A kinetic model for the premelting of a crystalline structure

An analytical kinetic approach to examine the premelting phenomenon is suggested by using a first passage time analysis. Premelting is considered to occur when the time of formation of a Frenkel type defect in the surface monolayer becomes sufficiently small. The mean time of defect formation on the surface lattice, i.e., the mean time necessary for a selected (surface-located) molecule to leave its lattice site and form a Frenkel defect, is calculated by using a first passage time analysis. The model is illustrated by numerical calculations for a crystalline structure composed of molecules interacting via the Lennard-Jones (LJ) potential. The lattice vectors in the plane parallel to the free surface of the crystal were assumed to be equal (to the lattice parameter) and the angle between them was varied. The model predictions of the Tammann temperature (of premelting) are very sensitive to the parameters of the LJ potential. In all the cases considered, the temperature dependence of the mean first passage time has two clearly distinct regimes: at low temperatures the dependence is sharp and at high temperatures it is weak.