On the meaning of the impingement parameter in kinetic equations for nucleation and growth reactions

If certain preconditions are met, the Johnson-Mehl-Avrami-Kolmogorov (JMAK) kinetic equation is exactly accurate for nucleation and growth reactions with linear growth and is, at least, a good approximation for nucleation and growth reactions with parabolic growth. These preconditions include randomly distributed product phases, isotropic growth and constant equilibrium state. Mechanisms causing deviations from these preconditions include: capillarity effect, vacancy annihilation, blocking due to anisotropic growth. It is shown that deviations lead to a modification of the overall transformation, which can be approximated well by a single equation: $$\alpha = 1 - \left[ {\frac{{\left\langle {k\left\langle T \right\rangle t} \right\rangle ^n_s }}{{\eta _i }} + 1} \right] ^{- \eta _i} $$ where α is the fraction transformed, η i is the impingement parameter, n s and k(T) are parameters that depend on growth geometry and growth rate. The factors which influence the impingement parameter are discussed.