Structural, Electronic, and Lattice Dynamics of PbTiO₃, SnTiO₃, and SnZrO₃: A Comparative First-Principles Study

Abstract

The properties of cubic (Pm3m, 221 space group) perovskite prototypes PbTiO₃ (PTO), SnTiO₃ (STO), and SnZrO₃ (SZO) were investigated via first-principles calculation using the density functional theory as implemented in CASTEP computer code. The lattice parameters of PbTiO₃ (as the reference compound) were calculated. The accuracy values of the calculation functional (GGA-PBEsol) were acceptable relative to the experimental values with typical error of approximately 0.6% underestimate. The independent elastic constants (C₁₁, C₁₂, and C₄₄) and bulk modulus, B, were obtained and analyzed. The density of state studies indicated hybridizations among anion O 2p, cation Pb 6s/Sn 5s and the Ti 3d/Zr 4d states of PTO, STO, and SZO. An indirect band gap was respectively obtained for both PTO and STO at the X-G point. A direct band gap was attained for SZO at the X-X point along the high-symmetry direction in the Brillouin zone. The born effective charge values of PTO, STO, and SZO were attributed to the responses of the bond charges to the displacement caused by the strong covalency between the cation orbital and O 2p (strong covalency A-O and B-O bonding). Results also reveal that anion O 2p, cation Pb 6s/Sn 5s, and Ti 3d/ Zr 4d states have played an important role in the instability of perovskite oxide. Comparative results from the PTO, STO, and SZO prototypes showed the calculated theoretical and experimental values were in good agreement.

Keywords:

• Elastic Constants
• Electronic Band Structure
• Density of States
• Lattice Dynamic
• Density-Functional Theory

Acknowledgements

This study was supported by the Fundamental Research grant Scheme by the Ministry of Higher Education, and Research Management Institute (RMI), Universiti Teknologi MARA Malaysia.