A theoretical model was proposed which described phason imperfections, in a quasi-periodic grain boundary in a polycrystalline solid, as dilatational flexes. Within the framework of this model, the elastic stress field of the quasi-periodic grain boundary was calculated as a stress field which was created by an ensemble of dilatational flexes (phason imperfections) that were located in the boundary. It was shown that there was a special elastic interaction between crystal lattice defects and quasi-periodic grain boundaries which comprised phason imperfections. The strengthening effect in plastically deformed polycrystalline solids was quantitatively described as being related to the above elastic interaction between lattice dislocations and quasi-periodic grain boundaries.

Special Interaction between Quasi-Periodic Grain Boundaries and Lattice Dislocations in Crystalline Solids. M.Y.Gutkin, I.A.Ovidko: European Physics Journal B, 1998, 1[4], 429-37