Reciprocal Lattice
Reciprocal Lattice
Reciprocal Lattice
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Metric tensor transformations<br />
⎛<br />
⎜<br />
⎝<br />
⃗a ∗ · ⃗a ⃗a ∗ ·⃗b ⃗a ∗ · ⃗c<br />
⃗b ∗ · ⃗a b∗ ⃗ ·⃗b b∗ ⃗ · ⃗c<br />
⃗c ∗ · ⃗a ⃗c ∗ ·⃗b ⃗c ∗ · ⃗c<br />
⎞<br />
⎛<br />
⎟ ⎜<br />
⎠ = M · ⎝<br />
⃗a · ⃗a ⃗a ·⃗b ⃗a · ⃗c<br />
⃗ b · ⃗a ⃗ b ·⃗ b ⃗ b · ⃗c<br />
⃗c · ⃗a ⃗c ·⃗b ⃗c · ⃗c<br />
⎞<br />
⎟<br />
⎠<br />
⎛<br />
⎝<br />
1 0 0<br />
0 1 0<br />
0 0 1<br />
⎞<br />
⎛<br />
⎠ ⎜<br />
= M · ⎝<br />
⃗a · ⃗a ⃗a ·⃗b ⃗a · ⃗c<br />
⃗ b · ⃗a ⃗ b ·⃗ b ⃗ b · ⃗c<br />
⃗c · ⃗a ⃗c ·⃗b ⃗c · ⃗c<br />
⎞<br />
⎟<br />
⎠ = M · G<br />
M = G −1<br />
F = G
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