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
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
X-ray Generation
X-rays
Cathode
e-
Anode
Intensity
Kα=1.54Å
Kβ=1.39Å
Wavelength (Å)
The emission spectra for Cu
Intensity Mass Absorption Coefficient
1.2
Monochromatic Radiation
is needed for Crystal
Structure Analysis
Kα
Kα
Kβ
Filters for Suppression of Kβ Radiation
Kβ
1.4
1.6
λ(Å)
Unfiltered
1.8
1.2
1.4
1.6
λ(Å)
Ni Filter
1.8
The dotted line is the Mass
Absorption coefficient for Ni
Interference and Bragg’s Law
AO=OB
Bragg Diffraction
occurs when
2AO=nλ
Sinθ=AO/d(hkl)
2d Sinθ=nλ
λ=wavelength of the
incident radiation
Cu Kα=1.54 Å
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)
Lattice Parameter Calculation
Miller Indices
Bragg’s Law
Silicon Powder
Knowing dhkl we can
calculate the lattice
parameters
X-ray Diffraction
Differentiate Crystal Structures
C (Graphite)
C (Diamond)
SiC
0.436 nm
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
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
X-ray Diffraction
Peak Intensities
1. Polarization Factor
2. Structure Factor
3. Multiplicity Factor
4. Lorentz Factor
5. Absorption Factor
6. Temperature Factor
α-Al2O3
X-ray Diffraction
Phase Identification
International Centre for
Diffraction Data (ICDD)
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.
X-ray Diffraction
Phase Identification
PDF # 72-0268 Iron Chloride
Hydrate
Iron Chloride Dihydrate
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.
Breakdown of the PDF-2 database
X-ray Diffraction
Quantitative Phase Analysis (QPA)
DIFFRAC.SUITE EVA
Fe 75, Ni 25 wt.%
X-ray Diffraction
X ray diffraction of semi-crystalline polymer and amorphous
polymer
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.
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.
When to Use Scherrer’s Formula
Crystallite size < 5000 Å
K ∗λ
t=
B ∗ cos θ B
t = thickness of crystallite
K = constant dependent on crystallite shape (0.89)
λ = X-ray wavelength
B = FWHM (full width at half max) or integral breadth
θB = Bragg angle
Residual Stress Measurements
using X-Ray Diffraction
X-ray Diffraction
Diffraction cones arise from randomly oriented
polycrystalline aggregates or powders
X-ray
Polycrystalline
Sample
Diffraction Cone forms
Debye Rings
X-ray Diffraction
2D Detector
Area Detector
Debye Rings
X-ray Diffraction
Types of Detectors
Scintillation detector
2D Area detector
 Small portion of Debye
 large 2θ and chi range measured
ring acquired
 scan necessary
 long measuring times
 measurement of oriented samples
simultaneously
 very short measuring times
 intensity versus 2θ by integration of
the data
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
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
X-ray Diffraction
Orientation
The intensity distribution of the
Debye ring reveals much
information about the texture of
the material being studied!
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.
X-ray Diffraction
224
Simulated pattern
of CuInSe2
204
213
213
112
Acquired XRD
pattern of a thin
film of CuInSe2
grown on a Mo
foil substrate
211
103
101
204
112
Orientation
X-ray Sources
Rigaku D/MAX 2200 Diffractometer
Anode Kα1(Å)
Comments
Best for inorganics. Fe and
Co fluorescence.
Cu
1.54060
Cr
High Resolution for large d2.28970 spacing. High attenuation
in air.
Co
1.78897
Used for ferrous alloys to
reduce Fe fluorescence.
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)
Electron Diffraction Zeiss Libra 200EF
Polycrystal
Single Crystal
EBSD – Electron Back-Scattered Diffraction in the SEM
Background Corrected Pattern
Averaged Background
Raw Pattern
EBSD – Electron Back-Scattered Diffraction in the SEM
Background Corrected Pattern
Indexed Pattern
4
12
2
10
1
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
500 μm
EBSD data – Maps
polycrystalline Al2O3
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
EBSD Phase Discrimination
bcc Fe
fcc Fe
Differences in interplanar
angles and spacings allow
similar-looking EBSD patterns
from bcc and fcc
Fe to be readily distinguished.
bcc Fe
fcc Fe
EBSD data – Maps
Phase distribution, texture, grain size / shape, boundary properties,
misorientation, slip system activity, intra-granular deformation....
Phase map
Orientation bcc
Orientation fcc
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
2
Hough transformation
Transforms x-y space
to ρ−θ space. Bands in
Hough space show as
points which are easier
to identify and extract
90
°
1
0
1
0
°
1
2
4
2
1
0
4
90
°
1
Format of Crystal Information
Band triplets
Solution #
# votes
S3 (best solution w/most votes)
S2 (2nd best solution w/ 2ndmost votes)
Euler Angles using Bung convention:
1. A rotation of φ1 about the z axis
followed by
2. A rotation of ϕ about the rotated xaxis followed by
3. A rotation of φ2 about the rotated zaxis
X-ray Diffraction
Phase Identification
Intensity Mass Absorption Coefficient
1.2
Kα
Kα
Kβ
Kβ
1.4
1.6
λ(Å)
Unfiltered
1.8
1.2
1.4
1.6
λ(Å)
Ni Filter
1.8