Reciprocal lattice of the 2023 Cambridge body-centered cubic basis
= Reciprocal lattice of the 2023 Cambridge body-centered cubic basis
For
$$
a_1=\frac a2(1,1,1),
\quad a_2=\frac a2(1,-1,1),
\quad a_3=a(0,0,1),
$$
a reciprocal basis is
$$
b_1=\frac{2\pi}{a}(1,1,0),
\quad b_2=\frac{2\pi}{a}(1,-1,0),
\quad b_3=\frac{2\pi}{a}(-1,0,1).
$$
Thus $\Lambda^*=(2\pi/a)\{(h,k,l)\in\mathbb Z^3:h+k+l\text{ even}\}$ and its shortest nonzero vectors have length $2\sqrt2\pi/a$.