The analytical theory of the crystallography of mechanical twinning

The crystallography of mechanical twinning is formulated on an analytical mathematical basis. The system of equations determining the correspondence matrix of lattices for type I and type II twinning is obtained and group properties of those matrices are investigated. This leads to a technique for determining the vector of twinning shear in terms of components of the metric tensor of basis, and is valid for all crystal structures. The atomic shuffles, accompanying the twinning shear are examined and general requirements satisfying the twin relation are established.

Keywords:

• Mechanical twinning
• shear