Low-frequency phonon modes and negative thermal expansion in A(MO(4))(2) (A = Zr, Hf and M = W, Mo) by Raman and Terahertz time-domain spectroscopy.

The low-frequency phonon modes of cubic ZrW(2)O(8) and HfW(2)O(8), and trigonal ZrMo(2)O(8) and HfMo(2)O(8) have been comparatively studied by Raman and terahertz time-domain spectroscopy. It is shown that there appear a number of distinctive low-frequency modes below 150 cm(-1) in the cubic ZrW(2)O(8) and HfW(2)O(8) in both Raman and terahertz spectra which are attributed to the librational and translational motions of the polyhedra whereas only one weak mode is present in the Raman but absent in the THz spectra of the trigonal ZrMo(2)O(8) and HfMo(2)O(8) in the same region, which is assigned to the interlayer breathing. It is found that the lowest optical phonon mode at about 40 cm(-1) disappears accompanied by obvious weakening of the lowest asymmetric stretching mode for ZrW(2)O(8) and HfW(2)O(8) across the order-disorder phase transition temperature. It gives direct evidence of reduction in the number of rigid unit modes (RUMs) in the high-temperature phase. It is shown that the correlated motions of the libration and transilation of the WO(4) tetrahedra and the ZrO(6)/HfO(6) octahedra with the out-of-phase asymmetric stretching of the two neighboring WO(4) tetrahedra contribute a large portion to the NTE in the low-temperature phase and some of the correlated motions may be destroyed across the order-disorder phase transition, causing a smaller negative thermal expansion in the high-temperature phase. The lack of RUMs in trigonal ZrMo(2)O(8) and HfMo(2)O(8) is the cause of their positive thermal expansion.