ZrV2O7 and HfV2O7, which show negative thermal expansion (NTE) in the high-temperature phase, were investigated using X-ray diffraction and heat capacity calorimetry. Two sharp anomalies due to successive phase transitions were observed in the temperature dependence of heat capacity at 345.5 K and 373.4 K for ZrV2O7 and 341.8 K and 370.3 K for HfV2O7. The smallness of their combined entropies of transition suggested that the phase transitions are of displacive type. Effective phonon densities of states (DOS) described by a simple model, and mode-Grüneisen parameters of the low-temperature phase were obtained through the spectrum analyses of heat capacities of ZrV2O7 and HfV2O7. Their effective phonon DOS's show the three features common to NTE compounds: low-energy phonon mode, high-energy phonon mode, and a wide phonon gap in between. The mode-Grüneisen parameter of low-energy modes corresponding to translational and librational vibrations of the constituent polyhedra is negative but with a small absolute value due to the distortion of V2O7 group in the low-temperature phase, resulting in positive thermal expansion. It is revealed that the release of the structural distortion upon the successive phase transitions with large volume increase leads to the NTE of ZrV2O7 and HfV2O7 in the high-temperature phase.

To study the relation between the structural characteristics and the phonon property in the negative thermal expansion (NTE) compounds, the heat capacities of Sc2W3O12 and Sc2Mo3O12 were measured. Spectrum analysis of heat capacity provided their effective phonon densities of states (DOS). The DOS of Sc2W3O12 shows three features; low-energy phonon modes with negative mode-Grüneisen parameter (γi) around 5 meV, high-energy phonon modes, and separation of phonon DOS into two regions with a wide gap. The relative contribution of γiCi, where Ci is heat capacity of each vibrational mode i, reveals that the low-energy phonon modes with negative γi cause the NTE and that the latter two features are necessary to maintain the NTE in a wide temperature range. Sc2Mo3O12 has the low-energy mode with the negative γi. This fact indicates that Sc2Mo3O12 potentially has the NTE property even in its low-temperature phase showing positive thermal expansion. A comparison of the phonon DOS with other oxides shows that the phonon features are common in the NTE oxides and related to their common chemical and structural characteristics, “strong bond” and “framework structure”. This finding gives us an important guide to search for new actual and/or potential NTE compounds.

Zr1−xLuxW2O8−y solid solutions were newly synthesized by a solid sate reaction method. X-ray diffraction (XRD) experiments from 90 to 560 K revealed that the solid solutions were of a single phase up to x = 0.04 and showed a negative thermal expansion. Order–disorder phase transition temperatures (Ttrs) and saturated order parameters (ηs) associated with WO4 orientational order were determined from the XRD results. The linear relationship between the normalized Ttrs and ηs obtained for Zr1−xMxW2O8−y (M = Sc, Y, In) in our previous study was also found for Zr1−xLuxW2O8−y. A heat capacity anomaly due to the order–disorder phase transition was detected for Zr0.96Lu0.04W2O8−y by a relaxation calorimeter. Ttrs of the solid solutions drastically decreased with increasing Lu content. The drastic suppression of Ttrs can be explained by the model assuming the existence of a local nano-region including the WO4 pairs having the orientational disorder.

ZrV2O7 and HfV2O7, which show negative thermal expansion (NTE) in the high-temperature phase, were investigated using X-ray diffraction and heat capacity calorimetry. Two sharp anomalies due to successive phase transitions were observed in the temperature dependence of heat capacity at 345.5 K and 373.4 K for ZrV2O7 and 341.8 K and 370.3 K for HfV2O7. The smallness of their combined entropies of transition suggested that the phase transitions are of displacive type. Effective phonon densities of states (DOS) described by a simple model, and mode-Grüneisen parameters of the low-temperature phase were obtained through the spectrum analyses of heat capacities of ZrV2O7 and HfV2O7. Their effective phonon DOS's show the three features common to NTE compounds: low-energy phonon mode, high-energy phonon mode, and a wide phonon gap in between. The mode-Grüneisen parameter of low-energy modes corresponding to translational and librational vibrations of the constituent polyhedra is negative but with a small absolute value due to the distortion of V2O7 group in the low-temperature phase, resulting in positive thermal expansion. It is revealed that the release of the structural distortion upon the successive phase transitions with large volume increase leads to the NTE of ZrV2O7 and HfV2O7 in the high-temperature phase.