Migration-Driven Hierarchical Crystal Defect Aggregation - Symmetry and Scaling Analysis

Abstract

Recently the hierarchical defect substructures were observed experimentally in several metals and alloys before and after fracture. The general models of crystal defect aggregation with appearance hierarchical defect substructures are proposed and considered in the wide range of scales. Their general group analysis is performed, and symmetries of the governing equations are identified. The models of defect aggregate growth are considered for several partial cases and compared with classical Lifshitz-Slyozov-Wagner theory of coarsening, Leyvraz-Redner scaling theory of aggregate growth, etc. The reduced equations of new models are generated and solved, and the general scaling solutions are given. The results obtained are illustrated by preliminary simulations.