“…Depending on how the local imperfections are deviated from the bulk structure, they are classified into vacancies, interstitial atoms, or dislocations [10]. Theories and algorithms are then developed to study the morphology, distribution and dynamics of these local structures, including molecular dynamics technique [1,22], Monte Carlo simulation [20,25], continuum phase-field approaches [29,9], and multi-scale methods [19]. When studying GB structures, the relative orientation and displacement, as well as the dividing planes of two grains, are essential variables.…”