Lecture21-XRD-AnalysisOfXRDSpectraI

# Lecture21-XRD-AnalysisOfXRDSpectraI - EMSE 312 –...

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Unformatted text preview: EMSE 312 – Diffraction Principles Lecture 21 Powder X-ray Diffraction (XRD) Techniques Analysis of XRD Spectra: Effects of Dislocations and Point Defects Indexing of XRD Patterns using First Principles Non-cubic Systems Ordered Phases EMSE 312 DIFFRACTION PRINCIPLES EMSE 312 – Diffraction Principles Diffraction Techniques - XRD • XRD Diffractogram Analysis – Peak Broadening – Other Effects?????? – STRAIN!!! Uniform Tension d d + Δ Uniform Compression d d − Δ Uniform Bending Ave d d = Tension Compression 2 θ 2 θ T ( ) 1 T 2 2 s i n 2 2 d d λ θ θ − ⎛ ⎞ = < ⎜ ⎟ + Δ ⎝ ⎠ Strain Free d 2 θ 2 θ I/I 1 2 2 s i n 2d λ θ − ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠ 2dsin θ λ = 2 θ 2 θ C ( ) 1 C 2 2 s i n 2 2 d d λ θ θ − ⎛ ⎞ = > ⎜ ⎟ − Δ ⎝ ⎠ 2 θ 2 θ B 1 B 2 2 s i n 2d λ θ − ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠ Tension Compression EMSE 312 – Diffraction Principles Diffraction Techniques - XRD • XRD Diffractogram Analysis – Peak Broadening – Point Defects!!! • Vacancies – Local increase in d-spacing • Interstitials – Local decrease in d-spacing I/I 2 θ 2 θ 2 θ V 2 θ 2 θ I 2 θ 1 2 2 s i n 2d λ θ − ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠ 2dsin θ λ = Strain Free Reference Asymmetric Peaks Asymmetric Peaks EMSE 312 – Diffraction Principles Diffraction Techniques - XRD • Stoichiometric Oxides (e.g., MO) – Non-stoichiometry – small deviation from stoichiometry • A) M/O > 1 – Excess M: M 1+x O – O Deficiency: MO 1-x • B) M/O < 1 – Excess O: MO 1+x – M Deficiency: M 1-x O – The density of the stoichiometric Oxide is different from that of the non-stoichiometric oxide, and depends on the type of point defects EMSE 312 – Diffraction Principles Diffraction Techniques - XRD • XRD Diffractogram Analysis – Peak Broadening – Deformation – Recovery/Recrystallization – Grain growth I/I 2 θ 2 θ 1 2 θ 2 2 θ 2 θ 1 2 θ 2 2 θ 2 θ 1 2 θ 2 2 θ 2 θ 1 2 θ 2 Reference EMSE 312 – Diffraction Principles 200 400 600 800 1000 1200 1400 20 40 60 80 100 Powder 1) Check for similar Peak Broadening- SAME GRAIN SIZE 2) Check for Asymmetric Peaks- SAME TYPE OF POINT DEFECTS ab #5 EMSE 312 – Diffraction Principles 50 100 150 200 250 300 350 400 450 500 20 40 60 80 100 Sintered 1) Check for New Peaks 2) Check for Absent Peaks 3) Increasing and Decreasing Intensities ab #5 EMSE 312 – Diffraction Principles EMSE 312 – Diffraction Principles Diffraction Techniques - XRD • XRD Diffractogram Analysis – Indexing – Comparison with the JCPDF Data Base • Hanawalt • Fink • Computer methods – First principle determinations • Lattice parameters from d-spacings • Atom positions from Intensities • DIFFICULT/ TEDEOUS EMSE 312 – Diffraction Principles Diffraction Techniques - XRD • XRD Diffractogram Analysis of Real Samples...
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## This note was uploaded on 12/01/2011 for the course EMSE 312 taught by Professor Lagerlof,p during the Spring '08 term at Case Western.

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Lecture21-XRD-AnalysisOfXRDSpectraI - EMSE 312 –...

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