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2DMater. 3 (2016) 035008 doi:10.1088/2053-1583/3/3/035008

PAPER

Abnormality in fracture strength of polycrystalline silicene

NingLiu1, JiawangHong2,3, Ramana Pidaparti1,4 andXianqiaoWang1,4

1 College of Engineering, University ofGeorgia, Athens, GA 30602,USA2 Department of AppliedMechanics, Beijing Institute of Technology, Beijing 100081, People’s Republic of China3 Research Institute of Advanced Structure Technology, Beijing Institute of Technology, Beijing 100081, People’s Republic of China4 Author towhomany correspondence should be addressed.

E-mail: rmparti@uga.edu and xqwang@uga.edu

Keywords: silicene, fracturemechanics, grain boundary,molecular dynamics, polycrystalline

Supplementarymaterial for this article is available online

AbstractSilicene, a silicon-basedhomologueof graphene, arouses great interest innano-electronic devices due toits outstanding electronic properties.However, its promising electronic applications are greatly hinderedby lack of understanding in themechanical strength of silicene. Therefore, in order to designmechanically reliable deviceswith silicene, it is necessary to thoroughly explore themechanicalproperties of silicene.Due to current fabricationmethods, graphene is commonly produced in apolycrystalline form; the samemayhold for silicene.Hereweperformmolecular dynamics simulationsto investigate themechanical properties of polycrystalline silicene. First, an annealingprocess isemployed to construct amore realisticmodeling structure of polycrystalline silicene. Results indicatethat amore stable structure is formeddue to the breaking and reformation of bonds between atoms onthe grainboundaries.Moreover, as the grain size decreases, the efficiency of the annealingprocess,whichis quantifiedby the energy change, increases. Subsequently, biaxial tensile tests are performedon theannealed samples inorder to explore the relationbetween grain size andmechanical properties, namelyin-plane stiffness, fracture strength and fracture strain etc. Results indicate that as the grain sizedecreases, the fracture strain increaseswhile the fracture strength shows an inverse trend. The decreasingfracture strengthmaybepartly attributed to theweakening effect from the increasing area density ofdefectswhich acts as the reservoir of stress-concentrated sites on the grainboundary. The observed cracklocalization andpropagation and fracture strength arewell-explained by a defect-pileupmodel.

1. Introduction

Silicene [1–4], a two-dimensional material composedof silicon atoms, stimulates great interest due to itsunique physical and mechanical properties. Com-pared with its two-dimensional carbon counterpartgraphene [5, 6], silicene has a similar but buckledhoneycomb structure, meaning that the atoms are notpurely in sp2 hybridized states. According to theor-etical investigations [7, 8], silicene exhibits propertiessimilar to those of graphene. Moreover, the puckeredstructure introduced in high symmetric configura-tions can be exploited in some electronic applications[9]. In view of the applications of silicene, a key issue ofthe mechanical properties of silicene, especially poly-crystalline silicene, has to be solved in order to clearlyunderstand the potential reliability in devices utilizing

this new material. Despite great efforts in studying themechanical properties of pristine silicene [10–13], themechanical properties of polycrystalline siliceneremain largely unexplored. For polycrystalline materi-als, grain size is one of the key factors influencingmechanical properties such as in-plane stiffness,fracture strength etc [14, 15]. Compared with DFT,molecular dynamics (MD) is an ideal method to studythe mechanical properties of polycrystalline silicenedue to its high computational efficiency and theresultant relatively large simulation system. Therefore,in this paper molecular simulations are performed tounderstand the mechanism of grain size dependenceofmechanical properties of polycrystalline silicene.

While the polycrystals for silicene have not beensynthesized, a recent investigation [16] has predictedthe existence of polycrystalline silicene. On the other

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hand, for graphene, the carbon homologue of silicene,polycrystals are fairly common when synthesized bychemical vapor deposition [17–19]. Compared withpristine graphene, polycrystalline graphene exhibitsmarkedly different mechanical [14, 20–22], electronic[23, 24], and thermal properties [25, 26] due to itsunique structure characteristics, such as varied grainorientations and the defects along grain boundaries.Here we would like to briefly review some investiga-tions on the mechanical properties of polycrystallinegraphene. Wei et al [27] explored the effect of penta-gon–heptagon defects on fracture strength, indicatingthat in addition to the density of defects, the detailedarrangements of defects can also influence the strengthof graphene. Song et al [15] performed a series of MDsimulations to study the fracture of polycrystallinegraphene, which indicates that as the grain size decrea-ses, fracture strength increases. The above phenom-enon can be well explained by a dislocation pileupmodel. Moreover, the role of grain boundary ends andjunctions is emphasized, which is ignored by previousstudies. In a subsequent research work, Song et al [28]also found that the curvature of the structure greatlyinfluences the stiffness and strength of polycrystallinegraphene under indentation. Becton et al [14] studiedthe effect of the annealing process on the mechanicalproperties of polycrystalline graphene via a series ofMD simulations. Results indicate that the annealingprocess is helpful to get amore stable structure of poly-crystalline graphene. Moreover, fracture properties,namely yield strength and ultimate strain of annealedsamples, are much higher than those of their unan-nealed counterparts for a given grain size. Never-theless, for silicene, there have been few investigationsinto this polycrystalline material. Therefore, the pur-pose of this work is to offer a few useful insights intothe understanding of mechanical properties of poly-crystalline silicene.

The process of annealing is a method designed toget a more stably structured polycrystalline material,namely transforming the local minimized state of thegrain boundaries and defects into a more stable state.With respect to MD simulations, the initial configura-tions of polycrystalline materials are generatedthrough relatively simple algorithms. However, thesamples generated by this process may be exponen-tially difficult to represent polycrystalline materialsrealistically due to its unstable structure. On the otherhand, it is very difficult to generate polycrystallinesamples by simulating the fabrication process becauseof the huge computation resources consumed and thedifficulties of determining an appropriate potential.Therefore, the annealing process makes the algor-ithmically generated samples more stable and henceallows them to better emulate experimental resultsusing minimal computation resources. For poly-crystalline graphene, the effect of the annealing pro-cess has been systematically studied by Becton et al[14]. However, for silicene, the efficiency of annealing

process to get amore stable structure and the effects onmechanical properties still remain unexplored.

Here we perform MD simulations to understandthe effect of the annealing process on polycrystallinesilicene samples with different grain sizes in terms ofstructural and energetic evolution when comparedwith the unannealed samples. For each given grainsize, a biaxial tension is then applied on the annealedsamples in order to obtain the relationship betweenthe grain size and mechanical properties, such as frac-ture strength, ultimate strength, in-plane stiffness etc.Finally, we will further discuss the fundamentalmechanisms behind these properties.

2.Methodology andmodels

Figure 1 shows the geometrical configuration ofsilicene here, which has been already identified andverified by investigations using density functionaltheory [8, 29, 30]. Figure 1(a) is a perspective view,indicating that unlike graphene, silicene has an in-plane puckered structure. Silicene atoms are distrib-uted on the top layer and bottom layer as shown infigure 1(b). The unit cell of silicene is composed of fouratoms as shown in figure 1(d), in which

a1 and

a2 are

basis vectors along the armchair and zigzag directions,respectively. Note that although all the bonds are thesame, they are classified into two types in this paperartificially. As is shown in figure 1(d), the bondsparallel to the armchair direction are defined as b1while all the other bonds are defined as b2. The bondlength and pucker height are the two dominatinggeometric parameters that control the structure ofsilicene, as shown in figure 1. Different values for thetwo parameters from previous investigations usingDFT are listed in table S1(see supporting informationfor details). In this investigation, 0.224 nm and0.0427 nm are taken as bond length and pucker sizefor silicene, respectively.

MD simulations are carried out with the opensource package LAMMPS based on the Stillinger–Weber (SW) potential developed by Zhang et al [30].The SW potential was initially developed for bulk sili-con systems [31], but has been successfully extended tomany othermaterials such asmolybdenum disulphide(MoS2) [32] and wurtzite GaN [33]. It has also beensuccessfully used to study the thermal properties ofsilicene, which captures well the structure character-istics validated by previous DFT investigations. Itsapplicability to study the mechanical properties areinvestigated by performing tensile tests on the pristinesilicene samples. The obtained results are comparedwith those from previous works, which turns out bereasonable. The details can be found in table S3 in thesupporting information. The SW potential consists oftwo terms, a two-body term describing the bondstretching interaction and a three-body term describ-ing the bond bending interaction, and is expressed as

2

2DMater. 3 (2016) 035008 NLiu et al

follows

å åÆ = +< < <

V V , 1i j i j k

2 3 ( )

e s s= - s s- - - -V A B r r e , 2p

ijp q

ijq r a

2ij

1( ) ( )[ ( ) ]

el q q= -gs s gs s- + -- -

3

V e cos cos ,r a r aijk3 0

2ij jk1 1

( )( )[ ( ) ( ) ]

where V2 and V3 are the two-body term and three bodyterm respectively; rij is the distance between atom iand j; qijk is the angle between bond ij and bond jk; q0

is the equilibrium angle between two bonds; all theother parameters such as A, B are the coefficientsrequired to fit when developing the potential. Forsilicene, there is only one type of bond and one type ofangle.

Here a square samplewith size ´48 nm 48 nm isconsidered as the initial simulation system. In order tostudy the effect of grain size on the mechanical strengthof silicene, polycrystalline silicene models with variedgrain size are generated throughVoronoimethods [34].In order to eliminate the randomness of themodels,fivesamples are created for each given grain size. All the

results depend on the grain size are averaged from thefive samples. Subsequently, due to the sparse nature ofthe grain boundaries from Voronoi method, thesemodels will be annealed byMD simulations to obtain aphysically more stable structure. The annealing process

can bebriefly described as follows. The time step is set tobe 1 fs. First, the models are heated gradually to a rela-tively high temperature, 1200 K in this investigation,during which energy minimization is done until therelative energy difference is less than -10 .12 The justifi-cation of the chosen temperature can be found in figureS3 (see supporting information for details). Then, themodelswill be kept at 1200 K for 100 ps and then gradu-ally cooled down to 0 K. During the annealing process,periodic boundaries and the NVT ensemble are adop-ted. After the annealing process, the models undergoequilibration in the NPT ensemble in order to removeinternal residual stress. Finally, polycrystalline silicenesheets are biaxially stretched in the NVT ensemble.During the tensile tests, the models are elongated at arate of 0.001 strain every 10 ps along the loading direc-tion. The justification of the chosen strain rate can befound in figure S4 (see supporting information fordetails).

Here the atomic vonMises stress, a property that isused in section 3, is defined by the followingexpression

where sij represents different component of atomicvirial stress computed by LAMMPS. Note that theatomic virial stress calculated by LAMMPS is in unitsof pressure*volume. It should be divided by a per-atom volume to get the unit of stress (pressure), but an

Figure 1.Geometrical configuration of silicene: (a) perspective view; (b) side view from the zigzag direction;(c) front view from thearmchair direction; (d) top view.

a1 and

a2 indicate the lattice basis vectors along the armchair and zigzag direction respectively.

s s s s s s s s s s= - + - + - + + +1

26 , 4v xx yy yy zz zz xx yz zx xy

2 2 2 2 2 2[( ) ( ) ( ) ( )] ( )

3

2DMater. 3 (2016) 035008 NLiu et al

individual atom’s volume is not well defined or easy tocompute. We assume that every atom occupies thesame volume. Therefore, the output stress is dividedby the evenly distributed volume.However, during thetensile test, the length along the out-of-plane directionof the simulation box varies, which brings someunrealistic fluctuations to the atomic von-Mises stress.In order to eliminate these fluctuations, atomic vonMises stress is multiplied by the out-of-plane length ofthe simulation box. That is why the unit for vonMisesstress in this work is Nm−1.

3. Results and discussion

3.1. General effects of annealingThe process of annealing is a method designed to get amore stably structured polycrystalline material. Dur-ing the annealing process, the polycrystalline samplesare heated to a point where the crystalline structureinside grains is maintained while the grain boundariesare partially fluid, permitting the bonds to break andreform into a more stable and robust configuration.Consequently, annealed polycrystalline graphene isexpected to experience an improvement in terms ofmechanical properties according to a recent invest-igation, such as fracture strain and yield strength [14].The main purpose of this work is to understand thedependence of the mechanical properties of polycrys-talline silicene on grain size after it has been annealed.Therefore, in this part, the effectiveness of our anneal-ing process will be discussed.Note that in this work thetime interval for the annealing process is set to be200 ps and the samples are only annealed once. Thejustification of the above choices can be found infigures S8, S9, and S10 in the supporting information.

Figure 2(a) shows the evolution of potential energyduring the annealing process. As displayed in thefigure, the potential energy increases at first due toheating, while the subsequent plateau and downstairsstages are due to the constant and decreasing temper-ature. The spikes of the curves in figure 2(a) are wherethe silicene undergoes the potential energy minimiza-tion, making the system reach a more stable statebefore another heating or cooling. The potentialenergy change after the process of annealing is differ-ent for different grain sizes.When the grain size is rela-tively large, 8 and 24 nm in figure 2(a), the potentialenergy decreases slightly. However, for silicene sam-ples with smaller grain size, 2 and 4 nm in figure 2(a),the potential energy experiences a big change duringthis period. The atomic structures at grain boundariesare reconstructed due to the formation and breakageof bonds. Subsequently, the silicene samples arecooled down to 0 K, resulting in the decrease of poten-tial energy seen at the end offigure 2(a).

Note that for samples with different grain size, thepotential energy change after annealing process is dif-ferent. Figure 2(b) shows the overall potential energychange due to the annealing process as a function ofgrain size. In figure 2(b), it can be seen that the poten-tial energy drops due to the annealing process decrea-ses as the grain size increases. Moreover, the slope ofthe curve in figure 2(b) decreases as the grain sizeincreases. The potential energy drop is mainly causedby the evolution of the grain boundary structure,namely the formation and breaking of bonds betweenatoms along the grain boundaries. Therefore, theabove phenomena indicated by figure 2(b) are causedby the decrease of density of defect atoms per area asthe grain size increases (see figure S11 in the

Figure 2.Potential energy change (a) during the annealing process; (b) after the annealing process for polycrystalline silicenewithdifferent grain size.

4

2DMater. 3 (2016) 035008 NLiu et al

supporting information). Figure 3 shows snapshots ofa sample before and after the annealing process, whichare colored in terms of potential energy. As we can seefrom figures 3(a) and (b), grain boundaries are lessvisible after annealing compared with before anneal-ing under the same potential scale bar, indicating thedecrease in the potential energy of the grain bound-aries. Figures 3(c)–(f) show that there are a lot of three-member and four-member rings on the grain bound-aries of the unannealed sample, which disappear in theannealing process as these structures are remarkablyunstable. Moreover, the dangling bonds, which arefairly common on the grain boundaries of the unan-nealed sample, disappear after the annealing process.

To demonstrate the importance of the annealingprocess, biaxial tensile tests are performed on a samplewith 6 nm grain size before and after the annealingprocess. Figure 4 shows the stress–strain relationshipof tensile tests, where the blue and red curves represent

the results before and after annealing process respec-tively. To eliminate the effect of out-of-plane dist-ortion on stress, force per unit length in terms of virialstress is used to represent the stress and hence the unitfor in-plane stiffness changes accordingly. At thebeginning of deformation, the stress of the annealedsample increases much faster than the unannealedsample. To understand the origin of this phenom-enon, the out-of-plane distortion before tension aremeasured, which are 2.3 and 4.2 nm for the annealedand unannealed sample. A smaller distortion of theannealed sample indicates a less crumpled configura-tion than its unannealed counterpart and hencemakesit behave less stretchable and stiffer under external for-ces. As the deformation goes further, the in-plane stiff-ness for both samples become much closer to eachother, approaching 48.23 and 49.18 Nm−1 for theunannealed and annealed sample respectively. Theslight difference of in-plane stiffness between the

Figure 3.Overall snapshots (a) before and (b)after the annealing process; zoomed-in snapshots (c) before and (d) after the annealingprocessmarked by the yellow ellipse; zoomed-in snapshots (e) before and (f) after the annealing processmarked by the red ellipse forthe polycrystalline silicenewith grain size 6 nm (the atoms are colored by potential energy).

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2DMater. 3 (2016) 035008 NLiu et al

annealed and unannealed samples may be attributedto the discrepancy between the structures of grainboundaries in these two samples. With respect to frac-ture properties, the annealed sample has a better per-formance than its unannealed counterpart in terms offracture strain and ultimate strength.

3.2. Grain size dependence of fracture propertiesIn order to understand the dependence of mechanicalstrength on grain size, biaxial tensile tests are per-formed on the annealed polycrystalline silicene sam-ples. Figure 5 shows the stress–strain curves forsilicene samples of different grain size, in which thestress is the mean value of normal stress of botharmchair and zigzag directions. As we can see, at thebeginning of deformation, the stress increases slowlyas the strain increases, due to the crumpled feature ofthe initial sample as indicated in the inset of figure 5.After being stretched by the external forces, the stressincreases much faster until the slope of the stress–

strain curve becomes almost constant. At the last stageof the deformation, the stress–strain curve is muchsteeper than the previous stages. The results of the in-plane stiffness at different stages during the process areshown in table S2 (see supporting information fordetails). The stages are chosen according to the out-of-plane distortion of the sample, where in the first stagethe out-plane thickness is bigger than 1, 0.5–1 nm inthe second stage and less than 0.5 nm in the last stage.Results about the in-plane stiffness at the last stage ofdeformation are plotted as a function of grain size,which is shown in figure 6(a). As the grain sizeincreases, the area fraction of the grain boundariesreduces with proportional to .

L

1 Therefore, the in-

plane stiffness are believed to linearly depend on .L

1

Furthermore, all the grain size dependent behaviors ofpolycrystalline silicene in the rest of the paper are also

fitted to a linear function of .L

1 From figure 6(a), a cleartrend of the increase of in-plane stiffness can beobserved as the grain size increases. This phenomenon

Figure 4. Stress–strain curves for a sample (grain size 6 nm) before and after the annealing process.

Figure 5. Stress–strain curves for polycrystalline silicene under biaxial tension (the inset pictures show the configurations at differentdeformation stages colored by out-plane position).

6

2DMater. 3 (2016) 035008 NLiu et al

can be attributed to the decreasing density of defectatoms as the grain size increases. Compared with thehighly ordered crystalline section of grain interiors,grain boundaries are composed of defect atoms thatcan accommodate the deformation easily under exter-nal forces. Therefore, polycrystalline silicene sampleswith smaller grain size, which means it has more grainboundaries and hence more defect atoms, tend toexperience a larger deformation under a certainamount of given external force, resulting in a smallermagnitude of in-plane stiffness.

As indicated in figure 5, fracture properties,namely ultimate strength and fracture strain, dependheavily on the grain size. To clearly see the relationshipbetween grain size and these fracture properties, bothultimate strength and fracture strain are plotted as afunction of grain size in figure 6(b). Figure 6(b) indi-cates that the maximum strain increases as grain sizedecreases while the ultimate strength shows an inversetrend. The obtained discrete data points are fitted to alinear function of ,

L

1 where the resultant fitting curve is

in good agreement with the data points. Therefore, thevarying trends of both fracture strain and ultimatestrength result from the variance of the fraction ofgrain boundaries as the grain size changes. Withrespect to the fracture strain, samples with smallergrain sizes possess more grain boundaries, the inher-ent instability of which may contribute additionaldegrees of freedom to the structure, therefore leadingto the increase of ultimate strain.

With respect to the ultimate strength, the decreasingtrend alongwith thedecrease of grain size for polycrystal-line silicene is different from that for polycrystalline gra-phene reported by Song et al [15]. Note that in the

previous paper about graphene, the grains possess reg-ular hexagonal shapes and hence regular line defects ongrain boundaries. The well-aligned pentagon/heptonpairs (5/7) along the grain boundary result in high pre-stress in the junctions where more than two neighborgrains interact with each other. As the grain size becomesbigger, the pre-stress in the junctions becomes higher,resulting in higher strength reduction. These defects canbe the origin of the ‘Pseudo Hall Petch’ strength reduc-tion and the underlying dislocation-pileup mechanism.However, in the current work, the shapes of grains aregenerated randomly, making the defects on the grainboundaries be distributed more irregularly. The well-aligned 5/7 pairs are not observed in the polycrystallinesilicene samples. Therefore, the ‘Pseudo Hall Petch’strength reduction may not hold for the polycrystallinesilicene in the current work. A defect-pileup model isproposed to explain the origin of the ‘inverse PseudoHall–Petch’ strength reduction. Our hypothesis is that asthe grain size is smaller, the higher density of defectatoms brings a higher stress concentration and hence ahigher probability of fracture. Typically, the densities perarea of the defects increases as the grain size decreases(see figure S11 for details). Hence the higher density ofdefect atoms brings a higher stress concentration.On theother hand, regardless of different grain sizes, the criticalatomic stress that drives the crack initiation almostremains a constant for silicene. Figure 6(c) shows themaximum atomic stress before breaking, which fluc-tuates around 11.3 Nm−1 as the grain size varies. Basedon this criterion, the density of atoms with von Misesstress higher than 9Nm−1 before crack initialization isplotted as a function of grain size in figure 6(d). It can beseen that as the grain size decreases the density increases,

Figure 6.Grain size dependence of (a) in-plane stiffness; (b) fracture strain andUltimate strength; (c)maximumatomic stresscalculated in terms of vonMises stress before fracture; (d)density per area of atomswith vonMises stress bigger than 9 N m−1.

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2DMater. 3 (2016) 035008 NLiu et al

indicating a higher probability to trigger cracks in spite ofa lower average stress. Note that the stress densities arefitted to a linear function of ,

L

1 which shows good agree-

mentwith orginal data.Hence the increase trendof stressconcentration can be attributed to the increase of defectdensities as the grain size decreases. Figure 7 shows thedistribution of stress before crack initiation for poly-crystalline silicene with 6 and 24 nm grain size respec-tively. It can be seen that for the samplewith 24 nmgrainsize, the spike is narrower and higher than that for the

sample with 6 nm grain size, indicating a more uniformdistribution of stress. Moreover, the stress where thespike appears for the sample with 24 nm grain size is big-ger, indicating a much higher ultimate strength. Theinset shows the contours of atomic von Mises stress forpolyscrystalline silicene sheets with 6 and 24 nm grainsize respectively. From it the stresses of atoms on thegrain boundaries are higher than that of those in theinterior of the grain. Therefore, the fracture of poly-crystalline silicene is mainly dominated by the stress

Figure 7.Probability density of atomic vonMises stress before crack initialization.

Figure 8.Zoomed-in view of the crack initialization for polycrystalline silicene (colored by atomic vonMises stress).

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2DMater. 3 (2016) 035008 NLiu et al

status of atoms on the grain boundaries instead of thosein the grain interior, which can be reconfirmed byfigure 8. Figure 8 shows the crack initiation processoccurring on the grain boundaries. These zoomed-insnapshots can be used to capture the detail of bond fea-tures in the dynamic crack progress on the grain bound-ary. When the cracks nucleate, the bonds on the grainboundary start to break, nucleating into a small hole.Under the external force, more bonds break, stress con-centration at small holes causes them to coalesce into bigones and subsequently cleave the areas between them,resulting in the propagation of the crack along the grainboundary.

4. Conclusions

In summary, we performed a series of MD simulationsto study the effect of annealing on polycrystallinesamples and the dependence of mechanical propertiesof annealed silicene samples on grain size. Results revealthat the annealing process decreases the potentialenergy of the polycrystalline samples, indicating amorestable structure after annealing, which results from theevolution of the structure of grain boundaries. More-over, as the grain size decreases, the effect of annealingbecomes more pronounced, due to the increasingrelative quantity of grainboundary atoms.Themechan-ical properties of polycrystalline silicene are shown todepend strongly on grain size. As the grain sizedecreases, the in-plane stiffness decreases due to theincreased area of grain boundaries and the resulting‘softer’ structure. Additionally, as the grain sizedecreases the fracture strain increases while the ultimatestrength decreases. The decrement of ultimate strengthin response to the decreasing grain size can be explainedby an increasing defect density. With a higher defectdensity, polycrystalline samples with smaller grain sizeshave a wider spread of atomic stress, which is caused bythe higher atomic stress of defect atoms on the grainboundary. Therefore, polycrystalline samples withsmaller grain size have a more vulnerable nature thantheir counterparts with bigger grain size. Furthermore,the fracture process is observed, which shows that thecracks initialize and propagate along the grain bound-ary, branch into themiddle of the grain andfinally resultin the breakdown of the whole sample. Utilizing theseresultswill allow for the design and fabrication of robusttechnologies which can incorporate the unique proper-ties of polycrystalline silicene.

Acknowledgments

NL and XW acknowledge supports from the NationalScience Foundation (Grant No. CMMI-1306065) andthe University of Georgia (UGA) Research Founda-tion. Calculations are performed at the UGAAdvanced Computing Resource Centre. JH acknowl-edges the support from the Thousand Young Talents

Program of China and the Special Program forApplied Research on Super Computation of theNSFC-Guangdong Joint Fund (the second phase).

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