Shuffling-controlled versus strain-controlled deformation twinning: The case for HCP Mg twin nucleation

• General mathematical definition of solid–solid transformation is given.
• Gibbs energy landscape of Mg{101¯2}〈101¯1¯〉 twinning nucleation was computed based on DFT.
• Minimum Gibbs energy paths of the twinning nucleation processes were computed based on DFT.
• HCP Mg{101¯2}〈101¯1¯〉 deformation twinning is local atomic shuffling-controlled in particular at the twin nucleation stage.

The atomistic pathways of deformation twinning can be computed ab initio  , and quantified by two variables: strain which describes shape change of a periodic supercell, and shuffling which describes non-affine displacements of the internal degrees of freedom. The minimum energy path involves juxta-position of both. But if one can obtain the same saddle point by continuously increasing the strain and relaxing the internal degrees of freedom by steepest descent, we call the path strain-controlled, and vice versa. Surprisingly, we find the {101¯2}〈101¯1¯〉 twinning of Mg is shuffling-controlled at the smallest lengthscale of the irreducible lattice correspondence pattern, that is, the reaction coordinate at the level of 4 atoms is dominated by non-affine displacements, instead of strain. Shuffling-controlled deformation twinning is expected to have different temperature and strain-rate sensitivities from strain-controlled deformation twinning due to relatively weaker strength of long-range elastic interactions, in particular at the twin nucleation stage. As the twin grows large enough, however, elastic interactions and displacive character of the transformation should always turn dominant.