Surface melting is by now a well established disordering phenomenon, occuring especially at the non-close-packed surfaces of metals and essentially on all surfaces of rare-gas solids and molecular systems. Surface melting occurs at temperature very close to bulk melting point Tm. For surfaces exhibiting premelting, a quasi-liquid layer (QLL) coats the solid-vapor interface lowering the total interfacial free energy. As temperature further increases toward Tm, such QLL may or may not diverges. The former is called complete surface melting while the latter is called blocked surface melting. Surface melting is very sensitive to the long-range interatomic interactions. The scaling of the thickness of the QLL is directly related to the power (or exponent) of the interatomic potential. To learn more, you may want check some of the pioneering studies of surface melting. The self diffusion on melting surface is particularly interesting, because of the important effect of the underlying crystalline periodic potential. Thus one would expect the atoms in the molten surface layer to reflect even in their diffusive behaviour the characteristics of the crystalline surface, such as discrete crystalline symmetry, anisotropy, etc. to learn more, you may want check some of the pioneering studies of diffusion on melting surfaces.