  We present results for the kinetics of phase separation in solid binary
mixtures ($A_1+A_2$) from Monte Carlo simulations of the Ising model in two
dimensions. The simulation results are understood via appropriate application
of the finite-size scaling theory. At moderately high temperatures, for
symmetric $(50:50)$ compositions of $A_1$ and $A_2$ particles the average size
of the domains exhibit power-law growth with the exponent having the
Lifshitz-Slyozov value of 1/3 from very early time. However, our analysis shows
that for low enough temperatures, the growth exponent at early time is smaller
than the Lifshitz-Slyozov value. For composition dependence, we find that at
moderate temperature, even for extreme off-critical composition, curvature
dependent correction to the growth law is weak which is counterintuitive in
this case that gives rise to droplet morphology. This is however consistent
with the recent understanding on curvature dependence of surface tension.
Results from rather general studies on the finite-size effects with the
variations of temperature and composition have also been presented.
