1-3 X-Ray Characterization of Materials.docx

7/28/2019 1-3 X-Ray Characterization of Materials.docx

1/15

University of Technology Department of Materials Engineering

Dr. Saad B. H . F ar id F ormer ly: Chief Researchers Currently: Assistant Professor

CChhaar r aacctteer r iizzaattiioonn oof f MMaatteer r iiaallss PPhhDD CCoouur r ssee:: 22001122--22001133 1- X-Ray Characterization of Materials Part12- X-Ray Characterization of Materials Part23- X-Ray Characterization of Materials Part34- Exam15- Particle Size Determination

6- Electron Microscopy of Materials7- Spectroscopic Methods of Characterization, Atomic spectrometry8- Spectroscopic Methods of Characterization, UV-Visible spectroscopy9- Spectroscopic Methods of Characterization, Infrared Spectroscopy

10- Spectroscopic Methods of Characterization, Raman Spectroscopy11- Dielectric Characterization of Materials12- Exam213- Thermal Analysis of Materials14- Open15- Open


2/15

Dr. Saad B. H. Farid X-Ray Characterization of Materials 1 | / /

X-Ray Character ization of M ater ials

Generation of M onochr omatic X-r ay

The schematic shows typical x-ray emission spectrum. For clarity, the figure indicates only the presence of continuous background and three characteristic wavelengths: K

1, K

2, and

K , which have high intensities.

The spectra of the unfiltered beams from a copper target (Z=29) filtered by nickel (Z=28)Left - the schematic of the x-ray emission spectrum shown as the solid line overlapped with the schematic of the function of the properly selected -filter material (dotted line).Right - the resultant distribution of intensity after filtering as a function of the wavelength

Figure 1: Schematic Electronic transitions in an atomEmission processes indicated by arrows


3/15


Modern filtration technique utilizing divergent Monochromators (Crystal monochromators include pyroliticgraphite, Si, Ge, and LiCl). Usually graphite Monochromator is employed.

Example for determination of Miller Indices

A point Lattice, each point mayrepresent atom(s) or molecule

A unit cell, the bold a, b and crepresents vectors of the unit cell.


4/15



5/15


Crystal Diffraction

Lattice spacing is typically 10-10

m = 1 In 1912, the German physicistvon L aue reasoned that, if crystals were

composed of regularly spaced atoms, and if x-rays were electromagneticwaves of wavelength about equal to the inter-atomic distance in crystals,then it should be possible to diffract x-rays by means of crystals.

Under his direction, experiments to test this hypothesis were carried out: a crystal of copper sulfate wasset up in the path of a narrow beam of x-rays and a photographic plate was arranged to record the presence of diffracted beams, if any. The very first experiment was successful and showed without doubtthat x-rays were diffracted by the crystal out of the primary beam to form a pattern of spots on the photographic plate.

These experiments proved, at one and the same time, the wave nature of x-rays and the periodicity of thearrangement of atoms within a crystal.

Typical Laue X-ray diffraction patternLaue X-ray diffraction YAlO3 - c-axis normal to picture

Max von Laue(1879-1960)

Laue 1912 1914 Nobel Prize

Each spot corresponds to a different crystal planeSome Applications:

alignment of single crystal info on unit cell info on imperfections, defects in crystalSymmetry of the pattern

Symmetry of the crystal


6/15


The account of these experiments was read with greatinterest by two English physicists, W. H. Bragg and his sonW. L. Bragg.

The latter, although only a young student at the time it was still the year 1912 successfully analyzed theLaue experiment and was able to express the necessary conditions for diffraction in a somewhat simpler mathematical form than that used by von Laue.

He also attacked the problem of crystal structure with the new tool of x-ray diffraction and, in thefollowing year, solved the structures of NaCl, KC1, KBr, and KI, all of which have the NaCl structure; thesewere the first complete crystal-structure determinations ever made.

Systemati c absences :It is the absence of certain (h k l)diffracted x-ray due to cancelationsof out of phase equivalentreflections

Di ff raction methods

Symmetry There are 32un ique combination of 2D symmetry elements calledpoint groups Glide planes : is the combination of a mirror reflection plane with corresponding translations (1/2 or

1/4 units) parallel to the plane, results in a total of five possible crystallographic glide (shift) planesoccurs.

Screw axes : Screw axes perform a rotation simultaneously with a translation along the rotation axis.In other words, the rotation occurs around the axis, while the translation occurs parallel to the axis.Crystallographic screw axes include, only two-, three-, four- and six-fold rotations

When glide planes and screw axes is added to them, we have230 un ique space symmetry calledspace groups

All are listed inI nternational tables for crystallography


7/15


Reciprocal lattice The concept of a reciprocal lattice was first introduced byEwald and it quickly became an important tool inthe illustrating and understanding of both the diffraction geometry and relevant mathematical relationships.Let a, b and c be the elementary translations in a three-dimensional lattice (called here adir ect lattice )A second lattice,reciprocal to the direct lattice, is defined by three elementary translationsa*, b* and c* ,

which simultaneously satisfy the following two conditions:

What is V, V* ?

The reciprocal lattice is what is seen in the diffraction photographsso that it is used to calculate the parameters of the direct lattice.Where is the reciprocal lattice?Reciprocal L attice and Ewal d's Sphere

Where and when the Bragg's condition is metWhich is the possible Braggs reflections(Related to the symmetry and beyond the scope of this lecture)

Oscillating, Weissenberg, precessionand de Jongh Bouman photographs


8/15



9/15


F or single crystals Structure factor 1. Structure amplitude: Shared by multiple atoms in

the unit cell2. Population factor: In general, gi =1/n, where n is

the multiplicity of the symmetry element3. Temperature factor: also known as "atomicdisplacement parameters; atoms are in acontinuous oscillating motion about their equilibrium positions

4. Atomic scattering factor: the ability to scatter radiation varies depending on the type of an atom5. Phase angle: "phase problem" in diffraction analysis; due to lost phase angles in measurable intensities

Intensity of powder diffraction peaks 1. Integrated intensity: The area under the peak fitted to Gaussian or Lorentz Distribution2. Scale factor: to compensate diffraction geometry and Sample shape3. Multiplicity factor : equivalent Braggs angle for reflections such as h00 , -h00 4. Lorentz-polarization factor : intensity that reaches the detectors1/sin2 5. Absorption factor: dependent on both the geometry and properties of the sample and the

focusing method6. Preferred orientation: departure from random distribution of the orientations of crystallites7. Extinction factor: back-reflection within the same crystallite and multiple crystallites

The chief problem in determining particle size from line breadths is todetermine B from the measured breadth B of the diffraction line. Of the many methods proposed, Warren's is the simplest. The unknown ismixed with a standard which has a particle size greater than 1000A,and which produces a diffraction line near that line from the unknownwhich is to be used in the determination. B

2=B

2

Measured-B2

Standardthen B=0.9 /tcos

Crystallite size, not crystal or particle size!

Single Crystal X-ray Crystallographyis a complete solution of CrystalStructure.

Also called The Phase Problem of X-ray Crystallography (FC calculations)This is beyond the Scope of this

presentation


10/15


The simulated powder diffraction pattern of copper (space group Fm3m, a =3.615 A, Cu K 1, K 2 radiation,Cu atom in 4(a) position with x = 0, y = 0, z = 0).

A powder diffraction file (PDF) of hydroxyapatite.(The International Centre for Diffraction Data, ICDD)

A typical card from the ASTM file isreproduced in Fig. 14-1. At the upper left appear the d values for the three strongest lines (2.28,1.50, 1.35A) and, in addition, the largest d value(2.60A) for this structure.

The lower right-hand portion of the card, givesd values listed versus the relative intensitiesI /I 1 ,expressed as percentages of the strongest line inthe pattern

Details are given of the method used for obtaining the pattern (radiation, camera diameter,method of measuring intensity, etc.), and areference to the original experimental work. Therest of the left hand portion of the card containsroom for various crystallographic, optical, andchemical data.

Two powder diffraction patterns of LaB6collected using different 's


11/15


Quali tative XRD Analysis

Basic principles. The powder pattern of a substance is characteristic of that substance and forms a sort of fingerprint by which the substance may be identified.

Analysis 1- Manual analysis and match2- Computerized match followed by manual analysis. The computer program is supplied with database of standard x-ray patterns of inorganic and/or organic compounds.Search criteria should be applied like expected number of elements and element types.In all analysis, nothing can be accomplished from scratch !!!

Quanti tative XRD Analysis Quantitative analysis by diffraction is based on the fact that the intensity of the diffraction pattern of a particular phase in a mixture of phases depends on the concentration of that phase in the mixture. Therelation between intensity and concentration is not generally linear, since the diffracted intensity dependsmarkedly on the absorption coefficient of the mixture and this itself varies with the concentration.

M ethods

Diffraction pattern of a powder specimen of h drox a atite

The experimental diffraction pattern of a silicon andAl2O3 mixture. Numbers with three digits mark theMiller indices of corres ondin cr stallo ra hic lanes


12/15


5. Rietveld refinement : of multiple phase samples may be used for relativelyaccurate quantitative analysis. It requiresknowledge of the atomic structure for each phase present in the mixture. It

refines the difference between observedand calculatedI hkl

6. Full pattern decomposition : does notrequire the atomic structure to be knownand it produces intensities of individualBragg peaks. Thus, multiple reflectionsfrom each phase can be used to computeintensity ratios required in methodsdescribed in items 1 through 4 above,which increases the accuracy of theanalysis. The use of multiple Bragg peaks in evaluating an average intensityratio, to some extent diminishes thedetrimental influence of preferredorientation as long as it remains small tomoderate. This method, however, requires lattice parameters and therefore, is applicable toindexed patterns only. The phasecomposition is actually determined usingany of the first four methods listed above

by using intensities of several strong or all Bragg peaks instead of a singlereflection.

Figure 4.24. Illustration of standard additionmethod of quantitative analysis. The plot of the Ia, hkl/I b, hkl intensity ratio as a function of the known amount (Ya) of added phase a. The point marked Ya(0) corresponds to the originaltwo-phase mixture. The unknown amount of phase a in the original sample is Xa.


13/15


X-ray F luorescence The most intense lines of this spectrum

are the K and K lines if the elementwere bombarded with x-rays of highenough energy (fluorescence). They are

always called "characteristic lines" toemphasize the fact that their wavelengthsare fixed and characteristic of the emittingelement.

The primary radiation (Fig. 15-1) causesthe sample to emit secondary fluorescentradiation, which is then analyzed in aspectrometer. This method, commonlyknown as fluorescent analysis, giveinformation about the chemical elements present in the sample, irrespective of their state of chemical combination or the phases in which they exist.

The wavelength of each spectral line iscalculable from the corresponding Braggangle and the interplanar spacing of theanalyzing crystal used.

The useful range of fluorescent wavelengths extends from about 0.5 to about 2.5A. The lower limit isimposed by the maximum voltage which can be applied to the x-ray tube, which is 50 kv incommercial instruments.

The two main problems in fluorescent analysis, namely the achievement of adequate intensity andadequate resolution

There is a common Mistake; it isthe calculation of relativecontents by simply dividingintensities!


14/15


Quali tative analysis In qualitative work sufficient accuracy can be obtained by automatic scanning of the spectrum, with

the counter output fed to a chart recorder. Interpretation of the recorded spectrum will be facilitated if the analyst has on hand (a) a table of corresponding values of and 2 for the particular analyzingcrystal used, and (b) a single table of the principal K and L lines of all the elements arranged in

numerical order of wavelength. Since it is important to know whether an observed line is due to an element in the sample or to anelement in the x-ray tube target, a preliminary investigation should be made of the spectrum emitted by the target alone. For this purpose a substance like carbon or plexiglass is placed in the sampleholder and irradiated in the usual way; such a substance merely scatters part of the primary radiationinto the spectrometer, and does not contribute any observable fluorescent radiation of its own. Thespectrum so obtained will disclose the L lines of tungsten, if a tungsten-target tube is used, as well asthe characteristic lines of whatever impurities happen to be present in the target.

Quanti tative analysis In determining the amount of element A in a sample, the single-line method is normally used: theintensity Iu of a particular characteristic line of A from the unknown is compared with the intensity Is of the same line from a standard, normally pure A.

The way in which the ratio Iu / Is varies with the concentration of A in the sample depends markedly onthe other elements present and cannot in general be predicted by calculation. It is therefore necessary toestablish the variation by means of measurements made on samples of known composition.

Figure 15-8 illustrates typical curves of this kind for three binary mixtures containing iron.

M atri x Effect in X-r ay Fl uorescence Anal ysis: These curves show that the intensity of a fluorescent line from element A is notin general proportional to the

concentration of A. This nonlinearbehavior is due mainly to two effects: (1) Matrix absorption : As the composition

of the alloy changes, so does itsabsorption coefficient As a result thereare changes both in the absorption of the primary radiation traveling into thesample and in the absorption of thefluorescent radiation traveling out.

(2) Multiple excitation : If the primary radiation causes element B in the specimen to emit its characteristicradiation, of wavelength fB, and if fB is less than KA, then fluorescent K radiation from A will beexcited not only by the incident beam but also by fluorescent radiation from B.

Specimen preparati on Metals and alloys may be converted to powder by filing or, if they are sufficiently brittle, by grinding in asmall agate mortar. In either case, the powder should be filed or ground as fine as possible, preferably to pass a 325-mesh screen, in order to produce smooth, continuous diffraction lines. The screened powder isusually annealed in evacuated glass or quartz capsules in order to relieve the strains due to filing or grinding.In addition, care should be taken to avoid the "preferred orientation" of the powder particles (crystals) as it isa usual practice in sampling of e.g. silicon powder.

Fluorescence

Wavelength Dispersive Systems WDS A wavelength dispersive spectrometer may be a single channel instrument in which a single crystal and asingle detector are used for the measurement of a series of wavelengths sequentially; or a multichannelspectrometer in which many crystal/detector sets are used to measure elements simultaneously. The angular dispersion d/d of a crystal of spacing 2d is given by:


15/15


It will be seen from Eq. (3-8) that theangular dispersion will be high when the2d-spacing is small. This is unfortunateas far as the range of the spectrometer isconcerned, because a small value of 2d

means in turn a small range of wavelengths coverable. Thus, as with theresolution and peak intensities, theobtaining of high dispersion can only beobtained at the expense of cutting downthe wavelength range covered by a particular crystal.

En ergy Disper sive Systems EDS The energy dispersive spectrometer consists of the excitation source and the spectrometer/detection system.The spectrometer/detector is typically a Si(Li) detector which is a proportional detector of high intrinsic

resolution. A multi-channel analyzer is used to collect, integrate and display the resolved pulses. Whilesimilar properties are sought from the energy dispersive system as with the wavelength dispersive system,the means of selecting these optimum conditions are very different. Since the resolution of the energydispersive system is equated directly to the resolution of the detector, this feature is of paramountimportance. I.e. this technique gives better resolution.

Measurements of filmthickness,

Stress measurements,

Micro-crack detection, Topography, Structure of thin films, Texture analysis etc

They are not merecharacterization of materialsbut tests for produced parts

1-3 X-Ray Characterization of Materials.docx

Documents

Transcript of 1-3 X-Ray Characterization of Materials.docx