  We analyse the finite-size corrections to the free energy of crystals with a
fixed center of mass. When we explicitly correct for the leading ($\ln N/N$)
corrections, the remaining free energy is found to depend linearly on 1/N.
Extrapolating to the thermodynamic limit ($N\to\infty$), we estimate the free
energy of a defect free crystal of particles interacting through an
$r^{-12}$-potential. We also estimate the free energy of perfect hard-sphere
crystal near coexistence: at $\rho \sigma^{3}$=1.0409, the excess free energy
of a defect-free hard-sphere crystal is $5.91889(4)kT$ per particle. This,
however, is not the free energy of an equilibrium hard-sphere crystal. The
presence of an finite concentration of vacancies results in a reduction of the
free energy that is some two orders of magnitude larger than the present error
estimate.
