Chemical and elastic effects on isostructural phase diagrams: Theɛ-Gapproach

Numerous theoretical models of temperature-composition phase diagrams of isostructural binary alloys are based on the configurational Ising Hamiltonian in which the many-body configurational interaction energies ${\varepsilon }^{\left(n\right)}$ are taken as (volume-independent) constants (the ‘‘ɛ-only’’ approach). Other approaches postulate phenomenologically composition-dependent but configuration- (σ-) independent elastic energies. We show that under the commonly encountered situation where molar volumes at fixed composition (x) do not depend on the state of order, a new approach is pertinent: We prove that the physically relevant Hamiltonian (the ‘‘ɛ-G approach’’) includes the configuration-dependent (but concentration-independent) ‘‘chemical’’ interaction energies ${\varepsilon }^{\left(n\right)}$, plus a composition-dependent (but configuration-independent) elastic energy G(x). We compute the elastic term G(x) from the structural and elastic properties of ordered intermetallic systems. We show that inclusion of G(x) into the conventional configurational (ɛ-only) Hamiltonian cures many of the shortcomings of such Ising models in describing actual alloy phase diagrams. In particular, addition of the elastic energy G(x) leads to the following features: (i) narrower single-phase regions and broader mixed-phase regions, (ii) shift of the triple point to substantially higher temperatures, (iii) the mixing enthalpies of the disordered phases become much closer to the experimental data, and (iv) the possibility of the occurrence of metastable long-range-ordered compounds inside the miscibility gap. Cluster-variation and Monte Carlo calculations on model Hamiltonians and on the Cu-Au system are used to illustrate these points.