Origin of {3 3 2} twinning in metastable β-Ti alloys

In this paper, the origin of image twinning, which is a unique twinning mode in metastable β-Ti alloys, was investigated. The possible twinning modes in metastable β-Ti alloys are derived by considering lattice instability in addition to the theory of the crystallography of deformation twinning. In order to consider lattice instability in the body-centered-cubic (bcc) structure, a modulated structure was proposed. We then clarify how the modulated structure facilitates image twinning preferentially compared to other possible twinning modes by evaluating the magnitude of twinning shear and the complexity of shuffle. It was found that the lattice instability makes image twinning, which is a major twinning mode observed in alloys with stable bcc structure, unlikely to occur because the lattice modulation causes additional shuffling to form the image twin. It was also found that image twinning is the most possible twinning mode in the modulated structure in terms of the magnitude of twinning shear and the complexity of shuffle. The new formation model of the image twin presented in this study can explain how the lattice instability preferentially activates the image twinning in metastable β-Ti alloys.