Rev.Adv.Mater.Sci. (RAMS)
No 2, Vol. 51, 2017, pages 130-148

ELASTIC MODELS OF DEFECTS IN 3D AND 2D CRYSTALS

A.L. Kolesnikova, M.Yu. Gutkin and A.E. Romanov

Abstract

We present the elastic models of defects in crystals exploring the framework of continuum mechanics of solids. The key feature of the defects attributed to zero-, one-, two- or three-dimensional ones is the dimension of the region of their eigenstrains. It is shown how from the elastic fields of defects of a lower dimension to build, by integration, the elastic fields of defects of a higher dimension. On the base of the elastic fields of infinitesimal dislocation loops, the fields of the circular dilatation line, the circular dilatation disk, and the cylindrical and hemispherical inclusions are derived in a step-by-step manner. In the final part of the paper, the elastic fields of defects in 2D crystals are considered.

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