Neutron diffraction studies using powder samples have been used to understand the complex sequence of low temperature phase transitions of NaNbO3 in the temperature range from 12 K-350 K. Detailed Rietveld analysis of the diffraction data reveal that the antiferroelectric to ferroelectric phase transition occurs on cooling around 73 K while the reverse ferroelectric to antiferroelectric transition occurs on heating at 245 K. However, the former transformation is not complete till down to 12 K and there is unambiguous evidence for the presence of the ferroelectric R3c phase coexisting with an antiferroelectic phase (Pbcm) over a wide range of temperatures. The coexisting phases and reported anomalous smearing of the dielectric response akin to dipole glasses and relaxors observed in the same temperature range are consistent with competing ferroelectric and antiferroelectric interactions in NaNbO 3 . We have carried out theoretical lattice dynamical calculations which reveal that the free energies of the antiferroelectric Pbcm and ferroelectric R3c phases are nearly identical over a wide range of temperature. The small energy difference between the two phases is of interest as it explains the observed coexistence of these phases over a wide range of temperature. The computed double well depths and energy barriers from paraelectric Pm 3m to antiferroelectric Pbcm and ferroelectric R3c phases in NaNbO 3 are also quite similar, although the ferroelectric R3c phase has a slightly lower energy.

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We report first principles density functional perturbation theory calculations and inelastic neutron scattering measurements of the phonon density of states, dispersion relations and electromechanical response of PbTiO 3 , BaTiO 3 and SrTiO 3 . The phonon density-of-states of the quantum paraelectric SrTiO 3 is found to be fundamentally distinct from that of ferroelectric PbTiO 3 and BaTiO 3 with a large 70-90 meV phonon band-gap. The phonon dispersion and electromechanical response of PbTiO 3 reveal giant anisotropies. The interplay of covalent bonding and ferroelectricity, strongly modulates the electromechanical response and give rise to spectacular signatures in the phonon spectra. The computed charge densities have been used to study the bonding in these perovskites. Distinct bonding characteristics in the ferroelectric and paraelectric phases give rise to spectacular vibrational signatures. While a large phonon band-gap in ATiO 3 perovskites seems a characteristic of quantum paraelectrics, anisotropy of the phonon spectra correlates well with ferroelectric strength. These correlations between the phonon spectra and ferroelectricity, can guide future efforts at custom designing still more effective piezoelectrics for applications. These results suggest that vibrational spectroscopy can help design novel materials.

Geometric frustration is a broad phenomenon that results from an intrinsic incompatibilityCompositionally graded ferroelectrics can thus be considered as the ``missing'' link that brings ferroelectrics into the broad category of materials able to exhibit geometric frustration. Our ab-initio calculations allow a deep microscopic insight into this novel geometrically frustrated system.Geometrically frustrated systems like spin ice and spin liquids reveal intriguing phenomena and are known to exhibit a degenerate manifold of exotic ground states [1][2][3][4][5][6][7][8] . Spectacular features of geometrically frustrated compounds include formation of complex microstructures 1-8 , strong deviation of macroscopic properties from well-known critical behaviors 9-10 and presence of topological defects, spiral states and curvature [11][12][13][14][15][16][17] . Here, we report the discovery that compositionally modulated ferroelectrics exhibit all these phenomena that are hallmarks of geometric frustration (GF).Practically, we investigated compositionally graded (Ba,Sr)TiO 3 (BST) compounds, which are systems that are promising candidates for applications as storage capacitors and dielectrics for the next generation of dynamic random access