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 Na0.5Bi0.5TiO3, Na0.5Bi0.5TiO3-5% BaTiO3, and Na0.5Bi0.5TiO3-8% K0.5Bi0.5TiO3 single crystals. It was found that Na0.5Bi0.5TiO3 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 A(1) 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 TF-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 9A(1)+9E and 36A ''+24A' modes for the rhombohedral and monoclinic phases of Na0.5Bi0.5TiO3, respectively.