Asymptotic Thickness of an Island

The an e 9o is found from the condition of mechanical equilibrium for three phases in the triple junction point. In our case, 

In the symmetrical case, the total thickness of the island becomes 

Note that a frozen-in concentration profile in the new phase is linear in the direction perpendicular to the initial a P contact 

in our model, the asymptotic thickness of the phase layer is determined by the characteristic size I, which, in turn, presents a combination of kinetic parameters D and k. It is highly essential to analyze the behavior of this combination when the homogeneity region of the phase tends to zero. The interdiffusion coefficient at IPB may acquire different forms, but it is always proportional to the second-order derivative 9 g/9, which tends to infinity with Ac tending to zero [28]. The reaction constant k is also proportional to the same second-order derivative. 

Within the model we have assumed that the boundary curvature can be neglected. To check this assumption, let us analyze the ratio of the following fluxes jcurv (caused by the curvature gradient) and jchem (caused by the concentration gradient) in a quasi-stationary approximation. In the general case, we have cD 9 (a Sip) cD ao, dp 

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