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 present numerical problems at low temperatures or for highly stoichiometric compounds. Under these conditions, their application to complex alloy Hamiltonians, with extended pair and multi-site interactions, is non trivial and can be very computer-time demanding. In this work, we investigate the application of a low-temperature expansion of the thermodynamic potentials for Hamiltonians with many pair and multi-site interactions. In this way, analytic expressions can be obtained for the free 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 the expansion, the low-temperature expansion is accurate up to temperatures where Monte Carlo simulations or cluster variation calculations are practical. Consequently, these three methods can be used as complimentary techniques to compute a single phase diagram. Furthermore, we also show that the coefficients of the low-temperature expansion can be computed from the same information used to build the cluster variational free energy, thereby making the low-temperature expansion very simple to use. We illustrate the application of this new approach by computing the fcc Pd-rich phase diagram of the Pd-V alloy.