### Abstract

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).

Original language | English |
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Pages (from-to) | 685-706 |

Number of pages | 22 |

Journal | Modelling and Simulation in Materials Science and Engineering |

Volume | 10 |

Issue number | 6 |

DOIs | |

State | Published - Nov 2002 |

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## Cite this

*Modelling and Simulation in Materials Science and Engineering*,

*10*(6), 685-706. https://doi.org/10.1088/0965-0393/10/6/306