Non-singular descriptions of dislocation cores: a hybrid ab initio continuum approach

Abstract

The core structure of straight and curved dislocations is studied by developing a hybrid approach that links the parametric dislocation dynamics method with ab initio calculations. The approach is an extension of the Peierls–Nabarro (PN) model, with the following features: (1) all three components of the displacement vector for atoms within the dislocation core are included; (2) the entire generalized stacking fault energy surface (GSFS) obtained from ab initio calculations is utilized; and (3) the method is generalized to treat curved dislocations. We combine the parametric dislocation dynamics (DD) approach for the interaction and motion of dislocations with ab initio calculations of lattice restoring forces. These forces, which are extracted from the GSFS (γ-surface), are calculated from both first-principles density functional theory (DFT) and the embedded-atom method (EAM). Dislocation core structures in aluminium and silver are determined. For straight dislocations, the results from the model are shown to be in excellent agreement with experiments for both Al and Ag. In contrast to undissociated dislocation loops in Al, it is found that the core width and the separations between partials in Ag vary along the angular direction measured with respect to the Burgers vector. It is also shown that the core-cutoff radius, which is usually employed in DD calculations to avoid singularities, must be adjusted as a function of loop size to account for the correct dislocation core energy.

Acknowledgements

The work conducted at UCLA was supported by the National Science Foundation through grant DMR-0113555 and by the Air Force Office of Scientific Research (AFOSR) grant number F49620-03-1-0031. NG and NK wish to acknowledge the support from NSF-NIRT Award Number: 0506841. GL and NK acknowledge the support from the US Army grant W911NF-04-1-0058. GL also acknowledges the support from the Department of Energy grant DE-FC02-06ER25791 and from the ACS Petroleum Research Funds PRF43993-AC10.