  A free energy functional for a crystal that contains both the symmetry
conserved and symmetry broken parts of the direct pair correlation function has
been used to investigate the crystallization of fluids in three-dimensions. The
symmetry broken part of the direct pair correlation function has been
calculated using a series in ascending powers of the order parameters and which
contains three- and higher-bodies direct correlation functions of the isotropic
phase. It is shown that a very accurate description of freezing transitions for
a wide class of potentials is found by considering the first two terms of this
series. The results found for freezing parameters including structure of the
frozen phase for fluids interacting via the inverse power potential u(r) =
\epsilon (\sigma/r)^{n} for n ranging from 4 to \infty are in very good
agreement with simulation results. It is found that for n > 6.5 the fluid
freezes into a face centred cubic (fcc) structure while for n \leq 6 the body
centred cubic (bcc) structure is preferred. The fluid-bcc-fcc triple point is
found to be at 1/n = 0.158 which is in good agreement with simulation result.

Soft Condensed Matter