Anharmonic Gruneisen theory based on self-consistent phonon theory: Impact of phonon-phonon interactions neglected in the quasiharmonic theory

We formulate a theory of thermal expansion based on the self-consistent phonon (SCP) theory, which nonperturbatively considers the anharmonic effect. We show that the Gruneisen formula holds within the SCP theory by replacing the phonon frequency by the SCP frequency. By comparing it with the quasiharmonic approximation (QHA), we derive explicit formulas of the correction to the QHA result. We show that the phonon anharmonicity gives a small correction of O(<(U) over cap (4)>/<(U) over cap (2)>) to the thermal expansion coefficient alpha, where (U) over cap (2) and (U) over cap (4) are the harmonic and the quartic terms of the potential energy surface. On the other hand, we show that the phonon anharmonicity gives two correction terms to the temperature (T)-dependent phonon frequency shift which are comparable to the original QHA term. In strongly anharmonic materials such as NaCl and MgO, these two correction terms tend to cancel out each other, which explains why QHA sometimes gives reasonable values for the T-dependent phonon frequency shift while it fails for thermal expansion.

Automated summary

In this study, a theory of thermal expansion based on the self-consistent phonon (SCP) theory is formulated, taking into account the anharmonic effect. The Gruneisen formula is shown to hold within the SCP theory by replacing the phonon frequency. By comparing with the quasiharmonic approximation (QHA), explicit formulas for the correction to the QHA result are derived. It is found that the phonon anharmonicity has a small correction to the thermal expansion coefficient alpha, but has comparable corrections to the temperature-dependent phonon frequency shift.