Unstable twin in body-centered cubic tungsten nanocrystals

Twinning is commonly activated in plastic deformation of low stacking-fault face-centered cubic (Fcc) metals but rarely found in body-centered cubic (Bcc) metals under room temperature and slow strain rates. Here, by conducting in situ transmission electron microscopy (TEM) at atomic scale, we discover that, in stark contrast to those in most Fcc metals, a majority of deformation twins in Bcc metals are unstable and undergo spontaneously detwinning upon unloading. Such unexpected instability of Bcc twins is found to be closely related to the prevalence of the inclined twin boundaries—a peculiar structure where twin boundaries are not parallel to the twinning plane, and the degree of instability is in direct proportion to the fraction of the inclined twin boundary. This work provides significant insights into the structure and stability of deformation twins in Bcc metals.

(1) where μ is the shear modulus, r is the radius of curvature and α is the coefficient (~2.1 for pure edge dislocation and ~6.3 for pure screw dislocation). Since is determined by the stacking fault energy, and it is estimated to be ~0.089 N m^-1. 8,9,10 Image force for edge dislocation, 7 where l is the distance from the surface, ν is the Poisson ratio, r is the radius and is the angle. The total force acting on the individual dislocation line on one twinning plane is expressed as： Considering the stacking of multiple twinning dislocation on different twinning planes (Supplementary Figure 8C), the average net force for the twin with N layers can be expressed as: Two cases are considered in Supplementary Figure 9A as follows: Case 1: 0 < ≤ 2 ⁄ . There is one assumption that the twinning partial keeps as a half-circle loop to propagate, the area fraction of MF f =100%.
where the assumption that the dislocation would keep as the original half-circle loop to move forward is made and the area fraction of MF f = B/2d.
As case 2 is developed, the balance ( ̅ = 0) can be reached and is determined.
Based on references [5,11], we assume that the layer number of the twin ≥ 6. One is found that the predicted value of for the spontaneous detwinning is much lower than the value (~ 60%) in the experiment. This difference can be ascribed to the following reasons. The first reason might be the neglect of the complex interaction between twinning partials in multiple (112) planes. Moreover, one simple assumption that the twinning partial keeps as the half-circle loop to propagate in case 2 is applied. Actually, the dislocation line may have higher curvature (higher restoring force and thus higher driving force for detwinning) rather than the half-circle loop due to the huge mobility difference between screw and edge dislocations and thus would get larger. Another reason might be the underestimation of the lattice friction according to the simulation result. Our experiment indicated that twinning partials were hard to fully penetrate the crystal in the Bcc nanocrystals, while either screw or edge partial dislocation shows relatively high mobility in simulation, 5,12 compared to the experimental observation. The potentials used for Bcc crystals in the simulation has a significant effect on the theoretical prediction, which leads to huge differences in the lattice resistance results. 3 It should be noted that the twin may nucleate from other surface sites and start as the formation of screw twinning partials. The screw part may dominate the dislocation type in this curved dislocation line, as shown in Supplementary Figure 8A. Owing to the dislocation line perpendicular to the view direction [1-10], for screw dislocation, it is difficult to find the propagation distance and thus hard to evaluate the image force.
The complicated geometry of this case makes it hard to do the quantitative analysis as before. But it is conceivable that detwinning is still dominated by the twin fault force or stacking fault force and there also would exist one critical point as discussed before that the dislocation tends to move reversely with a certain fraction of MF.