In this Letter we report Ising model simulations of the growth of allo
ys which predict quite different behavior near and far from equilibriu
m. Our simulations reproduce the phenomenon which has been termed ''so
lute trapping,'' where concentrations of solute, which are far in exce
ss of the equilibrium concentrations, are observed in the crystal afte
r rapid crystallization. This phenomenon plays an important role in ma
ny processes which involve first order phase changes which take place
under conditions far from equilibrium. The underlying physical basis f
or it has not been understood, but these Monte Carlo simulations provi
de a powerful means for investigating it.