Layering effect

The surface premelting of solids is explained in terms of a repulsive and attractive interactions between the solid-liquid and the liquid-vapor interfaces. Ercolessi et al. [31] showed how a crucial part of this interaction originates from the layering effects near the liquid metal surface. The layering effect [32,98,99] is density oscillations which are observable at the liquid surface of metals and semiconductors (See Fig. ). The layering effect was first noted in molecular dynamics simulations [33], and recently have been observed experimentally for Hg [34].

Figure: Density profile of the liquid surface of aluminum exhibits pronounced oscillations at the liquid-vapor interface. Figure from ref. [32].

The layering effect in metals is very similar to a layering of a fluid near a wall. It is presumed that the liquid-vapor interface acts as a sort of a rigid wall for the liquid metal. Different models has been proposed to explain the layering effect in metals, for instance, Rice et al. [35] claimed that the density oscillations are due to the coupling between the electronic and ionic profiles. The electron density profile decays very abruptly and generates an effective wall potential against which the ions need to rearrange themselves to reduce the energy cost and lay orderly.

The oscillation is characterized by a typical liquid periodicity, $2\pi/Q_0$, where $Q_0$ is the absolute value of the wave vector, at which the liquid radial distribution function has its maximum. Besides that periodicity, $2\pi/Q_0$, there is another one, a second oscillation at the solid-liquid interface. This is due to the crystal planes which induce density fluctuation in the liquid layer. The periodicity of this oscillation is given by the distance between the crystal planes, $a$, which in turn depends on the orientation $\{hkp\}$ of the planes of the underlying crystal.

These two distinct layering oscillations - one with the periodicity $2\pi/Q_0$ (tied to the liquid - vapor interface) and another with the periodicity of the interlayer spacing $a$ (tied to the solid - liquid interface) overlap and interfere inside the liquid film, provided that the separation between the solid-liquid and the liquid-vapor interfaces is small. The kind of interference depends strongly on the orientation of the underlying crystal. For the close packed face, for example (111) face of fcc crystals, the periodicities are match, e.g. $2\pi/Q_0=a$, and one have constructive interference (See Fig. ).

Figure: Comparison between the density profiles of the (111) and (110) surfaces of a Lennard-Jones crystal and gold obtained by MD simulations, from ref. [32].

The interference induces oscillation of the free energy, and the deepest minimum of the free energy of the close packed face is at zero thickness of the quasiliquid film as it is shown in Figure .

Figure: Variation of the surface free energies as a function of the interface separation $l$. Upper panel: the close packed (111) face of a fcc crystal, constructive interference. Lower panel: the least packed (011) face of a fcc crystal, deconstructive interference, from ref. [32].

The interfaces strongly attract each other and this attraction leads to the absence of surface premelting. In the opposite case, when $2\pi/Q_0 \ne a$ the interference is destructive, and therefore there is a repulsion between the interfaces and surface premelting is observed.