Discommensuration nucleation and growth by climb

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Abstract
A simple model for the solution of irreducibly two-dimensional problems in thin adlayers is constructed by a Peierls-type extension of the Frank–van der Merwe model. The energy of a discommensuration of finite length having either both ends within (a dislocation dipole) or one end within and one end on the periphery of a misfitting, nearly commensurate monolayer is derived. The energy is found to separate into the self-energy of the two dislocations (or of the one dislocation plus that of the ending of the discommensuration on the periphery), the energy of the connecting discommensuration, and a very small energy of interaction between the dislocations. The latter decreases exponentially with increasing dislocation separation. Both the nucleation energy and length are found to be smaller for a discommensuration on the periphery than for one within the adlayer. The nucleation lengths are found to be of the order of one lattice spacing at a misfit somewhat larger than the critical misfit for zero discommensuration energy. The nucleation energy is one to four times the surface migration energy. This would favor nucleation and growth of discommensurations in a monatomic epilayer by climb, starting from the periphery. The dislocations constitute the nuclei for the formation of threading dislocations in a layer-by-layer growth mode.