Dislocation Kink in a Crystal Model

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Abstract
A modified Frenkel—Kontorova dislocation model, with a piecewise linear substrate potential, is extended to two dimensions to describe the entire slip plane of the dislocation with one kink. Accurate solutions are found, with the aid of several analytic techniques and a digital computer, for the static configuration under applied stress. The kink Peierls stress σk P, the kink width w, and the kink energy F, are determined for a range of values of γ, the perfect crystal shear strength. σk P is found to be very sensitive to γ, and to have maxima of the order of 10−6 to 10−5, in units of the shear modulus. w and E are less sensitive to γ; w ranges from ∼4 to ∼30 lattice parameters, while E varies from several hundred to several thousand degrees Kelvin for typical crystal parameters.