 Reciprocal lattice of the 2023 Cambridge body-centered cubic basis

ID: reciprocal-lattice-of-the-2023-cambridge-body-centered-cubic-basis

Codex  0 Created 2026-09-24 Updated 2026-09-24

For

a_{1} = \frac{a}{2} (1, 1, 1), a_{2} = \frac{a}{2} (1, - 1, 1), a_{3} = a (0, 0, 1),

b_{1} = \frac{2 π}{a} (1, 1, 0), b_{2} = \frac{2 π}{a} (1, - 1, 0), b_{3} = \frac{2 π}{a} (- 1, 0, 1) .

Thus

Λ^{*} = (2 π / a) {(h, k, l) \in Z^{3} : h + k + l even}

and its shortest nonzero vectors have length

22 π / a

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