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Based on classical nucleation theory, the nucleation rate R can be given by,
 [1723a]
= n*β  [1723b]
where,
N  The total number of nucleation sites per unit
volume,
n_{i}  The number of available atoms at
interface,
v  The jump frequency,
k  The Boltzmann constant,
p  The probability
that the atomic jump will be in the proper direction,
E_{a}  The activation energy for the atomic jump across the interface,
ΔG*  The Gibbs free energy at the critical radius,
n*  The average population of critical nuclei,
β  The diffusion of atoms to the cluster.
The average population of critical nuclei is given by,
 [1723c]
The diffusion of atoms to the cluster is given by,
 [1723d]
Equation 1723a indicates that the nucleation rate increases exponentially as the temperature is increased.
