1. X-ray Diffraction and EBSD
Jonathan Cowen
Swagelok Center for the Surface Analysis of Materials
Case School of Engineering
Case Western Reserve University
October 27, 2014

2. Outline X-ray Diffraction (XRD)
History and background
Introduction to XRD
Practical applications
Electron Back-Scattered Diffraction (EBSD)
Introduction to EBSD
Types of information that can be drawn from EBSD

3. Discovery of X-rays and Modern XRD
Wilhelm Conrad Röntgen
1895: Discovery of X-ray
1901: awarded first Nobel prize winner for Physics
M.T.F. von Laue:
1912: Discovery of the diffraction of X-rays by single crystals , in cooperation with Friedrich and Knipping
Terms: Laue equation, Laue reflections
1914: Nobel prize for Physics
W.H. and W.L. Bragg:
1914: X-ray diffraction and Crystal Structure
Terms: Bragg‘s equation, Bragg reflections
1915: Nobel prize for Physics
Nearly two weeks after his discovery, he took the very first picture using X-rays of his wife Anna Bertha's hand. When she saw her skeleton she exclaimed "I have seen my death!"[5]
Max von Laue

4. The emission spectra for Cu
X-ray Generation
Anode
X-rays
Cathode e-
Wavelength (Å)
Intensity
Kα=1.54Å
Kβ=1.39Å
Vacuum tube-A bias potential of 45kV and an emission current of 40mA is used.
The emission spectra for Cu

5. Monochromatic Radiation is needed for Crystal Structure AnalysisKβ Kα
λ(Å)
Unfiltered
Ni Filter
Intensity Mass Absorption Coefficient
Filters for Suppression of Kβ Radiation
The dotted line is the Mass
Absorption coefficient for Ni

6. Interference and Bragg’s Law
AO=OB
Bragg Diffraction occurs when 2AO=nλ
Sinθ=AO/d(hkl)
2d Sinθ=nλ
Incident waves in phase—diffract off atomic planes (reflections)---AO=OB and when 2A0=nlamda we we have conditions that satisfy
the Bragg equation.
λ=wavelength of the incident radiation
Cu Kα=1.54 Å

7. Monochromatic X-rays using Diffraction
Graphite monochromator utilizes a highly orientated pyrolytic
graphite crystal (HOPG) mounted in a compact metal housing to provide
monochromatic radiation. This is usually an improvement over filters.
C (Graphite)

8. Lattice Parameter Calculation
Miller Indices
Bragg’s Law
Silicon Powder
Knowing dhkl we can calculate the lattice parameters

9. X-ray Diffraction Differentiate Crystal Structures
C (Graphite)
C (Diamond)
SiC
0.436 nm

10. Scintag Advanced X-Ray Diffractometer System
Conventional theta-theta scan
Rocking curves and sample-tilting curves
Grazing angle X-ray diffraction (GAXRD)
DMSNT software package is used to control the diffractometer, to acquire raw data and to analyze data.
PDF-2 database and searching software for identifying phases
Synchronous

11. X-ray Diffraction Typical Patterns
Amorphous Pattern
Crystalline Pattern
Amorphous patterns will show an absence of sharp peaks
Crystalline patterns will show many sharp peaks
The atoms are very carefully arranged
High symmetry
From peak locations and Bragg’s Law, we can determine the structure and lattice parameters.
Elemental composition is never measured
By comparing to a database of known materials, phases can be identified

12. X-ray Diffraction Peak Intensities
Polarization Factor
Structure Factor
Multiplicity Factor
Lorentz Factor
Absorption Factor
Temperature Factor
α-Al2O3
Lorentz-polarization factors take care of asymmetric tails of broad peaks especially at higher two theta values.

13. International Centre for Diffraction Data (ICDD)
X-ray Diffraction Phase Identification
International Centre for Diffraction Data (ICDD)
• The PDF-2 (Powder Diffraction File) database contains over 265K entries.
• Modern computer programs can determine what phases are present in any sample by quickly comparing
the diffraction data to all of the patterns in the database.
• The PDF card for an entry contains much useful information, including literature references.
Iron Chloride Dihydrate

14. X-ray Diffraction Phase Identification
PDF # Iron Chloride Hydrate
Iron Chloride Dihydrate
Inset

15. X-ray Diffraction Quantitative Phase Analysis (QPA)
External standard method
A reflection from a pure component.
Direct comparison method
A reflection from another phase within the mixture.
Internal standard method
A reflection from a foreign material mixed within the sample.
Reference Intensity Ratio (RIR)
Generalized internal standard method developed by the ICDD.
Some internal standards have been built into the database. As long as the phase and its associated PDF has been run with pure alpha alumina an internal correction for phase has been established. I is the maximum intensity of the strongest line from some component and I(corundum). I/I(cor) is a correction factor that can be applied to determine the percent of phase a.
Breakdown of the PDF-2 database

16. X-ray Diffraction Quantitative Phase Analysis (QPA)
DIFFRAC.SUITE EVA
Fe 75, Ni 25 wt.%

17. X ray diffraction of semi-crystalline polymer and amorphous polymer

18. X-ray Diffraction
XRD is a primary technique to determine the degree of crystallinity in polymers.
The determination of the degree of crystallinity implies use of a two-phase model, i.e. the sample is composed of crystalline and amorphous regions.

19. Smaller Crystals Produce Broader XRD Peaks
2nm
Gold Nanoparticle
Note: In addition to instrumental
peak broadening, other factors that
contribute to peak broadening
include strain and composition inhomogeneities.

20. When to Use Scherrer’s Formula
Crystallite size < 5000 Å
t = thickness of crystallite
K = constant dependent on crystallite shape (0.89)
l = X-ray wavelength
B = FWHM (full width at half max) or integral breadth
θB = Bragg angle

21. Residual Stress Measurements using X-Ray Diffraction
The planes parallel to the surface represent a case of zero residual stresses. The planes which are normal to the sample surface represent a maximum in the residual stress. All plane in between will therefore contain some

22. Polycrystalline Sample
X-ray Diffraction Diffraction cones arise from randomly oriented polycrystalline aggregates or powders
X-ray
We just talked about the difference between conventional XRD and the 2 dimensional XRD, but to understand how this two dimensional image was recorded? We have to start with the diffraction pattern in 3D space. This figure shows the pattern of diffracted x-rays from a single crystal and from a polycrystalline sample. The diffracted rays from a single crystal point to discrete directions each corresponding to a family of diffraction planes. The diffraction pattern from a polycrystalline (powder) sample forms a series diffraction cones if large number of crystals oriented randomly in the space are covered by the incident x-ray beam (Figure 2.2b). Each diffraction cone corresponds to the diffraction from the same family of crystalline planes in all the participating grains.
Polycrystalline Sample
Diffraction Cone forms Debye Rings

23. X-ray Diffraction 2D Detector
Area Detector
Debye Rings

24. X-ray Diffraction Types of Detectors
Scintillation detector
2D Area detector
Small portion of Debye ring acquired
scan necessary
long measuring times
large 2 and chi range measured simultaneously
measurement of oriented samples
very short measuring times
intensity versus 2 by integration of
the data

25. X-ray Diffraction Bruker D8 Discover
Small Beam diameter
Can achieve 200μm
Parallel Illumination
Forgives displacement errors
4 circle Huber goniometer
Dual beam alignment system

26. X-ray Diffraction Orientation
Polymers, due to their long chain structure, are often highly oriented.
Alignment of a sample in a drawing process causes orientation effects

27. X-ray Diffraction Orientation
The intensity distribution of the Debye ring reveals much information about the texture of the material being studied!

28. X-ray Diffraction of Conch Shells
In addition to identifying the CaCO3 as the Aragonite polymorph, X-ray diffraction patterns reveal a strong degree of crystallographic texture in the intact shell.
Aragonite is a polymorph of CaCo3 has an orthorhombic symmetry were as calcite has a trigonal symmetry

29. X-ray Diffraction Orientation
112
Simulated pattern of CuInSe2
204
101
224
103
211
213
Acquired XRD pattern of a thin film of CuInSe2 grown on a Mo foil substrate
112
213
204

30. X-ray Sources Anode Ka1(Å) Comments Cu Cr Co
Rigaku D/MAX 2200 Diffractometer
Anode
Ka1(Å)
Comments Cu
Best for inorganics. Fe and Co fluorescence. Cr
High Resolution for large d-spacing. High attenuation in air. Co
Used for ferrous alloys to reduce Fe fluorescence.

31. X-ray Diffraction Summary
Structure Determination
Phase Identification
Quantitative Phase Analysis (QPA)
Percent Crystallinity
Crystallite Size and Microstrain
Residual Stress Measurements (Macrostrain)
Texture Analysis
Single Crystal Studies (not a SCSAM core competency)

32. Electron Diffraction Zeiss Libra 200EF
Polycrystal
Electron diffraction ERD and EBSD by being very site specific. Single crystal diffraction patterns are easy to acquire. Particle sizes have to be on the order of tens of nanometers to acquire ring patterns as seen above.
Single Crystal

33. EBSD – Electron Back-Scattered Diffraction in the SEM
Background Corrected Pattern
Averaged Background
Raw Pattern
Static background -
Dynamic background – (takes in to account the intensity variation between phases)

34. EBSD – Electron Back-Scattered Diffraction in the SEM
Background Corrected Pattern
Indexed Pattern 1 2 10 12 4

35. EBSD data – Maps Beam scan provides orientation map of polycrystalline NaCl
300×300 grid
5 μm step
Analysis time: 36 minutes
The colors indicate
specific orientations

36. EBSD data – Maps
polycrystalline Al2O3

37. A single automated EBSD run can provide a complete characterization of the microstructure:
Phase distribution
Texture strength
Grain size
Boundary properties
Misorientation data
Slip system activity
Intra-granular deformation
Can collect XEDS simultaneously

38. EBSD Phase Discrimination
bcc Fe
fcc Fe
bcc Fe
fcc Fe
Duplex stainless steels.
Differences in interplanar angles and spacings allow similar-looking EBSD patterns from bcc and fcc
Fe to be readily distinguished.

39. Body- and Face-Centered Cubic Iron
EBSD
Body- and Face-Centered Cubic Iron
Plane
Intensity
No.
{110}
100% x6
{200}
51%
{112}
32%
x12
{220}
23%
{013}
17%
{222}
13% x4
{123}
10%
x24
bcc
Plane
Intensity
No.
{111}
100% x4
{200}
77% x3
{220}
38% x6
{113}
26%
x12
{222}
23%
{400}
16%
{133}
13%
{240}
12%
fcc
bcc h+k+l=2n (i.e. no {111})
fcc h, k, l all odd or all even

40. EBSD data – Maps
Phase distribution, texture, grain size / shape, boundary properties, misorientation, slip system activity, intra-granular deformation....
Phase map
Orientation bcc
Orientation fcc

41. Summary
XRD is a powerful tool for answering some specific questions about a given sample.
Phases present, QPA, orientation, residual stress, texturing, and crystallite size analysis.
XRD is extremely efficient for the characterization of samples.
Sample preparation time is minimal when compared to SEM/EBSD and TEM.
Data acquisition is straight forward and short set up times are required.
XRD will provide a larger sampling area and a more accurate averaged result of the lattice parameter, but EBSD will be more site specific.
EBSD yields similar results and all the same “specific questions” can be answered in one data set!

42. Hough Transformation 1 2 10 4 12 0°
-90°
90° 1 2 10 12 4
Hough transformation Transforms x-y space to r-q space. Bands in Hough space show as points which are easier to identify and extract relative angles.

43. Format of Crystal Information
Solution #
# votes
Band triplets
S3 (best solution w/most votes)
S2 (2nd best solution w/ 2ndmost votes)
Euler Angles using Bung convention:
A rotation of φ1 about the z axis followed by
A rotation of ϕ about the rotated x-axis followed by
A rotation of φ2 about the rotated z-axis

44. X-ray Diffraction Phase Identification

45. Intensity Mass Absorption CoefficientKβ Kα
λ(Å)
Unfiltered
Ni Filter
Intensity Mass Absorption Coefficient