Vibrational stability and melting

Abstract

The self-consistent phonon (SCP) theory is used to study the mechanical stability of crystals to vibration as temperature is increased. The temperature at which instability occurs, TI, depends sensitively on the approximation made to the SCP theory. In the self-consistent harmonic approximation, TI is 10-200 times the observed melting temperature TM, depending on the crystal considered. In higher approximations TI is reduced to (3-4)TM in all cases. Although the explicit character of the instability depends somewhat on the approximation, the instability is sudden, and takes place at a critical vibrational amplitude reminiscent of the Lindemann model of melting. © 1983 The American Physical Society.