Theoretical models for small ferroelectric particles predict a progressive decrease of the Curie temperature, spontaneous lattice strain, and polarization until the critical size corresponding to transition to the cubic phase and disappearance of ferroelectricity is reached. In contrast, the behavior of nanocrystalline $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ ceramics with a grain size of $\approx 30\mathrm{nm}$ is dominated by extrinsic effects related to the grain boundaries which mask the expected downscaling of properties. While the noncubic crystal structure, the high dielectric constant $(\approx 1600)$ and the variation of permittivity with temperature suggest a ferroelectric behavior, very slim, and nearly linear polarization hysteresis loops are observed. Evidence for the existence of a ferroelectric domain structure with domains extending over several grains and of polarization switching at local scale is given by piezoresponse force microscopy. The suppression of macroscopic ferroelectric hysteresis and switching originates from a frozen domain structure stable under an external field owing to the effects exerted by the grain boundaries, such as the clamping of the domain walls and the hindrance of polarization switching. Furthermore, the depolarization field originated by the low-permittivity nonferroelectric grain boundaries can cause a significant reduction of polarization. If the grain size is small enough, the ceramic is expected to undergo a “phase transition” to a polar phase with nonswitchable polarization. The $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ ceramics with grain size of $30\mathrm{nm}$ investigated in the present study are deemed to be close to this transition.

The complex elastic compliance and dielectric susceptibility of (Na0.5Bi0.5)1$-${}xBaxTiO3 (NBT-BT) have been measured in the composition range between pure NBT and the morphotropic phase boundary included, 0$\le${}x$\le${}0.08. The compliance of NBT presents sharp peaks at the rhombohedral/tetragonal and tetragonal/cubic transitions, allowing the determination of the tetragonal region of the phase diagram, up to now impossible due to the strong lattice disorder and small distortions and polarizations involved. In spite of ample evidence of disorder and structural heterogeneity, the R-T transition remains sharp up to x=0.06, whereas the T-C transition merges into the diffuse and relaxorlike transition associated with broad maxima of the dielectric and elastic susceptibilities. An attempt is made at relating the different features in the anelastic and dielectric curves to different modes of octahedral rotations and polar cation shifts. The possibility is also considered that the cation displacements locally have monoclinic symmetry, as for PZT near the morphotropic phase boundary.

BaSnxTi1−xO3 solid solutions with compositions in the range x = 0–0.20 were studied by combining analysis of the field-induced dielectric and ferroelectric properties with Raman spectroscopic investigations. By combining techniques, the detection of specific features related to the ferroelectric-to-relaxor crossover with increasing Sn content is possible. Detailed tunability analysis of the x = 0.05 composition indicated that multiple components contribute to the dc-field induced permittivity response; these components are active in different temperature and field ranges and could be assigned to a few polarization mechanisms. First order reversal curves (FORC) for the material clearly show a transition from ferroelectric-to-relaxor behavior with increasing x, confirming the conclusions from the Raman and dielectric studies. This was evidenced by the shift of the FORC distribution over coercivities toward zero field values. Raman measurements allow the identification of the separate phases with varying Sn content and temperature, indicating large regions of phase coexistence. The composition x = 0.20 is in a predominantly relaxor state. This is ascribed to a large range of phase coexistence and to the presence of polar nanoregions promoted by Sn substitution on the B site of the perovskite unit cell ABO3.

Complex dielectric susceptibility was used to investigate the relaxor properties and the ferroelectric phase transitions in (Na_1/2Bi_1/2)_1 − xBa_xTiO₃ (0 ≤ x ≤ 0.08) ceramics. XRD was used to characterize the ground states of poled and unpoled samples. Dielectric susceptibility vs. temperature studies allowed to obtain the relaxor properties and to identify the electric field-induced phase transitions in the morphotropic phase boundary (MPB) compositions (0.06 < x < 0.08) and the spontaneous relaxor-ferroelectric phase transitions in the rhombohedral compositions (x < 0.06). The frequency dispersion of the dielectric maximum at T_m was observed for all compositions, although of decreased extension for lower x. The relaxor properties have been analysed with Vogel-Fulcher law. The activation energy and attempt frequency for the MPB compositions are similar to those of classical relaxors like Pb(Mg_1/3Nb_2/3)O₃, while for rhombohedral compositions, they are similar to relaxor ferroelectrics with spontaneous relaxor-ferroelectric phase transitions, like Pb(Sc_1/2Nb_1/2)O₃. A relationship has been found between the relaxor dispersion degree and the hysteresis of the ferroelectric transition.