Reciprocal-space cluster expansions for complex alloys with long-range interactions

Abstract

Although widely recognized as a powerful tool to explore the influence of nonlocal interactions in crystals, reciprocal-space cluster expansions, in their most popular ``mixed-basis'' (MBCE) formulation, still suffer from restrictions severely limiting their application to complex crystallographies and multisite unit cells. In order to investigate such systems, we therefore propose here a complementary methodology labeled ``modified mixed-basis cluster expansion'' (M2BCE). The key idea is to bypass the currently admitted decomposition of reciprocal-space interactions $\mathrm{J\ifmmode \tilde{}\else \~{}\fi{}}$($\mathrm{kP\vec}$) into short- and long-range parts, which allows us to determine these quantities as a whole for an arbitrary set of $\mathrm{kP\vec}$ points. Our approach is essentially independent of the ``constituent strain energies'' ${E}_{\mathit{CS}}$, a key feature since these parameters, central from the very beginning in MBCE, may become exceedingly intricate to evaluate in many low-symmetry cases. The efficiency of M2BCE is illustrated on four-site unit-cell interstitial H-Zr.