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A crystallographic displacive model is proposed for the extension twins inmagnesium. It is based on a hard-sphere assumption previously used formartensitic transformations. The atomic displacements are established, and thehomogeneous lattice distortion is analytically expressed as a continuousangular-distortive matrix that takes the usual form of shear when thedistortion is complete. The calculations prove that a volume change of 3percents occurs for the intermediate states and that the twinning plane, evenif untilted and restored when the distortion is complete, is not fullyinvariant during the transient states. The crystallographic calculations alsoshow that the (90 deg, a) twins observed in magnesium nano-pillars and the (86deg, a) twins observed in bulk samples come from the same mechanism, the onlydifference being the existence of a slight obliquity angle (+/- 3.4 deg)required to reduce the strains in the latter case. Continuous features in thepole figures between the low-misoriented (86 deg, a) twin variants areexpected; they are confirmed by EBSD maps acquired on a deformed magnesiumsingle crystal. As the continuous mechanism of extension twinning is not asimple shear, a "virtual work" criterion using the value of the intermediatedistortion matrix at the maximum volume change is proposed in place of theusual Schmid's law. It allows predicting the formation of extension twins forcrystal orientations associated with negative Schmid factors.

Displacive model of deformation twinning in hexagonal close-packed metals. Case of the (90 deg, a) and (86 deg, a) extension twins in magnesium