An accidental visualization of the Brillouin zone in an Ni–W alloy via diffuse scattering

Solid state physics is built on the concept of reciprocal space. The physics of any given periodic crystal is fully defined within the Wigner–Seitz cell in reciprocal space, also known as the first Brillouin zone. It is a purely symmetry-based concept and usually does not have any eye-catching signature in the experimental data, in contrast with some other geometrical constructions like the Fermi surface. However, the particular shape of the Fermi surface of nickel allowed the visualization of the system of edges (skeleton) of the Wigner–Seitz cell of the face-centred cubic lattice in reciprocal space in three dimensions by the diffuse scattering of X-rays from Ni_1−xW_x (x = 0.03, 0.05, 0.08) single crystals. Employing a cluster-expansion method with first-principles input, it is possible to show that the observed scattering is inherent to the given nickel alloys and the crystal structures they form. This peculiar feature can be understood by considering the shape of the Fermi surface of pure nickel.