Free energy dissolution nucleus

Pit formation. If we consider a dissolution nucleus at a screw dislocation intersecting the surface which consists of a cylindrical hole of radius r, one atom layer deep (a), then the free energy of formation of this nucleus will be composed of a volume energy, surface energy, and elastic strain energy term, respectively, as follows ... 

It would therefore be expected that for nuclei with a radius smaller than the critical nucleus size, the Gibbs free energy can be minimized by dissolution, while at sizes larger than the aitical nucleus the Gibbs free energy can... 

In this relationship, the excess free energy for the formation of clusters AG first increases then decreases with the radius of the particles, r. The critical radius, r, is associated with a maximum excess free energy, AG. Accordingly, there exists a critical number of atoms, , in cluster A at the radius of r. When r < r, the system can lower its free energy by dissolution of clusters. Thus, these clusters are not thermodynamically stable and dissolve quickly, whereas some new clusters form due to spontaneous collisions. These unstable particles (A < A ) are known as clusters or embryos, and their numbers follow the Boltzmann distribution and decrease exponentially with increases of AG as described in Equation 10.4. When the radius of a cluster is larger than the critical value (r> r ), it becomes stable and is referred to as a nucleus. Thus, the expressions of critical radius r and maximum excess free energy AG can be obtained mathematically when dAG,/dr is equal to zero [22, 23, 28] ... 

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