Obtaining ising-like expansions for binary alloys from first principles

Many measurable properties of crystalline binary A_1-x B_x 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 2^N 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).