Effect of normal phonon-phonon scattering on the phonon relaxation time for metals

The phonon-phonon scattering relaxation time for metals is derived by an analysis that explicitly incorporates the Peierls condition that normal phonon-phonon scattering cannot equilibrate the phonon system. Numerical results are presented for potassium. These results demonstrate that at low temperatures, the Peierls condition leads to a very significant reduction of phonon-phonon scattering.