The electron-phonon interaction and melting of metals

Abstract

The minimum uncertainty product form of Heisenberg's Uncertainty Principle is applied to the electron-phonon interaction in metals in the free-electron and Debye approximations. Twice the Debye frequency follows as an upper limit to the electron-phonon scattering rate. This is an extension of an earlier application to the 3-phonon anharmonic scattering rate, and Lindemann's law of melting follows in both cases. Corrections and clarifications of the earlier work are included. It is shown that the electron-phonon relaxation time, the Debye zoneboundary phonon relaxation time, the ion-ion collision time on the liquid side of melting, and the inverse of twice the Debye frequency are all approximately equal at the melting point.