# X-ray Diffraction and EBSD

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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

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

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

Monochromatic Radiation is needed for Crystal Structure Analysis
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

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

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

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

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
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.

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

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

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

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

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 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

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

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

X-ray Diffraction 2D Detector
Area Detector Debye Rings

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

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. Aragonite is a polymorph of CaCo3 has an orthorhombic symmetry were as calcite has a trigonal symmetry

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

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.

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 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

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)

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

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

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 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.

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

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 10 4 12 -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.

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

X-ray Diffraction Phase Identification

Intensity Mass Absorption Coefficient
λ(Å) Unfiltered Ni Filter Intensity Mass Absorption Coefficient