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

Abstract

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 cm−1, the Eg mode at around 550–555 cm−1, and the Ag mode peaked at about 637 cm−1. 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.