Thermodynamic and dynamic stabilities of Li₄Mn₂O₅. (a) Calculated Li–Mn–O (T = 0 K) phase diagram. The Li₄Mn₂O₅ phase is slightly higher in energy (13.6 meV per atom) relative to the ground-state phase: a mixture of Li₂O and LiMnO₂. (b) Phonon dispersion of the ground-state Li₄Mn₂O₅ and (c) calculated temperature-dependent free energy of Li₄Mn₂O₅ (red dashed line), Li₂O (orange dotted line), and LiMnO₂ (green dotted line), as well as the stability (purple solid line) of Li₄Mn₂O₅ versus temperature relative to Li₂O and LiMnO₂ phase mixtures. Li₄Mn₂O₅ is dynamically stable and can be entropically stabilized at ∼ 1350 K.^[71]