We use a combination of first-principles density functional theoretical analysis and experimental characterization to understand the lattice dynamics, dielectric and ferroelectric properties of lead-free relaxor ferroelectric Na0.5Bi0.5TiO3 (NBT) system. Vibrational spectrum determined through our calculations agrees well with the observed Raman spectrum, and allows assignment of symmetry labels to modes. The calculated Born effective charges reveal (a) two distinct types of Ti ions at the B-site with anomalous dynamical charges differing by up 1.6e, and (b) Na and Bi ions at the A-site exhibit disparate dynamical charges of about 1 and 5.5e, respectively. Thus, there exist hetero-polar activity at both A and B-sites in NBT, and disorder associated with these hetero-polar ions is responsible for its relaxor behaviour. Large dielectric response of NBT arises primarily from phonons, and specifically the modes involving Bi-O (109 cm−1) and Ti-O (246, 276 cm−1) vibrations, respectively.

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