II. The simple cubic lattice and the body-centred cubic lattice
J. S. Wang · Proceedings of the Royal Society of London A Mathematical and Physical Sciences · 1938
Abstract The purpose of this paper is to apply the general theory developed in the preceding paper (quoted as I) to the simple cubic lattice and the body-centred cubic lattice. For these two lattices the nearest neighbours of an α site are all β sites and those of a β site are all α sites. The number of A atoms is now equal to that of B atoms and the number of α sites is equal to that of β sites. The structure of these two lattices is such that zαα = zββ = 0, zαβ = zβα = z, z' = 2z, (1) where z = 6 for the simple cubic lattice and z= 8 for the body-centred cubic lattice (cf. I, eqn, (25)). Since r = ½, eqn. (15) in I becomes rα = rβ = ½(1+ s), wα = wβ = ½(1 - s). (2) Now when the central site in an α site all the first shell sites are β sites, and when the central site is a β all the first shell sites are α sites. Hence we have only one parameter ϵ and one parameter ζ, namely ϵβ and ζα.