Thermodynamic Approach to Materials Showing Negative Thermal Expansion

In this paper, various thermodynamic approaches to the structural phase transitions and the phonon properties of the materials showing negative thermal expansion (NTE) in the wide temperature range are briefly reviewed through three families of the NTE compounds; ZrW2O8, ZrV2O7, A2B3O12 (A = trivalent cation, B = W or Mo) families. As for the structural phase transitions, the thermodynamic approaches provide us with elucidation of their mechanism from an entropic point of view. The NTE is closely related to phonon properties. Heat capacity measured by calorimetry enables us to estimate not only a Gruneisen function but also a distribution of phonon density of states, leading to specifying the phonon modes with negative mode-Gruneisen parameters. It is demonstrated that the thermodynamic approach is powerful to research the properties of the NTE materials.