Assignment for Vibrational Spectra of BaTiO3 Ferroelectric Ceramic Based on the First-Principles Calculation

A BaTiO3 ceramic was synthesized using a conventional solid-state reaction, and sintered at 1400 degrees C for 4 h. The pure tetragonal phase was confirmed by Rietveld refinement of the X-ray diffraction data. The Raman spectrum and the far infrared (FIR) reflective spectrum were obtained and analyzed using Lorentz fitting and the four-parameter semi-quantum model fitting, respectively. The Raman and FIR spectra were assigned based on first-principles calculations, and consideration of the splitting of the transverse optical modes and longitudinal optical modes. All the vibrational modes were represented by linear combinations of the symmetry coordinates deduced by group theory analysis. Among the 12 optical modes, the Raman-active-only mode, B-1, can be viewed as the wing-flapping vibration of the O4-O5 plane perpendicular to the z-axis in the O-6 octahedron. The A(1)((1)) mode and the E-(1) soft mode are split by the triply degenerate F-1u mode of cubic BaTiO3, resulting in the ferroelectric property of tetragonal BaTiO3. The appearance of the A(1)((1)) mode leads to crystal polarization along the z-axis and the E-(1) mode causes the large permittivity. These two modes can be described as vibration of the Ti atom against the O-6 octahedral cage along the z-axis [A(1)((1))] and on the xy-plane [E-(1)].