Kinetics of phase transformation in complex systems

Kinetics of phase transformation in complex systems, in which more than one subprocess with different nucleation and growth rates are involved, is studied. Based on probability theory, exact solutions for one-dimensional model systems are obtained. Corresponding derivations for two- and three-dimensional systems can be discussed. Analytical treatments are compared with Monte Carlo simulations using model systems of vast size. Strong nonlinear character is observed for the one-dimensional system, whereas linear superposition presents a rather good approach for two- and three-dimensional systems. This linear approximation provides a practical method particularly for theoretical modeling of crystal growth with different reactants or different products, and with tendencies of preferential nucleation or preferential growth.