Grain-Size-Controlled Mechanical Properties of Polycrystalline

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Grain-size Controlled Mechanical Properties of Polycrystalline Monolayer MoS Jianyang Wu, Pinqiang Cao, Zhisen Zhang, Fulong Ning, songsheng zheng, Jianying He, and Zhiliang Zhang Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b05433 • Publication Date (Web): 01 Feb 2018 Downloaded from http://pubs.acs.org on February 1, 2018

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Grain-size Controlled Mechanical Properties of Polycrystalline Monolayer MoS2 Jianyang Wu,1, 2, * Pinqiang Cao,1, 3 Zhisen Zhang,1 Fulong Ning,3 Song-sheng Zheng,4 Jianying He,2 and Zhiliang Zhang2, * 1

Department of Physics, Research Institute for Biomimetics and Soft Matter, Fujian Provincial Key Laboratory for Soft Functional Materials Research, Xiamen University, Xiamen 361005, P. R. China 2

NTNU Nanomechanical Lab, Department of Structural Engineering, Norwegian University of Science and Technology (NTNU), Trondheim 7491, Norway 3

Faculty of Engineering, China University of Geosciences, Wuhan, Hubei 430074, P. R. China 4

College of Energy, Xiamen University, Xiamen 361005, P. R. China

Abstract: Pristine monocrystalline molybdenum disulphide (MoS2) possesses high mechanical strength comparable to that of stainless steel. Large-area chemical-vapor-deposited monolayer MoS2 tends to be polycrystalline with intrinsic grain boundaries (GBs). Topological defects and grain size skillfully alter its physical properties in a variety of materials; however, the polycrystallinity and its role played in the mechanical performance of the emerging single-layer MoS2 remain largely unknown. Here, using large-scale atomistic simulations, GB structures and mechanical characteristics of realistic single-layered polycrystalline MoS2 of varying grain size prepared by confinement-quenched method are investigated. Depending on misorientation angle, structural energetics of polar-GBs in polycrystals favor diverse dislocation cores, consistent with experimental observations. Polycrystals exhibit grain size dependent thermally-induced global out-of-plane deformation, although defective GBs in MoS2 show planar structures that are in contrast to the graphene. Tensile tests show that presence of cohesive GBs pronouncedly deteriorates the in-plane mechanical properties of MoS2. Both stiffness and strength follow an inverse pseudo Hall-Petch relation to grain size, which is shown to be governed by the weakest link mechanism. Under uniaxial tension, transgranular crack propagates with small deflection, whereas upon biaxial stretching the crack kinkily grows with large deflection. These findings shed new light in GB-based engineering and control of mechanical properties of MoS2 crystals towards real-world applications in flexible electronics and nanoelectromechanical systems. Keywords: dislocation core; inverse pseudo Hall-Petch; grain boundary; MoS2; polycrystallinity; thermal annealing *

Email: [email protected], [email protected] Page 1 of 24

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Introduction Two dimensional (2D) transition metal dichalcogenide crystals (TMDCs), consisting of a transition metal layer sandwiched between two chalcogenide layers in a trigonal prismatic structure, have attracted enormous attention in recent years because of their distinctive electrical, optical and mechanical characteristics.1-4 Single-layer molybdenum disulfide (MoS2), as the most representative 2D TMDCs, is a typical direct gap semiconductor with an intrinsic band-gap of about 1.8 eV thanks to quantum confinement.5 Single-layer MoS2 also shows excellent intrinsic electronic mobility and high on-off ratios.6 Such a host of fascinating properties render single-layer MoS2 interesting not only for fundamental studies of novel physical phenomena but also for a wide range of novel applications in electronics systems, such as field-effect transistor, phototransistors, optoelectronics, nanoelectromechanical devices and so on.5-10 To realize the above-mentioned application potentials, scalable preparation of high-quality and large-area single-layer MoS2 crystals with low cost is highly desirable. Limited by the currently state-of-the-art fabrication approaches, including mechanical exfoliation, chemical exfoliation, and chemical vapour deposition (CVD) growth, however, it is still a daunting challenge to produce large-area pristine monocrystalline MoS2. For example, both mechanical and chemical exfoliations are limited to small flakes of single-layer pristine monocrystalline MoS2 and inevitably generate native crystalline defects in MoS2.3,

11-13

In contrast, CVD synthesis is capable of producing

high-yield and large-area MoS2, but a major disadvantage of this technique is that, as a consequence of multiple nucleation sites on substrates, it often results in the formation of polycrystalline microstructures consisting of multiple grains joined by a variety of grain boundaries (GBs).2, 3, 13-15 GBs in as-grown polycrystalline MoS2 appear as a kind of topological lattice defects. It has been well-documented that topological defects and crystalline domain size in graphene subtly alter its physical properties.14, 16-18 Consequently, a number of studies have recently been carried out to gain knowledge about the topological defects and crystalline size of MoS2, as well as their roles in electrical, magnetic, optical and thermal properties.19-30 Similar to graphene, three types of topological defects in monolayer MoS2, including point defects, dislocations and GBs, have been identified under various laboratory-settings. For example, using atomic-resolution annular dark field image on an aberration-corrected scanning transmission electronic microscope (ADF-STEM), Zhou et al.21 identified 6 different point defects in polycrystalline MoS2 grown by CVD, including Page 2 of 24


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monosulfur vacancy (Vs), disulfur vacancy (Vs2), vacancy complex of Mo and nearby 3-sulfur (VMoS3), vacancy complex of Mo nearby 3-disulfur pairs (VMoS6), and antisite defects where a Mo atom substituting a S2 column (MoS2) or a S2 column substituting a Mo atom (S2Mo). Based on the polygonal ring numbers, a variety of topological dislocation cores, including 5|7, 4|4, 4|6, 4|8 and 6|8 fold-rings, that primarily compose various GBs in CVD-grown polycrystalline MoS2, have been discovered by first-principle calculations and by ADF-STEM imaging. GB structures in CVD-grown MoS2 monolayers altered the electrical conductivity, whereas GBs in metal-organic CVD synthesized MoS2 sheets exhibited less disturbance on the spatial homogeneity of transport characteristics.20,

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Moreover, a size-dependent electrical performance was discovered in

polycrystalline MoS2 with nano-sized grains, but not in polycrystals with micro-sized grains.19, 24 Depending on the atomic structure of GBs, two types of long-range magnetic orderings in the polycrystalline MoS2 were generated; GBs composed of 5|7 dislocations were ferromagnetic while GBs made of 4|8 rings showed anti-ferromagnetic behavior.30 Because of destructive interference of waves from adjacent grains, GBs in polycrystalline MoS2 led to reduction in intensity of nonlinear optical response.23 Using 2-laser Raman thermometry, a 100-fold reduction in the in-plane thermal conductivity of polycrystalline MoS2 membranes with respect to the bulk was revealed, resulting from remarkable scattering on the GBs.28 Moreover, theoretical calculations showed a scaling trend of the thermal conductivity with the grain size of polycrystalline MoS2.28 There have also been a number of pioneering studies examining the mechanical properties of defect-free MoS2, both experimentally and theoretically.9, 31-37 Yet, very few attempts have been made to assess the effect of topological defects on the mechanical properties of MoS2 crystals.38-43 Using computer simulations, it was revealed that point defects, including V1S, V2S, VMo, VMoS2 and VMoS3, degrade the in-plane tensile properties of single-crystal MoS2 because of stress-concentration at the defect locations.39, 43 Very recently, in-situ experiments and molecular dynamics (MD) simulations showed that the crack propagating behavior in crystalline domain of CVD-grown monolayer MoS2 was governed by the concentration of point defects ahead of the crack tip zone and exposed environments.41,

42

For example, crack deflections occurred in sparse vacancy defects of MoS2

crystals, while, as a result of migration of vacancies in the strain fields into networks, a transition from brittle to ductile in fracture mechanism was discovered as the density of vacancy defects exceeds a critical value.42 Page 3 of 24


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Despite the above-mentioned studies, how the nature and presence of dislocation, GB and GB-junction (GBJ) defects as well as crystalline grain size influence the overall mechanical properties of CVD-synthesized monolayer MoS2 still remains unexplored and is of both scientific importance and technological significance for its application potentials in flexible devices. Here, large-scale MD simulation with first-principle based reactive empirical potential is adopted to examine the structures and in-plane mechanical characteristics of freely hanging polycrystalline MoS2. The 2D Voronoi polycrystals experiencing a confinement-quenched process show well-stitched GBs and GBJs composed of experimentally observed dislocation cores. Mechanical tests reveal that presence of GBs and GBJs significantly degrades the mechanical properties of MoS2 sheet. Stiffness and strength of polycrystals are markedly sensitive to the grain size, showing an inverse pseudo Hall-Petch weakening behavior. This grain size-induced weakening phenomenon can be depicted by a weakest-link mechanism. Polycrystals fail by brittle breakage of bonds at GBs and GBJs, and kinked transgranular crack propagation along armchair and zigzag directions is detected. Finally, it is shown that the limitation of mechanical performance of polycrystalline MoS2 with cohesive GBs can be possibly improved by controlling the grain size. Results and Discussion GB Structures in Polycrystalline MoS2 Large-area MoS2 produced by CVD is often of polycrystalline nature, where the internal pristine crystalline grains are stitched together by disordered GBs. Figures 1a and b show the perspective side- and top-viewed molecular structures of annealed polycrystalline MoS2 with average grain size of 12 nm, respectively, and with atoms colored according to their grain number and ring type. Apparently, as a result of misorientation angles between the crystal lattices of grains, Mo and S atoms locating at the GBs mostly form non-hexagonal ring structures, highlighting the networks of disordered GB in polycrystals. Figure 1c displays typical distribution of von Mises stress in polycrystalline MoS2 under stress-free loading condition. Rather heterogeneous atomic-level stress is presented in the vicinity of GBs and GBJs. For example, as a result of dislocation cores in the GBs, dipolar-like stress fields along the GBs are readily observed. In contrast, uniform atomic-level stress is observed in the bulk of grains. Clearly, stress concentrates locally at the GBs and GBJs. Local lattice is distorted by dislocation cores at the GBs and GBJs.

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Figures 1d and e present the zoomed-in microstructures of a GB loop and a double Y-shaped GBJ. It is revealed that GBs and GBJs are dominantly composed of diverse dislocation cores, including not only the conventional 5|7 ring pairs, but also intriguing 4|4, 4|6, 4|8 and 6|8 fold-rings, distinctly differing from GBs reported in graphene. Moreover, point defects like S and Mo vacancies are also present in polycrystals. Such complex GB structures in 2D-TMDCs have also been showed by recent first-principles calculations and experiments.12, 20-22, 44 As shown in Figures 1d and e, 5|7 and 6|8 dislocations coexist in GBs with intermediate inter-grain misorientation angles, and both type and density of dislocation are determined by the misorientation angle. For example, high-angle tilt GB belonging to grains 1 and 4 in Figure 1d consists of dense 5|7 and 6|8 dislocations, while low-angle tilt GB separating grains 2 and 5 primarily contains isolated 5|7 (non-closing Burger’s circuit as marked by a loop red-arrow in Figure 1d). In particular, the highest-tilt 60° GB shared by grains 1 and 4 in Figure 1e is mainly composed of connected 4|8 dislocation, which is consistent with recent theoretical and experimental data.20-22 In contrast to graphene with six-fold symmetry, bi-elemental MoS2 with three-fold symmetry has two types of 5|7, 6|8 and 4|6 dislocations, as highlighted in right side of Figure 1. Microscopically, Mo-rich 5|7 type of dislocation, labeled as Mo5|7, is structurally featured by a distinctive Mo-Mo homo-elemental bond shared by penta- and heptagon in the center of the dislocation core, whereas S-rich 5|7 dislocation (S5|7) has two S-S homo-elemental bonds connecting penta- and heptagon. 6|8 dislocations can be yielded by inserting Mo or S into the homo-elemental bonds of 5|7 structure, as by reaction of Mo5|7+S/2S → 6|8s, or S5|7+Mo → 6|8m. Notably, to our knowledge, only 6|8s dislocation has been experimentally identified in MoS2/WS2 so far.21,

45

On the contrary, 4|6 structures can be generated from 5|7

dislocations by deleting a single Mo or a pair 2S that originally form the homo-elemental bonds, as by reaction of Mo5|7-Mo → 4|6m, or S5|7-2S → 4|6s. Thermal Rippling Characteristics in Polycrystalline Monolayer MoS2 It is expected that structural defects and thermal-induced position fluctuations at finite temperature distort the free-standing 2D crystalline lattices. Consequently, a freely hanging 2D crystal is not strictly perfect planar but in fact possesses intrinsic microscopic roughening that is bound to modulate the electronic properties. Figure 2a shows the atomic landscape of out-of-plane displacement field of polycrystalline MoS2 with average grain size of 12 nm. The color code

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indicates atomic displacements along the out-of-plane (z) direction. Interestingly, free-standing MoS2 membrane exhibits a 2D checkerboard corrugated pattern h ( x , y ) = H sin(2π x / λ ) sin(2π y / λ ) , where H and λ

are the amplitude of out-of-plane fluctuation and the distance between

neighboring ripples, respectively. Intrinsically, the temporal and spatial alteration of Mo-S, S-S and Mo-Mo bond-lengths of isotropic polycrystalline MoS2 drives Mo and S atoms to occupy space in normal (z) direction, resulting in 2D ripples. Experimental characterizations, however, showed that substrate-hosted MoS2 films feature one-dimensional (1D) periodic ripple structures.46 One reason for this is that, due to distinctive mismatch in thermal expansion between MoS2 and substrate, MoS2 membrane is constrained and thus forms 1D ripple patterned morphology as temperature varies. In addition, smooth gradient field of out-of-plane displacement across GBs in MoS2 indicates planar structure of defective GBs, rather than vertical buckled/wrinkled topology that has been commonly observed in GBs of one-atomic thick graphene and boron nitride (BN).16-18,

47

Previous studies

showed that point defects and dislocation cores at GBs locally introduce marked levels of in-plane strain but negligible out-of-plane deformation to accommodate host lattice mismatch in MoS2/WS2.21, 45

Figure 2b plots atomic and mean out-of-plane corrugations against their positions in one planar (x) direction. Sinusoidal deformation of the monolayer polycrystal is identified, as indicated by a

 

sinusoidal function ( f ( x) = h0 + A sin  π x

1− c   ) that is fitted to the out-of-plane corrugation of all w 

atoms in the cell. To further quantify the spontaneously formed ripples, mean out-of-plane displacement amplitude of the whole MoS2 sheet with different nanograin size is calculated by

h =

N

N

i

i

∑ mi ( hi − hcom ) 2 / ∑ mi

(1)

where hcom is the center-of-mass position in the normal (z) direction of freely hanging polycrystals composed of N atoms, hi and mi are the position in the normal (z) direction and mass of the i atom, respectively. Figure 2c shows the calculated

h

h

as a function of grain size. It is found that the

of polycrystalline MoS2 remarkably depends on the grain size, i.e. decreasing with increasing

crystalline grain size. According to the elastic theory of thermal fluctuations in thin membranes, Page 6 of 24


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mean-square displacement in the normal (z) direction of the membrane is described by 48

h2 =∑ q

TN T ∝ L2 4 kS0q k

(2)

where L, S0, N and k are the edge length, area per atom, total atoms and bending rigidity of planar sample, respectively. T and q are the temperature and wave-vector, respectively. Therefore, although GBs do not cause vertical deformation, grain size dependence of

h

suggests that grain size

influences the out-of-plane structural flexibility of MoS2. Effect of Annealing Temperature on Mechanical Response of Polycrystals Metastable GB structures of MoS2 are susceptible to reconstruct and migrate during CVD and annealing processes. Such change of GB structures could greatly change its properties of MoS2 lattice. Figure 3 presents the overall uniaxial tensile stress-strain responses and top-viewed snapshots of polycrystalline MoS2 with mean grain size of 3 nm under annealing temperature ranging from 1000 - 3000 K for 1100 ps, respectively. It is observed that the annealing temperature has a profound effect on the mechanical response of polycrystalline MoS2; the ultimate strength reduces as the annealing temperature decreases. This indicates that high temperature annealing produces more mechanically robust polycrystalline MoS2 specimens. Such difference in mechanical response is attributed to the different scenarios of reconstruction and migration of GBs in the polycrystals under annealing processing. As shown in Figures 3b-f and S1, polycrystal, under different annealing temperatures, exhibits distinctive grain morphology and von Mises stress fields. Upon thermal annealing at 1000-2000 K, complex networks of GBs are detected, and limited changes in polycrystalline microstructures take place through reconstruction of GBs and merging of neighboring grains with low misorientation angle (Figures 3b-d). Under annealing beyond 2000 K, however, polycrystals show remarkable changes in polycrystalline grain morphology as result of large-scale coalesces of grains and reconstruction and migration of GBs (Figures 3e and f). Recently, it has also been reported the merging behavior of CVD-grown monolayer polycrystalline MoS2 via experimental characterizations.49 Additionally, point defects and isolated dislocation cores are present in as-coalesced grains of annealed polycrystal, as indicated by isolated non-hexagonal rings

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and irregular local stress in the grain interior (Figures 3e and f, S1e and f ). Effect of Annealing Time on Mechanical Response of Polycrystals Upon heating, polycrystalline MoS2 shows metastable GB structures that dynamically change. Figure 4 shows the resulting uniaxial tensile stress-strain curves and evolution of one typical grain in the polycrystalline MoS2 with average grain size of 3 nm along with annealing time up to 1100 ps at 2000 K. Similarly, the annealing time strongly affects the mechanical response of polycrystalline MoS2; both ultimate strength and failure strain are enhanced with increasing of annealing time, originating from that changes in GB and GBJ microstructures with the annealing process facilitate the stabilization of polycrystalline structures. This observation is in sharp contrast to polycrystalline graphene, where Gamboa showed a clear reduction in ultimate strength with increasing annealing time by MD simulations.50 As shown in Figures 4b-f, complex structural defects are identified in both GBs and GBJs. Plenty of dislocation cores and point defects in GBs and GBJs actively react to form derivative families, resulting in formation of cohesive GB and GBJ structures, as indicated by the decrease of gray region area in Figures 4b-f. For instance, during the annealing process, a defective structure consisting of 5|9+4|6 in the left GB of the captured grain shows a unique evolution pathway of 5|9+4|6 → 4+6|8m+6|8m → 5|6|8+4|6 → 6|8m+6|8m → 4+6|8m+6|8m. However, two neighboring S5|7 dislocations with vertical alignment are structurally stable during the thermal annealing. In addition, the effective interaction between specifically aligned dislocation cores also generates derivative families. For example, two neighboring 6|8m dislocations with vertical alignment in S-rich environment react first to form an intermediate motif of 6|8m + 4|9, and finally to yield 4|6|8s motif, whereas two vertically aligned 6|8m dislocations separated by a Mo-S bond are not able to generate derivative defects. This indicates that reconstruction of GBs and GBJs not only depends on the composed dislocations and their local environments but also on the arrangement of dislocations. Particularly, an isolated 6|8m dislocation core self-reconstructs to yield a 4|6s dislocation. As a whole, 6|8m dislocation tends to reconstruct, yet explaining the uncovery of 6|8m dislocation in CVD-grown MoS2 samples. Based on first-principle calculations, a series of glide of dislocation cores and two different migrating dislocations have been predicted.12, 51 The observed complex dynamics in GBs and GBJs are primarily attributed to the nature of flexible coordination of S atom and the relatively weak Mo-ligand bonds. This facilitates transformation of Page 8 of 24


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dislocation structures, resulting in dislocation glide and GB migration. Evolution of grain morphologies in a typically polycrystalline MoS2 with mean grain size of 3 nm during the annealing process at 2000 K is recorded in Movie S1. Grain Size-induced Weakening in Polycrystalline MoS2 Crystals In nanocrystalline materials, internal crystalline grain size governs their mechanical properties by either enhancement or weakening, depending on the distinctive microscopic deformation mechanisms.16-18, 52-54 Effect of grain size on the mechanical behaviors of polycrystalline MoS2 under external loading is therefore explored. Figures 5a and b show the typical stress-strain responses of polycrystals with seven different mean grain sizes subjected to uniaxial and biaxial straining, respectively. Three typical deformation stages are identified. Initial ramp of stress-strain curves is a characteristic of entropic elastic response, originating from nanoscale de-wrinkling of monolayer MoS2. This is in agreement with previous MD simulations of other 2D polycrystalline materials.17, 18, 47

The grain size dependent amplitude of intrinsically out-of-plane displacement (Figure 2c) explains

the difference in the initial stretching responses of polycrystalline MoS2. In the second stage, mechanical loads are directed on the bonds in the bulk of grains and GBs, and the stretching stress markedly increases as the increase of the applied strain. The stretching curves in this stage are also grain size dependent. In the last stage, the stretching stress sharply declines as the applied strain is over critical value, indicative of brittle rupture behavior. Figures 5c-h plot the Young’s modulus, ultimate strength and breaking strain of the polycrystals under uniaxial and biaxial tension as a function of mean grain size, respectively. For each mean grain size, eight samples are produced with different initial GB configurations for statistical mechanical analysis. For single-crystalline MoS2, the present simulation yields Young’s modulus of 158.2 and 157.7 GPa, ultimate strength of 27.3 and 26.6 GPa along armchair and zigzag directions (Figure S2), respectively, consistent with previous MD simulation and ab initio data.37, 42 Obviously, polycrystal shows a remarkable reduction in the in-plane mechanical properties, indicating that GBs and GBJs have a detrimental effect on the mechanical performance of MoS2. Such GB-induced weakening phenomenon has been identified in other latticed structures.16, 50, 55, 56 Dislocation-dominated GBs and GBJs in polycrystalline MoS2 show longer bonds than those in bulk of grains (Figures S3a-c, g and h). Because of coherent inharmonicity of those bonds, GBs and GBJs are highly Page 9 of 24


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stress-concentrated (Figure 1c and Figure S3d-f) and are mechanically weakened. GBs and GBJs behaving as weak links are the origin of apparent weakening behavior of MoS2. Moreover, polycrystal exhibits grain size dependent in-plane mechanical properties. As grain size is reduced, both uni- and bi-axial tensile stiffness and ultimate strengths decrease, showing an inverse pseudo Hall-Petch weakening behavior. Such grain size-induced weakening has also been discovered in nanocrystalline metals, graphene and methane hydrate.18, 52-54 Here the weakest-link model57 is employed to explain the weakening phenomenon in polycrystalline MoS2. The weakest-link model assumes that a brittle structure is made up of small substructures linked together, and that the brittle structure fails as any one of substructures or weakest links fails. It states that failure strength of a brittle structure follows a power-law relationship with the number of weak links in the structure. Based on the model, defective GBs and GBJs in present brittle polycrystalline MoS2 are the weak links and tend to initiate cracks. For 2D polycrystals with fixed edge-length, density of GBs and GBJs versus grain size follows power-law relation. Besides, it is observed that polycrystals with smaller grain size show a broader distribution of bond length, bond angle and stress (Figures S4 and S5), indicating higher maximum stress in GBs and GBJs of polycrystal with smaller grains. High stress concentration occurs on the GBs and GBJs where catastrophic failure of the polycrystal initiates. Such size-dependent stress-concentration mechanism is different from the polycrystalline graphene where grains stitched together by 5|7 dislocations are ideally hexagon-shaped.17 The above analysis explains the inverse pseudo Hall-Petch weakening in poycrystalline MoS2. For macroscopic polycrystalline MoS2 with micrometer-sized grains, the mechanical strength is expected to be close to the pristine MoS2. Therefore, polycrystal with large grains is preferred for achieving high tensile mechanical performance of monolayer MoS2 sheet. To further explore the failure mechanisms, deformation developments of polycrystals with different grain sizes under uniaxial and biaxial tensions are examined. Results reveal that polycrystals preferentially fail from GBs and GBJs and show both intergranular and transgranular cracking behaviors, independent of grain size. Figures 6a-i show the typical failure process of a polycrystal under uniaxial stretching. For more clarification, the corresponding deformational structures of the middle Mo-layer are individually captured and shown in Figure S6. It is observed that both the S- and Mo-layer show dipolar-like stress field in the vicinity of GBs and GBJs (Figures 6 and 6S). By comparison, Mo atoms are more stress-carried and thus are more critical to the Page 10 of 24


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strength of MoS2. This arises from that the 6-fold coordinated Mo atoms in sandwich-like MoS2 structure possess less flexibility to move than the 3-fold coordinated S atoms. Prior to failure, dipolar-like stress fields in the vicinity of GBs and GBJs remain (Figures 6a and S6a). However, the pattern of dipolar-like stress field changes; Motif of stress field transforms from dipolar to four-polar pattern, and motif of dipolar-like stress field reorients during the stretching (Movie S2). A close-up view of an upcoming cracking GB demonstrates its dislocation-dominated structure (Figure 6f). It is noticed that the polycrystal fails by direct breakage of Mo-S, S-S and Mo-Mo bonds in the GB accompanied by reconstruction of as-formed edges (Figures 6b and g), rather than dislocation motion. Such failure is attributed to the large pre-strain experienced by the bonds in dislocation cores along the GBs. After the intergranular crack is initiated, the stress field in the adjacent region is altered; stress on Mo atoms is strongly relieved (Figure S6b) while that on S atoms is negligibly changed (Figure 6b). Instead, high stress is concentrated at the Mo atoms at the crack tip (Figure S6b), driving the crack to propagate further along the GB. As the crack propagation reaches to the triple GBJ wherein the other two GBs make large angles to the loading direction, the crack initially grows into one adjoining grain along zigzag path, and then along armchair path (Figures 6c and S6c), and finally back to along zigzag path when it approaches another GB (Figures 6d and S6d). During the transgranular propagation, stress-concentration is highly localized at Mo atoms of the crack tip (Figure 6c), however, the stress on S atoms becomes remarkably relieved (Figure S6c). This reveals that the Mo atoms play a crucial role in load bearing while S atoms are very important in sustaining large stress at the sharp crack tip, in agreement with recent MD calculations.40 No evident lattice reconstruction in both tip regions is detected. As a result of complex structure at the crack-influenced GB region, two newly neighboring cracks develop into one adjoining grain along a zigzag path (Figure 6d), leaving two atomic chains at the GB and the grain interior near the GB, respectively (Figures 6h and i). It is also observed that the crack tip is blunter along armchair path than that along zigzag one (Figures 6h and i). This indicates high energy of armchair edge, agreeing with recent MD simulations. Crack edge reconstructs as the transgranular crack grows along armchair path. As transgranular crack propagates along a zigzag path, the as-formed S- and Mo-terminated edges show distinctly shaped hexagons at the edges as a result of their different surface energy. Tiny transgranular crack defection is found along the zigzag path, consistent with recent MD and experimental observations. Under biaxial tension, propagating crack is prone to branch out at finite Page 11 of 24


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GBs or GBJs and crack kinks are frequently observed as a consequence of complex stress state (Figure S7). For example, crack kinking from one zigzag plane to another zigzag plane is identified (Figure S7h), resulting in crack deflection of 60°. Moreover, another crack kinking from one zigzag plane to one armchair plane to another zigzag plane is discovered (Figure S7h), resulting in crack deflection of 30°. Similar to uniaxial tension, linear and branched Mo-S atomic chains are formed as cracks propagate (Figure S7g). To further reveal the brittle crack behaviors, mechanical behaviors of pre-cracked monocrystalline monolayer MoS2 under uniaxial tension are examined and shown in Figures S8 and 9. Fracture stress increases as the initial length of both zigzag- and armchair-edged pre-cracks reduces. The MD results can be described by the modiﬁed Griffith Criterion theory.58 Interestingly, monocrystalline monolayer MoS2 with either armchair or zigzag directional pre-cracks shows perfectly straight crack path, which is in sharp contrast to those in polycrystalline MoS2. Conclusion Defect-free monolayer MoS2 show high mechanical properties comparable to that of stainless steel. Yet, it is still a daunting challenge to produce large-area pristine MoS2. Driven by the need for large-area MoS2 in engineering practice, high-yield and large-area MoS2 can be broadly produced through CVD growth. However, mechanical properties of CVD-grown monolayer MoS2 with polycrystalline nature remain unknown. Using REBO forcefield-based classic MD simulations, the GB structures and mechanical properties of polycrystalline MoS2 with different grain size prepared by a confinement-quenched technique are studied. In contrast to the GBs of polycrystalline graphene, cohesive GBs of polycrystalline MoS2 are represented by complex structures dominantly composed of Mo- and S-riched 5|7, 4|4, 4|6, 4|8 and 6|8 dislocations. Those structures facilitate the development of the growth mechanism of CVD-synthesized polycrystalline MoS2. Those dislocation structures and their arrangements govern the mechanical properties of polycrystals. Intuitively, mechanical properties of polycrystal are enhanced while it progressively evolves toward pristine MoS2. Ripples driven by thermal stimulus spontaneously appear and the ripple amplitude is shown to be strongly dependent of grain size. Intrinsic planarity of GBs in polycrystals indicates the weaker suppression of thermal fluctuations by anharmonic coupling between bending and stretching modes than that of defect-free structure. Both uniaxial and biaxial tension tests of polycrystals show that their mechanical properties are remarkably grain size dependent in ways not previously identified. The Page 12 of 24


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inverses pseudo Hall-Petch effect is dictated by the weakest link mechanism, which shows the strength reduction with decreasing the grain size. Polycrystal fails in a brittle manner, where the transgranular in polycrystals is achieved by crack initiation at GBs or GBJs followed by rapid intergranular and transgranular Griffith cracking propagations in samples. The transgranular crack often deflects as a result of two distinct scenarios of stress fields of S and Mo layers at the sharp crack tip. The present work provides critical knowledge of GB structures and mechanical properties of polycrystalline MoS2, which is of significant importance for designing MoS2 with desirable mechanical properties for practical applications. ASSOCIATED CONTENT Supporting Information Simulation details including realistic Molecular Models of Polycrystalline MoS2, forcefield for polycrystalline MoS2 modeling, tensile testing MD simulations of polycrystalline MoS2 and pre-cracked monocrystalline MoS2. Supporting Table S1, Figures S1-9, Videos S1-3 and references. The Supporting Information is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author *E-mail: [email protected], [email protected]. Notes The authors declare no competing financial interests. Acknowledgments This work was financially supported by the National Natural Science Foundation of China (Grant No. 11502221 and 11772278), the Fundamental Research Funds for the Central Universities (Xiamen University: Grant No. 20720150015), the project sponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, the National Science Foundation of Fujian Province (Grant No. 2014J01209), “111” Project (B16029), Fujian Provincial Department of Science & Technology (2014H6022) and the 1000 Talents Program from Xiamen University. The computational resources were provided by Information & Network Center for Computational Science at Xiamen University and the Norwegian Metacenter for Computational Page 13 of 24


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Figures and captions

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Figure 1 Grains and GB structures in 2D polycrystalline MoS2. (a) Perspective view of a typical polycrystal in which grains are colored for clarification of grain morphology. (b) Top-view of a grain-textured polcrystal where gray-colored atoms indicate the as-formed GBs. (c) Distribution of von Mises stress field of a grain-textured polycrystal. GBs show a characteristic of dipolar-like stress field in GBs as a result of presence of dislocation cores in GBs. (d) and (e) Typical loop and Y-shaped GBs captured from the polycrystal. The black arrows indicate the zigzag direction of bulk of grain. Boundary misorientation angles are explained by the angles between the arrow vectors in the neighboring grains. GBs are composed of diverse dislocation cores, depending on boundary misorientation angles. Right of figure shows typical dislocation cores captured from GBs in polycrystal, and they are individually named according to the feature of ring-pairs for clarification. Figure 2 Structural characteristics of polycrystalline MoS2. (a) Topography of a 2D polycrystalline MoS2 sheet in which atoms are colored according to displacement in out-of-plane (z) direction. Significantly localized positive and negative Gaussian curvatures are detected. Smooth gradient of out-of-plane displacement in the vicinity of GBs indicates the planarity of GB structures, in sharp contrast to graphene where GBs show vertically local wrinkles. (b) Out-of-plane corrugation of a typical polycrystal along one planar (x) direction. Grey and bule points indicate individually atomic corrugations and average atomic corrugations as a function of their position along one planar (x) direction, respectively. Red solid curve indicates a sinusoidal fitting of the out-of-plane corrugation of all atoms in the box, revealing a sinusoidal out-of-plane deformation. (c) Mean out-of-plane fluctuation of polycrystals as a function of mean grain size. Figure 3 Mechanical responses of polycrystalline MoS2 with mean grain size of 3 nm under different annealing temperatures. (a) Uniaxial tensile stress-strain curves of polycrystal under annealing temperatures varying from 1000-3000 K. The inset is the initial grain morphology of the polycrystal where 278 grains are dyed according to their grain number. (b)-(f) Top-viewed grain-textured configurations of polycrystal after thermal annealing under temperatures of 1000-3000 K, respectively. The color code clearly explains the polycrystallinity of MoS2; Atoms belonged to hexagonal rings are aqua green colored, whereas other atoms forming non-hexagonal rings are colored for highlighting disordered GBs. Networks of GBs are significantly changed under elevated 2500 and 3000 K, indicating large-scale coalesce of grains and reconstruction of migration of GBs. Page 22 of 24


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Figure 4 Mechanical responses of polycrystalline MoS2 with mean grain size of 3 nm under different annealing times. (a) Uniaxial tensile stress-strain curves of polycrystal under annealing time varying from 0 - 1100 ps. The inset shows original grain morphology of the polycrystal where 278 grains are colored based on their grain number. (b)-(f) Top-views of one typically local structures captured from the polycrystal after thermal annealing from 0-1100 ps, respectively. The atomic configurations of topological defects are highlighted. GBs are apparently reconstructed to form more energy-favorable configuration during the thermal annealing process. Figure 5 Mechanical properties of polycrystalline MoS2 of varying mean grain size. (a) and (b) uniaxial and biaxial tensile stress-strain curves of polycrystal with grain size varying from 3 - 20 nm, respectively. Grain size-dependence of (c) uniaxial tensile modulus, (d) uniaxial tensile strength, (e) uniaxial failure strain, (f) biaxial tensile modulus, (g) biaxial tensile strength, (h) biaxial failure strain for polycrystalline MoS2 sheets with different mean grain sizes, respectively. Figure 6 Typically catastrophic failure process of polycrystalline MoS2. (a)-(e) Nucleation and propagation of both intergranular and transgranular cracks. Atoms in polycrystal are colored according to the values of von Mises stress. (f) Zoomed-in atomic configurations of one GB as marked by a black rectangle in (a) are highlighted. (g) Occurrence of dissociation of bonds in highlighted GB. Dash lines indicate the broken bonds. (h) and (i) Zoomed-in transgranular cracks along armchair and zigzag directions as marked by the black rectangles in (c) and (d), respectively.

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Grain-Size-Controlled Mechanical Properties of Polycrystalline

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