High-Component Ionic Cluster Expansions for Exploring Disordered Spaces

Cluster expansions coarse-grain the free energy of multi-component systems based on the possible configurations of species on a disordered crystal lattice. The modeling of configurational energetics in conjunction with Monte-Carlo methods enables finite temperature voltage curve calculations and the computation of phase diagrams. While cluster expansions can in theory be used for systems of any dimensionality, their application has generally been limited to binary or ternary alloys. When applied to high-component ionic systems, a number of practical challenges emerge, including charge-state assignment, atomic relaxations from the fixed lattice, and the fitting of predictive models from a large feature space. We demonstrate techniques to overcome these challenges in the fitting of a cluster expansion to the space of cation-disordered Mn-based spinel, a Li-ion cathode materials space within which the high energy density, high-rate partially disordered spinels lie. We then show how the cluster expansion can evaluate how the level of disorder between the 16d TM sites and vacant 16c octahedral sites affects the electrochemical properties of the disordered spinel. Through this thermodynamic analysis, we illustrate how cluster expansions can be applied to isolate and understand the effects of specific types of disorder.