A simple method for understanding the triangular growth patterns of transition metal dichalcogenide sheets

Abstract

Triangular nanoflake growth patterns have been commonly observed in synthesis of transition metal dichalcogenide sheets and their hybrid structures. Triangular nanoflakes not only show exceptional properties, but also can serve as building blocks for two or three dimensional structures. In this study, taking the MoS2 system as a test case, we propose a Matrix method to understand the mechanism of such unique growth pattern. Nanoflakes with different edge types are mathematically described with configuration matrices, and the total formation energy is calculated as the sum of the edge formation energies and the chemical potentials of sulfur and molybdenum. Based on energetics, we find that three triangular patterns with the different edge configurations are energetically more favorable in different ranges of the chemical potential of sulfur, which are in good agreement with experimental observations. Our algorithm has high efficiency and can deal with nanoflakes in microns which are beyond the ability of ab-initio method. This study not only elucidates the mechanism of triangular nanoflake growth patterns in experiment, but also provides a clue to control the geometric configurations in synthesis.

Atomic‐Scale Edge Morphology, Stability, and Oxidation of Single‐Layer 2H‐TaS2

“…[33][34][35] The triangular nanosheets of MoS 2 are the energetically favorable shape pattern in the different ranges of the chemical potential of sulfur. [36] For TaS 2 , the morphology variation from triangular to hexagonal shape was observed and attributed to the local changes of the Ta : S ratio of precursors. [14] We construct the phase diagram of the edge energy as a function of the sulfur chemical potential to determine preferred shape at various conditions according to the Wulff construction.…”

Homoepitaxial Growth of Large‐Scale Highly Organized Transition Metal Dichalcogenide Patterns

“…We also observed some three‐point star‐shaped MoS 2 crystals (Figure d). The observed morphological change originates from the anisotropic growth rates of different edges, where the relative stability of the edge structures is different under different sulfur chemical potential µ S . The formation energy (γ) for four different types of edges (Figure e) varies with µ S , as shown in Figure f.…”

Mo-Terminated Edge Reconstructions in Nanoporous Molybdenum Disulfide Film

“…In order to understand the formation mechanism of these edges, the formation energies of the different edges are calculated and plotted as a function of sulfur chemical potential 30 as shown in Figure 3a. Among the different edge terminations (DT (red), Mo-Klein (cyan), and S-ZZ edge (yellow)) along the S-ZZ chain direction, the S-ZZ edge shows increasing formation energy with decreasing sulfur chemical potential, in contrast to the other two edges.…”