New kinetic Monte Carlo computer simulations of the liquid to crystal
transition which include structural relationships are presented. The s
tructure of the nucleating phase is incorporated on an atomic scale in
the simulation of cluster dynamics. It is shown that the consideratio
n of these geometric factors requires extensions to the concepts of cr
iticality from that conventionally encountered in classical nucleation
theory with the use of the capillarity approximation. The implication
s of these findings on the analysis of homogeneous nucleation are disc
ussed.