  We present a phase field theory for binary crystal nucleation. In the
one-component limit, quantitative agreement is achieved with computer
simulations (Lennard-Jones system) and experiments (ice-water system) using
model parameters evaluated from the free energy and thickness of the interface.
The critical undercoolings predicted for Cu-Ni alloys accord with the
measurements, and indicate homogeneous nucleation. The Kolmogorov exponents
deduced for dendritic solidification and for "soft-impingement" of particles
via diffusion fields are consistent with experiment.
