- Nano Express
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The Effect of VMoS3 Point Defect on the Elastic Properties of Monolayer MoS2 with REBO Potentials
© Li et al. 2016
Received: 2 December 2015
Accepted: 15 March 2016
Published: 22 March 2016
Structural defects in monolayer molybdenum disulfide (MoS2) have significant influence on the electric, optical, thermal, chemical, and mechanical properties of the material. Among all the types of structural defects of the chemical vapor phase-grown monolayer MoS2, the VMoS3 point defect (a vacancy complex of Mo and three nearby S atoms) is another type of defect preferentially generated by the extended electron irradiation. Here, using the classical molecular dynamics simulation with reactive empirical bond-order (REBO) potential, we first investigate the effect of VMoS3 point defects on the elastic properties of monolayer MoS2 sheets. Under the constrained uniaxial tensile test, the elastic properties of monolayer MoS2 sheets containing VMoS3 vacancies with defect fraction varying from 0.01 to 0.1 are obtained based on the plane anisotropic constitutive relations of the material. It is found that the increase of VMoS3 vacancy concentration leads to the noticeable decrease in the elastic modulus but has a slight effect on Poisson’s ratio. The maximum decrease of the elastic modulus is up to 25 %. Increasing the ambient temperature from 10 K to 500 K has trivial influences on the elastic modulus and Poisson’s ratio for the monolayer MoS2 without defect and with 5 % VMoS3 vacancies. However, an anomalous parabolic relationship between the elastic modulus and the temperature is found in the monolayer MoS2 containing 0.1 % VMoS3 vacancy, bringing a crucial and fundamental issue to the application of monolayer MoS2 with defects.
The monolayer molybdenum disulfide (MoS2) is a graphene-like crystal with quasi-two-dimensional (2D) honeycomb lattice, consisting of a monatomic Mo-layer sandwiched between two monatomic S-layers. The pristine monolayer MoS2 holds many remarkable physical and chemical properties for its intrinsic direct bandgap of 1.8 eV  and high elastic modulus of ~0.2 TPa, which strongly promises for burgeoning 2D nanodevices, including transistor , field-effect transistor , phototransistors , nanomechanical resonator , and photodetector . However, the structural defects can be commonly observed [7, 8] or deliberately introduced  in the monolayer MoS2, which have significant influence on its electrical conductivity , electrical contacts , band-to-band tunneling , catalytic , photoluminescence , magnetism , and thermal conductivity .
Structural defects, nine types of point defects (including vacancies and antisite defects), have been recently defined and characterized via atomic resolution imaging and first-principle calculation [7, 8]. The monosulfur vacancy (VS) is the most common point defect, frequently observed in experiments for its lowest formation energy (1.1 eV) . So far, there are few documents concerning its impacts on the mechanical properties [17, 18], which can be momentous in MoS2 engineering applications. Dang and Spearot  conducted molecular dynamics (MD) nanoindentation simulations to investigate the VS effect on the mechanical behavior of monolayer MoS2. They revealed that the VS defects weaken the breaking force and induce displacive phase transformations under indentation. Gan and Zhao  performed first-principle calculations to show that the chirality effect on the mechanical properties of monolayer MoS2 becomes more and more significant with the increasing of strain, regardless of vacancies. Besides VS, VMoS3 (a vacancy complex of Mo and three nearby S atoms) is another type of defect preferentially generated by the extended electron irradiation . However, there is still a lack of reports on the VMoS3 effect on the mechanical properties of monolayer MoS2.
Hence, in this letter, the mechanical properties of monolayer MoS2 containing VMoS3 (V-MoS2) with defect fraction from 0.01 to 0.1 are first investigated under the constrained uniaxial tensile test (CUATT) using MD simulation with reactive empirical bond-order (REBO) potential [19–21]. The REBO interatomic potential has been recently utilized to calculate the breaking force of monolayer MoS2 with VS defects  and has been demonstrated to be more effective in simulating the elastic behavior of monolayer MoS2  than other interatomic potentials such as consistent valence force field (CVFF) and Stillinger-Weber (SW), under a small deformation (tensile strain ε < 5 %). Under the CUATT, the elastic properties of monolayer MoS2 sheets containing VMoS3 vacancies with defect fraction varying from 0.01 to 0.1 are obtained based on the plane anisotropic constitutive relations of the material. From our simulation results, it is found that the increase of VMoS3 vacancy concentration leads to the noticeable decrease in the elastic modulus but has a slight effect on Poisson’s ratio. The maximum decrease of the elastic modulus is up to 25 %. Increasing the ambient temperature from 10 K to 500 K has trivial influence on the elastic modulus and Poisson’s ratio for the monolayer MoS2 without defect and with 5 % VMoS3 vacancies. However, an anomalous parabolic relationship between the elastic modulus and the temperature is found in the monolayer MoS2 containing 0.1 % VMoS3 vacancy, which is in conflict with the previous work using the SW potential  and bringing a crucial and fundamental issue to the application of monolayer MoS2 with defects.
Specially, C 11 = C 22 implies the 2D isotropic material. Furthermore, the engineering constants E i and v ij will be derived from the elastic constants of C ij after the CUATT. The intrinsic elastic constants of C ij are extracted from the slope of a perfect linear range of stress-strain curves. A strain increment of ∆ε = 5 × 10−5 is used among energy minimizations and following MD simulations .
Results and Discussion
The thermal dependence of elastic properties of V-MoS2 is subsequently investigated with MD simulations, with a given defect fraction of 0.05 and under the temperature varying from 10 K to 500 K. Before the CUATT, the simulation box is relaxed for 20 ps with the NPT ensemble to bring the system to the desired temperature and pressure condition (0.1 bar). After the relaxation, the ensemble is switched to NVT, and the strain increment is applied via scaling the box length in the specified direction (zigzag for instance) and fixing the other orthogonal directions, to carry out the CUATT. The positions of system atoms are not remapped to the new box when the box is stretched, in order to keep the tensile stress consistent. In all MD simulations, the equations of motion are integrated by means of standard velocity - Verlet method with a 1-fs time step. The temperature and pressure conditions are controlled using the original Nose-Hoover thermostat and barostat.
As shown in Fig. 5, Poisson’s ratio ν 12 (circles) and ν 21 (squares) of the defect-free MoS2 sheets slightly decrease as the temperature increases, excluding the data of ν 12 at 300 K and 400 K. However, Poisson’s ratio ν 12(diamonds) and ν 21 (stars) of V-MoS2 sheets slightly fluctuate as the temperature increases, in which the maximum amplitude does not exceed 2 %. The fluctuation can be attributed to the vacancies, which allow the ambient atoms to vibrate violently. As for Young’s modulus, the defect-free MoS2 sheet and the V-MoS2 sheet both show little dependence on the system temperature.
The temperature dependence of the defect-free MoS2 sheet obtained from our simulations with REBO potential is entirely contrary to the work of Zhao etal.  using the SW potential, in which Young’s modulus of perfect monolayer MoS2 obviously decreases with increasing the ambient temperature from 4.2 K to 500 K. They obtained the maximum reduction of Young’s modulus more than 30 %. However, the temperature dependence of the defect-free MoS2 with REBO potential in this paper is comparable to that of graphene , in which the maximum reduction of Young’s modulus is about 5 % when the system temperature increases from 300 K to 700 K. We believe that such result distinction is mainly derived from the adoption of different interatomic potentials and the processing procedure, as the co-worker of Zhao published another totally different result , in which Young’s modulus of perfect MoS2 is independent to the temperature range from 0 K to 300 K.
In conclusion, we first investigate the mechanical properties and the thermal dependence of monolayer MoS2 containing VMoS3 vacancies with defect fraction varying from 0.01 to 0.1 under the constrained uniaxial tensile test using MD simulation with REBO potential. Our simulation results show that the VMoS3 vacancy concentration has noticeable influence on the elastic modulus but has a slight effect on Poisson’s ratio. Increasing the ambient temperature from 10 K to 500 K has trivial influence on the elastic modulus and Poisson’s ratio for the monolayer MoS2 without defect and with 5 % VMoS3 vacancies. However, an anomalous parabolic relationship between the elastic modulus and the temperature is found in the monolayer MoS2 containing 0.1 % VMoS3 vacancy and bringing a crucial and fundamental issue to the application of monolayer MoS2 with defects.
The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (Grant No. 50903017) and the Fujian Collaborative Innovation Center of High-End Manufacturing Equipment. MLL would like to thank the financial support from the China Scholarship Council during his visit to Rice University. The authors thanks Tao Liang for his support on the LAMMPs code of REBO potentials.
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