Small transition-metal dichalcogenide nanostructures down to subnanometer by two-dimensional material origami

Origami is a promising method for creating various structures from filmlike materials via local deconstruction rather than elastic bending. Transition-metal dichalcogenides (TMDCs) have high bending stiffness making the formation of highly curved nanostructures, such as nanotube or nanocages, via bending difficult. Here, we propose the use of two-dimensional (2D) material origami to build stable TMDC nanostructures. Various nanostructures, such as polygonal nanotubes or polyhedral nanocages, can be created by introducing line defects, which incurs only a very small energy penalty. Through first-principles calculations and high-resolution transmission electron microscopy imaging, we confirmed their stability and the possibility of synthesis experimentally via line defect formation. As an example, the widely observed TMDC nanowires are produced with this approach, and many experimentally observed nanostructures agree with these origami creases/line defects. This work opens a door to synthesize nanostructures of few-atomic-thick 2D materials for various potential applications.

Figure 1

Stability comparison between $\mathrm{Mo}{\mathrm{S}}_2$ nanoribbons with and without line defect. The black curve is the formation energy of nanoribbons bent by 38°, as functions of ribbon width $w$. The left inset shows four nanoribbons of different widths that are all bent by 38°. The horizontal green line is the formation energy of a nanoribbon with a sulfur vacancy crease, $\lambda$, which is constant for different $w$. However, $\lambda$ changes with different sulfur chemical potentials, ${\mu }_{\mathrm{S}}$, as denoted by the gradient blue-yellow shadow. The right inset is the front view of the initial and relaxed 2D and 3D atomic structures of $\mathrm{Mo}{\mathrm{S}}_2$ nanoribbon with a sulfur vacancy crease.

Figure 2

Structures and stability of $\mathrm{Mo}{\mathrm{S}}_2$ nanotubes with sulfur vacancy creases. (a) The relaxed structures of some $\mathrm{Mo}{\mathrm{S}}_2$ nanotubes with different number of sulfur vacancy creases along the zigzag direction, (m, n)-i, where $i=1,2,...,10$. (b) The formation energy per unit length of $\mathrm{Mo}{\mathrm{S}}_2$ nanotubes with $i$ sulfur vacancy creases, as a function of the curvature of the original tube ($i=0$) at ${\mu }_{\mathrm{S}}={\mu }_{{\mathrm{S}}_8\mathrm{bulk}}$. Dashed lines are the linear fitting lines. (c) The enlarged view of the gray region shown in (b). (d) The optimal number of sulfur vacancy creases, $i_{\mathrm{opt}}$, as a function of diameter of the nanotubes under different ${\mu }_{\mathrm{S}}$, where ${\mu }_{\mathrm{S}}={\mu }_{{\mathrm{S}}_8\mathrm{bulk}}$ is set as zero.

Figure 3

Electronic properties of $\mathrm{Mo}{\mathrm{S}}_2$ nanotubes with line defects. (a) Band structures of (12, 12) nanotube with different number of sulfur vacancy creases, $i=0$, 1, 2, and 6. The blue and red dots are the contributions from Mo and S atoms around defects, respectively. The insets are enlarged views around the Fermi level. (b) Decomposed charge density of CBM and VBM at the $\mathrm{\Gamma }$ point for the (12,12)-2 tube. (c) Enlarged front and side views of (b).

Figure 4

Evolution from $\mathrm{Mo}{\mathrm{S}}_2$ nanotube to nanowire. The formation energy per atom of zigzag $\mathrm{Mo}{\mathrm{S}}_2$ nanotubes with three evenly distributed sulfur vacancy creases, in S-rich (orange dots) and Mo-rich (blue dots) environments. The insets are the corresponding optimal structures. The leftmost one is the smallest possible structure (top and front views), which is exactly the experimentally observed $\mathrm{Mo}{\mathrm{S}}_2$ nanowire.

Figure 5

Structures and stability of $\mathrm{Mo}{\mathrm{S}}_2$ octahedron. (a) Construction of a $\mathrm{Mo}{\mathrm{S}}_2$ octahedron nanocages with vacancy creases. Side view and top view of a regular $\mathrm{Mo}{\mathrm{S}}_2$ triangle with ZZ Mo edges (a1) and ZZ S edges (a2). (a3) Side view and 3D views of a folded rhombus connected by (a1) and (a2). (a4) An integrated octahedron connected by four pieces of $\mathrm{Mo}{\mathrm{S}}_2$ shown in (a3). (b) Top view of optimized structures without (b1) and with (b2) vacancy creases and the formation energy comparison for them (c). The inset in (c) is the $\mathrm{M}{\mathrm{o}}_6{\mathrm{S}}_8$ cluster, the smallest possible structure of octahedrons with vacancy creases, which has been well known as a catalyst for hydrodesulfurization. (d) Snapshots taken during the AIMD simulation of the $\mathrm{Mo}{\mathrm{S}}_2$ octahedrons at 1100 K, without (d1) and with (d2) line defects.

Figure 6

Experimental evidences of vacancy creases in TMDC nanomaterials in the literature. (a) TEM micrograph of a $\mathrm{Mo}{\mathrm{S}}_2$ nanoparticle, atomic models with creases are shown for comparison [57]. Copyright 2010, the Royal Society of Chemistry. The red rectangles denote two concavelike surfaces. (b) TEM image of a $\mathrm{Mo}{\mathrm{S}}_2$ fullerene, in which the structures with vacancy creases are shown for comparison. Reproduced with permission [58]. Copyright 2000, American Chemical Society. (c) and (d) are scanning transmission electron microscopy images of $\mathrm{Mo}{\mathrm{S}}_2$ nanotubes, in which the structures with vacancy creases are shown for comparison. Reproduced with permission [21]. Copyright 2010, the Royal Society of Chemistry. (e1) The fast Fourier transform filtered image of HR-TEM micrograph of a $\mathrm{Mo}{\mathrm{S}}_2$ nanoparticle, reproduced with permission [27]. Copyright 2006, American Chemical Society. The red droplet denotes the sharp corners, which corresponds to creases of the $\mathrm{Mo}{\mathrm{S}}_2$ plane. (e2) Simulated TEM image using octahedron with vacancy creases.

Figure 7

Experimental evidences of sulfur vacancy creases. (a) HR-TEM image of the cross section of a $\mathrm{Mo}{\mathrm{S}}_2$ nanoparticle contains both sharp (yellow) and blunt (red) turns. Enlarged views are also shown. To show the sulfur vacancy crease in the sharp turn, a structure model is overlaid on it, where the cyan dash lines are Mo planes, white lines are interlayer gaps, the yellow lines are pairs of S atoms, and the yellow circles in the corners are S atoms without corresponding inner S atoms (sulfur vacancy crease). (b) HR-TEM image of a $\mathrm{Mo}{\mathrm{S}}_2$ nanoparticle with sharp turns. The region in the orange box has been enlarged and overlaid by a structural model.

Figure 8

A schematic view of introducing sulfur vacancy creases into a TMDC nanotube. (a) A regular nanotube. (b) A nanotube with surfur vacancy creases ($i=5$). (c) Expand the nanotube wall.