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 σ≡{σ_i;i=1,…,N}, with N sites i occupied by atom A (σ_i=−1), or B (σ_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_LDA[σ_i;i=1,…,N] by an analytic functional E_MBCE[σ_i;i=1,…,N]. We extend the method to bcc alloys, describing how to select N_σ ordered structures (for which LDA total energies are calculated explicitly) and N_F pair and multibody interactions, which are fit to the N_σ 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.