A generalized Peierls–Nabarro model for kinked dislocations

Abstract

We present a generalized Peierls-Nabarro model for curved dislocations incorporating directly the Peierls energies for both straight dislocations and dislocation kinks. In our model, the anisotropic elastic energy is calculated efficiently using the discrete Fourier transform on the discrete lattice sites of the slip plane, and the discreteness in both the elastic energy and the misfit energy is included. We have used our model to calculate the kink migration and nucleation energies of the 30 dislocations in silicon. The results agree well with those obtained using atomistic potentials and first principles calculations, and the experimental results.

Atomistic-to-continuum description of edge dislocation core: Unification of the Peierls-Nabarro model with linear elasticity

“…We considered the continuum displacement fields as identical for every atomic layer in the (121) direction, effectively neglecting core interactions between atomic layers. More sophisticated models based on Peierls-Nabarro can attain migration barriers quantitatively comparable to those found in atomistic simulations [15][16][17].…”

“…where the MSFK definition of Poisson's ratio (15) was used. This leads to the elastostatic equations:…”

Continuum approximation of the Peach–Koehler force on dislocations in a slip plane

“…We will employ the disregistry across the slip plane to represent the continuous distribution of dislocations, following the Peierls-Nabarro models (Peierls, 1940;Nabarro, 1947;Eshelby, 1949;Vitek, 1968;Xu and Argon, 2000;Koslowski et al, 2002;Movchan et al, 2003;Xiang et al, 2008;Wei et al, 2008).…”

“…(6) and (7) in Section 3. For distribution of dislocations in a single slip plane with all the possible Burgers vectors, a pair of disregistry functions will be enough, as in the Peierls-Nabarro models (Xu and Argon, 2000;Koslowski et al, 2002;Movchan et al, 2003;Xiang et al, 2008;Wei et al, 2008), which is being considered and the results will be presented elsewhere.…”

Derivation of Orowan's Law from the Peierls–Nabarro Model

“…In other words equation (1.1) simply describes the motion of dislocations by relaxation of the total energy (elastic + misfit). For a physical introduction to the Peierls-Nabarro model, see for instance [9], [14]; we also refer the reader to the paper of Nabarro [13] which presents an historical tour on the Peierls-Nabarro model. The Peierls-Nabarro model has been originally introduced as a variational (stationary) model (see [13]).…”