Ssp_8y - 3 Continued Scattering conditions(Laue conditions I K(r e G i K r r = G e iG r dr 3 2 2 I(K e G G i G K)r d 3r cf 1 x = 2 e ikx dk = e i

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3-7 Scattering conditions (Laue conditions) () IK re dr iK r G G iG r = −⋅ ρ ρρ 3 2 e G G iG K r −− 3 2 ( ) cf.: δ π xe d k e d k ikx i kx == −∞ −∞ 1 2 2 (wave packet with p x 0) ed r VG K V = = 3 0 for otherwise K k - k 0 ( ) IG G ∝ ρ 2 Scattering condition: G = K
3-8 No absorption () ρρ re G G iG r = −⋅ real () () ρ rr G G =⇒ = ** and with G G G G G G I = = * 2 Gh g k g l g =++ 12 3 II hkl hkl = (Friedel Rule) Consequences: Reflex pattern always has inversion center E.g.: 3-fold axis in lattice 6-fold axis in reflex pattern K = G K = k - k 0 k = k 0 = 2 π/λ λ continuum or crystal rotation! Fig. 3.4. Ewald construction. A point of the reciprocal lattice is chosen as arbitrary origin. The vector k 0 is drawn to point towards the origin. All points on a sphere with radius k 0 , centered around the starting point of k 0 obey the condition k = k 0 for elastic scattering. The Laue condition K = G is obeyed for all reciprocal lattice points intersecting the “Ewald sphere“.

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3-9 Miller indices hkl Fig. 3.5. (a) Illustration of Miller indices defined by intersections of the lattice planes with the coordinate axes in terms of integer multiples m, n, o of the base vectors. Here m =1, n =2, o =2. The Planes ( hkl ) are spanned by ma 1 - na 2 , oa 3 - na 2 .(b) The dashed planes are equivalent to the solid ones.
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This note was uploaded on 01/19/2010 for the course MATERIALS M504 taught by Professor Adelung during the Spring '02 term at Uni Kiel.

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Ssp_8y - 3 Continued Scattering conditions(Laue conditions I K(r e G i K r r = G e iG r dr 3 2 2 I(K e G G i G K)r d 3r cf 1 x = 2 e ikx dk = e i

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