Models of Etch-Pit Formation

From the geometrical arrangement of atoms around dislocations, it is Immediately obvious that screw dislocations should yield etch pits with slope, m, given by  

The change in the free energy, AG, for the nucleation of a diskshaped cavity of depth, h, and radius, r, at the site of a dislocation is given by  

The behavior of the free-energy curve is determined by taking the first two derivatives of A G, and equating them to zero. The first derivative, d AG ,/dr, gives a quadratic equation having two roots  

Thus for 1, there is an energy barrier for etch-pit nucleation at a dislocation site but the value of this barrier is less than that at the perfect surface. For = 1, there is a double root  

When 1, there is no real root, which means that there is no nucleation barrier for etch-pit formation. Thus, since increases with A/ (Eq. 78), there is a particular value of A above which dislocations open up spontaneously, Thecritical value of this A is obtained from Eq. 78for = 1, i.e., 

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