Kinetics of the surface-nucleated transformation of spherical particles and new model for grain-boundary nucleated transformations

Abstract

Equations for the transformed volume fraction of a spherical particle with nucleation on its surface, both nonisothermal and isothermal, are derived in the framework of Kolmogorov method adapted for this problem. Characteristic parameters governing the transformation kinetics are determined; the latter is studied with particular emphasis on the Avrami exponent temporal behavior. It is shown that the surface-nucleated transformation qualitatively differs from the bulk-nucleated one at large values of the characteristic parameters due to the one-dimensional radial growth of a new phase occurring after the complete transformation of the surface itself at the early stage of the process. This effect also manifests itself in the considered ensemble of size-distributed particles and in grain-boundary nucleated transformations. The logarithmic normal distribution inherent for the particles obtained by grinding is employed for numerical calculations and shown to stretch temporally the volume-fraction and Avrami-exponent dependences for the ensemble of identical particles. A new model for grain-boundary nucleated transformations alternative to the Cahn model of random planes is offered; it is based on the ensemble of size-distributed spherical particles with the possibility for a growing nucleus to cross grain boundaries. Transformation kinetics in the present model qualitatively differs from that of the Cahn model. In particular, the double-logarithmic volume-fraction plot at large values of the governing parameter ends by a characteristic bend observed on experimental curves for the crystallization of bulk metallic glasses. Originating from the closed geometry of grain boundaries and the one-dimensional radial growth of a new phase, this bend together with the form of the plot as a whole directly indicates to the grain (polycluster) structure of metallic glasses and nucleation at intercluster boundaries.