TEM SEM EBSD - VTK Gent...Karen Louise De Sousa Pesse 1 EBSD SEM TEM Study Guide 2016-2017 Taught...

Karen Louise De Sousa Pesse 1

EBSD

SEM TEM

Study Guide 2016-2017

Taught by: Prof. dr. ir.

Roumen Petrov

“If you quit now you will soon be back to where you

started. And when you started you were wishing to be

where you are now”


Table of Contents

1 GENERAL PART............................................................................................................................................................ 5

1.1 QUESTION 1................................................................................................................................................................ 5 1.1.1 GENERAL CONCEPT OF MICROSTRUCTURE 5 1.1.2 DEFINITION 5 1.1.3 GENERAL PRINCIPALS OF MICROSTRUCTURE CHARACTERIZATION 5 1.1.4 ELASTIC AND INELASTIC SCATTERED SIGNALS 6 1.1.5 STRUCTURE - PROPERTY RELATIONSHIPS 6 1.1.6 MICROSTRUCTURAL SCALE 6 1.2 QUESTION 2................................................................................................................................................................ 8 1.2.1 RESOLUTION OF THE IMAGING SYSTEMS 8 1.2.2 FACTORS WHICH INFLUENCE THE RESOLUTION OF THE IMAGING SYSTEM 8 1.2.3 RAYLEIGH CRITERION 9 1.3 QUESTION 3.............................................................................................................................................................. 10 1.3.1 INTERACTION OF THE RADIATION WITH THE MATTER 10 1.3.2 THE PENETRATION DEPTH 10 1.3.3 MATERIAL DAMAGE 13 1.4 QUESTION 4.............................................................................................................................................................. 14 1.4.1 SAMPLE PREPARATION - GENERAL REQUIREMENTS 14 1.4.2 SPECIFIC STEPS IN MACRO STRUCTURE SAMPLE PREPARATION 14 1.4.3 SPECIFIC STEPS IN MICRO STRUCTURAL SAMPLE PREPARATION 14 1.4.4 SURFACE EFFECTS AFTER GRINDING AND POLISHING 15 1.4.5 MECHANICAL POLISHING 16 1.4.6 ELECTROLYTIC POLISHING 17 1.4.7 CHEMICAL POLISHING 17 1.4.8 ETCHING, CLEANING AND KEEPING THE SAMPLES 18

2 LIGHT OPTICAL MICROSCOPY (LOM) .......................................................................................................................... 19

2.1 QUESTION 5.............................................................................................................................................................. 19 2.1.1 IMAGE FORMATION, PATH OF THE BEAM/LIGHT 19 2.1.2 LIMITATIONS 20 2.1.3 BRIGHT FIELD 21 2.1.4 DARK FIELD 21 2.1.5 DIFFERENTIAL INTERFERENCE CONTRAST (DIC) 21 2.1.6 POLARIZED LIGHT CONFIGURATION 22 QUESTION 6 ...................................................................................................................................................................... 23 2.1.7 LIGHT OPTICAL MICROSCOPY 23 2.1.8 RESOLUTION 23 2.1.9 NUMERICAL AND ANGULAR APERTURE 23 2.1.10 USEFUL MAGNIFICATION OF THE MICROSCOPE 25 2.1.11 LENS DEFECTS AND METHODS TO BE CORRECTED 26

3 QUANTITATIVE METALLOGRAPHY (QM) .................................................................................................................... 29

3.1 QUESTION 7.............................................................................................................................................................. 29 3.1.1 QUANTITATIVE METALLOGRAPHY (STEREOLOGY) 29 3.1.2 GRAIN SIZE DETERMINATION - VISUAL EVALUATION 29 3.1.3 GRAIN SIZE DETERMINATION – JEFRIES METHOD 30 3.1.4 GRAIN SIZE DETERMINATION (SALTICOV) 30 3.1.5 GRAIN SIZE DETERMINATION (LINEAR INTERCEPTION METHOD) 31 3.1.6 PHASE QUANTIFICATION 31


3.1.7 AUTOMATIC QUANTITATIVE ANALYSIS 31

4 X-RAY DIFFRACTION .................................................................................................................................................. 32

4.1 QUESTION 8.............................................................................................................................................................. 32 4.1.1 GENERAL THEORY (BRAGG’S LAW) 32 4.1.2 RECIPROCAL LATTICE 33 4.1.3 EWALD SPHERE 34 4.1.4 GENERATION OF X-RAYS 35 4.1.5 PENETRATION DEPTH 36 4.1.6 ABSORPTION 36 4.1.7 SAMPLE PREPARATION 37 4.2 QUESTION 9.............................................................................................................................................................. 38 4.2.1 APPLICATION OF X-RAY DIFFRACTION 38 4.2.2 METHODS FOR XRD MEASUREMENTS 39 4.2.3 DETERMINATION OF THE TYPE OF THE CRYSTAL LATTICE, PHASE ANALYSIS, DETERMINATION OF THE LATTICE PARAMETER 42 4.3 QUESTION 10 ............................................................................................................................................................ 44 4.3.1 APPLICATION OF X-RAY DIFFRACTION - QUANTITATIVE PHASE ANALYSIS QPA 44 4.3.2 INTERNAL STRESSES MEASUREMENT (RESIDUAL STRESS) 46 4.4 QUESTION 11 ............................................................................................................................................................ 49 4.4.1 TEXTURE 49 4.4.2 REPRESENTATION OF TEXTURE AND INDIVIDUAL CRYSTALLOGRAPHIC ORIENTATION 50 4.4.3 ORIENTATION DISTRIBUTION FUNCTION ODF 53 4.4.4 POLE FIGURE 54 4.4.5 INVERSE POLE FIGURE 54 4.5 QUESTION 12 ............................................................................................................................................................ 57 4.5.1 PRACTICAL ASPECTS OF TEXTURE MEASUREMENTS BY XRD - GEOMETRY OF THE MEASUREMENT SCHEME 57 4.5.2 SAMPLE PREPARATION 58 4.5.3 EXAMPLES 59 4.5.4 EXAMPLES OF ROLLING, TEXTURES, RECRYSTALLIZATION TEXTURES AND TRANSFORMATION TEXTURES IN FCC AND BCC CRYSTAL

STRUCTURES 60

5 SCANNING ELECTRON MICROSCOPY (SEM) ................................................................................................................ 62

5.1 QUESTION 13 ............................................................................................................................................................ 62 5.1.1 ARCHITECTURE OF SEM 62 5.1.2 TYPES OF FILAMENTS - ADVANTAGES AND DISADVANTAGES 63 5.1.3 INTERACTION OF THE PRIMARY BEAM WITH MATERIAL - EFFICIENCY OF SE AND BSE 64 5.2 QUESTION 14 ............................................................................................................................................................ 65 5.2.1 EDX AND WDX ANALYSIS IN SEM CHARACTERISTIC X-RAYS 65 5.2.2 DETECTORS PRINCIPLE 67 5.2.3 COMPARISON BETWEEN EDX AND WDX SPECTROSCOPY 69

6 ELECTRON MICROSCOPY TEM .................................................................................................................................... 70

6.1 QUESTION 15 ............................................................................................................................................................ 70 6.1.1 THE SAMPLE PREPARATION TECHNIQUES FOR TEM 70 6.1.2 GIVE SCHEMATIC DESCRIPTIONS OF DIFFERENT METHODS 71 6.2 QUESTION 16 ............................................................................................................................................................ 73 6.2.1 IMAGE FORMATION AND CONTRAST FORMATION IN A TEM 73 6.2.2 RESOLUTION IN TEM 73 6.2.3 BRIGHT AND DARK FIELD IMAGING 74 6.3 QUESTION 17 ............................................................................................................................................................ 75 6.3.1 OBJECTIVE APERTURE 75 6.3.2 WHAT IS SAD 75


6.3.3 HOW ARE SAD IMAGES ANALYSED FOR CUBIC MATERIALS? 76

7 ELECTRON BACKSCATTERED DIFFRACTION (EBSD) ...................................................................................................... 80

7.1 QUESTION 18 ............................................................................................................................................................ 80 7.1.1 DEFINITION 80 7.1.2 ARCHITECTURE 80 7.1.3 FORMATION OF KIKUCHI PATTERN. 81 7.1.4 BAND DETECTION 81 7.1.5 HOUGH TRANSFORM 82 7.2 QUESTION 19 ............................................................................................................................................................ 84 7.2.1 EVOLUTION OF ELECTRON BACK-SCATTER DIFFRACTION EBSD 84 7.2.2 ORIENTATION IMAGE ANALYSIS. 84 7.2.3 SPATIAL RESOLUTION AND ANGULAR RESOLUTION OF THE EBSD. 85 7.2.4 WHAT IS IQ, (BC) CI (MAD) 85 7.2.5 EXPERIMENT DESIGN PHILOSOPHY - WHAT KIND OF INFORMATION CAN BE OBTAINED FROM AN EBSD MEASUREMENT? (EXAMPLES) 88 7.2.6 SAMPLE PREPARATION FOR THE EBSD MEASUREMENT 88 7.2.7 COMPARE THE EBSD WITH THE XRD METHOD FOR TEXTURE CHARACTERIZATION. 89

8 3D MICROSTRUCTURE CHARACTERIZATION (3D-EBSD) ............................................................................................... 90

8.1 QUESTION 20 ............................................................................................................................................................ 90 8.1.1 OVERVIEW OF SPECIAL TECHNIQUES 90 8.1.2 3D-EBSD WITH FOCUSED ION BEAM 90 8.1.3 3D-XRAY DIFFRACTION 92

9 AFM/APM ................................................................................................................................................................ 93

9.1 QUESTION 21 ............................................................................................................................................................ 93 9.1.1 APM 93 9.1.2 FIELD ION MICROSCOPE 93 9.1.3 ATOM PROBE 93 9.1.4 SAMPLE PREPARATION 94 9.1.5 APPLICATIONS 94 9.1.6 AFM 95 9.1.7 CONTACT MODE AFM 95 9.1.8 NON-CONTACT MODE AFM 96 9.1.9 TAPPING MODE AFM 96 9.1.10 ADVANTAGES OF AFM 96 9.1.11 DISADVANTAGE OF AFM 96

PRACTICAL CLASSES ........................................................................................................................................................ 97

9.2 EXTRA ON EBSD ........................................................................................................................................................ 97

10 SOURCES ................................................................................................................................................................. 98


Materiaalkundige Micro-Analyse en Structuurbepaling:

Vragen voor examen 2016/2017 studiejaar

(Reading guide)

By Karen Louise de Sousa Pesse

1 General part 1.1 Question 1

General concept of the microstructure. Definition, General principles of microstructure characterization. Elastic and inelastic scattered signals. Structure –properties relationships.

Microstructural scales.

1.1.1 General Concept of Microstructure

1.1.2 Definition Microstructure is the identical arrangement in 3D space of atoms and all types of non -equilibrium

defects (Book – Physical Methods);

The small scale structure of a material, defined as the structure of a prepared surface of material as revealed by a microscope above 25x magnification (Wikipedia).

Totality of all thermodynamic non-equilibrium lattice defects in a space scale that ranges from Å to meters.

The arrangement of phases and defects within a material

1.1.3 General Principals of Microstructure Characterization The characterization of microstructures is mostly divided into 4 steps:

Probe Source (light, X-rays, Electrons) – Chose the correct method to analyse your material; Different probe signals can be used for characterizing the microstructure in different scale and different aspects.

Specimen Sample (polished and etched surface, thin films) – Chose the type of material and prepare it adequately to the method you chose;

Image Signal – Elastically or Inelastically scattered radiation, secondary signals)

Data Collection and processing, image interpretation


1.1.4 Elastic and Inelastic Scattered Signals Light scattering is one of the major physical processes that contribute to the visible appearance of most objects. Ex.: Backscattered electrons.

1.1.4.1 Elastic Scattered Signal – Equal amount of energy They have the same wavelength as the incident light, and are divided in:

Optical Imaging (real space): The distance of the image is directly proportional to the distance of the object, with a constant equal to the magnification.

Diffraction Spectra (reciprocal space): The scattering angle for the diffracted radiation is inversely proportional to the scale of the features of the object, so the distances in the diffraction pattern are inversely proportional to the separation of the features in the object.

1.1.4.2 Inelastically Scattered Signal – Lower final energy Scattered photons have a change in ener gy of a molecule due to a transition to another energy level: Ex.: X-Ray (XRD)

Energy Loss Spectra – electrons will undergo inelastic scattering, lose energy and have their paths slightly and randomly deflected;

Secondary Signals – Secondary Electrons are loosely bound outer shell electrons from the atom, which receive sufficient kinetic energy during inelastic scattering of beam electrons to be ejected from the atom and set into motion.

1.1.5 Structure - Property Relationships There are two types of structure properties:

Insensitive to Structure : Elastic Moduli, Thermal expansion coefficient, Specific Gravity

Sensitive to Structure : Yield Strength, Thermal conductivity and electrical resistivity and Fracture toughness;

1.1.6 Microstructural Scale The typical magnification lies on x104 for Microstructure; Common Techniques are Optical Microscopy, Electronic Microscopy, Transmission Electron Microscopy, and Atomic Force Microscopy; Characteristic Features (what you can see): Dislocations, Substructure, Grain and Phase boundaries, Precipitations phenomena;


Scale Macrostructure Mesostructure Microstructure Nanostructure

Typical magnification

x1 x102 x10

4 x10

6

Common techniques

Visual inspection X-ray radiography, Ultrasonic inspection

Optical microscopy SEM

OM, EM,TEM, AFM

X-ray diffraction Scanning Tunnelling Microscopy, HRTEM

Characteristic features

Production defects Porosity cracks and inclusions

Grain and particles size Phase morphology and anisotropy

Dislocation substructure Grain and phase boundaries, precipitations phenomena

Crystal and interface structure Point defects and point defects clusters

Resume:

Examples of non-equilibrium; lattice defects are:

Interstitial and Substitutional foreign atoms

Vacancies

Edge and Screw dislocations

Incoherent and coherent precipitations

Grain boundaries

Determination of the microstructure:

Which phase

Shape of the phase

Composition of the phase

Every characterizing system consists of four parts:

A source

A specimen

A signal resulting in the interaction between the source and the sample

A way to process the collected data


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1.2 Question 2

Resolution of the imaging systems. Describe the factors which influence the resolution of the imaging system. Rayleigh criterion.

1.2.1 Resolution of the imaging systems

To describe the microstructure in different scales, we need an appropriate resolution – not always the highest resolution is the best solution;

Def: Resolution is the minimum distance between two points from which they still can be recognized as 2 points;

One method is to illuminate the object over its entire surface by using a suitable source of radiation (photons, electrons or ions) and use a lens arrangement to form an image, by focusing the radiation that is either reflected or emitted from the object. A point on the object is f ocused to an equivalent point on an image plane.

1.2.2 Factors which influence the resolution of the imaging system

One of the most powerful tools to improve the resolution is the probe’s wave length (λ):

The resolution normal to the direction of the incident beam, often called spatial resolution, is influenced by the diameter of the incident beam, the wavelength of the incident radiation and the mean free path of the incident beam in the material.

This can be seen in the equation that defines resolution:

o Minimum separation distance between two points d

o Focal Length, the distance between observer and the points L (Lens system)

o Angle of resolution () which is obtained from d and L;

o Diameter of circular opening or diameter of lens aperture D;

o - Wavelength;

If one uses a second method, in which you direct a very narrow beam of radiation onto the object and detect the absorbed or reflected radiation, the reflected radiation allows an image of the surface to be build up. The spatial resolution will then be deter mined by the:

Diameter of the incident beam

Wavelength of the incident radiation

Scattering of the incident radiation within the object surface.


1.2.3 Rayleigh Criterion Airy disc: when one passes a laser beam through a pinhole aperture; it creates a specifi c

diffraction pattern of light the Airy pattern, which has a bright region in the centre

the Airy disk.

According to Rayleigh Criterion, two point sources cannot be resolved if their separation is less than the radius of an Airy Disk. The bigger the aperture (D), the smaller the angle you can resolve (formula);

The Rayleigh criterion for barely resolving two objects that are point sources of light, such as stars seen through a telescope, is that the centre of the Airy disk for the first object occurs at the first minimum of the Airy disk of the second.

However, while the angle at which the first minimum occurs (which is sometimes described as the radius of

the Airy disk) depends only on wavelength and aperture size D, the appearance of the diffraction pattern will vary with the intensity (brightness) of the light source . Because any detector (eye, film, digital) used to observe the diffraction pattern can have an intensity threshold for detection, the full diffraction pattern may not be apparent.

1.2.3.1 Rayleigh Scattering When light is incident on a material, certain resonance frequencies are absorbed in raising the atom to an excited state.

When the atom decays, that same frequency may be re -emitted in a random direction and not necessarily the direction of the incident beam.

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1.3 Question 3

Interaction of the radiation with the matter. Penetration depth and material damage caused by

photons, electrons and ions.

1.3.1 Interaction of the radiation with the matter

To characterize a microstructure, it is necessary to perturb the material by interacting in some way with it – to see a surface you have to bombard it with photons.

Objective: Obtain maximum information from material while causing the least amount of damage ;

When the radiation from the probe source strikes on the sample, interaction with the matter occurs. This interaction is measured and reveals the characteristics of the microstructure. Of course the intention is to obtain maximum information with the least amount of damage to the sample . A general rule is to initiate the examination of the sample with the lowest possible intensity . There are different kinds of radiation sources. The lowest intensity is obtained by using low energy photons. To obtain more information the source energy may be increased by using X-rays. Electrons have an even higher energy while ions have the highest energy. The more microstructural information one wants to obtain, the higher energy source needs to be used . Indeed, the higher the energy, the lower the wavelength and thus the h igher the resolution. However, this also damages the sample the most, because of the different penetration depths from the above radiation sources.

1.3.2 The penetration depth Also known as the mean free path of the incident beam, determines the depth and volume of material that will be sampled. You probe with one type of radiation – for example a beam of X-ray photons - and detect a second type – like emitted electrons.

The depth that a photon can penetrate in the bulk of a sample depends on the wavelength of the incident radiation and the material of the sample (more specifically the absorption coefficient of the material µ). This penetration depth determines the depth and volume of material that will be sampled. Of course a wavelength is needed that is of comparable size to the features being studied. Several kinds of radiation are applied: photons, electrons, neutrons, ions and atoms.


1.3.2.1 Photons

Are discrete quanta of electromagnetic radiation and identified by their wavelength , energy E and

frequency .

𝐸 = ℎ = ℎ𝑐/

The penetration of photons shows considerable and dramatic variations between different types of material and photon energy or wavelength.

The most important wavelengths for material characterization are

The infrared radiation (long wavelengths) investigate how specific wavelengths are absorbed;

The visible light shorter wavelengths used to obtain a visual image of the surface , penetration depth of 50 to 300 nm equal to a several hundred atom layers);

Ultraviolet radiation (shorter wavelength than previous, used to obtain information about the electron distribution in the surface atoms );

X-rays are even shorter wavelengths and maybe most used. The penetration depth of X-rays varies both with wavelength and material, and it is typically a few micrometers. The absorption coefficient µ increases with atomic number and determines the penetration depth. X-rays are produced by bombarding a metal target with high energy electrons to produce a band of white radiation.

Superimposed on the white rad iation are a series of discrete maxima whose wavelength and intensity is determined by the electron binding energies of the atom making up the metal target being bombard. These characteristic X-ray photons result from electrons falling into holes created in core electron levels by the incident electron beam with the emission of a photon whose energy is given by the energy difference between the electron shells.

The shortest wavelengths are obtained with gamma rays (10 -2 nm), and also the higher

energies. These rays can penetrate considerable distances through a material but the penetration depth varies inversely with the atomic number.


1.3.2.2 Electrons

The penetration depth varies with energy of

the electron and atomic number of the material the mean free path of electrons in elements of low atomic number is large and vice-versa; this is important because often the material is composed of different elements with different atomic numbers;

Electrons are widely used for analysis because of their wide energy spectrum (10 eV - 1 MeV), the flexibility of the electron optics , the strong interaction between the electron and the solids and the diffraction of the electrons (figure 2.6 from

physical methods). The penetration depth of electrons varies dramatically with both the energy E of the electron beam and the atomic number Z of the material that is being examined. The energy of the electrons is produced by the used voltage to accelerate the electrons in the microscope. The higher the voltage applied, the higher the electrons energy. Thus, the lower their wavelength, and therefore the higher the resolution, the higher the penetration depth.

Energy = Voltage; = Resolution; Penetration Depth

The penetration depth increases with decreasing atomic number . This has important consequences for any microstructural characterization since materials will invariably be composed of element s with different atomic numbers:

Images can present differences in terms of penetration of the electrons into the bulk and the backscattering of electrons by atoms of different atomic number. The obtained surface images will differ as the beam energy (and thus the penetration depth) is changed and different anal ysis will be obtained.

Many techniques detect electrons with low energies in the region of 0 to 2 keV where the effect of the material on the penetration depth is reduced. Up to 10 eV the very low energy causes the electrons to move very slowly and instead of colliding with the atoms of the material, they pass between them. Therefore the penetration depth is very high (and increasing with decreasing electron energy). These changes in penetration depth can be used in many ways to obtain additional microstructural information concerning a surface, but also indicates the great care that must be exercised when using electrons to probe a material.

1.3.2.3 Neutrons

Have a mass that is 1000 times more than the mass of electrons . They also have a wave character and diffract, but they are not electrically charged which means that their penetration depths will be much larger than those of electrons or X -rays (several millimeters) because they do not interact with the electron cloud surrounding the nucleus , only with the nucleus. Therefore neutrons are used to study the microstructure within the bulk of the material. A disadvantage is the fact that a nuclear reactor is needed to produce neutrons.


1.3.2.4 Ions or atoms

If ions penetrate a material, so much damage is caused that is more accurate to address the stopping distance than the penetration di stance;

Ions have an even larger mass. Depending on the energy the ions will either produce elastic (low energy) or inelastic (high energy) interactions. The elastic ones are limited to imaging the materials surface – in Ion Scattering Spectroscopy, the io ns reflect from the surface and do not perturb it as much as a high energy photon or electron. The high energy ions give rise to complex reactions and penetrate deep into the material . These ions can push out electrons, atoms, ions and ion clusters. Of course that the higher the energy, the deeper the penetration . With this type of radiation a lot of damage occurs . When an ion enters the material it will follow a path which is not necessarily normal to the surface and travel a distance b efore coming to rest at a point. The distance penetrated is determined by the kinetic energy of the incident ion , the atomic number of the ion and the atomic number of the material . Although extremely damaging, this method provides microstructural information that outweighs t he disadvantage.

1.3.3 Material Damage When radiation interacts with the material, damage always occurs.

1.3.3.1 Photon A photon source is regarded as the least damaging of the analytical probes. The damage caused is the result of heating and the degree and extent of this damage is determined by the penetration into the material, the energy of the radiation and the photon flux.

1.3.3.2 X-Rays As an example X-rays can cause the surface of certain oxides to be reduced and laser beams can burn holes through metal by heating to temperatures that result in the instantaneous melting and evaporation in the immediate vicinity of the beam. In some techniques this phenomenon is used as an advantage. However, as a general rule, if the results for a microstructural investigation can be obtained using a photon source, then this should be used.

1.3.3.3 Electrons Electrons are more damaging than photons because of their greater momentum. Again the resultant damage is related to the amount of energy or heat transferred to the material and to the thermal conductivity of the material. Even after a few minutes of observation, changes can be seen. In conventional instruments, the incident beam energy does not exceed 100 to 200 keV, however some instruments with more energetic electrons can cause atoms to be displaced from normal lattice positions by the transfer of momentum.

1.3.3.4 Ions/atoms When ions or atoms penetrate a material they either interact in essentially a totally non-damaging manner where they interact elastically with the surface or they cause severe damage where they interact inelastic with the surface. The damage is done by displacing atoms from their normal lattice positions , and a minimum energy is required by the ion to exceed the binding energy of the atom. The greatest damage is caused by this type of radiation. With ions it is even possible to cut a zone by “damaging”.


1.4 Question 4

Sample preparation. General requirements. Specific steps in micro- and macro-sample

preparation. Surface effects after grinding and polishing. Mechanical, chemical, electrolytic

polishing. Etching, cleaning and keeping the samples.

Metallographic Analysis: Analysis of the structure of metals (phases, morphology and distribution) to link to the properties and manufacturing process, by means of preparing the sur face of the material; can be a macro/micro structural analysis;

1.4.1 Sample Preparation - General Requirements Specimen must be representative;

All structural elements must be retained

No scratches/deformations on surface

No foreign matter must be introduced in the specimen surface

Specimen must be plane and highly reflective

Optimal price $$ per sample should be obtained

All preparations must be 100% reproducible

Goal: Prepare for observation the zone of the material that we are interested in! Do not change the microstructure in this zone during preparation procedure;

1.4.2 Specific Steps in MACRO structure sample preparation i. CUT the sample – size is dependent on the needs of the researcher; there is no size limitations

ii. GRINDING the samples with mechanical grinding papers up to #1000 grit SiC

iii. ETCHING – the etchants reveal the chemical heterogeneities in macrostructure

1.4.3 Specific Steps in Micro structural sample preparation i. Documentation of the material;

ii. SELECTION of the place that contains zone of interest

iii. CUT the sample – size depends on the needs of the researcher; surface usually do es not exceed 1,5-2cm2; depending upon the material, sectioning operation can be obtained by abrasive cutting disc (metals and metal matrix composites) or diamond cutting disc (ceramics, electronics, biomaterials, minerals); proper cutting required the correct selection of disc type (hardness) as well as proper cutting speed, load and coolant.

iv. PACKAGING or MOUNTING the samples depending on the shape and zone that must be observed – mould in polymer (cold or hot embedding) or metal sample holders (clamping); small samples are generally mounted in plastic compound (thermosets, epoxies or thermoplastics) for convenience in


handling and to protect the edges from the specimen being prepared; En grave identification with electro pen;

v. GRINDING – Mechanical grinding papers or honeycomb type diamond discs up to #4000 grit; purpose of grinding is to generate a FLAT SURFACE necessary for the next steps; It goes from COARSE grinding to FINE grinding, by implying a series of abrasives; Samples must be rotated 90˚ between stages

vi. POLISHING (mechanical, electrolytic, chemical, electromechanical, electrochemical); the purpose is to obtain a final surface free from marks; Diamond abrasives are the most utilize d in polishing (3µm and 1µm), aluminium oxide powders are also applied for general purposes.

vii. ETCHING (chemical – most common - or electrolytic); is used to highlight and identify microstructural features or phases present on the sample. Etchants are usuall y dilute acid or dilute alkalis in water, alcohol or some other solvent. The acid or base is placed on specimen surface for seconds or minutes depending on the rate attack on the phases and their orientation.

1.4.4 Surface Effects after Grinding and Polishing

i. During grinding and polishing, you remove the deformed surface from your material which does not represent the microstructure; the idea is to see the non -deformed layer of the sample;

ii. GRINDING removes saw marks and levels and cleans the specimen surface . Polishing removes the artefacts of grinding but very little stock. Grinding uses fixed abrasives —the abrasive particles are bonded to the paper or platen—for fast stock removal. Polishing uses free abrasives on a cloth; that is, the abrasive particles are suspended in a lubricant and can roll or slide across the cloth and specimen.

iii. As you decrease the average particle diameter (increasing SiC grit designation), you reduce the

depth of disturbed material (roughness and deformation) as you increase from 100 to 800 and then 1000 your grinding paper, this means the particles inside it are smaller, thus it will make a more refine polish on the surface, removing previous deformations and also removing deformations caused by grinding itself.

iv. At first you remove the deformed smear zone, then the fragmented zone and contours of equal deformation until you reach the non-deformed region (figure);


1.4.5 Mechanical Polishing

Parameters: Speed, pressure, Time, Lubrication and Cooling (SPTLC)

Labour is a major variable in the process

The process is to do grinding first, polishing second, and buffing third. In general, grinding permits far more aggressive abrading action than polishing. Likewise, polishing is a far more aggressive abrading action than buffing.

In grinding, polishing and buffing, labour is a major variable in the process. The requirement is for highly skilled labour with years of experience and a thorough knowledge of the art of their craft.

The basic mill plate and sheet metal finishes for stainless steel include five grades that have finishes that are produced mechanically by using abrasive compositions and buffing wheels. There is also available on the market what is generically known as 'non -directional No. 8."

Special mechanical polishing procedures ar e required for preparing metal surfaces, such as stainless steel, for electropolishing. Mechanical polishing and buffing cannot be viewed as an adequate substitute for electropolishing in most applications due to the embedded abrasives and compounds, exposed grain structure of the metal, and the lack of the non -particulating, non-contaminating, and non-outgassing characteristics of an electropolished surface.

A mechanically polished metal surface yields an abundance of scratches, strains, metal debris and embedded abrasives. Mechanical polishing fails to remove inclusions, but also tends to push them further into the surface and even increase them by further pickup of abrasive materials which can lead to future points of corrosion. In contrast, the electropolishing process results in a surface which is completely featureless. It reveals the true crystal structure of the metal without the distortion produced by the cold -working process that always accompanies mechanical finishing methods.

https://www.delstar.com/characteristics-of-the-electropolishing-process

https://www.delstar.com/characteristics-of-the-electropolishing-process

https://www.delstar.com/electropolishing


1.4.6 Electrolytic Polishing

Excellent method for deformation-free polishing, but restricted mainly to single phase materials;

In electropolishing, the metal is removed ion by ion from the surface of the metal object being polished;

In basic terms, the object to be electropolished is immersed in an electrolyte (typically phosphoric and sulphuric acid) and subjected to a direct electrical current. The object is maintained anodic, with the cathodic connection being made to a nearby metal conductor (see diagram). In electropolishing, the metal is removed ion by ion from the surface of the metal object being polished.

During electropolishing, the polarized surface film is subjected to the combined effects of gassing (oxygen), which occurs with electrochemical metal removal, saturation of the surface with dissolved metal and the agitation and temperature of the electrolyte. Electropolishing selectively removes microscopic high points or "peaks" faster than the rate of attack on the corresponding micro-depressions or "valleys."

Source: Delstar.com

1.4.7 Chemical Polishing https://en.wikipedia.org/wiki/Chemical -mechanical_planarization

Chemical mechanical polishing/planarization is a process of smoothing surfaces with the combination of chemical and mechanical forces. It can be thought of as a hybrid of chemical etching and free abrasive polishing.

The process uses an abrasive and corrosive chemical slurry (commonly a colloid) in conjunction with a polishing pad and retaining ring, typically of a greater diameter than the wafer. The pad and wafer are pressed together by a dynamic polishing head and held in place by a plastic retaining ring. The dynamic polishing head is rotated with different axes of rotation (i.e., not concentric). This removes material and tends to even out any irregular topography, making the wafer flat or planar.

Typical CMP tools, such as the ones seen on the right, consist of a rotating and extremely flat platen which is covered by a pad. The wafer that is being polished is mounted upside-down in a carrier/spindle on a backing film. The retaining ring (Figure 1) keeps the wafer in the correct horizontal position. During the process of loading and unloading the wafer onto the tool, the wafer is held by vacuum by the carrier to prevent unwanted particles from building up on the wafer surface.

https://en.wikipedia.org/wiki/Abrasive

https://en.wikipedia.org/wiki/Slurry

https://en.wikipedia.org/wiki/Colloid

https://en.wikipedia.org/wiki/Polishing

https://en.wiktionary.org/wiki/concentric

https://en.wikipedia.org/wiki/Topography

https://en.wikipedia.org/wiki/Polished

https://en.wikipedia.org/wiki/Wafer


1.4.8 Etching, Cleaning and Keeping the Samples Non-metallic inclusions are better observable in non -etched samples;

i. Etching is an important step for adequate further visualization of the sample. This technique uses chemical action to produce lines on metal samples, in order to view the metal specimen under an optical microscope. On figure 1(a), Titanium sample was not etched and observed in Keyence Light Optical Microscope, using bright field illumination, and figure (b) shows the etched sample with obvious microstructure.

ii. Etching is used to highlight and identify microstructural features or phases present . Etchants are usually dilute acid or dilute alkalis in water, alcohol or some other solvent.

iii. Etching occurs when the acid or base is placed on the specimen surface because (for seconds or several minutes) of the difference in rate of attack of the various phases present and their orientation. The etching process is usually accomplished by merely applying the appropriate solution to the specimen surface.

iv. The most common technique for etching is the chemical etching . Other techniques such as electrolytic, thermal and plasma etching have also found specialized applic ations.

Cleaning the samples the samples are first cleaned with ethanol. After polishing they are also cleaned with acetone. After this cleaning the sample must be dried. Without this cleaning there is a possibility of corrosion of the sample.

http://www.asminternational.org/documents/10192/3460742/06785G_Sample.pdf/ad6f8964 -40da-4ff3-a2f5-c4647e2a94d8

Figure 1: Difference in a) non-etched and b) etched sample of Titanium.


2 Light Optical Microscopy (LOM) 2.1 Question 5

Discuss the image formation, path of the beam/light and

limitations (resolution, in-depth sharpness) of light

optical microscopy. How does the image form during

the observation in bright field, dark field and

differential interference contrast?

2.1.1 Image Formation, Path of the Beam/Light

2.1.1.1 First Explanation The microscope increases the angle of observation;

The Reflected Light Optical or Metallurgical Microscope is ideal for samples in which light is unable to pass through. Thus, light is directed onto the surface and eventually returns to the microscope’s objective lens by specular or diffused reflection.

On the first step, a Tungsten-Halogen Lamp emits light through the Collector Lens, Condenser Aperture Diaphragm and Field Diaphragm. The condenser concentrates light onto the specimen while its diaphragm regulates resolution, contrast and depth of field;

The beam splitter (or half mirror) is an optical device that splits a beam of light in two, reflecting and transmitting light, and can be used to recombine separate light beams into a single path. Deviated light goes out of phase, causing destructive int erference with the direct light that has passed through non -deviated. (Some of the light passes undisturbed in its path – non-deviated light - and some light is diffracted when it encounters parts of the specimen);

The objective lens gathers light from the object being observed and focuses the light rays to produce a real and inverted image; this lens is the one at the bottom near the sample;

Then, light reflected from the surface of the specimen re -enters the objective and is directed to the eye -pieces – ocular lens placed near the focal point of the objective – magnifying the intermediate image.

The eye lens of the eyepiece magnifies this image which is then projected onto the retina;

Reflected Light Microscopy Illuminator. Light passes through collector lens, being controlled by aperture and field diaphragms. Afterwards, a half mirror reflects the light through the objective to illuminate the specimen. Source: Olympus


2.1.1.2 Another Explanation

i. An object O of height h is being imaged on the retina of the eye O’’.

ii. The objective lens (Lo b) projects a real and inverted image of O magnified to the size O’ and height h’ into the intermediate image plane of the microscope.

iii. This occurs at the eyepiece diaphragm, at the fixed distance fb + z’ behind the objective.

iv. In this diagram, fb represents the back focal length of the objective and z’ is the optical tube length of the microscope.

v. The aerial intermediate image at O’ is further magnified by the microscope eyepiece (Ley) and produces an erect image of the object at O’’ on the retina, which appears inverted to the viewer.

vi. The magnification factor of the object is calculated by considering the distance a between the object O and the objective (Lob) and the front focal length of the objective lens (f).

vii. The object is placed a short distance ( z) outside of the objective’s front focal length ( f), such that z + f = a.

viii. The intermediate image of the object, O’, is located at distance b, which equals the back focal length of the objective ( fb) plus (z’), the optical tube length of the microscope.

ix. Magnification of the object at the intermediate image plane equals h’ . The image height at this position is derived by multiplying the microscope tube length ( b) by the object height (h), and dividing this by the distance of the object from the objective: h’ = (h x b)/a.

x. Source: http://www.olympusmicro.com/primer/microscopy.pdf

2.1.2 Limitations

Resolution At very high magnifications with transmitted light, point objects are seen as fuzzy discs surrounded by diffraction rings (Airy Disks). The resolving power of a microscope is taken as the ability to distinguish between two closely spaced AIRY DISKS.

Diffraction Limit Finite limit beyond which it i s impossible to resolve separate points . The diffraction patterns are affected by both the wave length of the light, the refractive material used to manufacture the lens and the numerical aperture of the objective lens .

http://www.olympusmicro.com/primer/microscopy.pdf


2.1.3 Bright Field *It is important to know how to draw all of them

Among the illumination modes, Bright Field (BF) is the simplest of them. The light beam strikes the sample perpendicularly, relating bright areas to horizontal zones in which the beam returns unaffected, and darker areas to tilted zones where the recurrent beam is scattered (Figure 4, a). Although the Bright Field image suffers from lack of contrast details, it supplies a general outline of the overall features on the specimen. Grain boundaries have darker colours since less l ight goes through the objective lens.

2.1.4 Dark Field A very important technique in reflected light microscopy is the dark field, which allows, through and oblique illumination, to obtain a bright contrast in regions with a small inclination regarding the surface.

As you increase the tilt of vertical illuminator, waves are directed away from the objective . The waves go through the mirror assembly and oval mirror (Figure 4, b), passing through an outer sleeve next to the objective lens towards a concave mirror and then finally hit the sample surface at highly incident angle .

Bright features are formed by areas with relief contour that direct light back through the objective lens, however most of the light is not reflected back, hence the dark background.

On this technique, it is advised that the field and aperture diaphragms located in the vertical illuminator remain opened to their widest points , avoiding that the light beam illumina ting the mirror assembly is blocked.

2.1.5 Differential interference contrast (DIC)

Material Scientists typically employ the reflection mode , also known as episcopic light differential interference contrast (DIC) , in opaque specimens that are highly reflective and do not absorb or transmit significant amount of incident light. This te chnique yields more complete analysis of the surface structure.

Topographical differences like slopes, depressions and other discontinuities on the surface of the sample create optical path differences in the reflected beam, which will further be transformed to amplitude or intensity variation by the illumination mode. The image can often be interpreted as a three dimensional representative, although depth may be misleading. The rainbow patterns along the features is caused as various colours destructively interfere at different locations on the surface, since the formation of final image is the result of interference between two distinct wave fronts that reach the image plane out of phase.

A birefringent prism (also known as Nomarski prism) is placed in th e space above the objective and a polarizer is installed in the vertical i lluminator. The prism will then divide the polarized wave lengths into two orthogonal polarized beams that will hit the specimen, creating a lateral displacement in regions of surface relief. Flat surfaces do not display any features. Once the beam returns through the objective and prism, it goes through a second polarizer ( analyser). The interference produces an intermediate image that is captured by the eyepiece and then image is ma gnified.


2.1.6 Polarized Light Configuration Polarizers can be inserted into the vertical i lluminator before the mirror unit, as well as before light

enters the objective (Figure 4, c), enhancing contrast and improving the quality of the image obtained. Optically anisotropic samples alter the state of polarization during the reflection process. The reflected wave goes through the objective and is projected onto a second polarizer (the analyser) which filters depolarized wave fronts, letting them pass. The tech nique is important to distinguish isotropic and anisotropic materials.

Learn how to draw:


Question 6

Light optical microscopy. Resolution. Numerical and angular aperture. Useful magnification of

the microscope. Lens defects and methods to be corrected.

2.1.7 Light Optical Microscopy

Simpler method for the analysis of solid materials

Two modes are typically employed, based on the measurement of transmitted or reflected light, from transparent to opaque sample respectively.

For metallurgy, samples are mostly opaque, hence the usage of the Reflected Light Optical Microscope (also called Metallurgical Microscope)

The Reflected Light Optical or Metallurgical Microscope is ideal for samples in which light is unable to pass through (opaque materials). Thus, light is directed onto the surface and eventually returns to the microscope’s objective lens by specular or diffused reflection, using a system of mirrors, prisms and semi-mirrored glasses which allows the light beam to pass in one direction and refl ects in the other.

Due to the inherent difference in intensity or wavelength of the light absorption characteristics of the different phases, contrasts are observed. These contrasts can be enhanced by etching.

2.1.8 Resolution

The ability to discern fine detai ls within a magnified image is referred to as the resolution of a microscope.

Since light is used as the illumination source in optical microscopy, the resolution is expressed in the same unit as the wavelength of the light (nm ). The theoretical resolution, d, of any optical system may be calculated using Abbe’s equation.

n sinµ is the numerical aperture with sinµ being the angular aperture. N is the refracting index of the medium in which the lens operates (mostly 1).

2.1.9 Numerical and Angular Aperture Numerical aperture is a number that characterizes a range of angles, and within these angles a system can receive or emit light. NA = n sinµ


It is clear that the resolution depends mainly on the numerical aperture .

The bigger its value, the higher the resol ution (the smaller d).

This numerical aperture can be changed by changing the medium, for example using oil (n=1.54) instead or air (n=1).

The numerical aperture can also be enlarged by a bigger collecting angle; this angle is bigger when the focal distance is lower or the width of the objective lens is higher. Of cours e these changes are restricted by geometrical factors. Theoretically the maximum angular aperture is equal to one, but in practice it is restricted to a value of 0.95. This of course also l imits the resolution of the optical microscope.

The best resolution is obtained with the highest numerical aperture and the lowest wavelength. The shortest wavelength for visible light is blue: 450 nm. The best lense s have a collecting angle of 70° which means that the best angular aperture is equal to 0.94. The highest resolution lenses work in an oil medium with a refractive index of 1.56. Together this gives a maximum resolution of about 200 nm.

dm i n = 1.22 * 450 nm/(2*1.56*0.94) = 202 nm

When two points on the visualized sample are closer than 202 nm, they will not be distinguished by optical microscopy.

http://www.olympusmicro.com/primer/anatomy/numaperture.html

http://www.olympusmicro.com/primer/anatomy/numaperture.html


2.1.10 Useful Magnification of the Microscope Whereas the resolution is influenced by the objective, the magnification is influenced by the ocular .

It is important to see the difference between resolution and magnification:

Resolution involves the visibility of details o n the sample.

Magnification only enlarges the view, but this doesn’t mean that more details are obtained. The ocular only magnifies the intermediate image, without giving the additional details in it. For the latter, the objective needs to be adapted, so that the resolution is better and details are revealed.

The objective characteristics thus determine the main characteristics of the microscope, namely the useful magnification limits and the global (general) magnification because you can magnify the image all you want but when the resolution is not good enough at those magnifications, you will not see a thing. Therefore, it is important that the real magnification lies in the range of the minimal and maximal magnification determined by the objective.

W rea l = Wobj ect i ve * Wocu la r

Wobjec t ive ,m i n = 500 * numerical aperture

Wobjec t ive ,ma x = 1000 * numerical aperture

Wobjec t ive ,m i n < W rea l < Wobjec t iv e ,ma x

If W rea l is smaller than the minimal objective magnification, details visible for the objective are lost because the magnification is not high enough. When W rea l is bigger than the maximal objective magnification, a blurred image will be obtained, because the magnification is out of the range for a good resolution. Recapitulatory the objective determines the minimal and maximal magnification at which a good image (good resolution) is obtained. When the real magnification does not lie within this range, the image will be blurred. (For an example see lecture 2, slide 39)

Example: If a mignification of 500x is needed, this means Wmin < 500 < Wmax

This can be written as 500*A < 500 < 1000*A we needed A between 0,5 - 1

If there is one objective with this condition: A is 0,65 with a magnification of 50, the magnification of the ocular is between 10 (to have 500x magnification) and 13 (because the magnification cannot be bigger than 650) which left only the ocular with magnification of 10 .


2.1.11 Lens Defects and Methods to be corrected Lenses used in optical systems do not give perfect images because of defects and aberrations. Luckily correction methods are available (see also figure 5.2 in physical methods and figures in lecture on lens defects).

Spherical aberration: The rays which are deviated from the optical centre have a focal point which is different from the one of the central rays . As a consequence, the image is not sharp. This defect can be corrected by applying lens corrections and/or placing a diaphragm in front of the le ns, but this reduces the numerical aperture, which in turn reduces the resolution. Another solution is the use of aspheric lenses.

Spherical aberration occurs because spherical surfaces are not the ideal shape with which to make a lens, but they are by far the simplest shape to which glass can be ground and polished and so are often used. Spherical aberration causes beams parallel to but away from the lens axis to be focused in a slightly different place than beams close to the axis. This manifests itself as a blurring of the image. Lenses in which closer-to-ideal, non-spherical surfaces are used are called aspheric lenses. These were formerly complex to make and often extremely expensive, although advances in technology have greatly reduced the cost of manufacture for these lenses. Spherical aberration can be minimised by careful choice of the curvature of the surfaces for a particular application: for instance, a plano -convex lens which is used to focus a collimated beam produces a sharper focal spot when used with the convex side towards the beam.

Coma formation: The surroundings of a point are distorted like a comet. When a lens is corrected for spherical aberration, coma formation can still occur. This is a type of aberration that affects rays which lie off the axis of the lens. Coma arises from differences in refraction indices of the rays passing through the inner and outer zones of the lens. Under these conditions the point images as a comet shape. This effect can be reduced by the use of a suitable l ens aperture.

Another type of aberration is coma, which derives its name from the comet -like appearance of the aberrated image. Coma occurs when an object off the optical axis of the lens is imaged, where rays pass through the lens at an angle to the axis θ. Rays which pass through the centre of the lens of focal length f are focused at a point with distance f tan θ from the axis. Rays passing through the outer margins of the lens are focused at different points, either further from the axis (positive coma) or closer to the axis (negative coma). In general, a bundle of parallel rays passing through the lens at a fixed distance from the centre of the lens are focused to a ring-shaped image in the focal plane, known as a comatic circle. The sum of all these c ircles results in a V-shaped or comet-like flare. As with spherical aberration, coma can be minimised (and in some cases eliminated) by choosing the curvature of the two lens surfaces to match the application. Lenses in which both spherical aberration and coma are minimized are called bestform lenses.


Chromatic aberration: A light source consists of different wavelengths. Rays with different wavelength have a different refraction index, which results in a different focal point. This is called chromatic aberration. It can be solved by using double or multiple lenses.

Chromatic aberration is caused by the dispersion of the lens material, the variation of its refractive index n with the wavelength of light. Since from the formulae above f is dependent on n , it follows that different wavelengths of light will be focused to different positions. Chromatic aberration of a lens is seen as fringes of color around the image. It can be minimised by using an achromatic doublet (or achromat) in which two materials with differing dispersion are bonded together to form a single lens. This reduces the amount of chromatic aberration over a certain range of wavelengths, though it does not produce perfect correction. The use of achromats was an important step in the develop ment of the optical microscope. An apochromat is a lens or lens system which has even better correction of chromatic aberration, combined with improved correction of spherical aberration. Apochromats are much more expensive than achromats.

Astigmatism: If a lens does not have perfect axial symmetry , the image plane for objects lying in one direction differs from the image plane for objects lying in another direction (the image is formed asymmetrically). Consequently, vertical components of the image focus in a different plane compared with the horizontal components and no sharp image plane exists, only a plane of least confusion between two sharply focused images. In optical systems this is inherent and relates to the manufacturing quality of the glass lens.

Complex and expensive objectives are available which improve the correction for formation of undistorted images and colours.


There are two types of corrections: achromatic and apochromatic. The resolution in optical microscopes is thus determined/restricted by the lenses of the optical system.

Achromatic doublet (or achromat) in which two materials with differing dispersion are bonded together to form a single lens.

apochromat is a lens or lens system which has even better correction of chromatic a berration, combined with improved correction of spherical aberration

Sources: Lecture 2, slides 34 to 39,

Flewitt:”Physical methods for materials characterization -Second Edition”, Chapter 5. Parts 5.2 and 5.3 .


3 Quantitative Metallography (QM) 3.1 Question 7

Quantitative metallography (Stereology). Grain size determination (visual evaluation, Jeffries,

Salticov and linear interception method) Phase quantification. Automatic quantitative analysis.

3.1.1 Quantitative metallography (stereology) Stereology is a group of statistical methods (several measurements are necessary to obtain a reliable result) to obtain the size of the structural constituents and elements of a material. Also the quantity of the phases can be calculated. The main problem with m etals is them being opaque (non-transparent). Thanks to appropriate mathematical assumptions, extension to 3D characterization is possible. These methods are based on the Kavalieri principle: If the cross sections are equal or proportional then also the objects are equal or proportional (see figure below). For all the methods, it is important to know the magnification.

3.1.2 Grain size determination - visual evaluation The American Society for Testing of Materials (ASTM) has introduced a grain size number N which is def ined as

n = 2N- 1

where n is the number of grains in 10 -4 square inch, or in 0.0645 mm 2, or in 1 in2 under 100x magnification. (Verify that these three definitions are

equivalent). N provides an excellent characterization of the grain size of the material. For most microstructures N has a value between 0 and 8, but n can

be negative or greater than 8.

If we recalculate for 1mm², then

𝒏𝟎 = 𝟐𝑵+𝟑

Where n0 is the number of grains in 1mm 2.

n0 is actually two times n where n is the number of grains at a magnification of 100:1.

The average surface of the grains S = 1/ n 0.

The average grain diameter d = 1/√𝑛0

The ASTM number is then given by G = -6.64*log10 (d) -2.95 where d is the grain diameter given in mm.


K=2n for M=100:1 and

(Kx=2nx) for Mx = M

3.1.3 Grain size determination – Jeffries method This method is also based on counting the number of grains in a predetermined view field (mostly a circle with a certain diameter). It is important to work with an appropriate magnification. When the number of grains inside the view field is too low, the calculation will not be representative. 60 to 70 grains is good. When the magnification is set, the number of grains completely inside the view field is counted. This value is called p. Also the number of grains partially in the view field is counted. This value is called q. Next nx is determined; this is the number of grains at the current magnification Mx.

nx = p+k*q with k a correction coefficient (the lower p, the smaller k)

Now n0 (the number of grains in 1 mm²) can be calculated:

n0 = (2*nx * M²x)/M² with M the standard magnification equal to 100:1

n0 is also equal to two times n: the number of grains at the standard magni fication M (view field is 0.5 mm²). Then N can be calculated from the above relationship between N and n 0. Again the average surface of the grain S and the average grain diameter d can be calculated as before.

3.1.4 Grain size determination (Salticov) This method is based on counting the number of triple junction points inside a predetermined view field (mostly a circle with a certain diameter). A triple junction point is a point where 3 grains meet. K is the number of these triple junction points inside the view field. K is then equal to 2 times n for a standard magnification M of 100:1. At the current magnification M x, K x is equal to 2 times n x. n0 is then calculated as follows.

n0 = Kx * M²x/M²

Again from this, grain size number N, the average surface of the grains S and the average grain diameter d can be calculated.


3.1.5 Grain size determination (linear interception method) This method is based on counting the grains that intersect with a predetermined line. P L is the number of intercepts of grain boundaries per unit length of the test line (the exact length of the test line must be known) and the average or mean intercept length (or average grain diameter) is then:

L3 = d/PL

For example, if you cross a line of 15cm, use the scale bar to adjust to the size of measurement. If 20 intercepts were counted, the average size diameter will be N A = size of line/number of intercepts.

The ASTM grain size number n can be obtained from the Hillard relation.

n = -3.36-2.88*ln(L3) with L3 given in mm

The amount of grain boundary surface per unit volume is called Sv and is equal to two times P L.

Attention: Best method if the question is in diameters (and not in surface, which would be Jeffries)

3.1.6 Phase quantification The Rosival method is a linear method to quantify th e average phase fraction. For this some lines are drawn and the total number of scale divisions is called L. Here it is thus not important to know the length of the test lines but rather the fractions. Li is the number of divisions that lay in the black constituent (second phase). Lav is then equal to the sum of all Li divided by i with i the number of test lines. The volume fraction is then given by V = Lav/L. Sometimes for high anisotropic materials, a circle is used instead of a line.

For example: cross 4 lines on your picture of 15 cm each. Make traces every 0.5cm. How many times a trace passed the white phase? Get this number and find the percentage of white phase in your material.

3.1.7 Automatic quantitative analysis This method is done automatically by image processing. The phases are quantified by the delineation of the pixels that belong to different phases based on the light intensity or colour differences. Starting from an optical microscopy image or a SEM image, a masked image is produced and then a binary image (2 colours). From this binary image, different phases are quantified. The advantage is the easy and fast data collection and the repeatability of the results. This method is however very sensitive to the sample preparation (which is operator dependent). This is an important disadvantage. The best option for quantitative characterization is the orientation mapping with EBSD but this requires highly specialized equipment and sample preparation.


4 X-ray diffraction 4.1 Question 8

Give the general theory about X-ray diffraction (Bragg law, reciprocal lattice, Ewald sphere).

Generation of X-rays. Discuss also the penetration depth, absorption and sample preparation for

XRD examination.

4.1.1 General theory (Bragg’s Law)

Related to scattering of waves that h it a crystal Bragg diffraction occur when radiation (with comparable to atomic spacing d h kl) is scattered by atoms of a system and undergoes constructive interference .

𝑛𝜆 = 2𝑑𝑠𝑖𝑛𝛳 →when x-rays are scattered from a crystal lattice, peaks of scattered intensity are observed which correspond to the angle of incidence = angle of scattering;

X-Ray Diffraction (XRD) is based on the diffraction of incident X -rays on a sample. The beam of X-rays has a thickness of a few mm which means that XRD is a macroscopic technique. No local information is obtained and the technique is less sensitive to imperfections. X-rays are photons with a wavelength of the order of a fraction of a nanometer.

A sample, for example a metal, consists of different atomic layers corresponding to its crystal structure (see figure below). When X-rays are incident on the metal, they are reflected by the different atomic layers of the sample (the sample somewhat acts like a mirror).

Thomson effect: scattering of X-Rays by electrons: diffraction

Actually the Thomson effect occurs: The X-rays are elastically scattered by the electrons of the atoms. The atoms are polarized by the X-rays, acting like separate emitters. Only the waves with a common tangent to the wave front (coherent waves) can leave the material, the other waves interfere destructively. The path difference between the reflected X-rays of different atomic layers corresponds to the interplanar distance dhk l, between the atomic layers which is characteristic to the crystal stru cture. The reflected waves are detected only when constructive interference occurs (when the reflected wave lengths are coherent, in phase). This means that Braggs law needs to be fulfilled.


n ∗ λ = 2 ∗ dhkl ∗ sin θ

n is the order of diffraction , θ is the diffraction angle and actually determines the direction of the crystal planes with respect to the X-rays at which interference occurs. This angle is changed by rotating the sample. Constructive interference only occurs when the difference in path length equals an even number of times the wavelength of the source . If not the waves cancel out and no signal is detected. By measuring theta and knowing λ, the interplanar spacing can be determined and the crystal spacing identified. Also the lattice parameter or the miller indices can be obtained.

𝑑 =𝑎

√(ℎ2 + 𝑘2 + 𝑙2) 𝑓𝑜𝑟 𝑎 𝑐𝑢𝑏𝑖𝑐 𝑐𝑟𝑦𝑠𝑡𝑎𝑙

These values are compared to measurements of samples and with random orientations (powder). This means that XRD is a relative measurement.

4.1.2 Reciprocal Lattice The reciprocal lattice is constructed to aid the interpretation of diffraction from crystal lattices.

In real space crystal planes are defined by their intercepts on coordinate axis, usually with axis units being defined as the Miller Indices hkl.

Planes with intercepts hkl have families of planes nh, nk, nl that are parallel to hkl and contribute to a diffracted beam.

These planes are separated by a distance𝑑ℎ𝑘𝑙

𝑛.

Check https://www.youtube.com/watch?v=fZ0m8wustVk

In the reciprocal space reciprocal lattice is constructed for a defined crystal lattice by drawing a line from the origin, normal to the lattice plane hkl . This will be of length g = 1/dhkl = d*hkl and is equal to the reciprocal of the interplanar spacing d hk l. The reciprocal lattice points correspond both to planes with miller indices hkl and those with indices nh, nk, nl which al so contribute to diffraction. Thus, the reciprocal lattice defines a range of potential lattice sites that may lead to diffraction. A particular lattice type may be characterized by absent diffraction positions and the corresponding points in the reciprocal lattice will be missing. For example the reciprocal lattice of BCC is FCC and vice versa. Also an hkl vector in the reciprocal space is perpendicular to an hkl vector in the real space. The diffraction of an X-ray beam can be predicted from the reciproca l lattice using the Ewald construction or Ewald sphere.

Each spot is a set of planes in our unit cell;

The intensity of each spot is related to the amount of scattering matter on that set of planes

The distance g between spots is 1/dhk l;

1/dhkl

https://www.youtube.com/watch?v=fZ0m8wustVk


4.1.3 Ewald Sphere The Ewald Sphere is used to predict the reciprocal lattice of an X -ray diffraction. The Ewald circle

represents in reciprocal space all the possible points where planes (reflections) could satisfy the Bragg equation.

The incident X-ray beam is considered to pass through the origin (0 0 0) in both real and reciprocal space. A sphere is then drawn with a radius of 1/λ (diffraction sphere) inside a limiting sphere of

radius 2/.

The centre of the diffraction sphere is on the incident beam direction and position as well, as such that the surface of the sphere passes through the origin .

This sphere is known as the Ewald sphere or the diffraction sphere. Diffraction of the X -ray beam will

only occur if the Ewald sphere passes through a reciprocal lattice point r* hk l when another reciprocal point (that is not the origin) touches the sphe re, like r*, the Bragg condition is satisfied;

k1 represents the diffracted wave vector, k 0 the incident wave vector and g the reciprocal lattice vector corresponding to the diffracting planes.

The condition here for diffraction to occur is thus that the change in wave vector k1 must be equal to a vector of the reciprocal lattice (which is perpendicular to the hkl planes in real space and has a length of the order of the reciprocal of the interplanar spacing).

When the sample is rotated (and hence the r eciprocal lattice points and the Ewald sphere), different crystal planes can be analysed. Since the wavelength stays the same, so does the diameter of the Ewald sphere and no reciprocal lattice points outside a sphere of radius 2/λ can pass through the Ewald sphere and therefore cannot diffract the X-ray beam so that this is called the limiti ng sphere.

Please check https://www.doitpoms.ac.uk/tlplib/reciprocal_lattice/ewald.php

g=1/dhkl

https://www.doitpoms.ac.uk/tlplib/reciprocal_lattice/ewald.php


4.1.4 Generation of X-rays X-rays can most easily be produced by bombarding a material surface with relatively high energy electrons , which were accelerated by a certain voltage.

A preheated filament (mostly Tungsten) is used as a cathode and emits electrons which are accelerated to the anode by a positive voltage of 20-50 kV. The electrons generate X-rays after collision with the anode . The higher the atomic number of the material of the anode, the lower the wavelength of the produced X -rays. The X-rays escape through a Beryllium window.

In practice it is normal to use metals to produce X -rays for use in XRD because an intense beam of X -rays is desired and the good thermal conductivity of the metal allows the heat produced during bombardment with an intense high energy electron beam to be readily removed thus avoiding damage to the source.

When a high energy electron collides on the material, X-rays are produced in two ways. Because the incident electrons are decelerated by the material they emit a continuous spectrum of bremsstrahlung (inelastic scattering). The intensity of these X-rays is a function of the electrons energies and the atomic number of the target. The incident electrons also cause the surface atoms to be ionized by the removal of an inner shell electron. As the atom rearranges with electrons from outer orbitals falling into the hole created, energy is released in the form of a photon. The probability that these characteristic X -rays will be emitted increases with atomic number of the target. Normally these characteristic peaks are used to produce diffraction patterns in XRD.

Another explanation:

Sometimes the electron comes very close to a nucleus in the target and is deviated by the electromagnetic interaction. In this process, which is called bremsstrahlung (braking radiation), the electron loses much energy and a photon (X-ray) is emitted.

The high energy electron can also cause an electron close to the nucleus in a metal atom to be knocked out from its place. This vacancy is filled by an electron further from the nucleus. The difference in binding energy is emitted as a photon. This photon is detected as an x -ray line in the energy spectrum.


4.1.5 Penetration depth

The electrons generate X-rays after collision with the anode

Since the wavelength of the produced X-rays depends on the material of the anode on which the electrons are bombarded, a higher atomic number Z of this material causes the X-rays to have a lower wavelength.

Z =

This means that the X-rays have a higher energy which influences not only the resolution but also the penetration depth.

The penetration depth is higher when the energy of the X -rays is higher. The penetration depth also depends on the absorption coefficient of the material. (I recommend to read further on the third question 1.3.2.2).

Energy = Voltage; = Resolution; Penetration Depth

4.1.6 Absorption During the measurement a diffractogram is obtained.

This is a graph of the intensity in function of two times theta {I(2)}. The peaks on this graph correspond to constructive interference and the angle at which they occur is a characteristic for the material examined. This means that for the angle, the conditions of measurement do not have an influence on the dominant peaks, because they are only dependent on (and characteristic for) the crystal lattice type of the material . The intensity does depend on the conditions of measurement though; more precisely it depends on the source, scan speed and increment:

The scan speed is the speed at which the sample is scanned. When this speed is higher, the intensity of the peaks will be lower.

The increment is the step at which two theta is changed. The lower its value, the higher the resolution. The intensity of transmitted waves is never the same as the intensity of the incident X-ray beam because a part of the intensity is always absorbed by the m aterial. This absorption is described by the absorption coefficient of the material.

A high absorption coefficient is associated with a high atomic number.

I = I0 ∗ exp (−µ ∗ t)

This absorbed intensity is used for example the Thompson effect. Indeed the electrons inside the material elastically scatter the X-rays by emitting X-rays themselves in the electromagnetic field created by the incident X-rays. These X-rays have the same frequency and therefore the same energy as the incident X -rays. These created X-rays are then used for diffraction measurements.


4.1.7 Sample preparation

Easy For XRD the sample preparation is less intensive than for optical or other kinds of microscopy, since not an image is required for the sample analysis but only diffraction is meas ured. This means that there is no need for etching the sample. However the sample should be flat since diffraction occurs on parallel planes at different diffraction angles so polishing is still needed.

Solid Samples from unprepared pieces of metal to cut and polished metal samples. The ideal is a perfect flat surface. Irregular sample surfaces change the distance from the sample to the x-ray source and introduce error. All X -rays are calibrated based on a fixed sample -to-source distance, and changing this distance can vary your intensity.

Loose powder must be put into a plastic sample holder with a plastic support film; the more finely ground and homogeneous, the better is the analysis.

For X-ray diffraction we must have a single crystal. The crystals should be transparent and appear to

contain no flaws when viewed under the microscope. Crystals that are cloudy, have cracks, appear to have other crystals buried inside or intergrown crystals protruding from the side should be rejected.

Extra

Condition for planes (you better know this table):

H+K+L=2n BCC

H,K,L =>all or 2n or 2n+1 FCC


4.2 Question 9

Application of X-ray diffraction. Methods for XRD measurements (Laue, Debay-Sherrer).

Architecture of the X-ray diffractometer and focusing schemes. Determination of the type of the

crystal lattice, phase analysis, determination of the lattice parameter.

4.2.1 Application of X-Ray Diffraction

Qualitative, Quantitative and Texture

XRD is a very useful tool to identify crystalline phases and the orientation of a material. It is also a non-destructive method which is a large benefit.

XRD can also be used to determine some structural properties of a material. The lattice parameter, residual stresses, strain, grain size, phase composition and thermal expansion can be determined by using XRD. You can also measure the thickness of thin films and multilayers with XRD. T he texture can also be determined by using XRD.

XRD can be used in two different ways:

It can be used to determine the wavelength of the incident X -rays. This is done by using a known sample where you know the interplanar spacing d hk l. When you measure the diffraction angle θ you can calculate the wavelength λ from the Brag g’s law .

A second and more frequently used way to use the XRD is to calculate the interplanar spacing dhk l of a sample. Therefore, you use an X-ray source with known wavelength λ. The diffraction angle θ is measured by XRD and then you can calculate the in terplanar spacing from the Bragg’s law. When you know the interplanar spacing of the peaks you can calculate to which phase each peak belongs. In that way you can determine which phases are present in the material.

Identify phases and their composition

Orientation Atomic Arrangement (Structure of Crystals) -

Lattice parameter

Residual Stress

Grain Size Thermal Expansion Texture Measure thickness


4.2.2 Methods for XRD measurements There are two main methods for XRD measurements (Laue and Debye -Scherrer).

4.2.2.1 Laue Method

Determine orientation of large single crystal

White radiation is reflected from or transmitted through a fixed crystal;

Variation of wavelength

Each plane (that is suitable) d iffracts, turning into a different dot (diffraction pattern)

The Laue method is for the determination of the orientation of large single crystals and the type of lattice. Therefore white radiation is used. This implies that d hkl is fixed and λ changes . The white, polychromatic radiation provides the range of wavelengths necessary to ensure that the Bragg’s Law is satisfied for all planes. Each set of planes picks out and diffracts the particular wavelength from the white radiation. Each curve therefore corresponds to different wavelength. The spots lying on any one curve are reflections from planes belonging to one zone. Reflections from planes of the same zone all lie on the surface of an imaginary cone whose axis is the zone axis.

The Laue method can be done in two different ways: back-reflection Laue or Transmission Laue (see picture).

In the back-reflection method the film is placed between the source and the sample . The beams which are diffracted in a backward direction are recorded. The film intersects the imaginary cone, with the diffraction spots generally lying on a hyperbola

In Transmission Laue the film is placed behind the sample to record beams which are transmitted through the crystal. The film intersects the cone with the diff raction spots generally lying on an ellipse.

Crystal orientation is determined from the position of the spots. Each spot can be indexed using special

charts each spot is a particular plane. You can also use these methods to check if the crystal was bent or tilted, because the spots will be distorted.

Zone axis


4.2.2.2 Debye-Scherrer Method Incident beam of monochromatic X-ray interacts with

specimen.

This specimen must contain sufficient particles with the correct orientation to allow diffraction from diffracting planes when rotated in the x-ray beam;

The Debye-Scherrer method is also called the powder method.

The Debye-Scherrer camera is a flat cylinder. On the walls of the cylinder a photographic film is placed. Through illumination of the diffracted X-rays after developing segments of the diffraction cones shows.

Determination of lattice parameter and type of lattice

Here monochromatic X-ray source interacts with fine grained polycrystalline (notice the rings instead of dots) powders with random texture.

In a powder sample typically all possible orientations are present, so that always some crystals will have lattice planes that are oriented at the corresponding Bragg angle with respect to the incident beam.

The angle between the diffracted radiation and the transmitted radiation is always 2θ (2x the incident angle) . The diffracted beam intensity provides a measure of the distribution and position of atoms within the crystal.

Comparison of Debye-Scherrer ring and diffractogram


4.2.2.3 Bragg’s Method Not asked on the question*

Determination of different phases in the material

Diffractogram {I(2)}

The mostly used method is the Bragg-Brantano set-up (see picture). Here the source is fixed, the sample rotated with a speed θ/∆t and the detector moves with a speed of 2θ/∆t. The step size of turning determines the resolution of the measurement. The source is an X-ray tube with a filter (mostly Kβ-filter) that makes the beam monochromatic. It also has Soller-slits; these are some kind of apertures that focus the beam by cutting it.

With this method you can determine the l attice parameters and the type of lattice of the sample. The detector can be an ionization detector or and Scintillation detector (see EDX). We also have to watch out for fluorescence ; this problem can be solved by placing a filter in front of the detector .


4.2.3 Determination of the type of the crystal lattice, phase analysis, determination of the lattice parameter *This is often asked on the exam

One way to determine the type of crystal lattice is by analysis of a diffractogram. You can obtain quantitative phase fraction and lattice parameter information. In the next figure you can see a diffractogram of single crystal (one family of peak) and polycrystal (several peaks):

Now that we know the different methods, we try to determine the type of crystal lat tice. Therefore, we need the Bragg’s Law and the definition of dhkl:

If some information is given (n=1, 2 (rad), =0.7E-10m); you are able to find the Diameter and relate to the diffraction data tables:

28.6°

2= 14.3° 𝑥 180° = 𝜋 𝑟𝑎𝑑 14.3° = 0.249 𝑟𝑎𝑑 𝑠𝑒𝑛 0.249 𝑟𝑎𝑑 =

0.2464 𝑟𝑎𝑑

𝑑 = 0.7 ∗ 10−10

2 ∗ 0.2464⁄ = 1,42 Å

A table relating d and hkl can be given, or you will have to calculate it yourself.

This table will have information about which phase you are dealing with and your Miller Indices.


And if you have to calculate it yourself? We can play with these two formulas

When we substitute one formula in another and calculate sin²θ we get:

In this method the wavelength is kept constant and for the same type of lattice the interatomic distance a is off course constant as well. Consequently, for each two peaks of the same type of lattice is valid:

Here k is the reference peak. These ratios tell us to which phase the different peaks belong because each phase has different ratios that can be extracted from tables. Now that you know this, you can make the indexation of the diffraction pattern. Therefore you use the second part of the equation above and the fact that for BCC crystals the sum of h,k,l has to be even. For FCC structures h,k,l all have to be odd or even .

To get the right angle 2θ you have to pay attention to some details. The background has to be taken into account. You have to be careful with overlap of different peaks. Next to these two also a defocusing error and an error caused by absorption can be taken into account. Probably the best method to calculate the right θ is by determining at which angle the gravity centre of the peak is situated.

The lattice parameter can also be determined. Therefore, we use of:

*Past exam question

Interpolation

We can calculate a for all different θ hkl. To calculate the extrapolated a we plot all the calculated a’s versus the function f. The zero axis gives us the extrapolated a.

The lattice parameter can change with introducing of stresses or by changing the temperature.


4.3 Question 10

Application of X-ray diffraction. Quantitative phase analysis, internal stresses measurement.

4.3.1 Application of X-Ray Diffraction - Quantitative Phase Analysis QPA

X-Ray powder diffraction is one of the most powerful methods to perform QPA.

Each crystalline phase of the material gives a characteristic diffraction pattern independent from other phases

The intensity of a peak is proportional to its fraction

XRD can measure quantitative phase analyses. Therefore, you have to know the density ρ, absorption coefficient μ and the intensity of the phase I when it’s 100% . Then, by measuring the real intensity and the use of some formulas you can calculate the volume fraction of the phase in the material.

It has to be noted that you first have to clean up the spectra before starting the calculations ( subtract background, eliminate α2-peaks …)

The phase fraction of austenite in iro n can be calculated in this way:

K is a factor (instrumental factor constant) depending on the nature of the phase, selected diffraction line and geometry of the diffractometer.

Source: Rigaku


To calculate the volume fraction, one has to know the miller indices of your sample. Afterwards apply in the formula:

For example, for retained austenite:


4.3.2 Internal Stresses Measurement (Residual Stress) For this measurement, one will get a graph similar to this one:

In case of an unstressed sample, the graph would be a line with no change in y axis (n o variation in d); this graph is a change in d caused by compressive test, which can be seen because the interplanar spacing d of

the plane (311) is varying according to the angle (sin 2ψ) reduction in size.

To determine the residual stress on the practical class, the following formula was used:

E and are given. m is obtained from the curve plotted. If m is negative compressive.

Internal stresses are static multiaxial stresses and related strains, in an isolated material that isn’t subjected to an external force. These stresses cause a change in the interplanar spacing d hk l. In an XRD-measurement this can be measured by the change in diffraction angle 2θ in comparison to the stress-free state.

It has to be noted that this method is only valid for crystalline materials.

For a crystal that is free from stresses the Bragg’s law is valid. But influenced by an interal stress σ , the interplanar spacing d hk l chances from d0 to d in a uniform way. This means that the peak in the XRD -spectra shifts. (Learn how to draw this figure)

The influence of a non-uniform residual stress on microscale gives rise to a peak broadening whereas equal areas are in compression as there are in a tensile condition. Therefore there is no shift of the peak. This peak broadening can be calculated by differentiation of the Bragg’s Law.

Uniform residual strain – peak shift

Non-uniform residual strain – peak broadening


4.3.2.1 Sin2ψ method

Goal – find Residual Stress σΦ

Link the force applied on the lattice (and the change in d) to the stress that is left even when you are not applying a force anymore;

It is clear that the change in d hk l and so also the strains can be measured by XRD. To make the link between these strains and the residual stresses we make use of the elasticity theory (Hooke’s Law: [σ i j]=[E i j][ε i j]). In the general case of internal, homogenous, residual stress a spherical volume unit is changed to an ellipsoid. The axes of this ellipsoid are the main axis of the σ’s and ε’s. Planes that are perpendicular to these axes aren’t subjected to shear stresses (shear normal to the surface = 0) .

So when a material is anisotropic the mechanical properties are not depende nt on the direction, so at the surface of the material the following equations are valid (Hooke’s Law):

To determine the residual stress, we have to determine the residual stress σ Φ in an arbitrary direction in reference to the main axes. Theories have proven that therefore only two measurements have to be done; we have to calculate ε 3 and εψ:


A first measurement of dhk l is taken when the (hkl)-planes are parallel to the surface. Hereby we can calculate ε 3.

In a second measurement, dhkl is measured when the normal of same (hkl) -planes and the surface have angle of ψ between them (practically ψ is often 45°). In this way ε ψ can be determined.

When you know these two strains, you can easily calculate the residual stress. This method is called the sin² ψ-method.

Assuming that the stress normal to the surface is zero, the biaxial stresses σx = σy and taking into consideration the strain along a specific direction,

Sources:

Lecture 9, ”X-ray diffraction” slides 47 to 51,

Flewitt:”Physical methods for materials characterization-Second Edition”, Chapter 4. Parts 4.3.8, (file IP556_CH04.pdf)

B.C.De Cooman “Materiaalkundige observatietechniken” File: “Chapter 18.pdf” Chapters 3.6.1.”Meting van interne spanningen”

Practical classes report

Strain along a Specific Direction


4.4 Question 11 *Hot Question

Texture measurements: What is texture and how do we represent individual crystallographic

orientations and textures. What is a pole-figure, inverse pole figure and an ODF?

4.4.1 Texture

Polycrystalline materials

Preferential Orientation (planes are not random)

Texture is a term that is related to polycrystalline materials. Polycrystalline materials are an aggregate of single crystallites with all their individual orientation with respect to the sample reference system. Textured materials are materials in which the individual crystallites have a preferential orientation with respect to the sample reference system.

The opposite of a textured material is a textureless or random textured material.

By crystallographic orientation I actually mean the comparison of two different coordinate systems: the crystal reference system KC and the sample reference system KS. When the sample is a rolled material the sample reference system is often the rolling direction (RD), the transversal direction (TD) and the normal direction (ND).

Other specimens, such as a tensile test piece, a rod or a wire have only uniaxial symmetry and hence it is only necessary to specify one axis in the specimen coordinate system, the other two axes can be chosen arbitrarily.

The crystal coordinate system (K c) is specified by directions in the crystal. The choice of directions is in principle arbitrary, although it is convenient to adapt it to the crystal symmetry. For example, for orthogonal symmetry, [100],[010] and [001] al ready form an orthogonal frame and are often adopted as the crystal coordinate system.


4.4.2 Representation of Texture and Individual Crystallographic Orientation The representation of individual crystallographic orientations and textures can be done in diffe rent ways.

4.4.2.1 Rotational Matrix The first option is by the rotation orientation matrix [g] (see figure). Each column of the matrix [g] displays the direction cosines of a sample reference axis with respect to the crystal reference system K c.

Both rows and columns of the matrix are unit vectors, that is, the matrix is orthonormal and the inverse of the matrix is equal to its transpose. Since a crystal orientation needs only three independent variables to specify it, it is clear that the matrix, having nine n umbers, contains non-independent elements. In fact the cross product of any two rows (or columns) gives the third and for any row or column the sum of the squares of the three elements is equal to one.

4.4.2.2 Miller Indices

(hkl) crystallographic plane, paral lel to rolling plane

uvw crystallographic direction parallel to Rolling Direction

A second way of notating the orientation is by using Miller Indices (hkl)[uvw]. In this notation (hkl) is the crystallographic plane which is parallel to the rolling plane. Direction [uvw] is the direction that is parallel to the rolling direction. By using formulas it is possible to go from the rotation (orientation) matrix to the Miller Indices and vice versa. A very famous orientation is the Goss orientation (110)[100]. It is known for its very good electrical properties.


4.4.2.3 Euler Angles A third way to represent the orientation is by using Euler Angles . The Euler angles refer to three rotations which, when performed in the correct sequence, transform the sample coordinate system SCS (Xs Ys Zs) onto the crystal coordinate system CCS (Xc Yc Zc). There are several different conventions for expressing Euler angles but the most commonly used are those 3 steps formulated by Bunge:

i. Rotate the SCS around the ZS axis with an angle 1. The XS axis will then be in the XCYC-plane of the CCS.

ii. Rotate the SCS around the XS axis with an angle Φ until ZS coincides with ZC.

iii. Rotate the SCS around ZS again, but with an angle 2 until XS coincides with XC and Ys coincides with YC.

These rotations can be written analytically in the form of a matrix. By multiplying these three matrices you obtain t he rotation orientation matrix.

These three angles can be plotted in the Euler Space.

Symmetry reduces Euler Space

An Euler space is a 3D representation of orientations expressed in terms of its Euler angles. This red dot in the image is an

orientation expressed in terms of Euler angle , and its

coordinates are (1,Φ,2).


Each point in the Euler space determines only one crystallographic orientation , and each 3 Euler angles determine a position in the 3d space . The opposite is not true: the same crystallographic orientation can be represented with different Euler angles. The Euler space does not have linear borders. It‘s not a linear space.

Properties of the Euler Space:

In the most general case the Euler angles are defined in the range 0°≤ 1/2 ≤2π and 0°≤Φ≤π which defines the maximum size (volume = 8π²) of the Euler space, the so-called asymmetric unit (the maximum size of Euler space). However symmetries lead to a reduction in the size of the Euler space.

Crystal symmetry can reduce the Euler space. In general each n -fold symmetry axis reduces the Euler space by a factor of n. For example, in a Cubic crystal there are 24 equivalent ways of attaching a right -handed orthogonal reference system to a cube. This means that there are 24 equivalent points to represent one single cubic orientation in Euler space. So the fundamental zone V’=V/24.

Therefore: 0° ≤ 1 ≤ 2π

0° ≤ Φ ≤ π/2

0° ≤ 2 ≤ π/2

Here the three-fold axes aren’t included because they would lead to a too complex subspace. So for cubic crystals each orientation appears three times in the reduced Euler space.

Next to crystal symmetry also sample symmetry can reduce the Euler space. In samples deformed by rolling or more generally under a plane-strain deformation state, it is usually assumed that there is a two -fold symmetry axis parallel to each of the three sample axes (orthorhom bic sample symmetry). Therefore the Euler space is again reduced by a factor of 4.

Therefore: 0° ≤ 1 ≤ π/2

0° ≤ Φ ≤ π/2

0° ≤ 2 ≤ π/2

Step by step:

Different sample symmetries affect the range of the angle 1 reduce Euler Space

When there is no symmetry, 0° ≤ 1 ≤ 360°.

If one symmetry element is present, 0° ≤ 1 ≤ 180°.

If a two-folded symmetry axis is present, then we have 0° ≤ 1 ≤ 90°.

Crystal symmetry further reduces the size of the Euler Space by affecting the range of Φ and 2.

N-fold symmetry axis reduces Euler space by a factor of n


4.4.3 Orientation Distribution Function ODF A representation of the Euler space can be done with ODF (Orientation Distribution Function). ODF give a complete image of all the texture components that are present.

ODF f(g) is a probability density function describing the probability of finding a grain with an orientation g within a given distance in orientation space (∆g) of a specified orientation g 0 or alternatively the volume fraction of material oriented within ∆g of g 0.

The units of an ODF are time the random intensity.

A texture can be described by the Orientation Distribution Function (ODF);

Orientation g of each crystal in the sample is quantified

The orientation of this crystal is determined by the sample reference system

ODF = volume fraction of crystals with orientation g+dg

Random texture Constant f(g) = 1/8π2.

Texture function has a determined maximum

When you measure the texture grain by grain, and plot each orientation in the Euler space Obtain ODF.


4.4.4 Pole Figure Orientation can also be plotted as two dimensional projections in pole figures . Such figures can be useful for simplifying the analysis of the orientation distribution. A pole figure shows the position of a pole (a normal to a lattice plane) relative to the sample reference frame (RD, TD, ND). So it’s a stereographic projection that gives the distribution of one crystallographic direction in the material.

For rolling materials ND is typically chosen to be the North Pole. The RD-TD plane is the projection plane. To project a pole onto the pole figure you have to link the pole with the South Pole. The intersection of this line with the projection plane gives you the projection of the pole onto the pole figure.

So far, only individual poles have been considered. However one pole does not give the entire orientation information, since the crystal can still rotate about this particular pole. The orientation is fully characterized by three poles. Sometimes two poles are enough depending on the symmetry of the crystal and/or the poles.

So the pole figure is a semi-quantitative method. It shows the d istribution of <hkl> crystallographic poles with respect to the sample reference system. In a pole figure the sample reference system and the crystal pole <hkl> must be represented. A pole figure displays the sample symmetry (orthorhombic horizontal and vertical symmetric/ monoclinic only vertically). To conclude you have to know that one pole figure cannot represent the complete texture. You need in general three pole figures.

4.4.5 Inverse Pole Figure Instead of a pole figure you can also use the Inverse Pole Figure to display the orientation. In the inverse pole figure the orientation of the sample coordinate system is projected into the crystal coordinate system. So the reference system of the inverse pole figure is the crystal coordinate system and the ‘orientation’ is defined by the axes of the sample coordinate system (RD, TD, ND). According to the crystal symmetry it is not necessary to show the entire pole figure, but just one unit triangle. In an inverse pole figure the crystal reference system and the sample direction must be represented. Just like a normal pole figure an inverse pole figure displays the crystal symmetry and doesn’t represent the complete texture.

Pole Figure Sample Reference System

Inverse Pole Figure Crystal Reference System


This is a Pole Figure . It’s colours indicate a direction that can be seen in the triangle: Blue is 111, Red is 001 and green is 101. RD stands for Rolling Direction, ND is Normal Direction and TD is Transverse direction.

Also very important:

4.4.6 Kernel Average Misorientation (KAM)

For KAM calculation, the misorientation between the centre point of the kernel and all surrounding points in the kernel are calculated and averaged, which gives the local misorientation value of the centre pixel.

Substructures, having misorientation lower than 5°, are identified by kernel average misorientation (KAM).

This map has a value for each pixel equal to the average disorientation that pixel has with its neighbours.

While the Grain Average IQ-method is an average method that compares image qualities of different grains, the KAM-method is more local and compares orientation gradients between different points. This implies that the area selected based on the Grain Avera ge IQ-method will always correspond to the junction of several grains, whereas the area selected based on the KAM-method not.


Observe the relationship between colours.

Knowing this graph is very important.


4.5 Question 12

Practical aspects of texture measurements by XRD (geometry of the measurement scheme).

Sample preparation. Examples of rolling, textures, recrystallization textures and transformation

textures in FCC and BCC crystal structures.

4.5.1 Practical aspects of texture measurements by XRD - Geometry of the Measurement Scheme

Bragg’s Law is the law that governs XRD = 𝑠𝑖𝑛 = 𝑛/2𝑑

To discuss the practical aspects of a texture measurement we start with discussing the geometry of the arrangement. A texture measurement is most of the time done with a special diffractometer, equipped with a texture Goniometer (Euler-Cradle).

Texture Goniometer X-Ray source and X-Ray counter positioned

according to the Bragg angle 2

Eulerian Cradle Important piece of the Goniometer, that combined create multi-circle (four-angle) diffractometers.

With this equipment, one measure the texture using x-ray diffraction through a method called “Schulz Reflection Method”

Check:https://www.doitpoms.ac.uk/tlplib/crystallographic_texture/texture_measaurement.php

The method that is most commonly used is called the Schulz reflection method. In this method we have a sample holder that can make 4 different movements:

1) A translation (omega) to average the orientations by

measuring more grain orientat ions usually constant at 0°;

2) A rotation (phi) about the normal of the sample surface

3) A rotation (chi) χ about the orthogonal axis

4) The classical θ-2θ rotation

https://www.doitpoms.ac.uk/tlplib/crystallographic_texture/texture_measaurement.php

https://www.doitpoms.ac.uk/tlplib/crystallographic_texture/texture_measaurement.php


During a measurement there is a continuous rotation of the -angle and a step wise change of the χ -angle (for example 5°). Meanwhile the intensity of an (hkl) -plane reflection is measured for a fix ed Bragg angle.

The χ-angle normally only goes from 0 to 70° so we get an incomplete pole figure. Therefore you need to take three or four incomplete pole figures to get the total information of the total texture, orientation.

Typically is kept at 0°, because if you change it, there will be no more symmetry between the X -Ray source and X-Ray counter (which are perfectly positioned to satisfy the Bragg-Brentano arrangement, at

the Bragg angle ). When you do change , is to measure the quality of the crystal, and to derive exact peak shapes.

4.5.2 Sample Preparation It is clear that the surface of the sample that you want to investigate has to be as flat as possible. So you always have to be careful during the sample preparation that you don’t make any deep sc ratches on the surface during grinding. You also have to use a special kind of sample holder. Otherwise you would measure the mounting material and not the sample itself. Next to this there is no special sample preparation necessary for an XRD-measurement.

A sample with a flat surface is mounted on the sample holder with its normal direction parallel to the axis

of the rotation.

Azimuth

Sample

Detector

Source


4.5.3 Examples

This sample is rotated in its plane around the axis. This angle corresponds to the azimuth of a pole in a pole figure.

After a full rotation, the sample is tilted on the axis. and (pole figure radial angle) are defined in the

opposite direction = 90° - .

The limiting value of in the Bragg-Brentano focusing condition is when both incident and ref lected beam are parallel to the sample (90°), but usually 60 -85° are used. The limiting factor is mostly because the

intensity of a peak decreases with increasing .

By rotating the sample, the projection of the beam onto the samples surface becomes incre asingly elongated. Furthermore, different incident angles θ add an additional distortion of the projected beam. These things should also be kept in mind when doing a texture measurement. On the figures you can see

the different angles and .

In general, absorption of the X-rays increases with the atomic number of the analysed sample material and with the wavelength of the X-rays. Shorter wavelengths are less absorbed than large ones. However, there are some combinations of sample and target materials whic h yield anomalously high absorption. Absorption is undesirable in texture measurements so these combinations should be avoided.

For texture measurements the incoming X -rays have to be monochromatic. An X-ray source most of the time sends out continuous wavelengths with a sharp Kα -peak. Next to this peak it may also have a sharp Kβ-peak. This peak has to be taken out when we want monochromatic X -rays. Therefore the source has to be equipped with a Kβ-filter to reduce the intensity of this Kβ -peak.

Continuous contributions to the X-ray spectrum remain at wavelengths larger than Kα and at very short wavelengths. Although these intensities are relatively small compared to the Kα -intensity, they may become significant in the case of very sharp textures.

In this case we make use of truly monochromatic radiation. This can be obtained by using single crystal monochromators. The monochromator is best inserted in the primary beam between the X -ray tube and the sample.


4.5.4 Examples of rolling, textures, recrystallization textures and transformation textures in FCC and BCC crystal structures

Orientation Distribution Function ODF calculated from XRD measurement.

Transformation from FCC to BCC structure

ODF is a statistical way to plot an image Measurement of preferred orientations grain-by-grain gives discrete points in the Euler Space that can be plotted.

Some transformations and recrystallization processes can be simulat ed, and then compared to the ODF experiment to ensure its quality (by using XRD you can check i f these simulations are good or not).

For example the transformation from FCC to a BCC structure can be seen as a Kurdjumow-Sachs (K-S mechanism) (<112>90°) or Bain (<001>45°) transformation. By simulation you can see what the Orientation Distribution Function ODF should be. You can compare this image then with the actual image that you become.

Rolling The KS mechanism consists of distortion of matrix by a first shear and a second shear . From the lattice distortion matrix, one can obtain invariant normal pla nes.

Bain mechanism uniaxial tension in z direction and uniform expansion in x and y axis BCC material subjected to high strain, the lattice may be elastically distorted towards an FCC lattice, by activation of slip systems.

Transforming Austenite into Ferrite

For the bcc-fcc phase, these are the only plans that are more or less identical in each crystal.

So you can see that the K-S transformation texture is a good approximation for describing the FCC to BCC structure. You can also get differences in deformed and recrystallized st ructures as seen in the picture.


The deformation texture of low carbon steel is based on the Taylor Theory . This theory is based on two assumptions:

1) Macroscopic strain = microscopic strain

2) Dissipated plastic power is minimized

So a displacement is accommodated by a combination of 5 slip systems (out of 24).

This theory can also be checked by using simulations and XRD and as seen in the picture below you can se e that this theory is quite accurate .

Also the effect of recrystallization on the texture as the change in R-values (for deep drawing – those cups that we did in OCAS) can be determined by using XRD.

Significant effect on the deformation as a consequence of the - phase transformation deep drawing properties of TRIP steels;

KS relationship is used to convert crystallization textures to textures


5 Scanning Electron microscopy (SEM) 5.1 Question 13

Scanning Electron Microscopy (SEM). Architecture of SEM. Types of filaments-advantages and

disadvantages. Interaction of the primary beam with Material-Efficiency of SE and BSE.

5.1.1 Architecture of SEM

Scanning electron microscopes are composed of several parts.Based on the vacuum, 2 parts can be distinguished: an ultra-high vacuum chamber on top (starting pump, diffusion pump and possibly 2 ion pumps (IP)) and a normal vacuum chamber below (starting pump and diffusion pump).

The ultra-high vacuum is to protect the electron source and to have as little interaction

with air as possible.In this vacuum room, an electron gun and the Wehnelt cap are located. The Wehnelt cap is used to centre and locate the emitted electrons as good as possible (focusing and control of the electron beam), to group the electrons and to form a parallel beam (minimize cross-over).

The normal vacuum room contains: lenses, an x -ray detector, a BSE and a SE-detector, a stage, coils, apertures, valves...

Liquid Nitrogen cooling

Electron Gun

Vacuum Column

Condenser Lenses

IP – Lamps

SE – Secondary Electron Detector


5.1.2 Types of filaments - Advantages and Disadvantages Different types of electron sources are currently available: W (Wolfram or Tungsten), LaB 6 (Lanthanum Hexaboride) and FEG (Field Emission Gun). Both W and LaB6 are thermo-ionic emitters; FEG emits electrons

by field emission (room temperature).

W is a small wire and from the top of the curve, the electrons are emitted. This is a cheap source, but is not very efficient. The brightness is the lowest, and it has the highest cross-over diameter (decrease

resolution) and the highest energy width ∆E. An advantage is the relatively low vacuum (10−3 Pa).The optimal temperature is 2800 K. Higher temperatures don’t give higher electron densities so there is no use in raising the temperature since raising the temperature lo wers the l ifetime (≈ 100 hr) of the wire . Without the benefit of using a corrector, the energy width degrades resolution because of chromatic aberration .

Cheap (100-600$)

Low Vacuum

Not very efficient

Needs very high temperature

Low Lifetime (evaporates)

LaB6 is a small cone-shaped single crystal (110)-plane of LaB6. The electrons are captured by a Wehnelt -

cup. Optimal working temperature is 1400 -2000K. The properties of this kind of source are better than the properties of the tungsten wire, but worse than the FEG. It is used for about 500 hr (long lifetime). To

create the vacuum of 10−4 an extra IP is added.

Better lifetime than Tungsten W (lower evaporation)

Chemically reactive when hot Poison cathode

Expensive (1300 – 3000$)

Needs a high vacuum

Really half-way W and FEG

The FEG (Field Emission Gun) is super expensive (second hand is 7k$). No high temperatures are needed (RT) since anodes are strong enough to suck the electrons out of the tip. A first anode is used to suck the electrons out; a second anode is used as a Wehnelt-cap. The properties of the FEG are very good. High current stability (< 5%), excellent brightness, lower cross-over diameter, lower energy width,

large lifetime (>1 year). The biggest difficulty is the ultra-high vacuum (< 10−8 Pa). To establish this kind of vacuum, at least 4 pumps are used.

Not as stable as the others

Needs a super high vacuum

Not good for large specimen (empty magnification)

Works in room temperature

Better brightness

Long lifetime

Small crossover d better resolution

Very fine current density


Because the emitted electrons in the various types of guns are heated, their energy distribution is not a sharp peak. Instead, they have a Boltzmann distribution that can vary widely depending on the type of filament . For a good microscope, you want ∆E/E to be as small as possible, that is, the energy distribution to be a small fraction of the average energy of the electrons.

5.1.3 Interaction of the primary beam with Material - Efficiency of SE and BSE

Interaction with material

The electron beam suffers direction change, energy loss and absorption

The material is excited, ionised, create lattice defects, there is heat production and secondary radiation (electrons and x -rays);

There are two types of interaction: elastic an d inelastic (scattering).

o Elastic: electron-nucleus interaction, low energy release, diffraction

o Inelastic: Interaction electron-electron, large energy variation;

SE Secondary Electrons

Emitted by the surface of the material after impact

Inelastic interaction Collision between two electrons and variation in energy E; Low energy (less than 50 eV), low penetration depth

BSE Backscattered electrons;

High energy electrons originating in the electron beam.

They are reflected (or back scattered) by elastic scattering interactions with specimen atoms.

Small energy loose has high Energy deeper penetration depth

Interaction between electron and nucleus

The efficiency of SE and BSE: 𝛿 =#SE

#PE 𝜂 =

#BSE

#PE

#PE = Ratio of Primary Electron emitted

η is Z dependent the heavier the element the brighter the signal in the microscope ;

𝛿 shows no dependence with Z low penetration depth

SE efficiency is higher when the sample is tilted in the direction of the detector

BSE is not really influenced by the angle


5.2 Question 14

EDX and WDX analysis in SEM Characteristic X-rays. Detectors-principle. Comparison between

EDX and WDX spectroscopy.

5.2.1 EDX and WDX analysis in SEM characteristic X-Rays

EDX or EDS Energy Dispersive X-Ray Analysis

Goal: Identify the elemental composition of a specimen. The EDX analysis system works as an integrated feature of a Scanning Electron Microscope and cannot operate its own without it.

During EDX Analysis, the specimen is bombarded with an electron beam inside the scanning electron microscope.

The bombarding electrons collide with the specimen atoms’ own electrons , knocking some of them off in the process;

A position vacated by an ejected inner shell electron is eventually occupied by a higher-energy electron from an outer shell . The outer electron will give up some energy and emit an x -ray.

This energy depends on which shell it is transferring from, and which shell is going to.

The atom of every element re leases X-rays with unique amounts of

energy this is the identity of the atom from which the x -ray was emitted.

The output of an EDX analysis is an EDX spectrum Peaks corresponding to energy levels, each peak being unique to an atom (corresponding to a single element); the higher the peak in a spectrum, the more concentrated the element is in the specimen;

The EDX spectrum not only identifies the element corresponding to each peak. The type of x-ray can also be identified. An x -ray from the L

to the K shell is a K peak, and from MP to K shell is a K peak, and so on.

WDX Analysis or WDS Wavelength Dispersive X-Ray Analysis

The detector counts the X-rays in terms of characteristic wavelengths , and not energy.

It is very similar to EDX, but more expensive, time consuming (slower) and causes higher sample damage/chamber contamination because of the high beam currents required;

So why would someone use it? The analysis is better. Better energy resolution prevents peak overlap errors (picture) that are frequent in EDX and has lower background noise (more accurate quantitative analysis).


5.2.1.1 Quantification via X-ray - ZAF correction (It is not highly necessary to be mentioned)

Different atoms give different responses to x-rays:

• Z Atomic Number Effect:

Backscattered coefficient increases with atomic number Z premature loss of beam electrons before ionization resulting in x-ray production

Stopping power the rate of energy loss due to inelastic interaction increases with decreasing

atomic number (leading to the same result; these two factors tend to cancel one another)

Z Energy Loss (inelastic) lower Z = lower backscattered coefficient and high energy loss;

The higher the Z, the better the Intensity.

Two factors must be considered regardi ng atomic number: the backscatter coefficient and “stopping power”. The backscatter coefficient increases with atomic number —leading to the premature loss of beam electrons prior to ionization resulting in X -ray production. The rate of energy loss due to i nelastic interaction increases with decreasing atomic number —leading to the same result. These two factors tend to cancel one another.

• A X-Ray absorption Effect

Intensity lowers due to absorption of x-rays in the sample. Absorption is usually the biggest factor that must be considered in the measurement of composition by x -ray microanalysis. As an X-ray travels through the sample, it may be absorbed, giving up its energy entirely to an electron and ejecting the electron from its orbital. The probability that an X-ray will be absorbed depends on its energy and the energy with which the electron is bound to its nucleus. The probability of absorption increases as the X -ray energy approaches this binding energy from above and reaches a maximum when the X -ray energy is just greater than the binding energy. At this point there is a discontinuity (absorption edge) in the probability curve. Lower energy X-rays no longer have sufficient energy to overcome the binding energy and the probability of absorption drops to a lower value. The probability of absorption then increases again as the X -ray energy approaches the binding energy of a more loosely bound electron. An absorption curve [1] for a given element includes an absorption edge for each electron shell.

Absorption edges can be directly observed when the X -ray spectrum energy range spans the critical excitation energy for the absorber element in the sample [1]. At the absorption edge, the continuum background abruptly decreases for X -ray energies slightly above the edge because the mass absorption coefficient increases abruptly at the absorption edge.

As X-rays are generated deeper in the specimen, progressively greater fractions are lost to absorption. The ratio of the measured X-ray intensity to the generated X-ray intensity at some position in the sample is dependent on the: mass absorption coefficient; specimen density; and path length. The probability of X -ray absorption as a function of path length through the sample is given by Beer’s Law:

I/Io = exp (-μM ρd) where:

I/Io = fraction of X-rays transmitted;

d = thickness;

ρ = material density;

μm = mass absorption coefficient (available in published tables).


F: X-Ray Fluorescence Effect:

When an X-ray is absorbed by a sample atom, the absorbing atom is left in an excited state. It subsequently relaxes, emitting its own characteristic X-rays (secondary fluorescence). Since an X-ray can be absorbed only in an interaction with an electron having a binding energy less than the energy of the absorbed X -ray, the energy of the secondary fluorescence is necessa rily less than the energy of the primary X -ray. For example, in a Cu-Fe sample, Cu Kα radiation (8.04 keV) is of sufficient energy to excite Fe K radiation (K ab = 7.11 keV). As a consequence, the measured iron intensity would be enhanced due to fluorescenc e by copper, while the copper intensity would be suppressed due to strong absorption by iron. In practice, secondary fluorescence is only significant if the characteristic energy is within approximately 3 keV of the critical ionization energy. The fluoresc ence effect can be calculated with sufficient accuracy and it is usually the least important of the three factors.

5.2.2 Detectors Principle

WDS Principle

A beam of electrons is aimed at the sample. X -rays escape. On a certain distance on the imaginary Rowland circle or focusing circle, a well-known analytical crystal is placed. The crystal has specific lattice spacing d, well-known. When x-rays encounter the analytical crystal at a specific angle θ, only those x-rays that satisfy Bragg’s law are reflected an d a single wavelength is passed onto the detector . When the measurement is done, the intensities (*) are compared with those of standards containing known values of the elements of interest. Therefore, the fractions can be calculated.

The sample is often fixed, so the crystal and the detector have to move around the Rowland circle.

(*) Actually, not the intensit ies, but the x -rays are counted. This is done with a proportional counter. In a tube of 90% Ar and 10% CH4, x-rays are attracted to the cathode a nd can create a voltage. By measuring the voltage, the

fraction of a certain element can be measured.

All the X-Rays originating from the point source on the sample are diffracted over a great percentage of the crystal surface and are brought to focus at the same point on the detector, thus maximising the collection efficiency of the spectrometer.

Several different diffracting crystals with different crystal lattice spacing are normally used for WDS, in order to cover all of the wavelengths (energies) of interest, as well as to optimize performance in the different wavelength ranges.

Further reading: https://www.oxford-instruments.com/OxfordInstruments/media/nanoanalysis/brochures%20and%20thumbs/OI_AppNote_WDS_Explained.pdf

To maintain the correct geometrical relationship between specimen, crystal and detector for the full range of diffracted angles, it is necessary to maintain all three on the Rowland circle. This is accomplished by a mechanical goniometer which moves the crystal and detector so that correct diffraction conditions are maintained.

https://www.oxford-instruments.com/OxfordInstruments/media/nanoanalysis/brochures%20and%20thumbs/OI_AppNote_WDS_Explained.pdf




Detectors used in WDS are usually of the gas proportional counter type.

X-ray photons are diffracted into the detector through a collimator (receiving slit) , entering the counter through a thin window.

The photons are then absorbed by atoms of the counter gas.

A photoelectron is ejected from each atom absorbing an x-ray. The photoelectrons are accelerated to the central wire causing further ionization events in the gas, so that an “avalanche” of electrons drawn to the wire

produces an electrical pulse the inert gas is ionized by the radiation.

The detector potential is set so that the amplitude of this pulse is proportional to the energy of the X -ray photon that started the process. Electronic pulse height analysis is subsequently performed on the pulses to filter out noise.

EDS

EDS detector is made of an electron trap, a window, the crystal and a cryostat.

• Electron trap: To make sure the electrons don’t damage the window, electrons are ’trapped’ by a magnetic field and reflected by a very thin (20 nm) Al-film;

• Window: The window is made of Be or polymer. A window is necessary to overcome the pressure gradient between the vacuum EDS and atmospheric pressure. If the window would not exist, air molecules would condensate on the detector and disturb the measurements. Be is quite strong, but it absorbs low energy x-rays. With a Be window, elements below Na can’t be detected. A polymer film is a lot thinner and therefor better. It does not absorb x-rays, but a supporting grid has to be attached. Mostly polymer windows are used nowadays.

• The cryostat maintains a low temperature and is not in contact with the detector, but the side of the detector is in contact with the cryostat. The detector is cooled indirectly.

The detector is composed of Silicon (silicium). When an x-ray enters, a hole is created. This hole can be detected. If the energy of the x-ray is too low, it is absorbed by Be, if it is too high, it passes through the silicium. From Na till U are measurable.


5.2.3 Comparison between EDX and WDX spectroscopy

EDS is more commonly employed data collection and analysis with EDS is a relatively quick and simple process because the complete spectrum of energies is acquired simultaneously. Using WDX, the spectrum is acquired sequentially (as the full wavelength is scanned).

Although it takes longer to acquire the full spe ctrum, WD technique has better resolution compared to EDS

the typical resolution of ED is 70 to 130 eV, and WD resolution is 2 to 20 eV (source Oxford Instruments).

The ability to combine better resolution and higher count rates allow WDS to detect elements at an order of magnitude lower concentration than EDS . EDS, is not able to detect pieces less than 10 wt%, elements have to be heavier than beryllium. Even when measuring a precipitate, a part of the bulk will be measured since the spatial resolution is approximately the penetration depth. Accu racy is between 99 and 95%.

WDS is better in resolution, but cost more (often 4 detectors with different crystals needed) and is more time consuming. Since focusing is needed, mistakes are more easily made. Limit of detection is around 1 wt%.

While WDS technique has always been appreciated for its higher resolution and trace element capability, it has been traditionally viewed as more complex to set up, and WDS data is more tedious to obtain and interpret than EDS (says Oxford Instruments).

http://eesemi.com/edxwdx.htm

http://eesemi.com/edxwdx.htm


6 Electron Microscopy TEM 6.1 Question 15

Discuss the sample preparation techniques for TEM. Give schematic descriptions of different

methods.

6.1.1 The sample preparation techniques for TEM In transmission electron microscopy (TEM), a high -energy electron beam (~ 200 keV) interacts with an electron transparent (~ 100-150 nm thick) specimen in order to study the microstructure and composition. Preparation of such a thickness is both an art and a science. It needs the devising of suitable methods as well as realising/demonstrating them in a defined process with reproducibility. Also, utmost care is necessary in preparing and handling the specimens, as they are extremely thin and hence prone to bending and breaking.

Important things to notice when preparing the sample:

Electron transparent for a 100 keV, a thickness of less than 100 nm is required (depending on the material)

Representative the sample has to contain what you want to analyse

Stable under electron beam could be a problem in organic matter, but no problem in metals.

Polishing is mostly done by chemical polishing. But safety is needed. Polishing is often done with HCN, HF, HNO3 and HClO4. All of those

liquids are dangerous, even explosive.

The sample is placed on a supporting grid (lines, hexagonal, raster, split,...) The supporting grid is placed in a sample holder (single entry

holder) that is actually a stick with a O -ring as seal and a platform and a jewel bearing. The jewel bearing is to link the holder to the column; the stick is to insert the specimen and to be able to rotate it in the column. The O-seal is to make sure the vacuum is maintained. The platform is very different everywhere. Rotation, heating, cooli ng, double tilt, multiple specimens, bulk... If a special thing is needed, it will be made. A top entry holder is also possible, but very rare. The advantage is that tilting can be done in every direction, but the tilting

angle is limited.


6.1.2 Give schematic descriptions of different methods The method to prepare the specimens for TEM depends on what information is required. In order to observe TEM images with high resolution, it is necessary to prepare thin films without introducing contamination or defects. For this purpose, it is important to select an appropriate specimen preparation method for each material, and to find an optimum condition for each method.

The most common way to prepare a sample possible for the TEM are: replicas and foils (Twin-Jet

electropolishing) .

Replicas can be positive (the true surface) or negative (the inverse surface). Mostly they are made by C,

Cr or Pt. Negatives are made by evaporating C, Cr, or Pt on the sample and dissolving the metal sample is lost. A positive is made by adding a layer of plastic on top of the sample, removing the sample, evaporating C, Cr or Pt on the plastic and dissolving the plastic. These techniques are working fine, because the evaporation is stopped when the layer looks flat. This means that there are places only a few atoms thick, while others are the thickness of the bumps, which is also small enough since the bumps are not very well visible under the SEM.

A special kind of replica is the extractive replica to see the inclusions. By deep selective etching, the inclusions are almost loose. By evaporating a thin film of C, Cr of Pt on the etched specimen, the inclusions can be removed. This is in order to view the inclusions without background and knowing that no inclusion is hidden behind another. The particles can also be tested for orientation and composition, the shape can be seen and th e texture can be measured without interference from

the bulk material.

In the replicas, diffraction is useless. The information about the orientation is lost. Only the shape and some thicknesses can still be seen.

Other methods involve crushing the sample with an agate mortar and pestle (the flakes obtained are suspended in an organic solvent like acetone and dispersed with sonic bath), electropolishing, chemical polishing, ultramicrotomy for sectioning, ion milling (Argon ions are used for sputtering).

Focused Ion Beam A thin slice of the sample is cut by an ion beam o n a scanning ion microscope. The main advantage of this method is that it allows selective thinning at a desired location by cutting trenches in the sample.

6.1.2.1 Single Jet Method Polishing of a material of one side at a time. The sample is an anode , and can be polished by electrochemical action, by keeping it in an electrolyte and applying potential. The electrolyte, its temperature and bias voltage are important parameters in controlling the rate of dissolution of the sample.


6.1.2.2 Double Jet Method The double-jet technique enables the polishing of metal disks simultaneously from both sides and automatically stops the polishing operation when perforation occurs.

A twin jet electro-polisher can be used for diameter. This equipment has a sample holder which can accommodate sample discs with 3 mm diameter. The sample disc acts as the anode. It is positioned between two nozzles, which are also acting as cathodes. Both the sample disc and the nozzles are submerged in a suitable electrolyte. A small submersible pump, wh ich is a part of the equipment, pumps jets of the electrolyte through these nozzles on both sides of the sample. The thinning rate in the central portions of the disc is higher than at the edges that are relatively unaffected. Therefore, the perforation oc curs preferentially near the central region with a rim at the edges of the disc. The perforation can be identified using a light source and a light sensor that are placed on opposite sides of the sample. The edges near the perforation will have a wedge -shape with those next to the perforation having the desired thickness for electron transparency.

Obtain a sample between 100 and 200 μm thick. Use a holder to polish the sample

Thinning Cut 3 mm diameter discs of the foil

Electropolishing Pre-thin the central region (from 1 or 2 sides). The double-jet method is often used;

Often, the double-jet is enough. Ion thinning can also be done. This method is very clean, precise and a

larger zone of flat material is obtained. Disadvantage is the production time: 6 -10h. A sample can also

be made with FIB (Focused ion beam, with Ga +- ions). Ions cut pieces of the sample till the right shape,

thickness, and place are reached. With the electron beam you can investigate the sample. By using the FIB a very thin plate can be made. When this is welded to an ominprop (= needle) a small plate can be produced. Again, the cutt ing with ions takes a lot of time (at least 5h and probably more).

Notification: When using TEM for dislocation density, make sure not to bend the specimen. This will

change the dislocation density.

Source: Necip Ünlü - Preparation of high quality Al TEM specimens via a double-jet electropolishing technique .

D. V. Sridhara Rao1, K. Muraleedharan1 and C. J. Humphreys .TEM specimen preparation techniques .

Resume:

Prepare slices (cut with a blade)

Prepare TEM discs (disc punch or ultrasonic disc cutter, la pping/polishing)

Twin-jet electropolishing prepare electrolite, adjust temperature, specimen holder


6.2 Question 16

Discuss the image formation and contrast formation in a TEM. What determines the resolution in

a TEM and why? Explain the bright and dark field image formation in TEM and the way you can

obtain an image.

6.2.1 Image Formation and Contrast Formation in a TEM

Interpreting transmission images is tricky image has no depth sensitivity. You will not know what is surface and what is in the bulk.

The instrument often has 5 lens illumination system and a trend increasing the number of lenses to optimise the overall performance;

After leaving the source, electrons are formed into a cross -over and this demagnified source image is projected on to the specimen by two condenser lens.

The first condenser lens forms a demagnified image of about 1m diameter that is projected on to the specimen by a second condenser lens with magnification of about two. The final illumination

spot on the specimen is typically as small as 2m, which is sufficient to fill the viewing screen at the highest magnifications.

6.2.2 Resolution in TEM Almost all TEM’s are build the same way. The only difference is the energy of the electrons, ranging from 100 keV till 1,25 MeV. Mostly energie s of 200-300 keV are used. 1,25 Mev is to powerful and damages the sample. The electron sources are the same as in the SEM (W, LaB 6 or FEG). Again the wehnelt cup is used

to collect the electrons. The wehnelt cup is again a negatively loaded cup. The curre nt to load the cup cannot be too high or the electrons aren’t focused but repelled. Therefore, a bias resistor is implanted to change the current. A positivlely charged anode is behind the wehnelt cup to attract and accelerate the

electrons.Then, electromagnetic coils are placed to aim the beam, 2 condenser lenses create the focus, 2 fixed apertures and 1 modifiable, an alignment coil at the beginning makes sure the electrons stay in the

tube after the anode and a stigmator to correct stigma tism are in front of the specimen holder.After the specimen holder, 2 apertures are placed (1 is only used in diffraction mode), many lenses and a stigmator. At the end is a fluorescent screen or CCD camera. All is done in high vaccuum.

The resolution of a TEM image is determined according to the Reighleig criterion.

Since λ is proportional to 1/E1/2, higher energetic electrons (lower λ) give better resolution. Although, the resolution is also restricted due to aberration: spherical and chromatic ( ̸= between red, green, blue). why aberration?

When looking at the image of a TEM, contrast is made by absorption or diffraction. The thicker the sample the more absorption (Lambert-Beer). Contrast can also be because of diffraction (electrons are too wide scattered), or diffracted differently (phases).

Magnification is done by using lenses. An object of length l is magnified by a lens till L =q/p with q the distance from the lens till the image plane. The focal distance (f) is different from q. f is lower than q.

In imaging mode, you want rays that started at the same place to come exactly together on the phosphor screen. In diffracting mode, you want paral lel beams from different spots (= diffraction) to come together


at the same place on the phosphor screen. Both methods are quite the same, but the intermediate lens is changed in strength to go from diffraction mode to imaging mode.

6.2.3 Bright and dark Field Imaging Bright field and dark field images are the bas ic mode for viewing crystalline specimens in the transmission electron microscope. They provide the essential microstructural information fro m a specimen prior to having to resort to more specialist imaging or operating techniques. Although these images can be obtained over the complete range of accelerating voltages, we address here the range that covers both the conventional and medium

If an objective aperture intercepts all the diffracted beams and allows only the direct beam to pass, deficiency contrast occurs and a bright field image is formed.

In addition, the objective aperture can be used to select a single diffracted beam to produce a dark field image. If this is produced by tilting the incident electron beam, the astigmatism in the image is reduced.


6.3 Question 17

What are the functions of the objective aperture in TEM and where it is positioned? What does

change in the image when you insert and objective aperture. What is SAD and how are the SAD

images analysed for cubic materials?

6.3.1 Objective aperture Above the focal point or below it :

To reduce the effects of spherical aberration , apertures are introduced into the beam path. Apertures are circular holes in metal disks on the micron scale. The net effect of the aperture is to reduce the diameter of the disk of minimum confusion . However, that positive effect comes at the price of reduced beam current. Also, a very small aperture will display diffraction effects. The diameter of the aperture used will also affect the convergence angle of the beam and this in turn will affect its coherence as well as image properties such as depth of focus.

An objective aperture is situated within the beam path just below the objective lens. The objective aperture is important for several reasons. The aperture will:

Allow for signal selection (What you want to see)

Provide for contrast within the image

Decrease objective lens aberrations, spherical and chromatic, which will degrade image resolution.

Affect depth of field in the image – a smaller aperture giving better depth of field.

In diffraction mode, we remove the objective aperture and insert another aperture further down the column —a selected area diffraction (SAD) aperture, to select a portion of the sample from which the diffraction pattern arises.

6.3.2 What is SAD SAD is referred to as "selected" because the user can easily choose from which part of the specimen to obtain the diffraction pattern. Located below the sample holder on the TEM column is a selected area aperture , which can be inserted into the beam path. This is a thin strip of metal that will block the beam. It contains several different sized holes, and can be moved by the user. The effect is to block the entire electron beam except for the small fraction passing through one of the holes; by moving the aperture hole to the section of the sample the user wishes to examine, this particular area is selected by the aperture, and only this section will contribute to the SADP on the screen. This is important, for exampl e, in polycrystalline specimens. If more than one crystal contributes to the SADP, it can be difficult or impossible to analyse. As such, it is useful to select a single crystal for analysis at a time. It may also be useful to select two crystals at a time , in order to examine the crystallographic orientation between them.


6.3.3 How are SAD images analysed for cubic materials?

i. In order to analyse a SAEDP, firstly a parallelogram with the smallest g 1, g2 and g3 is chosen on the

spot electron diffraction pattern.

a. Measurement of the size of g1, g2 and g3 and the scale bar is done with a ruler.

b. The values are then compared with the actual size on the scale bar.

c. The length |g i| in nm -1 is determined using the scale bar ratio on the diffraction pattern;

Table 1: gi was calculated from the relation of scale bar on a ration 6cm 15 nm-1

.

Index i

𝒈𝒉𝒌𝒍⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ 𝒏𝒎−𝟏

𝒈𝒉𝒌𝒍⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ 𝐜𝐦

1 4.25 1.7

3 5.00 2.0

2 4.25 1.7

ii. Afterwards, the inter planar distance d i is determined by the equation

𝑑𝑖 =1

𝑔ℎ𝑘𝑙⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗


These values are then compared with the given table in the exercise:

Table 2: Determination of inter planar distances, d values, family planes and planes.

In order to find the plane (hkl), the following formula shall be applied:

ℎ1 + ℎ2 = ℎ3

𝑘1 + 𝑘2 = 𝑘3

𝑙1 + 𝑙2 = 𝑙3

Thus in {hkl}{111}, {111} and {002} we have:

1 − 1 = 0

1 − 1 = 0

1 + 1 = 2

And the plane will then be the column of numbers with the appropriate signal chosen .

i. In order to measure the angles, there are two possibilities:

a. The family planes are inserted in the formula

b. Draw an angle (using the protractor template)

Index i

𝒈𝒉𝒌𝒍⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ 𝒏𝒎−𝟏

dhkl nm

Family plane

{hkl}

Plane

(hkl)

1 4.26 0.234 {111} (111)

2 4.26 0.234 {111} (1̅1̅1)

3 4.92 0.203 {002} (002)

Figure 2: Angle masurement with protractor template.


The values obtained were the following:

1

= cos−1(ℎ1ℎ3 + 𝑘1𝑘3 + 𝑙1𝑙3)

√(ℎ12 + 𝑘1

2 + 𝑙12)(ℎ3

2 + 𝑘32 + 𝑙3

2)= cos−1

(0 + 0 + 2)

√12= 54.7°

2

= cos−1(ℎ2ℎ3 + 𝑘2𝑘3 + 𝑙2𝑙3)

√(ℎ22 + 𝑘2

2 + 𝑙22)(ℎ3

2 + 𝑘32 + 𝑙3

2)= cos−1

(0 + 0 + 2)

√12= 54.7°

Table 3: Interplanar angles for cubic system

𝝋𝟏 𝝋𝟐

Measurement 52° 56°

Calculation 54.7° 54.7°

The values correspond to each other and can be considered satisfactory.

On the second task, one must determine the crystal zone axis for the indexed diffraction spots (i.e. crystal planes in a real space). This can be obtained with the following formula:

< 𝑢𝑣𝑤 > = {111}𝑥{002} =

[𝑢 𝑣 𝑤10

1 10 2

]𝑢10

𝑣10

= 2𝑢 − 2𝑣 + 0w = < 22̅0 >

General Family of Directions

If we calculate the direction parallel to the electron beam specifically for one set of planes:

< 𝑢𝑣𝑤 > = (1̅1̅1)𝑥(002) = 2̅20

[𝑢 𝑣 𝑤1̅0

1̅ 10 2

]𝑢1̅0

𝑣1̅0

= −2u + 2v + 0𝑤 = 2̅20 = 1̅10

This is a particular solution for particular indices of planes, thus brackets should be square.

The zone axis is a direction in the crystal which is parallel to the electron beam. Thus this axis is 1̅10. Indices must be reduced to least numbers.

Figure 3: The electron beam is parallel to the zone axis direction. Source: Google


On another example:

On this one you might find families {002} and {113}, with {133} in the middle, however you cannot seem to apply the rules because 3 and 2 can never equal 3, r ight? But here we are talking about families, so {002} = (002), (020) and (200). If you use (020), should be able to find the r ight solution.

1 + 0 = 1

1 + 2 = 3

3 + 0 = 3

Thus the family of planes is (113), (020) and (133).

1

= cos−1(ℎ1ℎ3 + 𝑘1𝑘3 + 𝑙1𝑙3)

√(ℎ12 + 𝑘1

2 + 𝑙12)(ℎ3

2 + 𝑘32 + 𝑙3

2)= cos−1

(0 + 6 + 0)

√18 ∗ 4= 45°

2

= cos−1(ℎ2ℎ3 + 𝑘2𝑘3 + 𝑙2𝑙3)

√(ℎ22 + 𝑘2

2 + 𝑙22)(ℎ3

2 + 𝑘32 + 𝑙3

2)= cos−1

(1 + 3 + 9)

√19 ∗ 11= 25°

[𝑢 𝑣 𝑤10

3 32 0

]𝑖10

𝑗32

= −6𝑢 + 0𝑣 + 2𝑤 = 3̅01

(020)

(133)

(113)

1

2


7 Electron Backscattered Diffraction (EBSD) 7.1 Question 18

Explain the basic operational principles of the EBSD method. Formation of Kikuchi bands. Band

Detection. Hough Transform. Pattern Indexation

7.1.1 Definition EBSD – Electron Backscattered Diffraction: is a SEM based technique that provides crystallographic

orientation data necessary to understa nd the micro-structure property relationships for alloy design, materials characterization and failure analysis;

Steps necessary to produce an EBSD pattern in a SEM

Tilt the sample so that its surface makes an angle about 70° with the horizontal

Turn off the scan coils to obtain a stationary electron beam

Place a recording medium in front of the tilted specimen to capture the diffraction pattern: phosphor screen

7.1.2 Architecture EBSD system is attached to scanning electron microscope in one of the free ports us ually

perpendicular to the tilt axis of the microscope stage.

Operational System: Signal detector camera connected to a post -processing unit and a computer; Specialized hardware and software is used for post -processing the signal from the camera, analysis (indexation) of the acquired diffraction patterns and beam or stage control.

EBSD Cameras: detectors for forward scattered electrons – additional images with orientation or elemental contrast

OIM computer (orientation imaging microscopy) asks Microscope C ontrol computer to place a fixed electron beam on a spot on the sample;

A cone of diffracted electrons is intercepted by a specifically placed phosphor screen;

Incident electrons excite the phosphor, producing photons

A charge Coupled Device CCD Camera detects and amplifies the photons and sends the signal to the OIM computer for indexing;


7.1.3 Formation of Kikuchi pattern. What influences a Kikuchi Pattern? Which of those can be avoided by the researcher?

Is a SEM based technique → proper sample preparation is very important;

The patterns are observed when a fixed and focused electron beam is positioned on a tilted specimen:

TILT – Reduce the path length of backscattered electrons – 70° is ideal

Backscattered electrons escape from 30 -40 up to 100nm underneath the surface, hence there is a diffracting volume;

EBSD patterns (consisting of Kikuchi bands) are formed when a stationary electron beam interacts with a crystalline lattice in a highly tilted sample in the SEM.

The geometry of the band hold informatio n about crystal lattice in the diffracting volume;

The width and intensity of a band is related to the spacing of atoms in the corresponding crystal plane;

The symmetry of the crystal lattice is reflected in the pattern

The orientation of the crystal latti ce with respect to a laboratory reference frame can be determined from a pattern assuming the material is of a known crystal structure;

Remember → ↑atomic number Z↑ Backscattering

7.1.4 Band Detection There are two distinct artefacts: BANDS (planes) and POLES (vectors);

Bands are intersections of diffraction cones with the phosphorous screen; they correspond to a family of crystallographic planes

Bands widths are proportional to the inverse inter planar spacing

Intersection of multiple bands (planes) correspond to a pole of those planes (vector)


7.1.5 Hough Transform Bands are transformed to peaks

p =x cos T +y sin T

x and y are the coordinates of a pixel in the EBSD patter image (column and row)

p and T are the coordinates of lines that pass through the pixel

A PIXEL in the image space becomes a sinusoidal curve in the transform space

When applied to every pixel, the transform becomes a large set of si nusoidal curves

For each pixel in a line, possible values of p are calculated using the formula, with T ranging from 0 to 180 degrees

The curves will intersect at point that is the angle of the line and its position relative to the origin;

All the pixels in a band form a peak at the intersection of their individual sinusoidal curves;

A LINE IN IMAGE SPACE TRANSFORMS TO A POINT IN HOUGH SPACE

The basics of Hough Transform is to find aligned points in images that create lines

VERY IMPORTANT: https://www.youtube.com/watch?v=4zHbI-fFIlI

Teta and Ro parameters will define a line equation in terms of angle and radius

The point where the curves intersect gives a distance and angle, and they indicate the line which intersects the point being tested

https://www.youtube.com/watch?v=4zHbI-fFIlI


Pattern Indexation

Assuming the pattern is from a known structure, the first step is to identify the (hkl) indices of the strongest diffracting planes in the crystal;

A look up table is constructed from these planes

The bands identified by Hough transform are processed to extract geometrical relationship between bands and then compared to the table to identify potential (hkl) indices for the detected bands;

To correlate the bands with particular planes in the crystal lattice, and to identify the crystal orientation, the angles between the bands are calculated and compared to theoretical values; once the bands have been found, next step is to determine the orientation of the crystal lattice from the geometrical arrangement of the bands;

Often the first step in the EBSD process after pattern collection is indexing: this allows identification of crystal orientation at the

Resume:

Influences on EBSD:

beam current

accerlerating voltage

spotsize and tilt angle

features that can be seen are crystal latice

Latice parameter

orientation

Sources:

a. Lecture 7 ”EBSD” slides 1-26

b. V. Randle and O. Engler “Introduction to Texture Analysis-Macrotexture, Microtexture and Orientation Mapping” Chapter6 pages 127-151 and 157-176. –Recommended. (file Introduction to Texture Analysis.pdf)

c. Flewitt:”Physical methods for materials characterization-Second Edition”, Chapter 6. Parts 6.4.1., 6.4.2, 6.4.3 and 6.4.5 (file IP556_CH06.pdf)

d. Bob Hafner,” Introductory Transmission Electron Microscopy Primer” file “tem_primer.pdf”-Recommended

e. Practical classes report


7.2 Question 19

Evolution of electron back-scatter diffraction (EBSD. Orientation Image Analysis. Special

resolution and angular resolution of the EBSD. What is IQ, (BC) CI (MAD)? Experiment design

philosophy. What kind of information can be obtained from an EBSD measurement? (Examples).

Sample preparation for the EBSD measurement. Compare the EBSD with the XRD method for

texture characterization.

7.2.1 Evolution of electron back-scatter diffraction EBSD

30-50s: first observation of Kikuchi patterns

70s – Electron backscattered patterns recorded in the SEM

80s – Computer routines for interactive EBSD pattern evaluation

80s – Automated EBSD pattern analysis

90s – Orientation contrasting map

7.2.2 Orientation Image Analysis.

ORIENTATION IMAGING MICROSCOPY (OIM) – automation technique of the orientation measurement process using EBSD; in OIM the electro n beam is scanned over the specimen surface in a regular grid, at each pixel in the grid and EBSD pattern is captured and automatically indexed; the following data are calculated:

Crystallographic Orientation data

IQ Image Quality: a quality factor definin g the sharpness of the diffraction pattern

CI confidence index: a patented parameter indicating the degree of confidence that the orientation calculation is correct

Material Phase

Specimen data collection coordinates (x, y)


7.2.3 Spatial resolution and angular resolution of the EBSD.

7.2.3.1 Spatial Resolution: Def.: ability of the imaging modality to differentiate two objects; measure of how closely lines can

be resolved; ability to see fine detail

The spatial resolution of the technique is governed by the SEM elec tron optics as in conventional backscattered electron imaging. For high resolution imaging on Nano grains, high performance FE-SEMs are required, along with a small sample and short working distances ;

Minimum grain diameter for EBSD imaging is 10nm

The Spatial Resolution is primarily determined by

o SEM

o Geometry of the sample/lens/EBSD detector relationship (the specimen/microscope geometry: specimen → screen distance; specimen tilt; specimen height)

o Material (↑ Z - ↑ backscattered signal - ↑ pattern clarity)

o Accelerating Voltage (↑ voltage = ↑ brighter diffraction pattern, ↓ interference from EM fields, electron beam penetrates further and surface contamination/damage effects are minimized)

o Probe (beam) Current (narrow beam, ↑ current density)

o Pattern Clarity

7.2.3.2 Angular Resolution of Ebsd o AR of an individual EBSD pattern is usually 1°

o Important to determine misorientation between two crystal lattices (grains) – the accuracy is determined by measuring misorientation between adjacent sampling points in a single cry stal;

o The accuracy, or angular resolution of EBSD related directly to the precision with which the diffraction pattern can be indexed;

7.2.4 What is IQ, (BC) CI (MAD)

7.2.4.1 The image quality parameter IQ

describes the quality of an electron backscattered diffractio n pattern;

IQ = sum of detected peaks in the Hough Transform

The IQ is dependent on the material and condition, and is a function of the technique and parameters used to index the pattern as well as other factors such as video processing;

The greatest effect on the quality of diffraction patterns is the perfection of the crystal lattice in the diffracting volume;

Distortions of the crystal lattice lower quality of image;

IQ reveals grain boundaries and precipitates (black dots)

Gradients in IQ reveal dislocation structures


In the Oxford HKL software, the equivalent of the IQ is the Band Contrast Parameter (BC) and the Confidence Index or Indexation Reliability is quantified by the Minimum Angular Deviation (MAD);

MAD shows the difference between the measured value of the angles and the theoretical ones for the given crystal lattice;


7.2.4.2 CI Confidence Index Parameter that indicates the degree of confidence that the orientation calculation is correct

For a given diffraction pattern, several possible orientations may be found (that satisfy the diffraction bands detected by the image analysis routine);

The orientation is then “voted”: ex.: if you have 5 colors (bands) that can form different triplets (10 combinations), you can have several solutions. Each solutio n assigns an hkl to a band triplet; If a solution yields inter-planar angles within tolerance , a vote or an “x” is marked in the solution column;

The solution chosen will be the one with more votes

Once the solution is chosen, it is compared to the Hough a nd the angular deviation is calculated as the fit

6.010

410

tripletsband ofnumber

S2 of n votes - S1 of n votes

CI

Solution #

n votes

Ban

d t

rip

lets

S1 (solution w/most votes)

S2 (solution w/ 2nd

most votes)


7.2.5 Experiment design philosophy - What kind of information can be obtained from an EBSD measurement? (Examples)

A great advantage of the EBSD measurement is that the output data can be easy represented as text files which could be further exchanged, post -processed or exported to their programs for texture calculations, modelling; etc. A table can be obtained with:

Information for the scanned phase

X and y coordinates of the pixel from where the diffraction pattern was acquired

Orientation of the crystal in the point with coordinates x and y given by three Euler angles (phi1, phI, phi2)

Image Quality factors (BC, BS, IQ) and Confidence Index (CI, MAD)

7.2.6 Sample preparation for the EBSD measurement Sectioning/cutting

Mounting (convenience in handling specimens of difficult shapes or sizes/protect and preserve extreme edges or surface defects during preparation)

Grinding (different grits of sandpaper for 15 -20s)

Mechanical Polishing (diamond/alpha alumina solution 5-10 min)

7.2.6.1 Additional steps:

i. Vibratory polishing,

ii. Electro polishing (best quality of EBSD, but several bad aspects like surface relief, rounds sample edges, sensitive to polish parameters)

iii. Chemical etching (simpler technique, but surface relief is cre ated and any topography is enhanced)

iv. Ion etching

v. Ion Beam Milling (works on almost every type of material, but only small surfaces can be polished and takes long time to prepare; ion beam interacts with material and unstable phases can transform);

vi. Coating

7.2.6.2 Sample storage

i. EBSD is a surface technique – information is obtained at 10-50nm from the surface

ii. Any surface damage influences the result

iii. EBSD is a SEM technique – samples must be conductive

iv. Non-conductive samples require special measures

v. Selection of correct phase (crystal structure) is necessary


7.2.7 Compare the EBSD with the XRD method for texture characterization. The characterization of phase fractions with EBSD and XRD shows differences, due to interacting

volumes and the spatial resolution of differe nt methods.

The minimum detectable sample area in EBSD is 0.1µm of diameter while in XRD is 10 -100µm diameter;

The angular accuracy of EBSD is 0.5 -1.0°; XRD is 2°;

Applications of XRD are mostly for Grains; EBSD reaches Subgrains;

Sources:

Lecture 7 ”EBSD” slides 1-26

V. Randle and O. Engler “Introduction to Texture Analysis -Macrotexture, Microtexture and Orientation Mapping” Chapter 7; pages 157 -176. –Recommended (file Introduction to Texture Analysis.pdf)


8 3D Microstructure Characterization (3D-EBSD) 8.1 Question 20

Give an overview of the special techniques that are used to do a 3D microstructure

characterization. Explain details on 3D-EBSD with focused Ion beam and 3D-Xray diffraction.

WHY 3D: THE MATERIALS MICROSTRUCTURE IS OF 3D NATURE. THE STATISTICAL 3D METHODS GIVE AN

ACCURATE BUT NOT A COMPLETE DESCRIPTION OF THE MICROSTRUCTURE.

8.1.1 Overview of special techniques

Method

Multiple sectioning +OM or SEM or EBSD

Most simple

Destructive method

Multiple cutting or polishing

Atom probe microscopy

Destructive method

+ Chemical composition

No crystallographic structure

X-Ray tomography Non-destructive method

Uses x-rays to create cross-sections due to the difference in absorption

Used for non-metals: porosity of biological objects

3D XRD Non-destructive method

Texture + grain shape reconstruction

With variation of time and temperature (in situ: -4D)

3D EBSD with FIB Destructive method

Sectioning by FIB

Observation by EBSD

8.1.2 3D-EBSD with focused ion beam The geometry of the sample holder for 3D EBSD looks like the figure at right. The angles handle the geometrical condition. The perfect alignment of the ion beam and the electron beam is a critical point in this technique.


First the Ga+ beam glides over the sample and removes a thin layer. Then the Ga+ beam is stopped and the sample holder rotates. Now the e - beam reacts with the sample and the reflected electrons can be collected by the EBSD.

In each step you go deeper in the specimen by removing a thin layer. Then you put the EBSD patterns together and you get a 3D image.


8.1.3 3D-Xray diffraction High energy, short wavelength penetrate the sample

The primary beam (yellow) is stopped; the diffracted beam (red) gives the x -rays.

The sample can be heated up for some experiments.

Sources:

Lecture 12 ”3D microstructure characterization by means of combined FIB -EBSD method” slides 1 -26


9 AFM/APM 9.1 Question 21

What observation techniques stay behind the abbreviations AFM and APM? Discuss the

operational principle, requirements for the sample preparation and the application field.

9.1.1 APM APM stands for atomic probe field ion microscopy. APM combines two techniques

Field ion microscope: first microscope with atomic resolution

Atom probe: time-of-flight mass spectrometer: identification of atoms

9.1.2 Field ion microscope In this microscope a sharp (<50nm tip radius) is placed in an ultrahigh vacuum chamber, which is filled with an imaging gas such as argon, neon, hydrogen or helium. To avoid thermal emission, the tip is cooled to cryogenic temperatures (20-100K). A high positive voltage of 5 -20kV is applied to the tip, therefore the sample is placed on an electrically insulated stage. Imaging gas atoms adsorbed on the positive charged tip are ionized by the strong electric field in de neighborhood of the t ip. So the gas atoms are becoming positively charged and then being repelled from the tip. The ions are repelled in a direction perpendicular to the surface due to the curvature of the surface. A detector (fluorescent screen) is placed so as to collect these repelled ions.

When the voltage increase, we could have field evaporation. This means that an atom contains enough energy to evaporate from the surface. With this effect we are not restricted to the investigation of surface atoms because the next layer is available: 3D imaging is possible.

9.1.3 Atom probe A pulsed high voltage source (typically 0 -7 kV) is generated and applied to the specimen. The application of the pulsed voltage to the sample allows for individual ions at the sample surface to have their electric field, and hence atomic bonding, temporarily disrupted. This results in ejection of an ionized atom from the sample surface at a known time. The delay between application of the pulse and detection of the ion allows for the computation of a mass-to-charge ratio (time of flight).


9.1.4 Sample preparation

We need to have a very thin tip. We can do this with mechanical grinding (left image) of a rod or wire or with electro polishing (right image).

9.1.5 Applications You can determine the location and distribution of elements in alloys. You can also identify the elements segregated to dislocations. This technique is the only one who combine chemistry and morphology in 3D.


9.1.6 AFM AFM stands for atomic force microscopy.

AFM consist of a cantilever with a sharp tip (silica crystal) at its end that is used to scan the specimen surface. Forces between the tip and the surface leads to deflections.

These deflections caused by the surface topology are measured by a laser light. A laser l ight is reflected off the back of a cantilever and the light is collected by a 4 quadrant photodiode. The output signal is proportional to the deflection. The detection limit is approximately 0.1 A.

There are two primary modes of operation (imaging mode s). The static mode (contact mode AFM), where the force between the tip and the surface and the deflection is kept constant. The dynamic mode (non -contact mode AFM and tapping mode AFM), where the cantilever oscillate around resonance frequency and the change in oscillation, after reaction with the surface, gives information about the sample.

9.1.7 Contact mode AFM In contact mode, the force between the tip and the surface is kept constant during scanning by maintaining a constant deflection. The contact mode us es the repulsive force between the tip and the sample and uses a DC-detection method. Because the distance tip -sample changes, the applied voltage can determine the height of sample.

The disadvantage of this mode is that you can cause damage to the surf ace.


9.1.8 Non-contact mode AFM The non-contact mode uses attractive forces between the tip and the sample and uses an AC -detection method. The tip oscillates above the sample with a constant oscillation frequency or amplitude. The tip -sample distance is changing and the applied voltage is a measure for the height of the sample.

The non-contact AFM uses weaker forces so an AC-detection method is needed. This mode also requires vacuum due to adsorbents.

9.1.9 Tapping mode AFM In the tapping mode the tip oscillates above the sample with a constant amplitude. The amplitude changes when surface relief. The tip -sample

distance is changing and the applied voltage is a measure for the height of the sample.

With this mode, the surface isn’t damaged and there is no influ ence by adsorbent layer. It can be implemented in air. Even a very soft and fragile sample can be imaged with this mode.

9.1.10 Advantages of AFM The sample doesn’t have to be conductive and there is no surface preparation necessary. It is a 3D -imaging technique to investigate the surface of the specimen with a very good resolution: lateral resolution 5nm, vertical resolution 0.01 nm. There is no vacuum needed (except for non -contact mode) so air and liquid environment are possible.

9.1.11 Disadvantage of AFM You have only a small imaging area: 150µm by 150µm with µm height (if you increase x and y, you decrease z) (↔ SEM: mm by mm with mm depth of field). The imaging of the sample (several minutes) is slower than with SEM (nearly real-time). Drift in the image is also possible. It is required to have a good choice of the tip, otherwise you can get artifacts (see picture below).

Sources:

Lecture 13 ”Microstructure characterization by means of combined Atomic Force Microscopy, Atom Probe Microscopy and Laser Confocal M icroscopy”


Practical classes

EBSD, XRD, LOM/QM, SP, TEM, SEM

GROUP 4

9.2 Extra on EBSD

EBSD – Analysis technique based on a scanning electron microscope (SEM)

Measures the local crystal orientation with sub-micron spatial resolution

Can also be used for phase distribution analysis

When the electron beam hits the sample, a cloud of backscattered electrons is generated

A phosphor screen placed within this cloud transform each arriving electron into a photon, thus transforming the backscattered signal into a visible light signal;

The diffracted part of the backscattered electrons is highly anisotropic and when interacting with the phosphor it will create a KIKUCHI pattern

The kikuchi pattern is captured by a high speed and high sensitivity CCD camera placed behind the phosphor screen and transferred to a computer where it is being analyzed;

Hundreds of patterns per second can be acquired and analyzed due to state of the art hardware and software programming technology;

EBSD data is displayed and interpreted in real time; the phase distribution map reveals the presence of hard and brittle intermetallic phases; the orientation distribution map displays the local crystal orientations;

https://www.youtube.com/watch?v=Ny_lTzPnynY

https://www.youtube.com/watch?v=Ny_lTzPnynY


10 Sources

1. Lecture 1, slides 14 to 28;

2. Flewitt ”Physical methods for materials characterization -Second Edition”, Chapter 1.9 -Microstructure (only)(f i le IP556_CH01.pdf);

3. Lecture 1, slides 29 to 35;

4. Flewitt ”Physical methods f or materials characterization-Second Edition”, Chapter 1.9 -Microstructure (only)(f i le IP556_CH01.pdf);

5. Lecture 4, slides 1 to 30;,

6. Flewitt ”Physical methods for materials characterization -Second Edition”, Chapter 2.Parts 2.1, 2.2, and 2.3 Without 2.2.4. “Protons” (f i le IP556_CH02.pdf) ; I strongly recommend you to go through the rest of the Chapter 2 until Chapter 2.8

7. B.C.De Cooman “Materiaalkundige observatietechniken”Chapters 1.6.1.”Materiaalen en denciteiten” en chapter 1.6.2.”Basisformule van de microkarakterisat ie”

8. Lecture 2. Sl ides 1-26;

9. Practical c lasses notes and discussions;

10. Lecture 2, slides 27 to 56;,

11. Flewitt ”Physical methods for materials characterization -Second Edition”, Chapter 5. Parts 5.1, and 5.4

12. Practical c lasses report

13. Lecture 2, slides 34 to 39,

14. Flewitt:”Physical methods for materials characterization -Second Edition”, Chapter 5. Parts 5.2 and 5.3,


16. Lecture 2, slides 57 to 72



19. Flewitt:”Physical methods f or materials characterization-Second Edition”, Chapter 4. Parts 4.31, 4.3.2, 4.3.4 and 4.3.3 (4.3.3 only for information), (fi le IP556_CH04.pdf)

20. Website: http://www.matter.org.uk/diffraction/geometry/3D_reciprocal_latt ices.htm


22. B.C.De Cooman “Materiaalkundige observatietechniken”; Chapter 3.1, 3.2(Interactie tussen X -stralen en vaste stof); 3.3.1, 3.3.2 (Productie van X-stralen). In f ile “Chapter 16.pdf”


24. Flewitt:”Physical methods for materials characterization -Second Edition”, Chapter 4. Parts 4.3.5, 4.3.6 (fi le IP556_CH04.pdf)

25. B.C.De Cooman “Materiaalkundige observatietechniken”; In f ile “Chapter 16.pdf” Chapter 3.1.1,until 3.1.2


27. Lecture 9, ”X -ray diffract ion” s lides 47 to 51,

28. Flewitt:”Physical methods for materials characterization -Second Edition”, Chapter 4. Parts 4.3.8, (f i le IP556_CH04.pdf)

29. B.C.De Cooman “Materiaalkundige observatietech niken” Fi le: “Chapter 18.pdf” Chapters 3.6.1.”Meting van interne spanningen”


http://www.matter.org.uk/diffraction/geometry/3D_reciprocal_lattices.htm


31. Lecture 8 “Introduction to quantitative texture analysis”, sl ides 1 to 35,

32. B.C.De Cooman “Materiaalkundige observatietechniken” Fi le “Chapter 18.pdf” Chapter 3.6.2.”Textuuranalyse”

33. V. Randle and O. Engler “Introduction to Texture Analysis -Macrotexture, Microtexture and Orientation Mapping” Chapters 2.1 to 2.6. page 13-36.-Recommended. (f i le Introduction to Texture Analysis.pdf)


35. Lecture 9 ”X -ray diffract ion” slides 52 -60

36. Lecture 8 ”Introduction to quantitative texture analysis”, sl ides 36 to 52

37. V. Randle and O. Engler “Introduction to Texture Analysis -Macrotexture, Microtexture and Orientation Mapping” Chapter 3. Pages 41-54. and 61-88. –Recommended. (f ile Introduction to Texture Analysis.pdf)

38. Flewitt:”Physical methods for materials characterization -Second Edition”, Chapter 4. Parts 4.3.6, last part of the chapter, (fi le IP556_CH04.pdf)

39. B.C.De Cooman “Materiaalkundige observati etechniken” Fi le: Chapter 19.pdf” Chapter 3.6.2.3”Practische aspekten van de textuurmeting”


41. Lecture 6 ”Introduction to SEM” sl ides 1 -32

42. Flewitt:”Physical methods for materials characterization -Second Edition”, Chapter 6. Parts 6. 1,6. 2 and 6.3. (fi le IP556_CH06.pdf)

43. Bob Hafner ”Scanning Electron Microscopy Primer” –strict ly recommended ! Fi le “sem_primer.pdf”

44. B.C.De Cooman “Materiaalkundige observatietechniken” Files: “ Chapter 8.pdf” “Chapter 9.pdf”, “Chapter 11.pdf”and Chapter 12.pdf Chapters 2.3.1,(Elektronen bron), 2.3.2 (Elektronen optika), 2.3.3(Elektronen detektoren), 2.5 (Elementen van de elektronen microscopen)


46. Lecture 6 ”Introduction to SEM” sl ides 1 -32

47. Flewitt:”Physical methods for materials charac terization-Second Edition”, Chapter 6. Parts 6.1,6. 2 and 6.3. (fi le IP556_CH06.pdf)

48. Bob Hafner ” Energy Dispersive Spectroscopy on the SEM:A Primer ! File “eds_on_sem_primer.pdf” Recommended!

49. B.C. De Cooman “Materiaalkundige observatietechniken” Files: “ Chapter 11.pdf”, “Chapter 12.pdf” Chapters 2.4. (X-stralen spectrometers) en Chapter 2.5.5. (Microanal ize m.b.v. characteristieke X -stralen)


51. Lecture 11 ”Introduction to TEM” sl ides 21 -42

52. Flewitt:”Physical methods for materials char acterization-Second Edition”, Chapter 6. Parts 6.4.4. (fi le IP556_CH06.pdf)



55. Bob Hafner,” Introductory Transmission Electron Microscopy Primer” f i le “tem_primer.pdf” -Recommended

56. Flewitt:”Physical methods for materials characterization -Second Edition”, Chapter 6. Parts 6.4.1., 6.4.2, 6.4.3 and 6.4.5 (fi le IP556_CH06.pdf)



59. Flewitt:”Physical methods for materials character ization-Second Edition”, Chapter 6. Parts 6.4.1., 6.4.2, 6.4.3 and 6.4.5 (fi le IP556_CH06.pdf)




62. Lecture 7 ”EBSD” slides 1 -26

63. V. Randle and O. Engler “Introduction to Texture Analysis -Macrotexture, Microtexture and Orientation Mapping” Chapter6 pages 127-151 and 157-176. –Recommended. (f ile Introduction to Texture Analysis.pdf)

64. Flewitt:”Physical methods for materials characterization -Second Edition”, Chapter 6. Parts 6.4.1., 6.4.2, 6.4.3 and 6.4.5 (fi le IP556_CH06.pdf)



67. Lecture 7 ”EBSD” slides 1 -26

68. V. Randle and O. Engler “Introduction to Texture Analysis -Macrotexture, Microtexture and Orientation Mapping” Chapter 7; pages 157-176. –Recommended (fi le Introduction to Texture Analysis.pdf)


70. Lecture 12 ”3D microstructure characterizat ion by means of combined FIB-EBSD method” slides 1 -26

71. Lecture 13 ”Microstructure characterization by means of combined Atomic Force Microscopy, Atom Probe Microscopy and Laser Confocal Microscopy”

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