The effect of lattice vibrations on substitutional alloy thermodynamics

A long-standing limitation of first-principles calculations of substitutional alloy phase diagrams is the difficulty in accounting for lattice vibrations. A survey of the theoretical and experimental literature seeking to quantify the effect of lattice vibrations on phase stability indicates that they can be significant. Typical vibrational entropy differences between phases are of the order of 0.1 to ${0.2k}_{B}/\mathrm{atom},$ which is comparable to the typical values of configurational entropy differences in binary alloys (at most ${0.693k}_{B}/\mathrm{atom}).$ This article presents the basic formalism underlying ab initio phase diagram calculations, along with the generalization required to account for…