A progressive reduction of tetragonal distortion, heat of transition, Curie temperature, and relative dielectric constant has been observed on dense ${\mathrm{BaTiO}}_3$ ceramics with grain size decreasing from 1200 to $50\mathrm{nm}$. The correlations between grain size, extent of tetragonal distortion, and ferroelectric properties strongly support the existence of an intrinsic size effect. From the experimental trends the critical size for disappearance of ferroelectricity has been evaluated to be $10–30\mathrm{nm}$. The strong depression of the relative permittivity observed for the nanocrystalline ceramics can be ascribed to the combination of the intrinsic size effect and of the size-dependent “dilution” effect of a grain boundary “dead” layer.

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.

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.