Atomistic computation of the image force on a dislocation in a bicrystal I. Case of small difference between the elastic moduli of the two half-crystals

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Abstract
The image force on a dislocation near an interface separating two half-crystals of different elastic moduli is investigated by computer simulation. The 〈001〉 screw dislocation and the (100) interface between two bcc crystals have been chosen because the dislocation is undissociated and the anisotropic boundary conditions have an analytic form allowing accurate calculations. In the homogeneous medium, the dislocation core is found to be planar and to extend along a {110} dense plane but the core widths depend on the type of atomic potential utilized. To construct the bicrystal, the same potential is used in medium 2 as in medium 1, but multiplied by a factor α, equal to the desired ratio μ2/μ1 of shear moduli. The study is restricted here to values of α slightly larger than unity and sufficiently small for the lattice friction to remain everywhere larger than the image force. The dislocation is placed at distances x from the interface, ranging from 0 to 6a0, and for each stable position, the configuration and the total crystal strain energy E(x) are calculated; E(x) includes, in addition to the strain energy computed in the atomistic region, the elastic energy of the surrounding continuum. The computed energy curve E(x) differs notably from elasticity only in a region of few atomic distances from the interface. The image force on the dislocation, derived from the computed energies by finite differences, shows a broad peak in the interface region. The maximum is smaller than that derived in the same conditions from linear elastic energies. The peak shape is similar to that deduced from the Peierls-model-based calculation of Pacheco and Mura, but the atomistic simulation gives a lower peak with a larger extension and it is found that these two quantities are related to the core width of the dislocation.