  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 the 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 the 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. The kinetics of this process is shown to be governed
by the same characteristic parameter, as for a single particle, and
qualitatively differs from the Cahn-model one. In particular, the 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. This peculiarity 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.
