Fig. 1: First-principles density functional theory and density functional perturbation theory calculations of Na1/2Bi1/2TiO3-based ceramics.

Crystal structure diagrams of a Na1/2Bi1/2TiO3 in R3 phase, b Na1/2Bi1/2TiO3 with Ti3+ replacing Ti4+, c Mn4+-doped Na1/2Bi1/2TiO3, d Mn3+-doped Na1/2Bi1/2TiO3, and e Mn2+-doped Na1/2Bi1/2TiO3; f Polarization and g Displacements from density functional perturbation theory calculations.