  The application of the Young-Laplace equation to a solid-liquid interface is
considered. Computer simulations show that the pressure inside a solid cluster
of hard spheres is smaller than the external pressure of the liquid (both for
small and large clusters). That would suggest a negative value for the
interfacial free energy. We show that in a Gibbsian description of the
thermodynamics of a curved solid-liquid interface in equilibrium, the choice of
the thermodynamic (rather than mechanical) pressure is required, as suggested
by Tolman for the liquid-gas scenario. With this definition, the interfacial
free energy is positive, and the values obtained are in excellent agreement
with previous results from nucleation studies. Although for a curved
fluid-fluid interface there is no distinction between mechanical and thermal
pressures (for a sufficiently large inner phase), in the solid-liquid they do
not coincide, as hypothesized by Gibbs.
