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

TL;DR

This paper develops and analyzes hierarchical models of crystal defect aggregation, identifying symmetries and scaling laws, and compares them with classical coarsening theories, supported by simulations.

Contribution

It introduces new hierarchical defect aggregation models with symmetry analysis and scaling solutions, extending classical coarsening theories.

Findings

Models exhibit specific symmetry properties.

Scaling solutions match experimental observations.

Simulations support theoretical predictions.

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.