Structural unit and faceting description of Σ3 asymmetric tilt grain boundaries

Atomistic simulations are employed to investigate the structure of Σ3 asymmetric tilt grain boundaries (ATGBs) with boundary planes rotated about the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle 110 \rangle$$\end{document} misorientation axis in Cu and Al. Results show that the structural units (SUs) and faceting of all 25 Σ3 ATGBs in Cu and Al intermediate to the coherent twin boundary and the symmetric incoherent twin boundary can be completely defined in terms of SUs for these two symmetric boundaries. A structural unit and faceting description for Σ3 asymmetric tilt grain boundaries is presented. Interestingly, this description is identical for both low stacking fault energy Cu and high stacking fault energy Al; only the dissociation width of the D structural unit on the incoherent twin facet differs in Cu and Al. A model based upon the coincidence plot and the structural units of the Σ3 coherent and incoherent twin boundaries is shown to accurately describe the structural units and faceting for all calculated Σ3 asymmetric tilt grain boundaries in this study. This model can also be extended to continuum descriptions of these boundaries to facilitate higher scale computational models.