Screw misfit dislocations perpendicular to one or two free surfaces

When a screw dislocation pierces one or two free surface(s), noticeable elastic relaxation takes place nearby these surfaces. To refine the theoretical interpretation of an electron microscopy image this relaxation should be included in a precise imaging model. In the present work, the relaxation field is evaluated for a periodic set of misfit screw dislocations normal to the free surface of a semi-infinite or plate-like heterogeneous bicrystal. The proposed approach uses an appropriate combination of known biperiodic elastic fields. For a homogeneous medium and when the period increases, the results around a misfit screw dislocation converge to those of Eshelby and Stroh (1951) who considered an isolated translation screw dislocation.