Lecture22-XRD-AnalysisOfXRDSpectraII

Lecture22-XRD-AnalysisOfXRDSpectraII - EMSE 312 DIFFRACTION...

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EMSE 312 – Diffraction Principles Lecture 22 Powder X-ray Diffraction (XRD) Techniques Analysis of XRD Spectra: Indexing of XRD Patterns using First Principles Non-cubic Systems Ordered Phases EMSE 312 DIFFRACTION PRINCIPLES
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EMSE 312 – Diffraction Principles Diffraction Techniques - XRD • XRD Diffractogram Analysis – Indexing • Orthorhombic (3 unknown) – A can be determined from reflections of the type {h00} – B can be determined from reflections of the type {0k0} – C can be determined from reflections of the type {00l} • Solve equation systems from mixed indices 22 2 2 2 2 2 2 s in h k l Ah Bk Cl 4a 4b 4c λ λλ θ =++ = + + 2 2 Ac o n s t 4a == 2 2 Cc o n s t 4c 2 2 Bc o n s t 4b
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EMSE 312 – Diffraction Principles Diffraction Techniques - XRD • XRD Diffractogram Analysis – Indexing • Orthorhombic (3 unknown) – Solve equation systems from mixed indices 1 2 θ 2 2 3 2 2 ( ) 110 ( ) 111 ( ) 211 ( ) hkl 22 2 2 sin A h B k C l θ= ⋅+ 2 1 sin A B + 2 2 sin A B C ++ 2 3 sin 4A B C 21 Cs i n s i n ⇒= ( ) 32 A1 3 s i n s i n =− 2 1 Bs i n A
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EMSE 312 – Diffraction Principles Diffraction Techniques - XRD • XRD Diffractogram Analysis – Indexing •T r i c l i n i c (6 unknown) – Solve from 6 independent equations • mixed indices –e .g . – (100) – (110) – (111) – (102) – (112) – (122) a G b G c G β γ α hkl 1 g d ha * kb * lc * = =⋅ + +
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EMSE 312 – Diffraction Principles Diffraction Techniques - XRD • XRD Diffractogram Analysis – Indexing •T r i c l i n i c (6 unknown) a G b G c G β γ α 222 V abc 1 cos cos cos 2cos cos cos βγ =− −+ () 22 2 11 22 33 12 23 13 hkl 11 S h S k S l 2S hk 2S kl 2S hl dV =+ + + + + 2 11 Sb c s i n = 2 22 Sa c s i n = 2 33 b s i n = 2 12 b c c o s c o s c o s 2 23 S a bc cos cos cos γα 2 13 S ab c cos cos cos αβ
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EMSE 312 – Diffraction Principles Diffraction Techniques - XRD • XRD Diffractogram Analysis – Phase Transformations • Change of Structure – e.g., cubic to tetragonal • Change of Lattice Parameters Low T – Low Symmetry Orthorhombic (metastable) High T – High Symmetry Cubic Tetragonal Monoclinic
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EMSE 312 – Diffraction Principles Diffraction Techniques - XRD • XRD Diffractogram Analysis – Order-Disorder Transformations – Disordered phases • High T – Ordered Phases •L ow T
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EMSE 312 – Diffraction Principles Diffraction Techniques - XRD • XRD Diffractogram Analysis – Order-Disorder Transformations • Disorder (high Symmetry) • Order (low symmetry) F-Cell P-Cell DIFFERENT STRUCTURE FACTORS
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EMSE 312 – Diffraction Principles Diffraction Techniques - XRD • Order – Disorder Transformations – Example 1) CuZn
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EMSE 312 – Diffraction Principles Diffraction Techniques - XRD •D i s o r d e r – “Average Cu-Zn” atoms on Lattice Points •(C uZ n ) Ave at 0,0,0 and ½,½,½ ( ) ( ) () { } ( ) {} ( ) Disorder Disorder X gh k l A v e j j j j j X Ave j FF f e x p 2 i h u k v l w 11 1 f e x p2ih0 k0 l0 e x p2ih k l 22 2 f1 e x p i h k l θπ π == + + ⎧⎫
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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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Lecture22-XRD-AnalysisOfXRDSpectraII - EMSE 312 DIFFRACTION...

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