Research work · 1951
Note on Superlattices and Brillouin Zones
J. C. Slater
Physical Review
Abstract
In a number of alloys, such as CuPt, an ordered phase is formed below a definite temperature, in which atoms of the two sorts are localized in alternate layers. In some cases in the ordered phase an atom of each sort is surrounded by equal numbers of atoms of both sorts, so that the ordinary explanation of ordering, the preference of an atom to be surrounded by neighbors of the opposite type, does not apply. It is pointed out, however, that in such a case the Brillouin zone is split by the double periodicity in the lattice, with modification of the energy levels such that if the zone is approximately half-filled with electrons, the electronic energy is decreased by an amount proportional to the square of the degree of order. It is suggested that this decrease of energy is what stabilizes the ordered phase. It is also suggested that in some metals, a similar effect on the Brillouin zones would occur if alternate layers were slightly displaced in opposite directions along the normal to the planes. This also might stabilize such a structure, at low temperatures, leading to a narrow energy gap above the occupied levels, with consequent increase of resistance; this might explain the resistance increase of Mg and Au at low temperatures. The similarity of these effects to current theories of antiferromagnetism and of superconductivity is pointed out.