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July 5th, 2020 
A cylindrical pill-like cluster of radius r nucleates on a dislocation substrate. The freeenergy change per unit thickness is given by
? = ??
2?? + 2??? + ? ???(?)
(a) Sketch the plot of ? vs r. [note: as r = 0, ? = ]
(b)Find critical radius and critical Gibbs free energy of the nucleation.
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