Monte Carlo simulation of hard-sphere fluid and solid in a confined geometry

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Abstract
We study the structure of hard-sphere solids and fluids in a spherical cavity with Monte Carlo simulation for samples with up to 1024 particles. We found that at high densities for a fixed number of particles the density of the solid near the wall oscillates as the density is changed, as a consequence of the commensuration of the cavity radius with the hard-sphere spacing. As the size of the system is increased, the region in density over which this oscillation occurs is decreased; the amplitude of variation remains strong. We also computed the structure factor averaged over particles at different distances from the center. Even though the density exhibits a peak at the boundary, this local structure factor is much smaller at the boundary, indicating a decrease of crystalline order at the interface because of the presence of the wall. Our results suggests that it is melting and not nucleation that starts at the walls. Density-functional-type methods, which assume this local structure factor to be small, may still be useful to study melting in confined geometries.