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).