The electronic, phase stability and epitaxial strain properties of cubic and tetragonal structure of PbTiO3 and SnTiO3 were investigated using density functional theory (DFT) with space group (Pm3m) for cubic and (P4mm) for tetragonal for both structure within the GGA PBE-sol functional and were applied in a pseudo-potential plane wave using the CASTEP computer code. The results showed that the cubic PbTiO3 and cubic SnTiO3 have the minimum total energy within almost the tetragonal perovskite structure of the lattice parameter 3.937 Å and 3.916 Å respectively. The calculated electronic structure of SnTiO3 resembles that of PbTiO3 due to the Ti-3d states, Sn-5s and 5p states hybridize with the O-2p orbitals. The electronic properties showed that hybridizations happen among anion O 2p, special lone pair of ns2, and the Ti-3d states with an indirect bandgap at the X-G point. The energy band gap was evaluated from the division between the Ti-3d which the conduction band is and the upper of the O-2p valence band. It is achieved that the bond between Pb and O is ionic in the tetragonal state, while there is huge strength hybridization between Ti-3d and O-2p, which is significant for ferroelectricity in PbTiO3. It is shown that tetragonal is the steadiest when compared to other structures while the ilmenite structure is the least stable followed by a cubic, rhombohedral and orthorhombic. The out-of-plane c-axis strain is achieved to be largely oriented to PbTiO3 under large in-plane a-axis compressive strain.
