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      An iterative scheme for the generalized Peierls-Nabarro model based on the inverse Hilbert transform

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          Abstract

          A new semi-analytical iterative scheme is proposed in this work for solving the generalized Peierls-Nabarro model. The numerical method developed here exploits certain basic properties of the Hilbert transform to achieve the desired reduction of the non-local and non-linear equations characterizing the generalized Peierls-Nabarro model to a local fixed point iteration scheme. The method is validated with simple examples involving the 1D Peierls-Nabarro model corresponding to a sinusoidal stacking fault energy, and with calculations of the core structure of both edge and screw dislocations on the close-packed \(\{111\}\) planes in Aluminium. An approximate technique to incorporate external stresses within the framework of the proposed iterative scheme is also discussed with applications to the equilibration of a dislocation dipole. Finally, the advantages, limitations and avenues for future extension of the proposed method are discussed.

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          Most cited references 22

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          The size of a dislocation

           R. Peierls (1940)
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            Dislocations in a simple cubic lattice

             F Nabarro (1947)
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              Intrinsic stacking faults in body-centred cubic crystals

               V Vitek (1968)
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                Author and article information

                Journal
                02 July 2019
                Article
                1907.01165

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                physics.comp-ph cond-mat.mtrl-sci

                Condensed matter, Mathematical & Computational physics

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