Possible Twinning Operations during Directional Solidification of Multicrystalline Silicon

Twinning is an important phenomenon during crystal growth of multicrystalline silicon. During twinning, the nucleated new grain is in twin relation with the parent grain, and the twin relation mathematically could be operated through a transformation matrix (T matrix). We have derived the possible T matrices for twinning on the (111) facets, and some of them have not been well recognized before. As applied to the available electron backscatter diffraction (EBSD) data, we found that, in addition to the twist Σ3 operation, the well accepted mechanism for twin formation, there are four other possible twinning operations.