Transition of dislocation nucleation induced by local stress concentration in nanotwinned copper

Metals with a high density of nanometre-scale twins have demonstrated simultaneous high strength and good ductility, attributed to the interaction between lattice dislocations and twin boundaries. Maximum strength was observed at a critical twin lamella spacing (∼15 nm) by mechanical testing; hence, an explanation of how twin lamella spacing influences dislocation behaviours is desired. Here, we report a transition of dislocation nucleation from steps on the twin boundaries to twin boundary/grain boundary junctions at a critical twin lamella spacing (12–37 nm), observed with in situ transmission electron microscopy. The local stress concentrations vary significantly with twin lamella spacing, thus resulting in a critical twin lamella spacing (∼18 nm) for the transition of dislocation nucleation. This agrees quantitatively with the mechanical test. These results demonstrate that by quantitatively analysing local stress concentrations, a direct relationship can be resolved between the microscopic dislocation activities and macroscopic mechanical properties of nanotwinned metals.


Supplementary Notes
Supplementary Note 1: Step defects in as-deposited nanotwinned Cu.
Steps exist on twin boundaries (TBs) in the as-deposited nanotwinned copper.
Supplementary The left peak for the stress concentration in the blue trace is almost the same as that in the black trace. This finding suggests that different sizes of the strain gauge will not significantly influence the presentation of stress concentration around the steps on TBs in Supplementary Fig. 11a. In addition, the result of the strain analysis on the proximity of the step has also been plotted in Supplementary Fig. 11b. The strain gauge marked by a black box (indicated by a red arrow in Supplementary Fig. 11a and corresponds to the result in Fig. 4b) gives a strain distribution, presented as the red trace in Supplementary Fig. 11b. The strain distribution is almost the same as the left peaks of the strain from the large areas. Therefore, the selected strain gauge (marked by a black box and indicated by a red arrow in Fig. 4b) can represent the strain distribution of the stress concentration at the steps on TBs faithfully.

Supplementary Note 5:
The influence of step heights on the critical stress required for the emission of type I dislocations.
The critical stress has been measured for the nucleation of type I dislocations at steps with heights of 1 or 2 atomic layers (Supplementary Table 2). These results show that the critical stress values are roughly the same, which suggests that the stress required for dislocation emission would be constant at steps with one or two atomic layers. In addition, if we consider the dislocation emission from the steps as a process of dislocation dissociation, then the stress required for the dislocation nucleation should only be related to the Burgers vectors at the step and of the emitted dislocation and thus would be independent of the step height. Here, the critical shear stress required for dislocation emission can be estimated based on the assumption that the shear stress for dislocation dissociation corresponds to the attractive force between two parallel straight dislocations when the distance between them is equal to the core width of the initial dislocation. In this way, the shear stress is sufficient to dissociate the initial dislocation into two dislocations [5][6] . The radial force between two parallel dislocations can be given as where d is the distance between two dislocations, G is the shear modulus, ξ is the dislocation line vector, ν is the Poisson ratio, and b 1 and b 2 are Burgers vectors of the two parallel dislocations [5][6] . Therefore, the shear stress required for the dislocation emission at steps should be independent of the step height, if the Burgers vectors at the steps b 1 and of the emitted dislocation b 2 are constant for those steps. Combining the above results with the fact that more than 94% of steps have a height of no more than 2 atomic layers, it can be assumed that dislocation emissions from steps with one or two atomic layers are dominant variety of slips across twin lamellae during tensile deformation.

Supplementary Note 6: The stress state after the emission of type III dislocations.
Supplementary Fig. 12a (corresponding to the right image of Fig. 4d in main text) shows a HRTEM image taken after the emission of a type III dislocation. The corresponding strain distribution is shown in Supplementary Fig. 12b. The quantitative strain profile (Supplementary Fig. 12c) from a strain gauge marked by a black box (indicated by a red arrow) in Supplementary Fig. 12b indicates that the mean shear strain near the twin boundary/grain boundary (TB/GB) junction is 0.042  0.002, which corresponds to a local shear stress of 2.02  0.10 GPa.
Under the continuous tensile loading, several dislocations were observed being sequentially emitted from TB/GB junctions, as shown in Fig. 4d and Supplementary   Fig. 13a. This phenomenon is confirmed by the thickness of the twin lamella, as it was eleven {111} layers in the left image of Fig. 4d and fourteen {111} layers in Supplementary Fig. 13a, which suggests that three type III dislocations passed along the upper TB. In the meantime, no dislocation activity was observed on the lower twin boundary (the thickness of the lower twin lamella remains at 9 {111} layers during the loading process). Thus, the lower TB can be used as a reference for the change of the upper twin boundary.
The time between the left (t = 0 s) and right (t = 1 s) images of Fig. 4d is 1 s, which is sufficient for the stress concentration to accumulate again at the TB/GB junction after the first type III dislocation emitted from the TB/GB junction. Therefore, the local shear strain before the next dislocation emission (2.0 GPa, the right image of Fig. 4d) could be comparable to the strain before the first dislocation's emission (2.2 GPa, the left image of Fig. 4d) from the TB/GB junction. As shown in Supplementary Fig. 15d, the proportions of type III dislocations are different, 60-70% and 20-50% (indicated by red and green symbols). This finding suggests that the twin lamella spacing, rather than the grain boundary structure (presented as grain boundary misorientation angle here), plays a crucial role in the dislocation nucleation.
Supplementary Note 8: Determination of the shear strain during the large strain deformation. Supplementary Fig. 16a (corresponding to Fig. 6a), the included angle between the twin boundary and grain boundary is 112.9°. After the loading of external stress, the included angle becomes 111.1° (Supplementary Fig. 16b,

As shown in
In addition, the tensile displacement is about 85 μm at the time of capturing Fig. 6c, and thus the apparent strain is roughly estimated by the ratio of the tensile displacement to the length of the deformed area as about 4%. This agrees well with the above result of 3% shear strain at the time of Fig. 6c.
Supplementary Note 9: The mechanism of deformation with a large strain in nanotwinned Cu.
As described above, for < c in the incipient plastic deformation, dominant type III dislocations are emitted from TB/GB junctions and slip along the coherent twin boundaries, as shown in Fig. 6b. After the emission of abundant type III dislocations, as shown in the Fig. 6c, type I dislocations (like dislocations 1 and 2) were also observed to be emitted. Nevertheless, due to the limitation of the time resolution (0.5 second per frame) and spatial resolution of the in situ bright-field TEM observation, the detailed process of the emission of type I dislocations cannot be resolved at a large strain. One possibility is that type I dislocations are emitted from TB/GB junctions (e.g., dislocation 1 in Fig. 6c) or the inherent steps on TBs (e.g., dislocation 2). As shown in Supplementary Figs. 17a and 17b (bright-field images taken before (t= 5 s) and after (t= 5.5 s) the emission of dislocation 2), type III dislocations (indicated by blue arrows) were still moving, although other type III dislocations started to accumulate at the left side of the grain. These results suggest that dislocation 2 is likely emitted from an inherent step rather than a (still moving) type III dislocation. In addition, the stress will increase with the pile-up of type III dislocations and may be sufficient to trigger the emission of a type I dislocation. Nevertheless, as stated, the possibility of the emission of type I dislocations by the dissociation of piled-up type III dislocations cannot be completely excluded due to the above mentioned limits of in situ bright-field TEM observation. Notably, this emission of type I dislocations is different than the nucleation of type I dislocations (e.g., as shown in Supplementary Movie 4) that has often been observed without prior activity of type III dislocations in the incipient deformation.