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

Abstract

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.

Shifting the Shear Paradigm in the Crystallographic Models of Displacive Transformations in Metals and Alloys

“…The conclusions reached by both models are also convergent: "the {10-12} twinning plane cannot remain invariant during twinning" and a mechanism "without the need of twinning dislocations" is possible [139]. It is also interesting to note the very good agreement between the DTF calculations made by Ishii et al [144] and the analytical calculations presented in Section 9.1. For example, the energy landscape given by DFT presents an energy barrier due to shuffling, as if "something internal 'got stuck'" [144], and this barrier was found at the midway point of the transformation process, as with the maximum volume change calculated analytically (Figure 28e).…”

On the interaction of precipitates and tensile twins in magnesium alloys

“…The crystalline energy, ∆f (1 − ϕ)ϕ, is the potential energy landscape when an original parent crystal is sheared into a twin crystal orientation. ∆f is the energy barrier of the crystalline energy, which can be obtained by ab initio calculations [47]. The minima of the crystalline energy at ϕ = 0.0 and ϕ = 1.0 describe the equilibrium states of the parent and twin crystal, respectively.…”

Precipitation Behavior and Its Effects on Mechanical Properties in a Pre-Twinned Mg–6Al–1Zn Alloy

“…No fixed displacement vector exists during twinning for shuffling atoms; thus, the twin boundary is wrinkled. Based on first-principles density functional theory, Ishii et al 12) also indicated that the {1012} twinning of magnesium was shuffling-controlled when the reaction coordinate is at the level of four atoms. Liu et al 13) performed aberration-corrected transmission electron microscopy observations for the {1012} twin in magnesium and they found that no crystallographic mirror plane exists for twinning in magnesium.…”