Melting mechanism during fast heating

The behavior of an ideal crystal during fast heating when the settled life time of particles is substantially larger than the characteristic time of changing temperature is considered. A calculation model is a crystal with a simple cubic lattice, in which the interaction between particles is described by the Lenard–Jones potential. Disordering of the crystal on heating is considered to be a result of the formation of vacancies. Vacancies are shown to form during fast heating only in the case if the temperature is higher than a critical temperature $T_C$. An equation of state describing the behavior of a crystal with vacancies during fast heating has been derived. It is found that there is a temperature at which the crystal lattice losses the mechanical stability. This temperature is identified as the melting temperature on fast heating.