Ab initio multi-string Frenkel–Kontorova model for a b = a/2[111] screw dislocation in bcc iron

Abstract

We formulate a multi-string Frenkel–Kontorova (MSFK) model for a a/2[111] screw dislocation in bcc iron, and investigate the occurrence of degenerate and non-degenerate dislocation core structures as functionals of the law of interaction between the [111] strings of atoms forming the crystal. By comparing the effective inter-string interaction laws derived from ab initio density functional calculations and from semi-empirical interatomic potentials for α-iron, we show that it is the form of the function determining how the atomic strings interact with each other as a function of their relative one-dimensional displacement in the [111] direction that determines whether a degenerate or a non-degenerate screw dislocation core configuration has lower energy. We show that by constructing a one-dimensional inter-string interaction law, and by solving the MSFK equations, it is possible to easily predict the nature of the screw dislocation core, hence providing a simple yet effective check to aid the development of short-range semi-empirical interatomic potentials for bcc transition metals. Finally, we analyse the relation between the inter-string interaction law, and the shape and the height of the Peierls energy barriers separating the adjacent equilibrium configurations for a migrating screw dislocation.

Keywords:

• computer simulation
• dislocation theory
• core structure
• bcc iron
• Frenkel–Kontorova

Acknowledgements

We gratefully acknowledge stimulating and helpful discussions with V.V. Bulatov, W. Cai, P.M. Derlet, P.B. Hirsch, J. Marian, D. Nguyen-Manh, S.G. Roberts, D.G. Pettifor, and F. Willaime. This work was supported by the UK Engineering and Physical Sciences Research Council and by EURATOM through the EFDA Fusion Materials Modelling Programme. The views and opinions expressed herein do not necessarily reflect those of the European Commission.