CHARACTERIZATION OF LATTICE IMPERFECTIONS IN...

CHARACTERIZATION OF LATTICE IMPERFECTIONS IN NANOCRYSTALLINE

MATERIALS BY POSITRON ANNIHILATION, X-RAY DIFFRACTION AND OTHER METHODS

DISSERTATION SUBMITTED TO THE UNIVERSITY OF BURDWAN IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR

THE DEGREE OF DOCTOR OF PHILOSOPHY IN SCIENCE (PHYSICS)

ABHIJIT BANERJEE

MATERIAL SCIENCE LABORATORY DEPARTMENT OF PHYSICS

THE UNIVERSITY OF BURDWAN BURDWAN-713104

WEST BENGAL INDIA

2012

Dedicated to my parents

Late Mahadeb Banerjee

and

Basanti Banerjee

Prof. S. K. Pradhan, Ph.D. Department of Physics, Ex-Visiting Prof., University of Trento, Italy Ex-Visiting Prof., Central Michigan University, USA. Programme Coordinator, Centre of Advanced Study

THE UNIVERSITY OF BURDWAN GOLAPBAG, BURDWAN : 713 104

WEST BENGAL INDIA

Phone: (0342) 2657800 (O) (0342) 2657282 (R) Mobile: 09800162193 Fax : +91 342 2657800 e-mail: [email protected]

Date:

Certificate from the Supervisor

This is to certify that the research works incorporated in the dissertation entitled “Characterization of lattice imperfections in nanocrystalline materials by positron

annihilation, x- ray diffraction and other methods”, have been carried out at The

University of Burdwan, Burdwan by Abhijit Banerjee, M.Sc. under my supervision.

Mr. Banerjee has followed the rules and regulations as laid down by University of

Burdwan for the fulfillment of requirements for the degree of Doctor of Philosophy in

Science. As far as I know, any other worker anywhere has not published the results

included in the dissertation.

(Prof. Swapan Kumar Pradhan)

i

The dissertation reports the results of preparation and microstructure

characterization of some nanocrystalline materials of potential industrial applications

are prepared by (i) mechanical alloying the metal oxide ingredients in a high-energy

planetary ball mill and by (ii) chemical route (co-precipitation technique). The

microstructure characterization of the prepared materials has been investigated using

Positron annihilation lifetime (PAL), Positron annihilation spectroscopy (PAS)

experiments, X-ray powder diffraction data employing the Rietveld’s method of

structure/microstructure refinement and in some cases by Mössbauer spectroscopy,

high-resolution transmission electron microscopy (HRTEM), UV-Vis spectrometer.

The thesis is divided into two parts. Part I consists of three chapters and

provides a general idea about different types of lattice imperfections, microstructure

characterization of nanocrystalline materials with a brief review of earlier works,

theoretical background and present considerations of microstructure analysis and

experimental details of material preparation and characterization.

Part II consists of six chapters and is concerned with the experimental results of

the microstructure characterization of nanocrystalline materials prepared by different

preparation routes and phase stability study of the prepared nanomaterials at elevated

temperatures. For microstructure characterization by X-ray powder diffraction,

basically the Rietveld powder structure refinement method has been employed. From

X-ray line profile analysis, the lattice strain has been estimated which is considerably

high for all ball-milled samples. By the analysis of the PAL spectrum we have noticed

the nature of vacancy-type defects, vacancy clusters, and microvoids in different

kinds of nanomaterial. The other positron annihilation spectroscopy (PAS) technique,

Doppler broadening of the positron annihilation radiation line-shape measurement

have been used to study the momentum distribution of electron in a material.

Mössbauer spectra of all ball-milled Fe2O3 samples consist of a doublet which is

attributed to the superparamagnetic behaviour of ferromagnetic fine particles and a

broad sextet which is presumably due to high internal strain. The decrease in

hyperfine field, broadening of lines and asymmetry of line shape implies a broad

particle size distribution in the ball-milled sample. From the figures of high-resolution

transmission electron microscopes (HRTEM) we have measured the particle sizes of

Preface

PREFACE

ii

the unmilled and milled samples milled for different hours. Employing the UV-Vis

absorption spectroscopic method the changes in the band gap for direct transitions for

all the samples (milled and unmilled Fe2O3) have been measured.

Most of the experimental investigations have been carried out at the Materials

Science Laboratory of the Department of Physics of the University of Burdwan,

Burdwan under the supervision of Dr. S.K. Pradhan, Professor, Department of

Physics, University of Burdwan, Golapbag, Burdwan 713104, W. Bengal, India ;

Variable Energy Cyclotron Center, Department of Atomic Energy, 1/AF Bidhan

Nagar, Calcutta 700064, India; Department of Physics, University of Calcutta, 92

Acharya Prafulla Chandra Road, Kolkata 700 009, India; UGC-DAE Consortium for

Scientific Research , Kolkata 700 098, India.

Almost all the experimental results have already been published in the form of

research papers in different journals of international repute.

iii

ACKNOWLEDGEMENT

I would like to take this opportunity of expressing my word of thanks to Prof. S. K.

Pradhan, Department of Physics, The University of Burdwan for suggesting the

problem and for his continued interest with constant encouragement and guidance

during the progress of the investigation. Dr. Dirtha Sanyal, SOF, VECC, Salt Lake,

Kolkata and Dr. Mahua Chakroborty, Department of Physics, The University of

Calcutta are greatly acknowledged for their continuous help to complete the research

work. I would also thankful to Dr. Dipankar Das, Scientist, UGC-DAE Consortium

for Scientific Research, Kolkata; Dr. Udayan De, Scientist, VECC, Salt Lake,

Kolkata; Mr. Anindya Sarkar, Asst. Professor of Bangobasi College, Kolkata and Dr.

Hema Dutta, Asst. Professor of Vivakananda College, Burdwan. The cooperation of

colleagues of the Dept. of Physics of Burdwan University, Soumitra Patra, Amrita

Sen, Sumanta Sain, Anshuman Nandy, Sushovan Lala, Ujjwal Kumar Bhaskar are

also greatly acknowledged. I also thankful to the Secretary and Head Master and

colleagues of the Hatni P.C. Vidyamandir, Hatni, Hooghly. I also put my best regards

to Late Prof. Dilip Banerjee, Department of Physics, The University of Calcutta and

my parents for their constant mental support to complete the research work

successfully. Finally, I convey my great thanks to the authorities of the University of

Burdwan, Variable Energy of Cyclotron Center, Kolkata; The University of Calcutta;

UGC-DAE Consortium for Scientific Research, Kolkata; for providing the necessary

laboratory facilities for pursuing experimental research work.

Finally, I would like to thanks my family and my friends for their unceasing

inspiration, which helps me to carry on my research work and to make it successful.

Date: Dept. of Physics,

The University of Burdwan,

Golapbag, Burdwan-713104,

West Bengal, India. (ABHIJIT BANERJEE)

iv

Contents

PART: I Introductory remarks, Theoretical considerations and

Experimental considerations Page no.

CHAPTER-1: Introductory remarks 1-52 1.1 Introduction 2 1.2 Defect in crystals 3 1.2.1 Point defects 3 1.2.2 Line defects 4 1.2.2 (a) Edge dislocations 5 1.2.2 (b) Screw dislocation 5 1.2.3 Planar defects 6 1.2.3 (a) stacking faults 6 1.2.3 (b) Grain boundaries 7 1.2.4 Bulk defects 7 1.3 Types of imperfections 8 1.4 Background of X-ray crystallography 8 1.5 Imperfection of crystal investigated by X- ray, Positron annihilation and other methods: Direct and Indirect observations

9

1.6 A review on the microstructure characterization by X- ray powder diffraction 14 1.6.1 Past works on microstructural characterization using integral breadth, variance, Warren-Averbach method

15

1.6.2 Microstructural characterization using the Rietveld method 15 1.6.3 Recent works on microstructural characterization using modified Warren-

Averbach method 23

1.7 Review on Positron annihilation studies for lattice imperfection measurement 26 1.8 Review on research work done using Mössbauer spectroscopy 36 1.9 The aim and objectives of the present work 40 1.10 References 41 CHAPTER-2: Theoretical considerations 53-80 2.1 Introduction 54 2.2 X-ray line profile analysis: Theoretical considerations 54 2.3 Integral Breadth method 55 2.4 Different methods of X-ray diffraction pattern analysis 56 Limitations of different methods 2.4.1 Fourier method

57

2.4.2 Warren-Averbach method 57 2.4.3 Whole Powder Pattern Decomposition (WPPD) method 57 2.5 The Rietveld method 58 2.6 MAUD: a user friendly computer software based on Java for Materials Analysis

Using Diffraction 62

2.7 Positron annihilation technique 64 2.7.1 Positron Annihilation Spectroscopy (PAS) 64

v

2.7.1(a) Positron annihilation lifetime (PAL) measurement 66 2.7.1(b) Coincidence Doppler Broadened Positron Annihilation Radiation Line shape (CDBPARL) measurement

68

2.8 The Mössbauer effect 70 2.8.1 Fundamentals of Mössbauer Spectroscopy 73 2.8.1(a) Isomer Shift 74 2.8.1(b) Quadrupole Splitting 75 2.8.1(c) Magnetic Splitting (Hyperfine Interaction) 76 2.9 References 77 CHAPTER-3: Experimental considerations 81-109 3.1 Introduction 82 3.2 Different fabrication techniques of nano materials 82 3.2.1 Sol-gel method 82 3.2.1.1 Advantages of Sol-gel Technique: Sol-gel process 84 3.2.2 Ball- milling process 84 3.3 Potential of mechanical alloying 85 3.3.1 High energy ball-milling 85 3.3.2 The planetary ball-mill (P5) 86 3.3.3 Mechanism of a planetary ball mill 86 3.3.4 The merits and demerits of planetary ball-mill 87 3.3.5 The mechanochemical transformation during milling 88 3.3.6 Use of ball milling for synthesis of nanocrystalline materials 88 3.4 Preparation of powder specimens for X-ray powder diffractometry 89 3.4.1 Choice of radiation 89 3.4.2 Choice of instrumental standard 89 3.4.3 Recording of X-ray powder diffraction data 89 3.5 Transmission electron microscope (TEM) used for microstructure study 90 3.6 The outline of positron annihilation experiment 91 3.6.1 The Positron Source 93 3.6.2 The positron source preparation for positron annihilation experiments 94 3.6.3 Implantation profile 94 3.7 Positron Annihilation Lifetime (PAL) Measurement 95 3.7.1 The positron annihilation lifetime (PAL) spectrometer 95 3.7.2 Positron Annihilation Lifetime Data Analysis 97 3.7.2 (a) Mathematical analysis of the positron annihilation lifetime data 97 3.7.2 (b) Positron annihilation lifetime data analysis 98 3.8 Doppler Broadening of the Electron Positron Annihilation Radiation Measurement 98 3.8.1 Coincidence Doppler broadening of the electron positron annihilationradiation measurement

99

3.8.2 The coincidence Doppler broadening of the electron positron annihilation radiation (CDBEPAR) spectrometer

100

3.8.3 The Doppler broadening data analysis 101

3.8.3 (a) Line shape analysis 101

3.8.3 (b) Ratio-curve analysis 102 3.9 A outline of Mössbauer spectroscopy experiment 102 3.9.1 The Mössbauer Spectroscopy 102 3.9.2 Radiation Sources 105

vi

3.9.3 The Absorber 105 3.9.4 Detection and Recording Systems 105 3.9.5 Experimental set up of Mössbauer spectroscopy 106 3.10 References 107

PART: II

Experimental investigations on some nanomaterials

CHAPTER-4 Nanophase iron oxides by ball-mill grinding and their Mössbauer characterization

110-119

4.1 Introduction 111 4.2 Experimental details 111 4.3 Method of X-ray line profile analysis 112 4.4 Results and discussion 112 4.5 Conclusions 118 4.6 References 118 CHAPTER-5 Annealing effect on nano-ZnO powder studied from positron lifetime and optical absorption spectroscopy

120-133

5.1 Introduction 121 5.2 Experiment and data analysis 122 5.3 Results and discussion 123 5.4 Conclusions 130 5.5 References 131 CHAPTER-6 Particle size dependence of optical and defect parameters in mechanically milled Fe2O3

134-147

6.1 Introduction 135 6.2 Experimental outline 136 6.3 Results and discussion 138 6.4 Conclusions 146 6.5 References 146 CHAPTER-7 Microstructure, Mössbauer and Optical Characterizations of Nanocrystalline α-Fe2O3 Synthesized by Chemical Route

148-163

7.1 Introduction 149 7.2 Experimental outline 150 7.3 Method of microstructure analysis by Rietveld refinement 151 7.4 Results and Discussion 153

7.4.1 Microstructure Characterization Using XRD and HRTEM 153 7.4.2 Magnetic Characterization Using Mössbauer Spectroscopy 156 7.4.3 Optical Characterization Using UV-Vis Spectroscopy 159 7.5 Conclusions 161 7.6 References 161

vii

CHAPTER-8 Microstructural changes and effect of variation of lattice strain on positron annihilation lifetime parameters of zinc ferrite nanocomposites prepared by high enegy ball-milling

164-178

8.1 Introduction 165 8.2 Experimental method 166 8.3 Method of analysis 167 8.4 Results and discussion 167 8.4.1 X-ray diffraction analysis 167 8.4.2 Positron Annihilation Spectroscopy 172 8.5 Conclusions 177 8.6 References 177 CHAPTER-9 Microstructure and positron annihilation studies of mechanosysthesized CdFe2O4

179-192

9.1 Introduction 180 9.2 Experimental 181 9.3 Method of analysis 181 9.4 Results and Discussion 182 9.4.1 X-ray diffraction analysis 182 9.4.2 Positron Annihilation Spectroscopy 186 9.5 Conclusions 190 9.6 References 191 General conclusions 193 Future plan of research work 195 List of Publications 196

PART: I

Introductory remarks, Theoretical considerations and Experimental considerations

CHAPTER-1

Introductory remarks

INTRODUCTORY REMARKS CHAPTER-1

~ 2 ~

1.1 Introduction

Materials in nanocrystalline form are now being prepared widely because of

their wide range of applications in different fields. Structural imperfections in such

nanomaterials contribute a massive change in different properties of these materials.

Material characterizations in terms of detailed study of lattice imperfections in

particular, are essential for the systematic development of such nanomaterials as well

as for qualification of materials for design and fabrication. Today, there are several

techniques for material characterization. They often depend on how a given sample

responds to a probe. The probe may be electrons, positrons, neutrons, ions,

electromagnetic radiation (x-ray, gamma rays etc), ultra sound etc. In this dissertation,

positron annihilation lifetime (PAL) spectroscopy, X-ray powder diffraction (XRD)

and few other methods of microstructure characterization would be discussed which

are usually used for characterization of nanomaterials.

Positron annihilation lifetime (PAL) spectroscopy deals with the measurement

of the lifetime of positrons (~100-400 ps) in a solid. Positrons injected from a

radioactive source (like 22Na) get thermalized within 1-10 ps inside a solid and

annihilate with an electron of that material. It is well known that positrons

preferentially populate (and annihilate) in the regions where electron density,

compared to the bulk of the material is lower (e.g., vacancy-type defects, vacancy

clusters, and microvoids). The lifetime of positrons trapped in defects is

comparatively longer with respect to those that annihilate at defect free regions. An

analysis of the PAL spectrum thus throws light on the nature and abundance of

defects in the material. The other positron annihilation spectroscopy (PAS)

technique, Doppler broadening of the positron annihilation radiation line-shape

measurement is useful to study the momentum distribution of electron in a material.

Depending on the electron momentum, the 511-keV γ rays are Doppler shifted along

the direction of measurement. The wing region of the 511-keV spectra carries the

information about the annihilation of positrons with the core electrons. The momenta

of the core electrons are element specific and hence the atoms surrounding a defect

can be probed by proper analysis of the measured spectra.

The objects of the dissertation are to (i) synthesis of some nanocrystalline

materials by physical and chemical methods (ii) characterization of the

nanocrystalline materials in terms of lattice imperfections of different kinds primarily


~ 3 ~

employing X-ray powder diffraction method of line profile analysis and in some cases

by PAL, PAS, HRTEM and Mössbauer spectroscopy.

1.2 Defects in crystals Atoms may be arranged in many ways – tetragonal fashion or hexagonal

close-packed fashion or face centered cubic fashion or others. The reason that atoms

have a regular or homogeneous way to stack themselves is because such arrangement

results in a stable or low energy configuration. The homogeneously arranged portion

of atoms is called a phase.

It has been found that certain deviations of the crystals from their perfect

regularity i.e. the existence of certain imperfections, are required for accounting the

properties such as colour of crystals, plasticity, increased conductivity of pure

semiconductors, strength of crystals, melting and growth of crystals, luminescence,

diffusion of atoms through solids, etc. Thus, the concept that the atoms in the solids

are not arranged strictly in a perfect regular manner is also equally important. This

means that the actual crystals must behave as if containing essentially certain defects.

The real crystals are always imperfect in one respect or the other. The nature of

imperfections is better understood for some solids than for others. There are

essentially three kinds of imperfections that can occur in crystals: point defects, line

defects, and plane defects.

1.2.1 Point defects A point defect is very localized interruption in the regularity of the lattice. It

produces strain in the small volume of the crystal surrounding the defect, but does not

affects the perfection of more distant parts of the crystal. These defects may be in the

form of either impurities, or vacancies i.e. the unoccupied lattice sites, or vacancies

with the bound electrons/holes which are usually called as the colour centres

(Fig 1.1).


~ 4 ~

Fig.1.1 Different kinds of point defects.

1.2.2 Line defects The line defects are those which extend along some direction in an imperfect

crystal. One such defect can be considered as the boundary between two regions of a

surface which are perfect themselves but out of register with each other. In case of

crystals it arises, for example, when one part of the crystal shifts or slips relative to

the rest of the crystal such that the atomic displacement terminates within the crystal.

If the displacement dose not terminate within the crystal, but continues throughout the

crystal instead, it may not introduce any defect in the crystal. This emphasizes that it

is only the termination of the displacement which introduces the defect. This defect is

centered along a line which is also the boundary between the slipped and unslipped

regions of the crystal. This defect is commonly called a dislocation and the boundary

as the dislocation line (Fig.1.2).

Fig.1.2 The dislocation line


~ 5 ~

There are two basic types of dislocations: (a) Edge dislocation and (b) Screw

dislocation.

1.2.2 (a) Edge dislocations Edge dislocations are caused by the termination of a plane of atoms in the

middle of a crystal. In such a case, the adjacent planes are not straight, but instead

bend around the edge of the terminating plane so that the crystal structure is perfectly

ordered on either side. The analogy with a stack of paper may be noticed: if a half a

piece of paper is inserted in a stack of paper, the defect in the stack is only noticeable

at the edge of the half sheet [Fig. 1.3].

Fig. 1.3 Edge dislocation

1.2.2 (b) Screw dislocation The screw dislocation is more difficult to visualise, but basically comprises a

structure in which a helical path is traced around the linear defect (dislocation line) by

the atomic planes of atoms in the crystal lattice [Fig. 1.4].

Fig. 1.4 Screw dislocation


~ 6 ~

1.2.3 Planar defects These defects are those which have an areal extent. Planar defects are the most

serious defects. The stacking faults and grain boundaries are the most common

defects in the various types of planar defects.

1.2.3 (a) Stacking faults The stacking faults are usually produced during the grain growth of the

crystals. When close-packed layers grow one over the other to form a close- packed

crystal, it is possible for a layer to start stack incorrectly. A stacking fault results when

in the regular stacking sequence of a crystal one plane is out of sequence, while the

lattice on the either side of the fault is perfect. A crystal having this defect is usually

said to be twinned and the common plane is a twin plane.

Stacking faults occur in a number of crystal structures, but the common

example is in close-packed structures. Face-centered cubic (fcc) structures differ from

hexagonal close packed (hcp) structures only in stacking order. Both structures have

close packed

Fig. 1.5 Close packing of equal spheres

atomic planes with sixfold symmetry. The atoms form equilateral triangles. When

stacking one of these layers on top of another, the atoms are not directly on top of one

another [Fig. 1.5].The first two layers are identical for hcp and fcc, and labeled AB. If

the third layer is placed so that its atoms are directly above those of the first layer, the

stacking will be ABA. This is the hcp structure, and it continues ABABABAB.


~ 7 ~

However, there is another location for the third layer, such that its atoms are not

above the first layer. Instead, the fourth layer is placed so that its atoms are directly

above the first layer. This produces the stacking ABCABCABC, and is actually a

cubic arrangement of the atoms. A stacking fault is a one or two layer interruption in

the stacking sequence, for example, if the sequence ABCABABCAB were found in

an fcc structure.

1.2.3 (b) Grain boundaries Most of the material of practical importance consists of many small

interlocking crystallites or grains having random orientations. The boundary between

the two adjacent grains is called the grain boundary. It is a type of defect between the

two grains. Suppose the two grains, which can grow in size, are separated by a fairy

thick non-crystalline layer. Now as the grains grow, they force the atoms at their

surfaces to assume positions (consistent with their respective grains) in the region

between them. This process continues until two grains are separated by only few

atom-distance. At this distance, as the inter- grain forces come into play, each

competing grain pulls on the boundary layer atoms with comparable forces, and the

atoms thus assume positions that conform some kind of a compromise between the

requirements of the structure of either grain. Impurities such as foreign atoms,

interstitials, etc., which might be expelled by the grains during their growth are also

collected at the boundaries.

1.2.4 Bulk defects Voids are small regions where there are no atoms, and can be thought of as

clusters of vacancies. Impurities can cluster together to form small regions of a

different phase. These are often called precipitates.


~ 8 ~

1.3 Types of imperfections Point defects: Interstitial Extra atom in an interstitial site.

Schottky defect Atoms missing from correct sites.

Frankel defect Atom displaced to interstitial site creating

nearby vacancy.

Line defects: Edge dislocation Rows of atoms making edge of a

crystallographic plane extending only

part way in crystal. Burger vector is

normal to the line of dislocation.

Screw dislocation Rows of atoms about which a normal

crystallographic plane appears to spiral.

Burger vector is parallel to the line of

dislocation.

Planar defects: Lineage boundary Boundary between two adjacent perfect

regions in the same crystal that are

slightly tilted with respect to each other.

Grain boundary Boundary between two crystallites in a

polycrystalline solid.

Stacking fault Boundary between two parts of a closest

packing having alternate stacking

sequence.

Volume

imperfections

Transients:

Voids and precipitates Generate from cluster of vacancies,

interstitials and solute/ impurity atoms.

Generated and annihilated in a crystal

due to phonon-phonon, phonon-atom and

phonon-electron interactions.

1.4 Background of X- ray crystallography In the year 1912 Max Von Laue published his discovery that X- rays could be

diffracted by crystal [1]. In the next year, W. Lawrence Bragg [2] extended Laue’s


~ 9 ~

idea by showing that each diffracted beam can be considered as ‘reflection’ by an

array of parallel lattice planes with interplanar spacing dhkl, where hkl are miller

indices of the possible crystal face parallel to the array, provided that the beam of

wavelength λ is incident at a particular glancing angle θhkl to be ‘reflected’, naturally,

at the same angle and successfully interpreted the diffraction patterns of ZnS. This

idea of Laue brought a momentous change in the concept of crystalline solid. In 1914

W.H.Bragg and W.L.Bragg using orientation dependence of X-ray diffraction from a

single crystal solved the structure of NaCl, diamond, copper etc. as reported by

Mosley [3].

In the year 1916, Debye and Scherrer in Germany and in the year 1917 Hall in

the United States discovered independently ‘the powder method of X-ray’. In those

days powder diffraction patterns were recorded photographically and the primary

objective was to determine the atomic arrangement in metals and their alloys. As the

time passed by, the field of X-ray diffraction extends far beyond the early goal.

Sophisticated diffractometers were devised to produce diffractograms indicating the

locations of diffraction peaks as well as intensity of reflections very accurately in a

short time. Gradually, scientists are engaged their attention to the problems associated

with the behavior of metals under conditions of stress and strain, the influence of

alloying additions, the behavior of alloys at high temperatures, the anisotropy

produced by cold working, the production of intermetallic compounds with

semiconducting and thermoelectric properties etc. Recently, X-ray diffraction

methods are being used to study the microstructure in the grain size range of 10-4 to

10-8 cm and for identification of various phases present in the sample.

1.5 Imperfection of crystal investigated by X-ray, Positron Annihilation and other methods: Direct and Indirect observations J.G. Byrne [4] have been reviewed the different types of lattice imperfections

by the different types of methods. These methods can be categorized into two groups:

(1) Direct observations, (2) Indirect observations.

(1) Direct observations

(a) Etching and decoration technique

(b) Field ion microscopy (FIM)

(c) X- ray fluorescence (XRF)

(d) X- ray and synchrotron X- ray topography (XRT and SXRT)


~ 10 ~

(e) Secondary ion mass spectroscopy (SIMS)

(f) Auger and photoelectron spectroscopy (AES, XPS)

(g) High and low- energy electron diffraction (HEED, LEED)

(h) Transmission, scanning, scanning transmission and high resolution electron

microscopy (TEM, SEM, STEM, HREM)

(2) Indirect observations

(a) Mechanical properties studies

(b) Electrical resistivity

(c) Ultrasonic method

(d) Mössbauer spectroscopy

(e) Solid diffusion

(f) Quenching and annealing phenomena

(g) X-ray diffraction and small angle X- ray scattering

(h) Neutron irradiation

(i) Replica- electron microscopy

(j) Channeling studies

(k) Rutherford back scattering

(l) Positron annihilation techniques.

Detailed discussions of all these methods are beyond the scope of the thesis

and only a few ones are discussed below in brief:

X- ray diffraction topography [5,6] is an important and elegant tool to observe

directly lattice imperfections in as- grown single crystal. ‘Lang’ transmission

topography has been found to be a very powerful non-destructive method to

characterize crystal microstructure involving dislocations, stacking faults, precipitates,

grain boundaries etc. Topography with the use of synchrotron radiation in recent years

has become a powerful and challenging method.

Auger and photo-electron spectroscopy (AES, XPS) techniques are used to

identify the presence of physical and chemical imperfections (interstitials, precipitates

etc.) in the surrounding matrix elements.

The scanning electron microscopy (SEM) provides a direct means of

examining surface topography of a sample at high magnification with high resolution.


~ 11 ~

The transmission electron microscopy (TEM) is the most advanced and

probably the most versatile technique for direct observations of high density of lattice

imperfections amongst the listed direct methods. The electron source used in TEM

has a wavelength around hundredth of a nanometer, which means it has the power

hundred times better than the X-ray. We can determine the shape of the defect

structures and what kind of displacements has occurred to the atomic arrangements at

the defects. The energy of electron source in conventional TEMs is usually below 120

KeV.TEM was mainly developed at the Cavandish Laboratory in Cambridge by

Hirsch, Whelan and Howie [7] and by Ballman [8] in order to look at the dislocations

in a more direct confirmatory manner. In TEM an electron beam is accelerated to 100

to 2000 KV. This accelerated beam impinges on the thin sample placed in ultra high

vacuum chamber and gets diffracted. From the sample two beams emerge, one direct

and other diffracted beam. Out of these two, the undesired beam is suppressed, while

allowing the other beam to form an image on the photographic plate. Due to

displacement of atoms from their ideal position phase contrast is present in Bragg

diffraction, which helps to locate defects in crystal. In TEM dislocations appear as

dark lines and stacking faults give rise to interference fringes. It is also possible to

image other type of crystallographic defects, if the Burger vectors of dislocations and

displacement vectors of stacking faults are known. A good electron micrographs

originating from diffraction contrast, reveals the position of dislocation, stationary or

moving extended nodes and even separation of partials resulting in weak beam

technique to estimate stacking fault energy [9,10]. In recent years, million- volt

electron microscopes have come into existence so that a thicker specimen,

representative of bulk, may be used.

The energy of electron source of high resolution transmission electron

microscopy (HRTEM) is at least 200 KeV or even 1 MeV. The most important

difference between TEM and HRTEM is that TEMs cannot resolve atomic images,

but HRTEMs can and thus helps in studying the atomic and defect structures in the

vicinity of interfaces.

The measurements of broadening, shift and asymmetry of X- ray diffraction

line profile from polycrystalline specimens were developed by Warren school [11,12]

and have been extensively applied in the past decades [13] to elucidate qualitatively

as well as quantitatively the microstructure of the materials ( deformed, vapor-grown


~ 12 ~

etc.) characterized by various types of imperfections, namely, intrinsic, extrinsic, twin

or growth faults, coherently diffracting domain, residual stress, dislocation density

and stacking fault energy etc. In this method, analysis is done with individual

diffraction lines and hence this method fails to characterize the materials having low

symmetry where diffraction lines are found to be seriously overlapping. In 1966 H.

M. Rietveld suggested a method, known as Rietveld method, in which total X- ray

powder diffraction pattern is simulated and fitted with a suitable profile fitting

function and then structural refinement is carried out until the best fit is obtained

between the entire observed pattern and the entire calculated pattern [14]. In 1981,

Powley suggested whole-powder-pattern-decomposition method for refining unit-cell

parameters without reference to structural model. These methods have turned out to

be extremely elegant and powerful for studying the microstructures of various

materials [15].

Amongst the above-listed indirect methods Positron annihilation technique is

one of the most important methods to determine the different types of defects in the

materials. By this method we can easily detect the point defects, voids, cluster, micro-

voids which are not observed from X- ray diffraction pattern. To understand the

electron density distribution and electron momentum distribution in a defect-free

regions we can use an analysis of the PAL (positron annihilation lifetime) spectrum.

Positron annihilation spectroscopy (PAS) is well known non-destructive nuclear

technique. After entering a material positrons are trapped in the defect sites (lower

electron density region) in material such as dislocations, monovacancies, vacancy

clusters, micro voids, small and large angle grain boundaries etc. There is an another

technique to study the electron momentum distribution in the material is Doppler

broadening of the positron annihilation γ-ray radiation line shape (DBPARL) analysis.

In the DBPARL techniques positron from the radioactive 22Na source has been

thermalized inside the studied material and annihilate with an electron of the studied

material emitting two oppositely directed 511 KeV γ-rays. Depending upon the

momentum of the electron (p) these 511keV γ-rays are to be Doppler shifted by an

amount ±∆E (∆E=pLc/2) in the laboratory frame, where pL is the component of the

electron momentum, p, along the detector direction. Using high-resolution high-purity

germanium (HPGe) detectors one can measure the spectrum of Doppler-shift 511KeV

γ-rays. The wing region of the 511KeV spectra (higher value of pL) carries the


~ 13 ~


of the core electrons are element specific and hence the atoms surrounding a defect

can be probed by proper analysis of the measured spectra.

Positron annihilation lifetime (PAL) spectroscopy deals with the measurement

of the lifetime of positrons (~100-400ps) in a solid. Positrons injected from a radio-

active source (here 22Na) get thermalized within 1-10ps inside a solid and annihilate

with an electron of that material. It is well known that positrons preferentially

populate (and annihilate) in the regions where electron density, compared to the bulk

of the material, is lower (e.g., vacancy-type defects, vacancy clusters, and

microvoids). The lifetime of positrons trapped in defects is comparatively longer with

respect to those that annihilate and abundance of defects in the material.

In the indirect methods, Mössbauer technique is a very useful to determined

the superparamagnetic state and also ferromagnetic state by seeing the two- finger and

six- finger pattern of Mössbauer spectrum respectively. It is noted that the nature of

the Mössbauer spectrum depends on the relation between the time of measurement

and that of the magnetization vector relaxation. If the time of observation is much less

than the relaxation time, the particles exhibit ferromagnetism, while in the opposite

case one observes superparamagnetism. This Mössbauer spectroscopic [16,17,18,19]

technique is only one technique to detect the different phases/ states of magnetic

materials.

In 1958, R.L. Mössbauer in Germany, made a very important discovery in the

field of gamma-ray physics, which won him the Nobel prize in Physics in 1961.Under

certain circumstances, Mössbauer observed that gamma-rays could be emitted from

nuclei without any loss of energy due to the recoil of the emitting nucleus. As such

these gamma-rays have the same energy as the transition energy between the two

states. This type of transition is known as the recoilless transition and the effect is

known as Mössbauer effect. Mössbauer’s discovery has been used to test Albert

Einstein’s theory of general Relativity.

From Mössbauer effect we get some definitions which are given below:

(a) Hyperfine splitting of the nuclear energy levels:

Hyperfine splitting of the atomic energy levels arises from the magnetic

interactions of the nuclear magnetic moment with the magnetic field due to the orbital

electrons at the nucleus.


~ 14 ~

(b) Isomeric or chemical shift:

Mössbauer effect considered so far refers to identical atoms in the emitting

and absorbing systems, i.e., the atoms at the lattice sites have identical chemical

compositions. Hence whatever effects the electronic environment may have on the

nuclear levels are the same in both the emitting and absorbing atoms. If however, the

atoms in the two have different chemical compositions, then the nuclear levels will be

influenced by different amounts in the emitting and absorbing atoms.

Chemical shifts are usually very small (∆E/E ~ 10-12) and can be determined

by Mössbauer method by moving the source at velocities ~ 0.1mm/s relative to the

absorber. It has been found that Rex (nuclear radii in excited states) may be greater or

less than Rg (nuclear radii in ground states). For 57Fe, Rex < Rg by 0-1% while for 119Sn, Rex > Rg by 0.01%.

(c) Gravitational red shift:

R. V. Pound and G.A. Rebka (Jr.) carried out an experiment based on

Mössbauer method to measure the effect in the earth’s gravitational field (1960) on

the frequency of light. According to the General Theory of Relativity, a photon of

energy Eγ = (h/2π)ω behaves like a particle of mass m = Eγ / c2 in a gravitational field.

Hence in rising through a height l in the gravitational field of the earth, its potential

energy will increase by an amount ∆Egr = mgl = (Eγ/c2) gl , where g is the

acceleration due to gravity. Thus the energy of the photon will decrease by the same

amount. So the frequency of the light will decrease by ∆Vgr = ∆Egr /h = Eγ gl / c2 h ,

This decrease causes the light of shorter wavelength to shift towards longer

wavelength, an effect known as the gravitational red shift. In the reverse case, if light

moves downwards against the force of gravity, it will suffer a blue shift.

It may be mentioned that Mössbauer method has been used by Hay, Schiffer,

Cranshaw and Egelstaff (1960) to provide experimental verification of time-dilatation,

predicted by the Special Theory of Relativity.

1.6 A review on the microstructure characterization by X-ray powder diffraction

A large number of crystallographers had been studied on the nature of

imperfections introduced into crystalline materials as a result of growth and plastic

deformation processes for the past decades. As a complementary to electron

microscopy which is very useful for studying materials with little stacking fault, X-


~ 15 ~

ray diffraction methods are mainly of value in the investigation of high density of

stacking fault in heavily deformed materials. Experimental work in this field of study

has been adequately mentioned in the text of Wilson [20], Barrett and Massalski [21],

Warren [12], and Klug and Alexander [22]. Here we are discussing a short review on

the significant experimental and theoretical works that have been made in the recent

past on microstructure characterization of materials.

1.6.1 Past works on microstructural characterization using integral breadth, variance, Warren-Averbach method There are a large number of publications (theoretical as well as experimental)

between 1950-1970 embarking on comprehensive X-ray studies of crystallite size,

microstrain, stacking faults energies and dislocation densities in various metals, alloys

and compounds have been made adopting integral breadth, variance and Fourier

methods. Only the few significant references are mentioned here. These include:

Bertaut [23], Barrett [24], Warren and Averbach [25,26], Warren and Warekois [27],

Williamson and Smallman [28], Wagner [29,30], Michell and Hiag [31], Smallman

and Westmacott [32], Christian and Spreadborough [33], Cahn and Davies [34],

Vassamillet[35], Davies and cahn [36], Klein et al. [37], Welch and Otte [38], Alder

and Wagner [39], Foley, Cahn and Raynor [40], Vassamillet and Massalski [41],

Howie and Swann [42], Sundahl and Sivertsen [43], Koda et al.[44], Vassamillet and

Massalski [45], Nakajima and Numakura [46], Wagner and Helion [47], Lele et

al.[48,49], Otte [50], Sengupta and Quader [51], Goswami, Sengupta and Quader

[52], De and Sengupta [53], Rao and Rao [54], Delehouzee and Deruyttere [55],

Ahlers and Vassamillet [56].

1.6.2 Microstructural characterization using the Rietveld method

The Rietveld method was first reported at the seventh Congress of the IUCr in

Moscow by H.M. Rietveld in 1966 [57,58]. In 1974, the Rietveld refinement using

time-of-flight neutron powder diffraction data was performed for the first time to

analyze the monoclinic phase of KCN by Decker et al. [59]. In 1975, Carpenter et al.

attempted to apply Rietveld method to spallation pulsed neutron source data and

proposed a suitable peak shape function based on a convolution of separate rising and

falling exponential for representing the time dependence of the initial neutron pulse

[60]. In 1976, Windsor and Sinclair obtained a good fit for nickel data from a pulsed


~ 16 ~

neutron source at Harwell Linac [61] using Rietveld refinement. In 1977, Mueller et

al. used a tabulated numerical peak shape function to fit data for Th4D15 from the

ZING-P pulsed neutron source at Argonne and got satisfactory result. Till 1977 the

method was mainly used to refine structures from data obtained by fixed wavelength

neutron diffraction and a total of 172 structures were refined in this way before 1977

[62].

The application of the Rietveld method to X-ray patterns slowly developed,

primarily because of the asymmetric and non-Gaussian nature and multiple spectral

components in most X-ray diffraction profiles. In the mid-1970’s application of

Rietveld method was extended to X-ray data obtained with a diffractometer. Mackie

and Young [63], Malmros and Thomas [64], Young et al. [65], and Khattak and Cox

[66] gave the first application of Rietveld method to X-ray data. The work of Wiles

and Young in 1981 [67] marked the beginning of the much wider development of this

method.

The popularity of the Rietveld method led to the development of many

sophisticated computer programs, usually based on Rietveld’s original work [68].

Among these most widely used are:

(i) The DBWS program written by Wiles, Sakthivel and Young for main

frame computers and later adapted for PC use [69]. It operates with X-ray and neutron

diffraction data in angle-dispersive mode. The other version of this program are

LHPM [70], ALFRIET1 [71] to refine only f (x) by deconvoluting a split Pearson VII-

modeled g(x) from the observed data, ALFRIET2 [72] to refine structure with

incommensurate modulations and FULLPROF [73]. The latter version has been

written in to cover a variety of situations.

(ii) In 1987, Larson and Von Dreele [74] developed GSAS, which offers a

high flexibility and runs on a VAX-VMS machine and was recently adopted for PC

use. It works with angle dispersive and energy dispersive (time-of-flight) data. X-ray

and neutron diffraction data can be used simultaneously or independently in a

structure refinement. The program includes provisions for applying constrains on

bond lengths and angles.

(iii) XRS-82, The X-ray Rietveld System [75] is based on a collection of

crystallographic programs for the refinement of structures from single crystal data.


~ 17 ~

(iv) In 1992 Lutterrotti et al. developed a program, LS1 for simultaneous

refinement of structural and microstructural parameters [76] using psuedo-Voigt

function. Izumi (1995) developed another program, called RIETAN for joint

refinement with X-ray and neutron data under non-linear constraints [77-78].

Lutterotti et al. (1994) developed a user-friendly software, the MAUD, based on Java

platform, for material analyzing using diffraction pattern. It can perform simultaneous

crystal structure refinement, measurement of line-broadening, texture and quantitative

phase abundances of a mixed phase material [79-84].

Databases play a useful role in the course of structure determination for

detecting isostructural chemically related compounds. Among useful databases there

are:

-PDF-2 maintained, updated and marketed by the International Centre for

Diffraction Data (ICDD, http://www.icdd.com). The PDF contains experimental data

for over 87,500 substances and more than 49,000 patterns calculated from the ICSD

database. It is consulted after collecting the powder data.

-NIST Crystal Data File (CDF) is a compilation of crystallographic and

chemical data on more than 200,000 entries and is marketed by ICDD. This is a useful

database as soon as the unit cell is known from pattern indexing.

-Inorganic Crystal Structure Database (ICSD) contains a complete

crystallographic information over 50,000 inorganic structures (http://barns.ill.fr

/dif/icsd/).

-SDPD database contains references over 500 crystal structure determined ab

initio from powder diffraction data (http://sdpd.univ-lemans.fr/iniref.html).

Most programs used for the Rietveld method incorporate as iterative procedure

for pattern matching [85] by fitting a calculated pattern to the observed data without

the use of a structure model, but using constraints on the positions of reflections

allowed by the space group conditions. The accuracy of results obtained as the output

of refinement in the programs available for Rietveld analysis depends on the judicious

choice of the profile function. One can use a single function or convolution of two or

more functions for approximating the observed diffraction profiles. Pearson VII [86],

Split Pearson VII [87], and psuedo-Voigt [88] functions have been demonstrated to

give the best fit to the observed X-ray profile fitting [89-90] in structural and

microstructural analysis using Rietveld method. Dollase (1986) showed performance

of March function in Rietveld refinement [91] for preferred orientation measurement.


~ 18 ~

Many authors then incorporated March-Dollase function in Rietveld refinement codes

and confirmed Dollases’s evaluation. Another interesting and apparently very

powerful preferred orientation function was given by Ahtee et al. (1989) in which the

preferred orientation effect was modeled by expanding the orientation distribution in

spherical harmonies [92]. Wenk et al. introduced WIMV method for texture analysis

and got tremendous success [93].

The microstructural study by Rietveld method is now become very popular

among powder diffractionists. In 1988, Langford for the first time determined

crystallite size and microstrain using Rietveld method [94]. In 1993, Delhez et al.

developed a theory for the crystallite-microstrain separation [95] and reported that as

long as microstructure effects are isotropic, they can be accounted for easily in

Rietveld refinements. Bokhimi et al. [96] and Sanchez et al. [97] characterized the

particle size of magnesium and titanium oxides prepared by the sol-gel technique, by

using DBDW and WYRIET. Xiao et al. reported that the Rietveld refinement of

nanostructured hollandite powders do not converged well, due to anistropic effects

associated with a fiber axis in the b direction and fitted the powder pattern realized

with a highly packed sample taking into account the preferred orientation correction

and reducing the contribution of the narrowest reflections and reported a mean

crystallite size of 108 A0 with zero microstrain [98].

The Rietveld method can determine the degree of crystallinity in

semicrystalline materials. Riello et al. modeling the crystalline peak profiles by

psuedo-Voigt for a sample of polyethylene terephtalate and simultaneously

optimizing the background contributions estimated quantitatively the volume fraction

of silicate glass in ceramic by RIETQUAN [99].

Ungar et al. (1999) applied the dislocation based model of strain anisotropy in

the Fourier formalism of profile fitting and fitted the powder pattern of Li-Mn

(spinel), refining the parameters, namely the average dislocation density, the average

coherent domain size, the dislocation arrangement parameter and the dislocation

contrast factor[100]. In 1998, Popa developed a method especially for anisotropic

crystallite shape including the harmonic expansion [101] for better fitting of X-ray

profiles. In 1999, Scardi and Leoni reported that anisotropic line broadening of X-ray

diffraction profiles due to line and plane lattice defects can be Fourier modeled and a

detailed information on the defect structure (dislocation density and cut-off radius,

stacking and twin fault probabilities were refined together with the structural


~ 19 ~

parameters) can be obtained when applied to face-centered cubic structure materials

[102]. Ungar et al. established a simple preocedure for the experimental determination

of the average contrast factor of dislocations [103], in terms of a simple parameter q

which can be used in Rietveld structure refinement.

Studies on Rietveld refinement reveal that only size-effect is much easier to

handle than both size and microstrain. Being confirmed from the transmission

electron micrograph of the powder that only size effect is present, the size distribution

of single crystal nano particles can be estimated by two approaches. One approach

consists in Monte Carlo fitting of wide-angle X-ray scattering peak shape [104].

Another method applies maximum entropy for determining the column-length

distributions from size-broadened diffraction removing instrument broadening [105].

Line profile analysis is incorporated in Rietveld method for refinement of

crystallite size, microstrain, lattice distortion due to dislocations (edge/screw); planar

defects (twin and deformation faults) [106-107]. Lutterotti et al. analyzed the material

composed of silicate glass in ceramic matrix by the Rietveld method and determined

the content of amorphous phase in ceramic materials [108] and characterized its

defect structure.

Bokhimi et al. [109] prepared samples in the MgO-TiO2 system via the sol-gel

technique. Samples were characterized with X-ray powder diffraction and to quantify

the concentration and the crystallography of the phases in the samples, their

crystalline structures were refined using the Rietveld method.

Blouin et al. [110] followed the kinetics of formation and structural evolution of

nanocrystalline phases by mechanochemical reaction between Ti and RuO2 by

performing a Rietveld refinement analysis of X-ray diffraction profile.

Rixecker et al. [111] identified ternary phases with the cubic structure in both

the Fe-Nb-Si and Fe-Ta-Si systems formed during the crystallization of mechanically

alloyed amorphous materials during heat treatments. The X-ray powder diffraction

data were evaluated both by local line fit and by Rietveld analysis.

Wang et al. [112] prepared iron-doped titania photocatalysts with different

iron contents by using a sol-gel method in acidic media. The crystalline structures of

the various phases calcined at different temperatures were studied by using the

Rietveld technique in combination with XRD experiments.

Bose et al. [113] prepared five compositions of Cd-Ag alloy in different

phases and phase boundary regions have been prepared and analyzed both in the


~ 20 ~

annealed and cold-worked states employing Rietveld’s powder structure refinement

method and Warren-Averbach’s method of X-ray line profile analysis.

In 2002 Bose et al. synthesized nanocrystalline Ni3Fe in sol-gel method [114]

and made X-ray microstructure characterization of the same material employing

Rietveld’s powder structure refinement method, the Warren-Averrbach’s method and

the modified Williamson-Hall method.

Pratapa et al. [115] made a comparative study of single-line and Rietveld

strain-size evaluation procedures using MgO ceramics. Strain-size evaluations from

diffraction line broadening for MgO ceramic materials have been compared using

single-line integral-breadth and Rietveld procedures with the Voigt function.

Bid et al. [116] reported formation of fully stabilized c-ZrO2 phase from m-

ZrO2 phase in ball milling process without using any additive. Microstructural

parameters of ball milled ZrO2 milled at four different BPMR (ball to powder mass

ratio) and different milling hrs were obtained by Rietveld powder structure refinement

analysis.

Dutta et al. [117] prepared nanocrystalline V2O5 by high energy ball milling

and studied the anisotropic nature of particle size and strain through Rietveld’s

analysis.

Manik et al. [118] prepared for the first time of nanocrystalline orthorhombic

polymorphs of CaTiO3 by high energy ball milling method and studied the

microstructural parameters of the phases during its evolution and at different post-

annealing temperature.

The same author prepared Nanocrystalline powders of CaCu3Ti4O12 (CCTO)

by high-energy ball milling the powder mixture of CaO, CuO, TiO2 and studied

structural and microstructural changes in terms of lattice imperfections from the

analysis of X-ray powder diffraction data by Rietveld's powder structure refinement

method [119].

Sarkar et al. [120] made an application of Stephens’s phenomenological model

for anisotropic line broadening of ZrSiO4 sample and the Rietveld’s refinement with

and without the model showed that the model improved the quality of fit.

A large number of successful refinements by Rietveld method has been

reported; reviews have been given by Taylor (1985), Hewat (1986), Cheetham and

Wilkinson (1992), Young (1993), Harris and Tremayne (1996), Masciocchi & Sironi

(1997), Harris et al (2001) and Devid et al (2002). It was mentioned in a review report


~ 21 ~

by H.M. Rietveld himself that a total of 172 structures were refined before 1977. In

the period January 1987 to May 1989 a total of 341 papers were published with

reference to or using the Rietveld method, of which nearly half using neutron

diffraction. In the year 1991, the number of papers published with reference to the

Rietveld method is 257. In the year 1994 the number rises to 350. In a lecture in

XVIIIth IUCR conference at Glasgow, Scotland, H.M. Rietveld himself told that

now-a-days Rietveld method is used in more than 500 publications per year [121].

Recently Rietveld method is used in over 2000 publication per year.

Z. K. Heiba et al. [122] studied the mixed oxides Zn1-xMgxO (ZMO) prepared

as nano-polycrystalline powders and thin films by a simple sol–gel process and dip

coating method. Structural and microstructural analysises were carried out applying x-

ray diffraction (XRD) and Rietveld method. Analysis showed that for x < 0.25, Mg

replaces Zn substitutionally yielding ZMO single phase, while for x ≥ 0.25 two phases

are identified ZMO and MgO. Replacing Zn2+ by Mg2+ distorts the cation tetrahedrons

and decreases the lattice constants ratio c/a of the wurtzite ZMO which deviate the

lattice gradually from the hexagonal structure as Mg+2 increases. These distortions are

attributed to the difference in electronic configuration of the two cations which

suppress the paraelectric-ferroelectric phase transition in the ZMO wurtzite.

Lemine et al. [123] studied the effects of milling times on the mechanically

milled ZnO powder. The milled powders are analysed by X-ray diffraction (XRD)

and scanning electron microscope (SEM). In order to quantify these effects, analysis

by the Rietveld method is carried out. It is shown that the application of mechanical

milling is a simple technique to produce nanocrystalline powder. A clear reduction of

grain size with an increase of microstrain and lattice parameters is observed with

increasing milling time.

Sivestrini et al. [124] studied the synthesis, morphology and luminescence

properties of europium (III)-doped zirconium carbonates prepared as bulk materials

and as silicasupported nanoparticles with differing calcinations treatments are

reported. Transmission electron microscopy and X-ray diffraction analyses have,

respectively, been used to study the morphology and to quantify the atomic amount of

europium present in the optically active phases of the variously prepared

nanomaterials. Rietveld analysis was used to quantify the constituting phases and to

determinate the europium content. Silica particles with an approximate size of 30 nm


~ 22 ~

were coated with 2 nm carbonate nanoparticles, prepared in situ on the surface of the

silica core.

Tebib et al. [125] studied that the Elemental Fe and red phosphorus powders

with a composition close to FexP (x = 10, 15 and 20 wt. %) were mechanically alloyed

in a planetary ball mill under an argon atmosphere. Structural changes were studied

by X-ray diffraction. The complete dissolution of the elemental powders is achieved

within 3 h of milling. Detailed analysis of the X-ray diffraction patterns reveal the

formation of a Fe(P) solid solution with two structures (α-Fe1 and α-Fe2) having

different lattice parameters, crystallite size and microstrains.

Albores et al. [126] studied the ZnO nanorods synthesized by induced seeds

by chemical bath deposition using hexamethylenetetramine (HMT) as a precipitant

agent and zinc nitrate (ZN) as Zn2+ source at 90°C. The influence of reactants ratio

was studied from 2 to 0.25 ZN/HMT molar. Microstructural information was obtained

by Rietveld refinement of grazing incidence X-ray diffraction data. These results

evidence low-textured materials with oriented volumes less than 18% coming from

(101) planes in Bragg condition.

Vagadia et al. [127] carried out a comparative study of structural,

microstructural and magnetic properties of the two sets of Co-doped ZnO samples

synthesized by solid state reaction and sol-gel method. Rietveld refinement of the X-

ray diffraction data reveals single phase hexagonal wurtzite structure for all the

samples, while the tunnelling electron microscopy measurements show the presence

of nano-phase in the sol-gel grown Co-doped ZnO samples.

Abbas et al. [128] studied the nanocrystalline cobalt ferrite synthesized using

two different methods: ceramic and co-precipitation techniques. The nanocrystalline

ferrite phase was formed after 3h of sintering at 1000°C. The structural and

microstructural evolutions of the nanophase were studied using X-ray powder

diffraction and the Rietveld method. The refinement result showed that the type of the

cationic distribution over the tetrahedral and octahedral sites in the nanocrystalline

lattice was partially an inverse spinel. The transmission electronic microscope

analysis confirmed the X-ray results.

Cherian et al. [129] studied that the sol–gel auto-combustion method adopted

to prepare solid solutions of nano-crystalline spinel oxides, (Ni1−xZnx) Fe2O4

(0≤x≤1).The phases are characterized by X-ray diffraction (XRD), high-resolution


~ 23 ~

transmission electron microscopy, selected area electron diffraction, and Brunauer–

Emmett–Teller surface area. The cubic lattice parameters, calculated by Rietveld

refinement of XRD data by taking into account the cationic distribution and affinity of

Zn ions to tetrahedral sites, show almost Vegard’s law behavior.

1.6.3 Recent works on microstructural characterization using modified Warren- Averbach method

Leine et al. in 1980 investigated the microstructure of the spalat-cooled

Aluminium rich alloys using modified Warren-Averbach method [130]. Tonejc and

Aluminium in 1980 determined crystallite size, microstrain and stacking fault

probabilities for splat-quenched Ag- (6,8.2,11) at. % Sn alloys and compared the

results with cold-worked filings and bulk compressed alloys [131]. Delhez et al. in

1980 and 1982 modified the classical theory of Warren (1969) for single line analysis

and discussed about the errors involved in the analysis from theoretical aspects

[132,133]. Ghosh, De and Sengupta characterized the microstructures if Cu-Ge and

Ag-Al alloys in deformed state [134-136]. Ekstrom and Chafield using X-ray line

profile broadening analysis studied the milling behavior of commercial alumina

(Al2O3) powders [137]. Reddy and Suryanarayana reported that the microstrain is the

major source of line broadening in Ag-Cd-In and Ag-Cd-Zn alloys [138].

Bhikshamaiah and Suryanarayana determined the stacking fault energy in Ni and

dilute Ni-Fe alloys as a function of temperature [139]. Delhez et al. in 1986 and

Langford et al. in 1988 made a detailed discussion about systematic errors developed

due to truncation of experimental line profiles at a finite range [140,133]. Pradhan et

al. studied the microstructure of binary Cu-Al, Cu-Si and ternary Cu-Mn-Si and Cu-

Ge-Si alloys in the deformed state [141-144]. David and Bonnet observed stacking-

fault pyramid in the phase Ni73..5Al9 Ti 14Cr3.5, when deformed at 7400C [145]. Yang

and Wan studied the influence of Al on the stacking fault energy in Fe-Al-Mn-C

alloys [146]. Balzer et al. analyzed the line-broadening effects in superconductors and

reported that stacking fault energy increases with increasing Tc [147]. Vermeulen et

al. suggested a method for correcting errors arising due to truncation of line profiles

[148,149]. Rosengard and Skriver made a comparative study of intrinsic, extrinsic and

twin fault probabilities found in 3d, 4d and 5d transitional metals [150]. Pal et al.

studied the microstructure of (Ag, Cu)-Zn and Cu-Ni-Sn alloys [151,152]. Drits et al.

studied thickness distribution and microstrain for illite and illite-smectite crystallites


~ 24 ~

[153]. Chatterjee et al. studied microstructure of Pb(1-x)Snx alloys using the above

method [154] and Mukherjee et al. studied lattice imperfections in deformed

Zirconium-base alloys[155].

Jayan et al. [156] studied the Coarsening of nano-sized M23C6 carbide

precipitate in 2.25Cr–1Mo steel. Carbide specimens were prepared by electrochemical

extraction of boiler tube specimens subjected to extend ageing in a thermal power

plant. The crystallite size was computed by Warren-Averbach and integral breadth

methods from X-ray diffraction line profiles. It is found that coarsening of nano sized

M23C6 particles reflected in diffraction pattern as increased crystallite size with

ageing.

Ortiza et al. [157] studied the crystallite size, lattice microstrain, lattice

parameter, and formation of solid solutions of a nanocrystalline Al93Fe3Cr2Ti2 alloy

prepared via mechanical alloying (MA) starting from elemental powders have been

investigated using the Rietveld method of X-ray diffraction (XRD) in conjunction

with line-broadening analyses through the variance, Warren–Averbach, and Stokes

and Wilson methods. Detailed analyses using transmission electron microscopy

(TEM), scanning electron microscopy (SEM), and inductively coupled plasma-optical

emission spectroscopy (ICP) have also been conducted in order to corroborate the

formation of solid solutions and the grain size measurement determined from the

XRD analyses.

Haluska et al. [158] studied the nanostructural features of the gas-phase

displacement reaction 2Mg (g) +SiO2 -2MgO(s) + Si, where SiO2 is in the form of

diatom shells were studied via X-ray diffraction and Fourier methods. Diatomaceous

powder heated to 700 C in a sealed graphite cell in the presence of Mg vapor formed

MgO via a displacement reaction. Warren-Averbach analysis performed on samples

reacted for different times showed an initial sharp MgO grain size distribution which

broadened with time.

Uvarov et al. [159] determined the crystallite size by X-ray diffraction

methods for 210 TiO2 (anatase) nanocrystalline powders with crystallite size from 3

nm to 35 nm. Each X-ray diffraction pattern was processed using different free and

commercial software. The crystallite size calculations were performed using Scherrer

equation and Warren–Averbach method. Statistical treatment and comparative

assessment of the obtained results were performed for the purpose of an ascertainment

of statistical significance of the obtained differences.


~ 25 ~

Biju et al. [160] studied that the lattice strain contribution to the X-ray

diffraction line broadening in nanocrystalline silver samples with an average

crystallite size of about 50 nm using Williamson-Hall analysis assuming uniform

deformation, uniform deformation stress and uniform deformation energy density

models. The lattice strain in nanocrystalline silver seems to have contributions from

dislocations over and above the contribution from excess volume of grain boundaries

associated with vacancies.

Oba et al. [161] studied the origin of the ferromagnetism that appears in the

core region of Pd nanoparticles. In order to consider the contribution of crystal

structure to the appearance of ferromagnetism in the Pd nanoparticles, they performed

x-ray diffraction experiments and Warren-Averbach analysis. The results revealed

that the standard deviation of strain ∆ε showed a positive correlation with the

saturation magnetization, with the ferromagnetism appearing when ∆ε became larger

than about 0.5%. This suggests that the strains induce internal ferromagnetism in the

Pd nanoparticle.

Ebnalwaled et al. [162] studied the nanocrystalline Al-Mg-Mn synthesized by

ball milling technique. Microstructure of these alloys has been studied from X-ray

line broadening. The crystallite size of nanocrystalline Al-Mg-Mn system decreases

by increasing the Mg content, while the micro-strain, median diameter, increases by

increasing the Mg content.

Ganjkhanlou et al. [163] studied that Y2O3:Eu nanopowder was prepared by

urea solution combustion method. The samples were then characterized by X-ray

diffraction (XRD) and high resolution transmission electron microscopy (HRTEM).

The XRD patterns of samples were investigated by Warren-Averbach method in order

to determine crystallite size and strain distribution. An innovative method was

developed for prediction of dopant ion distribution in host lattice using Warren-

Averbach method and micro-strain distribution. Analyzing of Y2O3:Eu nanopowder

by this method revealed that the Eu ions preferentially accumulated in near the grain

boundaries more than the inner parts of crystallites.

Rivnay et al. [164] studied the crystallite size and cumulative lattice disorder

of three prototypical, high-performing organic semiconducting materials investigated

using a Fourier-transform peak shape analysis routine based on the method of Warren

and Averbach (WA). A simple analysis based on trends of peak widths and


~ 26 ~

Lorentzian components of pseudo-Voigt line shapes as a function of diffraction order

is also discussed as an approach to more easily and qualitatively assess the amount

and type of disorder present in a sample.

Wardecki et al. [165] studied that the microstructure of electrodeposited

nanocrystalline chromium (n-Cr) was studied by using synchrotron radiation (SR)

diffraction, SEM, TEM, and EDX techniques. The presence of the Cr oxide phases

was studied by performing X-ray diffraction studies at room temperature with a

laboratory X-ray diffractometer Seifert ID-3003 (Mo Ka radiation) operating at 40 kV

and 30 mA (University of Warsaw). The average column length and the microstrain

fluctuation were calculated from SR diffraction data by using the Warren-Averbach

method.

Back et al. [166] observed an optical study of Tb3+-doped Y2O3 nanocrystals

synthesized by Pechini-type sol–gel method. The particles are investigated in terms of

size and morphology by means of X-ray diffraction and transmission electron

microscopy analysis. The reflection broadening in the XRD patterns is attributed

mainly to three kinds of contributions: crystallite size, microstrain, and the instrument

itself. The Warren–Averbach method was used for the line profile analysis of

reflections to separate the effect of crystallite size and microstrain on reflection

broadening. The software based on Warren–Averbach Fourier transfer method was

used to calculate the distribution of crystallite size and microstrain of the samples

1.7 Review on positron annihilation studies for lattice imperfection

measurement The temperature dependence of positron annihilation in aluminum has been

investigated by Fluss et al. [167] over the range 20-435°C by simultaneous

measurements of positron lifetime and Doppler broadening of the annihilation

spectrum.

Krishnan et al. [168] studied that the preferential sensitivity of positrons

towards micro-defect domains which are not assessable by other techniques makes it

an attractive tool for many materials science problems. The study is intended as a

brief introduction on the principle of measurements and its potential is exemplified

with the help of results on some metallic and ceramic systems.


~ 27 ~

Chidambaram et al. [169] studied a positron annihilation study of the

icosahedral Al-Cu-Fe alloy system which has been carried out using both Doppler

broadening and lifetime measurement techniques.

Yongming et al. [170] have calculated the one- and two-dimensional angular

correlation distribution of electron-positron annihilation (ACAR) as well as the

electron momentum distribution (EMD) for graphite.

Hübner et al. [171] calculate the fraction of positrons reaching particle surface

(FPS). The presence of defects in the particles can drastically reduce FPS depending

on the defect concentration and capture rate. They demonstrate that for small-grained

materials the grain surface can influence the lifetime signal significantly.

Sandreczki et al. [172] studied that the positron annihilation lifetime

spectroscopy is used to monitor the sub-glass-transition-temperature (Tg) annealing of

a polycarbonate sample. The intensity of ortho-positronium annihilation decreases as

a stretched-exponential function of annealing time at Tg − 121 K.

Haung et al. [173] performed two-dimensional angular correlation of electron-

positron annihilation radiation (2D-ACAR) measurements on a series of porous

silicon with photoluminescence (PL) peak energy in the range from 1.6 to 2.0 eV. The

electron-positron momentum spectra of porous silicons can be well resolved into two

peaks with different line width. The result shows two distinct momentum spectra for

the studied samples.

Shantarovich et al. [174] studied that the positron annihilation lifetime (PAL)

spectroscopy was applied to measure free-volume size distribution in polymer

samples with unusually long lifetimes: in dense films of poly (trimethylsilylpropyne)

(PTMSP) and in porous membranes prepared from poly (phenylene oxide) (PPO).

PAL data were treated by finite-term lifetime analysis (PATFIT program) and

continuous lifetime analysis (CONTIN program).

Wurschum et al. [175] studied that the atomic free volumes and vacancies in

the ultrafine grained alloys Pd84Zr16, Cu 0.1 wt % ZrO2, and Fe91Zr9 were studied by

means of positron lifetime.

Staab et al. [176] investigate the changes in the microstructure on a nano-scale

(nano-structure) in technically used AlCuMg 2024 alloys. How the annihilation

parameters, i.e. the positron lifetimes and corresponding intensities, are changing

during natural and artificial aging is observing here. It turns out that positron

annihilation spectroscopy is very sensitive to changes occurring in the nano-structure


~ 28 ~

but which are not always reflected or measurable in the materials properties such as

hardness.

Dull et al. [177] studied an existing model that relates the annihilation lifetime

of positronium trapped in subnanometer pores to the average size of the pores is

extended to account for positronium in any size pore and at any temperature. This

extension enables the use of positronium annihilation lifetime spectroscopy in

characterizing nanoporous and mesoporous materials, in particular thin insulating

films where the introduction of porosity is crucial to achieving a low dielectric

constant, K.

Lizama et al. [178] studied that a series of thermoplastic/elastomer composite

particles has been prepared by two step emulsion polymerization techniques. The

morphology of the obtained composite particles as a function of the system

composition has been studied by transmission electron microscopy. Afterwards, a

correlation between the structural behavior of the composites and the ortho-

positronium lifetime and formation probability was also established. This correlation

can be explained in terms of free volume changes associated to phase transitions in

the particles.

Grafutin [179] studied that the measurements of positron lifetimes, the

determination of positron 3γ- and 2γ-annihilation probabilities, and an investigation of

the effects of different external factors on the fundamental characteristics of

annihilation constitute the basis for this promising method.

Zheng et al. [180] studied that the synthesis of nanoparticles SiO2 that have

enabled the processing of exciting new nanoparticle/epoxy composites. Ultrasonic and

mechanical methods were used to disperse the nanoparticles in epoxy resin. The

nanocomposites were characterized by tensile and impact testing as well as TEM

studies. Additionally, the effects of nanometer-sized SiO2 particles on free volume of

nanocomposites were studied using positron annihilation lifetime spectroscopy.

Mokrushin et al. [181] studied the measurements of the angular correlation of

annihilation radiation and infrared absorption spectra conducted with porous silicon

samples, containing capillary macropores with a diameter of about 1 m. The set of

data shows that a high proportion of Si-O bonds contribute to positron annihilation

and IR absorption for porous silicon. Annihilation parameters and estimated values of

the specific surface area point to the availability of a nanoporous system in the


~ 29 ~

macroporous silicon. Most likely the macropore surface is covered by the nanoporous

material to a thickness of 100-200 nm.

Nagai et al. [182] studied the irradiation-induced vacancy-type defects in Fe-

based dilute binary alloys ~Fe-C, Fe-Si, Fe-P, Fe-Mn, Fe-Ni, and Fe-Cu!, model

alloys of nuclear reactor pressure vessel steels by positron annihilation methods,

positron lifetime, and Coincidence Doppler Broadening (CDB) of positron

annihilation radiation. The vacancy-type defects were induced by 3 MeV electron

irradiation at room temperature. The defect concentrations are much higher than that

in pure Fe irradiated in the same condition, indicating strong interactions between the

vacancies and the solute atoms and the formation of vacancy-solute complexes.

Chen et al. [183] studied the defects in hydrothermal grown ZnO single

crystals studied as a function of annealing temperature using positron annihilation, x-

ray diffraction, Rutherford backscattering, Hall, and cathodoluminescence

measurements. Positron lifetime measurements reveal the existence of Zn vacancy

related defects in the as-grown state. The positron lifetime decreases upon annealing

above 600°C, which implies the disappearance of Zn vacancy related defects, and

then remains constant up to 900°C.

Galindo et al. [184] studied the colloidal silica particles introduced in methyl

silicate (SiO1.5CH3) coating (obtained from methyltrimethoxysilane as a precursor) to

increase the hardness, the elastic modulus and the fracture toughness. In order to

obtain a more detailed structural analysis Positron Beam Analysis (PBA) using the

Doppler Broadening (DB) and the 2D-Angular Correlation of Annihilation Radiation

(2D-ACAR) techniques was performed.

Chakrabarti et al. [185] studied the particle size of the ball-milled Bi2O3

powder has been determined by the x-ray powder diffraction method and transmission

electron microscopy. The absorption spectra, in the spectral range 300–1300 nm,

indicate an increase of the optical bandgap for both the direct and indirect transitions

due to the reduction of grain size. The defects introduced in Bi2O3 during grinding

have been investigated by the positron annihilation technique. Positron annihilation

results indicate an increase of defects due to ball milling.

Cassidy et al. [186] studied the high-density gas of interacting positronium

(Ps) atoms by irradiating a thin film of nanoporous silica with intense positron bursts

and measured the Ps lifetime using a new single-shot technique. When the positrons


~ 30 ~

were compressed to 3.3×1010 cm-2, the apparent intensity of the ortho-positronium

lifetime component was found to decrease by 33%.

Kuriplach studied [187] the nanoparticles embedded in a matrix can trap

positrons under certain conditions. In such cases nanoparticles can be effectively

studied by means of positron annihilation because positron annihilation characteristics

contain information related to nanoparticles' electronic and atomic structure.

Zheng et al. [188] studied that the effects of SiO2 nanoparticles on the

properties of glass-fiber composites show that the SiO2 nanoparticles can generally

promote their properties especially the bend strength that ends up with 69.4%

enhancement. This is attributed to the promoted bonding forces between glass fibers

and matrices owing to the presence of nanoparticles. The size and concentration of

free volume were tested by positron annihilation spectroscopy.

Kar et al. [189] studied that the quantum confinement effects in

nanocrystalline CdS studied using positrons as spectroscopic probes to explore the

defect characteristics. The lifetime of positrons annihilating at the vacancy clusters on

nanocrystalline grain surfaces increased remarkably consequent to the onset of such

finite-size effects. The Doppler broadened line shape was also found to reflect rather

sensitively such distinct changes in the electron momentum redistribution scanned by

the positrons, owing to the widening of the band gap.

Kar et al. [190] studied the Positron lifetimes measured in different

nanosystems of FeS2—granular samples, ribbons, oxidized ribbons, rods, and a

mixture of wires and tubes. To identify the positron trapping sites, the 511–511 keV

gamma rays coincidence-gated Doppler-broadened spectra were recorded and it

appeared that the trapping of positrons took place mainly in the vacancies created by

the absence of Fe2+ ions. The positron lifetimes in the nanogranular sample were

conspicuously larger compared to those in the coarse-grained bulk due to trapping and

annihilation at the grain surfaces.

Thosar et al. [191] studied the measurements of the value 2 and the intensity

I2 of the long component in the life-time spectra of positrons annihilating in some

simple unassociated, polar, and associated organic liquids are reported as a function of

temperature. A semi-empirical free volume model for the formation and quenching of

ortho-positronium atoms is developed for simple molecular materials to explain the

correlation between viscosity η, density ρ, and 2 observed in unassociated and polar


~ 31 ~

liquids. Such a correlation is not observed for associated liquids in which the presence

of hydrogen bonds between molecules apparently influences the annihilation process.

Roy et al. [192] studied the nanosize zinc ferrite samples with an average

particle size of 6–65 nm prepared by a new chemical reaction involving nitrates of Zn

and Fe and investigated for magnetic behaviour and defect structure. The sample with

an average particle size of 6 nm has considerable inversion in cation distribution as

shown by its hysteresis loop and increased magnetization.

Chakrabarti et al. [193] studied that Polyacrylonitrile (PAN)-based carbon

fibers, embedded with multi-wall carbon nanotubes (MWCNT) in different

concentrations, have been prepared by an electrospinning technique and investigated

using scanning electron microscopy, Raman, and positron annihilation spectroscopy.

An analysis of the positron lifetime and Doppler broadened spectral line shape has

been made. Positron lifetime spectra for all the samples give best fit for three distinct

lifetime components.

Biswas et al. [194] studied nanostructures of ZnS, both particles and rods,

synthesized through solvothermal processes and characterized by x-ray diffraction

and high resolution transmission electron microscopy. Positron lifetime and Doppler

broadening measurements were made to study the features related to the defect

nanostructures present in the samples. The nanocrystalline grain surfaces and

interfaces, which trapped significant fractions of positrons, gradually disappeared

during grain growth, as indicated by the decreasing fraction of ortho-positronium

atoms. The crystal vacancies present within the grains also trapped positrons. These

vacancies further agglomerated into clusters during the thermal treatment given to

effect grain growth.

Acosta et al. [195] studied the one of the basic mechanisms of radiation

embrittlement of steels is due to matrix damage. Embrittlement results in a raise in the

ductile-to-brittle transition temperature, which is used as indicator of the degradation

status of the material. The positron annihilation spectroscopy in lifetime set-up is used

for study the microstructural changes of matrix due to embrittlement.

Mishra et al. [196] studied the defects present in ZnO nanocrystals prepared

by a wet chemical method have been characterized by photoluminescence (PL) and

positron annihilation spectroscopy (PAS) techniques. The as-prepared sample was

heat treated at different temperatures to obtain nanocrystals in the size range of 19–39

nm. Positron annihilation spectroscopy has been employed to understand the


~ 32 ~

dynamics of the vacancy-type defects and their annealing behavior. The observed

variation of the defect related lifetime components with heat-treatment temperature

has been successfully explained by using a three-state trapping model. The results of

PL and PAS studies in the present case are found to be complementary to each other.

Nghiep et al. [197] studied the positron annihilation rate measurement in

Polyethylene Terephthalate (PET) films. The correlation between annihilation rates

and the PET film thickness was established.

Lichard et al. [198] studied the excitation curve of e+e- annihilation into four

charged pions in the ρ (770) region calculated using three existing models with ρ

mesons and pions in intermediate states supplemented by Feynman diagrams with the

a1(1260) π intermediate states.

Chaplygin et al. [199] shows that an effective method to define the size of

nano-objects (vacancies, vacancy, clusters, free pore volumes, cavities, and holes),

and their concentration and chemical composition, is positron annihilation

spectroscopy (PAS). A review of the state of the art of the application of the PAS

technique to probe nanostructures in porous silicon, silicon and single crystal quartz

samples is presented.

Ridder et al. [200] studied the production rates for two, three, four, and five

jets in electron-positron annihilation at the third order in the QCD coupling constant.

At this order, three-jet production is described to next-to-next-to-leading order in

perturbation theory while the two-jet rate is obtained at next-to-next-to-next-to-

leading order.

Itoh et al. [201] studied the three main classes of materials, metals,

semiconductors and polymers, studied by using the Positron annihilation lifetime

spectroscopy (PALS) technique which is a powerful tool for the investigation of

microstructure.

Sanyal et al. [202] studied the coincidence Doppler broadening of the positron

annihilation technique employed to identify the defects in thermally annealed 'as-

received' ZnO and thermally annealed ball-milled nanocrystalline ZnO. Results

indicate that a significant amount of oxygen vacancy has been created in ZnO due to

annealing at about 500 °C and above.

Cheng-Xiao et al. [203] studied the influence of dopants in ZnO films on

defects is investigated by slow positron annihilation technique. The dopant

concentration could determine the position of Fermi level in materials, while defect


~ 33 ~

formation energy of zinc vacancy strongly depends on the position of Fermi level, so

its concentration varies with dopant element and dopant concentration.

Ghoshal [204] studied the ZnO samples in the form of hexagonal-based

bipyramids and particles of nanometer dimensions synthesized through solvothermal

route and characterized by x-ray diffraction and transmission electron microscopy.

Positron annihilation experiments were performed to study the structural defects such

as vacancies and surfaces in these nanosystems. From coincidence Doppler

broadening measurements, the positron trapping sites were identified as Zn vacancies

or Zn–O–Zn trivacancy clusters. The positron lifetimes, their relative intensities, and

the Doppler broadened lineshape parameter S all showed characteristic changes across

the nano bipyramid size corresponding to the thermal diffusion length of positrons.

Tang et al.[205] studied the momentum density distributions determined by

the analysis of positron annihilation radiation in embedded nano Cu clusters in iron

were studied by using a first-principles method. A momentum smearing effect

originated from the positron localization in the embedded clusters is observed. The

smearing effect is found to scale linearly with the cube root of the cluster's volume,

indicating that the momentum density techniques of positron annihilation can be

employed to explore the atomic-scaled microscopic structures of a variety of impurity

aggregations in materials.

Heng et al. [206] investigated the nature of violet-blue emission from (Ge, Er)

co-doped Si oxides (Ge+Er+SiO2) using photoluminescence (PL) and positron

annihilation spectroscopy (PAS) measurements. The PL spectra and PAS analysis for

a control Ge-doped SiO2 (Ge+SiO2) indicate that Ge-associated neutral oxygen

vacancies (Ge-NOV) are likely responsible for the major emission in the violet-blue

band.

Das et al. [207] studied that the nanocrystalline samples of nickel oxide

synthesized through solvothermal and sol-gel routes, and the grain sizes determined

through x-ray diffraction and transmission electron microscopy. Fourier transform

infrared, optical absorption and positron annihilation spectroscopy studies were done

to characterize them further and study the defects at nanoscale. The onset of quantum

confinement effects is indicated by characteristic blue-shift in optical absorption

spectra and widening of the band gap. Positron annihilation parameters changed as a

result and the causes are discussed.


~ 34 ~

Mangalam et al. [208] studied the room temperature ferromagnetism in

nanoparticles of otherwise nonmagnetic materials attributed to point defects at the

surface of the nanoparticles. They have employed positron annihilation spectroscopy

to identify the nature of defects in multiferroic BaTiO3 nanocrystalline materials with

varying average particle sizes. Ratio curve analysis of the Doppler broadening profile

to a reference profile suggests that the defect is an oxygen vacancy. The decrease of

intensity of the intermediate lifetime component with increasing particle size indicates

a decrease of surface defect concentration. The large defect concentration in

nanocrystalline BaTiO3 can explain the observed room temperature ferromagnetism.

Oberdorfer et al. [209] studied the exact solution of a diffusion-reaction model

for the trapping and annihilation of positrons in grain boundaries of polycrystalline

materials with competitive trapping at intragranular point defects is presented.

Closed-form expressions are obtained for the mean positron lifetime and for the

intensities of the positron lifetime components associated with trapping at grain

boundaries and at intragranular point defects.

Hain et al. [210] investigated a friction stir welded (FSW) Al alloy sample by

Doppler broadening spectroscopy (DBS) of the positron annihilation line. The

spatially resolved defect distribution showed that the material in the joint zone

becomes completely annealed during the welding process at the shoulder of the FSW

tool, whereas at the tip, annealing is prevailed by the deterioration of the material due

to the tool movement.

R. Burcl et al. [211] studied the chemical composition of the material at the

annihilation sites (silicon atoms of the pore “wall”), the size of nanodefects, and their

concentration in porous silicon and single-crystal silicon wafers irradiated by protons

determined using the angular distribution of annihilation photons.

Wang et al. [212] studied the high purity ZnO nanopowders pressed into

pellets and annealed in air between 100o and 1200°C. The crystal quality and grain

size of the ZnO nanocrystals were investigated by x-ray diffraction. Positron

annihilation measurements reveal vacancy defects including Zn vacancies, vacancy

clusters, and voids in the grain boundary region. The voids show an easy recovery

after annealing at 100–700°C. However, Zn vacancies and vacancy clusters observed

by positrons remain unchanged after annealing at temperatures below 500°C and

begin to recover at higher temperatures. After annealing at temperatures higher than

1000°C, no positron trapping by the interfacial defects can be observed.


~ 35 ~

Acharya et al. [213] studied the Diffusion Trapping Model used to obtain the

positron annihilation Doppler broadening lineshape parameter in ZnO and O+, B+, N+,

Al+ implanted ZnO films. The concentration of vacancy clusters is found to be related

to the atomic number and the fluence of the implanted ion. The S-parameter is found

to be largest in the case of implantation of Al+ ions and is minimum for the

implantation of B+ ions. Thus, the vacancy clusters are found to be largest in the case

of Al+ implantation. The calculated results have been compared with the experimental

value.

Nambissan [214] reported that positron annihilation spectroscopy (PAS) is a

very useful tool to study the defect properties of nanoscale materials. The ability of

thermalized positrons to diffuse over to the surfaces of nanocrystallites prior to

annihilation helps to explore the disordered atomic arrangement over there and is very

useful in understanding the structure and properties of nanomaterials.

Pati et al. [215] studied the nanocomposites of Fe–NiO synthesized by the

mechanical milling technique. The phase purity of the sample was checked by X-ray

diffraction (XRD), which shows only lines of α-Fe and NiO. Presence of defects in

Fe–NiO nanocomposites ball-milled for prolonged durations is confirmed by positron

annihilation lifetime spectroscopy (PALS) measurements.

Simpson et al. [216] studied the silicon nanoclusters/nanocrystals (Si-nc) in

SiO2 matrix exhibit strong visible luminescence, and so are of interest in the pursuit of

a silicon-based light emitter for optoelectronics. They have investigated the formation

of Si-nc by implanting excess Si at 90 keV into SiO2 films and then annealing to form

nanoclusters by precipitation and ripening. Positron annihilation provides information

on vacancy-type defects produced during implantation. They suggest that defects may

play a key role in Si-nc formation.

Sarkar et al. [217] measured the room temperature positron annihilation

lifetime for single crystalline ZnO as 164 ± 1 ps. The single component lifetime value

is very close to but higher than the theoretically predicted value of ~154 ps.

Photoluminescence study (at 10 K) indicates the presence of hydrogen and other

defects, mainly acceptor related, in the crystal. The bulk positron lifetime in ZnO is

expected to be a little less than 164 ps.

Haynes et al. [218] studied the Fermi surface of the ferromagnetic shape-

memory alloy Ni2MnGa experimentally with two-dimensional angular correlation of

electron–positron annihilation radiation.


~ 36 ~

Maki et al. [219] studied the positron lifetime results under high-power steady-

state and transient optical excitation. The temperature dependences of transient and

steady-state measurements are studied, suggesting the possibility of analyzing the

positron trapping to extended defects and vacancy clusters in semiconductors.

1.8 Review on research work done using Mössbauer spectroscopy

Yuanzheng et al. [220] studied the nano-crystalline elemental iron powder

successfully formed by high-energy ball grinding. The x-ray diffraction, transmission

electron microscopy and Mössbauer spectroscopy were employed to follow the

structure changes in the process of mechanical grinding with milling time. The

broadening of Mössbauer spectrum is attributed to the large fraction of iron atoms

existing at the interfaces for the powder milled.

Ma et al. [221] studied the nickel ferrite ultrafine powders with different grain

sizes (8, 12, 20, 40 and 80 nm) synthesized chemically. Mössbauer spectra of 57Fe

nucleus in the samples composed of the nickel ferrite ultrafine powder before and

after the high pressure treatments have been measured. The superparamagnetic

relaxation is markedly suppressed by high pressure. The intensity of the sextets in

Mössbauer spectra increases with increasing the grain size or pressure.

Vijaya Kumar et al. [222] studied the magnetite nanorods prepared by the

sonication of aqueous iron (II) acetate in the presence of β-cyclodextrin. The

properties of the magnetite nanorods were characterized by x-ray diffraction,

Mössbauer spectroscopy, transmission electron microscopy, thermogravimetric

analysis, and magnetization measurements. The as-prepared magnetite nanorods are

ferromagnetic and their magnetization at room temperature is ~78emu/g.

Grave et al. [223] studied the various aspects, revealed by Mössbauer

spectroscopy, of structural and magnetic properties of Al-substituted small-particle

soil-related oxides. The ferrimagnetic-like behaviour reflected in the external-field

Mössbauer spectra (4.2 K, 60 kOe) of certain Al goethites is presented.

Predoi et al. [224] studied the two systems of nanoparticles with different

surface states have been prepared by sol-gel methods and analysed by X-ray

diffractometry, transmission electron microscopy, thermal analysis and temperature

dependent Mossbauer spectroscopy.


~ 37 ~

Malini et al. [225] studied the nanocomposites with magnetic components

possessing nanometric dimensions, lying in the range 1–10 nm, are found to be

exhibiting superior physical properties with respect to their coarser sized counterparts.

Magnetic nanocomposites based on gamma iron oxide embedded in a polymer matrix

have been prepared and characterized. The behaviour of these samples at low

temperatures have been studied using Mössbauer spectroscopy. Mössbauer studies

indicate that the composites consist of very fine particles of γ-Fe2O3 of which some

amount exists in the superparamagnetic phase. The cycling of the preparative

conditions were found to increase the amount of γ -Fe2O3 in the matrix.

Liu et al. [226] studied the Fe2O3–Al2O3 nano-composites synthesized by sol–

gel means. The properties of samples sintered at various thermal treatment

temperatures were investigated by X-ray diffraction (XRD) and Mössbauer

spectroscopy (MS). The experimental results show that the γ- to α-Al2O3

transformation occurs at lower temperature after iron oxide doping.

Chakraverty et al. [227] studied the theory of relaxation of single domain

magnetic nanoparticles, appropriate for analyzing measurements of Mössbauer

spectra, magnetization response, and hysteretic coercivity. With a special focus of

attention in the theoretical formulation is the presence of dipolar interaction between

the magnetic particles.

Sharma et al. [228] studied the nano particles of chromium substituted cobalt

zinc ferrite synthesized by a chemical co-precipitation method. X-ray diffraction

studies of the nano particles of CrxCo0.5−xZn0.5Fe2O4 (x = 0.1 to 0.5) heat-treated at

300 °C show that the particle sizes are in the range of 2 to 7 nm. Room temperature

Fe-57 Mössbauer spectra of all the samples show only two doublets, confirming the

presence of superparamagnetic relaxation in the nano particles. An exponential

decrease in the superparamagnetic blocking temperature, with increasing chromium

concentration, is observed for these samples.

Bahl et al. [229] demonstrate the exchange interactions between

antiferromagnetic nanoparticles of 57Fe-doped NiO varied by simple macroscopic

treatments. Mössbauer spectroscopy studies of the superparamagnetic relaxation

behaviour show that grinding or suspension in water of nanoparticles of NiO can

significantly reduce interparticle interactions.

Bandyopadhyay [230] write a comprehensive review on the recent

contributions of Mössbauer spectroscopy in materials science and engineering. After a


~ 38 ~

brief introduction to the basic methodology, examples of the application of 57Fe and 119Sn Mössbauer spectroscopy in both transmission and back-scattering mode are

presented and discussed.

Delcroix et al. [231] showed the Mössbauer spectra reflect the strong

sensitivity of the distribution of hyperfine magnetic field distributions (HMFDs) of

near equiatomic Fe–Cr alloys to the method of preparation of samples. Whatever the

way a bcc Fe0.51Cr0.49 alloy is prepared, powders produced from it by ball milling or

by filing exhibit a unique HMFD at room temperature.

Mukherjee et al. [232] studied the Fe–MgO nanocomposites synthesized by

the mechanical high-energy transfer technique characterized by x-ray diffraction

(XRD), transmission electron microscopy, Mössbauer spectroscopy and dc

magnetization studies. By varying the duration of milling, powder with different grain

sizes in the range 17–40 nm was produced. XRD and Mössbauer measurements could

not detect the presence of any form of iron oxide in the nanocomposites. Transmission

electron micrographs showed a shape transformation from spherical to acicular-like

geometry in the samples ball milled for more than 36 h.

Felner et al. [233] studied the 57Fe (1%) doped SrCoO3 obtained by high-

pressure method, investigated by magnetization and Mössbauer spectroscopy studies

(MS) in the temperature range 4.2 K to 300 K. The ferromagnetic ordering

temperature TC obtained is 272(2) K. Isothermal magnetization curves have been

measured at various temperatures, from which the saturation moments (M sat) have

been deduced.

Kiseleva et al. [234] used the Mossbauer spectroscopy and X-ray diffraction

for structural study of nanopowders resulting from a 60% Fe + 40% Al mixture after

mechanical activation, as well as their nanocomposite derivatives arising in the

process of self-propagating high-temperature synthesis. The different nature of the

iron-aluminum interaction in these nanotechnological processes is demonstrated.

Filoti et al. [235] showed that the laser pyrolysis became a useful tool,

providing various ways, in production of nano materials. The iron Mössbauer

spectroscopy is one very accurate method in evidencing the physical properties and

related processes in the nano scale compounds. The effect of pressure, laser spot area

and induced combustion, of gas mixture and laser power on the phase composition

and inside particle distribution, grain size as well as the related phenomena were

investigated by temperature dependent Mössbauer spectroscopy.


~ 39 ~

Thakur et al. [236] studied the nano-nickel-zinc-indium ferrite (NZIFO)

(Ni0.58Zn0.42InxFe2−xO4) with varied quantities of indium (x = 0,0.1,0.2) synthesized

via reverse micelle technique. The addition of indium in nickel-zinc ferrite (NZFO)

has been shown to play a crucial role in enhancing the magnetic properties. Room

temperature Mössbauer spectra revealed that the nano-NZFO ferrite exhibit collective

magnetic excitations, while indium doped NZFO samples have the ferromagnetic

phase. The dependence of Mössbauer parameters, viz. isomer shift, quadrupole

splitting, linewidth, and hyperfine magnetic field, on In3+ concentration has been

studied.

Lyubutin et al. [237] used a thermal reduction method developed to prepare

magnetite/hematite nanocomposites and pure magnetite nanoparticles targeted for

specific applications. The relative content of hematite α-Fe2O3 and magnetite Fe3O4

nanoparticles in the product was ensured by maintaining proper conditions in the

thermal reduction of α-Fe2O3 powder in the presence of a high boiling point solvent.

The structural, electronic, and magnetic properties of the nanocomposites were

investigated by 57Fe-Mössbauer spectroscopy, x-ray diffraction, and magnetic

measurements.

Andrade et al. [238] studied the nano-sized materials often present chemical,

electronic, magnetic, and mechanical properties that are potentially interesting for

many technological applications comparatively to their corresponding bulk properties.

This paper describes the main differences in magnetic properties among

nanomagnetite powders prepared by three methods: (I) reduction-precipitation of

ferric chloride by reaction with Na2SO3; (II) reduction of hematite with coal, and (III)

reduction of hematite with hydrogen gas. XRD and Mössbauer spectroscopy results at

298 K showed the clear effect of the preparation routes on the crystallographic

structure and crystallite size of the magnetic species.

Mishra et al. [239] studied the behavior of strain, magnetization, and

resistivity of a nanoporous Au0.55Fe0.45 alloy studied in situ during electrochemically

induced charge variations on the surface of the alloy. In situ Mössbauer spectra

recorded during charging and decharging showed a systematic variation in quadrupole

splitting.

Babilas [240] studied on Fe72B20Si4Nb4 metallic glass in form of ribbons. The

amorphous structure of tested samples was examined by XRD and TEM. Mössbauer

spectroscopy method was applied to comparison of structure in studied amorphous


~ 40 ~

samples with different thickness (cooling rates).The paper presents a structure

characterization of selected Fe-based metallic glass in as-cast state.

Chakrabarti et al. [241] reported that the Mössbauer Spectroscopic technique

is an important nuclear solid technique which has been used to probe the local

magnetic properties of a solid. They have reported Mössbauer spectroscopic studies

on different ferrites.

Antic et al.[242] studied that the structural and magnetic properties of

(Mn,Fe)3-δO4 nanoparticles synthesized by soft mechanochemistry using Mn(OH)2× 2

H2O and Fe(OH)3 powders as starting compounds. The Combined results of XRPD,

Mössbauer spectroscopy, and EDX analysis suggest that there is a deviation from

stoichiometry in the nanoparticle core compared to the shell, accompanied by creation

of cation polyvalence and vacancies. The value of saturation magnetization, MS, of

73.5 emu/g at room temperature, is among the highest reported so far among

nanocrystalline ferrite systems of similar composition.

Zakharova et al. [243] studied that the Mössbauer spectroscopy has been used

to study maghemite (γ-Fe2O3) particles with average dimensions on the microscopic

(~1 μm, “bulk” state) and nanoscopic (15 and 20 nm) levels. Data provided by this

method on the thickness of a surface region of magnetic nanoparticles and features of

their magnetic state have been analyzed.

1.9 The aim and objectives of the present work

Materials in nanocrystalline form are now being prepared widely because of

their wide range of applications in different fields. Structural imperfections in such

nanomaterials contribute a massive change in different properties of these materials.

Material characterizations in terms of detailed study of lattice imperfections in

particular, are essential for the systematic development of such nanomaterials as well

as for qualification of materials for design and fabrication. Today, there are several

techniques for material characterization. They often depend on how a given sample

responds to a probe. The probe may be electrons, positrons, neutrons, ions,

electromagnetic radiation (x-ray, gamma rays etc), ultra sound etc. In this research

work, Positron Annihilation Lifetime (PAL) spectroscopy, X-ray powder diffraction

(XRD) and few other methods of microstructure characterization would be discussed

which are usually used for characterization of nanomaterials.


~ 41 ~

Presently, oxides in its nanocrystalline phase become very important due to

their wide applications. The large surface to-volume ratio of these nanomaterials

makes them different from the bulk of the material. Among them, magnetic

nanomaterials have received special attention as they can be used in different fields

like magnetic resonance imaging, drug delivery agents, etc. Among different

magnetic nanoparticles, α-Fe2O3 has large applications in chemical industry. It can be

used as catalyst, gas sensing material to detect combustible gases like CH4 and C3H8

etc. Further, an unusual characteristic like superparamagnetism in nanocrystalline

state of these materials makes them object of great interest for fundamental studies.

Among different iron oxides, α-Fe2O3 is the most stable polymorph in nature under

ambient condition and can be easily found as mineral hematite. Again nanocrystalline

materials, semiconductors in particular (ZnO), are being widely investigated at

present because of their interesting electronic and optical properties which may find

applications in devices such as solar cells, light emitting diodes, ultraviolet (UV)

lasers, fluorescent displays, etc. Ferrites are a group of technologically important

materials used in magnetic, electronic and microwave fields. Magnetic

nanocrystalline materials hold great promise for atomic engineering of materials with

functional magnetic properties. Magnetic nanocrystals have been extensively applied

in magnetic recording medium, information storage, bio-processing and magneto-

optical devices. Usually, magnetic nanocrystals show superparamagnetic behaviour

below a certain critical size.

The objects of the dissertation are to (i) preparation of nanocrystalline oxide

materials of different kinds by mechanical alloying and chemical route, (ii) analyze

the structure and microstructure of the nanocrystalline materials by X-ray line profile

analysis employing the Rietveld structure and microstructure refinement and HRTEM

(iii) characterize the defect state of nanocrystalline materials in terms of lattice

imperfections employing Positron Annihilation Lifetime Spectroscopy, (iv) Magnetic

characterization of some magnetic nanoparticles using Mossbauer Spectroscopy (v)

measurement of optical band gap in some cases using UV-Vis absorption

spectrometer.

1.10 References [1] M. Laue, W. Friedrich and P. Knipping, Ann, Phys. Lpz., 41 (1912) 199.

[2] W.L. Bragg, Proc. Camb. Phil. Soc., 17 (1913) 43.


~ 42 ~

[3] H.G.J. Moseley, Phil. Mag. (1913) 1024.

[4] J.G. Byrne,’Recovery, Crystallization and Grain Growth’, McMillan Co., N.

Y. (1965).

[5] J.B. Newkirk, J. Appl. Phys., 29 (1958) 995.

[6] J.B. Newkirk, Trans. AIME., 215 (1959) 483.

[7] P.B. Hirsch, A. Howie and M.J. Whelan, Phil. Trans. Roy. Soc., A252 (1960)

499.

[8] W. Bollmann, Phys. Rev., 103 (1956) 1588.

[9] W.M. Stobbs and C.H. Sworn, Phil. Mag., 24 (1971) 1365.

[10] D.H.J. Cockayne, M.L. Jenkins and I.L. Ray, Phil. Mag., 24 (1971) 1383.

[11] B.E. Warren, Prog. Met. Phys., 8 (1959) 147.

[12] B.E. Warren, ‘X-ray diffraction’, Addision-Wesley, Reading, Mass, (1969).

[13] C.N.J. Wagner, Local Atomic Arrangement Studied by X-ray Diffraction’, ed.

J. B. Cohen and J.E. Hilliard, N.Y., Gordon Breach, (1966).

[14] H.M. Rietveld, Acta Crystallogr., A228 (1966) 21.

[15] G.S. Pawley, J. Appl. Cryst., 14 (1981) 357.

[16] E. Jartych, J.K. Zurawicz, D. Oleszak, M. Pekala, J. Mag. Matter, 208(2000)

221.

[17] S. Kumar, K. Roy, K. Maity, T.P. Sinha, D. Banerjee, K.C. Das, R.

Bhattacharya, Phys. Stat Sol. (a), 167 (1998) 12.


Bhattacharya, Phys., Stat Sol. (a) 175 (1999) 927.

[19] E. Jartych, J.K. Zurawicz, D. Oleszak, M. Pekala, J. Magn. Magn. Mater. 208

221 (2000).

[20] A.J.C. Wilson, ‘Mathematical Theory of X-ray Powder Diffractometry’

Centrex Publishing Co., Eindhoven, (1963) 66.

[21] C.S. Barrett and T.B. Massalski, ‘Structure of Metals’, McGraw-Hill, Inc., N.

Y. (1966).

[22] H.P. Klug and L.F. Alexander, ‘X-ray diffraction Procedures’, John-Wiley and

Sons., N. Y. (1974).

[23] E.F. Bertaut, C.R. Acad. Sci., Paris, 228 (1949) 492.

[24] C.S. Barrett, Trans. AIME, 188 (1950) 123.

[25] B.E. Warren and B.L. Averbach, J. Appl. Phys., 21 (1950) 595.

[26] B. E. Warren and B.L. Averbach, J. Appl. Phys., 23 (1952) 497.


~ 43 ~

[27] B.E. Warren and E.P. Warekois, Acta. Met., 3 (1955) 473.

[28] G.K. Williamson and R.E. Smallman, Phil. Mag., 1 (1956) 34.

[29] C.N.J. Wagner, Acta. Met., 5 (1957) 427.

[30] C.N.J. Wagner, Acta. Met., 5 (1957) 477.

[31] D. Michell and F.D. Hiag, Phil. Mag., 2 (1957) 15.

[32] R.E. Smallman and K.H. Westmacott, Phil. Mag., 2 (1957) 669.

[33] J.W. Christian and Spreadborough, Proc. Phys. Soc. (London), B70 (1957)

1151.

[34] R.W. Chan and R.G. Davies, Phil. Mag., 5 (1960) 1119.

[35] L.F. Vassamillet, J. Appl. Phys., 32 (1961) 778.

[36] R.G. Davies and R.W. Cahn, Acta. Met., 10 (1962) 621.

[37] M.J. Klein, J.L. Brimhall and R.A. Huggins, Acta. Met., 10 (1962) 13.

[38] D.O. Welch and H.M. Otte, Adv. X-ray Anal., 6 (1962) 96.

[39] R.P. I. Alder and C.N.J. Wagner, J. Appl. Phys., 33 (1962) 3451.

[40] J.H. Foley, R.W. Cahn and G.V. Raynor, Acta Met., 11 (1963) 355.

[41] L.F. Vassamillet and T.B. Massalski, J. Appl. Phys., 34 (1963) 3398.

[42] A. Howie and P.R. Swann, Phil. Mag., 6 (1961) 1215.

[43] R.C. Sundahl and J.M. Sivertsen, J. Appl. Phys., 34 (1963) 994.

[44] S. Koda, K. Nomaki and M. Nemoto, J. Phys. Soc. (Japan), 18 (1963) 118.

[45] L.F. Vassamillet and T.B. Massalski, J. Appl. Phys., 35 (1963) 2629.

[46] K. Nakajima and K. Numakura, Phil. Mag., 12 (1965) 361.

[47] C.N.J. Wagner and J.C. Helion, J. Appl. Phys., 36 (1965) 2830.

[48] S. Lele and T.R. Anatharamam, Z. Metallkunde, 58 (1967) 11.

[49] S. Lele and T.R. Anatharamam, Phil Mag., 58 (1967) 37.

[50] H.M. Otte, J. Appl. Phys., 38 (1967) 217.

[51] S.P. Sengupta and M.A. Quader, Acta. Cryst., 20 (1966) 798.

[52] K.N. Goswami, S.P. Sengupta and M.A. Quader, Acta. Cryst., 21 (1966) 243.

[53] M. De and S.P. Sengupta, Acta. Cryst., 24 (1968) 269.

[54] P.R. Rao and K.K. Rao, J Appl. Phys., 39 (1968) 4563.

[55] L. Delehouzee and A. Deruyttere Acta. Met., 15 (1967) 729.

[56] M. Ahlers and L.F. Vassamillet, ‘Adv. X-ray Analysis’, 10 (1967) 265.

[57] H.M. Rietveld, Acta Crystallogr., A228 (1966) 21.

[58] H.M. Rietveld Acta Cryst., 20 (1966) 508.


~ 44 ~

[59] D.L. Decker, R.A. Beyerlein, G. Roult and T.G. Worlton, Phys. Rev B., 10

(1974) 3584.

[60] J.M. Carpenter, M.H. Mueller, R.A. Beyerlein, T.G. Worlton, J.D. Jorgensen,

T.O. Burn et al., Proc. Neutron Diffraction Conf., Petten, The Netherlands, 5-6

Aug., (1975) 192.

[61] C.G. Windsor and R.N. Sinclair, Acta Cryst., A32 (1976) 395.

[62] A.K. Cheetham and J.C. Taylor, J. Solid State Chem., 21 (1977) 253.

[63] P.E. Mackie and R.A. Young, Acta. Cryst., A31 (1975) 198.

[64] G. Malmros, and J.O. Thomas, J. Appl. Cryst., 10 (1977) 7.

[65] R.A. Young, P.E. Mackie and R.B. Von Dreele, J. Appl. Cryst., 10 (1977)

262.

[66] C.P. Khattak and D.E. Cox, J. Appl. Cryst., 10 (1977) 405.

[67] D.B. Wiles and R.A. Young, J. Appl. Cryst., 14 (1981) 149.

[68] H.M. Rietveld, Acta Cryst., 29 (1969) 65.

[69] R.A. Young, A. Sakthivel, T.S. Moss and C.O. Paiva-Santos, J. Appl. Cryst.,

28 (1995) 366.

[70] S.A. Howard, ‘Advances in Material Characterization II’ ed R.L. Synder, R.A.

Condrate and P.F. Johnson (New York: Plenum) (1985) 43.

[71] R.J. Hill and C.J. Howard, Austral. Atomic Energy Comm Rep. No. M112,

(1986).

[72] D.P. Matheis and R. L. Synder, Powder Diffrac., 9 (1994) 28.

[73] J. Rodriguez-Carvajal, ‘Collected Abstract of Powder Diffraction Meeting’,ed.

J. Galy Toulouse, France, (1990) 127.

[74] A.C. Larson and R.B. Von Dreele, Los Alamos Nat. Lab. Report No.

LA_UR86-748 (1987).

[75] C. Baerlocher, XRS-82, The X-ray Rietveld system, Inst. fur Krist., ETH,

Zurich, (1982).

[76] L. Lutterotti, P. Scardi and P. Maistrelli, J. Appl. Cryst., 25 (1992) 459.

[77] F. Izumi, Nippon Kessho Gakkai Shi (J. Cryst. Soc. Jpn.), 27 (1985) 23.

[78] F. Izumi, Rigaku. J., 6 (1989) 10.

[79] M. Ferrari and L. Lutterotti, J. Appl. Phys., 76 (1994) 7246.

[80] Werner,P.E,Mater Sci.Forum.,79-82 (1991) 197-206.

[81] M. Ferrai, L. Lutterotti, S. Mathies, P. Polonioli, H.R. Wenk, Mater. Sci.

Forum., 228-231 (1996) 83.


~ 45 ~

[82] L. Lutterotti, S. Mathies, H.R. Wenk, A.J. Schultz, J. Richardson, J. Appl.

Phys., 81 (1997) 594.

[83] S. Mathies, L. Lutterotti, H.R. Wenk, J. Appl. Cryst., 30 (1997) 31.

[84] L. Lutterotti, S. Gialanella, Acta Materialia, 46 (1998) 101.

[85] A Le Bail, H. Duroy, J.L. Fourquet, Mater. Res. Bull., 23 (1988) 447.

[86] M.M. Hall Jnr., V.G. Veeraraghavan, H.Rubin, P.G. Winchell, J. Appl. Cryst.,

10 (1977) 66.

[87] J.I. Langford, J. Appl. Cryst. 11 (1978) 10.

[88] G.K. Wertheim, M.A. Butler, K.W. West, D.N.E. Buchanan, Rev. Sci.

Instrum., 11 (1974) 1369.

[89] R.A. Young, D.B. Wiles, J. Appl. Cryst., 15 (1982) 430.

[90] J.I. Langford, Prog. Cryst. Growth and Charact., 14 (1987) 185.

[91] W.A. Dollase, J. Appl. Cryst., 19 (1986) 267.

[92] M. Ahtee, M. Nurmela, P. Suortti, M. Jarvinen, J. Appl. Cryst., 22 (1989) 261.

[93] H.R. Wenk, S. Mathies, L. Lutterotti, Mater. Sci. Forum. 157-162 (1994) 473.

[94] J.I. Langford, R. Delhez, T.H. de Keijser, E.J. Mittemeijer, Austral. J. Phys.,

41 (1988) 173.

[95] R. Delhez, T.H. de Keijser, J.I. Langford, D. Louer, E.J. Mittemeijer, E.J.

Sonneveld, ‘The Rietveld Method’ ed by R. A. Young, Oxford University

Press, (1993) 132.

[96] X. Bokhimi, A. Morales, O. Novaro, T. Lόpez, E. Sánchez, R. Gόmez, J.

Mater. Research, 10 (1995) 2788.

[97] E. Sánchez, T. Lόpez, R. Gόmez, Bokhimi, A. Morales, O. Novaro, J. Solid

State Chem., 122 (1996) 309.

[98] Xiao, Bokhimi, Beniassa, Perez, Strutt, Yacaman, Acta Mater., 45 (1997)

1685.

[99] P. Riello, G. Fagherazzi, P. Canton, D. Clemente, M. Signoretto, J. Appl.

Cryst., 28 (1995) 121.

[100] T. Ungár, M. Leoni, P. Scardi, J. Appl. Cryst., 32 (1999) 290.

[101] N.C. Popa, J. Appl. Cryst., 31 (1998) 176.

[102] P. Scardi, M. Leoni, J. Appl. Cryst., 32 (1999) 671.

[103] T. Ungár, I. Dragomir, Á. Révész, A. Borbély, J. Appl. Cryst., 32 (1999) 992.

[104] P.E. Di Nunzio, S. Martelli, J. Appl. Cryst., 32 (1999) 546.

[105] N. Armstrong, W. Kalceff, J. Appl. Cryst., 32 (1999) 600.


~ 46 ~

[106] P. Scardi, M. Leoni, Y.H. Dong, Eur. Phys. Journal B, 18 (2000) 23.

[107] P. Scardi, Y.H. Dong, M. Leoni, Proceeding of EPDIC-7 Barcelona, (2000)

20.

[108] L. Lutterotti, R. Ceccato, R. Dal Maschio, E. Pagani, Mater. Sci. Forum, 278-

281 (1998) 87.

[109] X. Bokhimi, J.L Boldu, E. Munoz, O. Novaro, T. López, J. Hernandez, R.

Gómez and A. Garcia-Ruiz, Chem. Mat., 11 (1999) 2716.

[110] M. Blouin, D. Guay, R. Schulz, J. Mater. Sci., 34 (1999) 5581.

[111] G. Rixecker, R. Haberkorn, J. Alloy. Compd., 316 (2001) 203.

[112] J.A. Wang, R. Limas-Ballesteros, T. López, A. Moreno, R. Gómez, O.

Novaro, X. Bokhimi, J. Phys. Chem. B ,105 (2001) 9692.

[113] P. Bose, S.K. Shee, S.K. Pradhan, M. De, Mater. Engg., 12 (2001) 353.

[114] P. Bose, S. Bid, S.K. Pradhan, M. Pal, D. Chakravorty, J. Alloy. Compd., 343

(2002) 192.

[115] S. Pratapa, B. O'Connor, B. Hunter, J. Appl. Crystallogr., 35 (2002) 155.

[116] S. Bid, S.K. Pradhan, J. Appl. Cryst., 35 (2002) 517.

[117] H. Dutta, S.K. Pradhan, Mater. Chem. Phys., 77 (2003) 868.

[118] S.K. Manik, S.K. Pradhan, Mater. Chem. Phys., 86 (2004) 284.

[119] S.K. Manik, S.K. Pradhan, Physica E, 33 (2006) 160.

[120] A. Sarkar, P. Mukherjee, P. Barat, Z. Kristallogr. Suppl., 26 (2007) 543.

[121] H.M. Rietveld, proceedings of XVIIth IUCR conf. Scottland, (1999) 14.

[122] Z.K. Heiba, L. Arda, Crystal Research and Technology, 44 (2009) 845.

[123] O.M. Lemine, A. Alyamani, M. Bououdina, International Journal of

Nanoparticles, 2 (1-6) (2009) 238.

[124] S. Sivestrini, P. Riello, I. Freris, D. Cristofori, F. Enrichi, A. Benedetti, J

Nanopart Res., 12 (2010) 993.

[125] Tebib, Wassila; Alleg, Safia; Bensalem, Rachid; Greneche, Jean-Marc,

International Journal of Nanoparticles, 3 (3) (2010) 237.

[126] F. Pola-Albores, F. Paraguay-Delgado, W. Antúnez-Flores, P. Amézaga-

Madrid, E. Ríos-Valdovinos, M. Miki-Yoshida, Journal of Nanomaterials,

2011 (2011), Article ID 643126, 11 pages doi:10.1155/2011/643126.

[127] M. Vagadia, A. Ravalia, U. Khachar, P.S. Solanki, R.R. Doshi, S. Rayaprol,

D.G. Kuberkar, Materials Research Bulletin, 46 Issue 11 (2011) 1933.


~ 47 ~

[128] Y.M. Abbas, S.A. Mansour, M.H.Ibrahim, S.E. Ali, Journal of Magnetism and

Magnetic Materials, 323 Issue 22 (2011) 2748.

[129] C.T. Cherian, M.V. Reddy, G.V.S. Rao, C.H. Sow, B.V.R. Chowdari, J Solid

State Electrochem, 16 (2012) 1823.

[130] E.S.U. Laine, E.J. Hiltunen, M.H. Heinonen, Acta. Met., 28 (1990) 1565.

[131] A.M. Tonejc and A. Bonefacic, J. Mater. Sci., 15 (1970) 1561.

[132] R. Delhez, T.H. de Keijser, E.J. Mittemeijer, Acuuracy in Powder

Diffraction,’ ed S. Block, C.R. Hubbard, NBS spec. 567 (1980) 213.

[133] R. Delhez, Th. De Keijser, E.J. Mittemeijer, J.I. Langford, J. Appl. Cryst., 19

(1986) 459.

[134] S.K. Ghosh, M. De, S. P. Sengupta, J. Appl. phys., 54 (1983) 2073.

[135] S.K. Ghosh, M. De, S. P. Sengupta, J. Appl. phys., 56 (1984) 1213.

[136] S.K. Ghose, S. P. Sengupta, Metall. Trans. A, 16A (1985) 1427.

[137] T. Ekstrom, C. Chatfield, J. Mater. Sci., 20 (1985) 1266.

[138] S.V. Reddy, S.V. Suryanarayana, Bull. Mater. Sci., 8 (1986) 61.

[139] G. Bhikshamaiah, S.V. Suryanarayana, J. Less-Common Mat., 120 (1986)

189.

[140] R. Delhez, T.H. de Keijser, J.I. Langford, D. Louer, E.J. Mittemeijer, E.J.

Sonneveld, ‘The Rietveld Method’ ed by R. A. Young, Oxford University

Press, (1993) 132.

[141] S.K. Pradhan, A.K. Maity, M. De, S.P. Sengupta, J. Appl. Phys., 62 (1987)

1521.

[142] S.K. Pradhan, M. De, J. Appl. Phys., 64 (1988) 2324.

[143] S.K. Pradhan, M. De, Metall. Trans. A, 20(1989)1883.

[144] S.K. Shee, S.K. Pradhan, M. De, J. Alloys and Comps., 265 (1998) 249.

[145] D. David, R. Bonnet, Phil. Mag. Letts., 62 (1990) 89.

[146] W.S. Yang, C. N. Wan, J. Mater. Sci.,25 (1990) 1821.

[147] D. Balzer, H. Ledbetter, A. Rashko, Physica C, 185-189 (1991) 871.

[148] A.C. Vermeulen, R. Delhez, T.H. de Keijser, E.J. Mittemeijer, J. Mater. Sci.

Forum, 79-82 (1991) 119.

[149] A.C. Vermeulen, R. Delhez, T.H. de Keijser, E.J. Mittemeijer, J. Appl. Phys.,

71 (1992) 5303.

[150] M.N. Rosengard, H.L. Skriver, Phys. Rev. B., 47 (1993) 12865.

[151] H. Pal, S.K. Pradhan, M. De, Jpn. J. Appl. Phys., 32 (1993) 1164.


~ 48 ~

[152] H. Pal, S.K. Pradhan, M. De, Mater. Trans. JIM., 36 (1995) 490.

[153] V.A. Drits, D.D. Eberl, J. Srodon, Clays and Clay Minerals., 46 (1998) 38.

[154] P. Chatterjee, S.P. Sengupta, J. Appl. Cryst., 32 (2000) 1060.

[155] P. Mukherjee, S.K. Chattopadhyay, S.K. Chatterjee, A.K. Meikap, P. Barat,

S.K. Bandyopadhyay, P. Sen, M.K. Mitra, Metall.and Mater.Trans.A, 31

(2000) 2405.

[156] V. Jayan, M.Y. Khan, M. Husain, Science Direct, 58 (2004) 2569.

[157] A.L. Ortiz, L. Shaw, Acta Materialia, 52 (2004) 2185.

[158] M.S. Haluska, I. C. Dragomir, K.H. Sandhage, R.L. Snyder, Powder Diffr., 20

(2005) 306.

[159] V. Uvarovand, I. Popov, ScienceDirect, 58 (2007) 883.

[160] V. Biju, N. Sugathan, V. Vrinda, S.L. Salini, Journal of Materials Science, 43

(2008) 1175.

[161] Y. Oba, T. Sato, T. Shinohara, Phys. Rev. B, 78 (2008) 224417.

[162] A.A. Ebnalwaled, M. Abou Zied, Journal of Nano Research, 9 (2010) 61.

[163] Y. Ganjkhanlou, F.A. Hessari, M. Kazemzad, G. Darbandi, physica status

solidi (c), 7 (2010) 2667.

[164] J. Rivnay, R. Noriega, R.J. Kline, A. Salleo, M.F. Toney, Physical Review B-

Condensed Matter and Materials Physics, 84 Issue 4 (2011) Article no.

045203.

[165] D. Wardecki, R. Przeniosło, A.N. Fitch, M. Bukowski, R. Hempelmann, J

Nanopart Res.,13 (2011) 1151.

[166] M. Back, A. Massari, M. Boffelli, F. Gonella, P. Riello, D. Cristofori, R.

Ricco, F. Enrichi, J Nanopart Res.,14 (2012) 792.

[167] M.J. Fluss, L.C. Smedskjaer, M.K. Chason, D.G. Legnini, R.W. Siegel, Phys.

Rev. B, 17 (1978) 3444.

[168] R. Krishnan, D.D. Upadhyaya, Pramana, 24 (1985) 351.

[169] R. Chidambaram, M.K. Sanyal, P.M.G. Nambissan, P. Sen , J. Phys.:

Condens. Matter 2, (1990) 9941.

[170] L. Yongming, B. Johansson, R.M. Nieminen, J. Phys.: Condens. Matter, 3

(1991) 2057.

[171] C. Hübner, T. Staab, R. Krause-Rehberg, Applied Physics A: Materials

Science & Processing, 61 (2) (1995) 203.

[172] T.C. Sandreczki, X.Hong, Y.C. Jean, Macromolecules, 29 (11) (1996) 4015.


~ 49 ~

[173] C.C. Haung, I.M. Chang, Y.F. Chen, P.K. Tseng, Physica. B, Condensed

matter, 245 (1998) 9.

[174] V.P. Shantarovich, Z.K. Azamatova, Yu.A. Novikov, Yu.P. Yampolskii,

Macromolecules, 31 (12) (1998) 3963.

[175] R. Würschum, E. Shapiro, R. Dittmar, H. E. Schaefer, Phys. Rev. B, 62 (2000)

12021.

[176] T.E.M. Staab, E. Zschech, R. Krause-Rehberg, Journal of Materials Science,

35(18) (2000) 4667.

[177] T.L. Dull, W.E. Frieze, D.W. Gidley, J. Phys. Chem. B, 105 (20) 2001 4657.

[178] B. Lizama, R. López-Castañares, V. Vilchis, F. Vázquez and V. Castaño,

Materials Research Innovations, 5 (2) (2001) 63.

[179] V.I. Grafutin, E.P. Prokop'ev, (2002) Phys.-Usp. 45 59.

[180] Y. Zheng, Y. Zheng, R. Ninga, Materials Letters., 57 (2003) 2940.

[181] A. Mokrushin, I. Bardyshev, N. Serebryakova, V. Starkov, Physica Status

Solidi (a), 197 (2003) 212.

[182] Y. Nagai, K. Takadate, Z. Tang, H. Ohkubo, H. Sunaga, H. Takizawa, M.

Hasegawa, Physical Review B, 67 (2003) 224202.

[183] Z.Q.Chen, S.Yamamoto, M. Maekawa, A. Kawasuso, X.L. Yuan, T,

Sekiguchi, Journal of Applied Physics, 94 (2003) 4807.

[184] R.E. Galindoa, A.V. Veena, H. Schuta, C.V. Faluba, A.R. Balkenendeb, G.de

Withc, J.Th.M. De Hosson, Composites Science and Technology 63 (2003)

1133.

[185] M. Chakrabarti, S. Dutta, S. Chattapadhyay, A. Sarkar, D. Sanyal and A.

Chakrabarti, Nanotechnology, 15 (2004) 1792.

[186] D.B. Cassidy, S.H.M. Deng, R.G. Greaves, T. Maruo, N. Nishiyama, J.B.

Snyder, H.K.M. Tanaka, A.P. Mills, Jr. Phys. Rev. Lett., 95(2005) 195006.

[187] J. Kuriplach, Acta Physica Polonica A, 107 (5) (2005) 784.

[188] Y. Zheng, R. Ning, Y. Zheng, Journal of Reinforced Plastics and Composites,

24 (3) (2005) 223.

[189] S. Kar, S. Biswas, S. Chaudhuri, P.M.G. Nambissan, Phys. Rev. B, 72 (2005)

075338.

[190] S. Kar, S. Chaudhuri, P.M.G. Nambissan, Journal of Applied Physics, 97

(2005) 014301.


~ 50 ~

[191] B.V. Thosar, R.G. Laciu, V.G. Kulkarni, G. Chandra, physica status solidi (b),

55 (2006) 415.

[192] M.K. Roy, B. Haldar, H.C. Verma, Nanotechnology, 17 (2006) 232.

[193] K. Chakrabarti, P.M.G. Nambissan, C.D. Mukherjee, K.K. Bardhan, C. Kim,

K.S. Yang, Carbon, 44 (2006) 948.

[194] S. Biswas, S. Kar, S. Chaudhuri, P.M.G. Nambissan, J. Chem. Phys., 125

(2006) 164719.

[195] B. Acosta, A. Zeman, L. Debarberis, International Journal of Microstructure

and Materials Properties, 1 (3-4) (2006) 310.

[196] A.K. Mishra, S.K. Chaudhuri, S. Mukherjee, A. Priyam, A. Saha, D. Das, J.

Appl. Phys., 102 (2007) 103514.

[197] T.D. Nghiep, K.T. Tuan, N.D. Du, International Journal of Nuclear Energy

Science and Technology, 3 (4) (2007) 422.

[198] P. Lichard, J. Juran, Phys. Rev. D, 76 (2007) 094030.

[199] Y.A. Chaplygin, S.A. Gavrilov, V.I. Grafutin, E. Svetlov-Prokopiev, S.P.

Timoshenkov, Proceedings of the Institution of Mechanical Engineers, Part N:

Journal of Nanoengineering and Nanosystems, 221 (4) (2007) 125.

[200] A. Gehrmann-De Ridder, T. Gehrmann, E.W. Glover, G Heinrich, Phys Rev

Lett., 100 (17) (2008) 172001.

[201] Y. Itoh , A Shimazu , Y Sadzuka , T Sonobe , S Itai , Int J Pharm., 358(1-2)

(2008) 91.

[202] D. Sanyal, T.K. Roy, M. Chakrabarti, S. Dechoudhury, D. Bhowmick , A.

Chakrabarti, Journal of Physics: Condensed Matter, 20 (2008) 045217.

[203] P. Cheng-Xiao, W. Hui-Min, Z. Yang, M. Xing-Ping, Y. Bang-Jiao, Chin.

Phys. Lett, 25(12) (2008) 4442.

[204] T. Ghoshal, S. Biswas, S. Kar, S. Chaudhuri, P.M.G. Nambissan, J. Chem.

Phys., 128 (2008) 074702.

[205] Z. Tang, T. Toyama, Y. Nagai, K. Inoue, Z.Q. Zhu , M. Hasegawa, Journal of

Physics: Condensed Matter, 20 (2008) 445203.

[206] C.L. Heng, E. Chelomentsev, Z.L. Peng, P. Mascher, P.J. Simpson, , Journal

of Applied Physics, 105 (2009) 014312.

[207] S. Das, T. Ghoshal, P.M.G. Nambissan, Physica Status Solidi (C), 6(2009)

2569.


~ 51 ~

[208] R.V.K Mangalam, M. Chakrabrati, D Sanyal, A Chakrabati and A Sundaresan,

Journal of Physics: Condensed Matter, 21(2009) 445902.

[209] B. Oberdorfer , R. Würschum, Phys. Rev. B, 79 (2009) 184103.

[210] K. Hain, C. Hugenschmidt, P. Pikart, P. Böni, Sci. Technol. Adv. Mater., 11

(2010) 025001.

[211] R. Burcl, V.I. Grafutin, O.V. Ilyukhina, G.G. Myasishcheva, E.P. Prokop’ev,

S.P. Timoshenkov, Yu.V. Funtikov, Fizika Tverdogo Tela, 52 (4) (2010) 651.

[212] Wang, D. Chen, Z.Q. Wang, D.D. Qi, N. Gong, J. Cao, C.Y. Tang, Z., Journal

of Applied Physics, 107 (2010) 023524.

[213] A.D. Acharya, G. Singh, S.B. Shrivastava, Defect and Diffusion Forum,

Defects and Diffusion in Ceramics XI, 295-296 (2010) 1.

[214] P.M.G. Nambissan, J. Phys. Conf. Ser., 265 (2011) 012019.

[215] S.P. Pati, B. Bhushan, A. Basumallick, S. Kumar, D. Das, Materials Science

and Engineering B, 176, Issue 13, (2011) 1015.

[216] P.J Simpson, C.R Mokry, A.P Knights, J. Phys. Conf. Ser., 265 (2011)

012022.

[217] A. Sarkar, M. Chakrabarti, S.K Ray, D Bhowmick, D Sanyal, J. Phys.

Condens. Matter, 23 (2011) 155801.

[218] T.D. Haynes, R. J. Watts, J. Laverock, Zs Major, M.A. Alam, J. W. Taylor, J.

A. Duffy, S.B. Dugdale, New Journal of Physics, 14 (2012) 035020.

[219] J.M. Maki, T. Kuittinen, E. Korhonen, F. Tuomisto, New Journal of Physics,

14 (2012) 035023.

[220] Y. Yuanzheng, M. Xueming, D. Yuanda, H. Yizhen, W. Gengmiao, Chinese

Physics Letters, 9 (1992) 266.

[221] Y.G. Ma, M.Z. Jin, M.L. Liu, G. Chen, Y. Sui, Y. Tian, G.J. Zhang, Dr. Y.Q.

Jia, Materials Chemistry and Physics, 65 (2000) 79.

[222] R.V. Kumar, Y. Koltypin, X.N. Xu, Y. Yeshurun, A. Gedanken, I. Felner, J.

Appl. Phys., 89 (2001) 6324.

[223] E.D. Grave, C.A. Barrero, G.M.D. Costa, R.E. Vandenberghe, E.V. San, Clay

Minerals, 37 (4) (2002) 591.

[224] D. Predoi, V. Kuncser, G. Filoti, Romanian Reports in Physics, 56(3) (2004)

373.

[225] K.A. Malini, M.R. Anantharaman, A. Gupta, Bull. Mater., Sci., 27 (4) (2004)

361.


~ 52 ~

[226] M. Liu, H. Li, L. Xiao, W. Yu, Y. Lu, Z. Zhao, Journal of Magnetism and

Magnetic Materials, 294 (2005) 294.

[227] S. Chakraverty, M. Bandyopadhyay, S. Chatterjee, S. Dattagupta, A. Frydman,

S. Sengupta, P.A. Sreeram, Phys. Rev. B, 71 (2005) 054401.

[228] R.K. Sharma, O.Suwalka, N. Lakshmi, K. Venugopalan, A. Banerjee, P.A.

Joy, Materials Letters, 59 (2005) 3402.

[229] C.R.H. Bahl, S. Mørup, Nanotechnology, 17 (2006) 2835.

[230] D. Bandyopadhyay, International Materials Reviews, 51 (3) (2006) 171.

[231] P. Delcroix, G.Le. Caër, B.F.O. Costa, Journal of Alloys and Compounds,

434-435 (2007) 584.

[232] S. Mukherjee, S. Kumar, D. Das, Journal of Physics D: Applied Physics, 40

(2007) 4425.

[233] I. Felner, I. Nowik, S. Balamurugan, E. Takayama-Muromachi, Hyperfine

Interactions, 184 (1-3) (2008) 111.

[234] T.Y. Kiseleva, T.F. Grigor’eva, D.V. Gostev, V.B. Potapkin, A.N. Falkova,

A.A. Novakova, Moscow University Physics Bulletin, 63 (1) (2008) 55.

[235] G. Filoti, V. Kuncser, G. Schinteie, P. Palade, I. Morjan, R. Alexandrescu, D.

Bica, L. Vekas, Hyperfine Interactions, 191 (1-3) (2009) 55.

[236] S. Thakur, S.C. Katyal, A. Gupta, V.R. Reddy, M. Singh, J. Appl. Phys., 105

(2009) 07A521.

[237] Lyubutin, I.S. Lin, C.R. Korzhetskiy, Y.V. Dmitrieva, T.V. Chiang, Journal of

Applied Physics, 106 (2009) 034311.

[238] A.L Andrade, D.M Souza, M.C Pereira, J.D Fabris, R.Z Domingues, Journal

of Nanoscience and Nanotechnology, 9(3) (2009) 2081.

[239] A.K. Mishra, C. Bansal, M. Ghafari, R. Kruk, H. Hahn ,Phys. Rev. B, 81

(2010) 155452.

[240] R. Babilas, M. Kądziołka-Gaweł, R. Nowosielski, Journal of Achievements in

Materials and Manufacturing Engineering, 45 (2011) 7.

[241] M. Chakrabarti, S. Chattopadhyay, D. Sanyal, A. Sarkar, D. Jana, Materials

Science Forum, 699 (2012) 1.

[242] B. Antic, A. Kremenovic, N. Jovic, M.B. Pavlovic, C. Jovalekic, A.S. Nikolic,

G.F. Goya, C. Weidenthaler, J. Appl. Phys., 111 (2012) 074309.

[243] I.N. Zakharova, M.A. Shipilin, V.P. Alekseev, A.M. Shipilin, Technical

Physics Letters, 38 (2012) 55.

CHAPTER-2

Theoretical considerations

THEORETICAL CONSIDERATIONS CHAPTER-2

~ 54 ~

2.1 Introduction The X-rays powder diffraction technique is being used for many decades and

is still continuing due to its application in diffraction line profile analysis to study the

nature of crystal imperfections introduced during growth and plastic deformation of a

material. The earlier X-ray diffraction studies on cold- worked materials depict that

plastic deformation induces broadening of the X-rays diffraction profiles and such

peak broadening increases continuously with increase in degree of deformed. With the

use of modern techniques [1] like focussing curved crystal monochromator, counter or

solid state detector it is possible to locate and measure the shape of the X-ray

diffraction profiles with considerable accuracy. In the past decades extensive

theoretical and experimental studies have been made in this direction by Wilson [2],

Greenwough [1] and Warren [3]. A further development in this field was made by

Wagner [4], Warren [5] and Klug and Alexander [6], Enzo et al. [7], Langford et al.

[8], Mittemeijer et al. [9], Balzar et al. [10] and others. This chapter basically deals

with the various theoretical considerations in the X-rays diffraction line profile

analysis for microstructure characterization of polycrystalline and nanocrystalline

materials in terms of various lattice imperfections.

2.2 X-ray line profile analysis: Theoretical considerations When X-rays interact with the atoms, it gives rise to scattering in all

directions; in some of these directions the scattered beams will be completely in phase

and so reinforce each other to form diffracted beams following Bragg's law,

nλ sin θ2d = (2.1)

where λ is the wavelength of X-rays directed towards the set of parallel planes in a

crystal at an angle θ and n is the order of reflection, θ is called Bragg angle where

the maximum intensity occurs. At other angles there are little or no diffracted

intensities because of the destructive interference.

Each crystallographic phase in an ideal crystal has a characteristic set of d

spacings, which yields a discrete lines in the X-ray diffraction pattern at respective

Bragg anglesθ . But in the experiments with real crystals these discrete lines are

appear as peaks considerable amount of peak broadening. This is due to the facts that

it is hardly possible to have an incident beam composed of perfectly parallel and


~ 55 ~

monochromatic radiation and a real crystal always has some departures from an ideal

structure due to the presence of crystal imperfections.

Small crystallite size, microstrain inside the crystallites and stacking faults are

mainly responsible for broadening of line profiles. Some instrumental parameters like

slit widths, sample size, penetration in the sample, imperfect focussing, unresolved

1α and 2α peaks etc. also give some extraneous broadening to the line profile. All

these extraneous sources of broadening are grouped together under the name

"instrumental broadening".

The first step towards the determination of crystallite size from X-ray line

profile analysis was made by Scherrer in 1918 [11]. He reported that the line breadth

varies inversely with the size of the crystallites according to the equation,

cos θ )iβsam(βKλD

−= (2.2)

known as Scherrer formula, where λ is the wavelength, samβ and iβ are the measure

of line breadth of sample and instrumental ‘standard’ respectively, θ is the Bragg

angle, K is Scherrer constant ( )89.0K0.1 >> and D is an apparent crystallite size.

The Scherrer formula actually gives the length of the crystal in the direction of the

diffraction planes and it is evident from equation (2.2) that size broadening is

independent of the order of reflection. It is important to note that lattice strain effect,

which also contributes to the broadening is not considered in the Scherrer formula.

This formula is also unsuitable for the study of crystals where the strain broadening is

present. This limitation hinder the use of Scherrer formula in many sophisticated

problems, but it is still being used in some simple cases where the size of crystals is

fairly less than hundred angstroms and the line broadening is primarily due to small

crystallite size.

2.3 Integral Breadth method This is the oldest method of line profile analysis for determining crystallite

size and microstrain simulteneously. Scherrer [11] defined the breadth of a diffraction

line as its angular width in radians at a point where the intensity has fallen to half of

its maximum value. In 1926, Laue gave another definition of the breadth of a

diffraction line as the integrated intensity of a line profile above background divided

by peak height.


~ 56 ~

∫= )()( θθβ 2d2II1

p

(2.3)

Hall in 1949, assuming that peak-bordening due to small crystalline size and

lattice strain can be described by Cauchy functions, suggested that the total

broadening is given by

SD βββ += (2.4) where βD is the line breadth measured by Scherrer (eqn 2.2) and βS is the broadening

arising from microstrain which can be expressed as

θεβ tan4=S (2.5)

So, eqn (2.4) can be written in the form

θεθλβββ tan4cos +=+= DKSD (2.6)

or, λθελθβ sincos 4D1 += (2.7)

Thus from the corrected integral breadth β of the X-ray line profiles, a plot of

λθβ cos against λθsin should be a straight line and the intercept on the

λθβ cos axis will give D1 , the reciprocal of the crystallite size, while the slope

will give ε , the average microstrain.

2.4 Different methods of X-ray diffraction pattern analysis For a polycrystalline specimen consisting of sufficiently large (~10-4 cm) and

strain free crystallites, diffraction theory predicts that the lines of the powder pattern

will be exceedingly sharp. However, for a real crystal, peaks are broadened due to

size and lattice strain. Hence an analysis of breadths of strain and/or size broadened

diffraction lines will give quantitative information about the crystallite size and strain

of the deformed crystallites.

The crystallite size and microstrain can be determined from the X-ray

diffraction pattern with the help of the following methods:

(1) Integral Breadth Method ( William- Hall plot)

(2) Warren-Averbach method of line profile analysis

(3) Whole powder pattern fitting method

(4) Rietveld method


~ 57 ~

Limitations of different methods 2.4.1 Fourier method The principal sources of error in the Fourier (Warren-Averbach) analysis are:

(a) counting statistics;

(b) standard used to obtain g (instrumental) profiles;

(c) background determination;

(d) truncation of profiles at finite range;

(e) sampling interval (step length);

(f) choice of origin;

(g) limitations of approximation used in analysis.

These affect the analysis in different ways and by different amounts. Young et

al. [12] simulated the effect of (c), (d) and (e) and many other authors have since

discussed the treatment of errors in the Fourier method. Delhez et al. [13-14] have

given corrections for (a), (b) and (f). Procedures for improving the reliability of the

line profile analysis by the Fourier method have been represented by Zorn [15] and

Delhez et al.[16].

2.4.2 Warren-Averbach method The main drawbacks of Warren-Averbach method is the appearance of the

"hook effect". Two experimental errors giving rise to "hook" effect have been pointed

out are: (i) truncation of line profile and (ii) estimation of high background.

Crystallographers from all over the world tried their best to correct the "hook" effect,

but not a single established and valid procedure is found till date for the correction of

the "hook" effect.

Another drawback is that the method fails if the peaks are seriously

overlapping. Many materials having interesting technological applications display

diffraction patterns with overlapping peaks. Warren-Averbach method of line profile

analysis fails to characterize the microstructure of such materials.

2.4.3 Whole Powder Pattern Decomposition (WPPD) method Overlapping reflections at the same Bragg angle (intrinsic overlapping) can

not be perfectly decomposed by the WPPD methods. Thus the industrially important

materials, which usually exhibit severely overlapping lines are difficult to characterize


~ 58 ~

using this method. It has been found that the effective separation limit in pattern

decomposition (measured as the shortest 2θ distance between the two adjacent peaks)

ranges from 0.1 to 0.5 times the FWHM (generally~0.25) and it is influenced by

several factors, namely, counting statistics, the 2θ-range of data included in the

analysis, and the resolution of the data.

The above mentioned disadvantages have been overcome in the Rietveld

method. So, this is the best method of line profile analysis.

2.5 The Rietveld method The Rietveld method introduced by H. M. Rietveld [17] is a total pattern

fitting method in which all observable Bragg reflections are assigned with the

simulation of a proper diffraction pattern and subsequently a refinement is carried out

until the best fit is obtained between the observed and simulated pattern. To simulate

the diffraction pattern this method needs two models: a structural model based on the

approximate atomic positions of the materials and a non-structural model, which takes

care of the instrumental features and specimen features such as aberrations due to

absorption, specimen displacement, crystallite size and microstrain effects etc. The

quality of fit in the subsequent refinement depends on the choice of these starting

models and in order to get best fit a reasonably good starting model which is close to

the correct one is required. The structural model helps to determine the total intensity

of Bragg reflection along with their positions and the non structural model gives a

description of individual profile in terms of an analytical of other differentiable

functions ( pseudo-Voigt function, Pearson VII function and Gaussian, Lorentzian and

modified Lorentzian functions are widely used).

In all cases, the ‘best-fit’ sought is the best least-squares fit to all of the

thousands of intensities Io’s simultaneously. In order to improve fitting the model

parameters namely, atomic positions, thermal and site occupancy parameters,

parameters for background, lattice parameters, parameters representing instrumental

geometrical-optical features and specimen aberration (e.g. specimen displacement and

transparency), parameter for amorphous component, specimen reflection profile

broadening parameters (crystallite size and microstrain) and often parameter for

extinction effect are refined in steps with the calculation of residual at every steps.

The quantity minimized in the least-squares refinement is the residual Sy


~ 59 ~

( )∑ −=i

cioiiy IIWS 2 , (2.8)

where oii IW 1= , Ioi =observed (gross) intensity at the ith step, Ici =calculated

intensity at the ith step.

The best fit is said to obtain when yS reduces to minimum.

Many Bragg reflections contribute to the intensity yi , observed at any

arbitrarily chosen point, i, in the pattern. The calculated intensities, yci are determined

from the square of the absolute value of the structure factor, 2KF values calculated

from the structural model by summing of the calculated contributions from

neighbouring Bragg reflections plus the background:

( )∑ +−Φ=K

biKKiKKci IAPFLsI θθ 222 (2.9)

where S is the scale factor, K represents Miller indices, hkl for a Bragg

reflection, KL contains Lorentz polarization and multiplicative factor, Φ is a

reflection profile function which approximates the effect of both instrumental

features and specimen features such as aberration due to absorption, specimen

displacement, crystallite size and microstrain effects etc., KP is the preferred

orientation function, A is an absorption factor, KF is the structure factor for thK

Bragg reflection, biI is the background intensity at the thi step.

In the original Rietveld program, for angle dispersive data, the dependence of

the breadth H of the reflection profiles (measured as full-width-at-half-maximum,

FWHM ) was modelled as [18]

[ ] 212 WVUH ++= θθ tantan (2.10)

where U, V, and W are the refinable parameters.

This formula (termed as Caglioti formula) initially developed for the

‘medium’ (or less) resolution powder diffractometers and worked satisfactorily for

them, as did simple Gaussian reflection profile functions. Even though the

instrumental diffraction profiles of the typical X-ray powder diffractometers

operating on sealed-off X-ray tube or rotating anode sources are generally neither

Gaussian nor symmetric. The Caglioti relation was widely used for modeling the

instrumental broadening due to lack of anything better and simplified method. With

the reflection profiles from X-ray diffractometers and other comparatively high


~ 60 ~

resolution instruments, such as Guinier cameras and high-resolution neutron powder

diffractometers, another complication arises. Their instrumental profiles are

sufficiently narrow so that broadening of the intrinsic diffraction profile from

specimen defects such as microstrain and small crystallite size is a significant part of

the total broadening and in these cases instrumental broadening may not be modeled

by Caglioti relation.

An essential step in Rietveld method applying on data from modern X-ray

diffractometers is to examine the variation of FWHM (or integral breadth) with θ2

or ∗d and to compare this with the resolution curve of the instrument used. If the two

curves are identical, indicating that sample effects are negligible, then Caglioti

formula can be used to model breadth variation. If the curves differ, but the scattering

for the sample curve is not greater than that would be expected from counting

statistics or there is no marked 'anisotropy', on the average, then also one can model

the breadth of the profile with Caglioti formula, but this time U , V and W should be

treated as refinable parameters. But if the sample curve exhibits a scattering which is

θ2 or ∗d dependent, then the nature of 'anisotropic' breadth variation must be

ascertained and the dependence of breadth on hkl has to be modelled with special

care.

The quality of fitting is judged through the calculation of weighted residual

error, WR ,

( )21

22

⎥⎥⎦

⎤

⎢⎢⎣

⎡−= ∑∑

ioii

icioiiw IwIIwR (2.11)

which is then minimized through a Marquardt least-squares program[19]. The

e.s.d. is calculated following the method proposed by Scott [20] and finally, the

goodness of fit (GoF ) is established by comparing WR with the expected error, expR :

expRRGoF w= (2.12)

where, ( )21

2exp

⎥⎥⎦

⎤

⎢⎢⎣

⎡−= ∑

ioii IwPNR

oiI and ciI are the experimental and calculated intensities, respectively, iw ( oiI1= ) and N are the weight and number of experimental observations respectively and P is the number of fitting parameters.


~ 61 ~

Refinement continues till convergence is reached with the value of the quality

factor, GOF approaching 1, which confirms the goodness of refinement.

In general, sample induced line broadening includes contributions which are

independent of θ2 or ∗d , known as 'size effect' and which depends on θ2 or ∗d ,

known as 'strain effect'. There have been various attempts to make allowance for

smoothly varying (isotropic) microstructural effects in Rietveld programs. David and

Matthemam [21] modelled experimental line profile by means of a Voigt function

and assigned the 'Lorentzian' and 'Gaussian' components to the 'size' effects and the

instrumental broadening respectively. A different approach was adopted by Howard

and Snyder in the program SHADOW [22] who convoluted a Lorentzian simple line

profiles, assumed to be due to 'crystallite size' and/or 'microstrains', with

experimentally determined instrumental profiles, to match the observed data. The

simultaneous presence of isotropic 'size' and 'strain' effects was considered by

Thompson et al.[23]. They used a pseudo-Voigt function to model the overall line

broadening and assigned the Lorentzian components of the pseudo-Voigt functions to

'size' effects and Gaussian components to the combined 'strain' and instrumental

contributions.

An early attempt to model anisotropic line broadening in the Rietveld method

was made by Greaves [24] who assumed that the crystallites had the form of platelets

with thickness H and infinitely large lateral dimensions. In this case the contribution

to the integral breadth of reflection from plates parallel to the surface, in the

reciprocal unit, is simply H1 . In order to allow for the direction dependence of

microstrain, some assumptions are made regarding the stress distribution. If

microstrain is assumed to be statistically isotropic, then the anisotropy of the elastic

constants leads to a hkl dependence of strain. Thompson et al. [25] expressed

microstrain as a function of hkl and refined appropriate strain parameters based on

elastic compliances. Simultaneous anisotropic ‘size’ and ‘strain’ broadening was

incorporated in the Rietveld method by Le Bail [26] and Lartigue et al. [27]. The hkl

dependent nature of these quantities was modeled by means of ellipsoids and Fourier

series were employed to represent the line profiles. The number of microstructural

parameters to be refined was restricted by adopting Lorentzian function for ‘size’

contributions and an intermediate Lorentz-Gauss function for ‘strain broadening. In a

similar approach Lutterotti and Scardi [28] included crystallite size and microstrain as


~ 62 ~

refinable parameters, in the place of usual angular variation line-profile width.

Microstructural analysis based on approximate single line Fourier method was

introduced by Nandi et al. [29]. A program LS1 based on this approach was

developed by Lutterotti et al. [30]. In the field of materials analysis, there is a

constant demand for sophisticated tools, which can process enormous number of data

in a short time, deal with cases showing sample-induced anisotropy and extract more

information about the samples. In 1999, Lutteroti et al. developed a program, MAUD,

which is easy to use, can be applied to wide variety of materials and helps the user in

obtaining more information from data collected by traditional and new diffraction

instrument [31]. The outline and main features of MAUD are given here.

2.6 MAUD: a user friendly computer software based on Java for Materials Analysis Using Diffraction This program is written in Java, and run virtually in any computer

environment supporting the Java Virtual Machine with installers available for the

Macintosh and Windows platform.

The principal features of MAUD are:

(i) Simultaneous crystal structure refinement, line-broadening, texture (stress

under implementation) and quantitative phase analyses can be performed.

(ii) Multiple samples from different instruments can be analyzed at one time.

(iii) The diffraction patterns of a sample from different instruments, e.g. X-ray

tube, synchrotron, neutron constant wavelength and time of flight can be

analyzed simultaneously.

(iv) There is option for wizard or manual mode of refinement; the wizard mode

allows the user to select what kind of analysis the user needs to perform in

quantitative phase analysis, crystal structure analysis or texture analysis.

(v) There is option for adding different methodologies to the program by the

user without the need to recompile it or to know the internal structure of the

program. The plug-in-structure are included in instrument geometries and

correction/calibrations, data formats, line-broadening methods, texture

algorithms, peak intensity extraction, etc.

(vi) CIF (Crystal Information File) user friendly program is included. The

program uses, imports and supports CIF formats.


~ 63 ~

(vii) Various data format, Philips, Rigaku, Siemens, GSAS, D1B etc. can be used

for input files (only ASCII).

(viii) Unlimited number of data files can be analyzed at a time. Till now some

analyses have been done loading simultaneously more than 1000 datafiles

(from the SKAT diffractometer at Dubna).

(ix) Space group and symmetries relationships computed using SgInfo [32]

linked as a native library to the package for ease of analysis.

(x) Popa model has been included to analyze the cases having anisotropic

crystallite size and microstrain [33].

(xi) In order to give better accuracy in the results, the square-root of actual

intensity is plotted against θ2 in the fitted pattern, which gives magnified

image of the weaker peaks.

This program is an upgraded version of LS1 and the underlying theory is

almost same as that of LS1, except some modifications are made in crystallite size-

microstrain separation, texture analysis and defect parameters study. The basic

methodology for the crystallite size-microstrain separation are performed using the

theory developed by Delhez et al. [34] and the calculation of crystallite size and

microstrain is performed using the recently published method of Popa [33].

To analyze the texture of multiphase samples, in addition to the classical

March-Dollase formula, harmonic texture [35] and the WIMV method [36] are

included in order to obtain the entire orientation distribution function, provided a

sufficient number of spectra at different tilting angles are available for the refinement.

Thus it can be concluded that MAUD is an elegant method for material

characterization. The program has been successfully applied by Lutterotti to analyze

the Y2O3 CPD Round Robin sample, to analyze the texture of various multiphase

samples, to refine spectra with anisotropic peak broadening, quantitative analysis of

polymers and samples containing silica glass etc. [31].

In the present study, MAUD software has been extensively used to analyze

the microstructure of various industrially important multiphase ferrite materials. The

detailed results of each analysis will be described in the respective chapter of the

present dissertation.


~ 64 ~

2.7 Positron annihilation technique

Positron annihilation technique is a nuclear solid state technique to study the

electron number density, characterization of defects and the electron momentum

distributions in a material.

Depending upon different electron density sites in a material positron

annihilation lifetime states are different. The annihilation lifetimes of positrons with

free electrons in a material varies in the range ~ 100 - 150 ps. The electron density

distributions in defect sites are less from those of a perfect lattice and hence the

annihilation lifetimes are more. Thus, by measuring the positron annihilation lifetimes

in a material one can also obtain the information about the nature and the size of these

defect sites (Table 1).

Table 1: Possible defects and their sizes with the positron annihilation lifetime values.

2.7.1 Positron Annihilation Spectroscopy (PAS)

Positron annihilation spectroscopy (PAS) is a non-destructive nuclear solid

state technique [37,38] (shown in Fig.2.1), employing which one can study the

electronic structure, defect properties, electron density distribution (EDD) and

electron momentum distribution (EMD) in a material, e.g., metals, alloys, ceramic,

oxides, polymers, superconductors, magnetic materials, semiconductors,

nanocrystalline materials etc.


~ 65 ~

Energetic positrons injected from a radioactive source (e.g.,22Na, 64Cu, 58Co

etc.) get thermalized within 1-10 ps inside a solid and annihilate with an electron of

that material. It is well known that positrons preferentially populate (and annihilate) in

the regions where electron density, compared to the bulk of the material, is lower (e.g.

vacancy type defects, vacancy clusters, micro-voids). The lifetime of positrons

trapped in defects is comparatively longer with respect to those annihilate at defect

free regions. Analysis of PAL spectrum, thus, throws light on the nature and

abundance of defects in the material. The other PAS technique, Doppler broadening

of the positron annihilation radiation lineshape measurement is useful to study the

momentum distribution of electrons in a material [39,40]. Depending on the electron

momentum (p), the 511 keV γ-rays (electron-positron annihilated) are Doppler shifted

by an amount ± ∆E = pL c/2 in the laboratory frame where pL is the component of the

electron momentum (p) along the direction of measurement. Using high-resolution

high purity germanium (HPGe) detectors, one can measure the spectrum of Doppler

shift 511 keV γ-rays.

The wing region of the 511 keV spectra (higher value of pL) carries the


of the core electrons are element specific [41] and hence, the atoms surrounding a

defect can be probed by proper analysis of the measured spectra.

Mainly it has three principal categories:

(a) Positron annihilation lifetime (PAL) spectroscopy to measure the electron

density distribution (EDD) inside the sample,

Fig.2.1 Schematic diagram of defect characterization by Positron Annihilation Spectroscopy (PAS).


~ 66 ~

(b) Coincidence Doppler broadening of positron annihilation radiation line

shape (CDBPARL) spectroscopy to probe the electron momentum

distribution (EMD) inside the material under investigation,

(c) Angular correlation of annihilation radiation spectroscopy for better

understanding the electron momentum distribution in a material.

2.7.1 (a) Positron annihilation lifetime (PAL) measurement

The positron annihilation lifetime, τ, (which is the reciprocal of the positron

annihilation rate,

λ =1/τ = πro2c ∫ |Ψ+(r)|2n-(r)dr (2.13)

where n-(r) is the electron density at the annihilation site and the positron density

n+(r) = |Ψ+(r)|2, ro is the classical electron radius, c is the speed of light and r the

position

Fig.2.2. Experimental setup of PAL measurement for studying electron density distribution in a solid

vector is inversely proportional to the electron number density [42]. Therefore by

measuring the positron annihilation lifetime (~ 100-400 ps) in a solid one can obtain

directly the information about the electron density at the site of positron annihilation

[43]. Positron-electron annihilated gamma rays bear information regarding the nature,

concentration and the environments of the related defect species [44]. This is

understood by analyzing the PAL spectrum by different computer programs [45].

Therefore, the analysis of PAL spectrum, thus, throws light on the nature and

abundance of defects in the material. For positron annihilation studies, a 10 µCi 22Na


~ 67 ~

positron source (enclosed in thin mylar foils) has been sandwiched between two

identical plane faced pellets. The PAL spectrum, N(t) vs. t, has been measured with a

fast-slow coincidence assembly (shown in Fig.2.2.) with XP2020Q PMT coupled with

conical BaF2 crystals [46]. Here, N(t) is the number of coincidence events and t is the

time in ps. This spectrometer has the time resolution (TR) of 182±1 ps for the prompt 60Co γ-rays at the positron experimental window settings with the upper 60 % of the

Compton continuum of 1.276 MeV and 0.511 MeV γ- rays [47]. The measured

spectra have been analyzed by computer program PATFIT-88 [48] with necessary

source corrections to evaluate the possible lifetime components τi, and their

corresponding intensities Ii. All the lifetime spectra are found to be best fitted with

three lifetime components (variance of fit is less than one per channel), yielding a

very long (> 1.1 ns) positron lifetime component (τ3) with intensity 3-4%. A simple

but most convenient two-state trapping model [44, 42] assumes two processes:

(i) positron annihilation from Bloch state (in the bulk, non-defective lattice)

(ii) the same from a trapped state (in a defect).

According to its name, the model predicts a two-component fit of the PAL

spectrum. However, for the present samples, that makes the fitting parameters as well

as the significance of the fitting itself unreasonably poor. So, separate physical

process is necessary to analyze the spectrum data with another fitting parameter τ3.

The origin of τ3 is generally attributed to the formation of ortho-positronium and its

subsequent decay to para-positronium by pick-off annihilation [43]. In polycrystalline

samples, there always exist micro voids where positronium formation is favorable

[43,45]. Positronium formation, although more likely in voids, is not directly related

to defect trapping of positrons. Hence, it will not be discussed later on. Using the

above two-state trapping model, one can construct

the bulk lifetime, τB = (I1+I2)/(I1/τ1+I2/τ2)), (2.14)

and the average positron lifetime, τav = (τ1I1+τ2I2)/(I1+I2)) (2.15)

where τ1, τ2, I1 and I2 are the measured lifetime parameters. The shortest lifetime

component (τ1 ~ 145 ps) is generally attributed to free annihilation of positrons

[43,45,47]. However, in disordered systems, smaller vacancies [45,49] (like

monovacancies etc.) or shallow positron traps (like oxygen vacancies [50,51] in ZnO)

may be related with τ1. So, τ1 is indeed a weighted average of free and trapped


~ 68 ~

positrons, hence, it is sometimes called reduced bulk lifetime [44]. But the correlation

of τ1 with the material properties is not yet conclusive. So, this issue has not been

discussed much in this thesis. Finally, the most important lifetime component is the

intermediate one, τ2, which arises from the annihilation of positrons at defect sites

[44,42,43]. However, τ2 contains some error due to least-square fitting procedure of

the spectrum with finite statistics. In particular, when several types of defects may

exist in the system, it is better to choose statistically more accurate parameter, τav,

without assuming any model. Depending on the nature of defects and other defect

specific physical parameters, τ2 or τav gets the importance, as will be discussed later

on. Generally, the increase of τav reflects the overall enhancement of defects and τav >

τB indicates the presence of defect in the system.

2.7.1 (b) Coincidence Doppler Broadened Positron Annihilation Radiation Line shape (CDBPARL) measurement

The other PAS technique, Doppler broadening of the positron annihilation

radiation line shape measurement is useful to study the momentum distribution of

electrons in a material [44]. Depending

on the electron momentum (p), the 511

keV γ−rays (electron-positron

annihilated) are Doppler shifted by an

amount ± ∆E = pLc/2 in the laboratory

frame where pL is the component of the

electron momentum (p) along the

direction of measurement. Using high-

resolution high purity germanium

(HPGe) detectors, one can measure the

spectrum of Doppler shift 511 keV γ-rays

spectrum [52]. So, by analyzing the

CDBEPAR spectrum, identification of

atoms surrounding a defect can be done.

But, due to large background in the spectrum, the analysis becomes cumbersome and

becomes unambiguous. Use of the two detectors in coincidence [53,54] help to

Fig.2.3. Experimental setup of CDBPARL measurement for studying electron momentum distribution in a solid


~ 69 ~

suppress the background in measured Doppler broadened spectrum and hence, the

contributions of higher momentum electrons (core electrons) can be estimated

[55,56]. In the experiment, the two

detector coincidence Doppler broadened

electron-positron annihilation γ-radiation

(CDBEPAR) spectrum has been

measured by a HPGe detector (efficiency

13%, energy resolution of 1.3 keV for the

514 keV line of 85Sr) and a 3// × 3// NaI

(Tl) crystal coupled to a RCA 8850

photomultiplier tube placed at an angle of

180o [54] (shown in Fig.2.3). The peak to

background (607-615 keV) ratio is

14000:1 which allows successful analysis

of the wing region [47,57-60]. The

energy per channel of the multichannel

analyzer has been set to 22 eV. The peak

to background (607-615 keV) ratio has

been further enhanced to 105:1 by using another setup (at VECC, Kolkata) with two

identical HPGe detectors (Efficiency: 12

%; Type: PGC 1216sp of DSG,

Germany) having energy resolution of

1.1 keV at 514 keV of 85Sr and proper

∆E–E selection [61]. The energy per

channel in this set-up is 150 eV. The

CDBEPAR spectra have been recorded in

a dual ADC based - multiparameter data

acquisition system (MPA-3 of FAST

ComTec., Germany). The CDBEPAR

spectra for each sample have been

analyzed by evaluating the so-called

shape parameter (S-parameter) and wing

parameter (W-parameter) [44,42,54]. The S-parameter, calculated as the ratio of

Fig.2.4. Schematic representation of S-parameter

Fig.2.5 Schematic representation of W-parameter


~ 70 ~

counts in the central area of the 511 keV photo peak (|511 keV − Eγ | ≤ 0.86 keV) and

the total area of the photo peak (|511 keV − Eγ | ≤ 4.25 keV), represents the fraction of

positrons annihilating with the lower momentum electrons (Fig.2.4.). The W-

parameter, calculated as the ratio of counts in the wing region of the 511 keV photo

peak (1.6 keV ≤ | Eγ − 511 keV | ≤ 4 keV) and the total area of the photo peak,

represents the fraction of positrons annihilating with the higher momentum electrons

(Fig.2.5.). Ratio curve [55,58,62] from each CDBEPAR spectra of ZnO samples has

been constructed by dividing the counts at the same energy with that of a standard

CDBEPAR spectrum (spectrum of a 99.9999 % purity Al single crystal in the same

set up). However, a new type of ratio curve has been constructed with respect the un-

annealed as standard, which becomes more informative [47].

2.8 The Mössbauer effect In a resonance absorption experiment, the energy of incident radiation should

match exactly the energy separation between the two levels of the absorption system.

For example, radiation of a Na atom matches exactly the excitation energy of the

other Na atom and is, therefore, effectively absorbed by it. Applying the same logic to

irradiation and absorption of gamma-rays, the same electromagnetic radiation as in

the case of Na atoms only of higher energy being emitted by atomic nuclei, one would

come to the same resonant condition which requires that the energy separation

between the two levels in the source nucleus and those in the absorber nucleus should

be exactly equal. Therefore, both the source and the absorber nuclei must necessarily

be identical. Provided this, one would expect effective absorption and reemission of

gamma rays by identical nuclei, but this is not enough for observation of nuclear

resonant fluorescence. During the process of emission of a gamma ray by a nucleus, a

certain amount of excitation energy (the recoil energy – ER) is given to the nucleus to

conserve momentum. That is why the energy of the emitted gamma quantum Eg is

reduced by the same amount.

ER=p2/2M=Eg2/2Mc2, Eg=Eo-ER (2.16)

p being the momentum given to the nucleus, equivalent to momentum of the gamma

photon, and M the mass of the emitting nucleus. Similarly, whenever a gamma

quantum is absorbed, the energy transferred to the nuclear excitation is reduced by ER

due to the recoil energy imparted to the absorbing nucleus. For optical transitions the


~ 71 ~

energy loss to recoil is much smaller than the width of the absorption line, making

optical resonance fluorescence easily possible. But in the case of high energy nuclear

radiation, recoil energy is much larger than the line width which impedes nuclear

resonant fluorescence.

Nuclei in atoms undergo a variety of energy level transitions, often associated

with the emission or absorption of a gamma ray. These energy levels are influenced

by their surrounding environment, both electronic and magnetic, which can change or

split these energy levels. These changes in the energy levels can provide information

about the atom's local environment within a system and ought to be observed using

resonance-fluorescence. There are, however, two major obstacles in obtaining this

information:

(i) the 'hyperfine' interactions between the nucleus and its environment are

extremely small,

(ii) the recoil of the nucleus as the gamma-ray is emitted or absorbed

prevents resonance.

In a free nucleus during emission or absorption of a gamma ray it recoils due

to conservation of momentum, just like a gun recoils when firing a bullet, with a

recoil energy ER. This recoil is shown in Fig.2.6. The emitted gamma ray has ER less

energy than the nuclear transition but to be resonantly absorbed it must be ER greater

than the transition energy due to the recoil of the absorbing nucleus. To achieve

resonance the loss of the recoil energy must be overcome in some way.

Fig.2.6 Recoil of free nuclei during emission or absorption of gamma ray.

As the atoms will be moving due to random thermal motion the gamma-ray

energy has a spread of values ED caused by the Doppler effect. This produces a

gamma-ray energy profile as shown in Fig.2.7. To produce a resonant signal the two

energies need to overlap and this is shown in the red-shaded area. This area is shown

exaggerated as in reality it is extremely small, a millionth or less of the gamma-rays

are in this region, and impractical as a technique.


~ 72 ~

Fig.2.7 Emission and absorption profile of recoiled gamma rays.

What Mössbauer discovered is that when the atoms are within a solid matrix

the effective mass of the nucleus is very much greater. The recoiling mass is now

effectively the mass of the whole system, making ER and ED very small. If the

gamma-ray energy is small enough the recoil of the nucleus is too low to be

transmitted as a phonon (vibration in the crystal lattice) and so the whole system

recoils, making the recoil energy practically zero: a recoil-free event. In this situation,

as shown in Fig.2.8, if the emitting and absorbing nuclei are in a solid matrix the

emitted and absorbed gamma-ray is the same energy: resonance.

Fig.2.8 Recoilless emission and absorption of gamma rays by the source and the

absorber both embedded in respective lattice sites.

If emitting and absorbing nuclei are in identical, cubic environments then the

transition energies are identical and this produces a spectrum as shown in Fig.2.9 a

single absorption line.

Fig.2.9 Simple Mössbauer spectrum from identical source and absorber.


~ 73 ~

We can achieve resonant emission and absorption and use it to probe the tiny

hyperfine interactions between an atom's nucleus and its environment. The limiting

resolution now that recoil and doppler broadening have been eliminated is the natural

linewidth of the excited nuclear state. This is related to the average lifetime of the

excited state before it decays by emitting the gamma-ray. For the most common

Mössbauer isotope, 57Fe, this linewidth is 5x10-9ev. Compared to the Mössbauer

gamma-ray energy of 14.4keV this gives a resolution of 1 in 1012, or one sheet of

paper in the distance between the Sun and the Earth. This exceptional resolution is of

the order necessary to detect the hyperfine interactions in the nucleus.

As resonance only occurs when the transition energy of the emitting and

absorbing nucleus match exactly and the effect is isotope specific. The relative

number of recoil-free events (and hence the strength of the signal) is strongly

dependent upon the gamma-ray energy and so the Mössbauer effect is only detected

in isotopes with very low lying excited states. Similarly, the resolution is dependent

upon the lifetime of the excited state. These two factors limit the number of isotopes

that can be used successfully for Mössbauer spectroscopy. The most used is 57Fe,

which has both a very low energy gamma-ray and long-lived excited state, matching

both requirements well.

2.8.1 Fundamentals of Mössbauer Spectroscopy As shown previously the energy changes caused by the hyperfine interactions

we want to look at are very small, of the order of billionths of an electron volt. Such

miniscale variations of the original gamma-ray are quite easy to achieve by the use of

the doppler effect, i.e. the gamma-ray source moves towards and away from the

absorber. This is most often achieved by oscillating a radioactive source with a

velocity of a few mm/s and recording the spectrum in discrete velocity steps.

Fractions of mm/s compared to the speed of light (3x1011mm/s) gives the minute

energy shifts necessary to observe the hyperfine interactions. For convenience the

energy scale of a Mössbauer spectrum is thus quoted in terms of the source velocity,

as shown in Fig.2.10.


~ 74 ~

Fig.2.10 A typical Mössbauer spectrum showing the velocity scale and motion of

source relative to the absorber.

With an oscillating source we can now modulate the energy of the gamma-ray

in very small increments. Where the modulated gamma-ray energy matches precisely

the energy of a nuclear transition in the absorber the gamma-rays are resonantly

absorbed and we see a peak. As we're seeing this in the transmitted gamma-rays the

sample must be sufficiently thin to allow the gamma-rays to pass through, other wise

the relatively low energy gamma-rays are easily attenuated.

In Fig.2.10 the absorption peak occurs at 0mm/s, where source and absorber

are identical. The energy levels in the absorbing nuclei can be modified by their

environment in three main ways: by the Isomer Shift, Quadrupole Splitting and

Magnetic Splitting.

2.8.1 (a) Isomer Shift The isomer shift originates from the non-zero volume of the nucleus and the

electron charge density due to s-electrons within it. This leads to a monopole

(Coulomb) interaction, modifying the nuclear energy levels. The difference in the s-

electron environment between the source and absorber thus results in a shift in the

resonance energy of the transition. This leads to an overall shift of the whole spectrum

in the positive or negative direction depending upon the s-electron density, and

determines the position of the centroid of the spectrum.

As the shift cannot be measured directly it is referred relative to a known

absorber, viz. 57Fe Mössbauer spectra is often referred relative to alpha-iron at room

temperature. The isomer shift is very useful parameter for determining valency states,

ligand bonding states etc. for the samples under study.


~ 75 ~

The isomer shift is useful for determining valency states, ligand bonding

states, electron shielding and the electron-drawing power of electronegative groups.

For example, the electron configurations for Fe2+ and Fe3+ are (3d)6 and (3d)5

respectively. The ferrous ions have less s-electrons at the nucleus due to the greater

screening of the d-electrons. Thus ferrous ions have larger positive isomer shifts than

ferric ions.

2.8.1 (b) Quadrupole Splitting Nuclei in states with an angular momentum quantum number I > 1/2 have a

non-spherical charge distribution. This produces a nuclear quadrupole moment. In the

presence of an asymmetrical electric field (produced by an asymmetric electronic

charge distribution or ligand arrangement) this splits the nuclear energy levels. The

charge distribution is characterised by a single quantity called the Electric Field

Gradient (EFG).

In the case of an isotope with I = 3/2 excited state, such as 57Fe or 119Sn, the

excited state is split into two substates mI = ±1/2 and mI = ±3/2. This is shown in

Fig.2.11, giving a two line spectrum or 'doublet'.

Fig.2.11 Quadrupole splitting for a 3/2 to 1/2 transition. The magnitude of quadrupole

splitting, ∆, is also shown.

The magnitude of splitting, ∆ is related to the nuclear quadrupole moment, Q,

and the principle component of the Electric Field Gradient (EFG), Vzz, by the relation

(2.17)


~ 76 ~

2.8.1(c) Magnetic Splitting (Hyperfine Interaction) In the presence of a magnetic field the nuclear spin moment experiences a

dipolar interaction with the magnetic field i.e, Zeeman splitting. There are many

sources of magnetic fields that can be experienced by the nucleus. The total effective

magnetic field at the nucleus, Beff is given by:

Beff = (Bcontact + Borbital + Bdipolar) + Bapplied (2.18)

the first three terms being due to the atom's own partially filled electron shells. Bcontact

is due to the spin on those electrons polarising the spin density at the nucleus, Borbital is

due to the orbital moment on those electrons, and Bdipolar is the dipolar field due to the

spin of those electrons.

This magnetic field splits nuclear levels with a spin of I into (2I + 1) substates.

This is shown in Fig.2.12 for 57Fe. Transitions between the excited state and ground

state can only occur where mI changes by 0 or 1. This gives six possible transitions

for a 3/2 to 1/2 transition, giving a sextet as illustrated in Fig.2.12, with the line

spacing being proportional to Beff.

Fig.2.12 Magnetic splitting of the nuclear energy levels.


~ 77 ~

The line positions are related to the splitting of the energy levels, but the

line intensities are related to the angle between the Mössbauer gamma-ray and the

nuclear spin moment. The outer, middle and inner line intensities are related by:

3 : (4sin2θ)/(1+cos2θ) : 1 (2.19)

meaning the outer and inner lines are always in the same proportion but the middle

lines can vary in relative intensity between 0 and 4 depending upon the angle the

nuclear spin moments make to the gamma-ray. In polycrystalline samples with no

applied field this value averages to 2 (as in Fig.2.12) but in single crystals or under

applied fields the relative line intensities can give information about moment

orientation and magnetic ordering.

These interactions, Isomer Shift, Quadrupole Splitting and Magnetic Splitting,

alone or in combination are the primary characteristics of many Mössbauer spectra

[63-71].

2.9 References [1] G.B. Greenough, Progr. Metal. Phys., 3 (1952) 176.

[2] A.J.C. Wilson, Proc. Roy. Soc., London, A180 (1942) 277.

[3] B.E. Warren, Prog. Met. Phys., 8 (1959) 147.

[4] C.N.J. Wagner, 'Local Atomic Arrangements Studied by X-ray Diffraction',

ed. J.B. Cohen and J.E. Hilliard, N.Y., Gordon Breach (1966).

[5] B.E. Warren, 'X-Ray diffraction', Addison-Wesley, (1969).

[6] H.P. Klug, L.F. Alexander, 'X-Ray diffraction Procedures', John-Wiley and

Sons., N.Y. (1974).

[7] S. Enzo, G. Fagherazzi, A. Benedetti, S. Polizzi, J. Appl. Cryst., 21 (1988)

536.

[8] J.I. Langford, A.J.C. Wilson, Proc. Symp. On Crystallography and Crystal

Fection, ed. G.N. Ramashandran, N.Y. Academic press, (1963) 207.

[9] E.J. Mittemeijer and R. Delhez, J. Appl. Phys., 49 (1978) 3875.

[10] D. Balzar, J. Res. Natl. Inst. Stand. Tech., 98 (1993) 321.

[11] P. Scherrer, Gittinger Nachrichten., 2 (1918) 98.

[12] R.A. Young, R.J. Gerdes and A.J.C. Wilson, Acta Cryst., 22 (1967) 155.


~ 78 ~

[13] R. Delhez, Th.H. de. Keijser and M.J. Mittemeijer, 'Accuracy in Powder

Diffraction', NBS special publication No.567 ed. S. Block and C. R. Hubbard,

NBS: Washington, DC 213 (1980) 213.

[14] R. Delhez, Th.H. de. Keijser, M.J. Mittemeijer and Fresenius, Z. Anal. Chem.,

312 (1982) 1.

[15] G. Zorn, Aust. J. Phys., 41 (1988) 237.

[16] R. Delhez, Th.H.de. Keiser, M.J. Mittemeijer and J.I. Langford, Aust. J. Phys.,

41 (1988) 213.

[17] H.M. Rietveld, J. Appl. Cryst., 2 (1969) 65.

[18] G. Caglioti, A. Paoletti and F.P. Ricci, Nucl. Instrum., 3 (1958) 223.

[19] W.N. Schreiner and R. Jenkins, X-Ray Spectrom., 8 (1983) 33.

[20] H.G. Scott, J. Appl. Cryst., 16 (1983) 156.

[21] W.I.F. David and J.C. Matthewman, J. Appl. Cryst., 18 (1985) 461.

[22] S.A. Howard and R.L. Snyder, Mat. Sci. Res. Symp. on Advances in Mat.

Res., 19 (1985) 57.

[23] P. Thompson, D.E. Cox and J.B. Hastings, J. Appl. Cryst., 20 (1987) 79.

[24] C. Greaves, J. Appl. Cryst., 18 (1985) 48.

[25] P. Thompson, J.J. Reilly and J.M. Hastings, J. Less. Com. Met., 129 (1987)

105.

[26] A. Le Bail, Proc.10th Colloque Rayons X, Siemens, Grenoble, (1985) 45.

[27] C. Lartigue, A. Le Bail and A. Percheron-Guégan, J. Less. Com. Met., 129

(1987) 65.

[28] L. Lutterotti and P. Scardi, J. Appl. Cryst., 23 (1990) 246.

[29] R.K. Nandi, H.K. Kuo, W. Schlosberg, G. Wissler, J.B. Cohen, B. Crist Jnr, J.

Appl. Cryst., 17 (1984) 22.

[30] L. Lutterotti, P. Scardi and P. Maistrelli, J. Appl. Cryst., 25 (1992) 459.

[31] http://www.iucr.org/iucr-top/comm/cpd/Newsletters/no21may1999/art17/art17.htmm

[32] R.W. Grosse-Kunstleve, Acta Cryst., A55 (1999) 383.

[33] N.C. Popa, J. Appl. Cryst. 31 (1998) 176.

[34] R. Delhez, Th.H. de. Keiser, J.I. Langford, D. Louër, M.J. Mittemeijer and E.

J. Sonneveld, 'The Rietveld method', ed. R.A. Young (Oxford:IUCR/OUP)

(1995) 132.

[35] L. Lutterotti, P. Polonioli, P.G. Orsini and M. Ferrari, Materials and Design

Technology ASME, PD-Vol. 62 (1994).


~ 79 ~

[36] H.R. Wenk, S. Matthies and L. Lutterotti, Mater. Sci. Forum, 157-162 (1994)

473.

[37] R. Krause-Rehberg, HS. Leipner, Positron Annihilation in Semiconductors.

Heidelberg: Springer; 1999.

[38] P. Hautojarvi, C. Corbel, Positron Spectroscopy in Solids, edited A.

Dupasquier, A.P. Millis Jr. (IOS Press, Ohmsha, Amsterdam, 1995), 491.

[39] U. De, D. Sanyal, S. Chaudhuri, P.M.G. Nambissan, Wolf Th, Wühl H. Phys

Rev B, 62 (2000) 14519.

[40] M .Chakrabarti, A. Sarkar, S. Chattapadhayay, D. Sanyal, A.K Pradhan, R.

Bhattacharya, D. Banerjee, Solid State Commun., 128 (2003) 321.

[41] U. Myler, P.J. Simpson, Phys. Rev. B, 56 (1997) 14303.

[42] P, Hautojärvi, C. Corbel, Positron Spectroscopy of Solids. In: Dupasquier A,

Mills AP Jr, editors. IOS Press: Amsterdam; (1995) 491.

[43] D. Sanyal, D. Banerjee, U. De, Phys Rev B, 58 (1998) 15226.

[44] R. Krause-Rehberg, and H.S. Leipner, Positron Annihilation in

Semiconductors (Springer, Berlin, 1999), Chap. 3, 61.

[45] Z.Q. Chen, M. Maekawa, S. Yamamoto, A. Kawasuso, X.L. Yuan, T.

Sekiguchi, R. Suzuki, T. Ohdaira, Phys Rev B, 69 (2004) 035210.

[46] A. Banerjee, B.K. Chaudhuri, A. Sarkar, D. Sanyal, D. Banerjee, Physica B,

299 (2001) 130.

[47] S. Dutta, M. Chakrabarti, S. Chattopadhyay, D. Jana, D. Sanyal, A. Sarkar, J

Appl Phys., 98 (2005) 053513.

[48] P. Kirkegaard, N.J. Pedersen, M. Eldrup, Report of Riso National Lab (Riso-

M-2740), 1989.

[49] P.M.G. Nambissan, C. Upadhyay, H.C. Verma, J Appl Phys., 93 (2003) 6320.

[50] F. Tuomisto, V. Ranki, K. Saarinen, D.C. Look. Phys Rev Lett., 91 (2003)

205502.

[51] F. Tuomisto, K. Saarinen, D.C. Look, G.C. Farlow, Phys Rev B, 72 (2005)

085206.

[52] M. Chakrabarti, S. Dutta, S. Chattopadhayay, A. Sarkar, D. Sanyal, A.

Chakraborti, Nanotechnology, 15 (2004) 1792.

[53] K.G. Lynn, A.N. Goland, Solid State Commun., 18 (1976) 1549.

[54] M. Chakrabarti, A. Sarkar, S. Chattapadhayay, D. Sanyal, A.K. Pradhan, R.

Bhattacharya, D. Banerjee, Solid State Commun., 128 (2003) 321.


~ 80 ~

[55] R.S. Brusa, W. Deng, G.P. Karwasz, A. Zecca, Nucl Instr and Meth B, 194

(2002) 519.

[56] V.J. Ghosh, M. Alatalo, P. Asoka-Kumar, B. Nielsen, K.G. Lynn, A.C.

Kruseman, P.E.Mijnarends, Phys Rev B, 61 (2000) 10092.

[57] F. Tuomisto, A. Mycielski, K. Grasza, Superlatt and Microstr, 42 (2007) 21.

[58] M. Chakrabarti, A. Sarkar, D. Sanyal, G.P. Karwasz, A. Zecca, Phys Lett A,

321 (2004) 376.

[59] M. Chakrabarti, S. Chattopadhyay, A. Sarkar, D. Sanyal, A. Chakrabarti,

Physica C, 416 (2004) 25.

[60] M. Chakrabarti, D. Bhowmick, A. Sarkar, S. Chattopadhyay, S. Dechoudhury,

D. Sanyal, A. Chakrabarti, J Mater Sci, 40 (2005) 5265.

[61] D. Sanyal, T.K. Roy, M. Chakrabarti, S. Dechoudhury, D. Bhowmick, A.

Chakrabarti, J Phys Condens Matter, 20 (2008) 045217.

[62] P. Asoka-Kumar, M. Alatalo, V.J. Ghosh, A.C. Kruseman, B. Nielsen, K.G.

Lynn, Phys Rev Lett., 77 (1996) 2097.

[63] Mössbauer Spectroscopy and its Applications, T.E. Cranshaw, B.W. Dale,

G.O. Longworth and C.E. Johnson, (Cambridge Univ. Press: Cambridge)

1985.

[64] Mössbauer Spectroscopy, D.P.E Dickson and F.J. Berry, (Cambridge Univ.

Press: Cambridge) 1986.

[65] The Mössbauer Effect, H Frauenfelder, (Benjamin: New York) 1962.

[66] Principles of Mössbauer Spectroscopy, T.C. Gibb, (Chapman and Hall:

London) 1977.

[67] Mössbauer Spectroscopy, N.N Greenwood and T.C Gibb, (Chapman and Hall:

London) 1971.

[68] Chemical Applications of Mössbauer Spectroscopy, V.I Goldanskii and R.H

Herber ed., (Academic Press Inc: London) 1968.

[69] Mössbauer Spectroscopy Applied to Inorganic Chemistry Vols. 1-3, G J Long,

ed., (Plenum: New York) 1984-1989.

[70] Mössbauer Spectroscopy Applied to Magnetism and Materials Science Vol. 1,

G J Long and F Grandjean, eds., (Plenum: New York) 1993.

[71] M. Chakrabarti, S. Chattopadhyay, D. Sanyal, A. Sarkar, D. Jana, Material

Science Forum, 699 (2012) 1.

CHAPTER-3

Experimental considerations

EXPERIMENTAL CONSIDERATIONS CHAPTER-3

~ 82 ~

3.1 Introduction

Nanocrystalline oxides can be prepared by different methods, e.g., sol–gel,

hydrothermal, chemical vapor phase deposition, calcinations of hydroxides, radio

frequency sputtering, gas condensation technique, high-energy ball-milling process,

etc. Among these the high-energy ball-milling process has many potential advantages.

The main advantage is large quantities of samples can be produced in a very short

time, and the process is relatively simple and inexpensive without any effect of

chemical contamination.

3.2 Different fabrication techniques of nano materials Nanomaterial fabrication techniques are two types: (a) Chemical methods

(Bottom-up approach) (b) Physical methods (Top-down approach).

(a) Chemical methods (Bottom-up approach): It has five different types:

(i) Sol gel

(ii) Chemical vapor deposition beam epitaxy

(iii) Co-precipitation

(iv) Dip-coating

(v) Spin-coating

(b) Physical methods (Top-down approach): There are three different types such as:

(i) Physical vapor deposition,

(ii) Ball-milling, and

(iii) Molecular Beam Epitaxy (MBE)

Again the Physical vapor deposition technique has three different parts which are

(i) Sputtering

(ii) Pulsed laser deposition

(iii) Ion plating.

Here we have used two techniques for sample preparation; one from chemical

methods and another from physical methods which are discuss below in brief:

3.2.1 Sol-gel method This is a bottom-up approach, where materials and devices are built from

molecular atoms which assemble themselves chemically by principles of molecular

recognition i.e. this approach starts with atoms and molecules and create larger


~ 83 ~

nanostructures. The sol-gel process is a wet-chemical technique (chemical solution

deposition) widely used recently in the fields of materials science and ceramic

engineering. Such methods are used primarily for the fabrication of materials

(typically a metal oxide) starting from a chemical solution (sol, short for solution)

which acts as the precursor for an integrated network (or gel) of either discrete

particles or network polymers. Typical precursors are metal alkoxides and metal

chlorides, which undergo hydrolysis and polycondensation reactions to form either a

network “elastic solid” or a colloidal suspension (or dispersion) – a system composed

of discrete (often amorphous) sub-micrometre particles dispersed to various degrees

in a host fluid. Formation of a metal oxide involves connecting the metal centers with

oxo (M-O-M) or hydroxo (M-OH-M) bridges, therefore generating metal-oxo or

metal-hydroxo polymers in solution. Thus, the sol evolves towards the formation of a

gel-like diphasic system containing both a liquid phase and solid phase whose

morphologies range from discrete particles to continuous polymer networks.

A sol is a dispersion of the solid particles (~0.1-1 mm) in a liquid where only

the Brownian motions suspend the particles. A gel is a state where both liquid and

solid are dispersed in each other, which presents a solid network containing liquid

components.

The precursor sol can be either deposited on a substrate to form a film (e.g. by

dip-coating or spin-coating), cast into a suitable container with the desired shape (e.g.

to obtain monolithic ceramics, glasses, fibers, membranes, aerogels), or used to

synthesize powders (e.g. microspheres, nanospheres). [Fig.3.1]

Fig.3.1 Sol-Gel process


~ 84 ~

The reagent grade Fe(NO3)3.9H2O has been used as precursor for the

preparation of nanocrystalline α-Fe2O3 powder by chemical route. Initially, a solution

of Fe(NO3)3.9H2O is made with distilled water. A few drops of concentrated nitric

acid have been added to keep the pH level of the solution in acidic range. This

solution is then stirred for 1 h and then poured into a plastic flat-bottomed container

and left for three days in ambient atmosphere for gelation. The gel is then evaporated

to obtain “as-prepared” sample in powder form.

3.2.1.1 Advantages of Sol-gel Technique: Sol-gel process- (a) Can produce thin bond-coating to provide excellent adhesion between the

metallic substrate and the top coat.

(b) Can produce thick coating to provide corrosion protection performance.

(c) Can easily shape material into complex geometries in a gel state.

(d) Can produce high purity products because the organo-metallic precursor of the

desired ceramic oxides can be mixed, dissolved in a specified solvent and

hydrolyzed into a sol, and subsequently a gel, the composition can be highly

controllable.

(e) Can have low temperature sintering capability, usually 200-600 0 C.

(f) Can provide a sample, economic and effective method to produce high quality

coatings.

3.2.2 Ball- milling process A ball-mill is a type of grinder used to grind materials into fine powder for use

in paints, pyrotechnics and ceramics. Ball mills rotate around an axis, partially filled

with the material to be ground plus the grinding medium. An internal cascading effect

reduces the material to a fine powder. There are different types of ball milling

machine viz.

• Tumbler mill:- Energy depends on diameter and speed of drum. Primarily

used for large-scale industrial applications.

• Attrition mill:- High energy, small-industry scale (<100 kg).

• SPEX mill:- High energy, research-scale.


~ 85 ~

• Planetary mill (Pulverisette 5):- Medium-high energy research miller (<250

g). This can be used universally for high speed grinding of solid or liquid

inorganic samples for synthesis, analysis, quality control or material testing. It

is also used to mix and homogenize dry samples, emulsions or pastes.

3.3 Potential of mechanical alloying

Mechanical alloying (MA) is normally a dry, high energy ball milling

technique that has been employed in the production of a variety of commercially

useful and scientifically interesting materials. The formation of an amorphous phase

by mechanical grinding of a Y-Co intermetallic compound in 1981 [1] and in the Ni-

Nb system by ball milling of blended elemental powder mixtures in 1983 [2] brought

about the recognition of MA as a potential non equilibrium processing technique.

Beginning from the mid 1980s, several investigations have been carried out to

synthesize a variety of stable and metastable phases, including supersaturated solid

solutions, crystalline and quasi-crystalline intermediate phases and amorphous alloys

[3-7]. In addition it has been recognized that powder mixtures can be mechanically

activated to induce chemical reactions, i.e, mechanochemical reactions at room

temperature or at least at much lower temperatures than normally required to produce

pure metals, nanocomposites and a variety of commercially useful materials [8,9].

Efforts have also been under way since the early 1990s to understand the process

fundamentals of MA through modeling studies [10]. Because of all these special

attributes, this simple but effective processing technique has been applied to metals,

ceramics, polymers and composite materials.

3.3.1 High energy ball-milling High-energy milling usually refers to a dry milling process where fracture and

cold welding are the dominant processes. This technique was first introduced for

Oxide Dispersion strengthened (ODS) alloys in the late 1960s and has since been

extensively explored for many metallic, ceramics, metallic-ceramic systems [11],

ceramic-ceramic systems.

Different types of ball mills, such as attrition mills, vibratory ball mills, and

planetary ball mills, are used for different purposes. The milling balls and bowls are

generally made of same material depending upon mechanical performance, and


~ 86 ~

contamination considerations. A few of the common materials are crome-steel,

zirconia, alumina, agate and tungsten carbide.

3.3.2 The planetary ball-mill (P5)

The laboratory planetary mill “pulverisette 5” (Fig.3.1) has been used for mechanical

alloying. It can be used for high speed grinding of solid or liquid inorganic and

organic samples for synthesis of nanocrystalline materials of different kind. It is also

used to mix and homogenise dry samples, emulsions or pastes.

Fig.3.1 Planetary Mill (pulverisette 5)

3.3.3 Mechanism of a planetary ball mill

The material to be ground is crushed and torn apart by grinding balls in 2 or 4

grinding bowls. The centrifugal forces created by the rotation of the grinding bowls

around their own axis and the rotating

supporting disc are applied to the grinding bowl

charge of material and grinding balls.

Since the directions of rotation of

grinding bowls and supporting disc are opposite

(Fig.3.2), the centrifugal forces are alternately

synchronised and opposite. Thus friction results

from the grinding balls and the material being Fig.3.2 Grinding mechanism of Planetary mill.


~ 87 ~

ground alternately rolling on the inner wall of the bowl, and impact results when they

are lifted and thrown across the bowl to strike the opposite wall. The impact is

intensified by the grinding balls striking one another. The impact energy of the

grinding balls in the normal direction attains values up to 40 times higher than

gravitational acceleration. Loss-free comminution is guaranteed by a hermetic seal

between grinding bowls and lid-even if suspensions are being ground.

The mechanics of this mill are characterized by the rotation speed of the disk,

Ω, that of the container relative to the disk, ω, the mass, m, size, and number of balls,

the radius of the disk, R, and the radius of the container, r. Gaffet [12] has shown that

depending on the relative values of ω/Ω and r/R, two extreme regimes may be

achieved: 1) the ball rolls on the inner surfaces of the container or 2) it escapes and

impacts an opposite portion of the surface. For both cases the energy transferred per

unit area scales with mΩ2 and the frequency of the occurrence of the impacts scales

with ω. The power induced to the powder sample therefore scales as P ∝ ml2Ω2ω

where l2 is a characteristic area of the order R2 or rR for the rolling or impact regime

respectively.

3.3.4 The merits and demerits of planetary ball-mill Merits 1. This method has the advantage of a top-down method for obtaining nano or

amorphous materials.

2. Room temperature synthesis of the material is possible.

3. Alloying and complete solid solubility of materials can be done.

4. Solid state amorphization of materials can be achieved.

5. The nanosized particles can be achieved in a short duration of time.

6. Energy of the milling media can be controlled by a large number of parameters,

such as, BPMR, rpm, duration of milling, size of balls/bowls etc.

Demerits 1. Possibility of contamination from milling media.

2. Stickiness of material during dry milling.

3. Excessive heating of material during milling.

4. Combustible liquids with boiling point <1200C can not be used.


~ 88 ~

5. Difficult to measure the transient temperature of the material surfaces during

milling.

6. Agglomeration of nanoparticles.

3.3.5 The mechanochemical transformation during milling Powder transformation during milling

is driven by the collisions between balls or

between balls and the vial. A number of

processes work simultaneously on the sample

but their relative importance differs during the

course of a milling experiment. In the

beginning, mixing of the constituent powders

dominates, after sometime fragmentation and

coalescence, and finally amorph-ization or

phase transformation. The Fig.3.3 illustrates

the milling action on powder trapped between colliding surfaces of two balls. The

pressure on these particles is very high and while some of them are fragmented others

are joined together by cold welding or localized melting. Plastic deformation and

joining of particles stacked on top of each other lead to a layered structure which is

continuously refined by further fracture and joining. Milling is usually considered

complete when these layers can no longer be observed. The final result can be an

amorphous mixture, a solid solution of one phase in the other, or a new phase formed

during milling depending on the thermodynamics of the system and the milling

parameters. Compounds normally developed only at elevated temperature or under

high pressure are often formed during high-energy milling.

3.3.6 Use of ball milling for synthesis of nanocrystalline materials Nanocrystalline α-Fe2O3 powders at different milling time are prepared by ball

milling the analytical grade α-Fe2O3 powder in open air at room temperature. A

number of nanocrystalline ferrites have been prepared and studied for this dissertation

by mechanical alloying the stoichiometric mixture of metal oxides in a high energy

planetary ball mill. All the starting materials are of analytical grade (purity >99%).

The methods of preparation of different polycrystalline ferrites are described in detail

F ig . 3 .3 B al l-pow d er col li si on o f pow d er m ix ture dur ing m ec ha ni ca l a llo yin g.


~ 89 ~

in the following sections. Nanosized ZnO powder is prepared by ball milling the

analytical grade ZnO powder for 3 hours. However, detailed preparation techniques

are described in respective sections.

3.4 Preparation of powder specimens for X-ray powder diffractometry The experimental powder samples were placed inside a rectangular slot (2cm.

X 1.5cm.) of the standard aluminium sample holder (M/S Philips). The sample was

pressed by a small aluminium hammer for better packing of the powder grains and the

upper surface of the sample facing the X-rays was made perfectly flat and smooth to

avoid error due to sample displacement.

3.4.1 Choice of radiation The proper choice of radiation depends on the nature of the sample under

experiment and the purpose for which the diffraction pattern is to be used. In this

study, CuKα radiation (λ=1.54184 A0) was used for recording of the diffraction

patterns of all the samples.

3.4.2 Choice of instrumental standard For instrumental broadening correction a specially processed Si standard (Van

Berkum, 1994) was used. The resolving of (111) reflection of Si at even ~28.40 2θ

into Kα1 and Kα2 components indicates that the instrumental broadening is very small.

The U, V, W coefficients of Caglioti formula (FWHM varies non-linearly with

increasing scattering angle) asymmetry and Gaussian content (vary linearly with

increasing scattering angle) were estimated and incorporated in the Rietveld software

as instrumental broadening.

3.4.3 Recording of X-ray powder diffraction data To carry out the Rietveld powder structure refinement of multiphase system,

the XRD pattern should be extremely accurate and clear. In order to obtain such high

quality line profile of XRD data, digitized step-scan data from a diffractometer of

high resolving power should be used and the X-ray generator must be highly

stabilized. The data fluctuation due to statistical errors can be minimized to a

considerable extent by recording large number counts.


~ 90 ~

In the present study, the X-ray powder diffraction step scan data were

recorded at room temperature and stored in a PC coupled with the diffractometer

using Ni-filtered CuKα radiation from a highly stabilized and automated Philips X-ray

generator (PW 1830) operated at 35kV and 25 mA. The generator is coupled with a

Philips X-ray powder diffractometer consisting of a PW 3710 mpd controller, PW

1050/37 goniometer, and a proportional counter. The step scan data of the

experimental samples was recorded for the entire angular range 15-900 2θ in step size

0.020 2θ and for 10sec counting time per each step. For experiment, 10 divergence slit,

0.2 mm receiving slit, 10 scatter slit were used.

3.5 Transmission electron microscope (TEM) used for microstructure study

Transmission electron microscopy

(TEM) (fig.3.4) is a microscopy technique

whereby a beam of electrons is transmitted

through an ultra thin specimen, interacting

with the specimen as it passes through. An

image is formed from the interaction of the

electrons transmitted through the

specimen; the image is magnified and

focused onto an imaging device, such as a

fluorescent screen, on a layer of

photographic film, or to be detected by a

sensor such as a CCD camera.

Fig3.4 Model HR-TEM 2100F, JEOL

TEMs are capable of imaging at a significantly higher resolution than light

microscopes, owing to the small de Broglie wavelength of electrons. This enables

the instrument's user to examine fine detail even as small as a single column of atoms,

which is tens of thousands times smaller than the smallest resolvable object in a light

microscope. TEM forms a major analysis method in a range of scientific fields, in

both physical and biological sciences. TEM investigations for this dissertation were

made utilizing a JEOL high resolution transmission electron microscope (Model HR-

TEM 2100F) operated at 200kV.


~ 91 ~

Transmission electron microscopy (TEM) specimens were prepared from ball

milled powders dispersed in doubly distilled acetone and mixed well under ultrasonic

vibrator to avoid agglomeration of the fine particles. A drop of this finely dispersed

colloidal solution was placed on the 3mm disc and the disc kept overnight under

vacuum to get completely dry and well distributed fine particles over the entire area of

the carbon coated grid. After drying, the grid was mounted in the sample holder of the

microscope for observation.

Transmission electron microscopy (TEM) with TECNAIS-TWIN (FEI

Company) electron microscope operating at 200 kV has been used to estimate the

average particle size of the different hour ball-milled Fe2O3 samples. Powder

ultrasonically dispersed in alcohol was put on a standard microscope grid for the TEM

work.

3.6 The outline of positron annihilation experiment In this experiment the positron annihilation lifetime can be measured with a

slow-fast coincidence assembly. In such a set-up there are two detectors, each

consisting of a BaF2 scintillator (25 mm in diameter and 25 mm long) coupled to

Philips XP2020Q photomultiplier tube. For each temperature, a total of ~ 106

coincidence counts, in form of N(t) vs. t data, is typically recorded with 8000:1 or so

peak to background ratio. For positron annihilation experiments, 22Na-source is the

most suitable and hence most widely used. It emits one 1.27 MeV γ-ray almost

simultaneously with the positron so that the former is considered as the birth signal of

the positron. The eventual “death” or annihilation of this positron with an electron of

the sample can be recorded by detecting one of the two 511 keV annihilation γ-rays.

Coincidence electronics measures the time gap between the detections of the birth and

death signals of the positron. The resolving time, FWHM of the lifetime spectrometer,

is measured with a 60Co. The recorded N(t) vs. t data is analyzed after necessary

source correction by a suitable computer programme e.g., POSITRONFIT, PATFIT-

88. From a measured positron annihilation lifetime spectrum, N(t) vs. t, one can

calculate the possible positron lifetime components, حi , and their intensities, Ii. These

lifetime components will correspond to individual characteristic lifetime of the

components, if the sample is a mixture of non-interacting components. However, if

the sample is single component substance, element or compound, with a characteristic

Bloch lifetime, detection of two or more lifetime components indicate the presence of


~ 92 ~

one or more trapping site (s) or other physical processes like positronium formation.

The lifetime for annihilation from the positron-trap turns out to be longer of the two

lifetime components and denoted by 2ح. Here lifetime for annihilation from the Bloch

state, called حB and supposed to probe the intrinsic properties of the material, can be

easily shown to be given by the equation no. (2.14) in chapter-2.

So, in a trapping model, حB and 2ح are the physically significant quantities,

with 2ح resulting from annihilation in regions of lower electron density. Without

assuming any model, a mean positron lifetime which is shown in equation no. (2.15)

in chapter-2.

From a multichannel analyzer we get the Doppler broadened spectrum of N

(E) vs. E, the central portion of the spectrum corresponds to annihilation with very

low momentum electrons, e.g., the valence electrons. The annihilation of positrons

with higher momentum electrons, e.g., the core electrons are distributed over the

wings of this spectrum because they are more strongly Doppler shifted.

For the CDBEPAR (coincidence Doppler broadening of the electron positron

annihilation γ- radiation) measurement, two identical HPGe detectors (Efficiency:

12%; Type: PGC 1216sp of DSG, Germany) having energy resolution of 1.1 keV at

514 keV of 85Sr have been used as two 511 keV γ-ray detectors, while the CDBEPAR

spectra have been recorded in a dual ADC-based multiparameter data acquisition

system (MPA-3 of FAST ComTec., Germany). A 10µCi 22Na positron source

(enclosed in between thin Mylar foils) has been sandwiched between two identical

and plane faced pellets [13]. The peak-to-background ratio of this CDBEPAR

measurement system, with ± ∆E selection, is ~105:1 [14,15]. The CDBEPAR

spectrum has been analyzed by evaluating the so-called lineshape parameters [14,16]

(S parameter). The S parameter is calculated as the ratio of the counts in the central

area of the 511 keV photo peak (|511 keV- Eγ| ≤ 0.85 keV) and the total area of the

photo peak (|511 keV- Eγ| ≤ 4.25 keV). The S parameter represents the fraction of

positron annihilating with the lower momentum electrons with respect to the total

electrons annihilated. The statistical error is ~ 0.2% on the measured lineshape

parameters. The CDBEPAR spectra for the unmilled and the milled samples have

been also analyzed by constructing the ‘‘ratio-curves’’ [14,15,17] with respect to

defects-free 99.9999% pure Al single crystal (reference sample).


~ 93 ~

3.6.1 The Positron Source Several nuclei emit positrons but there are only a few which are suitable for

the positron annihilation experiments. For positron annihilation experiments the

source should be such that there is continuous and steady flow of positrons from the

source. This source may be either the positron beam or a natural β+ emitting

radioactive source. In the experiments we use β+ emitting natural radioactive source.

The nuclei which are suitable for the positron annihilation experiments should have

the following characteristic properties:

• The source must emit a distinct γ ray after the emission of the positron from

the source. This prompt γ ray can be treated as the birth signal of the positron.

• The source must have a long half life so that the user can perform a series of

measurements with the same source.

• The source must emit positrons with sufficiently high end point energy so that

they can penetrate well inside the material under study.

• The source must have high positron yield.

• The source must be easily producible.

Considering the above all properties, 22Na source is the most suitable positron

(β+) source for the positron annihilation experiments. The decay scheme of this 22Na

is shown in Fig.3.5.

Fig.3.5 The decay scheme of 22Na.

The half-life of 22Na is ~ 2.6 years with 90.4 % of the decay via emission of

β+ particle. The end-point energy of the β+ particle feeding the 2+ state in 22Ne is


~ 94 ~

545.4 keV. The 2+ excited state in 22Ne deexcites to the ground state (0+) by emitting

a γ-ray of energy 1.274 MeV. The half-life of the excited (2+) state is 3.7 ps, which is

much smaller than the positron lifetime in matter. Thus, the 1.274 MeV γ-ray is

considered as the birth signal of the β+ particle as the emission of β+ particle from the

nucleus 22Na and the emission of 1.274 MeV γ-ray from the nucleus of 22Ne is almost

simultaneous.

3.6.2 The positron source preparation for positron annihilation experiments About 10 µCi 22Na enclosed between two thin (2 µm) nickel foils has been

used as the positron source for the positron annihilation experiments. Carrier free,

high specific activity (~ 1.1 mCi per ml) 22NaCl dissolved in dilute HCl procured

from E.I. DuPont de Nemours & Co., Inc., (France) has been used for the preparation

of the positron source. In case of nickel covered 22Na β+ source a fraction of positrons

may be annihilating within the source cover (nickel foil). These annihilations

contribute additional lifetime components in the lifetime spectrum. In order to

eliminate this contribution, source correction is necessary. For this purpose, positron

annihilation lifetime spectrum has been recorded with a defects free 99.9999 % pure

Al single crystal. In pure Al, positron has only one lifetime component of value 166 ±

1 ps. Thus the remaining lifetime component (if any) is due to source itself. In the

present experiments, with Ni covered 22Na β+ source, in addition to 166 ±1 ps (98 %)

a second lifetime component of 743 ± 10 ps with 2 % intensity has been observed.

The lifetime component of 743 ± 10 ps with 2 % intensity is due to the annihilation of

positrons inside the source and Ni foil and has been considered as the source

component. This component is found to be temperature independent, and hence used

in the temperature dependent positron annihilation measurements.

3.6.3 Implantation profile From a radioactive source, positrons enter into the material and penetrate up to

a certain depth inside the material. The positron implantation profile [18] for this case

is

I (x) = I (0) e-αx (3.1)

where I(0) is the initial positron density, I(x) is the positron density at a distance x and

α is the absorption coefficient of the material for positrons. The value of α can be

obtained from the following equation


~ 95 ~

α = (16 ± 1) ρ(Emax)-1.43 cm-1 (3.2)

where ρ is the density of the material under study in gm cm-3 and Emax is the end

point energy of the positron on MeV. For 22Na source, the value of Emax is 0.545

MeV. From this value of Emax, the relation between penetration depth and the

absorption coefficient is

1 / α = 0.026 / ρ cm (3.3)

3.7 Positron Annihilation Lifetime (PAL) Measurement On entering inside a material positrons from a radioactive source (here 22Na

source), gets thermalized and annihilates with an electron by emitting two oppositely

directed 511 keV γ- rays. One of these two 511 keV γ-rays is a signature of the

annihilation of the positron with an electron and hence considered as the death signal

of the positron. After 3.7 ps of the emission of β+ from 22Na source, the daughter

nucleus, 22Ne, de-excites to the ground state by emitting a γ-ray of energy 1.274 MeV,

which is considered as the birth signal of the positron. The timing interval between

the birth signal (1.274 MeV γ-ray) and the death signal (511 keV γ-ray) is considered

as the lifetime of the positron inside the material.

3.7.1 The positron annihilation lifetime (PAL) spectrometer The lifetime of the positron annihilation inside a material can vary from 100

ps to several nanoseconds. These sub-nanosecond lifetimes have been measured by a

standard nuclear technique, gamma-gamma coincidence technique. As the positron

annihilation lifetime values are very small (~ 100 ps) the detection of the γ-rays

should be very fast. The positron annihilation lifetimes have been measured with a

fast-fast coincidence assembly consisting of two constant fraction differential

discriminators (Fast ComTech Model number 7029A). The detectors are 25-mm-long

× 25-mm tapered to 13 mm – diameter cylindrical BaF2 scintillators optically coupled

to Philips XP2020Q photomultiplier tubes. The resolving time (full width at half

maximum, FWHM), measured with a 60Co source and with the proper energy window

(700 keV to 1320 keV for the start channel and 300 keV to 550 keV for the stop

channel) of the fast-fast coincidence assembly is 180 ps [19]. During the

measurement, temperature was kept constant at 300 K. Altogether 20 measurements

have been carried out (each positron annihilation lifetime spectrum of about 5 × 106

coincidence counts) to ensure the repeatability of the measurements. Measured


~ 96 ~

positron annihilation lifetime spectra have also been analyzed by computer

programme PATFIT-88 [20] with necessary source corrections. The details of the

lifetime set up have been shown in the block diagram of Fig.2.2, chapter-2.

Fig.3.6 The plot of the channel shift of the 60Co prompt coincidence peak for different known values of the delay.

By using by using 60Co source the lifetime spectrometer has been calibrated.

The 60Co source emits two prompt γ ray of energy 1173.2 keV and 1332.5 keV in a

time gap of 0.7 ps. To calibrate the TAC some known delay is given to the stop pulse

so that the centroid of the 60Co prompt coincidence spectrum shifts by a number of

channels in the MCA. The time per channel of the TAC has been calculated from the

slope of the peak channel shift vs. time delay curve (Fig.3.6).

Fig.3.7 A typical positron lifetime spectrum. The prompt time resolution of the system using 60Co is also shown in the figure.


~ 97 ~

The delay per channel in this coincidence assembly is 26.2 ps. Fig.3.7 shows a

typical positron annihilation lifetime spectrum in some material at room temperature.

3.7.2 Positron Annihilation Lifetime Data Analysis For each lifetime spectrum 106 or more coincidence counts has been recorded

with 8000:1 random ratio. The system stability has been checked frequently during

the progress of the experiment.

3.7.2 (a) Mathematical analysis of the positron annihilation lifetime data The positron annihilation lifetime spectrum is an exponential spectrum (in the

form e-λt where λ is the annihilation rate in the material). The time dependent positron

annihilation decay spectrum F(t) for N discrete state is given by

(3.4)

where τi ( = 1/λi) is the positron lifetime in the ith state and Ii is the relative intensity.

Due to the spectrometer contribution in the measured spectra with the resolution

function R(t), the lifetime spectrum is modified as

(3.5)

The contents of channel n of the experimental lifetime spectrum is expressed as

(3.6) where C is the constant background due to random coincidence.

The positron annihilation lifetime component can be obtained from the

measured spectrum either by using the least square method or by the integral

transform method. In the integral transform method, the lifetime spectrum is

considered as the Laplace transform and the lifetime component is obtained by its

inverse. The positron lifetime components have been evaluated here by using the

widely used least square method.

To evaluate the lifetime parameters from the measured spectrum computer

programs (PATFITT – 88) have been used here. This program consists of two parts:

RESOLUTION and POSITRONFIT.

The shape of the resolution function has been evaluated by using

RESOLUTION program.

The shape of the resolution function is determined by the sums of the shifted

Gaussians. The output of the RESOLUTION program describes the width of this


~ 98 ~

Gaussians. POSITRONFIT program has been used to evaluate the lifetime

components. It is necessary to perform the source correction before evaluating the

lifetime components. The contribution of the source component in the lifetime

spectrum has been subtracted from the measured spectra. Then, by fixing the shape

parameters of the resolution function the positron annihilation lifetime components

have been evaluated from the measured spectra by using the POSITRONFIT program.

3.7.2 (b) Positron annihilation lifetime data analysis The positron lifetime component τi and its relative intensity Ii can be evaluated

from the measured positron annihilation lifetime spectrum N(t) vs. t. In case of single

crystal only one lifetime component exists whereas for polycrystalline samples the

number of lifetime states will be different depending upon the sample property. In the

two state trapping model [21] it is assumed that the smallest lifetime component, τ1, is

due to the positron annihilation in the bulk of the material and the longer lifetime

component, τ2, is due to the positron annihilation at the defect sites in the material.

We can calculate the annihilation lifetime in the Bloch state (called τB), and the mean

positron lifetime (τav) from the equation (2.14) and equation (2.15) in chapter-2

respectively.

3.8 Doppler Broadening of the Electron Positron Annihilation Radiation Measurement After entering a material positrons get thermalized and then annihilate with

electron. In the center of mass frame, the energy of the annihilating photon is exactly

moc2 = 511 keV (mo is the rest mass of the electron or the positron) and the two

photons are moving exactly in the opposite direction. But due to the electron-positron

pair momentum, p, the 511 keV annihilation γ-rays are Doppler shifted by an amount

± ∆E in the laboratory frame with

± ∆E = pLc/ (3.7)

Fig.3.8: Schematic representation of Doppler shift of the annihilating γ- rays along the detector direction.


~ 99 ~

pL (p cos θ) is the component of the electron momentum, p, along the direction of the

detection of the annihilating γ-rays. Fig. 3.8 represents the Doppler shift of the

electron positron pair along the detector direction due to non-zero momentum of the

electron positron pair. So by measuring the Doppler shift of these 511 keV γ-photons

one can study the momentum distributions of the electrons at the positron annihilation

site.

3.8.1 Coincidence Doppler broadening of the electron positron annihilation radiation measurement One can measure the Doppler broadening of the electron positron annihilation

γ-radiation (DBEPAR) spectrum using a high resolution HPGe detector. The central

portion of the DBEPAR spectrum (as shown in Fig.3.9) represents those 511 keV γ-

rays, which are less Doppler shifted, i.e., coming from the annihilation of positrons

with the lower momentum electrons. Similarly, the wing portion of the DBEPAR

spectrum represents those 511 keV γ-rays, which are more Doppler shifted, i.e.,

coming from the annihilation of positrons with the higher momentum electrons, e.g.,

core electrons. Now it is very important to study the annihilation of positrons with the

core electrons in a particular material. Hence it is very important to increase the

statistics of the counts in the DBEPAR spectrum, particularly in the wing portion.

Unfortunately, the Compton part of the 1.274 MeV γ-ray is always present in the

photo-peak of the 511 keV γ-rays and is more prominent as a background in the wing

portion of the DBEPAR spectrum. The typical peak to background ratio is ~ 50:1.

Using two HPGe detectors in opposite direction one can increase the peak to

background ratio better than 105:1 [22]. For the coincidence Doppler broadening

(CDB) measurement, two identical HPGe detectors (Efficiency: 12 % ; Type : PGC

1216sp of DSG, Germany) having energy resolution of 1.1 keV at 514 keV of 85Sr

have been used as two 511 keV γ- ray detectors, while the CDB spectra have been

recorded in a dual ADC based - multi parameter data acquisition system (MPA-3 of

FAST ComTec., Germany). The peak to background ratio of this CDB measurement

system [22] with ± ∆E selection is ~ 105:1. The CDB spectrum has been analyzed by

evaluating the ratio curve analysis [15].


~ 100 ~

Fig.3.9: A typical Doppler broadening spectrum with two detectors in coincidence [one HPGe and another NaI(Tl) detectors].

3.8.2 The coincidence Doppler broadening of the electron positron annihilation radiation (CDBEPAR) spectrometer The block diagram of such a Coincidence DBEPAR (CDBEPAR)

spectrometer used, is shown in Fig.2.3 in chapter-2, which is discussed earlier.

A total of ~ 6 × 106 to 107 coincidence counts have been recorded under the

photo-peak of the 511 keV γ-ray CDBEPAR spectrum at a rate of 110 counts per

second. The CDBEPAR spectrum is recorded in a PC based 8k multi-channel

analyzer. The energy per channel of the multichannel analyzer is kept at 22 eV (as

shown in Fig. 3.10).

Background has been calculated from 607 keV to 615 keV energy range of the

spectrum. The achieved peak to background ratio in the present case is ~ 14000:1.

The system stability has been checked frequently during the progress of the

experiment. For the energy calibration of the set up, the 383.7 keV γ-ray from 133Ba,

411.1 keV and 444 keV γ-ray from 152Eu and 661.6 keV γ-ray from 137Cs source have

been used.


~ 101 ~

Fig.3.10: Calibration of the coincidence Doppler broadening spectrometer using standard monoenergetic γ-rays.

3.8.3 The Doppler broadening data analysis

3.8.3 (a) Line shape analysis The coincidence Doppler broadening of the electron positron annihilated 511

keV γ-ray spectrum has been analyzed by evaluating the so called line-shape

parameters [23] (S-parameter) and (W-parameter). The S-parameter is calculated as

the ratio of the counts in the central area of the 511 keV photo peak ( | 511 keV - Eγ |

≤ 0.85 keV ) and the total area of the photo peak ( | 511 keV - Eγ | ≤ 4.25 keV ). The

S-parameter represents the fraction of positron annihilating with the lower momentum

electrons with respect to the total electrons annihilated. During all measurements, the

value of the S parameter is kept fixed around 0.45 to 0.5 by suitable selecting the

energy range. The W-parameter represents the relative fraction of the counts in the

wings region (1.6 keV ≤ |Eγ -511 keV| ≤ 4 keV) of the annihilation line with that

under the whole photo peak ( | 511 keV - Eγ | ≤ 4.25 keV ). The W-parameter

corresponds to the positrons annihilating with the higher momentum electrons. The

schematic representations of the S parameter and W-parameter are shown in Fig.2.4 &

Fig.2.5 in chapter-2 respectively. The statistical error is 0.2% on the measured line-

shape parameters.


~ 102 ~

3.8.3 (b) Ratio-curve analysis Ratio curve analysis [16,24] have been followed to identify the contributions

of the valence and the core electron momentum involved in the annihilation process.

Ratio-curve is defined as point to point ratio of area normalized CDBEPAR spectrum

of the material under study with an area normalized CDBEPAR spectrum of reference

sample. Reference sample should be a highly pure defects free sample. We have been

taken defects free 99.9999% pure Al single crystal and 99.9999% pure Cu single

crystal as reference samples.

3.9 An outline of Mössbauer spectroscopy experiment The Mösbauer spectroscopy represents one of the great achievements in

experimental physics. I first describe the principle of energy modulation using

Doppler velocity, which is a key step in observing a Mössbauer spectrum. This

technique is well developed and well documented in the literature [25,26]. Next, I

describe the Mössbauer radiation sources and the γ -ray detectors. These sources and

detectors must possess certain particular properties and are specially prepared. The

data acquisition system is relatively simple, which I briefly deal with.

3.9.1 The Mössbauer Spectroscopy The Mösbauer spectroscopy is a recoilless γ- ray emission and subsequent

absorption spectroscopy. To obtain the resonance curve of a nucleus absorbing γ-rays,

the energy of the incoming γ-ray must be modulated. This is achieved using the

Doppler effect, in which the perceived frequency of a wave is different from the

emitted frequency if the source is moving relative to the receiver. Suppose the source

and the receiver have a relative velocity of v, then the perceived frequency of the γ-

radiation is

(3.8)

where f0 is the frequency of the radiation when the source is at rest, c is the speed of

light, and θ is a small angle between the relative velocity and the γ-ray direction.


~ 103 ~

To obtain a typical Mössbauer spectrum, vmax< 1 m s-1, thus v/c << 1 and a very good

approximation of the above equation is

, or, (3.9) Mössbauer spectrometer has a velocity transducer based on equation (3.9)

modulating the γ -ray energies in order to observe the resonance curve. In most cases,

the source undergoes a mechanical motion, whereas the absorber is at rest so that it is

easier to change its temperature or to apply an external magnetic field to the absorber.

The velocity transducers are generally operated in two modes: constant

velocity and velocity scan. The first is the simplest, developed in the early 1960s. In

this case the spectrum is recorded ‘‘point by point’’ throughout the selected velocities

provided that the measurement time interval at each velocity is fixed. The Mössbauer

spectrometers used at the present time are almost exclusively constructed using the

second mode, in which the source scans periodically through the velocity range of

interest. If every increment/decrement in velocity between adjacent points is the same,

the source motion must have a constant acceleration, and the velocity-scanning

spectrometer becomes a constant-acceleration one. For recording the transmitted γ -

rays, each velocity has its own register (usually called a channel) which is

sequentially held open for a fixed, short time interval synchronized with the velocity

scan. The number of channels, i.e., the number of velocity points, is usually chosen to

be 256, 512, or sometimes 1024, etc.

Fig.3.11 shows a block diagram of a velocity-scanning spectrometer in

transmission geometry. It consists of a radiation source, an absorber, a detector with

its electronic recording system, a clock signal and a function generator, a drive circuit,

and a transducer.

The radiation source is not monochromatic. For example, in addition to

emitting the 14.4-keV γ-rays, a 57Co source also emits γ-rays and x-rays of other

energies. In order to pick out the signal due to the 14.4-keV radiation, a single-

channel analyzer (SCA) is placed behind the amplifier. Fig.3.12 shows various control

signals and an observed spectrum.

The clock generates a synchronizing signal, which sets the starting moment

(t =0) for velocity scanning. A triangular wave from the waveform generator begins to

increase (decrease) from its minimum (maximum), and the first channel also begins to


~ 104 ~

open. After that, each channel is opened in turn by an advance pulse alone. The

velocity of the transducer is scanned linearly from –vm to + vm

Fig.3.11 Block diagram of a Mössbauer spectrometer in transmission geometry. Fig.3.12 Various control signals in a constant-acceleration spectrometer and an absorption spectrum. and a spectrum taken during the linear ramp is stored in one half of the total channels.

Then, the velocity decreases from +vm back to -vm, completing a backward scan,

during which the measured data are stored in the other half of the available channels.

Therefore, in one scan period, a multiscaler or a computer will record two spectra,

which are mirror images of each other. In order to obtain a spectrum with a good

signal-to-noise ratio, hundreds of thousands of scans are usually necessary. An

occasional synchronization problem would have no impact, because it recovers at the

next scan period. One obvious advantage of using a constant-acceleration


~ 105 ~

spectrometer is that the stability requirement is not as strict as in a constant-velocity

spectrometer. If instability, such as a discrimination voltage drift at SCA, should

cause a decrease in the absorbed line intensities during one scan or several scans, it

has a small effect on the absolute intensities but no effect on the positions and the

shape of the spectral lines because this process is equivalent to shortening the

experiment duration slightly. Another advantage is that this mode can make full use of

digital technology, improving the properties of the spectrometer and allowing

automatic data acquisition.

3.9.2 Radiation Sources Among the isotopes in which the Mössbauer effect has been observed, 40K is

the lightest one. 57Fe and 119Sn are the most popular Mössbauer isotopes, whose decay

schemes are shown in Fig.3.13. 57Fe is by far the most important one, for more than

69% of research work involves 57Fe.

Fig.3.13 Nuclear decay schemes of 57Co and 119Sn. 3.9.3 The Absorber In Mössbauer spectroscopy, the absorber is usually the sample to be

investigated. In transmission geometry, the thickness of the absorber significantly

affects the quality of the spectrum and must be carefully chosen.

3.9.4 Detection and Recording Systems If we take the 57Co source, it emits γ-rays of 136, 122, and 14.4 keV and x-

rays of 6.3 keV (Fig.3.14), with an approximate intensity ratio of 1:10:1:13.

Therefore, the 14.4 keV Mössbauer radiation is only a small part of the total radiation,

and what is worse is that the flux of 14.4 keV γ-rays is attenuated considerably after

going through a typical sample, but the flux of the 122 keV γ-rays will be decreased


~ 106 ~

0 50 100 150 200 2501x105

2x105

3x105

4x105

8.568

5.273

1.784-0.835

-4.337

-8.025Cou

nts

Channel Number

very little. Consequently, the detector must be highly efficient for the 14.4 keV γ-rays,

but be as insensitive as possible to the 122 keV γ-rays. As to the γ-rays with energies

below 14.4 keV, they will be discriminated against by the single-channel analyzer if

they have been detected. The most widely employed detectors are proportional

counters and NaI(Tl) scintillation counters, followed by semiconductor detectors [27].

Fig.3.14 Schematic diagram showing various processes of secondary radiation as γ-rays from a 57Co source travel through the absorber towards the detector. 3.9.5 Experimental set up of Mössbauer spectroscopy Mössbauer spectroscopy has been successfully employed in our laboratory on

different system. Mössbauer spectra have been recorded using a CMTE constant

acceleration drive (Model-250) with a 5 mCi 57Co source in Rh matrix. A Xe filled

proportional counter was used as detector.

The sample was made vibration free using home made arrangements. Recoil

spectral analysis [28] software was used for quantitative evaluation of Mössbauer

spectra. The isomer shift was calculated with respect to metallic iron (α-Fe) at room

temperature.

Fig.3.15 Room temperature Mössbauer spectra for standard enriched 57Fe2O3 sample


~ 107 ~

0 50 100 150 200 250-12

-8

-4

0

4

8

12

Velo

city

(mm

/sec

)

Channel Number

Zero Channel = 128.8Velocity/Channel = 0.096

Fig.3.16 Velocity per channel calibration curve of the Mössbauer spectrometer

Room temperature 57Fe Mössbauer spectra for all the samples have been

recorded in the transmission configuration with constant acceleration mode. A gas

filled proportional counter has been used for the detection of 14.4 keV Mössbauer γ -

rays, while a 10 mCi 57Co isotope embedded in an Rh matrix has been used as the

Mössbauer source. The Mössbauer spectrometer has been calibrated with 95.16%

enriched 57Fe2O3 and standard α-57Fe foil. Fig.3.15 and Fig.3.16 show the spectrum of

the 57Fe2O3 and the velocity per channel calibration curve of the Mössbauer

spectrometer respectively. The Mössbauer spectra have been analyzed by a standard

least square fitting program (NMOSFIT).

3.10 References [1] E. Ermakov, E.E. Yurchikov, V.A. Barinov, Phys. Met. Metallogr., 52(6)

(1981) 50.

[2] C.C. Koch, O.B. Cavin, C.G. McKamey, J.O. Scarbrough, Appl. Phys. Lett.,

43 (1983) 1017.

[3] C.C. Koch, In: R.W. Cahn editor. Processing of metals and alloys of Materials

Science and Technology-a comprehensive treatment, Weinheim, Germany:

VCH Verlagsgesellschaft GmbH, 15 (1991) 193.


~ 108 ~

[4] C. Suryanarayana, Bibiography on mechanical alloying and

milling,Cambridge, UK: Cambridge International Science Publishing, 1995.

[5] C. Suryanarayana, Metals and Materials, 2 (1996) 195.

[6] M.O. Lai, and L. Lu, Mechanical alloying, Boston, MA: Kluwer Academic

publishers, 1998.

[7] B.S. Murty, S. Ranganathan, Internat. Mater. Rev., 43 (1998) 101.

[8] G. Heinicke, Tribochemistry, Berlin, Germany: Akademie Verlag, 1984.

[9] P.G. McCormick, Mater. Trans. Japan Inst. Metals, 36 (1995) 161.

[10] D.R. Maurice, T.H. Courtney, Metall. Trans., A21 (1990) 289.

[11] P.R. Soni, Mechanical Alloying: Fundamentals and Applications, Cambridge

International Science Publishing, Cambridge (2000).

[12] E. Gaffet, Materials Science and Engineering A, (1990)

[13] M. Chakrabarti, A. Sarkar, S. Chattopadhyay, D. Sanyal, In: Martins BP (ed)

New topics in superconductivity research. Nova Science, New York, (2006).

[14] M. Chakrabarti, D. Sanyal, A. Chakrabarti, J Phys Condens Matter, 19 (2007)

236210.

[15] D. Sanyal, M. Chakrabarti, T.K. Roy, A. Chakrabarti, Phys Lett A, 371 (2007)

482.

[16] Hautojarvi P, Corbel C (1995) In: Dupasquier A, Mills AP Jr (eds) Positron

spectroscopy of solids. IOS Press, Amsterdam, p 491; In: Krause-Rehberg R,

Leipner HS (eds) Positron annihilation in semiconductors, Springer Verlag,

Berlin, 1999.

[17] K.G. Lynn, A.N. Goland, Solid State Commun., 18 (1976) 1549.

[18] W. Brandt, R. Paulin, Phys. Rev. B, 15 (1977) 2511.

[19] D. Sanyal, M. Chakrabarti, A. Chakrabarti, Solid State Communications, 150

(2010) 2266.

[20] P. Kirkegaard, N.J. Pedersen and M. Eldrup: Report of Riso National Lab,

(Riso- M-2740), 1989.

[21] W. Brandt and A. Dupasquier (Eds.), Positron Solid State Physics, North-

Holland, Amsterdam, 1983.

[22] N. Kumar, D. Sanyal, and A. Sundaresan: Chem. Phys. Lett., 477 (2009) 360.

[23] P. Hautojarvi (Eds.), Positron in Solids, Springer-Verlag, Berlin, (1979) 4.

[24] R.S. Brusa, W. Deng, G.P. Karwasz and A. Zecca: Nucl. Instr. & Meth. B, 194

(2002) 519.


~ 109 ~

[25] R.L. Cohen and G.K. Wertheim. Experimental methods in Mössbauer

spectroscopy. In Methods of Experimental Physics, vol. 11, R.V. Coleman

(Ed.), pp. 307–369 (Academic Press, New York, 1974).

[26] G. Longworth. Instrumentation for Mössbauer spectroscopy. In Advances in

Mössbauer Spectroscopy: Applications to Physics, Chemistry and Biology,

B.V. Thosar and P.K. Iyengar (Eds.), pp.122–158 (Elsevier, Amsterdam,

1983).

[27] Yi-Long Chen and De-Ping Yang, Mössbauer Effect in Lattice Dynamics,

Experimental Techniques and Applications.


Sekiguchi, R. Suzuki, T. Ohdaira: Phys. Rev. B, 69 (2004) 035210.

PART: II

Experimental investigations on some nanomaterials

CHAPTER-4

Nanophase iron oxides by ball-mill grinding and their Mössbauer characterization

CHAPTER-4

~ 111 ~

4.1 Introduction

In the recent years nanocrystalline materials have been extensively

investigated due to their unusual properties as well as application potentials [1]. The

iron oxides, α-Fe2O3 (hematite) and Fe3O4 (magnetite), for example, are important

electrical and magnetic materials. Mössbauer spectra [2] of fine particles of α-Fe2O3,

produces by a chemical impregnession process and supported on a high area silica, in

different sizes, have been recorded before the name nanophase was coined. Among

various methods of producing nanomaterials, ball-milling [3] has potential for large

scale production and is being further developed. Particle size reduction and possible

chemical transformation of the sample during ball-milling are believed to be

influenced by ball-to-powder mass ratio (BPMR), duration of milling time, milling

environment, milling speed etc. as well as type of ball-mill itself. Recently, Zdujic et

al. [4] reported the results of ball milling of α-Fe2O3 powder in air and in ‘closed

atmosphere’ milling conditions using a planetary ball mill and showed that the

mechanochemical treatment of iron oxides was very sensitive to milling conditions.

Recently, structural and magnetic properties of nanophase materials have been

investigated by X-ray powder diffraction [1,5,6,14] and Mössbauer spectroscopic

[1,7-9] techniques. The present work is devoted to X-ray powder diffraction line

profile analysis and Mössbauer studies on differently ball-milled α-Fe2O3 fine

particles. It is noted that the nature of the Mössbauer spectrum depends on the relation

between the time of measurement and that of the magnetization vector relaxation. If

the time of observation is much less than the relaxation time, the particles exhibit

ferromagnetism, while in the opposite case one observes superparamagnetism. Also,

the relaxation time of superparamagnetic particles increases with particle volume, as

detailed later. Therefore, in ferromagnetic samples consisting mainly of nanoparticles,

the Mössbauer spectrum is usually a superposition of a superparamagnetic doublet,

corresponding to particles of smaller size, and a Zeeman sextet, corresponding to

large ferromagnetic particles [10,11].

4.2 Experimental details

Analytical grade α-Fe2O3 powder was used as the starting material for milling

in Fritsch Pulverisette 5 planetary ball mill. Two hardened-steel vials of 80 cm3

volume, each charged with 30 hardened-steel balls of 10 mm diameter were used for

CHAPTER-4

~ 112 ~

milling, keeping the angular velocity of the supporting disc at 31.42 (300 rpm) rad s-1.

The powder was milled in air atmosphere without any additives (dry milling) under

‘closed’ milling conditions, i.e., the vials were not opened during all the milling

periods. In all the experiments, the ball-to-powder mass ratios (BPMR) of 30:1 and

35:1.have been tried.

The X-ray powder diffraction (XRD) step scan data (0.020 2θ) were collected

on a Philips PW 1710 automatic diffractometer with CuKα radiation. The Mössbauer

spectra have been recorded in transmission geometry using a constant acceleration

type. Mössbauer spectrometer with a 5mCi Co57 source in a Pd matrix. A Xe-filled

proportion counter has been used as detector. The data have been acquired in the

MCS mode in a multichannel analyzer. Mössbauer spectra of α-Fe2O3 fine particles

produced by ball-milling have been recorded at room temperature.

4.3 Method of X-ray line profile analysis

In the present study, the Scherrer formula [12] has been used only for grain

size (D) determination and Warren-Averbach method of Fourier analysis of line

profile [12] for estimation of both the particle size (coherently diffracting domain)

(De) and r.m.s strain (<ε2>1/2) of unmilled and all the ball-milled α-Fe2O3 samples.

Mössbauer spectra for all the samples are fitted by least-square fitting programme

with Lorentzian line shape. The isomer shift (IS), line width, quadrupole splitting

(QS) internal hyperfine field (Hn) are obtained from best fitted Mossbauer spectra

lines.

4.4 Results and discussion

We have considered the most prominent reflections of α-Fe2O3 (012), (104),

(110), (113), (024), (116), (214) and (030) for X-ray line profile analyses (XRLPA).

The reflections of transformed Fe3O4 and Fe1-xOx are very weak and/or completely

overlapped with α-Fe2O3 reflections and are not considered for XRLPA. As some of

the peaks of α-Fe2O3 are partially overlapping [Fig. 4.1], it is prime necessity to

estimate the correct background of the X-ray spectra in the vicinity of overlapping

region in order to obtain the accurate values of peak-position maxima, peak

intensities, full-width at half-maxima (FWHM) and Gaussianity of the experimental

profiles. The Scherrer formula [12] for grain size (D) estimation or Warren-Averbach

CHAPTER-4

~ 113 ~

20 30 40 50 60 70

0

100

200

300

400

500

2θ (degree)

3= FeO2= Fe3O41= α-Fe2O3

112

12

12

1131

(030

)(2

14)

(116

)

(024

)

(113

)(110

)

(104

)

(012

)

1

123

0h

20h

15h

10h

5h

Inte

nsity

(arb

.uni

t)method of Fourier analysis of line shapes [12] for determination of particle size (De)

and r.m.s. strain, <ε2> 2/1 have been used after the correction for background by a

standard profile fitting procedure [13]. For peak fitting, the most suited pseudo-Voigt

peak shape function has been used, as recommended by Young and Wiles [14]. The

said function has the following refinable parameters: peak-height (I), peak area (S),

peak maximum position (2θmax), full width at half maxima (FWHM), an asymmetry

parameter (A) and gaussianity of the peak (G) and background parameters (linear/non

linear). Two weighting schemes can be used during the profile fitting: (a) unweighted

refinement (wI =1) and (b) weight equals to the reciprocal of the standard deviation.

Refinement uses the Marquardt minimization algorithm. The adopted software [13]

allows simultaneous fittings of upto 15 overlapping peaks of mixed Gaussian and

Lorenzian type. For both the Scherrer equation and Warren-Averbach analyses and a

specially prepared polycrystalline Si is used as ‘instrumental standard’ [15]. The

results of X-ray powder diffraction line profile analysis on differently ball-milled

samples of α-Fe2O3 is presented in Table 4.1.

Fig. 4. 1 X-ray powder diffraction patterns for different periods of ball-milling of α-Fe2O3

CHAPTER-4

~ 114 ~

Table 4.1 Results of X-ray powder diffraction line profile analysis on differently ball-milled samples with α-Fe2O3 (0h) denoting the as-supplied or the starting material.

Sample (milling time)

hkl

Lattice

parameter

(nm)

Particle size (nm) R.m.s. strain (103) Scherrer Warren-Averbach Warren-Averbach

(D)hkl (D)av (D)hkl (D)av 2/12hkl⟩⟨ε 2/12

av⟩⟨ε

Fe2O3 (0hrs.)

012 104 110 113 024 116 214 030

a=0.50250 c=1.36838

57.05 54.91 61.61 53.12 62.69 62.40 80.94 65.38

62.26 29.8 32.4 30.1 59.8 35.3 27.6 36.7 30.0

35.2 1.71 1.37 1.03 1.32 0.79 0.58 0.41 0.47

0.96

Fe2O3 (5hrs.)

BPMR= 30:1

012 104 110 113 024 116 214 030

a=0.50281 c=1.37402

8.08 8.04 9.56 6.93 6.85 7.59 6.74 7.84

7.70

5.02 3.01 6.54 3.29 3.20 3.62 3.00 3.21

3.86

9.97 7.60 6.16 6.06 5.09 4.21 4.25 3.81

5.89

Fe2O3 (10hr)

BPMR= 35:1

012 104 110 113 024 116 214 030

a=0.50320 c=1.37751

8.16 10.70 9.69 9.64 7.75 10.21 7.72 9.10

9.12

6.16 4.67 3.93 3.85 3.15 4.85 5.46 3.62

4.46

10.38 4.99 5.44 4.82 4.93 3.15 4.44 3.38

5.19

Fe2O3 (15hr)

BPMR= 35:1

012 104 110 113 024 116 214 030

a=0.50380 c=1.37638

8.20 9.91 10.41 11.66 10.83 8.87 12.59 10.72

10.39

3.27 3.95 5.89 6.41 4.37 4.25 5.12 5.26

4.81

9.53 5.76 5.04 3.79 3.56 3.61 2.44 2.58

4.53

Fe2O3 (20hr)

BPMR= 30:1

012 104 110 113 024 116 214 030

a=0.50391 c=1.37664

10.39 9.27 9.02 9.97 7.45 9.95 6.96 12.29

9.41

5.00 5.17 3.61 7.93 4.11 4.04 2.85 5.01

4.71

6.92 4.94 5.89 2.36 4.92 3.54 4.39 2.45

4.42

CHAPTER-4

~ 115 ~

Table 4.2 Mössbauer parameters for differently ball-milled α-Fe2O3

.Sample (milling time)

IS (mm/s)

a( 5612 ∆−∆ ) (mm/s)

QS (mm/s)

Hn (Tesla)

FWHM Γ(mm/s)

Relative Intensity(%)

Fe2O3(0h) Six-finger Doublet Single line

0.41

– –

0.22

– –

-0.08

– –

51.82

– –

0.34

– –

100 0 0

Fe2O3(5h) Six-finger Doublet

0.37 0.38

0.197

–

0.15 2.33

49.467

–

–

0.71

84.09 15.91

Fe2O3(10h) Six-finger Doublet Single line

0.48 0.40

–

0.008 – –

0.087 1.79

–

49.13 – –

– 2.27

–

80.52 19.48

0 Fe2O3(15h) Six-finger Doublet Single line

0.37 0.40

–

0.01 – –

0.27 1.69

–

48.89 – –

– 1.22

–

77.18 22.82

0 Fe2O3(20h) Six-finger Doublet Single line

0.35 0.64

–

0.167 – –

0.038 2.33

–

49.867 – –

– 1.89

–

74.22 25.78

0

)( 5612 ∆−∆a is the energy difference between lines 1 and 2 of the sextet, minus the energy difference between lines 5 and 6 of the sextet (line 1 is at extreme left). All the values of Mössbauer parameters have been calculated using α-Fe as standard. Mössbauer spectra for all the samples (Table 4.2) are fitted by least-square

fitting programme [16] with Lorentzian profiles to determine the line positions, line

width and peak-intensities. The continuous lines represent the computer fitted data,

where as the dot represents the experimental data. The isomer shift (IS), quadrupole

splitting (QS), internal hyperfine field (Hn), obtained from best fitted Mössbauer

spectra lines are presented in Table 4.2. Two typical spectra of bulk or as-supplied α-

Fe2O3 and 5h ball-milled α-Fe2O3 powder samples are shown in the Fig.4.2(a),(b),

respectively. The Mössbauer spectra of different ball-milled α-Fe2O3 samples consist

of a sextet and doublet.

Mössbauer spectrum of the bulk α-Fe2O3 sample, having particle size 35.2 nm

according to Warren-Averbach calculations, shows a six-finger pattern having

IS=0.41 mm/s and Hn=51.82 Tesla, which is in agreement with earlier findings [2].

Kundig and Bommel [2] have obtained only a central doublet with samples having

CHAPTER-4

~ 116 ~

particle size ~18nm or lower. They attributed the doublet to the superparamagnetic

state. In our case,

Mössbauer spectrum consisted of a sextet (predominating in intensity) and a

broad central doublet for particle sizes much smaller than 18nm (Table 4.2).

However, the Mössbauer spectra of the 5h milled sample is best fitted with a sextet, a

doublet and a single line of very weak relative intensity (0.01%). This single line

having an IS=0.64mm/s can be attributed to Fe1-xOx phase. It is interesting that the

relative intensity of the doublet increases as particle size decreases (corresponding to

longer milling time). So the doublet is attributed to the superparamagnetic behaviour

of ferromagnetic fine particles. One still needs an explanation for the additional

presence of the sextet that obviously indicates a ferromagnetic ordering in the

samples. Appearance of this ferromagnetic ordering can be explained either from the

theory of superparamagnetic relaxation or from a presence of larger particles (at

least>18nm) in high proportion. However, XRD analysis does not detect such high

proportion of larger particles. Therefore the only option remaining is to explain the

appearance of sextet from the theory of superparamagnetic relaxation. The

superparamagnetic relaxation time is given by

)/exp(0 kTKVττ = (4.1)

where 0τ depends only slightly on temperature and is of the order of 10-9-10-12, k is

Boltzman constant, T is the temperature, K is the magnetic anisotropic energy

constant, and V is the volume of the particle.

Now the time of relaxation τ at a fixed temperature depends both on the

particles volume V and anisotropy energy constant K. The nature of the Mössbauer

spectrum of magnetic nano-particles depends on the correlation between the time of

observation (τobs) and that of magnetization vector ralaxation (τ). For all the samples

we have obtained complex Mössbauer spectra consisting of a sextet and a doublet,

implying that obsττ ≅ . The time of relaxation τ at a fixed temperature depends both

on particle volume V and anisotropic phase constant K. In our case, particle sizes

smaller than that in the experiments of Kundig and Bommel [2], which should lead to

a predominant superparamagnetic doublet. Predominance of the sextet in our patterns

can be explained through a possible variation of the anisotropy constant K for

deferently ball-milled samples presumably due to internal strain (Table 4.1). It is

CHAPTER-4

~ 117 ~

noted that according to the model of collective magnetic excitations, the hyperfine

magnetic field of small magnetic

Fig.4.2 (a) Mössbauer spectrum of bulk or as supplied α-Fe2O3. And (b) Mössbauer spectrum of 5h ball-milled α-Fe2O3. particles depends on particles size and broadening of the Mössbauer lines can be

explained by a particle size distribution [17,18]. The magnetic splitting in a

Mössbauer spectrum of small magnetic particles is generally smaller than that found

in a microcrystal and if the samples contain a broad size distribution, the magnetic

splitting of the spectra of those particles will be different. Superposition of all these

spectra gives rise to asymmetric and broadened Mössbauer pattern. In the present

experiment, hyperfine field (Hn) obtained for the fine particle is ~49 Tesla, that for

bulk sample H is ~51.8 Tesla, and the lines are asymmetric and broadened. The

reduction in Hn, broadening of lines and asymmetry of line shape suggest not only a

CHAPTER-4

~ 118 ~

broad particle size distribution but also a fluctuation of the magnetization vector in a

direction close to the easy direction leading to the so-called collective magnetic

excitations.

4.5 Conclusions The particle size of α-Fe2O3 reduces to nanometric order within a few hours of

ball milling and becomes almost constant after 5h of milling. From X-ray line profile

analysis, the lattice strain has been estimated which is considerably high for all ball-

milled samples. Mössbauer spectra of all the ball-milled sample consists of a doublet

which is attributed to the superparamagnetic behaviour of ferromagnetic fine particles

and a broad sextet which is presumably due to high internal strain. The decrease in

hyperfine field, broadening of lines and asymmetry of line shape implies a broad

particle size distribution in the ball-milled sample.

4.6 References [1] E. Jartych, J.K. Zurawicz, D. Oleszak, M. Pekala, J. Mag. Mat., 208 (2000)

221.

[2] W. Kundig, H. Bommel. Phys. Rev. B ,142 (1966) 327.

[3] A.S. Edelslein, R.C. Camurata (Eds.), ‘Nanomaterials’, IOP, Bristol, (1994).

[4] M. Zdujic, C. Jovalekic, Lj. Karanovic, M. Mitric, D. Poleti, D. Skala, Mat.

Sci. Engg., A245 (1998) 109.

[5] S.K. Shee, S.K. Pradhan, M. De, J. Alloys and Compounds, 265 (1998) 249.

[6] H. Pal, S.K. Pradhan, M. De, Jpn. J. Appl. Phys., 35 (1996) 1836.


Bhattacharya, Phys. Stat. Sol. A, 167 (1998) 12.


Bhattacharya, Phys. Stat. Sol. A, 175 (1999) 927.

[9] E. Jartych, J.K. Zurawicz, D. Oleszak, M. Pekala, Nanostructured Mater., 12,

(1999).

[10] M.A. Polikarpov, I.V. Trushin, S.S. Yakimov, J. Magn. Magn. Mater, 116

(1992) 372.

[11] D.H. Jones, Hyperfine Interactions, 47 (1989) 289.

[12] B.E. Warren, X-ray diffraction, Addision-Wesley, (1969) 264.

CHAPTER-4

~ 119 ~

[13] A. Benedetti, G. Fagherazzi, S. Enzo and M. Battagliarin, J. Appl. Cryst., 21

(1988) 543.

[14] R A. Young, D.B. Wiles, J. Appl. Cryst., 15 (1982) 430.

[15] J.G.M. Van Berkum, Ph.D. Thesis, Delft University of Technology, The

Netherlands, (1994).

[16] E. von Meerwall, Comput, Phys. Commun. 9 (1975) 430.

[17] S. Morup, J.A. Dumesic, H. Topsoe, in: R.L. Cohen (Ed.), Application of

Mossbauer Spectroscopy, Vol. II, Academic Press, New York, (1980) 1.

[18] S. Morup, M.B. Madsen, J. Franck, J. Magn. Magn. Mater, 40 (1983) 163.

CHAPTER-5

Annealing effect on nano-ZnO powder studied from positron lifetime and optical absorption spectroscopy

CHAPTER-5

~ 121 ~

5.1 Introduction Nanocrystalline materials, semiconductors in particular, are being widely

investigated at present because of their interesting electronic and optical properties

which may find applications in devices such as solar cells, light emitting diodes,

ultraviolet (UV) lasers, fluorescent displays etc.[1-4]. Surface phenomena dominate

nanomaterial properties over their respective bulk features due to high surface to

volume ratio. Grain surfaces are defect rich and engineering on these defects offer a

scope to tune the useful material properties [5]. Here, we employ mechanical milling

or ball milling technique to reduce the grain size of powder ZnO material. This

technique is advantageous for large scale and cost effective production of

nanocrystalline materials without any effect of chemical contamination [6].

Recently, room temperature UV lasing has been reported in ZnO samples

with grain size few tens of a nanometer[7,8]. It has also been found that

incorporation of low density defects in ZnO lattice sometimes helps to obtain

improved crystalline quality through proper choice of annealing environment and

temperature [9]. In this way, the extent of disorderness and so also the characteristic

emission from the material can effectively be controlled. A better understanding on

the generation and recovery of defects in ZnO, particularly defects at grain surfaces,

has thus of immense potential to reach optimized annealing conditions. Suitable

defect characterization technique like positron annihilation lifetime spectroscopy has

been proved to be helpful [3,10-13] in this regard. Usually, positrons injected inside

a solid from a radioactive source (here 22Na) get thermalized and annihilate with an

electron. It is well known that positrons preferentially populate in the regions where

electron density, compared to the bulk of the material, is lower (e. g., vacancy type

defects, vacancy clusters, micro-voids). For materials with nanometer scale grain

size, positrons diffuse [14,15] to the surface region of the grains, which are rich in

open volume defects. Hence the electron-positron annihilated γ-rays bear the

lifetime of positrons, which provides information regarding the nature and

abundance of defects at the grain surface[3,13,15,16]. Simultaneous investigation of

UV-VIS (ultraviolate-visible) photon absorption by the sample elucidate, as detailed

later, the defect dependent optical processes in such technologically important

semiconductors.

CHAPTER-5

~ 122 ~

5.2 Experiment and data analysis

As supplied polycrystalline ZnO powder (purity 99.9 % from Sigma-Aldrich,

Germany) samples have been ball-milled (ball : mass = 35:1) by a Fritsch Pulverisette

5 planetary ball-mill grinder for 3 hours and then annealed at ten different

temperatures (between 210-1200 °C) for 4 hours followed by slow cooling (30 °C/h)

in air. Henceforth, the milled but unannealed sample will be termed as nano-ZnO. X-

ray diffraction (XRD) of all the samples have been recorded in a Philips PW 1710

automatic diffractometer with CuKα radiation. The average grain size of the powdered

samples has been determined by Scherer’s formula [17]:

Dhkl = Kλ/β cosθ (5.1)

where Dhkl is the average grain size, K the shape factor (taken as 0.9), λ is the x-ray

wavelength, β is the line width at half maximum intensity (here 101 peak of the ZnO

spectrum fitted with a gaussian) and θ is the Bragg angle. Standard method [17] to

deduct the contribution of instrumental broadening in β has been taken into account.

Different sets of samples have been pressed into pellets (~1 mm thickness

and 10 mm diameter) for positron annihilation lifetime (PAL) study. A 10-µCi 22Na

positron source (enclosed in thin mylar foils) has been sandwiched between two

identical plane- faced pellets. The PAL spectra have been measured with a fast-slow

coincidence assembly [18] having 182±1 ps [12] time resolution. Measured spectra

have been analyzed by computer program PATFIT-88 [19] with necessary source

corrections to evaluate the possible lifetime components τi, and their corresponding

intensities Ii. The two state trapping model [20] predicts a two-component fitting of

the spectrum, the shorter one (τ1) from free annihilation of positrons and the other

(τ2) from trapped positrons at defects. One can also construct, without assuming any

model, the average positron lifetime (τav = (τ1I1+τ2I2)/(I1+I2)), which represents the

defective state of the sample as a whole [19,21]. It is to be noted that τav is free from

errors, if any, arising from particular fitting procedure.

The electronic absorption spectra of the ZnO samples have been recorded on

a Hitachi U-3501 spectrophotometer in the wavelength range of 300–1100 nm. The

spectral absorption coefficient α(λ) has been evaluated [3,22] from the spectral

extinction coefficient, k(λ), using the following expression:

α(λ) = 4πk(λ)/λ (5.2)

CHAPTER-5

~ 123 ~

where λ is the wavelength of the absorbed photon.

5.3 Results and discussion The XRD spectra of the ZnO samples, ball milled and subsequently annealed

at 600° C and 1200° C, have been shown in Fig.5.1.

Fig.5.1 X-ray diffraction patterns for the nano-ZnO and annealed ZnO samples. Insets show the corresponding full width at half maximum FWHM) for (002) peak.

Mechanical milling reduces the average grain size from 76±1 nm (as-supplied

ZnO) to 22±0.5 nm (nano-ZnO). Annealing at elevated temperatures induce an

agglomeration of grains in the sample however, appreciable grain growth occurs only

above 425 °C (Fig.5.2). It is interesting to note that the average grain size of the

samples annealed higher than 776±8 °C (as estimated from Fig.5.2) becomes larger

than that of the as supplied or non-milled material. Chen et al.[9] have reported

similar

CHAPTER-5

~ 124 ~

Fig.5.2 Variation of grain size with annealing temperature. The annealing temperature of nano-ZnO sample has been taken as 30 °C (room temperature). The solid line is a guide to the eyes, and the dotted line is the reference line indicating the grain size for the nonmilled (as-supplied) sample.

observation in single crystalline ZnO where initial amorphization by energetic Al+

irradiation and subsequent heat treatment dramatically improve the crystalline quality

and so also the band edge emission. Increase of average grain size, in our case,

continues up to 1100 °C annealing temperature and reaches to 139±2 nm. Reduction

of the grain size for ~ 15 nm in 1200 °C annealed sample is, probably, due to

thermally generated defects at both Zn and O sites [23].

PAL analysis reveals a three-component lifetime fit, the third (τ3) and the

longest (~ 1400 ps with intensity 3-4 %) being due to the positron annihilation from

positronium [21] like atoms. Formation of positroniums generally occurs in the form

of ortho-positronium inside large voids in the material. Ortho-positroniums

subsequently decay as para-positronium by pick-off annihilation giving rise to such

a long lifetime ~ 1200 – 3000 ps. In polycrystalline samples there always exist void

spaces where positronium formation is favourable [12]. To note, positronium

formation in the material is a separate physical process not related to positron

trapping at defects. τ1 is generally attributed to the free annihilation of positrons

[21,24]. However in disordered systems, smaller vacancies [9,16] (like

monovacancies etc.) or shallow positron traps (like oxygen vacancies [25] in ZnO)

may be mixed with τ1. In the present investigation, τ1 from different ZnO samples

show considerable variation with annealing temperature (Table 5.1). τ1, here, is

indeed a weighted average of free and trapped positrons. But these sites are not

CHAPTER-5

~ 125 ~

major positron traps and their correlation with the material properties is not yet

conclusive. The most important lifetime component is the second one (τ2), which

indicates qualitatively the nature and size of the vacancy [20] and its relative

intensity (I2) quantifies the abundance of that vacancy with respect to some standard

of the same material. Here, τ2 increases from 326±3 ps to 343±3 ps due to

mechanical milling (Fig.5.3(a)).

Table 5.1. Table showing the c-axis lattice parameter (from XRD), band tailing parameter, E0 (from optical absorption) and part of the PAL parameters for the ZnO samples. For comparison the corresponding values of the as-supplied (nonmilled) material has been shown. The annealing temperature of nano-ZnO sample has been taken to be room temperature (RT) ~ 30 oC.

Sample Annealing

temperature (oC)

c-axis

(Å)

E0

(meV)

τ1

(ps)

I1

(%)

I2

(%) as-supplied

ZnO RT 5.160 92 147±2 38.0±0.5 58.0±0.5

nano- ZnO RT 5.242 316 173±2 32.3±0.2 64.5±0.2 210 5.172 320 181±2 29.8±0.2 66.4±0.3 250 5.168 300 214±2 47.0±0.2 49.4±0.2 300 5.166 255 201±2 41.3±0.2 55.0±0.2 350 5.182 201 184±2 36.4±0.2 60.2±0.3 425 5.197 226 186±2 40.9±0.2 55.2±0.2 600 5.177 214 159±2 31.6±0.2 64.1±0.3 800 5.258 258 163±2 50.4±0.2 46.0±0.2 900 5.264 386 151±2 57.9±0.3 38.3±0.2 1100 5.272 523 151±2 59.7±0.3 35.8±0.2 1200 5.279 676 153±2 61.5±0.3 34.2±0.2

CHAPTER-5

~ 126 ~

Fig.5.3 Variation of (a) τ2 (positron lifetime at defects) and (b) τav (average positron lifetime) with annealing temperature. The dotted lines are the reference lines corresponding to the error bars of the average positron lifetime and positron lifetime at defects (indicated by solid line) for nonmilled ZnO sample. The annealing temperature of nano-ZnO sample has been taken as 30 °C (room temperature). The inset of lower panel shows the variation of I2 with grain size. The same parameters of the nonmilled ZnO are representedby the dashed lines in the inset.

Enhanced vacancy clustering near the grain surfaces as a result of milling can

be understood. While annealing the nano-ZnO material an increase of τ2 with initial

annealing up to ~ 300 °C has been found. This is similar to what we have observed for

as-supplied ZnO [12]. Probably, the supply of small thermal energy helps intra-grain

zinc vacancies to migrate towards the grain surfaces, which are universal sink of

defects. In this way, small size Zn vacancies (monovacancies etc.) assemble near the

grain surfaces and τ1 grows accordingly (Table 5.1). Part of such vacancies

agglomerate to form larger size vacancy clusters causing and increase of τ2 also. Such

process can be understood as an intrinsic feature of granular ZnO systems that causes

the increase of positron lifetime up to some annealing temperature ~ 300 °C. The

variation of average lifetime (τav) with annealing temperature is more or less similar

CHAPTER-5

~ 127 ~

with that of τ2 (Fig.5.3(b)). τav starts to decrease above annealing temperature of 425

°C, interestingly, which is very close to the temperature from where XRD spectrum

shows a substantial grain growth. One should note here that positrons have a specific

affinity towards cationic defect sites, which are generally negatively charged in these

II-VI semiconductors [10,24]. So, the reduction of τ2 as well as τav above 425 °C

annealing represents a lowering of Zn vacancy defects at the grain boundaries and

consequently grain growth occurs. Mobility of interstitial Zn defects above 425 °C

may be the reason of Zn vacancy annihilation [26]. It can be estimated from figure

5.3(b) that above 700±50 °C annealing temperature the annealed sample becomes less

defective compared to the non-milled one. Similar conclusion has been reached while

discussing the grain size variation of the annealed samples and the related temperature

zone is also close to that have been estimated from the variation of grain size (776±8

°C). In view of the qualitative probing by two different techniques such consistency is

remarkable. Alternatively, our results altogether confirm the clustering of cationic

vacancies at grain boundaries in ZnO nanocrystals. At the same time, it can also be

concluded that majority of such cation vacancies, incorporated artificially either by

particle irradiation [9,26] or by mechanical milling (present case), in ZnO gets

recovered in between 700-800 oC. Compared to 1100 °C annealed sample, the defect

lifetime (τ2) has been found to be increased for 1200 °C annealed sample. Chen et

al.[27] have also found an increase of positron lifetime above 1000 °C in single

crystal ZnO. Such increase of positron lifetime is due to the enhancement of cationic

vacancy sites. A reflection of the large number of thermal vacancy generation, anionic

as well as cationic, is also evident from the lower grain size of the 1200 °C annealed

sample with respect to the 1100 °C annealed one (Fig.5.2). Here we should briefly

mention the variation of I2 (i.e., the relative intensity of τ2) due to annealing. I2 is

related (but not proportional) to the abundance of defects in the material that gives

rise to a positron lifetime of τ2. It has been mentioned earlier that in materials with

few tens of nanometer grain size, most of the defects reside near the grain surfaces

where positrons annihilate. With annealing induced grain growth the ratio of surface

to bulk region decreases in the material. Hence, in our nano-ZnO system also, we

should expect a correlation [15] between I2 and the grain size and that has been

plotted in the inset of Fig.5.3 (a). A general trend of lowering I2 with increasing grain

size can be identified although below 38 nm, there exists some subtle features which

CHAPTER-5

~ 128 ~

are not understood at this stage. Below certain grain size, other type of defects such as

dislocations, microstrain etc., which are very much likely in such mechanically milled

nano-systems, may partly contribute to I2.

The photon energy dependence of the optical absorption coefficients of the

milled and annealed samples has been shown in Fig.5.4.

Fig.5.4 (Color online) Absorption coefficients near the UV edge as a function of photon energy for the ZnO samples annealed at different temperatures. The optical band gap (Eg) of the samples have been estimated from the well

known expression [28] for direct transition

αE = A(E - Eg)1/2 (5.3)

where E(=hc/λ) is the photon energy and A is a constant. Standard extrapolation of

absorption onset [28] to αE = 0 (where E = Eg) has been figured for selected samples

(Fig.5.5) along with the modification of band gap due to annealing (inset of Fig.5.5).

The nano-ZnO has a lower optical band gap (3.11 eV) compared to the nonmilled or

as-supplied one (3.22 eV), which is probably due to its more granular nature [29].

CHAPTER-5

~ 129 ~

Fig. 5.5 (Color online) Plots of (αhν)2 vs photon energy for (a) as-supplied ZnO sample, (b) nano-ZnO sample, (c) sample annealed at 600 °C, and (d) sample annealed at 1200 °C. The inset shows the variation of band gap withannealing temperature.

Annealing above 900 °C temperature induces a red-shift in the band gap,

which is consistent with earlier reports [24,30,31]. Possible reason may be the

increase of oxygen vacancy related disorder for annealing at high temperature.

Enhanced oxygen vacancy in ZnO lattice is also evident from the expansion [12,32]

of c-axis lattice parameter above 800 °C annealing as shown in Table 5.1.

Fig.5.6 (Color online) Plots of ln(α) vs photon energy for (a) as supplied nonmilled ZnO sample, (b) nano-ZnO sample, (c) sample annealed at 350 °C, and (d) sample annealed at 1200 °C to show the linear variation of the respective curves. The inset shows the same curves in a broader region.

CHAPTER-5

~ 130 ~

We further plotted for all the samples ln (α) vs. E graph (Fig.5.6) just below

the band edge (E < Eg) to understand the band tailing effect due to

enhancement/reduction of defects with annealing. According to the theory [28], α(E)

should follow

α(E) = α0 exp(E/E0) (5.4)

with α0 is a constant and E0 is an empirical parameter. E0 has been estimated from

reciprocal of the slope by fitting the linear part of the respective ln(α) vs. E curves.

Any defect or disorder in the lattice gives rise to localized states within the band gap

(band tailing) and E0 describes the width of such localized states [29]. Enhancement

of E0 indicates the increase of disorder in the system. It has been found that the 350

°C annealed sample shows a lowest E0 value (Table 5.1). Interestingly, we have also

observed a reduced E0 due to annealing of as supplied ZnO near the same temperature

zone [33]. However, the degree of disorderness as reflected from the value of E0 is

higher for nano-ZnO along with its annealed counterparts than the as-supplied

material. E0 starts increasing steeply with the increase of annealing temperature from

and 800 oC. In contrast, the PAL investigation reveals (discussed earlier) a

considerable lowering of defects due to annealing above 700±50 oC. This is due to the

fact that relative trapping probability of positrons at an oxygen vacancy is much

weaker compared to that of a zinc vacancy. Within 700-800 oC most of the zinc

vacancies are recovered but at this stage thermally generated oxygen vacancies

become dominant defects in ZnO lattice. Oxygen vacancy and its related disorder

create localized defect states within the band gap resulting an increase of the band

tailing parameter E0 and a red shift of the band gap.

5.4 Conclusions

We have studied the effect of mechanical milling and subsequent annealing in

air at temperatures between 210-1200 °C on high purity ZnO by XRD, PAL and

optical absorption spectroscopy. The grain size has been reduced to 22±0.5 nm (nano-

ZnO) from the 76±1 nm (as-supplied ZnO) due to milling. The XRD analysis reveals

a substantial grain growth in nano-ZnO above 425 °C temperature. Distinct decrease

of the average lifetime of positrons also starts from the same temperature. This

indicates a lowering of defect concentration, mostly cationic, due to annealing above

425 °C. Such a reduction of defects continues up to 1100 °C annealing and little

CHAPTER-5

~ 131 ~

above 700 °C the sample becomes less defective, even better than the as supplied

ZnO. However, the band tailing parameter (E0), which has contributions from all

possible disorder, does not reflect a lowering of defects for high temperature

annealing (>700 °C). Enhanced oxygen vacancy concentration is responsible for such

an increase of E0. These oxygen vacancies are less sensitive to positron spectroscopic

measurements. Only increase or decrease of the zinc vacancies is reflected in the PAL

results. The annealing induced grain growth occurs due to the recovery of such zinc

vacancies the majority of which reside near the grain surfaces. PAL results, thus, bear

a qualitatively similarity with the findings from XRD analysis. Oxygen vacancy

related disorder (>800 °C) mainly contributes to the modification of UV-VIS

absorption spectrum and thus positron lifetime and optical absorption spectroscopy

provide different scenario regarding the defective state of the material.

5.5 References [1] Shalish, H. Temkin, and V. Narayanamurti, Phys. Rev. B, 69 (2004) 245401.

[2] X.T. Zhou, P.S.G. Kim, T.K. Sham, and S.T. Lee, J. Appl. Phys., 98 (2005)

024312.

[3] M. Chakraborty, S. Dutta, S. Chattopadhyay, A. Sarkar, D. Sanyal, and A.

Chakrabortyi, Nanotechnology, 15 (2004) 1792.

[4] M. Bredol, and H. Althues, Solid State Phenom., 99-100 (2004) 19.

[5] Y.S. Wang, P.J. Thomas, and P. O’Brien, J. Phys. Chem. B, 110 (2006) 4099.

[6] A. Urbieta, P. Fernández, and J. Piqueras, J. Appl. Phys., 96 (2004) 2210.

[7] G. Tobin, E. McGlynn, M.O. Henry, J.P. Mosnier, J.G. Lunney, D.

O’Mahony, and E. dePosada, Physica B, 340-342 (2003) 245.

[8] U. Özgür, Ya. I. Alivov, C. Liu, A. Teke, M. A. Reshchikov, S. Doğan, V.

Avrutin, S.-J. Cho, and H. Morkoç, J. Appl. Phys., 98 (2005) 041301.


Sekiguchi, R. Suzuki, and T. Ohdaira, Phys. Rev. B, 69 (2004) 035210.

[10] R. Krause-Rehberg, and H. S. Leipner, Positron Annihilation in

Semiconductors, (Springer, Berlin, 1999), Chap. 3, pp. 61.

[11] F. Tuomisto, V. Ranki, K. Saarinen, and D.C. Look, Phys. Rev. Lett., 91

(2003) 205502.

CHAPTER-5

~ 132 ~

[12] S. Dutta, M. Chakrabarti, S. Chattopadhyay, D. Sanyal, A. Sarkar, and D.

Jana, J. Appl. Phys., 98 (2005) 053513.

[13] M. Chakraborti, D. Bhowmick, A. Sarkar, S. Chattopadhayay, and S.

DeChoudhuri, D. Sanyal, A. Chakraborti, J. Mater. Sci., 40 (2005) 5265.

[14] A. Dupasquier, and A. Somoza, Mater. Sci. Forum, 175-178 (1995) 35.

[15] V. Thakur, and S.B. Shrivastava, M.K. Rathore, Nanotechnology, 15 (2004)

467.

[16] P.M.G. Nambissan, C. Upadhyay, and H.C. Verma, J. Appl. Phys., 93 (2003)

6320.

[17] B.D. Cullity, Elements of X-ray Diffraction (Addison-Wesley Publishing

Company, Inc., Philippines, 1978), Chap. 9, 284.

[18] A. Banerjee, A. Sarkar, D. Sanyal, P. Chatterjee, D. Banerjee, and B.K.

Chaudhuri, Solid State Commun., 125 (2003) 65.

[19] P. Kirkegaard, N. J. Pedersen, and M. Eldrup, Report of Riso National Lab

(Riso-M-2740), 1989.

[20] P. Hautojarvi, and C. Corbel, Positron Spectroscopy in Solids, edited A.

Dupasquier, A.P. Millis Jr. (IOS Press, Ohmsha, Amsterdam, 1995), 491.

[21] D. Sanyal, D. Banerjee, and U. De, Phys. Rev. B, 58 (1998) 15226.

[22] A.A. Dakhel, and F.Z. Henari, Cryst. Res. Technol., 38 (2003) 979.

[23] Z.Z. Zhi, Y.C. Liu, B.S. Li, X.T. Zhang, D.Z. Shen, and X.W. Fan, J. Phys. D:

Appl. Phys., 36 (2003) 719.

[24] R.M. de la Cruz, R. Pareja, R. Gonzalez, L.A. Boatner, and Y. Chen, Phys.

Rev. B, 45 (1992) 6581.

[25] F. Tuomisto, K. Saarinen, D.C. Look, and G.C. Farlow, Phys. Rev. B, 72

(2005) 085206.

[26] Z.Q. Chen, M. Maekawa, A. Kawasuso, S. Sakai, and H. Naramoto, Physica

B, 376-377 (2006) 722.

[27] Z.Q. Chen, S. Yamamoto, M. Maekawa, A. Kawasuso, X.L. Yuan, and T.

Sekiguchi, J. Appl. Phys., 94 (2003) 4807.

[28] J. Pancove, Optical Processes in Semiconductors (Prentice-Hall, Englewood

Cliffs, New Jersey, 1979).

[29] V. Srikant, and D.R. Clarke, J. Appl. Phys., 81 (1997) 6357.

CHAPTER-5

~ 133 ~

[30] N.R. Aghamalyan, I.A. Gambaryan, E.Kh. Goulanian, R.K. Hovsepyan, R.B.

Kostanyan, S.I. Petrosyan, E.S. Vardanyan, and A.F. Aerrouk, Semicond. Sci.

Technol., 18 (2003) 525.

[31] R. Hong, J. Huang, H. He, Z. Fan, and J. Shao, Appl. Surf. Sci., 242 (2005)

346.

[32] H. Kim, A. Piqué, J.S. Horwitz, H. Murata, Z.H. Kafafi, C.M. Gilmore and

D.B. Chrisey, Thin Solid Films, 377-378 (2000) 798.

[33] S. Dutta, S. Chattopadhyay, A. Sarkar, M. Sutradhar, and D. Jana, (to be

submitted).

CHAPTER-6

Particle size dependence of optical and defect parameters in mechanically milled Fe2O3

CHAPTER-6

~ 135 ~

6.1 Introduction Presently, oxides in its nanocrystalline phase become very important due to

their wide applications. The large surface-to- volume ratio of these nanomaterials

makes them different from the bulk of the material [1]. Among them,magnetic

nanomaterials have received special attention as they can be used in different fields

like magnetic resonance imaging, drug delivery agents, etc. [2]. Further, the

observation of peculiar characteristics like superparamagnetism [3] in the nanoparticle

phase of such materials makes these materials objects of great interest for

fundamental studies. Among different magnetic nanoparticles, α-Fe2O3 has large

applications in chemical industry [4]. It can be used as catalyst, gas sensing material

to detect combustible gases [5] like CH4 and C3H8 etc. α-Fe2O3, generally a

rhombohedrally centered hexagonal structure [6], is the most stable polymorph in

nature under ambient condition and can be easily found in mineral hematite.

Nanocrystalline oxides can be prepared by different methods, e.g., sol–gel [7],

hydrothermal [8], chemical vapor phase deposition [9], calcinations of hydroxides

[10], radio frequency sputtering [11], gas condensation technique [12], high-energy

ball-milling process [13, 14], etc. Among these the high-energy ball-milling process

has many potential advantages. The main advantage is large quantities of samples can

be produced in a very short time, and the process is relatively simple and inexpensive.

In the present work, ball-milling process has been adapted to prepare nanocrystalline

Fe2O3 samples. The optical and defect properties of the prepared nanocrystalline

samples have been studied by employing UV spectroscopy and coincidence Doppler

broadening of the electron positron annihilation γ-radiation (CDBEPAR)

spectroscopy, respectively. Employing the UV absorption spectroscopic method [15]

the changes in the band gap for direct transitions for all the samples (milled and

unmilled Fe2O3) have been measured. The defect parameter in the band gap has also

been estimated from the optical absorption data. During the preparation of

nanocrystalline oxides by the ball-milling process, large numbers of defects are

introduced in the material [14–16]. In the nanocrystalline phase the surface-to-volume

ratio is very high, hence the surface defects play important role in determining the

optical, magnetic, and electronic properties of the material. Thus it is very important

to study these defects. Presently, CDBEPAR spectroscopic technique, a powerful

technique to study the defects in a material [17, 18], has been employed to study the

CHAPTER-6

~ 136 ~

defects in the different hour ball milled as well as the unmilled samples. In the

CDBEPAR spectroscopic technique, positron from the radioactive (22Na) source is

thermalized inside the material under study and annihilate with an electron emitting

two oppositely directed 511 keV γ -rays. Depending upon the momentum of the

electron (p) these 511 keV γ-rays are Doppler shifted by an amount ±∆E in the

laboratory frame, where ∆E = pLc/2; pL being the component of the electron

momentum p toward the detector direction. By using two identical high-resolution

HPGe detectors one can measure the Doppler shifts of these 511 keV γ -rays [18]. The

wing part of the 511 keV photo peak carries the information about the annihilation of

positrons with the higher momentum electrons, e.g., core electrons of different atoms.

Thus by measuring the Doppler broadening of the 511 keV γ -ray and proper analysis

of the CDBEPAR spectrum [14] one can identify the electrons with which positrons

are annihilating.

6.2 Experimental outline α-Fe2O3 of purity 99.998% (Alfa Aesar, Johnson Matthey, Germany) has been

milled in a Fritsch Pulverisette 5 planetary ball mill grinder with agate balls for

different hours to achieve lower particle size. The ball-to-powder mass ratio has been

fixed to 12:1. The powder X-ray diffraction (XRD) data has been collected in a

Philips PW 1710 automatic diffractometer with CuKα radiation. In each case scanning

has been performed in between the 2θ range 20–90˚ in a step size of 0.02˚. The

average particle size of the sample has been calculated from Williamson–Hall plot

[19]

(6.1)

where D is the average particle size, β is the full width at half maximum (FWHM), K

is a constant (= 0.89), λ is the wavelength; θ is the Bragg angle, and ε is the strain

introduced inside the sample. The XRD patterns (Fig.6.1) for differently milled and

unmilled samples show α-Fe2O3 lines only, implying that none of the other oxide

phases have been developed during ball milling. Transmission electron microscopy

(TEM) with TECNAI S-TWIN (FEI Company) electron microscope operating at 200

kV has been used to estimate the average particle size of the different hour ball-milled

Fe2O3 samples. Powder ultrasonically dispersed in alcohol was put on a standard

microscope grid for the TEM work.

CHAPTER-6

~ 137 ~

Fig.6.1 X-ray diffraction pattern for the unmilled and milled samples

For the CDBEPAR measurement, two identical HPGe detectors (Efficiency:

12%; Type: PGC 1216sp of DSG, Germany) having energy resolution of 1.1 keV at

514 keV of 85Sr have been used as two 511 keV γ-ray detectors, while the CDBEPAR

spectra have been recorded in a dual ADC-based multiparameter data acquisition

system (MPA- 3 of FAST ComTec., Germany). A 10 µCi 22Na positron source

(enclosed in between thin Mylar foils) has been sandwiched between two identical

and plane faced pellets [20]. The peak-to-background ratio of this CDBEPAR

measurement system, with ± ∆E selection, is ~105:1 [21, 22]. The CDBEPAR

spectrum has been analyzed by evaluating the so-called lineshape parameters [17, 21]

(S parameter). The S parameter is calculated as the ratio of the counts in the central

area of the 511 keV photo peak (|511 keV − Eγ | ≤ 0.85 keV) keV_and the total area of

the photo peak (|511 keV − Eγ | ≤ 4.25 keV) The S parameter represents the fraction of

positron annihilating with the lower momentum electrons with respect to the total

electrons annihilated. The statistical error is ~0.2% on the measured lineshape

parameters. The coincidence DBEPAR spectra for the unmilled and the milled

samples have been also analyzed by constructing the ‘‘ratio-curves’’ [18, 21, 22] with

respect to defects-free 99.9999% pure Al single crystal (reference sample). The

electronic absorption spectra [23] of the Fe2O3 nanoparticles have been recorded on

HitachiU-3501 spectrophotometer in the wavelength range of 200–1,500 nm.

CHAPTER-6

~ 138 ~


Figure 6.1 represents the XRD pattern for the unmilled, 1, 6, 10, and 20 h

milled samples. Particle size as calculated from the Williamson–Hall plot for the

unmilled sample is 120 nm. Figure 6.2 shows the Williamson–Hall plot for 2 h milled

sample. Particle size and the strain introduced inside the samples due to ball milling

have been calculated from the intercepts and slope of the straight line fitted curve as

shown in Fig. 6.2. Table 6.1 represents the particle sizes and strain values for the

unmilled and the milled samples (calculated from the Williamson–Hall plot). From

Table 6.1 it is clear that the strain increases with increasing milling hour. Increase of

strain with the milling hour suggests the formation of defects in the milled sample.

Figure 6.3 shows the variation of particle size with milling hour. From Fig. 6.3 it is

clear that with the ball-milling process the particle size cannot be lowered

continuously, rather it becomes saturated after some specific milling hour. Figure

6.4(a)–(c) represents the TEM micrographs for the unmilled, 10 and 20 h milled

samples, respectively. From the TEM pictures the measured particle sizes are 206, 14,

and 10 nm for unmilled, 10 h milled, and 30 h milled

Fig.6.2 Willamson–Hall plot for 1 h milled sample

CHAPTER-6

~ 139 ~

Table 6.1 Value of strain for the unmilled and different hour ball milled samples

Fig.6.3 Variation of particle size (estimaetd from Scherrer formula and Williamson–Hall plot) with milling hour samples, respectively. The lattice parameters ‘‘a’’ and ‘‘c’’ for the unmilled and

milled samples have been calculated from different diffraction lines of the XRD

pattern (Fig.6.1). Figure 6.5 shows the variation of the lattice parameters ‘‘a’’ and

‘‘c’’ with milling hour. From Fig. 6.5 it is observed that both the lattice parameters

(‘‘a’’ and ‘‘c’’) decrease with increasing milling hour. This clearly indicates that with

milling, large number of defects have been introduced inside the milled samples. To

observe the effect of milling in the band gap, the optical absorption spectroscopic

technique has been used. The spectral absorption coefficient, α, is defined as [24]

(6.2)

CHAPTER-6

~ 140 ~

where k(λ) is the spectral extinction coefficient obtained from the absorption curve

and λ is the wavelength. Figure 6.6 represents the absorbance curve for unmilled, 8 h

milled, and 20 h milled samples. The inset of Fig. 6.6 shows the absorbance curve in

some specific wavelength region. From Fig. 6.6 it has been observed that in case of

ball-milled (8 and 20 h) samples the absorption maxima occur at 303 and 306 nm,

whereas for the unmilled sample the absorption maximum is at 304 nm. Thus the

position of the absorption maxima remains almost the same for the unmilled and the 8

h milled samples, whereas for the 20 h milled sample it is on the longer wavelength

side (306 nm). The band gap, Eg (for a direct transition between the valence and

conduction band), is obtained by fitting the experimental absorption data with the

following equation

αhν ~ A(hν - Eg)1/2 (6.3)

for a direct transition, [25] where hν is the photon energy, a is the absorption

coefficient Eg is the band gap, and A is a characteristic parameter independent of

photon energy.

Fig.6.4 TEM micrographs for (a) unmilled (b) 10 h milled and (c) 30 h milled Fe2O3 samples, respectively

CHAPTER-6

~ 141 ~

Fig.6.5 Variation of lattice parameters (‘‘a’’ and ‘‘c’’) with milling Hour

Fig.6.6 Absorbance curve for unmilled, 8 h, and 20 h milled samples

Figure 6.7(a), (b) represent the absorption curves of different ball-milled

Fe2O3 powder for direct transition. The value of band gap Eg (for direct transition) has

been obtained from the intercept of the extrapolated linear part of the (αhν)2 versus hν

curve with the energy (hν) axis. The band gap for direct transition (estimated from

Fig. 7a, b) for the unmilled sample is 2.62 eV at the wavelength 473 nm, whereas for

1, 4, 6, 8, 10, and 20 h milled samples it is 2.59, 2.56, 2.54, 2.52, 2.49, and 2.49 eV at

479, 485, 489, 493, 497, and 498 nm, respectively. The variation of the band gap (for

direct transition) with the inverse of particle size (D) follows a linear fit with a

negative slope (Fig.6.8). The decrease of band gap with decreasing particle size may

be due to the enhanced band bending effect [26, 27] at the particle boundaries or may

be due to the defects introduced in the milled samples.

CHAPTER-6

~ 142 ~

Fig.6.7 (a) Absorption spectra for unmilled and 4 h milled samples for direct transition. (b) Absorption spectra for 8 and 20 h milled samples for direct transition

In the energy region hν < Eg, i.e. near the band edge, the absorption coefficient follow

the relation [23]

α = α0exp(hν / E0) (6.4)

where α0 is a constant and E0 is an empirical parameter which represents the width of

the band tail states. E0 may be considered as the defect parameter in the band gap

energy value [26]. E0 can be obtained from the slope of the linear part of ln(α) versus

E curve in the E<Eg region. Figure 6.9 shows the ln(α) versus E curve for the

unmilled, 8 h, and 20 h milled samples. The values of E0 as calculated from the

intercept of the extrapolated linear part of the ln(α) versus hν curve with the energy

(hν) axis are plotted in Fig.6.10 with inverse of the particle size (D). It is clear from

Fig.6.10 that with lowering the particle size (by increasing milling hour) the defect

parameter E0 increases linearly. This confirms that lowering the particle size by

increasing milling hour, a large number of defects have been introduced inside the

samples

CHAPTER-6

~ 143 ~

Fig.6.8 Variation of band gap (Eg) with the inverse of particle size (1/D)

Fig.6.9 Plots of ln(α) versus photon energy (E) for unmilled, 8 h, and 20 h milled

samples

Fig.6.10 Variation of E0 with the inverse of particle size (1/D)

.

CHAPTER-6

~ 144 ~

To identify the defects, CDBEPAR measurement technique has been employed. In

case of nanocrystalline materials, the positron diffusion length plays an important

role, as after entering a material the positron becomes thermalized and diffuses inside

the material. The typical positron diffusion length is ~100 nm [28], which is larger

than the average particle size of the milled samples. Therefore, compared to the

unmilled sample (particle size ~120 nm), positrons annihilate more at the grain

surfaces in the milled samples. Figure 6.11 represents the variation of S parameter

with milling hour, where S parameter increases with milling hour. In general, the

increase of the S parameter suggests either the positrons are less annihilating with the

core electrons or an increase of the number of lower momentum electrons at the

positron annihilation site [17, 20–22]. Thus from the variation of S parameter with

milling hour it can be concluded that either positrons are less annihilating with the

core electrons of Fe and O or more annihilating with the lower momentum electrons.

To identify the nature of defects in the milled samples, the CDBEPAR spectra for the

unmilled and ball milled Fe2O3 have been analyzed by constructing the ratio curve

[20, 29] with the CDBEPAR spectrum of the defect-free 99.9999% pure Al single

crystal (Fig.6.12). From Fig.6.12 it is clear that there is a peak at ~10 x 10-3 m0c and a

flat region at ~20 x 10-3 m0c for unmilled, 1 h, and 20 h milled samples. Using the

relation E = p2/4m0 the kinetic energies of the electrons corresponding to momentum

pL ~ 10 x 10-3 m0c and 20 x 10-3 m0c comes out to be ~ 13 and 51 eV, respectively.

The annihilation of positrons

Fig.6.11 Variation of S parameter with milling hour

CHAPTER-6

~ 145 ~

Fig.6.12 Ratio of the experimental electron positron momentum distributions for unmilled, 1, 20, and 30 h milled Fe2O3 samples to the electron positron momentum distributions for the defect-free 99.9999% pure Al single crystal

with 2p core electrons of oxygen and 3d core electrons of Fe are mainly contributing

to the peak at 10x10-3 m0c, while the annihilation of positrons with the 3p core

electrons of Fe contribute to the flat region (pL ~ 20 x 10-3 m0c).

Fig.6.13 Ratio of the experimental electron positron momentum distributions for 1 and 20 h milled Fe2O3 samples to the electron positron momentum distributions for the unmilled Fe2O3 samples

Figure 6.13 represents the ratio curve for the ball-milled Fe2O3 with respect to

unmilled Fe2O3. A broad dip from the momentum range ~ 7 x 10-3 m0c to ~ 22 x 10-3

m0c is prominent (Fig.6.13) in the 20 h milled sample. Thus from Figs. 12 and 13 it

can be concluded that positrons annihilation with the core electrons (both 3d and 3p)

of Fe decreases with increasing milling hour. This indicates the formation of cation

CHAPTER-6

~ 146 ~

type of defects (Fe vacancy) at the grain surface of the milled Fe2O3 system, which is

in agreement with the earlier observation of formation of cation type of defects in

different oxide samples due to the ball-milling process [14, 15].

6.4 Conclusions

Nanocrystalline Fe2O3 samples have been prepared by the ball-milling

process. Particle sizes of the milled and the unmilled samples have been estimated

from XRD pattern and TEM micrographs. The strain introduced inside the sample

increases with ball milling hour. Ratio curve analysis of the CDBEPAR spectra for

the different hour milled and unmilled samples indicates the formation of cation type

of defects at the grain surfaces due to the ballmilling process. Direct optical band gap

decreases with decreasing particle size but the defect parameter (as calculated from

the band tail near the absorption edge of the absorption spectra) increases linearly

with milling hour (or decreasing particle size). Finally, it has been concluded that due

to ball milling the average particle size of the Fe2O3 decreases, but due to the

formation of cation type of defects the optical band gap decreases.

6.5 References

[1] Henglin, Chem Rev., 89 (1989) 1861.

[2] K.A. Hinds et al, Blood, 102 (2003) 867; S.R. Rudge, T.L. Kurtz, C.R

Vessely, L.G. Catterall, D.L. Williamson, Biomaterials, 21 (2000) 1411.

[3] D.H. Jones, Hyperfine Interact, 47 (1989) 289.

[4] N. Mimura, I. Takahara, M. Saito, T. Hattori, K. Ohkuma, M. Ando, Catal

Today, 45 (1998) 61.

[5] L. Huo, W. Li, L. Lu, H. Cui, S. Xi, J. Wang, B. Zhao, Y. Shen, Z. Lu, Chem

Mater, 12 (2000) 790.

[6] R. Zboril, M. Mashlan, D. Petridis, Chem Mater, 14 (2002) 969.

[7] R. Pascual, M. Sayer, C.V.R.V. Kumar, L. Zou, J Appl Phys, 70 (1991) 2348.

[8] X. Wang, X. Chen, X.C. Ma, H. Zheng, M. Ji, Z. Zhang, Chem Phys Lett., 384

(2004) 391.

[9] E.T. Kim, S.G. Yoon, Thin Solid Films, 227 (1993) 7.

CHAPTER-6

~ 147 ~

[10] X. Bokhimi, A. Morales, M. Portilla, A. Gracia-Ruiz, Thin Solid Films, 12

(1999) 589.

[11] W.G. Luo, A.L. Ding, H. Li, Integr Ferroelectr, 9 (1995) 75.

[12] R. Birringer, H. Gleiter, H.P. Klein, P. Marquardt, Phys Lett A, 102 (1984)

365.

[13] D. Michel, E. Gaffet, P. Berther, Nanostruct Mater, 6 (1995) 667.

[14] M. Chakrabarti, D. Bhowmick, A. Sarkar, S. Chattopadhyay, S. Dechoudhury,

D. Sanyal, A. Chakrabarti, J Mater Sci, 40 (2005) 5265. doi:10.1007/s10853-

005-0743-3.

[15] M. Chakrabartii, S. Dutta, S. Chattopadhyay, A. Sarkar, D. Sanyal, A.


[16] B.Q. Zhang, L. Lu, MO. Lai, Physica B, 325 (2003)120.

[17] Hautojarvi P, Corbel C (1995) In: Dupasquier A, Mills AP Jr (eds) Positron

spectroscopy of solids. IOS Press, Amsterdam, p 491; In: Krause-Rehberg R,

Leipner HS (eds) Positron annihilation in semiconductors, Springer Verlag,

Berlin, 1999.

[18] K.G. Lynn, A.N. Goland, Solid State Commun, 18 (1976) 1549.

[19] G.K. Williamson, W.H. Hall, Acta Metall, 1 (1953) 22.

[20] M. Chakrabarti, A. Sarkar, S. Chattopadhyay, D. Sanyal, (2006) In: Martins

BP (ed) New topics in superconductivity research. Nova Science, New York.

[21] M. Chakrabarti, D. Sanyal, A. Chakrabarti, J Phys Condens Matter, 19 (2007)

236210.

[22] D. Sanyal, M. Chakrabarti, T.K. Roy, A. Chakrabarti, Phys Lett A, 371 (2007)

482.

[23] J. Pancove (1979) Optical processes in semiconductors. Prentice- Hall,

Englewood Cliffs, NJ.

[24] A.A. Dakhel, F.Z. Henari, Cryst Res Technol, 38 (2003) 979.

[25] J. Tauc, Mater Sci Bull, 5 (1970) 72.

[26] S. Dutta, S. Chattopadhyay, M. Sutradhar, A. Sarkar, M. Chakrabarti, D.

Sanyal, D. Jana, J Phys Condens Matter, 19 (2007) 236218.

[27] V. Srikant, D.R. Clarke, J Appl Phys, 81 (1997) 6357.

[28] M.J. Puska, R.M. Nieminen, Rev Mod Phys, 66 (1994) 841.

[29] U. Myler, P.J. Simpson, Phys Rev B, 56 (1997) 14303.

CHAPTER-7

Microstructure, Mössbauer and optical characterizations of nanocrystalline α-Fe2O3

synthesized by chemical route

CHAPTER-7

~ 149 ~

7.1. Introduction

Nanostructured materials (oxides) nowadays attract lots of attention as their

structure and properties can be manipulated by changing the surface to volume ratio

[1], preparation process [2], annealing temperature [3], and by changing the crystallite

size [4]. Properties of the nanomaterials can also be controlled by incorporating

different types of defects inside nanocrystals [5]. Nanocrystalline magnetic metal

oxides have received special attention as they can be used in different fields, for

example, magnetic resonance imaging [6], drug delivery agents [7], and so forth.

Further, an unusual characteristic like superparamagnetism [8] in nanocrystalline state

of these materials makes them object of great interest for fundamental studies. Among

different magnetic nanoparticles, α-Fe2O3 is a very common magnetic material as it

has potential applications in chemical industry [9]. It can be used as catalyst, gas

sensing material to detect combustible gases [10] like CH4 and C3H8, and so forth.

Among different iron oxides, α-Fe2O3 is the most stable polymorph in nature under

ambient condition and can be easily found as mineral hematite. Hematite has a

rhombohedrally centered hexagonal structure of the corundum type with a

closepacked oxygen lattice in which two-thirds of the octahedral sited are occupied by

Fe (III) ions [11]. Nanocrystalline α-Fe2O3 powders have been prepared by different

preparation techniques like sol-gel [12], hydrothermal [13], chemical vapor phase

deposition [14], calcinations of hydroxides [15], radio frequency sputtering [16], gas

condensation technique [17], and high-energy ball-milling process [18, 19]. K¨undig

et al. [20] measured the Mössbauer spectra of Fe57 in α-Fe2O3 as a function of particle

size and temperature and noticed that bulk α-Fe2O3 changed in the sign of the

quadrupole interaction in going through the Morin transition temperature, 263 K.

They reported the superparamagnetic behavior of α-Fe2O3 when the particle size is

less than 13 nm and as the particle size gradually increased, it became ferromagnetic.

Giri et al. [21] prepared single-phased α-Fe2O3 nanoparticles using a hydrothermal

synthesis method in aqueous-organic microemulsion under mild alkaline condition.

They confirmed the uniformity of nanocrystalline α-Fe2O3 particles both by XRD and

HRTEM studies and obtained sextet pattern for these crystallites from the Mössbauer

study. Lemine et al. [22] studied the effect of high-energy ball milling on α-Fe2O3

particles and characterized the ball-milled powders by the Rietveld analysis based on

XRD patterns and Mössbauer spectroscopy and revealed that the magnetic hyperfine

CHAPTER-7

~ 150 ~

field was affected by the grain size. Sahu et al. [23] noticed the phase transformation

reaction in nanocrystalline α-Fe2O3 powder induced by ball milling under both air and

oxygen atmospheres. They revealed that the transformation of α-Fe2O3 to Fe3O4 and

finally to FeO occurs in both atmospheres depending upon the oxygen partial

pressures. In none of the above cases, detailed microstructure characterization and

oxygen vacancies in α-Fe2O3 lattice have been estimated by the Rietveld method of

structure refinement, and magnetic structures have been corroborated to the

microstructure parameters and oxygen vacancies. The purposes of the present work

are to (i) establish a correlation in between microstructure parameters and oxygen

vacancies with magnetic properties of nanocrystalline α-Fe2O3 and postannealed

powders and (ii) estimate the optical band gaps of nanocrystalline α-Fe2O3 under the

influence of lattice distortion. Optical band gaps of as-prepared and postannealed

samples have been measured by the UV-Vis absorption spectroscopic method. Goyel

et al [24] measured the direct band gap 2.5 eV of nanocrystalline Fe2O3 powder

synthesized by modified CVD technique. Fu et al. [25] reported that the α-Fe2O3

nanoparticles exhibited n-type semiconducting (SC) properties under ambient

conditions with a band gap of 2.2 eV. Sahana et al. [26] reported that the band gap for

α-Fe2O3 nanoparticle was 2.3 eV, and bandgap increases by the decreasing size of

Fe2O3 crystallites which was manifested in terms of the quantum confinement effect.

7.2. Experimental outline

In the present study, reagent grade Fe(NO3)3, 9H2 O has been used as

precursor for the preparation of nanocrystalline α-Fe2O3 powder by chemical route.

Initially, a solution of Fe(NO3)3, 9H2 O is made with distilled water. A few drops of

concentrated nitric acid have been added to keep the pH level of the solution in acidic

range. This solution is then stirred for 1 h and then poured into a plastic flat-bottomed

container and left for three days in ambient atmosphere for gelation. The gel is then

evaporated to obtain “as-prepared” sample in powder form [27]. The dry powder is

then annealed in open air at different temperatures, 300C, 350C, and 500C for 1 h

in a precisely controlled furnace.

The X-ray powder diffraction data of as-prepared and annealed samples have

been recorded in a Philips PW 1830 X-ray powder diffractometer using Ni-filtered

CuKα radiation. In each case, step-scan data have been obtained in the 20–80 2θ in a

CHAPTER-7

~ 151 ~

step size of 0.02 and 5 sec/step counting time. All experimental patterns are fitted

very well and the structure and microstructure parameters like crystallite size, lattice

parameters, oxygen concentration, and displacement of oxygen atoms in α-Fe2O3

lattice are obtained from the Rietveld analysis [22–26].

Transmission electron microscopy with TECNAI STWIN (FEI Company)

electron microscope operating at 200 kV has been used to estimate the average

crystallite size of different nanocrystalline α-Fe2O3 samples. A pinch of powder was

ultrasonically dispersed in alcohol, and a drop of the solution was put on a 300 mesh

copper grid for the transmission electron microscopy work.

Room temperature 57Fe Mössbauer spectra for all samples have been recorded

in the transmission configuration with constant acceleration mode. A gas filled

proportional counter has been used for the detection of 14.4 keV Mössbauer γ-rays,

while a 10mCi 57Co isotope embedded in an Rh matrix has been used as the

Mössbauer source. The Mossbauer spectrometer has been calibrated with 95.16%

enriched 57Fe2O3 and standard α-57Fe foil. The Mossbauer spectra have been analyzed

by a standard least square fitting program (NMOSFIT).

The UV-Vis absorption spectra of all samples have been recorded in a Hitachi

U-3501 spectrophotometer in the wavelength range 200–800 nm.

7.3. Method of microstructure analysis by Rietveld refinement In the present study, we have adopted the Rietveld’s powder structure

refinement analysis [28–33] of X-ray powder diffraction data to obtain the refined

structural parameters, such as atomic coordinates, occupancies, lattice parameters,

thermal parameters, and so forth, and microstructure parameters, such as crystallite

size and r.m.s. lattice strain. The Rietveld’s software MAUD 2.06 [31] is specially

designed to refine simultaneously both the structural and microstructure parameters

through least-squares method. The instrumental broadening for the present

experimental setup has been obtained using a specially prepared Sistandard, free from

all kinds of lattice imperfections. The peak shape is assumed to be a pseudo-Voigt

(pV) function with asymmetry because it takes individual care for both the crystallite

size and strain broadening of the experimental profiles. The background of each

pattern is fitted by a polynomial function of degree 4. The theoretical X-ray powder

diffraction pattern is simulated containing all structure and a trial set of microstructure

CHAPTER-7

~ 152 ~

parameters of rhombohedral α-Fe2O3 phase. A detailed mathematical description of

the Rietveld analysis has been reported elsewhere [28–31]. Considering the integrated

intensity of the peaks as a function of structural and microstructure parameters, the

Marquardt least-squares procedures are adopted for the minimization of the difference

between the observed and simulated powder diffraction patterns and the minimization

was monitored

Fig.7.1 X-ray powder diffraction patterns for different α- Fe2O3 sample.

Fig.7.2 Variation of lattice parameter with temperature of α-Fe2O3 samples.

using the reliability index parameters, Rwp (weighted residual error), and Rexp

(expected error) defined respectively as

CHAPTER-7

~ 153 ~

(7.1)

where I0 and Ic are the experimental and calculated intensities, wi(= I/I0) and N are the

weight and number of experimental observations, and P the number of fitting

parameters. This leads to the value of goodness of fit (GoF) [28–31].

(7.2)

Refinement continues till convergence is reached with the value of the quality factor,

GoF very close to 1 (varies between 1.1 and 1.7), which confirms the goodness of

refinement.

Fig.7.3 Variation of crystallite size of α-Fe2O3 samples with temperature.

7.4. Results and Discussion 7.4.1. Microstructure Characterization Using XRD and HRTEM The nanocrystalline α-Fe2O3 powder is prepared from the ferric-nitrate

solution and then annealed at 300C, 350C, and 500C in open air. Figure 7.1 shows

the X-ray powder diffraction patterns of these samples. It is evident from the figure

that all strong α-Fe2O3 reflections appear clearly in the XRD pattern of as-prepared

CHAPTER-7

~ 154 ~

sample with significant peak broadening. The peak broadening reduces, and intensity

of all reflections increases continuously with increasing annealing temperature up to

500C. The intensity ratios of all reflections agree well with the reported pattern

(JCPDS File # 33-0664, Space group: R3-cH (hexagonal setting)). For microstructure

characterization of these samples, the Rietveld structure and microstructure

refinement method has been adopted in the present study, and all experimental data

are fitted with the simulated XRD patterns containing only the α-Fe2O3 phase. All

experimental patterns are fitted very well and the structure and microstructure

parameters are obtained from the Rietveld analysis. Both the “a” and “c” lattice

parameters of α-Fe2O3 lattice are significantly large in “as-prepared” sample than the

reported values (a = 5.0356 A° , c =13.7489 A° ) [34] and decrease continuously

(Figure 7.2) towards the reported values with increasing annealing temperature up to

500C. It signifies that the lattice of the “as-prepared” sample contains a significant

amount of lattice strain and almost strain-free α-Fe2O3 lattice is obtained after

annealing the powder at 500C for 1hr. Considering all reflections the Rietveld

analysis reveals that the shape of α-Fe2O3 crystallites is isotropic in nature and their

size variation with increasing annealing temperature is shown in Figure 7.3. The

crystallite size of the “as-prepared” powder is ~18nm and remains almost unchanged

up to 300C and then increases sharply to ~54nm after annealing the powder at 500C

for 1 h. Figures 7.4(a) and 7.4(b) depict the HRTEM image of as-prepared powder

sample. It is evident from the image that particles are almost spherical in shape, and

average particle size is ~18nm which is very close to that obtained from X-ray

analysis. The as-prepared lattice is highly strained which is clearly evidenced by the

presence of Moire fringe in the HRTEM image.

The Rietveld analysis reveals that the “as-prepared” α-Fe2O3 powder is not

completely stoichiometric, and there are significant amount of oxygen vacancies

present in the α-Fe2O3 lattice and oxygen atoms are displaced from their stable

position. The variation of oxygen concentration with increasing annealing temperature

is shown in Figure 7.5. In as-prepared lattice, ~20 mol% oxygen positions remain

unoccupied and with increasing annealing temperature, most of the positions are

occupied and the lattice approaches towards the stoichiometric oxygen concentration

and after annealing at 500C, it becomes saturated and only 4 mol% oxygen positions

CHAPTER-7

~ 155 ~

remain unfilled. It seems that all oxygen positions in α-Fe2O3 powder may not be

completely filled up even after annealing the powder sample at higher temperatures.

Fig.7.4(a) HRTEM image of Fig.7.4(b) HRTEM image of α-Fe2O3 α-Fe2O3 crystallites in unannealed. crystallites in 300C annealed sample.

Fig.7.5 Variation of oxygen concentration with temperature.

Fig.7.6 Variation of displacement of oxygen with temperature.

CHAPTER-7

~ 156 ~

From the analysis it is also revealed that the displaced oxygen atoms in the

nonstoichiometric “as-prepared” sample (z = 0.29) approach towards their normal

positions (z = 0.32) as in the bulk α-Fe2O3 (ICSD Code No. 82904) (Figure 7.6).

These observations indicate that the nonstoichiometric and heavily distorted as-

prepared α-Fe2O3 lattice approaches gradually towards stoichiometric and perfect

lattice configuration with increasing annealing temperature.

7.4.2. Magnetic Characterization Using Mössbauer Spectroscopy Figures 7.7(a) and 7.7(b) show the room temperature Mössbauer spectra for

the as-prepared and 350C annealed samples, respectively. It is clear from these

figures that the as-prepared sample shows a doublet type of Mössbauer spectra, and

no ferromagnetic nature (six line pattern of Mössbauer spectra) has been observed.

This clearly indicates that the as-prepared α-Fe2O3 powder is superparamagnetic in

nature. The 350C annealed sample and all other annealed samples (300C and 500C)

show sextet patterns in Mössbauer spectra confirming the appearance of

ferromagnetic nature in these annealed samples From the experimental Mössbauer

spectra both isomer shift (IS), quadrupole splitting (QS), and hyperfine field (HF)

have been calculated by a standard leastsquare fitting program, NMOSFIT. Values of

the IS, QS, and HF for as-prepared and 500C annealed samples are summarized in

Table 7.1.

Table 7.1 Values of the Mössbauer parameters, IS, QS, and HF for the “as-prepared”

and 500C annealed Fe2O3 samples.

Sample IS (mm/sec) Line width (mm/sec) HF (Tesla) QS (mm/sec)

Nanocrystalline Fe2O3

0.42 10.41±0.482 - 0.7934

5000C annealed Fe2O3

0.36 3.95±0.23 78.8 -0.1250

From Table 7.1 it has been observed that the nanocrystalline as-prepared sample

shows enhanced IS, line width, and QS values in comparison to the annealed sample.

In the as-prepared sample there are two components. The first one is the grain

consisting of all atoms located in the lattice of the crystallites, and the second one is

CHAPTER-7

~ 157 ~

the interfacial component consisting of all the atoms situated in the grain boundaries

of the crystallites.

Fig.7.7 (a) Room temperature Mössbauer spectrum “as-prepared”α-Fe2O3 sample

Fig.7.7 (b) Room temperature Mössbauer spectrum for the for annealed α-Fe2O3

sample.

The enhanced IS, line width, and QS for the as-prepared sample may be due to

the reduction of the electron density at the interfacial site in presence of lattice

imperfections. The HF value for the 350C annealed sample is also higher than that of

the standard α-Fe2O3 sample (52 T). This enhanced HF value may be due to the low

electron density at the interfacial site in this annealed sample compared to the bulk

standard α-Fe2O3 sample. From the Rietveld analysis it has been shown that the

oxygen concentration increases gradually with annealing temperature, and displaced

oxygen atoms approach towards their equilibrium positions during annealing. It

CHAPTER-7

~ 158 ~

suggests that the as-prepared distorted lattice contains significant amount of lattice

imperfections, and the enhancement in all magnetic parameters may be attributed to

the high density of point defects in the as-prepared sample.

Fig.7.8 Variation of ratio of superparamagnetic fraction of α-Fe2O3 particles to the ferromagnetic fraction with the crystallite size.

Figure 7.8 represents the variation of ratio of superparamagnetic fraction of α-Fe2O3

particles to the ferromagnetic fraction with increasing crystallite size. This fraction

has been calculated by directly integrating the absorptions lines. It indicates that both

superparamagnetism and ferromagnetism persist in these nanoparticles. From

Mössbauer spectroscopy measurements It has been reported earlier [22] that there are

two kinds of particles which coexist in the sample: nanostructured and micrometric

hematite. Nanostructured particles result in superparamagnetism, and relatively bigger

particles having less lattice imperfections are responsible for ferromagnetism. This

nature of change in magnetic behaviour with change in particle size is already noticed

by several researchers [20–22, 24–26]. It is evident from the variation that

superparamagnetism in as-prepared sample caused mainly due to lattice imperfections

in α-Fe2O3 lattice for the following possible reasons. (i) Oxygen vacancy in the lattice

reduces the Fe-O dipoles; (ii) displacement of oxygen atoms from their equivalent

positions enhances the Fe-O bond lengths; (ii) magnetic dipoles are randomly oriented

in presence of lattice imperfections.

CHAPTER-7

~ 159 ~

7.4.3. Optical Characterization Using UV-Vis Spectroscopy

Optical band gaps of as-prepared and all annealed samples have been

measured using UV-Vis absorption spectroscopic technique. The spectral absorption

coefficient, α, is defined as [35]

(7.3)

where k(λ) is the spectral extinction coefficient obtained from the absorption

curve and λ is the wavelength. Figure 7.9 represents the absorbance curve for as-

prepared and all annealed samples. It is clearly observed that the absorption maxima

occur around ~ 475nm for all the samples. Thus the position of the absorption maxima

remains almost the same for the nanocrystalline as-prepared and the annealed

samples.

Fig.7.9 UV-Vis absorption spectra for different α-Fe2O3 samples.

The band gap, Eg (for a direct transition between the valence and conduction

band), is obtained by fitting the experimental absorption data with the following

equation:

(7.4)

for a direct band gap transition, [35] where hν is the photon energy, α is the

absorption coefficient, Eg is the band gap, and A is a characteristic parameter

independent of photon energy. Figures 7.10(a) and 7.10(b) represent the absorption

curves of as-prepared and 500C annealed powders for direct transition.

CHAPTER-7

~ 160 ~

Fig. 7.10(a) Band gap estimation for unannealed (as-prepared) sample.

Fig. 7.10(b) Band gap estimation for annealed sample.

The value of band gap Eg (for direct transition) has been obtained from the intercept

of the extrapolated linear part of the (αhν)2 versus hν curve with the energy (hν) axis.

The band gap for direct transition (estimated from Figures 7.10(a) and 7.10(b)) for the

as-prepared nanocrystalline sample is 2.65 eV at the wavelength 468 nm, whereas for

the annealed sample the value reduces to 2.50 eV. Thus the as-prepared and annealed

α-Fe2O3 nanoparticles are n-type semiconductor which was already noticed earlier

[24–26] and there is a red shift in the band gap with annealing of the samples.

CHAPTER-7

~ 161 ~

7.5. Conclusions Nanocrystalline α-Fe2O3 crystallites of size ranging 18 to 54nm have been

prepared by chemical synthesis. The Rietveld analysis reveals that the “as-prepared”

α-Fe2O3 powders are not completely stoichiometric, and significant oxygen vacancies

are noticed in the α-Fe2O3 lattice. With increasing annealing temperature the lattice

approaches towards the stoichiometric oxygen concentration. The “asprepared”

sample shows superparamagnetic behavior at the Mössbauer spectra whereas the

annealed samples show both superparamagnetic and ferromagnetic behaviors. From

Mössbauer spectra it has been observed that the nanocrystalline as-prepared sample

shows enhanced IS, line width, and QS values compared to the annealed samples

which may be due to the reduction of the electron density at the interfacial site. From

UV-Vis absorption spectra it has been observed that the band gaps of the annealed

samples are lower than the as-prepared samples and all samples belong to n-type

semiconductors.

7.6 References [1] Henglein, Chemical Reviews, 89 (1989) 1861.

[2] J. Drbohlavova, R. Hrdy, V. Adam, R. Kizek, O. Schneeweiss, and J. Hubalek,

Sensors, 9 (2009) 2352.

[3] S. Volden, A.L. Kjøniksen, K. Zhu, J. Genzer, B. Nystr¨om, and W.R.

Glomm, ACS Nano, 4 (2010) 1187.

[4] M. Chakrabarti, S. Dutta, S. Chattapadhyay, A. Sarkar, D. Sanyal, and A.


[5] M. Chakrabarti, A. Banerjee, D. Sanyal, M. Sutradhar, and A. Chakrabarti,

Journal of Materials Science, 43 (2008) 4175.

[6] H. Basti, L. Ben Tahar, L.S. Smiri et al., Journal of Colloid and Interface

Science, 341 (2010) 248.

[7] K.A. Hinds, J.M. Hill, E.M. Shapiro et al., Blood, 102 (2003) 867.

[8] D.H. Jones, Hyperfine Interactions, 47-48 (1989) 289.

[9] N. Mimura, I. Takahara, M. Saito, T. Hattori, K. Ohkuma, and M. Ando,

Catalysis Today, 45 (1998) 61.

[10] L. Huo, W. Li, L. Lu et al., Chemistry of Materials, 12 (2000) 790.

CHAPTER-7

~ 162 ~

[11] R. Zboril, M. Mashlan, and D. Petridis, Chemistry of Materials, 14 (2002)

969.

[12] R. Pascual, M. Sayer, C.V.R.V. Kumar, and L. Zou, Journal of Applied

Physics, 70 (1991) 2348.

[13] X. Wang, X. Chen, X. Ma, H. Zheng, M. Ji, and Z. Zhang, Chemical Physics

Letters, 384 (2004) 391.

[14] E.T. Kim and S.G. Yoon, Thin Solid Films, 227 (1993) 7.

[15] X. Bokhimi, A. Morales, M. Portilla, and A. Garc´ıa-Ruiz, Nanostructured

Materials, 12 (1999) 589.

[16] W.G. Luo, A.L. Ding, X.T. Chen, and H. Li, Integrated Ferroelectrics, 9

(1995) 75.

[17] R. Birringer, H. Gleiter, H.P. Klein, and P. Marquardt, Physics Letters A, 102

(1984) 365.

[18] D. Michel, E. Gaffet, and P. Berthet, Nanostructured Materials, 6 (1995) 667.

[19] M. Chakrabarti, D. Bhowmick, A. Sarkar et al., Journal of Materials Science,

40 (2005) 5265.

[20] W. Kündig, H. Bömmel, G. Constabaris, and R.H. Lindquist, Physical

Review, 142 (1966) 327.

[21] S. Giri, S. Samanta, S. Maji, S. Ganguli, and A. Bhaumik, Journal of

Magnetism and Magnetic Materials, 285 (2005) 296.

[22] O.M. Lemine, M. Sajieddine, M. Bououdina, R. Msalam, S. Mufti, and A.

Alyamani, Journal of Alloys and Compounds, 502 (2010) 279.

[23] P. Sahu, M. De, and M. Zdujić, Materials Chemistry and Physics, 82 (2003)

864.

[24] R.N. Goyal, A.K. Pandey, D. Kaur, and A. Kumar, Journal of Nanoscience

and Nanotechnology, 9 (2009) 4692.

[25] X. Fu, F. Bei, X. Wang, X. Yang, and L. Lu, Journal of Raman Spectroscopy,

40 (2009) 1290.

[26] M.B. Sahana, C. Sudakar, G. Setzler et al., Applied Physics Letters, 93 (2008)

Article ID 231909.

[27] A.E. Gash, T.M. Tillotson, J.H. Satcher, J.F. Poco, L.W. Hrubesh, and R.L.

Simpson, Chemistry of Materials, 13 (2001) 999.

[28] H.M. Rietveld, Acta Crystallographica, 22 (1967) 151.

[29] H.M. Rietveld, 2 (1969) 65.

CHAPTER-7

~ 163 ~

[30] R.A. Young and D.B. Willes, Journal of Applied Crystallography, 15 (1982)

430.

[31] L. Lutterotti, “Maud Version 2.14,” 2009, http://www.ing

.unitn.it/~Luttero/maud.

[32] B. Ghosh and S.K. Pradhan, Journal of Alloys and Compounds, 477 (2009)

127.

[33] S. Patra, B. Satpati, and S.K. Pradhan, Journal of Applied Physics, 106 (2009)

Article ID 034313.

[34] S. Dutta, S. Chattopadhyay, A. Sarkar, M. Chakrabarti, D. Sanyal, and D.

Jana, Progress in Materials Science, 54 (2009) 89.

[35] J. Tauc, Materials Research Bulletin, 5 (1970) 721.

CHAPTER-8

Microstructural changes and effect of variation of lattice strain on positron annihilation lifetime

parameters of zinc ferrite nanocomposites prepared by high energy ball-milling

CHAPTER-8

~ 165 ~

8.1 Introduction Ferrites are a group of technologically important materials used in magnetic,

electronic and microwave fields. Magnetic nanocrystalline materials hold great

promise for atomic engineering of materials with functional magnetic properties [1-3].

Many magnetic nanocrystals show superparamagnetism in single domain particles

below a certain critical size. Magnetic nanocrystals have been extensively applied in

magnetic recording medium, information storage, bio-processing and magneto-optical

devices [4-5]. The sulfur absorption capacity of milled zinc ferrite increases with

decreasing crystallite size due to structure–reactivity relationship at high temperature.

Crystalline ZnFe2O4 (cubic, a = 0.8441nm, space group: Fd−

3 m, Z = 8; ICDD

PDF #22-1012) is a normal spinel at room temperature. Spinel structure is made up by

a cubic close-packed array of oxygen atoms with tetrahedral (T) and octahedral (O)

cavities. In the normal 2–3 spinels, one-eighth of the T sites and one-half of the O

sites are filled by the divalent (A) cations (Mg2+, Zn2+, Mn2+, Cd2+, etc.) and the

trivalent (B) cations (Al3+, Fe3+, Cr3+ etc.), respectively, in the ratio AB2O4. The

structural formula of zinc ferrite is usually written as (Zn1−δ2+Feδ3+)[Znδ2+Fe2−δ

3+]O42−,

where round ( ) and square [ ] brackets denote T and O sites of co-ordination,

respectively, and δ represents the degree of inversion (defined by the fraction of the T

sites occupied by B cations). There are two ordered configuration stable at low

temperature, the one with δ = 0 (normal spinel) and the other with δ = 1 (inverse

spinel). When the temperature increases, disorder takes place, since A and B cations

undergo increasing intersite exchange over the three cation sites per formula unit (one

T and two O sites). The completely random distribution of A and B cations over the

three cation sites corresponds to δ = 2/3, which is asymptotically approached at very

high temperatures. Same type of cation distribution is also observed in ball-milled

samples [6-7]. The change in temperature or the change in milling parameter may

result in change in the degree of inversion. It has been found that a metastable

nanoscale structural state of mechanosynthesized ZnFe2O4 is characterized by a

substantial displacement of Fe3+ cations to tetrahedral sites and of Zn2+ cations into

octahedral sites. The inverse–normal transition in mechanosynthesized zinc ferrite

proceeds rapidly in the temperature range 885–1073K and the activation energy of the

transition is E ~72 kJ mol-1 [6].

CHAPTER-8

~ 166 ~

Formation of nanocrystalline ZnFe2O4 as normal and inverse spinel structures

was noticed after ball-milling the stoichiometric mixture of ZnO and α-Fe2O3

powders in open air for different lengths of time. Formation of nanocrystalline

materials in the process of ball-milling leads to significant amount of structural and

microstructural defects which can be characterized by X-ray diffraction and positron

annihilation spectroscopy studies.

The powder patterns of almost all the ball-milled materials, milled at different

milling time are composed of a large number of overlapping reflections of α-Fe2O3,

ZnO and ZnFe2O4 (normal and inverse spinel) phases. The Rietveld analysis based on

structure and microstructure refinement [8-9] was adopted for precise determination

of several microstructural parameters as well as relative phase abundance of such

multiphase material.

The purpose of the present work is to characterize defect states of the zinc

ferrite nanocomposites by positron annihilation lifetime spectroscopy (PALS) and

establish their relationship with microstructure parameters obtained from X-ray

analysis. PALS is a powerful technique to characterize defects in solid materials [10].

A nanostructured material contains unlimited grain boundaries and these boundaries

are rich in lattice defects. Thus, PALS method can be effectively used to characterize

nanostructures in terms of lattice imperfections. To the best of our knowledge, this

type of analysis will help to understand the nature of deformation generated in the

process of mechanical alloying in nanocrystalline ferrite powders.

8.2 Experimental method High-energy ball-milling of ZnO (M/s Merck, 99% purity) and α-Fe2O3 (M/s Glaxo,

99% purity) mixture in 1:1 mol% was conducted in a planetary ball mill (Model P5,

M/S Fritsch, GmbH, Germany). The time of milling was varied from 30 min to 10 h

depending upon the rate of formation of zinc ferrite phase. The step-scan data (of step

size 0.020 2θ and counting time 5 s) for the entire angular range (15–800 2θ) of the

unmilled mixture and all ball-milled samples were recorded using Ni-filtered CuKα

radiation from a highly stabilized and automated Philips X-ray generator (PW 1830)

operated at 35 kV and 25 mA.

For PALS measurements, about 12 µCi 22Na activity was deposited and dried

on a thin aluminium foil and was covered with an identical foil. This assembly was

CHAPTER-8

~ 167 ~

used as the positron source. The source correction was determined using a properly

annealed defect- free aluminium sample. The PALS system used was a standard fast-

fast coincidence set-up with two identical 1-inch tapered off BaF2 scintillator

detectors fitted with XP 2020Q photomultiplier tubes. The time resolution obtained

using 60Co source with 22Na gates was 285 ps. All lifetime spectra were analysed

using PATFIT 88 [11] programme.

8.3 Method of analysis The Rietveld’s powder structure refinement analysis [12-15] of X-ray powder

diffraction data using the Rietveld software MAUD 2.26 [9] revealed the refined


thermal parameters etc. and microstructural parameters, such as crystallite size and

r.m.s. lattice strain etc The experimental profiles were fitted with the most suitable

pseudo-Voigt (pV) analytical function15 because it takes individual care for both the

crystallite size and strain broadening of the experimental profiles. Positron

annihilation lifetime data were deconvoluted with three lifetime components using the

PATFIT programme. A total source correction of 10 % had been deducted while

analysing the spectra.


8.4.1 X-ray diffraction analysis: Figure 8.1 shows the X-ray powder diffraction patterns of unmilled and ball milled

mixture of ZnO and α-Fe2O3 powders milled for different durations. The powder

pattern of unmilled mixture contained only the individual reflections of ZnO and α-

Fe2O3 phases and the precursors were free from impurities. It was noticed that in the

course ball milling the mixture, ZnFe2O4 phase was formed and its amount increased

gradually with increasing milling time. After 30 min milling, the formation of

ZnFe2O4 was noticed clearly with the appearance of (220) (2θ = 29.950) and strongest

(311) (2θ = 35.30) reflections in the XRD pattern.

CHAPTER-8

~ 168 ~

Fig.8.1. X-ray powder diffraction patterns of unmilled and ball milled ZnO - α-Fe2O3 mixture (1:1mol%) at BPMR 40:1.

It may also be noticed that the content of ZnO phase was reduced to a large

extent in comparison to α-Fe2O3 phase. It indicated that the ZnO phase was much

prone to deformation fault as all the reflections were sufficiently broadened due to

reduction in particle size and accumulation of lattice strain in the course of milling.

As a result, solid-state diffusion between ZnO and α-Fe2O3 nanoparticles enhanced

extensively with increasing milling time. In the course of further milling, broadening

as well as degree of overlapping of neighbouring reflections were increased with

increasing milling time. After 2.5h of milling, except the strongest (104) (2θ = 33.180)

reflection, all other reflections of α-Fe2O3 were disappeared completely in the XRD

pattern. It was the indication of either (i) significant reduction in content of the phase

or (ii) significant increase in peak-broadening due to reduction in particle size and

accumulation of lattice strain aroused from the high energy impact of milling or due

to both these effects. Concurrently, an incredible change in intensities of ZnFe2O4

reflections was observed in the XRD pattern. The rate of mechanosynthesis of

ZnFe2O4 was then increased rapidly in course of milling. After 6.5h milling, all

reflections of starting precursors were completely disappeared and it appeared that the

CHAPTER-8

~ 169 ~

ZnFe2O4 phase was completely grown up as the intensity distribution of the XRD

pattern resembled perfectly in accordance with the ICDD PDF # 22-1012. It was

reported earlier that the present process of mechanosynthesis of zinc ferrite at room

temperature by ball milling may also lead to the formation of a metastable inverse

spinel structure. The inverse spinel zinc ferrite was derived by a substantial

displacement of Fe3+ cations to tetrahedral (T) sites and equal amount of Zn2+ cations

into octahedral (O) sites of the cubic close-packed anionic sublattice. After 2.5h

milling, when the formation of ZnFe2O4 was almost completed, verification for

formation of inverse spinel structure along with normal spinel was made because

without considering the inverse spinel, fitting quality of XRD powder data was poor.

Figure 8.2 shows the comparison of the quality of profile fitting in the 2.5h and

10h-milled samples with and without consideration of inverse spinel structure of

ZnFe2O4.

Fig.8.2. Calculated (-) and experimental( )X-ray powder diffraction patterns of ball milled ZnO - α- Fe2O3 (a) for 2.5h without inverse spinel (b) for 2.5h with inverse spinel (c) for 10h without inverse spinel (d) for 10h with inverse spinel revealed by Rietveld powder structure refinement analysis.

CHAPTER-8

~ 170 ~

It is evident that from the figure that the inclusion of the inverse spinel with

normal one improved the profile fitting quality significantly. It indicated towards the

coexistence of both the normal and inverse spinel structures of ZnFe2O4 in the

samples prepared with higher milling time.

Figure 8.3 shows the dependence of relative phase abundances of different

phases with increasing milling time.

Fig.8.3. Variation of phase content (wt.%) of different phase with increasing milling time

The content (wt.%) of ZnO decreased rapidly but that of α-Fe2O3 decreased

slowly with increasing milling time. After 2.5 and 6.5 h milling, ZnO and α-Fe2O3

phases disappeared completely from the respective XRD patterns. The formation of

normal spinel phase was noticed after 30 min of milling and its content increased

continuously (9.4–41.3 wt.%) up to 2.5 h milling. Simultaneously, almost equal

amount (40.1 wt.%) of inverse spinel phase was noticed to form. Content of normal

phase remained almost unchanged up to 10 h milling but that of inverse phase

increased to a large extent after 6.5h milling when α-Fe2O3 was completely utilized

for making exact stoichiometric (1:1 mol%) Zn-ferrite phase. This sudden increase in

CHAPTER-8

~ 171 ~

inverse phase content was essentially due to occupancy of octahedral vacancies by

Fe3+ cations of inverse spinel structures [16].

The nature of variation of crystallite sizes (D) of ZnO, α-Fe2O3 and ferrite

phases are shown in figure 8.4(a).

Fig.8.4(a). Variation of crystallite size of ZnO, Fe2O3, ZnFe2O4 and inverse ZnFe2O4 with increasing milling time.

Crystallite sizes of all the phases were considered to be isotropic. The

crystallite size of ZnO decreased rapidly to ~11nm within 30min milling and then

decreased slowly with increasing milling time. Crystallite size α-Fe2O3 phase was

reduced from ~75nm to ~13nm within 30min ball milling and then decreased slowly

to a saturation value ~7nm. Normal ZnFe2O4 phase was formed after 30min of milling

with ~19nm crystallite size and then reduced to ~10nm after 2.5h of milling. This

decrease in normal spinel crystallite size was manifested in the growth very small

crystallite size of ~6nm of inverse spinel phase after 2.5h of milling. After complete

formation of both spinel phases, heat energy produced by high energy impacts was

utilised to release the accumulated strain inside the nanoparticles and as a result, the

crystallite size increased to a small extent. This effect may also be explained as the

agglomeration of nanometric particles by re-welding mechanism.

CHAPTER-8

~ 172 ~

The nature of variation of r.m.s lattice strain with increasing milling time is

shown in figure 8.4(b).

Fig.8.4(b). Variation of r.m.s strain of ZnO, Fe2O3, ZnFe2O4 and inverse ZnFe2O4 with increasing milling time.

It is obvious that the strain value of normal spinel lattice increased very

rapidly within 30 min and then increased very slowly with increasing milling time,

but after 2.5 h milling, lattice strain suddenly started to release and after 5h milling it

reached a saturation value and remained almost unchanged with increasing milling

time. This nature of variation corroborates the variation of particle size with

increasing milling time.

8.4.2 Positron Annihilation Spectroscopy:

Positron annihilation lifetime spectra (PALS) all the ball-milled samples were

deconvoluted using three lifetime-components τ1, τ2 and τ3 with corresponding

intensities I1, I2 and I3 respectively. In general, for bulk polycrystalline samples, the

shortest positron lifetime (τ1) is assigned to the free annihilation of positrons at

defect-free sites, the intermediate lifetime (τ2) is assigned to the lifetime of positrons

trapped at the defect sites (mono or di-vacancies) and the longest one (τ3) to the pick-

off annihilation of o-Ps atoms formed inside large voids. But, in the case of

polycrystalline samples with crystallite size of the order of a few tens of nanometers,

CHAPTER-8

~ 173 ~

the assignments of lifetime parameters are different. When crystallite sizes become

smaller compared to the mean positron diffusion length (~100 nm), positrons pass

through the grains and annihilate mainly in the grain boundary regions. In this case,

the shortest lifetime (τ1) represents the weighted average of positron lifetimes at the

grain boundary defects (mono or di-vacancies) and the lifetime corresponding to

annihilation with free electrons residing at the grain boundaries. The intermediate

lifetime τ2 corresponds to annihilations at the triple junctions. Triple junctions are

open volumes present at the intersection of three or more grain boundaries and their

size is of the order of 8-10 missing atoms. The fraction of positrons that gets

annihilated inside a grain depends on the positron ‘trapping capability’ of the defects

present at the grain boundaries. The more is the positron trapping at grain boundary

defects, the less is the probability of annihilation with free electrons inside a grain.

Fig.8.5. Variation of mean-lifetime (τm) for ZnO + α-Fe2O3 nanocomposites as a function of ball-mill duration.

Figure 8.5 shows the variation of mean positron lifetime (τm) for ZnO + α-

Fe2O3 nanocomposites as a function of ball-milling duration. τm is related to average

defect density and is defined as

321

332211

IIIIII

m ++++

=ττττ . (8.1)

CHAPTER-8

~ 174 ~

For a given type (size) of defect, higher the defect density larger will be the

value of τm. It is clear that τm remains more or less constant throughout the ball-

milling process. This implies that the overall defect density, as seen by the positrons

remains more or less constant although ball-milling is expected to introduce several

changes in structure and phase content of the nanocomposite. To obtain an insight into

the positron capture mechanism at various trapping centers, the variation of the

individual lifetime parameters with ball-milling duration is to be seen.

Figure 8.6 shows the variation of positron lifetimes τ1, τ2 and intensity I2 with

milling duration. Before milling, i.e. at milling duration t = 0 h, lifetime τ1 may be

ascribed to free annihilation of positrons in the bulk α-Fe2O3 and ZnO crystals.

Fig.8.6. Variation of τ1, τ2 and I2 for ZnO + α-Fe2O3 nanocomposites as a function of ball-mill duration. Positron trapping can be also expected in the grain boundary defects of α-Fe2O3 as its

average crystallite size is ~75 nm (Figure 8.4(a)), which is less than positron diffusion

length in solids. τ2 may be ascribed to the lifetime of positrons trapped at the defect

sites viz., grain boundary defects in ZnO and triple-junctions of α-Fe2O3 nanocrystals.

After 30min of milling, the XRD analysis shows that the sample contains nanocrystals

of ZnO, α-Fe2O3 and ZnFe2O4 (Figures 8.1 and 8.3). Hence the shortest lifetime (τ1)

after milling the mixture for 30min, may be assigned to the mixed lifetime of

positrons trapped at defects (mono or di-vacancies) present at the grain boundaries of

all the nanocrystals (ZnO, α-Fe2O3 and ZnFe2O4) present in the sample and also to the

CHAPTER-8

~ 175 ~

free annihilation inside these nanocrystalline grains. The intermediate lifetime (τ2) has

been assigned to the lifetime of positrons trapped at the triple junction formed at the

intersection of three or more nanocrystalline grains. Similar assignment of lifetimes

was seen to successfully explain the results obtained in case of ZnO nanocrystals [17].

τ1 and τ2 in this case can be expressed as follows

( )∑ +=1i

BiiGBii nn τττ (8.2)

and,

( )∑=i

TPiinττ 2 (8.3)

where i stands for species of nanocrystalline grains viz., ZnO, α-Fe2O3 or ZnFe2O4,

GB stands for grain-boundary, B stands for bulk i.e. the defect free sites inside a grain,

n stands for the fraction of positrons annihilating in a particular site (GB or B) of a

particular type of grain i, and TP stands for triple junction.

Upto a milling duration of 3.5 h, τ1 shows a slight increasing trend. This is

because of the fact that the crystallite sizes become smaller as the ball-milling

duration is increased which in turn increases the surface area to volume ratio. As a

result of this, the contribution from the annihilation at grain boundary increases

resulting in the increase in the value of τ1. However τ2 shows a decreasing trend as

milling hour changes from 30 min to 2.5 h and remains more or less same up to

milling time 3h. The fall in τ2 may be ascribed to the decrease in weight percentage of

α-Fe2O3 (from 58.6 to 14.9 %) with increase in milling time. Disappearance of α-

Fe2O3 from the sample in the course of milling indicates decrease in the contribution

of triple junctions to τ2. It can also be seen that the corresponding intensity I2, which

gives an idea of the defect concentration related to τ2, maintains a steady value up to

3.5 h of milling. Another point to be noted is that though the wt% of α-Fe2O3 phase

changes, τ1 still remains more or less constant in the region of 2.5 to 3.5 h of milling.

A decrease in wt% could have decreased the contribution of annihilation at triple

junction of α-Fe2O3 nanocrystals. This may be explained as following manner. Since

the crystallite size of α-Fe2O3 was also seen to decrease in this region, the fraction of

positrons annihilating at the grain boundaries becomes more, thereby compensating

CHAPTER-8

~ 176 ~

the decrease in the value of τ1. However τ1 was seen to decrease after milling the

sample for 5 h. The phase content of the sample at this stage includes α-Fe2O3,

normal spinel ZnFe2O4 and inverse spinel ZnFe2O4 phases. Their content and grain

sizes do not change much in this milling stage compared to the previous milling stage

(3.5 h). The only change is a substantial decrease in r.m.s. strain value of the normal

spinel ZnFe2O4 structure [18]. Lattice strain depends on the lattice imperfection and

lattice imperfections may arise from the non-stoichiometric composition of the crystal

structure. In this case, decrease in r.m.s. strain value of the normal spinel ferrite

structure strongly indicates the removal of vacancy type defects, which arises out of

non-stoichiometric composition in the ferrite structure. The removal of defects, from

the normal spinel structure, leads to a decrease in contribution of defect related

lifetime to the lifetime component τ1, leading to a reduction in its value. After 6.5 h of

milling, τ1 again increases. At this milling stage, it was seen that the α-Fe2O3 phase

completely vanishes from the composite sample. Simultaneously, the wt.% of inverse

spinel component also increases after milling the sample for 6.5 h. This indicates a

reduction in the contribution of the free annihilation of positrons in the α-Fe2O3

crystals as well as of the annihilation at the grain boundary defect sites in the inverse

spinel structure resulting in an overall increase in τ1 value. However, as the complete

solid solution of α-Fe2O3 results in increase the wt.% of inverse spinel ZnFe2O4, the

value of τ2 did not change at this stage.

Fig.8.7 Variation of τ3 and I3 for ZnO + α-Fe2O3 nanocomposites as a function of ball-mill duration.

CHAPTER-8

~ 177 ~

Figure 8.7 shows the variation of τ3 and I3 as a function of ball-mill duration.

Except an initial increase, value of τ3 remains more or less steady. However, I3 shows

some fluctuations in its behavior. These fluctuations do not correlate themselves

anyhow to the structural changes and hence are not discussed in this article.

8.5. Conclusions The quantitative analysis of the XRD data evaluated on the basis of Rietveld’s

powder structure refinement method yielded detailed information about the structure

and microstructure of mechanosysthesized nanoscale zinc ferrite as well as the

distribution of cations in the spinel ferrite. The main feature of the structural disorder

of mechanosynthesized zinc ferrite was the defect induced inverse spinel phase

transition. The degree of inversion increased rapidly with increasing milling time and

then wt% of inverse phase approached towards a saturation value. Positron

annihilation lifetime data shows that the mean lifetime τm does not change much with

ball milling durations. This implies that the overall defect density, as seen by the

positrons remains more or less constant during milling. The variation of individual

lifetimes τ1 and τ2 and corresponding intensities I1 and I2 shows evaluation of different

phases with milling duration and confirms the formation of inverse spinel ferrite

structure.

8.6 References [1] A.Goldman, Modern Ferrite Technology, Van Nostrand Reinhold, New York;

(1990).

[2] B.M. Berskovsky, V.F. Mcdvcdcv and M.S. Krakov , Magnetic Fluids:

Engineering Applications, Oxford: Oxford University Press, (1993).

[3] R.E. Ayala and D.W. Marsh, Industrial & Engineering Chemistry Research,

30, (1991), 55.

[4] L.A. Bissett and L.D. Strickland , Industrial & Engineering Chemistry

Research, 30 (1991), 170.

[5] R.O. Sack and M.S. Ghiorso, Contributions to Mineralogy and Petrology, 106

(1991), 474.

CHAPTER-8

~ 178 ~

[6] P. Druska, U. Steinike and V. Sepelak. Journal of Solid State Chemistry, 146

(1999), 13.

[7] C.N. Chinnasamy, A. Narayanasamy, N. Ponpandian, K. Chattopadhyay, H.

Guerault, and J-M. Greneche, Journal of Physics Condensed Matter, 12 (2000)

7795.

[8] L. Lutterotti, P. Scardi and P.Maistrelli, Journal of Applied Crystallography,

25 (1992) 459.

[9] L. Lutterotti. MAUD version 2.26. 2011; http://www.ing.unitn.it/~maud/.

[10] R. Krause-Rehberg and H.S. Leipner, Positron Annihilation in

Semiconductors. Solid-State Sciences, Berlin, Springer, (1999) 127.

[11] P. Kirkegaard and M.Eldrup, Computer Physics Communications, 3 (1972)

240.

[12] H. M. Rietveld. Acta Crystallographica, 22 (1967) 151.

[13] H. M. Rietveld, Journal of Applied Crystallography, 2 (1969) 65.

[14] S. Sain, S. Patra and S.K. Pradhan, Journal of Physics D,44 (2011) Article ID

075101, 8 pages.

[15] R.A. Young and D.B. Willes, Journal of Applied Crystallography, 15 (1982)

430.

[16] Q-M. Wei, J-B. Li and Y-J. Journal of Materials Science. 36 (2001) 5115.

[17] A.K. Mishra, S.K. Chaudhuri, S. Mukherjee, A. Priyam, A. Saha and D.Das,

Journal of Applied Physics, 102 (2007) 103514.

[18] S. Bid and S.K. Pradhan, Materials Chemistry and Physics, 82 (2003) 27.

CHAPTER-9

Microstructure and positron annihilation studies of mechanosysthesized CdFe2O4

CHAPTER-9

~ 180 ~

9.1 Introduction The synthesis of nanocrystalline spinel ferrite has been investigated intensively

in recent years due to their potential applications in high-density magnetic recording,

microwave devices and magnetic fluids [1, 2]. High-energy milling is a very suitable

solid-state processing technique for preparation of nanocrystalline ferrite powders

exhibiting new and unusual properties [3–6]. Reports on synthesis of nanocrystalline

cadmium ferrite by high-energy ball milling of CdO and α-Fe2O3 mixture are very

few [7, 8]. The phase transformation kinetics and microstructure characterization of

ball-milled ferrites have been studied in detail in our previous work. Crystalline

CdFe2O4 (Cubic, a = 0.86996 nm, space group: Fd−

3 m, Z = 8; ICDD PDF #22-1063)

is normal spinel at room temperature. Spinel structure consists of a cubic close-

packed array of oxygen atoms with tetrahedral (A) and octahedral (B) cavities. In the

normal 2–3 spinels, one eighth of the A sites and one half of the B sites are filled by

the divalent cations (Mg2+, Zn2+, Mn2+, Cd2+ etc.) and the trivalent cations (Al3+, Fe3+,

Cr3+ etc.) respectively in the ratio AB2O4. When the temperature increases above a

critical limit, disorder takes place, since A and B cations undergo increasing intersite

exchange over the three cation sites per formula unit (one A and two B sites). Lattice

imperfections and phase transformations kinetics of ball-milled nanocrystalline

materials can be resolved by X-ray characterization technique based on structure and

microstructure refinement [9–13]. The powder patterns of almost all the ball-milled

materials, milled at different milling time are composed of a large number of

overlapping reflections of α-Fe2O3, CdO and CdFe2O4 phases. Rietveld’s analysis

based on structure and microstructure refinement [11, 14] has been adopted in the

present analysis for precise determination of several microstructural parameters as

well as relative phase abundance of individual phases.

The purpose of the present work is: (i) to prepare nanocrystalline CdFe2O4

from the stoichiometric mixture (1:1mol%) of powdered reactants containing α-Fe2O3

and CdO by high energy ball-milling at room temperature (ii) to determine the

relative phase abundances of spinel ferrite and other phases (iii) to characterize the

prepared materials in terms of several structural/microstructural defect parameters

(changes in lattice parameters, particle sizes, r.m.s. lattice strains) employing

Rietveld’s powder structure refinement method [9, 10, 12–14] and (iv) to study the

CHAPTER-9

~ 181 ~

defects and microstructural evolution of different phases with milling time by positron

annihilation lifetime spectroscopy[15, 16].

9.2 Experimental Accurately weighed starting powders of CdO (55.43 wt%) (M/s Merck, 99%

purity) and α-Fe2O3 (44.57 wt%) (M/s Glaxo, 99% purity) were hand-ground by an

agate mortar- pestle in a double-distilled acetone medium for more than 30 min. High-

energy ball-milling of unmilled stoichiometric homogeneous powder mixture(1: 1

mol%) was conducted in a planetary ball mill (Model P5, M/S Fritsch, GmbH,

Germany). Milling of powder mixture was done at room temperature in hardened

chrome steel vial using hardened chrome steel balls. The time of milling varies from

30 min. to 25 h depending upon the rate of formation of cadmium ferrite phase.

The X-ray powder diffraction profiles of the unmilled mixture and ball-milled

samples were recorded using Ni-filtered CuKα radiation from a highly stabilized and

automated Philips X-ray generator (PW 1830) operated at 35 kV and 25 mA. The

generator is coupled with a Philips X-ray powder diffractometer consisting of a PW

3710 mpd controller, PW 1050/37 goniometer, and a proportional counter. The step-

scan data (of step size 0.020 2θ and counting time 5 s) for the entire angular range

(15–800 2θ) of the experimental samples were recorded and stored in a PC, coupled

with the diffractometer.

For PALS measurements, about 12 µCi 22Na activity was deposited and dried

on a thin aluminium foil and was covered with an identical foil. This assembly was

used as the positron source. The source correction was determined using a properly

annealed defect free aluminium sample. The PALS system used was a standard fast-

fast coincidence set-up with two identical 1-inch tapered off BaF2 scintillator

detectors fitted with XP2020Q photomultiplier tubes. The time resolution obtained

using 60Co source with 22Na gates was 285 ps. All lifetime spectra were analysed

using PATFIT 88 [17] programme.

9.3 Method of analysis In the present study, we have adopted the Rietveld’s powder structure

refinement analysis [9-13] of X-ray powder diffraction data to obtain the refined


CHAPTER-9

~ 182 ~

thermal parameters etc. and microstructural parameters, such as particle size and

r.m.s. lattice strain etc. The Rietveld software MAUD 2.33 [14] is specially designed

to refine simultaneously both the structural and microstructural parameters through a

least-squares method. The peak shape was assumed to be a pseudo-Voigt function

with asymmetry. The background of each pattern was fitted by a polynomial function

of degree 4. In the present study, refinements were conducted without refining the

isotropic atomic thermal parameters.

Microstructure characterization of unmilled and all the ball milled powder

samples has been made by employing the Rietveld’s whole profile fitting method

based on structure and microstructure refinement [9-14]. The experimental profiles

were fitted with the most suitable pseudo-Voigt (pV) analytical function [12] because

it takes individual care for both the particle size and strain broadening of the

experimental profiles. Positron annihilation lifetime data were deconvoluted with

three lifetime components using the PATFIT programme. A total source correction of

10 % had been deducted while analysing the spectra.

9.4 Results and Discussion 9.4.1 X-ray diffraction analysis The fitted XRD powder patterns of unmilled CdO+α-Fe2O3 (1:1mol %)

homogeneous mixture and some of the selected patterns of ball-milled mixture

powders are presented in Fig.9.1. The powder pattern of unmilled mixture contains

only the individual reflections of CdO (ICDD PDF #5-0640) and α-Fe2O3 (ICDD

PDF #33-0664) phases. The intensity ratio of individual reflections is in accordance

with the stoichiometric composition of the mixture. It is evident from the figure that

in the course of ball milling, the peak broadening increases and CdO peaks are much

broaden in comparison to α-Fe2O3, implies that particle size of CdO reduces faster

than α-Fe2O3 phase. The formation of CdFe2O4 phase is first noticed clearly in the

XRD pattern of 5h milled powder with the appearance of isolated (220) (2θ = 29.040;

I/I0 = 60%) and (440) (2θ = 60.170; I/I0 = 35%) reflections.

CHAPTER-9

~ 183 ~

2 0 3 0 4 0 5 0 6 0 7 0 8 0

5 0 0 0

1 0 0 0 0

1 5 0 0 0

I o - I c

I o - I c

I o - I c

I o - I c

7 h

C d OF e 2 O 3

C d F e2O

4

I o - I c

2 5 h

5 h

P u r e

2 h

Inte

nsity

(arb

. uni

t)

2 θ ( d e g r e e )

Fig. 9.1 X-ray powder diffraction patterns of unmilled and ball milled CdO-α-Fe2O3 mixture (1:1mol%) The content of CdO phase has been reduced more rapidly in comparison to α-

Fe2O3 phase and except the isolated (200) (2θ = 38.3180; I/I0 = 88%) reflection, all

other reflections of CdO do not appear apparently in the XRD pattern of 5h milling

sample, because (i) small CdO particles contain huge amount of lattice strain arising

from high energy milling and (ii) the wt% of CdO has been reduced significantly

within this period of milling. As the milling goes on, peak broadening as well as

degree of overlapping of neighbouring reflections increases gradually. After 7 h of

milling, intensities of all CdFe2O4 reflections have been increased and relatively

strong (220), (311), (511) and (440) reflections are distinctly appeared in the XRD

pattern. In the mean time, all the reflections of CdO have been completely

disappeared and the peak intensities of α-Fe2O3 reflections have been reduced further.

Up to 10 h of milling, intensities of CdFe2O4 and α-Fe2O3 reflections increase and

decrease respectively. After 15 h of milling, wt% of α-Fe2O3 phase increases in

expense of CdFe2O4 phase and this trend continues upto 25 h of milling. The above

observations about phase transformation kinetics of nonstoichiometric ball milled

CHAPTER-9

~ 184 ~

powder mixture clearly reveals the following facts: (i) particle sizes of both the

starting materials reach a critical size within 5 h of milling and through the solid state

diffusion of highly active particles of both the phases the particles of CdFe2O4 phase

has been formed (ii) a significant amount of α-Fe2O3 phase does not take part in

ferrite formation and as a result the prepared ferrite is a non-stoichiometric one (iii)

increase in α-Fe2O3 content in expense of ferrite phase at higher milling due to

formation of nanocrystalline α-Fe2O3–CdFe2O4 solid solution.

0 4 8 12 16 20 240

15

30

45

60

75

90 CdO Fe2O3

CdFe2O4

Wt%

Milling time (h)

Fig. 9.2 Variation of phase content (wt.%) of different phase with increasing milling time.

Figure 9.2 shows the variation of relative phase abundances of different phases

with increasing milling time. The content (wt%) of CdO decreases very rapidly

whereas the wt% of α-Fe2O3 increases almost with the same rate with increasing

milling time. After 5h of milling, the wt% of α-Fe2O3 phase drops suddenly, this in

turn, results in formation of considerable amount of CdFe2O4 phase. After 7h of

milling when reflections of CdO phase completely disappear from XRD pattern (Fig.

1), the wt% of CdFe2O4 phase increased considerably at the expense of both the CdO

and α-Fe2O3 phases. Further milling in between 10-15h reveals that the wt% of α-

Fe2O3 phase increases at the expense of the CdFe2O4 phase. This trend of wt%

variation of these two phases continues till the end of ball milling up to 25h. The

CHAPTER-9

~ 185 ~

phase transformation kinetics of ferrite phase formation clearly reveals the following

facts: (i) increase in wt% of α-Fe2O3 up to 3h of milling is due to solid state diffusion

of CdO into α-Fe2O3 matrix (ii) the CdFe2O4 phase is formed from CdO-α-Fe2O3 solid

solution (iii) the increase in wt% of α-Fe2O3 phase at the expense of CdFe2O4 phase is

due to the formation of α-Fe2O3-CdFe2O4 solid-solution phase and (iv) the prepared

CdFe2O4 phase is a non-stoichiometric one because a considerable amount of α-Fe2O3

phase does not take part in CdFe2O4 phase formation even after 25h of ball milling.

5 10 15 20 25

2

3

4

5

6

0 5 10 15 20 254

6

8

10

60.0

60.5

61.0

61.5

0 1 2 3 4 52

4

6

220

222

224

(c) CdFe2O

4

L KPa

rticl

e si

ze (n

m)

Milling time (h)

(b) α-Fe2O

3Pa

rticl

e si

ze (n

m)

Milling time (h)

(a) CdO

Par

ticle

siz

e (n

m)

Milling time (h)

Fig. 9.3 Variation of particle size of CdO, α-Fe2O3 and CdFe2O4 with increasing milling time.

The natures of variations of particle size (D) of CdO, α-Fe2O3 and CdFe2O4

phases are shown in Fig.9.3. Except CdFe2O4 phase, particle sizes of other two phases

are found to be isotropic. Particle size of CdO phase decreases sharply from ~224nm

to ~7nm (Fig.9.3a) within 30min of ball milling and then slowly to ~3nm within 5h of

CHAPTER-9

~ 186 ~

milling. Particle size of α-Fe2O3 phase reduces less rapidly (Fig.9.3b) than CdO phase

and within 30min of milling it drops from ~61nm to ~11nm and reaches lowest value

of ~6nm within 2h of milling. It is then interesting to note the particle size of this

phase increases constantly with increasing milling time. The initial reduction and then

expansion of particle size value with increasing milling time is due to the well-known

fracture and re-welding mechanism of nanocrystalline particles [18, 19]. It is obvious

that during size reduction, particle fracture and during expansion (particle

agglomeration) re-welding of nanoparticles has been manifested. In contrast to the

particle size variation of these phases, the CdFe2O4 particles grow with a very small

isotropic size (~5nm) after 5h of milling (Fig.9.3c). Within 10h of milling, the particle

size becomes anisotropic and the degree of anisotropy increases with increasing

milling time. Particle size along the two major reflection directions [311] and [220]

has been estimated and their variation with increasing milling time is shown in Fig.

9.3c. It is evident from the figure that the particle size along [311] remains almost

constant but along [220] decreases continuously up to 25h of milling indicates that

(220) plane is more prone to deformation fault than most dense (311) plane of cubic

CdFe2O4 phase. It indicates that the oxygen vacancies have been created during ball-

milling on the (220) plane and one filled up by the substitution of the Cd atoms and

the mismatch in atomic size of these atoms may result in reduction in particle size

along [220]. All these observations regarding the particle size variation of all three

phases suggest that CdFe2O4 phase has been formed when particle size of α-Fe2O3

solid solution phase reduces to a minimum value of ~6nm, because the initial particle

size of Cd-ferrite is ~5 nm and it grows with growing oxygen vacancy with increasing

milling time.

9.4.2 Positron Annihilation Spectroscopy All the lifetime spectra of the samples were deconvoluted using three lifetime-

components τ1, τ2 and τ3 with corresponding intensities I1, I2 and I3 respectively.

Since the particle sizes of the constituents becomes less than the mean positron

diffusion length (~100 nm) within a short time during milling, positrons pass through

the grains and annihilate mainly in the grain boundary regions. In this case the

shortest lifetime (τ1) represents the weighted average of positron lifetimes at the grain

boundary defects (mono or di-vacancies) and the lifetime corresponding to

CHAPTER-9

~ 187 ~

annihilation with free electrons residing at the grain boundaries. The intermediate

lifetime τ2 corresponds to annihilations in the triple junctions. Triple junctions are

open volumes present at the intersection of three or more grain boundaries and their

size is of the order of 8-10 missing atoms. The fraction of positrons that gets

annihilated inside a grain depends on the positron ‘trapping capability’ of the defects

present at the grain boundaries. The more is the positron trapping at grain boundary

defects, the less is the probability of annihilation with free electrons inside a grain.

Therefore τ1 and τ2 in the present case may be expressed as follows.

( )∑ +=1i

BiiGBii nn τττ (9.1)

and,

( )∑=i

TPiinττ 2 (9.2)

where i stands for species of nanocrystalline grains viz., CdO, α-Fe2O3 or CdFe2O4,

GB stands for grain-boundary, B stands for bulk i.e. the defect free sites inside a grain,

n stands for the fraction of positrons annihilating in a particular site (GB or B) of a

particular type of grain i, and TP stands for triple junction.

The longest lifetime τ3 is attributed to the pick-off annihilation of ortho-

positroniums formed in the air trapped at the junction of sample-source sandwich.

0 5 10 15 200.20

0.21

0.22

0.23

0.24

0.25

0.26

0.27

0.28

0.29

0.30

Mea

n Li

fetim

e (n

s)

Ball - Mill Duration (h)

Fig. 9.4. Variation of mean-lifetime for CdO + α-Fe2O3 nanocomposites as a function of ball-mill duration.

CHAPTER-9

~ 188 ~

Figure 9.4 shows the variation of mean lifetime of cadmium ferrite nano-

composite as a function of ball-mill duration. τm is related to average defect density

and is defined as

321

332211

IIIIII

m ++++

=ττττ . (9.3)

For a given type (size) of defect, higher the defect density larger will be the

value of τm. The mean lifetime was seen to increase up to a ball-milling duration of 5

hrs. This is in good agreement with the XRD results where it was shown that the grain

size of the both CdO and α-Fe2O3 nanocrystals decrease. This might have resulted in

an increase in the surface to volume ratio, which in turn led to an increased trapping

of positrons at the grain boundaries. For rest of the ball milling process the mean

lifetime maintains a more or less same value indicating that the defect density remains

same thereafter.

To obtain an insight into the positron capture mechanism at various trapping

centers, the variation of the individual lifetime parameters with ball-milling duration

is to be seen.

0 5 10 15 200.1520.1600.1680.1760.1840.192

0.3000.3150.3300.3450.360

3035404550

τ1

Life

time

(ns)

Ball Mill Duration (hrs)

τ2

Life

time

(ns)

I2

Inte

nsity

(%)

Fig 9.5 Variation of τ1, τ2 and I2 for CdO + α-Fe2O3 nanocomposites as a function of ball-mill duration.

Figure 9.5 shows the variation of lifetime parameters viz., τ1, τ2 and I2. The

shortest lifetime component τ1 is seen to increase up to 5 hour milling duration . This

CHAPTER-9

~ 189 ~

increase is due to creation of defects associated with the reduction in grain size of

both CdO and α-Fe2O3. τ2 and I2 remain more or less constant up to 5 hour milling

duration. This indicates that the size and volume fraction of triple junctions remain

more or less same in that period of milling. During 5 to 10 hour ball milling duration

both τ1 and τ2 were seen to decrease. XRD results showed that CdO at this stage no

more exists in the composite whereas CdFe2O4 has formed. So contribution of CdO to

positron annihilation at grain surfaces, triple junctions or in the grain itself has

disappeared leading to a decrease in the value of τ1 and τ2. It may also be noted that

XRD results have indicated an upward trend for the size of α-Fe2O3 particles after 5

hour ball milling. This creates a reduction of the size of the triple junctions associated

with this component, which may also cause reduction of τ2. The increase of I2 after 5

hour ball milling is attributed to formation of CdFe2O4 phase and creation of

associated triple junctions. After 10 hour ball milling, the increase in τ1 is assigned to

lattice defects in the CdFe2O4 phase which is supported by the observed increasing

trend of r.m.s strain in the 311 direction (Table 9.1) as deduced from the XRD

analysis.

Table 9.1. Microstructure parameters of ball-milled CdO-Fe2O3 (1:1mol.%) powder revealed from Rietveld’s X-ray powder structure refinement method.

The slight increase of τ2 and decrease of I2 after 10 hour milling are attributed

to formation of larger vacant spaces at the triple junctions at the cost of smaller spaces

because of continuous reduction of size of the CdFe2O4 phase.

Milling time(h)

CdFe2O4

Lattice parameter (nm)

Particle size (nm)

r.m.s.strain<ε2>1/2 X 103

Wt.%

[220] [311] [220] [311]

5 0.8663 5.1 5.1 6.68 6.68 45.8 7 0.8657 5.5 5.5 7.848 7.848 58.5 10 0.8652 4.3 5.4 7.448 8.968 59.4 15 0.8646 3.3 5.6 8.336 12.07 55.1 20 0.8641 2.5 5.8 8.951 18.213 41.3 25 0.8639 2.2 5.7 7.986 23.397 36.0

CHAPTER-9

~ 190 ~

0 5 10 15 201.8

1.9

2.0

2.1

2.2

2.3

2.4

1.2

1.4

1.6

1.8

2.0

τ3

Life

time

(ns)

Ball mill duration (h)

I3

Inte

nsity

(%)

Fig 9.6 Variation of τ3 and I3 for CdO + α-Fe2O3 nanocomposites as a function of ball-mill duration The fluctuations in the values of τ3 and I3 (Fig.9.6) is not connected to the structural changes and hence are not discussed. 9.5 Conclusions Microstructure characterization and phase transformation kinetic studies of

high-energy ball milled stoichiometric (1:1 mol%) CdO + α-Fe2O3 powder mixture

have been investigated by Rietveld analysis of X-ray powder diffraction data. The

experimental results reveal that the ball milled prepared Cd-ferrite phase is a non-

stoichiometric one.

The microstructure characterization of ball milled samples in terms of lattice

imperfections lead to the following important conclusions:

(i) the nanocrystalline Cd-ferrite phase is formed after 5h of milling from the

nanocrystalline CdO - α-Fe2O3 solid-solution.

(ii) the increase in α-Fe2O3 phase at higher milling time in expense of Cd-ferrite

phase is due to the formation α-Fe2O3 – CdFe2O4 solid solution.

(iii) a stoichiometric Cd-ferrite phase can not be prepared by just ball milling the

stoichiometric powder mixture even for a longer duration (25h).

CHAPTER-9

~ 191 ~

(iv) the anisotropy in particle size and lattice strain of ball milled Cd-ferrite phase

arises due to continuous creation of oxygen vacancies and occupation of these

vacant sites by smaller Cd atoms on (220) plane during milling.

(v) variation of positron annihilation mean lifetime with milling time indicates

increase of defect density in the composite up to 5 h milling , beyond that the

defect density remains more or less same. The variation of individual lifetime

parameters indicate disappearance of CdO phase from the composite and

formation of CdFe2O4 phase after 5 h milling. It also shows enhancement of

α-Fe2O3 particle size after 5h milling and formation of lattice defect in

CdFe2O4 after 10 h milling.

9.6 References [1] Goldman, Modern Ferrite Tech, Nostrand Reinhold, New York, 1990.

[2] B.M. Berskovsky, V.F. Mcdvcdcv, M.S. Krakov, Magnetic Fluids:

Engineering Applications, Oxford University Press, Oxford, 1993.

[3] V. Sepelak, A.Yu. Rogachev, U. Steinike, D. Chr. Uccker, F. Krumcich, S.

Wibmann, K.D. Becker, The synthesis and structure of nanocrystalline spinel

ferrite produced by high-energy ball-milling method, Mater. Sci. Forum 235-

238 (1997) 139.

[4] V. Sepelak, A. Yu, Rogachev, U. Steinike, D. Chr. Uccker, S. Wibmann, K.D.

Becker, Structure of nanocrystalline spinel ferrite produced by high-energy

ball-milling method, Acta Crystallogr. Suppl. A52 (1996) C367.

[5] S.J. Stewart, M.J. Tueros, G. Cernicchiaro, R.B. Scorzelli, Magnetic size

growth in nanocrystalline copper ferrite, Solid State Commun. 129 (2004)

347.

[6] M. Sinha, H. Dutta, S. K. Pradhan, Phase Stability of Nanocrystalline Mg–Zn

Ferrite at Elevated Temperatures, Japn. J .Appl. Phys. 47 (2008) 8667.

[7] C.N. Chinnasamy, A. Narayanasamy, N. Ponpandian, R. Justin Joseyphus, K.

Chattopadhyay, K. Shinoda, B. Jeyadevan, K. Tohji, K. Nakatsuka, H.

Guérault, J.-M Greneche, Structure and magnetic properties of nanocrystalline

ferrimagnetic CdFe2O4 spinel, Scripta Mater. 44 (2001)1411.

[8] N.M. Deraz, M.M. Hessien, Structural and magnetic properties of pure and

doped nanocrystalline cadmium ferrite, J. Alloys Compd. 475 (2009) 832.

CHAPTER-9

~ 192 ~

[9] H.M. Rietveld, Line profiles of neutron powder-diffraction peaks for structure

refinement, Acta Cryst. 22 (1967) 151.

[10] H.M. Rietveld, A profile refinement method for nuclear and magnetic

structures, J. Appl. Crystallogr. 2 (1969) 65.

[11] L. Lutterotti, P. Scardi, P. Maistrelli, LSI- a computer program for

simultaneous refinement of material structure and microstructure, J. Appl.

Crystallogr. 25 (1992) 459.

[12] R.A. Young, D.B. Wiles, Profile shape functions in Rietveld refinements, J.

Appl. Crystallogr. 15 (1982) 430.

[13] R.A Young, The Rietveld Method, Oxford University Press/IUCr, Oxford,

1996, pp. 1.

[14] L. Lutterotti, Maud version 2.33, 2011 <http://www.ing.unitn.it/~maud/>.

[15] A.K. Mishra, S.K. Chaudhuri, S. Mukherjee, A. Priyam, A. Saha, D. Das, Characterization of defects in ZnO nanocrystals: Photoluminescence and

positron annihilation spectroscopic studies, J.Appl. Phys. 102 (2007) art.

no.103514.

[16] R. Krause-Rehberg, H.S. Leipner, Positron Annihilation in Semiconductors,

Solid-State Sciences, Springer, Berlin, 1999.

[17] P. Kirkegaard, M. Eldrup, POSITRONFIT: A versatile program for analysing

positron lifetime spectra, Comput. Phys. Commun. 3 (1972) 240.

[18] S Bid, S. K. Pradhan, Preparation and microstructure characterization of ball-

milled ZrO2 powder by the Rietveld method: monoclinic to cubic phase

transformation without any additive, J. Appl. Crystallogr. 35 (2002) 517.

[19] N. J. Welham, Room temperature reduction of scheelite (CaWO4), J. Mater.

Res. 14 (1999) 619.

~ 193 ~

General conclusions

In the present dissertation, industrially important nanomaterials have been

prepared by (i) high energy ball-milling technique and (ii) sol-gel method. Different

kinds of characterization have been made employing X-ray powder diffraction,

positron annihilation technique, transmission electron microscopy, Mossbauer

spectroscopy and band gap measurement by UV-Vis spectrometer. Microstructure

characterization in terms of several lattice imperfections like change in lattice

parameters, particle size, r.m.s. lattice strain, dislocation density etc. has been made

employing basically the modified Warren-Averbach’s method of X-ray line profile

analysis and the Rietveld’s X-ray powder structure refinement method. Both the

Warren-Averbach and Rietveld methods of analysis indicate the anisotropy in particle

size and lattice strain values. Again the particle sizes have been calculated by the

transmission electron microscope (TEM) experiment. The point defects, voids,

cluster, have been detected by the positron annihilation experiments. Super

paramagnetic state of the nanocrystalline Fe2O3 has been identified by the Mossbauer

experiment In the band gap experiment the value of band gap energy Eg (for direct

transition) has been obtained from the intercept of the extrapolated liner part of the

(αhν)2 versus hν curve with the energy (hν) axis. However , the following most

important findings can be treated as general conclusions of the present dissertation:

(1) From X-ray line profile analysis, the lattice strain has been estimated which is

considerably high for all ball-milled α-Fe2O3 samples. Mössbauer spectra of α-

Fe2O3 ball-milled sample consists of a doublet which is attributed to the

superparamagnetic behaviour of ferromagnetic fine particles and a broad sextet

which is presumably due to high internal strain. The decrease in hyperfine field,

broadening of lines and asymmetry of line shape implies a broad particle size

distribution in the ball-milled sample.

(2) The XRD analysis reveals a substantial grain growth in nano-ZnO above 425 °C

temperature. Distinct decrease of the average lifetime of positrons also starts

from the same temperature. This indicates a lowering of defect concentration,

mostly cationic, due to annealing above 425 °C. Such a reduction of defects

continues up to 1100 °C annealing and little above 700 °C the sample becomes

less defective, even better than the as supplied ZnO. However, the band tailing

~ 194 ~

parameter (E0), which has contributions from all possible disorder, does not

reflect a lowering of defects for high temperature annealing (>700 °C).

(3) The strain introduced inside the nanocrystalline Fe2O3 samples increases with

ball milling hour. Ratio curve analysis of the CDBEPAR spectra for the

different hour milled and unmilled samples indicate the formation of cation type

of defects at the grain surfaces due to the ball milling process. Due to ball

milling, the average particle size of the Fe2O3 decreases, but due to the

formation of cation type of defects the optical band gap decreases.

(4) From Mössbauer spectra it has been observed that the nanocrystalline α-Fe2O3

as-prepared by chemical synthesis sample shows enhanced isomer shift (IS), line

width, and quadrupole splitting (QS), and hyperfine field (HF) values compared

to the annealed samples which may be due to the reduction of the electron

density at the interfacial site. From UV-Vis absorption spectra it has been

observed that the band gaps of the annealed samples are lower than the as-

prepared samples and all samples belong to n-type semiconductors.

(5) The quantitative analysis of the XRD data evaluated on the basis of Rietveld’s

powder structure refinement method yields detailed information about the

structure and microstructure of mechanosysthesized nanoscale zinc ferrite as

well as the redistribution of cations from the spinel ferrite. The main feature of

the structural disorder of mechanosynthesized zinc ferrite is the mechanically

induced inversion spinel structure. Positron annihilation lifetime data shows that

the mean lifetime τm does not change much with ball milling durations. This

implies that the overall defect density, as seen by the positrons remains more or

less constant during milling. In the positron annihilation lifetime data the

variation of individual life times τ1 and τ2 and corresponding intensities I1 and I2

shows evaluation of different phases with milling duration and confirms the

formation of inverse spinel ferrite structure.

(6) The nanocrystalline Cd-ferrite phase is formed after 5h of milling from the

nanocrystalline CdO - α-Fe2O3 solid-solution. The experimental results reveal

that the ball milled prepared Cd-ferrite phase is a non-stoichiometric one. The

variation of individual lifetime parameters indicate disappearance of CdO phase

from the composite and formation of CdFe2O4 phase after 5 h milling. It also

~ 195 ~

shows enhancement of α-Fe2O3 particle size after 5h milling and formation of

lattice defect in CdFe2O4 after 10 h milling.

Future plan of research work

In completing the present dissertation, I acquired knowledge about the

characterization of lattice imperfections in nano-crystalline materials by positron-

annihilation, x-ray diffraction and other methods. I have got interest in preparation of

nanocrystalline materials by high-energy ball milling because the materials change

their different properties with the different milling time. I wish to prepare

nanocrystalline multiphase materials. The microstructure characterization and

measurement of physical properties would be helpful to establish correlation between

microstructure and property.

~ 196 ~

List of publications

(1) “Nanophase iron oxides by ball-mill grinding and their Mössbauer

characterization”, S. Bid, Abhijit Banerjee, S. Kumar, S.K. Pradhan, Udayan

De, D. Banerjee,

Journal of Alloys and Compounds, 326, 292-297, (2001).

(2) “Annealing effect on nano-ZnO powder studied from positron lifetime and

optical absorption spectroscopy”, Sreetama Dutta, S. Chattopadhyay, and D.

Jana, Abhijit. Banerjee, S. Manik, and S. K. Pradhan, Manas Sutradhar, A.

Sarkar

Journal of Applied Physics, 100, 114328 (2006).

(3) “Particle size dependence of optical and defect parameters in mechanically

milled Fe2O3”, Mahuya Chakrabarti , Abhijit. Banerjee , D. Sanyal, Manas

Sutradhar, Alok Chakrabarti

J Mater Sci, 43, 4175–4181, (2008).

(4) “Microstructure, Mössbauer and Optical Characterizations of

Nanocrystalline α-Fe2O3 Synthesized by Chemical Route”, Abhijit

Banerjee, Soumitra Patra, Mahuya Chakrabarti, Dirtha Sanyal, Mrinal Pal,

Swapan Kumar Pradhan,

ISRN Ceramics, Volume 2011, Article ID 406094, 8 pages, (2011).

(5) “Microstructural changes and effect of variation of lattice strain on positron

annihilation lifetime parameters of zinc ferrite nanocomposites prepared by

high enegy ball-milling”, Abhijit.Banerjee, S. Bid, H. Dutta, S. Chaudhuri,

D. Das and S. K. Pradhan ,

Material Research (in press) (2012).

~ 197 ~

(6) “Microstructure and positron annihilation studies of mechanosysthesized

CdFe2O4”, Abhijit. Banerjee, S. Bid, H. Dutta, S. Chaudhuri, D. Das and

S.K. Pradhan,

Communicated to Acta Physica Polonica

CHARACTERIZATION OF LATTICE IMPERFECTIONS IN...

Documents

Transcript of CHARACTERIZATION OF LATTICE IMPERFECTIONS IN...