Polymorphic Mode with Shape Optimization

If the system has the kinetic opportunity of shape optimization, the resulting nucleation barrier decreases, as expected. In the case of full optimization, the surface AG (u, Cx) does not reveal a minimum. After passing the saddle point, it is always favorable to increase the volume by transversal growth, but keeping limited the longitudinal size along the direction of the gradient. A critical diffusion zone width, close to the experimental value, is obtained at a = 4 x 10 J/atom. This result implies that, for this parameter a and the diffusion zone width K = 3.5 nm. 

Full shape adaptation may be limited by kinetics and geometry of the process. The most probable is the case when the shape optimization is restricted to the following the linear size of the supercritical nucleus must not be less than the size of a single unit cell (0.7 nm). In this case, the critical width of the diffusion zone which is close to the experimental result is obtained at a = 1.5 x 10 J/atom. When the diflFusion zone is 3 nm wide, the barrier amounts to lOOke T (nucleation is prohibited), and at 4 nm to 30k T (nucleation is possible). 

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Figure 5.7 Polymorphic mode with shape optimization at a = 4 x 10 J/atom ...

Therefore, the transversal mode with shape optimization gives us the same qualitative results as the polymorphic mode ... 

The polymorphic mode of nucleation is characterized by the conservation of the concentration profile, which is a reasonable assumption if the system has no time to redistribute atoms inside and outside the nucleus in the process of lattice transformation. For the polymorphic mode, we also consider the two cases discussed earlier (i) without shape optimization (rp = 1) and (ii) with shape optimization. 

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