Short-Range Order and Li$_x$TM$_{4-x}$ Probability Maps for Disordered Rocksalt Cathodes

Short-range order (SRO) in the cation-disordered state is a controlling factor influencing the probability of finding Li$_{4}$ tetrahedron clusters in disordered rocksalt (DRX) cathode materials. However, the prevalent Li$_4$ probability below the random limit across reported DRX compositions has not been systematically investigated, active strategies to surpass the random limit of Li$_4$ probability are lacking, and the fundamental ordering behavior on the face-centered cubic (FCC) lattice remains insufficiently explored. This research quantitatively examines pair SRO parameters and Li$_x$TM$_{4-x}$ probabilities via exhaustive Monte Carlo mapping across a simplified subset of the parameter space. The results indicate that, in the disordered state, the Li$_4$ probability is governed by the nearest neighbor (NN) pair-wise SRO parameter, and that these quantities do not necessarily represent a simple attenuation of their corresponding low-temperature long-range order, particularly for the important cases of Layered and Spinel-like orderings. Strategies are proposed to mitigate or even reverse the lithium and transition metals mixing tendency of NN pair SRO to achieve Li$_4$ probabilities that exceed the random limit. This study advances the fundamental thermodynamic understanding of ordering behaviors, which can be generalized to any FCC system.