
Transformation
Rate
· If there are
S nucleation sites per unit volume, the atomic concentration of critical nuclei,
X^{* }, is given by: X^{*} = (n^{*}/ S) = exp{ ΔG^{*}(T)/ kT}, where n^{*} is the number
of critical
nuclei per unit volume. · These nuclei must be stabilized by the addition of other atoms
( which causes the Gibbs function to decrease) through a diffusion
controlled
process. · The transport rate
for diffusion depends upon the activation
energy for bulk diffusion
G_{D},
with the form: exp(G_{D}/kT) · The formation rate of stable nuclei, (dN/dt), then depends
on both the concentration of critical nuclei and their stabilization rate:
(dN/dt
) = A exp (G_{D}(T) / kT) exp(ΔG^{*}(T) / kT) where A is a constant.


