Kinetics and Microstructural Control

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.