Adaptive cluster expansions and redox-dependent atomic ordering

An adaptive cluster expansion (ACE) methodology is presented which enables exploration of atomic ordering interactions in solids as a function of the redox environment. A previously developed cluster expansion methodology is augmented via inclusion of explicit effective charge dependence within the topological cluster basis. This augmentation produces an enhanced fit precision across a wide composition range and the ability to directly control the model's redox state during Monte Carlo system equilibrations. The approach is validated in applications to yttria-stabilized zirconia (YSZ) and the perovskite (La _0.8, Sr_0.2)(Cr_0.8, Ru_0.2)O _2.9 (LSCR), where significant variability in atomic ordering is seen across redox space. A locally adaptive lattice Monte Carlo sampling, utilizing the ACE methodology, is developed and validated in applications to determine the 0 K ground state configurations of YSZ and LSCR supercells with varying redox conditions. These equilibrations have direct relevance to solid-oxide fuel cell applications, whose components are subject to widely varying redox environments. The superior convergence of ACE results in a smaller number of numerically significant expansion terms, not only speeding the analysis but also permitting a physical interpretation of their meaning.