X-ray Diffraction and EBSD

X-ray Diffraction and EBSD

Jonathan Cowen

Swagelok Center for the Surface Analysis of Materials

Case School of Engineering

Case Western Reserve University

Outline

• X-ray Diffraction (XRD)

• History and background

• Introduction to XRD

• Practical applications

• Electron Back-Scattered Diffraction (EBSD)

• Introduction

to 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

Anode X-rays Cathode e -Wavelength (Å) In ten sity K_α=1.54Å K_β=1.39Å

X-ray Generation

Monochromatic Radiation

is needed for Crystal

Structure Analysis

The dotted line is the Mass Absorption coefficient for Ni

K_β K_β K_α K_α λ(Å) Unfiltered λ(Å) Ni Filter 1.2 1.4 1.6 1.8 1.2 1.4 1.6 1.8 In ten sity M as s Ab so rp tio n C o ef ficien t

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

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 d_hkl we can calculate the lattice

parameters

Lattice Parameter Calculation

Miller Indices

X-ray Diffraction

Differentiate Crystal Structures

C (Graphite) C (Diamond) SiC

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

• 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 Diffraction

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

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 Diffraction

Phase Identification

Iron Chloride Dihydrate

PDF # 72-0268 Iron Chloride Hydrate

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.

X-ray Diffraction

Quantitative Phase Analysis (QPA)

DIFFRAC.SUITE EVA

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

Note: In addition to instrumental

peak broadening, other factors that

contribute to peak broadening

include strain and composition

inhomogeneities.

Gold Nanoparticle

When to Use Scherrer’s Formula

Crystallite size < 5000 Å

B

cos

B

K

t

θ

λ

∗

∗

=

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

Residual Stress Measurements

using X-Ray Diffraction

Polycrystalline Sample

X-ray Diffraction

Diffraction cones arise from randomly oriented polycrystalline aggregates or powders

X-ray

Diffraction Cone forms Debye Rings

Area Detector

X-ray Diffraction

2D Detector

X-ray Diffraction

Types 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 detector Scintillation detector

• Small Beam diameter • Can achieve 200μm • Parallel Illumination

• Forgives displacement errors • 4 circle Huber goniometer

• Dual beam alignment system

X-ray Diffraction

Polymers, due to their long chain structure, are often highly oriented.

X-ray Diffraction

Orientation

Alignment of a sample in a drawing process causes

X-ray Diffraction

Orientation

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

Orientation Simulated pattern of CuInSe₂ Acquired XRD pattern of a thin film of CuInSe₂ grown on a Mo foil substrate 101 11 2 103 ₂11 213 204 224 11 2 213 204

X-ray Sources

Anode Kα₁(Å) Comments

Cu 1.54060 Best for inorganics. Fe and Co fluorescence.

Cr 2.28970 High Resolution for large d-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

EBSD – Electron Back-Scattered Diffraction in the SEM

Raw Pattern Averaged Background

1 2

10

12 4

EBSD – Electron Back-Scattered Diffraction in the SEM

300×300 grid 5 μm step

Analysis time: 36 minutes

500 μm

EBSD data – Maps

Beam scan provides orientation map of polycrystalline NaCl

The colors indicate specific orientations

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

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

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 1 0 1 2 4 1 2 1 0 4 1 2 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 by

2. A rotation of ϕ about the rotated x-axis followed by

3. A rotation of φ₂ about the rotated z-axis Solution # # votes B a n d t ri p le ts

S3 (best solution w/most votes) S2 (2nd _{best solution w/ 2}nd_{most votes)}

X-ray Diffraction

K_β K_β K_α K_α λ(Å) Unfiltered λ(Å) Ni Filter 1.2 1.4 1.6 1.8 1.2 1.4 1.6 1.8 In ten sity M as s Ab so rp tio n C o ef ficien t