COMPUTATION OF ALLOY PHASE-DIAGRAMS AT LOW-TEMPERATURES

Standard statistical-mechanics techniques for alloy-Ising models such as Monte Carlo simulations or the cluster variation method usually pre sent numerical problems at low temperatures or for highly stoichiometr ic compounds. Under these conditions, their application to complex all oy Hamiltonians, with extended pair and multi-site interactions, is no n trivial and can be very computer-time demanding. In this work, we in vestigate the application of a low-temperature expansion of the thermo dynamic potentials for Hamiltonians with many pair and multi-site inte ractions. In this way, analytic expressions can be obtained for the fr ee energies from which temperature-composition phase diagrams for any alloy can easily be computed regardless of the complexity of the Ising energy expression. It is demonstrated that with only a few terms in t he expansion, the low-temperature expansion is accurate up to temperat ures where Monte Carlo simulations or cluster variation calculations a re practical. Consequently, these three methods can be used as complim entary techniques to compute a single phase diagram. Furthermore, we a lso show that the coefficients of the low-temperature expansion can be computed from the same information used to build the cluster variatio nal free energy, thereby making the low-temperature expansion very sim ple to use. We illustrate the application of this new approach by comp uting the fee Pd-rich phase diagram of the Pd-V alloy. (C) 1998 Elsevi er Science B.V.