Analytical methods for the calculation of the elastic interaction of point defects with dislocation loops in hexagonal crystals

The Green’s function method for hexagonal crystals within the Lifshitz–Rosenzweig (1947) and Kröner (1953) approaches has been used to obtain analytical expressions for the energy of elastic interaction of radiation-induced point defects with dislocation loops of three types: the basal edge dislocation loop (cloop), the basal shear dislocation loop, and the edge $a$-loop (bedding plane $\{11\bar20\}$, Burgers vector $\mathbf{b}^{\mathbf{D}}$ = 1/3$\langle$1120$\rangle$). In the case of the basal edge dislocation loop, a similar expression has been obtained independently by solving the equilibrium equations using the Elliott method. A numerical comparison of the derived expressions for zirconium has demonstrated a complete identity of the results obtained within the approaches considered in this study.