Figure 1

HR-TEM images showing the formation of line defects under electron irradiation at 80 kV. (a) The initial configuration with a certain number of S vacancies already present. (b) and (c) Intermediate configurations illustrating formation of defect lines through agglomeration of nearby vacancies. (d) The final configuration after 220 s, where a large number of defect lines can be seen. Examples of single vacancy (SV) and double vacancy (DV) lines are highlighted. The shape of the DV line has changed from that shown in (c). The HR-TEM frames are low pass filtered in order to reduce Poisson noise. An unprocessed region is shown in the upper-right corner of (a).Reuse & Permissions

Figure 2

Comparison of experimental and simulated TEM images. (a,d) Examples of experimental HR-TEM images of the SV and DV lines with filtering applied as in Fig. 1. Various models of the vacancy lines: (b) and (c) single vacancy line, (e) amd (f) two neighboring vacancy lines in the same S layer, (g) and (h) two vacancy lines coinciding in top and bottom layers, and (i) and (j) two vacancy lines in staggered configuration, The atomic structures (b), (e), (g), and (i) are obtained from DFT calculations and used to simulate TEM images (c), (f), (h), and (j). Note that the bottom and side views are shown. In order to differentiate between atoms in the two S layers, they are colored differently: orange for the top layer and yellow for the bottom layer. Magenta circles denote the initial vacancy positions. For DV lines, the local shrinkage of the lattice is quantified by a ratio of the length of line segments (solid red lines) in pristine lattice and around the defect. (k) Formation energies for all considered models as a function of the number of constituting single vacancies (the number of missing S atoms). The DV lines always have even number of vacancies. The extrapolation to longer lines is also shown. The insets are the side views of the atomic models presented in (b), (e), (g), and (i).Reuse & Permissions

Figure 3

(a) Four sequential AC-HRTEM images showing vacancy diffusion events (highlighted by red line segments). (e) and (f) Calculated diffusion paths in the cases of (e) diffusion of S atom to a nearest-neighbor single vacancy site, (f) diffusion of S atom to a vacancy site in the presence of another nearby vacancy on the same side of the layer [position shown with a circle (magenta)]. In this case, there are two inequivalent paths. The respective energy barriers are given in (g).Reuse & Permissions

Figure 4

Lattice strain (shrinkage) as a function of vacancy concentration. The strain is isotropic in the case of isolated vacancies, but strongly anisotropic for vacancy lines. Strains in the direction parallel and perpendicular to the line are denoted by ${\epsilon }_{\left|\right|}$ and ${\epsilon }_{\perp }$, respectively. (b) Strain field for DV line defect. The arrows denote atom displacement from its original position in a pristine lattice to its position in a defective lattice. The arrow length is artificially increased for visualization purposes.Reuse & Permissions

Figure 5

AC-HRTEM images of the MoS${}_2$ flake edge: (a) the initial configuration and (b) after 818 s of irradiation. The white horizontal lines are guides to the eye. (c) Magnification of the final configuration showing large concentration of lines, predominantly oriented parallel to the edge.Reuse & Permissions

Figure 6

A sketch illustrating the formation and energetics of vacancy lines near the MoS${}_2$ flake edge with referential orientation. The energies are normalized to the number of isolated vacancies, and calculated at the 3.1$\%$ vacancy concentration.Reuse & Permissions

Figure 7

Energy (per atom) for foreign species substituting S atoms in SV (a) and DV (c) vacancy lines. Several references are used for the energy of the substituting atom: isolated atom (pluses, blue), molecules with H (crosses, green), and dimer molecules (dots, red). Density of states (DOS) for SV (b) and DV (d) vacancy lines, and for lines filled with various substituting species. In each case, the two curves correspond to the two spin (up and down) components. The filled DOS denotes occupied states (filled up to Fermi level). Gray areas mark for the valence and conduction bands. Examples of the atomic structures are also shown in the case of N substituted to the SV or DV line.Reuse & Permissions