Anisotropy's impact on the deformation of an infinite bicrystal caused by an interfacial dislocation

The study of elastic deformations associated with interfacial dislocation networks plays a fundamental role in understanding the physical properties of crystalline materials. These networks, located at the interface between two crystals, significantly influence the mechanical, thermal and electrical behaviors of materials. Despite their importance, these phenomena have received relatively little attention in the scientific literature. This gap is largely explained by the difficulty of analyzing these complex systems under realistic experimental conditions, particularly using advanced techniques such as transmission electron microscopy (TEM) or high-resolution transmission electron microscopy (HRTEM), which take into account the anisotropy of materials. In this context, the present work focuses on the anisotropic elasticity specific to each crystal constituting a bicrystal. The main objective is to model and understand the elastic fields that emerge at the interface of an infinite bicrystal when a unidirectional network of mismatch dislocations is present. To do this, an analytical approach based on Fourier series was adopted. The coefficients of these series are calculated by numerical inversion of a system of twelve linear equations with twelve complex unknowns. The results obtained by this method are illustrated through specific applications. The Al/Al and Cu/Cu single crystals, as well as the Al/Cu bicrystal, serve as examples to demonstrate the effectiveness and relevance of the proposed approach.