Body-centered cubic lattice

A body-centered cubic lattice consists of the points of a cubic lattice together with their body centers. Its reciprocal lattice is face-centered cubic.

In a body-centred cubic lattice of conventional edge $a$, a lattice site has eight nearest neighbours along body half-diagonals at distance $\sqrt{3}a/2$, then six next-nearest neighbours along the coordinate axes at distance $a$. There are two sites per conventional cell, so identical atoms of mass $m$ and mass density $\rho$ obey $\rho a^3=2m$. Specifying a neighbour shell matters: the nearest and next-nearest distances differ.

Fora reciprocal basis isThus ${\Lambda }^{\ast }=(2\pi /a)\{(h,k,l)\in {\mathbb{Z}}^3:h+k+l\text{ even}\}$ and its shortest nonzero vectors have length $2\sqrt{2}\pi /a$.