Mixed-basis cluster expansion for thermodynamics of bcc alloys

To predict the ground-state structures and finite-temperature properties of an alloy, the total energies of many different atomic configurations s;hsi ; i=1, . . . ,Nj, with N sites i occupied by atom A ssi=−1d, or B ssi = +1d, 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 2N possible configurations. The “mixed-basis cluster expansion” (MBCE) method allows to parametrize LDA configurational energetics ELDAfsi ; i=1, . . . ,Ng by an analytic functional EMBCEfsi ; i=1, . . . ,Ng. We extend the method to bcc alloys, describing how to select Ns ordered structures (for which LDA total energies are calculated explicitly) and NF pair and multibody interactions, which are fit to the Ns 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.