Structures and energies of computed silicon (001) small angle mixed grain boundaries as a function of three macroscopic characters

Understanding how dislocation structures vary with grain boundary (GB) characters enables accurate controls of interfacial nano-patterns. In this atomistic study, we report the structure-property correlations of Si (001) small angle mixed grain boundaries (SAMGBs) under three macroscopic GB characters (tilt character, twist character, and an implicit rotation character between them). Firstly, the SAMGB energies are computed as a function of tilt angle, twist angle and rotation angle, based on which a revised Read-Shockley relationship capable of precisely describing the energy variations span the three-dimensional GB character space is fitted. Secondly, GB structural transitions from dislocation to amorphous structures are given as a function of tilt angle, twist angle and dislocation core radii. The proportion, topology and structural signatures of different SAMGB types defined from the ratio between the tilt and twist angles are also presented. Thirdly, by extracting the transformation of metastable SAMGB phases, the formation mechanisms of SAMGB structures are characterized as energetically favorable dislocation glide and reaction, from which the dislocation density function is derived. The relevant results about SAMGB energies and structures are validated and supported by theoretical calculations and experimental observations, respectively.