Na${}_{0.5}$Bi${}_{0.5}$TiO${}_3$ (NBT) and its derivatives have prompted a great surge in interest owing to their potential as lead-free piezoelectrics. In spite of five decades since its discovery, there is still a lack of clarity on crucial issues such as the origin of significant dielectric relaxation at room temperature, structural factors influencing its depoling, and the status of the recently proposed monoclinic ($Cc$) structure vis-à-vis the nanosized structural heterogeneities. In this work, these issues are resolved by comparative analysis of local and global structures on poled and unpoled NBT specimens using electron, x-ray, and neutron diffraction in conjunction with first-principles calculation, dielectric, ferroelectric, and piezoelectric measurements. The reported global monoclinic ($Cc$) distortion is shown not to correspond to the thermodynamic equilibrium state at room temperature. The global monocliniclike appearance rather owes its origin to the presence of local structural and strain heterogeneities. Poling removes the structural inhomogeneities and establishes a long-range rhombohedral distortion. In the process the system gets irreversibly transformed from a nonergodic relaxor to a normal ferroelectric state. The thermal depoling is shown to be associated with the onset of incompatible in-phase tilted octahedral regions in the field-stabilized long range rhombohedral distortion.

The structure-property correlation in the lead-free piezoelectric ($1-x$)(Na${}_{0.5}$Bi${}_{0.5}$)TiO${}_3$-($x$)BaTiO${}_3$ has been systematically investigated in detail as a function of composition ($0<x\le 0.11$), temperature, electric field, and mechanical impact by Raman scattering, ferroelectric, piezoelectric measurement, x-ray, and neutron powder diffraction methods. Although x-ray diffraction study revealed three distinct composition ranges characterizing different structural features in the equilibrium state at room temperature: (i) monoclinic ($Cc$)+rhombohedral ($R$3$c$) for the precritical compositions, $0\le x\le 0.05$, (ii) cubiclike for $0.06\le x\le 0.0675$, and (iii) morphotropic phase boundary (MPB) like for $0.07\le x<0.10$, Raman and neutron powder diffraction studies revealed identical symmetry for the cubiclike and the MPB compositions. The cubiclike structure undergoes irreversible phase separation by electric poling as well as by pure mechanical impact. This cubiclike phase exhibits relaxor ferroelectricity in its equilibrium state. The short coherence length (∼50 Å) of the out-of-phase octahedral tilts does not allow the normal ferroelectric state to develop below the dipolar freezing temperature, forcing the system to remain in a dipolar glass state at room temperature. Electric poling helps the dipolar glass state to transform to a normal ferroelectric state with a concomitant enhancement in the correlation length of the out-of-phase octahedral tilt.

The lead free ferroelectric Na${}_{1/2}$Bi${}_{1/2}$TiO${}_3$ (NBT) is shown to exhibit electric-field-induced monoclinic ($Cc$) to rhombohedral ($R$3$c$) phase transformation at room temperature. This phenomenon has been analyzed both from the viewpoint of the intrinsic polarization rotation and adaptive phase models. In analogy with the morphotropic phase boundary systems, NBT seems to possess intrinsic competing ferroelectric instabilities near room temperature.

We have carried out a detailed Rietveld analysis of x-ray powder diffraction data of ${\mathrm{Pb(Zr}}_x{\mathrm{Ti}}_{\text{1−x}}){\mathrm{O}}_3$ (PZT) compositions across the morphotropic phase boundary (MPB) region $\text{(x=0.515,}$ 0.520, 0.525, 0.530). It is shown that the structure of PZT is pure tetragonal for $\text{x⩽0.515}$ with space group P4mm. In the MPB region, $\text{0.515<x<0.530,}$ the tetragonal and monoclinic (space group: Cm) phases are found to coexist as a result of a first order phase transition between the low temperature monoclinic and high temperature tetragonal phases. Further, arguments are advanced to show that the hitherto believed rhombohedral structure ${\mathrm{(F}}_R^{\mathrm{HT}})$ of PZT for $\text{0.530⩽x⩽0.62}$ is more likely to be monoclinic.