Anharmonic interactions in diamond‐type crystals

Abstract

The potential energy of diamond, Si, and Ge crystals has been expanded in a double power series of the infinitesimal strain parameters and phonon coordinates. Third and fourth order expansion coefficients have been fitted to give reasonable agreement with the Grüneisen parameters of the individual modes of vibration, the mean Grüneisen parameters and thermal expansion coefficients, the third order elastic constants and the temperature dependence of the elastic constants. Calculations have been made for the mass operators of normal mode spropagating in the [100] and [111] directions. The relative renormalization of the low energy TA modes in Ge and Si is of the order of 10% while it is one order of magnitude less for phonons of the other branches.