Hard-sphere displacive model of extension twinning in magnesium

A crystallographic displacive model is proposed for the extension twins in magnesium. The atomic displacements are established, and the homogeneous lattice distortion is analytically expressed as a continuous angular-distortive matrix that becomes a shear when the distortion is complete. The calculations prove that a volume change of 3% occurs for the intermediate states. The twinning plane, even if untilted and restored when the distortion is complete, is not fully invariant during the transient states. The crystallographic calculations also show that the (90°, a) twins observed in nano-pillars and the (86°, a) twins observed in bulk samples differ only by a slight obliquity angle (3.4°). Continuous features in the pole figures between the low-misoriented (86°, a) twin variants are expected; they are confirmed by EBSD maps acquired on a single crystal of magnesium. As the continuous mechanism of extension twinning is not a simple shear, a “virtual work” criterion using the value of the intermediate distortion matrix at the maximum volume change is proposed in place of the usual Schmid’s law. It allows predicting the formation of extension twins for crystal orientations associated with negative Schmid factors.