Kinetics of nucleation and halt-in-growth processes in a thin layer

The methods of determining the kinetic exponents in the equation, dX/dV_ex = (1 - X)^2-y, used for nucleation and halt-in-growth processes where X is the transformed fraction, V_ex the KJMA extended volume fraction which is related to time t, and γ is the overlap factor which accounts for the overlap between a crystallite and a phantom crystallite, are presented. The applications of the Kolmogorov-Johnson-Mehl-Avrami plot (γ = 1) and the Austin-Rickett plot (γ = 0) to this process are inappropriate, because the overlap factor is 0 < γ < 1. The impingement exponent 2-γ and the time exponent are determined from the linear relation of ln{[(1 -X)^γ-1 - 1]/(1 - γ)} versus In t. From the value of γ, the crystal shape and growth dimension can be estimated by referring to the mathematical value of γ. The methods of evaluating the activation energy, Q, are presented using the Arrhenius relation. The value of Q is not directly related to the overlap factor γ; however, γ appears as a constant term in the expression for Q.