The density functional theory is used to calculate vibrational spectra, suggest dependencies of total energies and frequencies on BaF2 and PbF2 crystal lattice constants, and obtain the density of two phonon states in PbF2 crystal weighted by thermal occupation numbers. Due to the order-of-magnitude difference between metal and fluorine masses, acoustic and optical branches are determined by metal and fluorine vibrations, respectively. Therefore, phonon spectra can be demonstrated in two Brillouin zones, namely fluorine lattice and sublattice, the number of optical branches being decreased twice. Based on the suggested dependencies of total energies in the crystal and squared frequencies on the lattice parameter, anharmonicity constants are identified. It is shown that with increasing temperature the frequency attenuates. For PbF2 crystal, anharmonicity constants are shown to be higher than for BaF2 crystal, and this fact is supported by the experiment. The model of the density of two phonon states in PbF2 crystal shows that the temperature broadening of Raman frequency is more substantial than that of the infrared active phonon frequency.
fluorite density functional phonon spectrum anharmonicity frequency attenuation sublattice
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