  We reconsider the applicability of classical nucleation theory (CNT) to the
calculation of the free energy of solid cluster formation in a liquid and its
use to the evaluation of interface free energies from nucleation barriers.
Using two different freezing transitions (hard spheres and NaCl) as test cases,
we first observe that the interface-free-energy estimates based on CNT are
generally in error. As successive refinements of nucleation-barrier theory, we
consider corrections due to a non-sharp solid-liquid interface and to a
non-spherical cluster shape. Extensive calculations for the Ising model show
that corrections due to a non-sharp and thermally fluctuating interface account
for the barrier shape with excellent accuracy. The experimental solid
nucleation rates that are measured in colloids are better accounted for by
these non-CNT terms, whose effect appears to be crucial in the interpretation
of data and in the extraction of the interface tension from them.
