  The free energies of the FCC, BCC, HCP and Simple Cubic phases for hard
spheres are calculated as a function of density using the Fundamental Measure
Theory models of Rosenfeld et al (PRE 55, 4245 (1997)), Tarazona (PRL 84, 694
(2001)) and Roth et al (J. Phys.: Cond. Matt. 14, 12063 (2002)) in the Gaussian
approximation. For the FCC phase, the present work confirms the vanishing of
the Lindemann parameter (i.e. vanishing of the width of the Gaussians) near
close packing for all three models and the results for the HCP phase are nearly
identical. For the BCC phase and for packing fractions above $\eta \sim 0.56$,
all three theories show multiple solid structures differing in the widths of
the Gaussians. In all three cases, one of these structures shows the expected
vanishing of the Lindemann parameter at close packing, but this physical
structure is only thermodynamically favored over the unphysical structures in
the Tarazona theory and even then, some unphysical behavior persists at lower
densities. The simple cubic phase is stabilized in the model of Rosenfeld et
al. for a range of densities and in the Tarazona model only very near
close-packing.
