Revision of the Statistical Mechanics of Phonons to Include Phonon Line Widths

摘要

Zubarev in 1960 obtained the smeared Bose-Einstein (B-E) function in order to take into account the fact that the eigenenergy associated with a fixed phonon wave vector q and fixed polarization index j is not precisely defined but instead, is smeared by phonon-phonon and phonon-electron interactions. The ratio GAMMA(qj)/ omega (qj) is often quite small, i.e., of the order of 0.01 or less, where GAMMA is the phonon linewidth and h-bar omega is the eigenenergy. However, in strongly anharmonic crystals GAMMA/ omega may be as large as 0.3 at certain points of the Brillouin zone. In such dramatic cases one would suspect that such phonon linewidths would have some observable effect on the thermodynamic properties. The purpose of this work is to derive the expression for the average free energy per mode for a crystal having large phonon linewidths and to test the properties of the thermodynamic functions derivable from the average free energy per mode. (ERA citation 08:056685)