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Surface melting can be regarded as a case
of wetting [27], namely a wetting of the solid by its own melt. As in the case of adsorption of
a gas onto a hard wall one may observe complete or incomplete wetting, depending on
whether the quasiliquid thickness diverges or remains finite as
. By
the same analogy, the case of nonwetting corresponds to an absence of surface
melting, e.g. the surface remains dry up to .
What makes the surface premelt or remain dry?
If a single crystal is cleaved along it plane, where are
the crystallographic indices, then the surface free energy per unit of area
is
defined as the work needed to create a unit area of dry
surface (the subscript 'sv' refers to the solidvapor interface). On the other hand,
the free energy of a surface that at is covered with a thick melt layer, is
given by
, where the indices 'sl' and 'sv' refer
to the solidliquid and liquidvapor interfaces, respectively (See Fig. ).
Figure:
The solidliquid and liquidvapor interfaces

Surface melting will only occur if there is a gain in the free energy, that is, if

(3.1) 
On the other hand, if
, then the surface will remain dry up to .
The sign and magnitude of
depend not only on the material, but also
on the surface orientation. In general the most open crystal faces, e.g. the (011) face for fcc crystals and
(111) for bcc crystals, are most likely to exhibit surface melting. For a system exhibiting complete
wetting there is a unique relation between the temperature and the equilibrium thickness of
the quasiliquid layer . The fact that there is a finite equilibrium thickness of the film
at a given temperature is a result of balance between two opposite thermodynamic forces.
On one hand, the quasiliquid becomes more liquidlike for increasing layer thickness, which results
in some gain in the free energy. This corresponds to an effective repulsive force between the solid
liquid and liquidvapor interface. The effective interaction energy between the interfaces at
either side of the quasiliquid layer is given by
,
where is the thickness of the film,
is a characteristic length scale over which the crystalline order decays [23,26]
as it is measured from the crystalquasiliquid interface, and is a positive constant which
is called the Hadamar constant. On the other hand there is the free energy cost associated with supercooling
of the quasiliquid layer. For a layer of thickness the energy cost per unit of area is ,
where is the latent heat of melting per unit volume. This yields an attractive force between
the two interfaces.
The total free energy of the surface covered with a melt layer of thickness is:

(3.2) 
The equilibrium thickness is the value of for which is minimal, i.e. . Let us define
define a crossover thickness as a thickness for which the longrange contribution to is equal
to the shortcontribution
. Consequently two different regime
are considered. The first regime is for
, where the system is governed by the shortrange exponentially
decaying interactions and the equilibrium thickness is given by:

(3.3) 
where the reduced temperature is given by . This kind of logarithmic divergence of
is characteristic for metals and semiconductors.
But for raregas crystals (or if is approached veryvery closely [23]) the longrange force
must eventually dominate the melting behavior in the second regime
. The shortranged force
will dampen out and one is left with van der Waals type dispersion forces. Thus minimizing with respect
to yields:

(3.4) 
Here it is implied that and the liquid is less dense than the solid. This power law
was tested in numerous experiments carried out with raregas crystals. The agreement between the theoretical
prediction and the experimental results is very good.
Next: Landau model of surface
Up: Surface melting
Previous: Preface
20030115