Hard-sphere displacive model of deformation twinning in hexagonal close-packed metals. Revisiting the case of the (56, a) contraction twins in magnesium

Contraction twinning in magnesium alloys leads to new grains that are misoriented from the parent grain by a rotation (56°, a). The classical shear theory of deformation twinning does not specify the atomic displacements and does not explain why contraction twinning is less frequent than extension twinning. The paper proposes a new displacive model in line with our previous work on martensitic transformations and extension twinning. A continuous angular distortion matrix that transforms the initial hexagonal close-packed (h.c.p.) crystal into a final h.c.p. crystal is determined such that the atoms move as hard spheres and reach the final positions expected by the orientation relationship. The calculations prove that the distortion is not a simple shear when it is considered in its continuity. The (0-11) plane is untilted and restored, but it is not fully invariant because some interatomic distances in this plane evolve during the distortion process; the unit volume also increases up to 5% before coming back to its initial value when the twinning distortion is complete. Then, the distortion takes the form of a simple shear on the (0-11) plane with a shear along the direction [18,-5,-5] of amplitude 0.358. Experiments are proposed to validate or disprove the model.