Thermodynamiccriteria are derived for the occurrence of surface-induced melting and freezing in a semi-infinite system. Use is made of a mean-field theory of the Landau-type.The parameters which enter the Landau free energy functional are expressed in terms of known interfacial free energies. Expressions are obtained for the order parameter profile in the surface region and for the temperature-dependent thickness of the molten (frozen) surface layer. The results explain recent observations of surface melting (or nonmelting)at differently oriented crystal faces of Pb and account for the general absence of surface-induced freezing effects in liquids.

Ion-shadowing and -blocking experiments on a cylindrical single crystal of Pb reveal a strongly orientation-dependent disordering (melting) of the surface with increasing temperature. The thickness of the disordered surface layer is found to diverge logarithmically as the bulk melting point is approached. The process of disordering is shown to be driven by an orientation-dependent difference in free energy between the surface in its ordered and liquid states.PACS numbers: 68.35.Rh, 68.35.Md, 68.45.Gd The possible role of the surface in initiating the melting of a solid has long been debated. l A recent observation of surface melting on an atomic level 2 has created a surge of renewed interest in the phenomenon. 3 " 6 Our present state of knowledge can be summarized as follows. Surface melting is an intrinsic effect. 7 It involves a positional disordering of the lattice in the surface region just below the bulk melting point and is to be distinguished from "surface roughening." As the temperature T approaches the bulk melting point T m , the melted layer thickness d is predicted to diverge as \\n(T m -T)\ or as (T m -T) ~r, depending on whether the acting forces are of short or long range. 8,9 The melted layer is not a true liquid, since the underlying lattice induces some crystalline order in it. 10 Hence it is usually referred to as a "quasiliquid."Several predictions have been made regarding a variation in melting behavior with surface orientation. 3,11 Crystal faces with open packing of atoms are expected to melt readily, whereas close-packed faces may not melt at all below T m . Such a trend has been observed by Stock 12 in optical emission measurements on spherical Cu monocrystals which were heated up to T m .In this Letter we report the first measurements of melted-layer thickness as a function of surface orientation and temperature. With use of medium-energy ion scattering, the presence of melting-related disorder was detected in the outermost atomic layers of a Pb crystal which was cylindrically cut so as to expose a range of surface orientations. The number of disordered monolayers at a given temperature in the vicinity of T m was found to vary dramatically with surface orientation. A simple thermodynamic model quantitatively explains this result.A cylindrical specimen was spark cut from a singlecrystal Pb bar of high purity. 13 The cylinder surface exposes a 73° range of crystallographic orientations along the [TlO] zone of the stereographic triangle. The orientation of a particular face on the cylinder is defined by the angle 0 between its normal and the [112] axis (Fig. 1). The surface was prepared as in Ref. 7. It was found to be well ordered as seen with low-energy electron dif-fraction and ion channeling. With Auger-electron spectroscopy it was checked that the surface was atomically clean. No segregation of impurities was observed with increasing T. The surface temperature was monitored by a pyrometer which was calibrated against a Pt resistance. The temperature scale was fixed by the bulk m...

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