Kinetics of solid-state transformation subjected to anisotropic effect: Model and application

In the present work, a growing particle subjected to anisotropic effect, if not influenced by other particles, is assumed to be an isotropically growing particle with constant volume. Accordingly, how to describe the anisotropic growth just becomes how to solve the blocking effect arising from the anisotropic growth. Following the statistical description of Johnson-Mehl-Avrami-Kolmogorov kinetics, the blocking effect was investigated further. Consequently, a series of analytical models for solid-state transformation, where a particle undergoes 1-scale blocking, k-scale blocking and infinite-scale blocking, were developed. On this basis, it was analytically proved for the first time that the classical phenomenological equation accounting for the anisotropic effect (f=1-[1+(ξ-1)^xe] ^-1/ξ-1) corresponds to an extreme case where a particle encounters infinite-scale blocking. From the model analysis, the anisotropic effect on the transformation depends on two factors: the non-blocking factor γ and the blocking scale k. From the model calculations, the Avrami exponent, subjected to the anisotropic effect, changes as a function of the transformed fraction, whereas the effective activation energy is not affected by the anisotropic effect. The present models were adopted to describe isothermal crystallization of amorphous Fe₃₃Zr₆₇ ribbons; good agreement with the published results was achieved.