Lattice theory of surface melting

We have developed a lattice theory of surface melting based on minimization of the free energy with respect to two spatially varying order parameters—density and ‘‘crystallinity.’’ The partition function is evaluated using mean-field and free-volume approximations on a lattice. Direct application is made to (100) and (110) Lennard-Jones crystal surfaces. It is shown that on the coexistence line and very close to the triple-point temperature $T_M$ a quasiliquid layer forms on the crystal-gas interface. The thickness of the layer grows asymptotically as ($T_M$-T${)}^{\mathrm{-}1/3}$, in good agreement with the recent experiments on Ar films. A change from long- to short-range interparticle attraction reduces the growth behavior to logarithmic, while a switch of the potential tail from attractive to repulsive can block altogether the growth of the quasiliquid layer. It is further shown that in cases where no in-plane disorder can arise no surface melting occurs and the crystal-vapor interface can even be overheated. Within the present mean-field approximation, surface melting is found to be continuous without any singularities below $T_M$ in the surface free energy, which is explicitly calculated. The decay of the ‘‘crystallinity’’ order parameter at the quasi-liquid-gas interface is predicted to be a ‘‘stretched exponential’’ in the long-range case and power law in the short-range case.