Obtaining Ising-like expansions for binary alloys from first principles

Many measurable properties of crystalline binary A1−xBx alloys, such as phase diagrams and excess thermodynamic functions, could be predicted via lattice statistical mechanics methods if one knew the `configurational energy'. The latter describes the energy at T = 0 for each of the 2N possible occupation patterns of the N lattice sites by an A or a B atom. Traditional approaches described the configurational energy either via empirically fitted, truncated Ising Hamiltonians, or through highly approximated coherent-potential constructs. We illustrate here the alternative approach of `mixed-basis cluster expansion' which extracts from a set of ab initio local density approximation calculations of the total energies of a few ordered A–B compounds a complete configurational energy function. This method includes both pair and multibody terms, whose number and range of interaction are decided by the variational procedure itself, as well as long-range strain terms. In this paper, we describe the computational details of this method, emphasizing methods of construction, interpolations, fits and convergence. This procedure is illustrated for Ni–Pt, Cu–Au and ScS–S (where denotes cation vacancy). The parameters of the final expansions are provided on our webpage (http://www.sst.nrel.gov).