Comment on “Surface layers on ice” by C. A. Knight

The term surface melting refers to the melting of a layer of fluid on the surface of a solid at temperatures below the bulk melting point of the solid. It is an equilibrium phenomenon, well established (as shown below) both experimentally and theoretically on a wide range of solids. The melted material is liquidlike, and the surface-melted or disordered region is often called a "quasi-liquid layer" (QLL). The existence of a QLL at equilibrium can be understood by consideration of a thought experiment in which a fresh solid/ vapor interface is created on a solid at a temperature T below the bulk melting temperature (by cleaving the solid, for instance). (We consider here a one-component system, as does K.) In this thought experiment, the solid, or crystal, structure is intact up to the surface in the first instant after the new surface is created. The system free energy consists of a volume term and a term proportional to the surface area. We ask under what conditions the evolution to equilibrium requires formation of a QLL. Let us imagine that a QLL of depth h exists on the surface. Let the surface area be A and the depths of the solid (vapor) layers be L,(L,,), where the subscripts "s" and "v" refer to solid and vapor phases. Let the surface free energy per unit area be %,,(h). Since the pressure is not uniform in this system, it is convenient to express the conditions of mechanical and thermodynamic equilibrium in terms of the grand potential, 12 -= F G, where F(G) are the Helmholtz (Gibbs) free energies. 12 = -p l/ + 3,A in each phase of surface area A, surface energy % pressure p, and volume V. Let the pressure in the bulk phases be p and let that in the surface-melted layer be p'. We have