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We present a Monte Carlo method for evaluating the difference between the free energies of two crystal structures. The method uses a biased sampling of atomic displacements to favor configurations of one structure that can be replaced by corresponding configurations of the other through a Monte Carlo switch of the lattice. The configurations of both structures can be sampled in a single process, and the difference between their free energies evaluated from their measured probabilities. The method is applied to the free energies of the fcc and hcp phases of hard spheres.
Bruce et al. (Mon,) studied this question.