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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Anomalous thermal expansion behaviour of several open frame-work compounds has been extensively investigated using the techniques of inelastic neutron scattering and lattice dynamics. These compounds involve increasing level of structural complexity and flexibility, which leads to increased values of thermal expansion coefficients approaching colossal values. In several compounds, neutron inelastic scattering experiments have produced quantitative estimates of the anharmonicity of phonons over a range of low energies, and thereby explained the observed thermal expansion quantitatively. The anharmonicity is found to be an order of magnitude larger than that in usual materials. Lattice dynamical calculations have correctly predicted the observed anharmonicity in the neutron experiments and revealed the overall nature of phonons involved. In compounds showing negative thermal expansion, the phonons responsible have rather low energies up to 10 meV. In most compounds, the anharmonic phonons span all over the Brillouin zone, while in some cases the specific phonons are limited to certain wave-vectors. The nature of specific phonons responsible for anomalous behavior is found to be different in all these compounds.These phonons generally involve transverse vibrations, librations and internal distortions of the polyhedral units. The paper reviews recent advances in the understanding of anomalous thermal expansion behaviour.

). We have measured the temperature dependence of phonon spectra in these compounds and analyzed them using ab-initio calculations. The spectra of the two compounds show large differences that cannot be explained by simple mass renormalization of the modes involving Zn (65.38 amu) and Ni (58.69 amu) atoms. This reflects the fact that the structure and bonding are quite different in the two compounds. The calculated pressure dependence of the phonon modes and of the thermal expansion coefficient, α V , are used to understand the anomalous behavior in these compounds. Our ab-initio calculations indicate that it is the low-energy rotational modes in Zn(CN) 2 , which are shifted to higher energies in Ni(CN) 2 , that are responsible for the large negative thermal expansion. The measured temperature dependence of the phonon spectra has been used to estimate the total anharmonicity of both compounds. For Zn(CN) 2 , the temperature-dependent measurements (total anharmonicity), along with our previously reported pressure dependence of the phonon spectra (quasiharmonic), is used to separate the explicit temperature effect at constant volume (intrinsic anharmonicity).