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# Anomalous slip in body-centred cubic metals

## Abstract

Crystal strength and plastic flow are controlled by the motion and interaction of dislocations, the line defects carrying atomic shear increments. Whereas, in most crystals, deformation develops in the crystallographic planes in which the glide force acting on dislocations is maximum, plasticity in body-centred cubic metals is more complex. Slip systems in which the resolved shear stress is not the highest can dominate at low temperature, leading to anomalous slip1,2. Using in situ tensile tests in a transmission electron microscope we show that anomalous slip arises from the high mobility of multi-junctions3, that is, junctions between more than two dislocations, which glide at a velocity several orders of magnitude larger than single dislocations. These multi-junctions result from the interaction of a simple binary junction with a gliding dislocation. Although elasticity theory predicts that these binary junctions should be unstable in crystals with a weak elastic anisotropy such as tungsten, both experiments and atomistic simulations reveal that such junctions can be created under dynamic conditions, in agreement with the existence of anomalous slip in almost all body-centred cubic metals, including tungsten4,5.

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## Data availability

Video sequences corresponding to the different figures describing results of in situ experiments are available as Supplementary Information. Configurations and input files used for atomistic simulations are available from the corresponding authors.

## Code availability

Atomistic simulations have been performed with the open-source computer code Lammps developed and maintained at the Sandia National Laboratories. Lammps is available at https://lammps.sandia.gov. Results of these simulations have been analysed with Ovito, available at https://www.ovito.org.

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## Acknowledgements

Atomic simulations in this work were performed using HPC resources from GENCI-CINES and -TGCC (grant no. 2021-096847). B.B. and E.C. acknowledge funding by the French Tripartite Institute (CEA-EDF-Framatome) through the ICOMB project.

## Author information

Authors

### Contributions

D.C. designed the study and performed the in situ TEM straining experiments. B.B. and E.C. performed the atomistic simulations and developed the elastic model. All the authors discussed the results, prepared the manuscript and reviewed the paper.

### Corresponding authors

Correspondence to Daniel Caillard or Emmanuel Clouet.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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## Extended data figures and tables

### Extended Data Fig. 1 Glide of isolated screw dislocations in niobium.

Frames a and b follow the motion of the same dislocations at two different times. The image in c is obtained by taking the difference between these two frames and enlightens the dislocations motion in the time interval with initial and final positions appearing respectively in black and white. This dislocation motion is sketched in frame d with initial and final positions of gliding dislocation drawn respectively with solid and dashed lined. The slip traces left on the thin foil surface by the gliding dislocations, noted ‘tr’, correspond to non-crystallographic slip planes. The dislocations straighten along their screw orientation when gliding with a slow and steady motion at an average velocity of the order of 5 nm/s. Four dislocation families with different Burgers vectors $${{\bf{b}}}_{1}$$, $${{\bf{b}}}_{2}$$, $${{\bf{b}}}_{3}$$, and $${{\bf{b}}}_{4}$$ are identified and can be distinguished in the images thanks to their different directions and lengths in projection.

### Extended Data Fig. 2 Glide of a dislocation network in niobium.

The same dislocation network is imaged in ac at three different times, using the diffraction vector g1 = (010). Two other diffraction vectors, g2 = (011) and $${g}_{3}=(0\bar{1}1)$$, are used in d and e to determine Burgers vectors by extinction just after time t = 14 s as in c. The network is made of two interacting screw dislocation families with Burgers vectors $${{\bf{b}}}_{1}=1/2[\bar{1}1\bar{1}]$$ and $${{\bf{b}}}_{2}=1/2[111]$$, forming horizontal junctions with Burgers vector $${{\bf{b}}}_{JR}=[010]$$ through the reaction $$1/2[\bar{1}1\bar{1}]+1/2[111]=[010]$$. This network glides in the average plane $${P}_{12}=(10\bar{1})$$ containing the three dislocation families, leading to the horizontal slip traces visible in all images, especially in e with diffraction vector g3 where dislocations 2 are out of contrast. The slip traces are clearly distinct for different emerging dislocations 1 and 2, which shows that the network is not entirely contained in a single P12 plane. The image difference f between a and c highlights the motion of the fastest node of the network, leading to a velocity of about 15 nm/s.

### Extended Data Fig. 3 Rapid glide of a node connecting four screw dislocations in niobium.

Three different events are shown, all corresponding to the same mechanism as in Figs. 1 and 2 where four screw dislocations connected to a node glide in two different planes over a large distance in less than 40 ms. The event in ab was obtained in the same area as in Extended Data Fig. 2 after further deformation. The second set (de) was obtained in the same sample in a neighbouring area and precedes the event described in Fig. 2. The last event (gh) comes from the same sample as that described in Fig. 1 after a rather large amount of deformation. The two sets of traces are remarkably similar for each sample, namely c and f on the one hand, i and Fig. 1c on the other.

### Extended Data Fig. 4 Mechanism leading to anomalous slip.

A network formed by $${{\bf{b}}}_{1}$$ and $${{\bf{b}}}_{2}$$ screw dislocations in P12 plane is intersected by dislocations $${{\bf{b}}}_{3}$$ which glide in the principal slip system. The interaction results in the creation of highly mobile junctions, leading to long-distance glide of $${{\bf{b}}}_{1}$$ and $${{\bf{b}}}_{2}$$ dislocations in a single P12 plane and of $${{\bf{b}}}_{3}$$ and $${{\bf{b}}}_{4}$$ dislocation in many parallel slip P34 planes.

## Supplementary information

### Supplementary Discussion

We present in this Supplementary Discussion the elastic energy model used to study the relaxation of the four-dislocation node and the stability of the <100> junction in BCC metals, as well as additional atomic simulations performed in Nb, W and Mo to study the mobility of coplanar dislocation networks and the dynamic formation of <100> junctions.

### Supplementary Video 1

Rapid glide of a four-dislocation node in niobium strained at 95K. The node connecting four screw dislocations moves rapidly to the left and leaves four horizontal traces on the thin foil surfaces. The video sequence corresponds to Fig. 1 of the main text.

### Supplementary Video 2

Formation and rapid glide of a four-dislocation node in niobium strained at 95K. Dislocation 3 first approaches the horizontal junction reaction (JR). Then, the node moves rapidly to the left and leaves four horizontal traces. Finally, dislocation 4 makes a dipole, allowing the identification of its Burgers vector. The video sequence corresponds to Fig. 2 of the main text. Its velocity has been increased by a factor of 3.

### Supplementary Video 3

Formation of a [010] junction in tungsten strained at 373K. A horizontal [010] junction appears at the intersection of two gliding 1/2 <111> screw dislocations. The video sequence corresponds to Fig. 4 of the main text.

### Supplementary Video 4

Steady motion of straight screw dislocations in niobium strained at 95K. The 1/2 <111> screw dislocations are gliding with a viscous motion corresponding a mobility controlled by a Peierls mechanism, that is, by the nucleation and propagation of kink pairs. The video sequence corresponds to Extended Data Fig. 1.

### Supplementary Video 5

Cooperative glide of screw dislocations forming a hexagonal network in niobium strained at 95K. The horizontal segments are <100> junctions. The video sequence corresponds to Extended Data Fig. 2.

### Supplementary Video 6

Rapid glide of a four-dislocation node in niobium strained at 95K. The node connecting four screw dislocations moves rapidly to the left and leaves four horizontal traces on the thin foil surfaces. The video sequence corresponds to Extended Data Fig. 3a,b.

### Supplementary Video 7

Rapid glide of a four-dislocation node in niobium strained at 95K. The node connecting four screw dislocations moves rapidly to the left and leaves four horizontal traces on the thin foil surfaces. The video sequence corresponds to Extended Data Fig. 3d,e.

### Supplementary Video 8

Rapid glide of a four-dislocation node in niobium strained at 95K. The node connecting four screw dislocations moves rapidly to the left and leaves four horizontal traces on the thin foil surfaces. The video sequence corresponds to Extended Data Fig. 3g,h.

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Caillard, D., Bienvenu, B. & Clouet, E. Anomalous slip in body-centred cubic metals. Nature 609, 936–941 (2022). https://doi.org/10.1038/s41586-022-05087-0

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