EQUILIBRIUM POSITION OF MISFIT DISLOCATIONS AT PLANAR INTERFACES

The equilibrium position of misfit dislocations at interfaces is analysed within linear elasticity theory. Calculations are performed for an isolated dislocation as well as for an infinite array of dislocations in an infinite bicrystal. Analytic expressions are obtained for the image forces on the dislocation array due to the elasticity discontinuity. The position of the dislocations is determined by the balance between image forces and coherency forces on the dislocations. An equilibrium position is obtained in crystal I with smaller shear modulus G1. The equilibrium stand-off distance is proportional to the inverse of the lattice misfit and increases with the ratio of the shear moduli, G2/G1, and of the Poisson's ratios, nu2/nu1, respectively. The calculated stand-off distance of misfit dislocations in Nb adjacent to a Nb-Al2O3 interface is smaller by a factor of 2 than the experimentally observed distance. This discrepancy can be explained qualitatively by the higher core energy of a dislocation in the vicinity to the elastically rigid Al2O3 compared to the core energy of a dislocation in bulk Nb.