Ferroelectrics Of Ba <sub> 0.5 </ Sub> Sr <sub> 0.5 </ Sub> Tio <sub> 3 </ Sub>, Of Srtio <sub> 3 </ Sub>, The Srzro <sub> 3 </ Sub > Theoretical Study Of Electronic Structure And Optical Propert

Ferroelectric materials are the subjects being extensively investigated and used because of their piezoelectricity, electro-optic, photorefractive and nonlinear optical effect. The theory on ferroelectric materials is important for the uses of the materials. Many theoretical tools and models had been used to study ferroelectrics, such as Landau theory, pseudo-spin model, and lattice dynamic model. These researches are helpful for understanding the mechanism of ferroelectric properties and for promoting the application of the materials. With the developments of density functional theory and computer technology, the first-principles calculations have become the routine and useful methods for studying the ferroelectric materials (especially for perovskite oxides). At early stage, the first-principles calculations were used to study the properties of bulk ferroelectrics. Recently, they have been used to study complex systems, such as solid solutions, superlattices, and doped systems. The theoretical results which have been obtained are in good agreement with experiments.In this dissertation, we have studied the electronic and optical properties of Ba_0.5Sr_0.5TiO₃, SrTiO₃, and SrZrO₃ systems by the first-principles calculations based on the density functional theory. Our calculation tool is CASTEP package embedded in the Materials Studio.The main contents of the dissertation are as follows:(1) Investigations on lattice constant, band structure, density of states, bond populations, electron density, and optical properties of Ba_0.5Sr_0.5TiO₃ system have been carried out. The obtained results show that the conduction band and the valence band are derived from the hybridization between titanium 3d orbitals and oxygen 2p orbitals. In the conduction band, titanium 3d orbitals play the primary role, while in the valence band, oxygen 2p orbitals play the primary role. The bond between Ti and O is covalent. The band gap of Ba_0.5Sr_0.5TiO₃ is indirect with the value 3.2eV. There are four peaks in the imaginary part of the electronic dielectric function located at about 5.4, 8.7, 20.9, and 23.5eV, respectively. The absorption coefficient is as large as10⁵cm^-1, and the absorption is mainly localized in the low energy region. The peak of the energy-loss spectrum is located at about 13.8eV. The refractive index n(0) equals 2.1. These results are in good agreement with experiments.(2) The first-principles calculations have been presented on cubic SrTiO₃ and SrZrO₃ perovskites under hydrostatic pressure. Lattice constant, bulk modulus, band structure, density of states, and the electronic dielectric function have been studied. The obtained results show that the general features of the energy bands of the two compounds are similar, the valence bands are primarily dominated by O 2p states, their top is reached at R point; the conduction bands are dominated by Ti 3d and Zr 4d states, their bottom is reached at the G point. Both of the two compounds are the indirect band gap insulators. Compared with SrTiO₃, the band gap of SrZrO₃ is larger and the bandwidths of SrZrO₃ are smaller. This is due to the fact that the interaction between Ti and O is more covalent than that between Zr and O, and moreover, the hybridization between Zr 4d and Sr 5s is stronger than that between Ti 3d and Sr 5s in the upper conduction bands. With the increase in hydrostatic pressure, the lattice constants decrease, and the band gaps increase almost linearly for the two compounds. The main peak of the imaginary part of the electronic dielectric function increases for SrZrO₃, and decreases for SrTiO₃. They have nearly the same energy shift towards high energy region. The dielectric function of SrTiO₃ decreases slowly and the variation of the dielectric function for SrZrO₃ is negligible with the increase in hydrostatic pressure. The obtained results are in good agreement with the available experimental results and previous theoretical calculations.