Mixed-basis cluster expansion for thermodynamics of bcc alloys

Abstract

To predict the ground-state structures and finite-temperature properties of an alloy, the total energies of many different atomic configurations $\mathbf{\ensuremath{\sigma}}\ensuremath{\equiv}{{\ensuremath{\sigma}}_{i};i=1,\dots{},N}$, with $N$ sites $i$ occupied by atom A $({\ensuremath{\sigma}}_{i}=\ensuremath{-}1)$, or B $({\ensuremath{\sigma}}_{i}=+1)$, must be calculated accurately and rapidly. Direct local-density approximation (LDA) calculations provide the required accuracy, but are not practical because they are limited to small cells and only a few of the ${2}^{N}$ possible configurations. The ``mixed-basis cluster expansion'' (MBCE) method allows to parametrize LDA configurational energetics ${E}_{\mathrm{LDA}}[{\ensuremath{\sigma}}_{i};i=1,\dots{},N]$ by an analytic functional ${E}_{\mathrm{MBCE}}[{\ensuremath{\sigma}}_{i};i=1,\dots{},N]$. We extend the method to bcc alloys, describing how to select ${N}_{\ensuremath{\sigma}}$ ordered structures (for which LDA total energies are calculated explicitly) and ${N}_{F}$ pair and multibody interactions, which are fit to the ${N}_{\ensuremath{\sigma}}$ energies to obtain a deterministic MBCE mapping of LDA. We apply the method to bcc Mo-Ta. This system reveals an unexpectedly rich ground-state line, pitting Mo-rich (100) superlattices against Ta-rich complex structures. Predicted finite-$T$ properties such as order-disorder temperatures, solid-solution short-range order and the random alloy enthalpy of mixing are consistent with experiment.