Negative thermal expansion emerging upon structural phase transition in ZrV2O7 and HfV2O7

ZrV(2)O(7) and HfV(2)O(7), 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 ZrV(2)O(7) and 341.8 K and 370.3 K for HfV(2)O(7). 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 ZrV(2)O(7) and HfV(2)O(7). 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 V(2)O(7) 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 ZrV(2)O(7) and HfV(2)O(7) in the high-temperature phase.