The energy of a prismatic dislocation loop in an isotropic elastic cylinder was derived, resulting in semi-analytic expressions. Analytic expressions were obtained in two limits: when the radius of the dislocation loop approaches the cylinder radius and when the radius of the dislocation loop was much smaller than the cylinder radius. These expressions could be used to predict the critical condition for misfit dislocation formation in semiconducting nanowires.

Energy of a Prismatic Dislocation Loop in an Elastic Cylinder. W.Cai, C.R.Weinberger: Mathematics and Mechanics of Solids, 2009, 14[1-2], 192-206