Does mixed grain boundary follow the principles of superposition?

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 character. Here, we demonstrated that the structures and stress fields of mostly mixed GBs could be considered as the superposition of their tilt and twist GB components by computationally examining 26.8 million large-scale structures of 4964 unique silicon mixed GB characters. The results indicate that low angle mixed GB is formed by the dislocation interactions between its decomposed tilt and twist components, while various complex sub-structures with dislocation stress but without conventional dislocation core structures are discovered on twin and structural unit GBs. A universal Read-Shockley model that physically captures the energy trends of the mixed GB is proposed, and its superiority, universality and transferability are proven in a variety of GB structures across different lattices. We confirm the validity of this work by comparing the results with experimental observations and first-principles calculations. Earlier works should now be reassessed in the light of these findings.