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-rays

Cathodee-

Wavelength (Å)

Inte

nsit

y

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

nsit

y M

ass

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 instrumental

peak 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

BcosB

Kt

t = thickness of crystalliteK = constant dependent on crystallite shape (0.89)l = 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 2 and chi range measured simultaneously

measurement of oriented samples very short measuring times intensity versus 2 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 CuInSe2 grown on a Mo foil substrate

101

112

103

211

213

204

224

112

213

204

X-ray Sources

Anode Ka1(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 1.78897Used for ferrous alloys to reduce Fe fluorescence.

Rigaku D/MAX 2200 Diffractometer

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

Raw PatternAveraged BackgroundBackground Corrected Pattern

1

2

10

124

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 -r q 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 t

rip

lets

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 1.8

Inte

nsit

y M

ass

Abs

orpt

ion

Coe

ffic

ient