Approximate Solution of the Peierls Equation for Screw Dislocations with Threefold Symmetry

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Abstract
Within the framework of the Peierls model an integral equation for the dislocation density distribution of 〈111〉 screw dislocations with threefold symmetry in b.c.c. crystals is derived. The dislocation core, described by a density of infinitesimal Burgers vectors, is extended along three {110} half‐planes intersecting at angles of 120° and acting as slip planes. The integral equation is approximately solved by an inversion procedure and by assuming appropriate functions with adjustable parameters representing the stresses along the slip planes. The results are in qualitative agreement with atomistic calculations reported in the literature. The total energy proves to be lower than in a planar Peierls model.

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