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.

Supercritical water is a green solvent used in many technological applications including materials synthesis, nuclear engineering, bioenergy, or waste treatment and it occurs in nature. Despite its relevance in natural systems and technical applications, the supercritical state of water is still not well understood. Recent theories predict that liquid-like (LL) and gas-like (GL) supercritical water are metastable phases, and that the so-called Widom line zone is marking the crossover between LL and GL behavior of water. With neutron imaging techniques, we succeed to monitor density fluctuations of supercritical water while the system evolves rapidly from LL to GL as the Widom line is crossed during isobaric heating. Our observations show that the Widom line of water can be identified experimentally and they are in agreement with the current theory of supercritical fluid pseudo-boiling. This fundamental understanding allows optimizing and developing new technologies using supercritical water as a solvent.