Modeling intercalation chemistry with multi-redox reactions by sparse lattice models in disordered rocksalt cathodes

Abstract: Modern battery materials can contain many elements with substantial site disorder, and their configurational state has been shown to be critical for their performance. The intercalation voltage profile is a critical parameter to evaluate the performance of energy storage. The application of commonly used cluster expansion techniques to model the intercalation thermodynamics of such systems from \textit{ab-initio} is challenged by the combinatorial increase in configurational degrees of freedom as the number of species grows. Such challenges necessitate efficient generation of lattice models without over-fitting and proper sampling of the configurational space under charge balance in ionic systems. In this work, we introduce a combined approach that addresses these challenges by (1) constructing a robust cluster-expansion Hamiltonian using the sparse regression technique, including $\ell_0\ell_2$-norm regularization and structural hierarchy; and (2) implementing semigrand-canonical Monte Carlo to sample charge-balanced ionic configurations using the table-exchange method and an ensemble-average approach. These techniques are applied to a disordered rocksalt oxyfluoride Li${1.3-x}$Mn${0.4}$Nb${0.3}$O${1.6}$F$_{0.4}$ (LMNOF) which is part of a family of promising earth-abundant cathode materials. The simulated voltage profile is found to be in good agreement with experimental data and particularly provides a clear demonstration of the Mn and oxygen contribution to the redox potential as a function of Li content.