Lattice-gas model to understand voltage profiles of ${\mathrm{LiNi}}_x{\mathrm{Mn}}_{2-x}{\mathrm{O}}_4/\mathrm{L}\mathrm{i}$ electrochemical cells

Lattice-gas models were used to study lithium intercalation in Ni-substituted spinel ${\mathrm{LiNi}}_x{\mathrm{Mn}}_{2-x}{\mathrm{O}}_4$ $(0<x<~0.5).$ Both mean-field theory and Monte Carlo simulations have been used to calculate voltage profiles of ${\mathrm{LiNi}}_x{\mathrm{Mn}}_{2-x}{\mathrm{O}}_4/\mathrm{L}\mathrm{i}$ electrochemical cells. Plateaus near 4.7 and 4.1 V in the voltage profiles are believed to be related to the removal of electrons from states on the Ni $3d$ $e_g$ level and from the Mn $3d$ $e_g$ level, respectively. The structure in the voltage profiles can be qualitatively explained using nearest-neighbor repulsive interactions between Li atoms in adjacent $8a$ sites, next-nearest-neighbor attractive interactions, and a binding energy to those sites that changes abruptly by 0.6 eV when all $1-2x$ available sites for electrons in Mn $3d$ levels are empty. Assuming that $2x$ specific sites have one binding energy and the other $1-2x$ sites have another is not successful in modeling the order-disorder transitions in the data. This implies that the either the Ni and Mn $3d$ bands are delocalized or that a specific localized Ni or Mn $e_g$ level can be reduced by a Li atom in any of a number of neighboring sites.