Unlimited Nucleation

Suppose that Da, Di, and Dp are effective diffusion coefficients in phases a, I, and p. Let nuclei of phase 1 form a layer of thickness Axi = between a and p. Considering ACa, Aci, and Acp 1, the equation of flux balance at moving phase boundaries is 

As it follows from Equation 3.40, (dA%/dt) becomes positive, and growth of phase 1 is allowed at 

The suppression time ti of phase 1 growth from the nuclei is called the incubation time, if one neglects the time required for nuclei formation. 

---

So far, we use the model that assumes the fact that critical nuclei of aU phases, allowed by the phase diagram, appear at once (the unlimited nucleation model). It is known that the growth of a new phase from the nucleus is energetically favorable only in the case of nucleus size exceeding some critical value la, determined from the extremum condition of Gibbs thermodynamic potential. In a one-component substance, the extremum condition is expressed simply by the derivative of G with respect to the nucleus size being equal to zero ... 

---