Thermodynamic Stability of Low- and High-Index Spinel LiMn₂O₄ Surface Terminations

Density functional theory calculations are performed within the generalized gradient approximation (GGA+U) to determine stable terminations of both low- and high-index spinel LiMn2O4 (LMO) surfaces. A grand canonical thermodynamic approach is employed, permitting a direct comparison of off-stoichiometric surfaces with previously reported stoichiometric surface terminations at various environmental conditions. Within this formalism, we have identified trends in the structure of the low-index surfaces as a function of the Li and O chemical potentials. The results suggest that, under a range of chemical potentials for which bulk LMO is stable, Li/O and Li-rich (111) surface terminations are favored, neither of which adopts an inverse spinel structure in the subsurface region. This thermodynamic analysis is extended to identify stable structures for certain high-index surfaces, including (311), (331), (511), and (531), which constitute simple models for steps or defects that may be present on real LMO particles. The low- and high-index results are combined to determine the relative stability of each surface facet under a range of environmental conditions. The relative surface energies are further employed to predict LMO particle shapes through a Wulff construction approach, which suggests that LMO particles will adopt either an octahedron or a truncated octahedron shape at conditions in which LMO is thermodynamically stable. These results are in agreement with the experimental observations of LMO particle shapes.