Sample preparation and introduction of cracks

The monolayer MoS 2 samples were grown on sapphire using chemical vapour deposition20, and then transferred to TEM grids using the polymethyl methacrylate (PMMA) method as a free-standing sheet21. Excellent quality of the as-grown MoS 2 crystal was confirmed by TEM (Supplementary Fig. 1), revealing the sulfur deficiencies lower than 1% (Supplementary Table 1). Owing to the high specific surface area, it was inevitable that some organic adsorbents remained on the sample surface after transfer (Supplementary Fig. 2). Absorbents on the MoS 2 surface can be activated and evaporated gradually by electron beam irradiation. From a mechanical point of view, these loosely contacting adsorbents can stabilize the 2D samples in the cracking process that we will discuss later. The vacuum in the JEOL ARM-200F TEM is >2 × 10−5 Pa and all TEM measurements were conducted at room temperature under 80 kV. During the in situ observation of cracking, the electron beam was kept sufficiently low or entirely turned off and only turned on (beam intensity 0.01 pA nm−2) for taking images with a short exposure time (0.32 s; see Supplementary Fig. 1 and Supplementary Table 1 for more defect analysis in MoS 2 in all experimental conditions). The occurrence of the beam damage on MoS 2 requires much higher beam intensity (Supplementary Fig. 1)22.

According to the criterion of continuum fracture mechanics, a crack starts to grow when the maximum stress intensity (K) on the sample exceeds the critical stress intensity factor (K c , fracture toughness). We confirmed that crack propagation is preferably initiated at some pores (either in pristine samples or newly created by condensed electron beam; see dark-field (DF) TEM images in Fig. 1a,b) that is congruent with the fact that the stress intensity factor is proportional to the square root of the dimension of defects3. The cracks can quickly run through the entire sampling area (suspended on 1 μm holes of the TEM grid, Fig.1a,b), or can stop in the centre because of relaxation of stresses and stabilization by adsorbents (Supplementary Fig. 3). We also note that the crack does not usually follow the grain boundaries (Fig. 1a), similar to previous findings8. In the following part, our discussion will be restricted to intragranular cracking.

Figure 1: TEM observations of cracks of monolayer MoS 2 . (a) Dark-field image of one crack initiated from the left pore through the entire hole, finally reaching the right pore, avoiding the grain boundary. Scale bar, 200 nm. (b) A similar crack initiated from the centre pore. Scale bar, 200 nm. (c) Bright-field image at the higher magnification reveals the microscopic cracking path. Scale bar, 45 nm. (d) The same crack as (a) after 70 s and several steps on the post crack surface are highlighted. The red triangles in c,d mark the same area on the sample. Scale bar, 30 nm. (e) HRTEM image for a cracked surface. Scale bar, 1 nm. (f) HRTEM image for an emitted dislocation close to a crack tip. Scale bar, 300 pm. Full size image

Figure 1c,d presents two snapshots of cracking during 70 s. Generally, straight cracking surfaces can be seen, whereas the cleavage plane of monolayer MoS 2 is determined by diffraction as the close-packed planes or a zigzag edge. The high-resolution transmission electron microscopy (HRTEM) image of the post cracking surfaces shows the two opposite S-terminated edge and Mo-terminated edge by direct decohesion (Supplementary Figure 4). Owing to the tensile stress direction not being exactly perpendicular to any cleavage plane, the nominal cracking direction is between [ ] and [ ] (Fig. 1c–e, and Supplementary Fig. 5). In addition to these proofs of brittleness, we also found some irregular steps or defective sites (highlighted by white triangles in Fig. 1d) on the crack surfaces. More importantly, dislocations that are absent in the pristine sample can be seen by HRTEM close to the crack tip (Fig. 1f). This dislocation structure consists of 4–6 cores with Burgers vector (Supplementary Fig. 6), and dislocation cores in MoS 2 may have more types23. These phenomena suggest that there might be other mechanisms accounting for the 2D MoS 2 cracking apart from decohesion.

In situ observation of fracture

Figure 2a–d presents one case of in situ cracking during 40 s by HRTEM images. There is one dislocation (labelled by ‘T’) near the crack tip. After 10 s, the dislocation climbs along the cracking direction by 1 nm. The geometric phase analysis (GPA)24 was carried out on the original TEM images at 10 s, and the axial strains, shear strain and lattice rotation are presented in Fig. 2e–h. The dislocation at the crack tip is highlighted in Fig. 2e. The distribution of the tensile strain ɛ 22 at the crack tip zone in Fig. 2f resembles the tensile strain distribution for normal Mode I cracking25. However, the shear strain also exists (ɛ 12 in Fig. 2f). Meanwhile, the local strain field near the crack tip is not uniform but contains a lot of high-frequency fluctuations (Fig. 2e–g) that can be attributed to the easy three-dimensional (3D) fluctuations of 2D materials13 when subjected to complex stress field near the crack tip. Because of the coexistence of tensile, shear and tear stress, the crack of MoS 2 here should be a mixed mode (I, II and III) cracking25. At the crack tip, because of the large strain gradient in the crack tip zone, the two parts of the monolayer MoS 2 crystals on the two sides of the dislocations can have some angle difference that can be locally considered as 2 nm-sized grains.

Figure 2: In situ TEM series revealing crack propagation and dislocation climb. (a–d) The in situ TEM image series showing a crack propagation at 0, 10, 25 and 40 s. All the images are aligned to show the same area (drift compensation) by aligning far-field less strain zones. Cracks are highlighted within the white-dashed lines in the lower right corners. The atomic models for perfect MoS 2 and multislice TEM image simulations of the atomic model corresponding to experimental TEM conditions are shown in the inset of a. The electron beam was turned off during the cracking process but only turned on to take images (exposure time 0.32 s), to exclude additional electron beam effect on the cracking. There is one edge dislocation at 0 s, highlighted by ‘T’. It starts to climb because of the stress of the crack tip at 10 s, and disappears at 40 s when the crack extends further. Scale bar (a), 1 nm. (e,f) The GPA strain analysis of the 10 s image. The box in e highlights the corresponding area shown in the HRTEM images in a–d. Axial strains with directions marked in the upper right corners in e,f, shear strain shown in g and rotation shown in h. Scale bar (e), 5 nm. Full size image

The dislocation dynamics near the crack tip was investigated by more in situ TEM observations. For example, in Fig. 3a, the crystallinity is perfect near the crack tip (including areas 1, 2 and 3). After 10 s, the crack propagates to area 2 and there is a new dislocation in area 3 (Fig. 3b). The GPA strain analysis for the image at 10 s shows that the maximum tensile strain (ɛ 22 ) direction is towards the newly emitted dislocation (Fig. 3c). After 90 s, the crack passed through areas 2 and 3 and arrived at area 4 (Fig. 3d). By identifying the positions for all the unit cells in Fig. 3a,b, we can plot the atomic displacement map with vectors (Fig. 3e). Figure 3e shows the atomic model for the emission of a dislocation on the surface near the crack tip. The red box highlights the dislocation emission zone. It can be easily seen that the slip plane connecting the crack surface and the dislocation core is ( ) plane. After the emission of this dislocation by gliding toward one side of the crack (right side here), the axial strain field at the crack tip (Fig. 3c) is different from the strain field when one dislocation stays in front of the crack path (Fig. 2e,f). The mode I tensile strain (ɛ 11 ) for the original cracking direction becomes lower, whereas tensile strain (ɛ 22 ) is higher and the direction from crack tip to the dislocation has the maximum ɛ 22 , and therefore the crack turns direction in area 2. Except for the dependence of crack propagation paths on the dislocation emissions as we observed here, other factors including external stress and surface adsorbents can also play a role to determine the crack path.

Figure 3: The in situ TEM observation of dislocation emission and crack turning. (a,b) The in situ TEM observation of cracking at 0 and 10 s. Electron beam is off during cracking and only turned on for imaging. The series images are spatially aligned (drift compensation). There is no dislocation in view at 0 s, whereas one fresh dislocation emerges in the box at 10 s, highlighted by ‘T’. Scale bars, 1 nm. (c) The GPA strain analysis for the axial strains at 10 s. Scale bar, 2 nm. (d) TEM image showing the crack turn after 90 s. All the related positions on the samples are labelled as 1, 2, 3 and 4 in a,b,d. The maximum tensile stress direction in c is in agreement to the following crack path in d, showing that the emission of one dislocation can change the strain field near the crack and thus turn the crack direction. Scale bar, 2 nm. (e) The atom displacement mapping between 0 and 10 s. All the unit cell locations in monolayer MoS 2 are determined by Gaussian fitting of the TEM images in a,b and then the displacement vector of each unit cell between 0 and 10 s can be calculated by subtraction. The displacement vectors are presented directly in e, and the colour stands for the displacement magnitude. Relative slip between two planes and creation of one dislocation can be seen clearly inside the red box. There are several surface atoms lost during cracking. Full size image

As mentioned before, the surface absorbents function to stabilize the cracking process that makes it possible for in situ observations. We performed in situ cracking experiments in the pristine sample, as well as the sample after low-intensity beam shower without beam damage (defect analysis shown in Supplementary Table 1) for 10 and 25 min, respectively. Supplementary Figure 8 presents three cases of cracking by strain maps corresponding to the three conditions. The amount of absorbents on the MoS 2 surface is reduced by increasing time of beam shower, confirmed by the direct TEM observations (Supplementary Figure 7). Mode I tensile strain (ɛ 22 ) decreases with less amount of absorbents (Supplementary Fig. 8), in agreement to the greater stabilization effect by more amount of absorbents. The statistics on the cracking speed and emitted dislocation density per unit length of crack is presented in Supplementary Table 2. Smaller absorbents on the sample generate larger number of dislocations. The reason for this is that larger strain at the crack tip and slower cracking speed for the sample with more absorbents allows the dislocations at the crack tip to climb with the propagating crack (supplementary Figure 8). Meanwhile, with smaller absorbents, the newly emitted dislocations have less time to move and dislocations will be caught up by the propagating crack and escape from the surface, and then another new dislocation is emitted in the following cracking process (Supplementary Fig. 8). The local strain change caused by the removal of adsorbents may influence the cracking path. However, the ability of emitting dislocations is intrinsic for MoS 2 , and the emitted dislocations can significantly change the stress field at the crack tip and affect the cracking path prominently (Fig. 3).

According to our observations, the blunting of the crack tip with a radius of up to 2 nm in MoS 2 can be identified during cracking (Supplementary Fig. 9) in line with the emission of a large density of dislocations. The maximum dislocation density occurs right at the forefront of the crack tip, whereas the post-cracking part has fewer dislocations, partially because of the released dislocations after cracking, leaving steps and corrugations. The material constant, the size of the plastic zone (r c ) at the crack tip, can be estimated by models or simulations26; for the plane stress condition, where σ Y is the yield stress. For monolayer MoS 2 , the observed r c is equal to 2–5 nm. Linear fracture mechanics can be applied if the cracking is brittle and r c <<a, where a is the characteristic dimension of intrinsic defects in the object. However, near the cracks our monolayer MoS 2 sample has only sulfur vacancy defects, implying that a approaches 0 nm. This implies a higher probability of generating plasticity.

Environmental assistance of cracking in 2D material

TMD materials have been known to be susceptible to environment18,27. In the following we will discuss about the environment-assisted cracking of monolayer MoS 2 , the so-called stress corrosion crack (SCC). For SCC, the K IC usually becomes smaller because of a chemical reaction assisted by release of the decohesion energy. Meanwhile, the yield stress also decreases. The as-grown monolayer MoS 2 sample on a sapphire substrate was exposed to ultraviolet (UV) light with controlled humidity inside the chamber (see Methods)27. Highly oxidative chemical groups, such as O 3 and oxygen-related radicals, can be created under UV that can quickly react with MoS 2 . This method was first applied to visualize the grain boundaries of 2D materials28.

The scanning electron microscopy image of a MoS 2 sample after 2 min of UV exposure is shown in Fig. 4a with that of the pristine sample in the inset. A high density of crack patterns was observed. The MoS 2 monolayer is subject to a biaxial in-plane stress mainly caused by the robust adhesion between MoS 2 and the sapphire substrate29. The grain boundaries between the triangular-shaped MoS 2 single crystals can first be determined by the rather straight lines (Fig. 4a). A zoom-in DF-TEM image (Fig. 4b) clearly reveals the triply branched cracking, stemming from some point defects (∼50 nm size). The angle between crack directions is 120° and the initial directions of cracks are all along the [ ] (zigzag) direction (Fig. 4b), as determined by electron diffraction (see Supplementary Fig. 10) that is the same as the cracking plane in the pristine sample. The ageing effect after cracking can be excluded, because the crack retains a uniform width. We also note that the cracks propagate in a random manner in another MoS 2 sample subject to the same UV treatment conditions after being transferred onto the TEM grid (Supplementary Fig. 11). Instead, in pristine MoS 2 sample on sapphire, the cracks interact with each other because of the elastic field induced by MoS 2 –sapphire interactions. Because the monolayer MoS 2 is ultrathin, all the cracks can be treated as steady-state (low strain rate) semi-infinite crack propagation in linear elasticity theory30. Therefore, the triply branched cracks have to turn their direction clockwise (or counterclockwise) coherently to satisfy the elastic stress/strain equilibrium (Fig. 4b).

Figure 4: Stress corrosion cracking of monolayer MoS 2 . (a) Scanning electron microscope image of crack pattern generated after 2 min of UV light exposure under humid conditions on MoS 2 . Scale bar, 2 μm. Inset shows an image of the as-grown sample. Scale bar, 5 μm. (b) TEM dark-field image of triple crack paths initialized from one defect similar to (a). Scale bar, 100 nm. Inset highlights the crack. Scale bar, 20 nm. (c,d) Magnified images of two areas in a, two cracks meet in the centre and are curved by each other because of the strain field. The three theoretically simulated paths using linear elasticity theory with different r c are fitted with the experimental paths. Scale bar (c), 150 nm. Scale bar (d), 200 nm. (e) Schematic showing the stress state of two meeting cracks. Full size image

By applying a linear elastic field under a biaxial stress condition in classical fracture mechanics and assuming that the stress field (out of plastic zone) extends to a distance r c from the crack tip, we can simulate the crack path between two cracks that approach to each other (see Supplementary Note 1). The shape of the crack path does not depend on the far-field stress but relies on r c . Figure 4c,d shows two examples of cracks approaching and finally merging with different initial conditions (tip spacing x and cracking angle α, Fig. 4e). The experimental images are overlaid with the cracking paths simulated with different r c . More brittle materials (smaller r c ) can turn the direction of cracking easily when affected by other elastic fields (the scheme can be found in Fig. 4e). The extreme case for r c =0 will be a straight line. The experimental cracking paths (Fig. 4c,d) are located between r c =5 nm and r c =10 nm.

On the other hand, the post SCC cracking MoS 2 sample is rechecked by high-resolution scanning transmission electron microscope (STEM) and electron energy loss spectra (EELS) (Supplementary Fig. 12). The pre-edge background subtracted EELS spectra shows that the cracking under UV induces stoichiometric deficiencies for sulfur near the crack (∼5 nm from the crack surface/edge) as compared with the region away from the crack. The large local strains near the crack tip will elevate the chemical reaction speed and thus lead to higher defect concentrations near the crack tip. Density functional calculations reported that the dislocations dynamics can be much easier in defective MoS 2 (ref. 31). Consequently, the greater sulfur deficiencies will increase the plasticity (emission and dynamics of dislocations). By EELS line scan and STEM images, we confirmed the width (dimension) of this higher deficiency zone near crack under UV environment attack is ∼5–8 nm, in congruent with the continuum mechanics simulation results. Therefore, by continuum mechanics modelling and EELS we conclude that the tip plastic zone for SCC of MoS 2 is 5–10 nm. This value is larger than that associated with pure cracking (2–5 nm). However, this is not contradictory to the usual plasticity enhancement of ceramic materials under corrosive environment32.