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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
GD,
with the form: exp(-GD/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 (-GD(T) / kT) exp(-ΔG*(T) / kT)
where A is a constant.
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