  One of the major challenges towards understanding and further utilizing the
properties and functional behaviors of grain boundaries (GB) is the complexity
of general GBs with mixed tilt and twist characters. Here, we report the
correlations between mixed GBs and their tilt and twist components in terms of
structure, energy and stress field by computationally examining 7040 silicon
GBs. Such correlations indicate that low angle mixed GBs are formed through the
reconstruction mechanisms between their superposed tilt and twist components,
which are revealed as the energetically favorable dissociation, motion and
reaction of dislocations and stacking faults. In addition, various complex
disconnection network structures are discovered near the conventional twin and
structural unit GBs, implying the role of disconnection superposition in
forming high angle mixed GBs. By unveiling the energetic correlation, an
extended Read-Shockley model that predicts the general trends of GB energy is
proposed and confirmed in various GB structures across different lattices.
Finally, this work is validated in comparison with experimental observations
and first-principles calculations.
