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.

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.

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.

In this paper, molecular dynamics simulations were performed to investigate the atomic-scale imaging of a typical two-dimensional monolayer: molybdenum disulfide (MoS 2 ). With a constant height mode, force-displacement curves of tips along a straight-line scanning path indicate resonant waveforms and the periodicities are capable of characterizing lattice parameters of monolayer MoS 2 . Some characteristic sites in the forcedisplacement curves arise only for tips with a radius of less than 3 Å under 1.47 Å tip-sample distance, which correlated to the atoms next to the scanning path. Such characteristic sites can be reproduced by using tips with a radius of 7 Å via increasing the tip-sample distance. The underlying mechanism was illustrated by the number of interactive atoms between the tip and the sample. The work may shed light on the atomic force microscope (AFM) operation when one expects to achieve high-resolution AFM imaging of 2D materials with a worn AFM tip.