A Lie-algebra-based description of disclination densities and the quantification of partial disclinations in deformed polycrystalline metals

Crystalline defects (e.g., dislocations, disclinations and grain boundaries) play a critical role in determining the mechanical and functional properties of metallic materials. From a physical point of view, dislocations and disclinations are the two fundamental types of topological defects in crystals, which originate from the breaking of translational symmetry and rotational symmetry, respectively. In spite of extensive studies on dislocations in the literature, the effects of disclinations on mechanical properties of metals have not been well recognized, partially due to the lack of an appropriate description for the rotational nature of disclinations. Here we suggest a Lie-algebra-based method to quantify the rotational properties of disclinations, which leads to a convenient way to determine disclination density distribution directly from Electron Backscatter Diffraction data. Through quasi-in-situ Electron Backscatter Diffraction characterizations, three major formation mechanisms of disclinations have been identified in deformed polycrystalline Mg alloys, i.e., dislocation-grain boundary interaction, dislocation redistribution and twin-twin reaction, all of which can be treated as topological reactions among various types of defects under a general framework. Our work not only suggests a new mathematical tool to investigate the interactions and reactions among multiple types of crystalline defects, but also provides a new insight to understand the deformation behaviors of metals and alloys based on dislocation/disclination theory.