Maximum overheating and partial wetting of nonmelting solid surfaces.

Surfaces which do not exhibit surface melting below the melting point (nonmelting surfaces) have been recently observed to sustain a very large amount of overheating. We present a theory which identifies a maximum overheating temperature, and relates it to other thermodynamical properties of the surface, in particular to geometrical properties more readily accessible to experiment. These are the angle of partial wetting, and the nonmelting-induced faceting angle. We also present molecular dynamics simulations of a liquid droplet deposited on Al(111), showing lack of spreading and partial wetting in good agreement with the theory. PACS numbers: 68.10.Cr, 68.45.Gd, 61.50.Jr Typeset using REVTEX 1 For a long time crystal overheating above the bulk melting temperature Tm has been believed to be impossible, at least in the presence of a free clean surface. The standard argument [1,2] is that surface premelting will always take place and act as an ubiquitous seed for the liquid to grow. The well-known surface melting of Pb(110) [3,4] provided a first microscopic evidence of how liquid nucleation takes place on a solid below Tm. It was only a little later that simulations of Au(111) [5] and newer experiments on Pb(111) [6] and Al(111) [7] demonstrated microscopically that the opposite could also happen, namely that certain surfaces may exhibit nonmelting up to and in fact even above the melting point [5,8]. A solid bounded by such surfaces can therefore be overheated, although in a metastable state, above Tm. Métois et al. have first shown that small Pb particles with strictly (111) facets are easily overheated by a few degrees above Tm [9]. Even more strikingly, Herman et al. found that a flat nonmelting Pb surface can be overheated by as much as 120 K above Tm [10]. This implies that the free energy of a crystal surface can have a local minimum for zero liquid thickness. As in other nucleation problems one should thus expect the metastable overheated state to survive up to some instability temperature Ti > Tm, where the barrier finally disappears (fig. 1, inset). At present, however, there is no further available understanding of this phenomenon. In particular, there are no means to calculate Ti and possibly connect it with other quantities which are more readily measurable in a surface experiment. At a more microscopic level, it is very desirable to understand the different behavior of a nonmelting and of a melting surface, against nucleation of the liquid. In this Letter, we introduce a simple theory of surface nonmelting which predicts the existence of a Ti, and connects its value with apparently unrelated geometrical quantities. These are the partial wetting angle θm which a drop of melt will form with that crystal surface at T = Tm, and the faceting angle θc of a vicinal surface. The angle θm has also been rather commonly measured in the past, a few early examples being the (0001) face of Cd [11] and the (100) faces of several alkali halides [12]. The nonmelting-induced faceting [13,14] angle θc has been well characterized experimentally and theoretically for (111) vicinals of Au [13,15], Cu [16] and Pb [13,14,17,18]. The connection we find between θm, θc and 2 Ti offers new insight in nonmelting surfaces. At a microscopic level, we substantiate this connection with molecular dynamics (MD) simulations of Al(111), which demonstrate both the non-spreading of a liquid drop at Tm, and the overheating of the flat face. The predicted relationship between θm, θc and Ti is found to be in excellent agreement with the simulation results, as well as with experiments. (i) Theory: Consider a liquid film of thickness l, sandwiched between semiinfinite solid and vapor, and let l grow from zero (no liquid) to a finite value. The change in free energy per unit area takes the standard form [4] ∆F (l) = ρLl(1− T/Tm) + ∆γ(l) (1) where ρ is the liquid density, L the latent heat of melting, and ∆γ(l) the difference between the overall free energy of the two interacting solid-liquid (SL) and liquid-vapor (LV) interfaces separated by a distance l, and the free energy of the solid-vapor (SV) interface. By definition, ∆γ(0) = 0. Assuming short-range forces only, this term can phenomenologically be written as ∆γ(l) = ∆γ∞[1 − exp(−l/ξ)] where ∆γ∞ ≡ γSL + γLV − γSV is the net free energy change upon conversion of the SV interface in two non-interacting SL and LV interfaces, and ξ is a correlation length in the liquid. For a melting surface ∆γ∞ < 0, and, for Tw < T < Tm, ∆F will have a minimum at l0(T ) = ξ ln [Tm|∆γ∞|/(Tm − T )Lρξ] which is the mean-field thickness of the melted film [4]. The wetting temperature defined by l0(Tw) = 0 is Tw = Tm (1− |∆γ∞|/Lρξ). For a nonmelting surface, ∆γ∞ > 0, and we move over to T > Tm. Here, ∆F (l) will instead have a local minimum at l = 0, the absolute minimum for l → ∞, and a maximum at a critical thickness