1. Diffraction: Electron and X-ray Electron probe microanalysis
EPMA and SEM
Diffraction:
Electron and X-ray
Electron Backscattered Diffraction
Orientation Contrast Imaging
Updated 3/10/2018

2. Why do we care?
Up to now, we have only been concerned with determining sample chemistry quantitatively by EPMA and SEM
Chemistry is only half the story. How to tell polymorphs, like coesite from quartz, both are SiO2?
All minerals and most geologic and synthesized materials have a crystalline structure (except amorphous)
Diffraction uses either electron or x-ray sources to characterize the crystal structure
Bulk (XRD), micro (XRD, EBSD) or nano (TEM) diffraction techniques are used
Electron Back Scatter Diffraction (EBSD) is a relatively new technique for micro-diffraction by SEM

3. Electron Backscatter Diffraction: Its Importance
Phase Identification (crystal structure + chemistry from EDS)
Orientation Determination/Mapping

Provide important insights into
Microstructure
Crystallography
Materials Physical Properties
All this in an accessible “tool” (=SEM) where features are easily found at low to high magnification.

4. Coherent Scattering
When x-rays or electrons interact with matter, the dominant effect is scattering.
Considering x-rays and electrons as waves we deal with coherent scattering (rather than as particles, where we deal with incoherent scattering)
For coherent scattering, x-rays and electrons are scattered with no loss of energy, and give rise to scattered radiation of the same wavelength
This discussion (above) is taken mainly from Andre Guinier’s X-ray Crystallographic Technology, a 1952 translation of his 1945 classic
Some of the following material is taken from Jim Connolly’s highly recommended UNM CXRD class notes:

5. Constructive Interference: X-rays
The distance between atoms (dhkl) are on the same order of size as the wavelength of an x-ray Cu Ka =1.54Å)
Interference phenomena is concentrated in directions related to the crystal lattice
The intensity of the diffracted x-rays gives rise to peaks for each set of wave vectors which make up diffraction patterns
The positions of the atoms in the material (the crystal lattice of the solid) and the wavelength of the x-rays determines the positions and intensities of the diffracted peaks.
Another kind of scattering, incoherent (Compton), is easiest understood in terms of the particle nature of photons: the photon deviates from path and electron takes part of its energy. The scattered photon has lost energy (so has a longer wavelength), and there is no relationship between the phases of the two waves. There is no interference and of little significance here (though it is for XRF) and we will not consider it further.

6. Diffraction Methods
Laue method: a single crystal is held stationary in a beam of monochromatic x-ray radiation. The crystal diffracts the discrete values of l for which {hkl} planes exist of spacing dhkl and incidence angle q. To determine symmetry of a crystal.
Rotating-crystal method: a single crystal is rotated about a fixed axis in a beam of monchromatic x-rays. The variation in q brings different atomic planes into position for reflection.
Powder (Debye-Scherrer-Hull) method: a finely powdered sample is placed in a holder in a monochromatic x-ray beam, with the angle q gradually changing due synchronous movement of holder and detector. Assuming random orientation of the tiny crystallites, there will be diffraction off of different {hkl} planes at specific angles.

7. Diffraction, or coherent scattering
Intensity
Gas
Intensity
Diffraction angle 2q
Liquid
Amorphous
Intensity
Diffraction angle 2q
Crystal
Diffraction angle 2q

8. Bragg’s Law
Incident x-ray l
Scattered x-ray l q
dhkl

9. S. W. Bailey XRD Laboratory
A353 Weeks

10. Powder X-ray DiffractometerLN
Dewar
X-ray tube
Specimen
Detector
X-ray Diffractometer
Controller and
Data Collection 2θ θ
X-ray tube HV
Crystal
Detector
(Moving)
(Fixed)
(Moving)

11. New XRD with 2-D detector powder and single crystals

12. XRD Applications
Crystallographic structural analysis and unit-cell calculations
Quantitative determination of amounts of different phases (in multi-phase mixture) by peak-ratio calculations
Quantitative determination of phases by whole-pattern (Rietveld) refinement
Determination of crystallite size from peak broadening
Determination of crystallite shape from peak symmetry
Study of thermal expansion by using in-situ heating stage.

13. Ewald Sphere 18x larger X-ray diffraction EBSD
CuKα x-ray λ= Å e- (20 kV) λ = Å
|k| = = 0.65 Å |k| = = Å-1 1 λ
Aluminum
fcc
a=4.05 Å
d(200)=2 Å
g(200)=1/d(200)=0.5 Å
The Ewald sphere is a geometric construction used in electron, neutron, and X-ray crystal-lography which demonstrates the relationship between: the wavevector of the incident and diffracted x-ray beams, the diffraction angle for a given reflection, the reciprocal lattice of the crystal.

14. Shoji Nishikawa and Seishi Kikuchi The Diffraction of Cathode Rays by Calcite. Proc. Imperial Academy (of Japan) 4 (1928)
Kikuchi recognized the importance of a divergent electron beam being diffracted -- how the spreading of the incident beam (by inelastic scattering in upper surface of sample)
Orientation mapping (OIM, orientation imaging microscopy)
Phase identification by step by step deduction of pattern point group symmetry, though some problems; other technique is to determine approx value of unit cell volume from measured lattice spacing and interplanar angles, together with EDS, searching a database for possible matches, then match angles
L-R: Yoshio Nishina, Seishi Kikuchi, Niels Bohr, laboratory in Japan Nishina Memorial Foundation, courtesy AIP Emilio Segre Visual Archives

15. a 2-D pattern with 3-D information
Kikuchi bands:
a 2-D pattern with 3-D information

16. EBSD
The sample is tilted steeply (55-70°) which enhances the number of HV electrons able to undergo diffraction and escape the surface
The HV electrons are scattered by the electrons of the atoms in the upper ~40 nm of the sample, scattering from electrons in {hkl} planes
Kossel cones are the set of wave vectors for a given {hkl} and intersect with a phosphor screen forming Kikuchi patterns
Electron backscatter diffraction (EBSD) is a technique for determining crystallographic information of submicron regions of flat polished samples. It has made possible studies of microtextures, phase identification (of polymorphs), grain boundary distribution, and deformation microstructures.
EBSD is also known by the names backscatter Kikuchi diffraction BKD, or electron backscatter pattern EBSP. The phenomenon has been known since 1928 by Kikuchi, who noted ‘remarkable lines’ resulting from electron diffraction thru a thin mica crystal. Two research groups (in UK) started working on EBSD ~1973, and it has only been commercially available since 1994.
In many cases it replaces more time-consuming/difficult TEM or XRD,or possibly electron channeling studies, with the benefit of SEM’s point by point high spatial resolution (<1 mm) together with its ability to scan large areas (~cm). It is relatively inexpensive ($50-100K), in being an add-on attachment to a previously existing SEM.
The Kikuchi pattern provides information about the crystal structure:
Point symmetry of the crystal lattice
Width and intensity of bands are related to dhkl and the unit volume
Angles between bands are related to the angles between {hkl} planes

17. EBSD Specimen preparation is important: crystalline surface is the key
The surface layer of most samples is damaged from mechanical polishing by diamond grit/paste
The damaged layer is removed by polishing with either colloidal silica or alumina (which also produces a chemical etch)
EBSD analysis on non-conductive samples can be done in VP-SEM
However high vacuum operation with a very thin coating such as 1 nm of Ir appears to yield better results than VP-SEM

18. EBSD CAMERAS
Modern CCD-based EBSD systems can index patterns at up to 1800 patterns / second. This enables very rapid and rich microstructural maps to be generated.
Recently, CMOS detectors have also been used in the design of EBSD systems. The new CMOS-based systems permit pattern indexing faster than CCD-based predecessors. Modern CMOS-based EBSD detectors are capable of indexing patterns up to 3000 patterns / second
Goldstein et al, 2018, p. 499
Source: Wikipedia

19. Prior et al. (1999) American Mineralogist: 84, 1741-1759.
EBSD
Prior et al. (1999) American Mineralogist: 84,

20. EBSD Patterns
The goal is to obtain SHARP Kikuchi bands like these! Not always possible on real samples (e.g. rocks)!

21. EBSD in Operation Very briefly, some of the key steps in doing EBSD:
Correctly polish the sample surface IF it has been ground flat. Natural crystals do NOT need polish.
Load the candidate crystals’ data into the software, if not already, acquire it from source such as American Mineralogist database at U of AZ
Load sample, move camera to correct location, select kV and beam current, locate area with SE or BSE
Acquire a background
Acquire a pattern
Index the pattern

22. Indexing EBSD Patterns
“Indexing” means identifying the crystal orientation at the single volume of the sample from where a pattern was collected. With EBSD software, pattern bands are typically detected via a mathematical routine called a “Hough transform”, in which every pixel in Hough space denotes a unique line/band in the EBSD Pattern (EBSP). The Hough transform is used to enable band detection, which are difficult to locate by computer in the original EBSP. Once the band locations have been detected it is possible to relate these locations to the underlying crystal orientation, as angles between bands represent angles between lattice planes. Thus when the position / angles between some number of bands (e.g. 9-12) are known an orientation solution can be determined.

23. Hough Transform
The “Hough Transform” algorithm takes the straight lines of the Kikuchi patterns and transfers them into points, which are then easier for the image analysis software built into the EBSD software to find.
Here the point is (r, theta)
Next, the angles between bands in patterns are compared with a lookup table of the candidate phase crystal structures.
When a consistent set of indices is found, the pattern is tentatively considered “indexed” – with some “MAD”, mean angular deviation, a measure of slop in the match. You’d like the lowest MADs, like 0.3, but sometimes you have to live with something a little under 1.0

24. EBSD Uses:
Mapping
Phase Identification

25. Orientation Mapping
In geology, in the past, a “Universal Stage” was used to map out orientation of crystals in a thin section. This took a LONG time and a lot of skill. Actually, UW-Madison was a leader in this, with the work of our mineralogist “Con” Emmons ( ).
This was mounted onto the stage of a petrographic (polarized light) microscope.

26. Phase/Orientation Mapping
Today, with EBSD, large regions (even whole thin sections!) can be mapped at ~25-50 micron resolution overnight.

27. Grain/Orientation Mapping
Above, EBSD of a dual phase steel with both austenite and ferrite. (a) Band contrast map (a measure of pattern sharpness, reflecting grain structure). (b) Orientation map of the autenite phase (colors) with the grey the underlain band contrast map showing the ferrite.
Goldstein et al, 2018, p. 497

28. Orientation Maps
Crystallographic orientations may be displayed in various ways.
Pole figure maps. These answer the question: Where does a particular crystallographic direction or plane fall in space relative to some arbitrary physical sample direction or plane?
Inverse pole figure maps. These answer the question: What crystallographic poles or planes are preferrentially parallel or perpendicular to a specific sample direction?
Goldstein et al, 2018, p. 505

29. Inverse Pole Figure
Goldstein et al, 2018, p. 497

30. From Microscopy Today, Jan/Feb 1993

31. EBSD: Phase Identification
There are many phases with similar or the same chemistry, for which EBSD is a very useful tool, for example:
CaCO3: calcite, aragonite, vaterite
TiO2: rutile, anatase, brookite
SiO2: cristobalite, trydimite, coesite, stishovite, a and b quartz
Iron rich “Steel”: ferrite (BCC) and austenite (FCC)

32. Transmission Kikuchi Diffraction
TKD:
Transmission Kikuchi Diffraction
Improved spatial resolution is possible if the sample is thinned, so that the electrons scatter even less than in regular tilted-bulk sample EBSD
CaCO3: calcite, argonite, vaterite
TiO2: rutile, anatase, brookite
SiO2: cristobalite, trydimite, coesite, stishovite, a and b quartz
Iron rich “Steel”: ferrite (BCC) and austenite (FCC)

33. Orientation Contrast Imaging
The upper two diodes detect backscattered electrons (BSE imaging)
Intensity varies with mean atomic number (Z) and is proportional to Z1.7
The lower two diodes detect forescattered electrons (OC imaging)
Intensity varies due to differences in crystal orientation >> Z
Exact same sample area

34. Orientation Contrast Imaging
The control of the lattice on the variation in BSE intensity with exit beam trajectory is known as channeling-out (and diffracted beam)
The control of the lattice on the variation in BSE intensity with incident beam trajectory is known as channeling-in
Prior et al. (1999) American Mineralogist: 84,

35. Banded Iron Formation
Diffraction:
Electron and X-ray

36. Some References
Goldstein et al, 2018, Scanning Electron Microscopy and X-Ray MicroAnalysis, Chapter 29 (by Joe Michael), Characterizing Crystalline Materials in the SEM.
Prior, D.J. et al. (1999) The application of electron backscatter diffraction and orientation contrast imaging in the SEM to textural problems in rocks. American Mineralogist: 84,
Introduction to X-Ray Powder Diffraction, by Jim Connolly (notes for U NM EPS ,
Modern Powder Diffraction by D. L. Bish and J. E. Post (eds), Mineralogical Society of America Reviews in Mineralogy, Vol 20, 1989
Electron Backscatter Diffraction in Materials Science, Edited by Adam J. Schwartz, Mukul Kumar and Brent L. Adams, Kluwer/Plenum, 2000, ISBN X (25 articles)
An Atlas of Electron Backscatter Diffraction Patterns by D. J. Dingley, K. Baba-Kishi, and V. Randle, 1994, Institute of Physics Publishing.