  We carry out molecular dynamics (MD) and Monte Carlo (MC) simulations to
characterize nucleation in liquid clusters of 600 Lennard-Jones particles over
a broad range of temperatures. We use the formalism of mean first-passage times
to determine the rate and find that Classical Nucleation Theory (CNT) predicts
the rate quite well, even when employing simple modelling of crystallite shape,
chemical potential, surface tension and particle attachment rate, down to the
temperature where the droplet loses metastability and crystallization proceeds
through growth-limited nucleation in an unequilibrated liquid. Below this
crossover temperature, the nucleation rate is still predicted when MC
simulations are used to directly calculate quantities required by CNT.
Discrepancy in critical embryo sizes obtained from MD and MC arises when
twinned structures with five-fold symmetry provide a competing free energy
pathway out of the critical region. We find that crystallization begins with
hcp-fcc stacked precritical nuclei and differentiation to various end
structures occurs when these embryos become critical. We confirm that using the
largest embryo in the system as a reaction coordinate is useful in determining
the onset of growth-limited nucleation and show that it gives the same free
energy barriers as the full cluster size distribution once the proper reference
state is identified. We find that the bulk melting temperature controls the
rate, even though the solid-liquid coexistence temperature for the droplet is
significantly lower. The value of surface tension that renders close agreement
between CNT and direct rate determination is significantly lower than what is
expected for the bulk system.
