Engineered defects to modulate fracture strength of single layer MoS2: An atomistic study
Introduction
MoS2 is one of the most widely studied layered transition metal dichalcogenides (TMDs). Single layer MoS2 (SLMoS2) is an excellent super-conductor with a direct bandgap of 1.8 eV [1], this specific property of SLMoS2 is very promising to overcome the limitations of gapless graphene as such it can potentially play a tremendous role on widespread application areas in the field of energy conversion [2] and storage [3], photodetectors, integrated logic circuits, transistor [4], sensors [5], hydrogen evolution reactor (HER) [6], and optoelectronics [7]. In addition to excellent electronic properties, SLMoS2 also possesses some impressive mechanical properties including a well-balanced stiffness and flexibility that make it a favourable candidate for filler in nano-materials like nano-porous filter for water desalination [8].
The possibility of frequent exposure to elevated temperature and harsh chemical environment during manufacturing and real-life applications makes SLMoS2 susceptible to the growth and evolution of defects. Multi-atom defects such as cracks and pores can cause mechanical properties to compromise severely. Such defects are inevitable in many situations and often they are deliberately impressed upon the nanostructures to harness desired properties, especially in terms of electrical and optical properties and even to enhance mechanical stability for some nanomaterials. For example, MoS2 monolayers originated from chemical vapour deposition (CVD) usually exhibit much lower carrier mobility compared to the mechanically exfoliated SLMoS2. It is because, generally, various defects in 2-D sheets [[9], [10], [11]] are prevalent in chemical growth processes. In the applications of TMDs as nano-catalysts and dry lubricants, defects due to radiation damage are unavoidable and can cause severe structural damages if not carefully fabricated and maintained. SLMoS2 filters with nano-pores have emerged very recently exploiting their promising performance for membrane separation and pores which play the central role in this regard [12]. Suppression of defect formation is not possible or desired in such cases. One way to leverage the effort would be to engineer the defects and adopting a stress-engineering approach to minimize such defect induced damages and enhance the mechanical properties, if possible. Such enhancements were previously documented for several nanomaterials and it may be a curious research question if such an approach is suitable for TMD family of nanomaterials, including SLMoS2. Therefore, it is essential to investigate the effect of size and behaviour of deliberate poring and cracking on the mechanical properties of SLMoS2 not only to predict and prevent the mechanical failure but also to investigate if such defects can be exploited to enhance the mechanical properties itself.
Due to the widespread availability in nature, bulk MoS2 is a well-studied layered TMD. However, for the case of single to few-layer MoS2, the amount of study is still wanting. Bertolazzi et al. [13] exfoliated single and double layer MoS2 and measured the in-plane elastic modulus and the failure strength. Their measurement showed the strength of SLMoS2 to be close to the theoretical strength limit of Mo–S covalent bonds. Li [14] performed ab initio calculations to measure the strength of SLMoS2 and reported that the failure mechanism is attributed to the out of plane relaxation of atoms, different from non-buckled honeycomb structure of graphene. Moreover, distinct defect formation, reconstruction and their stability have been observed in case of SLMoS2 [9]. Bao et al. [15] used classical molecular dynamics (MD) simulations to investigate the crack propagation mechanism and fracture toughness of SLMoS2 and found that energy release rate in the fracture process decreases with increasing initial crack length, crack angle and temperature. They reported crack tip blunting due to stress concentration immediately before fracture propagation. Sulfur vacancy defects in MoS2 was reported to alter the crack propagation path of SLMoS2, resulting in an enhanced fracture toughness. Wang et al. [16] introduced patterned array of precisely controlled sub-nanometer (nm) pores down to 0.6 nm on SLMoS2 and showed the stability of pore adjacency closer than 5 nm. Although few studies were conducted concerning the mechanical properties and fracture mechanism aspects of pristine and cracked SLMoS2, there is a knowledge gap for porous SLMoS2, their elastic properties and fracture mechanism under tensile loading. Additionally, there is not enough computational or experimental study that helps to answer if mechanical properties of pre-cracked SLMoS2 sheets can be enhanced by prefabricated array of cracks or pores, as can be speculated from similar healing phenomenon previously found in Graphene [17] and Silicene [18].
In this work, we studied the mechanical properties of centrally-cracked and centrally-pored SLMoS2 at temperatures of 1K and 300K varying the crack size from 1.5 nm to 5.5 nm and diameter of the pore from 1 nm to 3 nm at a fixed strain rate. We compared the fracture strength and stress intensity factor against the Griffith theory. Additionally, geometries with central-crack and central-pore and the temperature effect on the crack-pore and primary crack-auxiliary crack combinations have also been investigated by varying temperature from 1K to 500K. To find out the interactions between crack-pore and primary crack-auxiliary cracks, we determined stress-strain relationship, stress and displacement distributions for different auxiliary crack and pore positions around the central primary crack, for both armchair and zigzag directional loading at 1K and 300K temperature. Finally, we also elucidate the fracture mechanism in all the cases studied here.
Section snippets
Methodology
We created 30 nm × 30 nm SLMoS2 sheets using a MATLAB [19] script. The effective thickness of the nanosheet is taken to be 0.61 nm [20]. It has been reported that in order to avoid size effects of finite dimension, the minimum dimension (either length or width) of nanosheet must be at least ten times the maximum half crack length present in the sheet [21,22]. Therefore, to study the effect of crack length on the fracture strength of SLMoS2 nanosheet, five cracks of different lengths
Method validation
In order to validate the approach used in the study, we applied uniaxial tension to both armchair and zigzag directions of the pristine 30 nm × 30 nm single layer MoS2 at 1K and 300K temperatures. The corresponding stress-strain curves are shown in Fig. 2. The calculated fracture strength and Young's modulus are then compared with literature [[20], [28]]. The comparison between the results is shown in Table 1. It is evident from the comparison that the results predicted in the present study are
Stress-strain relationships for nano-porous SLMoS2
The fracture strength of porous SLMoS2 largely depends on the pore size. Such dependency can be found in Fig. 3 for five nanopores with diameters between 1 and 3 nm for both armchair and zigzag loading directions. Detailed stress-strain relations are presented in Supplementary Fig. S2 (b),(d) (in armchair loading) and (a),(c) (in zigzag loading), where the calculated stress is the nominal stress in the SLMoS2. Here, single nanopore is located at the centre of the sheet. Thus, the size of the
Conclusion
In summary, we performed molecular dynamics simulations to investigate the mechanical properties and fracture behaviour of deliberately cracked and pored SLMoS2 structure. We checked the result for different crack lengths and pore diameters. Increase in crack length and pore diameter leads to degradation of fracture strength, matching with the general trend of Griffith's brittle fracture model. However, Griffith's prediction underestimates the fracture stress, indicating the limitation of the
Author contribution
All authors contributed equally.
Declaration of competing interest
There are no conflicts to declare.
Acknowledgement
The authors of this paper would like to convey their thankfulness to Multiscale Mechanical Modeling and Research Network (MMMRN) group of BUET for their technical support. M.M.I acknowledges the support from Wayne State University startup funds.
References (48)
- et al.
Transition metal oxide nanoparticles as efficient catalysts in oxidation reactions
Nano-Struct. Nano-Objects
(2018) - et al.
Graphene nanoscrolls fabricated by ultrasonication of electrochemically exfoliated graphene
Nano-Struct. Nano-Objects
(2017) - et al.
Tailoring fracture strength of graphene
Comput. Mater. Sci.
(2018) Fast parallel algorithms for short-range molecular dynamics
J. Comput. Phys.
(1995)- et al.
Investigation on mechanical properties of polycrystalline W nanowire
Comput. Mater. Sci.
(2017) - et al.
Atomistic simulations of nanoscale crack-vacancy interaction in graphene
Carbon
(2017) - et al.
Fracture toughness of graphene
Nat. Commun.
(2014) - et al.
Mode-I stress intensity factor in single layer graphene sheets
Comput. Mater. Sci.
(2016) - et al.
Few-layer MoS2: a promising layered semiconductor
ACS Nano
(2014) - et al.
Enhancement of photovoltaic response in multilayer MoS2 induced by plasma doping
ACS Nano
(2014)