Lecture14-Review

Lecture14-Review - EMSE 312 DIFFRACTION PRINCIPLES Lecture...

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EMSE 312 – Diffraction Principles Lecture 14 Review – Part 1 Crystallography Fourier Transforms – Optical Diffraction Basic properties of X-rays Braggs Law – Real Space and Reciprocal Space Stereographic Projections Laue Backscattering EMSE 312 DIFFRACTION PRINCIPLES
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EMSE 312 – Diffraction Principles Crystallography - Review •C r y s t a l – Macroscopic Scale: • A Solid of Uniform Chemical Composition which is formed with Plane Faces each making Precise Angles with one another. – Microscopic Scale: •Atoms, or Groups of Atoms, Repeated Regularly in Three Dimensions. – Translation Symmetry [Lattice] – Symmetry of the Group of Atoms at each Lattice Point [Motif]
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EMSE 312 – Diffraction Principles Symmetry Motif : the fundamental part of a symmetric design that, when repeated, creates the whole pattern Operation : some act that reproduces the motif to create the pattern Element : an operation located at a particular point in space
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EMSE 312 – Diffraction Principles Lattice Translations Conventions: Conventions: 1. Cell edges should, 1. Cell edges should, whenever possible, whenever possible, coincide with coincide with symmetry axes or symmetry axes or reflection planes reflection planes 2. If possible, edges 2. If possible, edges should relate to each should relate to each other by lattice other by lattice ’s s symmetry. symmetry. 3. The smallest possible 3. The smallest possible cell (the reduced cell) cell (the reduced cell) which fulfills 1 and 2 which fulfills 1 and 2 should be chosen should be chosen
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EMSE 312 – Diffraction Principles Lattice Translations – Real Space •B a s i s V e c t o r s • Lattice Parameters • Lattice Points at • u, v, w all Integers • Miller Indices – Specific Directions – Family of Directions a;b;c G G G aa ; bb ; cc = == G G G ;; α βγ Ru a v b w c = ⋅+ G G GG [ ] uvw
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EMSE 312 – Diffraction Principles Lattice Translations – Reciprocal Space • Basis Vectors • Lattice Parameters • Plane Normals for • h, k, l all Integers • Miller Indices – Specific Planes – Family of Planes a*;b*;c* G G G a* a * ;b* b* ;c* c* === G G G *; *; * α βγ Gh a * k b * l c * = ⋅+ G G GG ( ) hkl { } hkl () b c ab c a* × ⋅× = G G G G ca b b * × × = G G G G G G c cab * × × = G G G G
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EMSE 312 – Diffraction Principles Lattice Translations – Reciprocal Space • Note!!! – Different Definitions of Reciprocal Space • Solid State Physics • Materials Science • Why? where () b c ab c a* 2 π × ⋅× = G G G GG G ca b b *2 × × = G G G G G G c cab × × = G G G G hkl 1 G d = G Gh a * k b * l c * = ⋅+ G G G G b c c a* × = G G G G b b * × × = G G G G G G c * × × = G G G G
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a b Unit Cell
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a b b* a* x x Unit Cell
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a b b* a* x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
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a* a b b* x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
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Lecture14-Review - EMSE 312 DIFFRACTION PRINCIPLES Lecture...

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