A topologically correct method of dislocations construction for atomistic modeling

Abstract We discuss the deep topological reasons why dislocation quadrupoles should be used for the construction of dislocations containing edge components. We demonstrate that contrary to all other currently used methods, this approach exactly preserves the topology of the order parameter field (atomic displacements in a crystal with defects relative to a defect-free crystal) of a dislocation-free crystal with periodic boundary conditions even for small simulation volumes and, thus, restores the verity of the material frame indifference principle, broken in other techniques. Using dislocation quadrupoles for edge and mixed dislocations, we have developed a careful procedure for relaxation of atomic positions around a dislocation core which enables one to achieve arbitrary low dislocation densities characteristic for real crystals. As a demonstration of the method capabilities, we have constructed a simulation volume with as low dislocation density as 1.5 · 10 14 m - 2 , which is realistic in deformed crystals, and one can easily lower this value as desired. All details of dislocation construction process are explicitly specified, making it very easy to reproduce our results. FCC Al crystal is used as a test case.