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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
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
• 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
Discovery of X-rays and Modern XRD
Anode
X-raysCathode
e-
Wavelength (Å)
Inte
nsity
Kα=1.54Å
Kβ=1.39Å
X-ray Generation
The emission spectra for Cu
Monochromatic Radiation is needed for Crystal Structure Analysis
The dotted line is the Mass Absorption coefficient for Ni
Kβ
Kβ
Kα
Kα
λ(Å)Unfiltered
λ(Å)Ni Filter
1.2 1.4 1.6 1.8 1.2 1.4 1.6 1.8
Inte
nsity
Mas
s Abs
orpt
ion
Coe
ffic
ient
Filters for Suppression of Kβ Radiation
Interference and Bragg’s Law
AO=OBBragg Diffraction occurs when 2AO=nλSinθ=AO/d(hkl)2d Sinθ=nλ
λ=wavelength of the incident radiation
Cu Kα=1.54 Å
Monochromatic X-rays using Diffraction
C (Graphite)
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.
Bragg’s Law
Knowing dhkl we can calculate the lattice
parameters
Lattice Parameter CalculationMiller Indices
Silicon Powder
X-ray DiffractionDifferentiate Crystal Structures
C (Graphite) C (Diamond) SiC
0.436 nm
Scintag Advanced X-Ray Diffractometer System
Conventional theta-theta scanRocking curves and sample-tilting
curvesGrazing 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
• 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
Amorphous Pattern Crystalline Pattern
X-ray DiffractionTypical Patterns
X-ray DiffractionPeak Intensities
1. Polarization Factor
2. Structure Factor
3. Multiplicity Factor
4. Lorentz Factor
5. Absorption Factor
6. Temperature Factor
α-Al2O3
X-ray DiffractionPhase Identification
Iron Chloride Dihydrate
• 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.
International Centre for Diffraction Data (ICDD)
X-ray DiffractionPhase Identification
Iron Chloride Dihydrate
PDF # 72-0268 Iron Chloride Hydrate
X-ray DiffractionQuantitative 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.Breakdown of the PDF-2 database
X-ray DiffractionQuantitative Phase Analysis (QPA)
DIFFRAC.SUITE EVA
Fe 75, Ni 25 wt.%
X-ray DiffractionX ray diffraction of semi-crystalline polymer and amorphous
polymer
X-ray DiffractionXRD 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.
Smaller Crystals Produce Broader XRD Peaks
Note: In addition to instrumentalpeak broadening, other factors that contribute to peak broadening include strain and composition inhomogeneities.
Gold Nanoparticle
2nm
When to Use Scherrer’s FormulaCrystallite size < 5000 Å
BcosBKt
θλ
∗∗
=
t = thickness of crystalliteK = constant dependent on crystallite shape (0.89)λ = X-ray wavelengthB = FWHM (full width at half max) or integral breadthθB = Bragg angle
Residual Stress Measurements using X-Ray Diffraction
PolycrystallineSample
X-ray DiffractionDiffraction cones arise from randomly oriented
polycrystalline aggregates or powders
X-ray
Diffraction Cone forms Debye Rings
Area Detector
X-ray Diffraction2D Detector
Debye Rings
X-ray DiffractionTypes of Detectors
Small portion of Debye ring acquired
scan necessary long measuring times
large 2θ and chi range measured simultaneously
measurement of oriented samples very short measuring times intensity versus 2θ by integration of
the data
2D Area detectorScintillation detector
• Small Beam diameter• Can achieve 200μm
• Parallel Illumination• Forgives displacement errors
• 4 circle Huber goniometer• Dual beam alignment system
X-ray DiffractionBruker D8 Discover
Polymers, due to their long chain structure, are often highly oriented.
X-ray DiffractionOrientation
Alignment of a sample in a drawing process causes
orientation effects
X-ray DiffractionOrientation
The intensity distribution of the Debye ring reveals much information about the texture of the material being studied!
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.
X-ray Diffraction of Conch Shells
X-ray DiffractionOrientation
Simulated pattern of CuInSe2
Acquired XRD pattern of a thin film of CuInSe2grown on a Mo foil substrate
101
112
103
211
213
204
224
112
213
204
X-ray Sources
Anode Kα1(Å) Comments
Cu 1.54060 Best for inorganics. Fe and Co fluorescence.
Cr 2.28970High Resolution for large d-spacing. High attenuation
in air.
Co 1.78897 Used for ferrous alloys to reduce Fe fluorescence.
Rigaku D/MAX 2200 Diffractometer
X-ray DiffractionSummary
• 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)
Electron Diffraction Zeiss Libra 200EF
Polycrystal
Single Crystal
EBSD – Electron Back-Scattered Diffraction in the SEM
Raw PatternAveraged BackgroundBackground Corrected Pattern
1
2
10
12 4
EBSD – Electron Back-Scattered Diffraction in the SEM
Background Corrected Pattern Indexed Pattern
300×300 grid
5 μm step
Analysis time: 36 minutes
500 μm
EBSD data – MapsBeam scan provides orientation map of polycrystalline NaCl
The colors indicate specific orientations
polycrystalline Al2O3
EBSD data – Maps
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
bcc Fe fcc Fe
bcc Fe fcc Fe
EBSD Phase Discrimination
Differences in interplanar angles and spacings allow similar-looking EBSD patterns from bcc and fcc Fe to be readily distinguished.
Phase distribution, texture, grain size / shape, boundary properties, misorientation, slip system activity, intra-granular deformation....
EBSD data – Maps
Orientation bcc
Orientation fcc
Phase map
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!
Hough Transformation
1
2
10
12
4
12
10
4
12
0°
-90°
90°
Hough transformation Transforms x-y space to ρ−θ space. Bands in Hough space show as points which are easier to identify and extract relative angles.
Format of Crystal Information
Euler Angles using Bung convention:1. A rotation of φ1 about the z axis
followed by2. A rotation of ϕ about the rotated x-
axis followed by3. A rotation of φ2 about the rotated z-
axis
Solution #
# votes
Ban
d tr
iple
ts
S3 (best solution w/most votes)S2 (2nd best solution w/ 2ndmost votes)
X-ray DiffractionPhase Identification
Kβ
Kβ
Kα
Kα
λ(Å)Unfiltered
λ(Å)Ni Filter
1.2 1.4 1.6 1.8 1.2 1.4 1.6 1.8In
tens
ity M
ass A
bsor
ptio
n C
oeff
icie
nt
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