Fig. 4: Examples of high-energy cation configurations predicted by the CE per spinel formula unit (f.u.), LiMn2O4, where the scenarios are Li+ or Mn2+ insertions onto vacant sites in spinel (48f or 8b).
From: Approaches for handling high-dimensional cluster expansions of ionic systems
The defect energies are calculated as either \(E^{final} - E^{initial} - \mu _{tet}^{Li^ + }\) for Li+ insertion and \(E^{final} - E^{initial} - \mu _{tet}^{Mn2 + }\) for Mn2+ insertion. The chemical potentials are calculated, starting from the spinel structure, as: \(E\left( {Li_8Mn_{16}O_{32}} \right) - E\left( {Li_7Mn_{16}O_{32}} \right) = \mu _{Li^ + }\) and \(E\left( {Li_7Mn_1^{2 + }Mn_{16}O_{32}} \right) - E\left( {Li_7Mn_{16}O_{32}} \right) = \mu _{Mn^{2 + }}\). a The Li+-occupied 48f site face-shares with two Mn, resulting in a +0.052 eV/spinel f.u. increase in energy. b Adding Li+ to a more metal-rich cluster, the 8b site, results in an even higher increase in energy: +0.071 eV/spinel f.u. c The Mn2+-occupied 48f site, face-sharing with two Mn, has a +0.067 eV/ spinel f.u. increase while the (d) Mn2+-occupied 8b site increases by +1.12 eV/ spinel f.u.
