Plasticity resulted from phase transformation for monolayer molybdenum disulfide film during nanoindentation simulations

Self-Assembly of MoS2 Monolayer Sheets by Desulfurization

Self-assembled structures of two-dimensional (2D) materials exhibit novel physical properties distinct from those of their parent materials. Herein, the critical role of desulfurization on the self-assembled structural morphologies of molybdenum disulfide (MoS₂) monolayer sheets is explored using molecular dynamics (MD) simulations. MD results show that there are differences in the atomic energetics of MoS₂ monolayer sheets with different desulfurization contents. Both free-standing and substrate-hosted MoS₂ monolayer sheets show diversity in structural morphologies, for example, flat plane structures, wrinkles, nanotubes, and folds, depending on the desulfurization contents, planar dimensions, and ratios of length to width of MoS₂ sheets. Particularly, at the critical desulfurization content, they can roll up into nanotubes, which is in good agreement with previous experimental observations. Importantly, these observed differences in the molecular structural morphologies between free-standing and substrate-hosted MoS₂ monolayer sheets can be attributed to interatomic interactions and interlayer van der Waals interactions. Furthermore, MD results have demonstrated that the surface-driven stability of MoS₂ structures can be indicated by the desulfurization contents on one surface of MoS₂ monolayer sheets, and the self-assembly of MoS₂ monolayer sheets by desulfurization can emerge to adjust their surface-driven stability. The study provides important atomic insights into tuning the self-assembling structural morphologies of 2D materials through defect engineering in the future science and engineering applications.

Mechanical Properties of Monolayer MoS2 with Randomly Distributed Defects

The variation of elastic constants stiffness coefficients with respect to different percentage ratios of defects in monolayer molybdenum disulfide (MLMoS2) is reported for a particular set of atomistic nanostructural characteristics. The common method suggested is to use conventional defects such as single vacancy or di vacancy, and the recent studies use stone-walled multiple defects for highlighting the differences in the mechanical and electronic properties of 2D materials. Modeling the size influence of monolayer MoS2 by generating defects which are randomly distributed for a different percentage from 0% to 25% is considered in the paper. In this work, the geometry of the monolayer MoS2 defects modeled as randomized over the domain are taken into account. For simulation, the molecular static method is adopted and study the effect of elastic stiffness parameters of the 2D MoS2 material. Our findings reveals that the expansion of defects concentration leads to a decrease in the elastic properties, the sheer decrease in the elastic properties is found at 25%. We also study the diffusion of Molybdenum (Mo) in Sulphur (S) layers of atoms within MoS2 with Mo antisite defects. The elastic constants dwindle in the case of antisite defects too, but when compared to pure defects, the reduction was to a smaller extent in monolayer MoS2. Nevertheless, the Mo diffusion in sulfur gets to be more and more isotropic with the increase in the defect concentrations and elastic stiffness decreases with antisite defects concentration up to 25%. The distribution of antisite defects plays a vital role in modulating Mo diffusion in sulfur. These results will be helpful and give insights in the design of 2D materials.

Atomic Simulation of Nanoindentation on the Regular Wrinkled Graphene Sheet

Surface landscapes have vague impact on the mechanical properties of graphene. In this paper, single-layered graphene sheets (SLGS) with regular wrinkles were first constructed by applying shear deformation using molecular dynamics (MD) simulations and then indented to extract their mechanical properties. The influence of the boundary condition of SLGS were considered. The wrinkle features and wrinkle formation processes of SLGS were found to be significantly related to the boundary conditions as well as the applied shear displacement and velocity. The wrinkling amplitude and degree of wrinkling increased with the increase in the applied shear displacements, and the trends of wrinkling wavelengths changed with the different boundary conditions. With the fixed boundary condition, the degree of graphene wrinkling was only affected when the velocity was greater than a certain value. The effect of wrinkles on the mechanical characterization of SLGS by atomic force microscopy (AFM) nanoindentation was finally investigated. The regular surface wrinkling of SLGS was found to weaken the Young's modulus of graphene. The Young's modulus of graphene deteriorates with the increase in the degree of regular wrinkling.

Hysteresis and its impact on characterization of mechanical properties of suspended monolayer molybdenum-disulfide sheets

The hysteresis phenomenon frequently arises in two-dimensional (2D) material nanoindentation, which is generally expected to be excluded from characterizing the elastic properties due to the imperfect elastic behaviour. However, the underlying mechanism of hysteresis and its effect on the characterization of the mechanical properties of 2D materials remain unclear. Cyclic loadings are exerted on the suspended monolayer molybdenum-disulfide (MoS2) films in atomic force microscopy (AFM) nanoindentation experiments. The elastic hysteresis loops are observed for most of the force-displacement curves. The friction/wear between the AFM silicon tip and the MoS2 monolayer is deemed to be dominant compared to the friction between the monolayer and the silicon dioxide substrate after the analysis, as determined using the finite element method (FEM) simulation. The loading force-displacement curves instead of the unloading curves have been used to deduce the elastic mechanical properties using a modified regression equation. The mean value of the obtained Young's modulus of monolayer MoS2, E, is equal to 209 ± 18 GPa, which is close to the inherent stiffness value, predicted by first principles calculation. Our results have confirmed that it is not obligatory to exclude the sample data with hysteresis behaviour for characterizing the elastic properties of 2D materials. In addition, all sample sheets have finally been penetrated and the mean breaking stress value, σmax, is 36.6 ± 0.9 GPa, determined using the radius value of the worn tip. Furthermore, the effect of the loading force and the shape/size of the suspended monolayer MoS2 sheets on the hysteresis behaviour in the 2D nanoindentation have also been analyzed and discussed, exhibiting interesting trends. Our findings provide guidance for the characterization of the mechanical properties of 2D materials using the AFM nanoindentation and the experimental samples with elastic hysteresis behaviour.

Mechanical properties of molybdenum diselenide revealed by molecular dynamics simulation and support vector machine

Despite the spurring interests in two-dimensional transition metal dichalcogenide (TMDC) materials, knowledge on the mechanical properties of one of their important member, i.e., molybdenum diselenide (MoSe2) is scarce and remains an open topic. In this work, the mechanical properties of h-MoSe2 and t-MoSe2 were systematically investigated using classical molecular dynamics (MD) simulations combined with machine learning (ML) techniques. The effects of chirality, temperature and strain rate on fracture strain, fracture strength and Young's modulus were characterized in both armchair and zigzag directions. For h-MoSe2, the fracture strengths were 13.6 and 13.0 GPa for armchair and zigzag chiralities, respectively, at 1 K and strain rate of 5 × 10-4 ps-1; the corresponding fracture strains were 0.23 and 0.27. The Young's moduli in armchair and zigzag directions exhibited similar values of 100.9 and 99.5 GPa, respectively. For t-MoSe2, much lower fracture strengths of 6.1 and 6.3 GPa, fracture strains of 0.13 and 0.15, and Young's moduli of 83.7 and 83.0 GPa were predicted under the same conditions. A total of 700 MD simulation cases were calculated under different impact factors and initial conditions, which were subsequently fed into the support vector machine (SVM) algorithm for ML modeling. After training, the ML model could predict the mechanical properties of both MoSe2 types given only the input features such as chirality, temperature and strain rate.

Characterization of Frictional Properties of Single-Layer Molybdenum-Disulfide Film Based on a Coupling of Tip Radius and Tip⁻Sample Distance by Molecular-Dynamics Simulations

Lateral-force microscopy is a powerful tool to study the frictional properties of two-dimensional materials. However, few works distinctly reveal the correlation between the tip radius with the tip⁻sample distance and the frictional properties of the two-dimensional (2D) materials. We performed molecular-dynamics simulations to study the atomic-scale friction of a typical two-dimensional single-layer molybdenum disulfide (SLMoS₂). The effects of tip radius and tip⁻sample distance on the frictional properties were analyzed and discussed. The frictional force⁻sliding-distance curves show typical stick⁻slip behaviors, and the periodicity can be used to characterize the lattice constants of SLMoS₂. Sub-nanoscale stick-slip movements occur in one-lattice sliding periods along with only the armchair (AC) direction and only when the tip radius is smaller than 3 Å with 1.47 Å tip-sample distance. At the same tip⁻sample distance, a smaller tip can provide a more detailed characterization and higher-precision frictional properties of SLMoS₂. A larger tip is capable of providing comparative frictional properties of SLMoS₂ at a proper vertical tip⁻sample distance, compared with the small tip.

Phase Transition of Single-Layer Molybdenum Disulfide Nanosheets under Mechanical Loading Based on Molecular Dynamics Simulations

The single-layer molybdenum disulfide (SLMoS2) nanosheets have been experimentally discovered to exist in two different polymorphs, which exhibit different electrical properties, metallic or semiconducting. Herein, molecular dynamics (MD) simulations of nanoindentation and uniaxial compression were conducted to investigate the phase transition of SLMoS2 nanosheets. Typical load-deflection curves, stress-strain curves, and local atomic structures were obtained. The loading force decreases sharply and then increases again at a critical deflection under the nanoindentation, which is inferred to the phase transition. In addition to the layer thickness, some related bond lengths and bond angles were also found to suddenly change as the phase transition occurs. A bell-like hollow, so-called residual deformation, was found to form, mainly due to the lattice distortion around the waist of the bell. The effect of indenter size on the residual hollow was also analyzed. Under the uniaxial compression along the armchair direction, a different phase transition, a uniformly quadrilateral structure, was observed when the strain is greater than 27.7%. The quadrilateral structure was found to be stable and exhibit metallic conductivity in view of the first-principle calculation.

First-Principles Study on the Structural and Electronic Properties of Monolayer MoS₂ with S-Vacancy under Uniaxial Tensile Strain

Monolayer molybdenum disulfide (MoS₂) has obtained much attention recently and is expected to be widely used in flexible electronic devices. Due to inevitable bending in flexible electronic devices, the structural and electronic properties would be influenced by tensile strains. Based on the density functional theory (DFT), the structural and electronic properties of monolayer MoS₂ with a sulfur (S)-vacancy is investigated by using first-principles calculations under uniaxial tensile strain loading. According to the calculations of vacancy formation energy, two types of S-vacancies, including one-sulfur and two-sulfur vacancies, are discussed in this paper. Structural analysis results indicate that the existence of S-vacancies will lead to a slightly inward relaxation of the structure, which is also verified by exploring the change of charge density of the Mo layer and the decrease of Young’s modulus, as well as the ultimate strength of monolayer MoS₂. Through uniaxial tensile strain loading, the simulation results show that the band gap of monolayer MoS₂ decreases with increased strain despite the sulfur vacancy type and the uniaxial tensile orientation. Based on the electronic analysis, the band gap change can be attributed to the π bond-like interaction between the interlayers, which is very sensitive to the tensile strain. In addition, the strain-induced density of states (DOS) of the Mo-d orbital and the S-p orbital are analyzed to explain the strain effect on the band gap.

Effects of atomic vacancies and temperature on the tensile properties of single-walled MoS2nanotubes

Using molecular dynamics simulations, we study the effects of Mo and S atomic vacancies and different temperatures on the tensile properties of single-walled MoS₂nanotubes through a series of tensile tests.