ANHARMONICITY EFFECTS IN CaF₂ AT LOW TEMPERATURE

Abstract
Using the framework of the rigid ion model, we have calculated the lifetime of longitudinal acoustic phonons in CaF₂ at low temperature. The decay mode 1→1 + t is strongly anisotropic and of one order of magnitude smaller than the decay mode 1→t + t. For each single decay mode, the long-wavelength approximation which yields the ν⁵ dependence of 1/τ, is valid for ν ≤ 2.5 THz. At higher frequencies, the competing decay modes show different deviances which, curiously, cancel each other so that the total life-time can be well approximated by the long-wavelength limit up to 5.5 THz. We have also calculated the temperature dependence of the second and third order elastic constants and a good agreement is found with the available experimental data.