Twinning path determined by broken symmetry: A revisit to deformation twinning in hexagonal close-packed titanium and zirconium

Deformation twinning is one of the major deformation mechanisms in crystals, which plays an important role in determining the mechanical properties of metals and alloys. One of the important issues to understand twinning mechanisms is the determination of the deformation path. However, due to a lack of theoretical tools, a fundamental relationship between symmetry breaking and the deformation path has not been established in materials science, which conceals the physical origin of deformation twinning. Utilizing a graph approach for deformation pathways, we show that twinning modes in hexagonal close-packed (hcp) titanium and zirconium are dictated by both the symmetry of hcp and the symmetry breaking associated with the bcc to hcp transformation. Our work not only opens another avenue to investigate the symmetry and symmetry breaking in hcp crystals, but also provides insight into the physical origin of crystalline defects.