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Homogeneous nucleation and growth in a simplest two-dimensional phase fieldmodel is numerically studied using the cell dynamics method. Whole process fromnucleation to growth is simulated and is shown to follow closely theKolmogorov-Johnson-Mehl-Avrami (KJMA) scenario of phase transformation.Specifically the time evolution of the volume fraction of new stable phase isfound to follow closely the KJMA formula. By fitting the KJMA formula directlyto the simulation data, not only the Avrami exponent but the magnitude ofnucleation rate and, in particular, of incubation time are quantitativelystudied. The modified Avrami plot is also used to verify the derived KJMAparameters. It is found that the Avrami exponent is close to the idealtheoretical value m=3. The temperature dependence of nucleation rate followsthe activation-type behavior expected from the classical nucleation theory. Onthe other hand, the temperature dependence of incubation time does not followthe exponential activation-type behavior. Rather the incubation time isinversely proportional to the temperature predicted from the theory ofShneidman and Weinberg [J. Non-Cryst. Solids {\bf 160}, 89 (1993)]. A need torestrict thermal noise in simulation to deduce correct Avrami exponent is alsodiscussed.

Direct numerical simulation of homogeneous nucleation and growth in a phase-field model using cell dynamics method