Epitaxial phase diagrams of SrTiO3, CaTiO3 , and SrHfO3 : Computational investigation including the role of antiferrodistortive and A -site displacement modes

Ground-state epitaxial phase diagrams are calculated by density functional theory (DFT) for ${\mathrm{SrTiO}}₃, {\mathrm{CaTiO}}₃$, and ${\mathrm{SrHfO}}₃$ perovskite-based compounds, accounting for the effects of antiferrodistortive and $A$-site displacement modes. Biaxial strain states corresponding to epitaxial growth of (001)-oriented films are considered, with misfit strains ranging between $\ensuremath{-}4%$ and 4%. Ground-state structures are determined using a computational procedure in which input structures for DFT optimizations are identified as local minima in expansions of the total energy with respect to strain and soft-mode degrees of freedom. Comparison to results of previous DFT studies demonstrates the effectiveness of the computational approach in predicting ground-state phases. The calculated results show that antiferrodistortive octahedral rotations and associated $A$-site displacement modes act to suppress polarization and reduce the epitaxial strain energy. A projection of calculated atomic displacements in the ground-state epitaxial structures onto soft-mode eigenvectors shows that three ferroelectric and six antiferrodistortive displacement modes are dominant at all misfit strains considered, with the relative contributions from each varying systematically with the strain. Additional $A$-site displacement modes contribute to the atomic displacements in ${\mathrm{CaTiO}}₃$ and ${\mathrm{SrHfO}}₃$, which serve to optimize the coordination of the undersized $A$-site cation.