A multi-string Frenkel-Kontorova (MSFK) model for a a/2[111] screw dislocation in body-centered cubic iron was formulated, and the occurrence of degenerate and non-degenerate dislocation core structures was investigated as functions 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, it was shown that it was the form of the function which determined how the atomic strings interact with each other as a function of their relative one-dimensional displacement in the [111] direction that determined whether a degenerate or a non-degenerate screw dislocation core configuration had the lower energy. This was shown by constructing a one-dimensional inter-string interaction law, and by solving the MSFK equations, it was 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 body-centered cubic transition metals. Finally, the relationship 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 was analysed.

Ab initio Multi-String Frenkel-Kontorova Model for a b = a/2[111] Screw Dislocation in BCC Iron. M.R.Gilbert, S.L.Dudarev: Philosophical Magazine, 2010, 90[7-8], 1035-61