Reciprocal Lattice

Reciprocal vector
(x⃗a) · (h ⃗a ∗ ) + (y ⃗ b) · (k ⃗ b ∗ ) + (z⃗c) · (l ⃗c ∗ ) = 1
can be written as
where
hx + ky + lz = 1
r xyz ⃗ · r ⃗∗ hkl
= 1
⃗ r ∗ hkl = h ⃗a ∗ + k ⃗ b ∗ + l ⃗c ∗
if
⃗ r ∗ hkl || ˆ n hkl
| ⃗ r ∗ hkl | = 1
d hkl
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