A cylindrical pill-like cluster of radius r nucleates on a dislocation that emerges from the substrate. The free-energy change per unit thickness is given by
∆G =πr^2∆G, + 2myr + A - B Inr, where A - B Inr represents the dislocation energy within the cluster. 0).
(a) Sketch ∆G vs r (note at r= 0, G
(b) Determine the value of r*.
(c) Show that when ∆G, B/ry >+, ∆G monotonically decreases with r,
but when ∆G, B/ay² < there is a turnaround in the curve. (The latter case corresponds to a metastable state and associated energy barrier.)