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 T~, depending on the crystal considered. In higher approximations Tl is reduced to-. (3-4)T~in all cases. Although the exphcit 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.

Melting as a first‐order phase transition in a system of defects

“…In terms of the surface potential, it is where E = -U/2 is the bulk value of the vacancy formation energy (9). Substituting c., (z,) into (20) Equat,ion (34) represents the implicit temperature dependence of the number L of disordered monolayers as well as the orientation dependence of surface melting.…”

Estimation of Mechanical Stability and Resistance of Microporous Materials Prepared by Pyrolysis

“…The approaches employed include * statistical mechanics and thermodynamics (9}11), * perturbation methods (12, 13), * interface and colloid theory (14,15), * phonon theory (16), and * cumulative damage theory (17). All of these methods can be used in an analytical or a numerical form.…”

Mechanical lattice instability and thermodynamical properties in classical solids

“…To this issue, the mechanical melting was also addressed in the past by using extensively the self-consistent phonon theory (SCPT), [28][29][30][31][32][33][34][35][36][37][38][39][40] which represents a suitable method to take into account the anharmonic effects of the atomic oscillations. Within this microscopic approach, the breaking of the self-consistent solution of the SCPT is thought to represent the mechanical instability of the solid phase, and it defines a maximum temperature T * which was commonly assumed as an upper estimation of the melting temperature (the variational free energy obtained by the SCPT is an upper bound of the exact free energy).…”