Peierls Stress Dependence on Dislocation Width

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Abstract
A numerical calculation of the Peierls stress and energy in the Frenkel—Kontorova dislocation model is reported. The calculated stresses are compared with the theoretical predictions of V. L. Indenbom that they decrease exponentially and I. M. Lifshitz that they decrease as the inverse fifth power with dislocation width. The results are in essential agreement with those of Indenbom. The Peierls stress and energy values obtained by Indenbom are, however, only about half those of the present calculation. This is, perhaps, due to the fact that Indenbom, like Peierls and Nabarro, uses a continuum approximation to determine the atom positions. The present method has particular advantages for calculating the small difference in energy between the unstable and stable dislocation configurations and for verifying that this difference is indeed the minimum barrier. When the elastic constants of polycrystalline copper are used, the present model predicts a Peierls stress to shear‐modulus ratio of 6×10−5, which is about an order of magnitude less than the value obtained by Seeger in his interpretation of the Bordoni experiment on copper.

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