A phase diagram of a Lennard-Jones solid at kT/epsilon greater-than-or
-equal-to 0.8 is constructed by our recent perturbation theory. It sho
ws the stability of the face-centered-cubic phase except within a smal
l pressure and temperature domain, where the hexagonal-close packed ph
ase may occur. The theory predicts anharmonic contributions to the Hel
mholtz free energy (important to the crystal stability) in good agreem
ent with Monte Carlo data.