Reciprocal Lattice

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$LSM 5.504 / PCMC 7.702 Cristallographie - Diffraction des Rayons X-$

Metric tensor transformations ⎛ ⎝ ⃗a ∗ ⃗b ∗ ⃗c ∗ ⎞ ⎛ ⎠ = G −1 · ⎝ ⃗a ⃗ b ⃗c ⎞ ⎠ and G = F T · G ∗ · F = G T · G ∗ · G G −1 · G = G −1 · G · G ∗ · G I = G ∗ · G <strong>Reciprocal</strong> tensor G ∗ = G −1 18 / 26
19 / 26 Transformation in reciprocal space ⎛ ⃗r ∗ = (h k l) · ⎝ ⎛ (h k l) · G −1 · ⎝ ⃗a ⃗ b ⃗c ⃗a ∗ ⃗b ∗ ⃗c ∗ ⎞ ⎛ ⎠ = (h ′ k ′ l ′ ⎜ ) · ⎝ ⎞ ⎛ ⎠ = (h k l) · G −1 · F T ⎜ ⎝ ⃗a ∗′ ⃗b ∗′ ⃗c ∗′ ⃗a ′ ⃗b ′ ⃗c ′ ⎛ (h k l) · G −1 · F T · G ′ ⎜ ⎝ ⎞ ⎟ ⎠ = ⎞ ⎟ ⎠ = ⃗a ∗′ ⃗b ∗′ ⃗c ∗′ ⎞ ⎟ ⎠
Page 1 and 2: Reciprocal space Ernesto Estévez R
Page 3 and 4: 3 / 26 Definition We can add metric
Page 5 and 6: Definition ⃗ r ∗ hkl || ˆ n hk
Page 7 and 8: 6 / 26 Equation of a plane ⃗n = (
Page 9 and 10: 8 / 26 Equation of a plane vwx( ⃗
Page 11 and 12: Equation of a plane vwx( ⃗ b ×
Page 13 and 14: 10 / 26 Equation of a plane [ ] [ ]
Page 15 and 16: Some history Gibbs (1839-1903) Gibb
Page 17 and 18: Reciprocal vector r⃗ hkl ∗ · (
Page 19 and 20: Metric tensor transformations ⎛
Page 21 and 22: 16 / 26 Metric tensor transformatio
Page 23 and 24: 17 / 26 Metric tensor transformatio
Page 25: 18 / 26 Metric tensor transformatio
Page 29 and 30: Point symmetry transformation in re
Page 35 and 36: Fourier transform and reciprocal ve
Page 37 and 38: Fourier transform of the lattice Di
Page 39: 26 / 26 Fourier transform of the la

Reciprocal Lattice

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