Phonons and anomalous thermal expansion behaviour in crystalline solids

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.