Coexistence of Ferroelectric Phases and Phonon Dynamics in Relaxor Ferroelectric Na_0.5Bi_0.5TiO₃ Based Single Crystals

A combination of polarized Raman technique, infrared reflectance spectra, and first-principles density-functional theoretical calculations were used to investigate structure transformation and lattice vibrations of Na_0.5Bi_0.5TiO₃, Na_0.5Bi_0.5TiO₃–5%BaTiO₃, and Na_0.5Bi_0.5TiO₃–8%K_0.5Bi_0.5TiO₃ single crystals. It was found that Na_0.5Bi_0.5TiO₃ is of a two-phase mixture with rhombohedral and monoclinic structures at room temperature. Correspondingly, three Raman-active phonon modes located at 395, 790, and 868 cm⁻¹, which were previously assumed as A₁ modes of rhombohedral phase have been reassigned as A^′′, A^′, and A^′ modes of monoclinic phase in the present work. In particular, a strong low-frequency A^′′ mode at 49 cm⁻¹ was found and its temperature dependence was revealed. Two deviations from linearity for the abrupt frequency variation in the A^′′ mode and Ti–O bond have been detected at temperatures of ferroelectric to antiferroelectric phase transition T_F–AF and dielectric maximum temperature T_max. The appearance of Na–O vibrations at 150 cm⁻¹ was found below T_max, indicating the existence of nanosized Na⁺TiO₃ clusters. The observed Raman and infrared active modes belonging to distinct irreducible representations are in good agreement with group-theory predictions, which suggests 9A₁+9E and 36A^′′+24A^′ modes for the rhombohedral and monoclinic phases of Na_0.5Bi_0.5TiO₃, respectively.