Lattice dynamics and anharmonicity of CaZrF6 from Raman spectroscopy and ab initio calculations

Very recently it has been found that CaZrF6 exhibits a very large and isotropic negative thermal expansion (NTE), even greater than the current most popular NTE materials. In this work, the vibrational dynamics of CaZrF6 has been investigated by temperature-dependent Raman spectroscopy combined with ab initio calculations. As expected on the basis of the group theory for CaZrF6, three Raman-active modes were identified: the F2g mode peaked at about 236 cm1, the Eg mode at around 550e555 cm1, and the Ag mode peaked at about 637 cm1. The temperature dependence of their frequencies follows an unusual trend: the F2g mode, due to bending vibrations of fluorine atoms in the linear Ca-F-Zr chain, is hardened with increasing temperature, while the Ag mode, corresponding to Ca-F-Zr bond stretching vibrations, is softened. We explain this anomalous behavior by separating implicit and explicit anharmonicity for both F2g and Ag modes. In fact, cubic anharmonicity (three-phonon processes) is observed to dominate the higher-frequency Ag phonon-mode, quartic anharmonicity (four-phonon processes) is found to dominate the lower-frequency F2g phonon-mode. As a result, the large NTE of CaZrF6 cannot be accurately predicted through the quasi-harmonic approximation.