  We describe a Monte Carlo scheme which, in a single simulation, yields a
measurement of the chemical potential of a crystalline solid. Within the
isobaric ensemble, this immediately provides an estimate of the system free
energy, with statistical uncertainties that are determined precisely and
transparently. An extension to multiple occupancy ("cluster") solids permits
the direct determination of the cluster chemical potential and hence the
equilibrium conditions. We apply the method to a model exhibiting cluster
crystalline phases, where we find evidence for an infinite cascade of critical
points terminating coexistence between crystals of differing site occupancies.
