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

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 alpha-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.