| Summary: | 碩士 === 中國文化大學 === 材料科學與奈米科技研究所 === 95 === In this thesis, we are studied the density of state, energy band structure, phonon dispersion relation and vibration modes of cubic, tetragonal and hexagonal structure of BaTiO3 by ab initio calculation.
Our first-principles calculation result shows that the existence of imaginary phonon of cubic BaTiO3 corresponds to a structural instability under ambient condition. The density of state and phonon band structures of the cubic BaTiO3 system is consistent with several literatures although those literatures are using several different lattices parameters with this thesis.
Based on the group theorem, there are 15 vibration modes of cubic structure BaTiO3. The vibration modes can be classified five types; the first type is moving modes. The second type is that the vibration direction of Ba-atoms is opposite to others atoms. The third type is the vibration direction of Oxygen atoms on Ti-O planes are opposite to the Oxygen atoms on Ba-O planes. The fourth type is the Ba and O in the Ba-O plane, which are vibrated in opposite ways. The other type is that the vibration directions of Oxygen atoms on Ba-O planes are opposite to the Oxygen atoms and Ti-atom on Ti-O planes.
The first-principles calculation result shows that there is no the existence the imaginary phonon of tetragonal BaTiO3 phase, which means the tetragonal phase is more stable than the cubic phase. Because of the LO-TO energy splitting, there are discontinued of phonon band structure at Γ point.
The calculation result shows that the hexagonal structure BaTiO3 is existence the energy band of the Fermi surface. The unit cell of hexagonal BaTiO3 is included 30 atoms, there are 90 vibration modes in the hexagonal BaTiO3, which is due to the phonon bands are very high density and degeneracy. The results are predicted that there is no mode existence during 550-620cm-1 and 650-720cm-1, which is consistent with the literature report.
Those 90 modes can be label as 7 kinds. The first kind is movement modes that are included 5 modes. The second kind is only Oxygen vibrations that are included 36 modes. The third kind is only Ba-atoms vibrations that are included 10 modes. The fourth kind is only Ti-atoms vibration that is only 1 mode. The fifth kind is only Oxygen and Ti-atoms vibration, which are included 31 modes. The sixth kind is only Oxygen and Ba-atoms vibration that are included 2 modes. The seventh kind is only Ba-atoms and Ti-atoms vibrations, which are included 6 modes.
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