FU

DOI: 10.1002/adem.201600112

LLPAPER

Mechanical Properties of the Boron Nitride Analog ofGraphyne: Scaling Laws and Failure Patterns**

By Matthew Becton, Xiaowei Zeng and Xianqiao Wang*

Recent years have witnessed the explosive growth of interest in novel two-dimensional materialsbeyond graphene, such as the boron nitride analogue BNyne. Here, the authors perform steeredmolecular dynamics (MD) simulations to probe the structure, mechanical properties, and failure ofBNyne with a range of triple-single-bond linker numbers. The authors develop a set of general scalinglaws for the cumulative effects of linkers based on MD, allowing extrapolation to extended BNynes.Results indicate that the number of linkers, and thus density, is a vital metric of material strength andstiffness. We find that BNyne is stronger in the armchair direction but stiffer in the zigzag direction.These findings are promising as the application of this strong, anisotropic 2D material becomes closerto reality.

1. Introduction The mechanical stability combined with h-BN’s natural

The past decade has seen an explosion of 2D material-related research, as these advancing edge materials havedemonstrated tremendous promising applications in elec-tronics, energy storage, composites, and biomedicine due totheir outstanding physical properties which are unable to beseen in bulk materials.[1] Following graphene’s meteoric risein popularity since its discovery, many other 2D materialshave begun to be investigated. Of the many kinds of 2Dmaterials currently drawing attention, boron nitride (BN) hasbecome a major topic of research due to its structuralequivalency to carbon allotropes and its outstanding me-chanical,[2] thermodynamic,[3] chemical,[4] and electronic[5,6]

properties. Hexagonal boron nitride (h-BN) is an atomiclattice structure similar to graphene, but composed of theheterogeneous atoms boron and nitrogen in place of carbon.

[*] Dr. X. Wang, Dr. M. BectonCollege of Engineering, University of Georgia, 712G Boyd, 200D.W. Brooks Drive, Athens, Georgia 30602, USAE-mail: xqwang@uga.eduDr. X. ZengDepartment of Mechanical Engineering, University of Texas atSan Antonio, San Antonio, Texas 78249, USA

[**] The authors acknowledge support from the National ScienceFoundation and University of Georgia (UGA) start-up fund.The facility support for modeling and simulations from theUGA Advanced Computing Resource Center are greatlyappreciated. Competing financial interests: the authors declareno competing financial interests. (Supporting Information isavailable online fromWiley Online Library or from the author.)

DOI: 10.1002/adem.201600112 © 2016 WILEY-VCH VerlaADVANCED ENGINEERING MATERIALS 2016,

sliding has enabled its fantastical applications in bulklubrication for decades;[7] however, with the explosive growthof interest in many disparate 2D materials, focus has shiftedtoward the applicability of h-BN at the nano-scale, such as aninsulator used as a foil to the conductor graphene,[8] a spin-filter for spintronic devices,[6,9] and a nanoscale filler as astrengthening component in ceramic composite materials.[10]

Following the discovery/invention of graphene, a type ofmaterials called “graphynes” have been making an impact fortheir promising properties as well. Graphynes are a family of2Dmaterials composed entirely of carbon similar to graphene;but whereas all of the atoms in graphene are sp2-hybridizedwith three neighbors apiece, graphynes all contain apercentage of sp1-hybridized acetylenic triple-single-bondlinkers, with the percentage and geometry of linkers definingthe type of graphyne.[11,12] The inclusion of single and triplebonds and an enlarged lattice gives graphynes markedlydifferent properties when compared with pristine graphene,opening new avenues and giving new alternatives toconventional energy storage,[13] electronics,[14] and filtra-tion[15] technologies. Applying the expanded structure ofgraphyne to BN, a new class of 2D materials called “BNyne”has been theorized with boron and nitrogen in a graphyne-like sheet with analogous connecting triple-single-bondchains.[16] This fusion combines the heterogeneous atoms ofBN and the heterogeneous bonding of graphynes to create atruly unique brand of nanostructured materials. Here, wefocus on the regular linking of BN aromatic groups withidentical and isotropic triple-single bond chains (see Figure 1),maintaining hexagonal symmetry and facilitating systematiccomparison between systems and assessment of the

g GmbH & Co. KGaA, Weinheim wileyonlinelibrary.com 1

Fig. 1. Bond-map comparison of BNyne structures. (a) BN, (b) 1-BNyne, (c) 3-BNyne, (d) 6-BNyne. In thisimage, the horizontal direction is “armchair,” and the vertical direction is “zigzag.” Blue atoms are nitrogen,yellow represents boron. The black lines depict the lattice length aL for each BNyne (a1¼ a2¼ aL).

M. Becton et al./Mechanical Properties of BNyne

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mechanical performance of BNynes. This class of materials isextremely novel, and as such is equally poorly understood.However, understanding the mechanical properties of thesematerials which are so full of potential will make it easier tocharacterize and manufacture them. Therefore, investigatingthe mechanical properties of BNynes and characterizing theresults by the number of linkers in order to better understandthe potential of this material will be the focus of this paper. Inthe following sections, we will discuss the computationalmethods for the tensile tests, explain the models, andcharacterize the results. In this manner, we hope to contributeto the development of BNynes.

2. Computational Model and Methods

First, an originally developed program is utilized togenerate a lattice structure of BNynes with the specificnumber of acetylene-like, triple-single-bond, linkers of inter-est. In what follows, molecular dynamics simulations basedon the open-source code LAMMPS[17] are employed toperform the tensile and fracture simulations of PBN. Toaccurately capture the behavior of BNynes, the Tersoffpotential is utilized, which takes the following form:

E ¼ 12

Xi

Xj 6¼i

f C rij� �

f R rij� �þ bijf A rij

� �� � ð1Þ

Here, fR is a repulsive two-body term while fA is anattractive three-body term managed by the bij bond function.

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The parameters of the Tersoff potentialutilized here for BN were documented byMatsunaga,[18] and are included in theSupplementary Materials Table S1. TheBNyne types tested in this paper are labeledbased on the number of triple-single-bondlinkers between hexagons, from 1 to 6. For thepurpose of convenience, boron nitride islabeled as 0-BNyne due to its lattice beingidentical to a case of there being 0 linkers. Forthe tensile tests, the simulated sample is a20� 20 nm2 square sheet under NVT ensem-ble using a Nose–Hoover thermostat tocontrol the temperature. The standard veloc-ity-Verlet time integration algorithm with atimestep of 1 fs is used to preserve a balancebetween accuracy and computational cost. Inthis work, the initial plane of the nanosheet isconsidered to be the x–y plane, the directionof tension is the x direction, and perpendicu-lar to the nanosheet is the z direction. Thelattice distance varies due to the expandedlattice for different numbers of linkers, andthe lattice distance for each L-BNyne islabeled as aL, where L indicates the numberof linkers. The boundaries are aperiodic so asto prevent self-interference in the sample, anda randomized initial velocity is applied to

each atom in accordance with the sample temperature withsum zero linear and angular momenta. The sample thenundergoes energy minimization following the Polak–Ribiereconjugate gradients method until the relative energy differ-ence between successive steps is less than 10�20, and thefinalized per-atom binding energy is listed in the Supplemen-tary Materials Table S2.

Prior to applying tensile loading, the sample takes a longenough time to relax such that there is minimal prestressinside the sample. The tensile test process is as follows: theenergy-minimized L-BNyne structure is kept at 1K usingNos�e–Hoover thermostatting, so as to minimize the effects ofthe randomized temperature profile. In order to provide thetensile force to the sample, both ends of the sample are pulledvia a virtual spring with a spring constant of 100 eV A�2. Thepulling speed is set as 2.5 nmns�1, which is slow enough tohave negligible velocity-dependent effects on the results asevidenced by Figure S1 of the Supplementary Materials.

3. Results and Discussion

3.1. Effect of Lattice Length on Mechanical PropertiesThe focus of this study is to investigate the mechanical

behavior of several varieties of BNyne structures under tensileloading, and accordingly an important factor in the propertiesof the final structure is the composition of the initial sample.The integer of triple-single-bond linkers L between hexagonalcells in this study is varied from 1 to 6, with 0-BNyne being h-

im DOI: 10.1002/adem.201600112ADVANCED ENGINEERING MATERIALS 2016,

0 0.5 1 1.50

50

100

150

200

Strain

Stre

ss (G

Pa)

BNyne-1BNyne-2BNyne-3BNyne-4BNyne-5BNyne-6

0 0.2 0.4 0.6 0.8 1 1.2 1.40

20

40

60

80

100

120

140

160

Strain

Stre

ss (G

Pa)

BNyne-1BNyne-2BNyne-3BNyne-4BNyne-5BNyne-6

(a)

(b)

Fig. 2. Stress–strain curves for BNynes in the (a) armchair and (b) zigzag directions.

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BN as shown in Figure 1. Each BNyne structure is a crystallattice, the same as BN, and as such each structure has its ownlattice length, defined here as aL for L-BNynes and a0 forhexagonal boron nitride. As the lattice length of the unit cell inthis 2D crystal structure grows larger, the atomic density ofthe BNyne decreases by the square of the lattice length. Inorder to characterize this structural uniqueness and providethe ease for the analysis, we define the scaled lattice length aLand the scaled density DL as follows:

aL ¼ aLa0

ð2Þ

DL ¼ rLr0

ð3Þ

Here, rL is the density of the L-BNyne and r0 is the densityof 0-BNyne, or pristine hexagonal boron nitride. Using thescaled lattice length makes it easier to see how the unit cell ofthe BNyne structure affects its mechanical properties; it hasbeen shown for the structurally similar graphynes that manymechanical properties can be interpreted accurately as afunction of the inverse lattice spacing.[12] As BNynes havesimilar structures, the number of triple-single-bond linkersand the resulting lattice spacing may very well also play asimilarly large effect on the properties of each sample; as suchthe mechanical properties of BNynes in this text are posed toshow their relation to the lattice spacing aL.

For this work, two sets of tensile tests are performed foreach sample: along the “armchair” direction of the crystallattice, and along the “zigzag” direction of the crystal lattice.For calculations of stress, the thickness of the BNyne sheet wastaken to be 3.3 A, as has been shown for layered graphite andBN structures.[19]

First, uniaxial loading along the armchair direction in theBNynes was performed. Here, we introduce the per-atomstress tensor as follows:

Sab ¼ �½mvavb þ 12

XNp

n¼1ðr1 aF1 b þ r2 aF2 bÞ ð4Þ

where a and b can take on values of x, y, and z to represent thesix tensor values of xx, xy, xz, yy, yz, and zz. The first term in theequation is the kinetic energy contribution to the per-atomstress, while the second term is a summation of all pairwiseinteractions in the simulation. All of the per-atom stresses aresummed up and the result divided by the volume of thesample to get the stress in the direction of tension, whichwould be the xx stress in this case. The resulting stress–straincurves for the BNynes in the armchair direction are depictedin Figure 2a. Judging from these curves, we can see that 1-BNyne has very similar ultimate strength as that of pristineBN, around 160GPa, while for larger L the strength rapidlydecreases.[20] There are two distinct phases before failure: i) upuntil just before 50% strain the stress rises gently as strainincreases, and the curves are distinct according to the number

DOI: 10.1002/adem.201600112 © 2016 WILEY-VCH Verlag GADVANCED ENGINEERING MATERIALS 2016,

of linkers the BNyne has; ii) at approximately 50% strain,however, each of the BNyne samples cease stretching and thestress builds up rapidly until failure with very little change inthe strain. These two phases shall be henceforth referred to asthe initial loading phase and the secondary loading phase.This particular phenomenon is due to the unique structure ofBNynes, and is discussed in detail in the section onmechanical failure. It is worthwhile to note that after thisbuild-up of stress, the number of linkers L determines thestress upon failure, with a larger L, and thus a more sparsestructure, thematerial becomesweaker and less elastic. This ismost clear with small L, as the difference between the curvesof 1-BNyne and 2-BNyne is very pronounced.

This trend is clearly seen in Figure 3, which is the fittedtrend of the ultimate stress for each type of BNyne, plottedagainst the inverse of the scaled lattice length (ai

�1). It is clearthat the ultimate stress increases in a linear fashion relative toai

�1, such that a greater L has a larger ai and thus a smallerai

�1. A linear trend is fitted to this data to represent thetensile strength (TS) of each L-BNyne as a function of theinverse of the scaled lattice length with the followingequation:

TSL ¼ b �ai�1 þ c ð5Þ

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0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.650

100

150

200

250

αL-1

Tens

ile S

tren

gth

(GPa

)

Armchair DataArmchair Fit (R2 = 0.939)Zigzag DataZigzag Fit (R2 = 0.979)

0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6100

150

200

250

300

350

αL-1

Elas

tic M

odul

us (G

Pa)

Armchair DataArmchair Fit (R2 = 0.999)Zigzag DataZigzag Fit (R2 = 0.988)

1 2 3 4 5 60

100

200

300

400

500

600

700

L

Spec

ific

Mod

ulus

Ys Armchair Data

Armchair TrendlineYs Zigzag Data

Zigzag Trendline

0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.620

40

60

80

100

120

140

160

180

αL-1

Toug

hnes

s (G

J/m

3 )

Armchair DataArmchair Fit (R2 = 0.937)Zigzag DataZigzag Fit (R2 = 0.949)

(a) (b)

(c) (d)

Fig. 3. (a) Ultimate stress, (b) elastic modulus, (c) specific modulus, and (d) toughness as a function of inverse-scaled lattice length for armchair and zigzag BNynes.

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For armchair BNynes, R2¼ 0.939 and b¼ 243.54 andc¼ 53.674. BNynes display a similar trend in the stress–straincurves from tensile stress in the zigzag direction as in thearmchair direction, shown in Figure 2b. It can be seen thataround 50% strain, once again the BNynes of various L ceasetheir initial stretching phase and load up stress until failure.As Figure 3a demonstrates, the ultimate strengths of BNynesin the zigzag direction are inferior to those of the same BNynein the armchair direction. This is due to the way stresses arealigned along linker chains, as will be shown in the followingsections. However, the same linear dependence of ultimatestrength on the lattice length can be seen in this relationship,although with parameters b¼ 274.54 and c¼–5.7362. Thisresults in an R2¼ 0.979, showing that this is a robust fit to thisrelationship. The steeper slope for this equation in the zigzagdirection indicates that not only is the ultimate strength muchless for all values of L, but that the strength decreases moresharply as L increases and the lattice spacing gets larger. Thedirection of stresses along the linker chains is what causes thislowered strength, as the chains in zigzag formation do notsupport pure linear stressing, with the angled chains insteadintroducing shear stress into the structure, causing earlierfailure. This phenomenon is shown clearly in the proceedingsection on failure in BNynes.

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Shown by the tensile strength results, as the lattice lengthincreases due to a larger number of linkers between BNhexagonal rings it creates a less mechanically robust structure;a claim which is further supported by the trend shown inFigure 3b. It can be seen from this figure that every L-BNyne ismuch less stiff than pristine BN, which has an elastic moduluson the order of 716–950GPa.[20] This is due once again to thequalitative difference between BN and BNyne, which is theinclusion of triple-single-bond linkers which act similarly to aspring with a different constant than that of the basehexagonal unit. Figure 3b shows the relationship betweena�1L and elastic modulus, which forms a trend similar to the

one for ultimate stress. Elastic modulus here is defined as thechange in stress over the change in strain, for smalldeformations (e< 5%). A trendline is fitted to each data setin Figure 3b to represent the stiffness of each L-BNyne as afunction of the inverse of the scaled lattice length with thefollowing equation:

YL ¼ b �ai�1 þ c ð6Þ

For armchair BNynes, the fit is superb as R2¼ 0.999, withparameters b¼ 439.71 and c¼ 24.475. While the strength ofBNynes in the zigzag direction is lessened due to the quirks of

& Co. KGaA, Weinheim DOI: 10.1002/adem.201600112ADVANCED ENGINEERING MATERIALS 2016,

M. Becton et al./Mechanical Properties of BNyne

FULLPAPER

geometry, the opposite is true for the stiffness. Figure 3cdepicts the elastic modulus of BNynes in the zigzag directionas a function of scaled lattice length. By comparing thesevalues with those in the armchair direction, it is clear that thestiffness of zigzag BNynes is higher for all values of L. Thetrendline fitted to this data has a good R2¼ 0.988 andparameters b¼ 395.27 and c¼ 73.893. The increased stiffnessof BNynes in the zigzag direction is related to their geometry,as the same diagonal linkers which account for decreasedstrength also have the effect of increasing the elastic modulusduring tension. Similarly, the density-scaled specific modulus(density being the same for zigzag and armchair alike),although it keeps a linear trend, is overall of a higher value forzigzag BNynes, as can be seen in Figure 3c. As the chainsbetween rings become longer, there is an associated decreasein the stiffness of the material, which is likely due to theincreased flexibility afforded by the sparseness of cross-linksbetween load-bearing chains. The elastic modulus is directlyrelative to the areal density in each L-BNyne, and to show thiswe define the specific modulus Ys as the modulus of elasticitydivided by the scaled density:

Ys ¼ YL

DLð7Þ

Here, YL is the elastic modulus of each L-BNyne. The graphof specific modulus versus linker number is plotted inFigure 3c, where we can easily see that, when areal density isaccounted for, the stiffness of each BNyne is approximatelythe same. This is due to accounting for the amount of area each“spring” covers of the total sample.

The toughness of a material is the amount of energyabsorbed during fracture. Accordingly, the toughness of a

Fig. 4. “Unraveling” phenomenon occurring during failure of armchair 4-BNyne (a) initial loading phase, (b)secondary loading phase, (c) failure, (d) unraveling, and (e) unraveled.

material is a good metric of how useful itcould be in high-impact or high-stressenvironments. Figure 3d displays the tough-ness of BNynes; from this figure, it can beseen that toughness decreases drastically forL greater than 1 (L¼ 1 is the first data point).A trendline is fitted to each set of data torepresent the toughness of each L-BNyne as afunction of the inverse of the scaled latticelength with the following equation:

TL ¼ b �ai�1 þ c ð8Þ

Armchair BNynes show larger toughnessvalues compared with their zigzag counter-parts, with the fitted trendline havingR2¼ 0.937 and parameters b¼ 294.81 andc¼–23.631. For toughness, there follows asimilar relationship as that displayed forstrength, wherein the values for zigzagBNynes fall far behind those of armchairBNynes, demonstrating that these materialsare strongly anisotropic. The relationship

DOI: 10.1002/adem.201600112 © 2016 WILEY-VCH Verlag GADVANCED ENGINEERING MATERIALS 2016,

between toughness and scaled lattice length is shown in,where it is fitted with a trend having R2¼ 0.949 andparameters b¼ 198.19 and c¼–22.453. These parametersdemonstrate the reliance of the toughness of each BNyne asa function of the inverse of the scaled lattice length, and thusthe number of triple-single-bond linkers. The fact that theslope of the line is far less than the equation for armchairBNynes demonstrates exactly how anisotropic this material iswhen it comes to toughness. It is easily seen from these figuresthat strength, stiffness, and toughness all sharply decline after1-BNyne, while the properties are more similar for L values of4, 5, and 6. This is due to the great relative change each linkerstructure introduces in structure for L-BNynes from 0 to 1 and1 to 2 when compared with the structural changes going from4 to 5, 5 to 6, etc.

The ultimate strength and toughness of zigzag-orientedBNynes are inferior to those of armchair BNynes of the samenumber of linkers, but the Young’s Modulus is superior,indicating that these materials are uniquely anisotropic. ForBNynes, the zigzag orientation is shown tobenotably stiffer yetweaker (in terms of both strength and toughness) than thearmchair orientation. However, in both cases 1-BNyne is muchsuperior to the other BNynes, with much less differentiationamong higher L values. However, to uncover more clues as tothe behavior of BNynes under tensile failure, further investiga-tion is needed. Thus, after characterizing the basic mechanicalpropertiesofBNynes, itwouldbebeneficial togetafirmgraspofthemode of failure observed inBNynes along the twoprincipledirections by taking a close look at the failure process.

3.2. Failure Mechanism of BNyneTo further understand the reasons for the mechanical

properties displayed by BNynes along either direction, it is

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M. Becton et al./Mechanical Properties of BNyne

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highly beneficial to take a close-up look at how deformation

and failure occurs in BNynes. For each failure, it was noticedthat the bonds to break are those in the hexagonal rings,specifically those bonds which do not run parallel to thedirection of tension. This causes the structure to degenerateinto individual strands of boron–nitrogen chains; this processwe will refer to as “unraveling.” To better observe thisphenomenon, Figure 4 displays the entire process of failurefrom the beginning of loading until full unraveling. Thefailure of 4-BNyne is displayed as a representative of thefailure of BNynes in the armchair direction in Figure 4. Thestages of pre-failure are shown in Figure 4a and b. These twoimages are indicative of the initial and secondary loadingphases displayed in Figure 2. For the initial loading phase, thesample stretches noticeably while the force increases. Afterthe critical strain, the sample drastically reduces the rate ofstretching while stress builds up until failure, such that strainincreases imperceptibly until a ring linker fails and the failurecascades rapidly. In Figure 4c, the initial sudden failure isdisplayed, a close-up of which is shown in Figure 5. It can beseen that a single layer of linkers snap before any further

Fig. 5. Close-up of sudden onset failure in armchair 4-BNyne. Shown is a stress-map of4-BNyne (a) before and (b) after the sudden failure onset.

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damage is done, and as Figure 4d and e illustrate, the materialbegins to unravel until a mere one or two single chains areconnected. These images allow one to see clearly that thelinear chains which run across the sample in the x directionsupport the majority of the stress, with very little stresssupported by the cross-linkers which connect hexagonal ringsoblique to the x direction. Figure 6 details an extreme close-upof the bond structure at failure, making it obvious that failureoccurs from the breaking of the hexagonal boron–nitrogenrings, while, as can be seen from Figure 4e, the linear BNchains are the last part of the structure to break. The two-atom,sp-hybridized bonds in the triple-single-bond linkers andresultant BN chains are quite strong along the line of force,with failure stemming from sp2-hybridized bonds which arenot parallel with the tensile force. This specific mode of failureis due to the contribution of two factors: that the bonds in thechains are at least as strong as the bonds in the rings, and thatthe cross-links induce a shear component to the stress on thehexagonal rings, as can be seen fromSupplementaryMaterialsFigure S3. For the first factor, the bonds of the linear chains can

Fig. 6. Detailed flat close-up of sudden onset failure in armchair 4-BNyne. Shown is abond-map of 4-BNyne (a) before and (b) after the sudden failure onset. Blue atoms arenitrogen, yellow represents boron.

& Co. KGaA, Weinheim DOI: 10.1002/adem.201600112ADVANCED ENGINEERING MATERIALS 2016,

Fig. 7. Stress map of failure of 4-BNyne in the zigzag direction; (a) initial loading phase, (b) secondary loadingphase, (c) failure, (d) unraveling, (e) unraveled.

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be approximated as having at least the tensilestrength of the bonds in the hexagonal units ifwe consider them analogous to the single-chain form of carbon, carbyne, which hasbeen shown to have similar strength to that ofthe hexagonal structure, graphene.[21] It hasbeen shown by ab initio calculations that B–Nmonochains are at least as stable energeticallyas C–C monochains.[22] For the second factorcan be seen in the stress map in Figure 5, thecross-linker chains contribute a compressiveforce (in blue) to the sides of the hexagonalunits. This compressive force, coupled withthe tension from the chains along thedirection of tension, leads to a shear stress(see Supplementary Materials Figure S3)which causes the hexagonal unit to firstdistort, as the bond angles change but notbond length. This distortion more easilyallows the hexagonal unit to fail in such a

way that the cross-linking chains become an “extension” ofsorts for the chains already under tension (as is depicted inFigure 6), temporarily relieving stress in the linear chainswhile also distorting the entire structure, leading to furtherfailure. This diagonal failure process is similar to the “shearbands” seen in the failure of ductile or quasi-brittle nano-materials.[23] Since the entire structure is held together by thehexagonal rings, BNynes with larger L values have fewerrings to support the tensile load, and thus fail at a lower load,as evidenced in Figure 3. For BNynes in the zigzag direction,wewill show that, while there are similarities with ring failure

Fig. 8. Close-up bond map of deformation during tension along the zigzag direction. The sample is 4-BNyne (a)in-plane before tension, (b) cross-linkers bulging out-of-plane during tension, and (c) the compressed cross-linkers during the secondary loading phase. Coloration is based on the absolute value of z for each atom, based onthe initial plane being |z|¼ 0.

and unraveling phenomena, the deformationof the sample up to failure is a markedlydifferent process.

BNynes under the zigzag loading directionunravel in a similar manner when comparedwith the armchair direction; however, even forlarger values ofL there is no orderly initial rowof broken linkers as is seen for the armchairdirection for BNynes. This is due to thedifferentway stress accumulates for thezigzagmode samples, which in turn leads to adifferent mode of destruction upon failure.The deformation, failure, and subsequentunraveling phenomenon are shown in Fig-ure 7. As the material is stretched along the xdirection, it undergoes a far larger decreasealong the y direction (perpendicular to tensiondirection) than occurs for BNynes in thearmchair direction. The linear chains whichsupport the majority of the stress for thearmchair BNynes are now along the y direc-tion, and during the tensile process theysupport no stress, instead bulging out of planeas the tension causes the oblique cross-links tobe stretched along the x direction, as is shown

DOI: 10.1002/adem.201600112 © 2016 WILEY-VCH Verlag GADVANCED ENGINEERING MATERIALS 2016,

with a close-up view in Figure 8. Thisfigure is colored based onthe absolute valueof z for eachatom,with the initial planeof thesample set as |z|¼ 0. The stress-map in Figure 7 demonstratesthat most of the tensile stress is concentrated in the hexagonalunits,while the bulgingout-of-plane cross-linkers are subject tocompressive stress due to the squeezing effect in the ydirection.Similar to the behavior in the armchair direction, the materialfails at the hexagonal units, as the oblique chains are pulledapart from one another by the strong force in the x directioncaused by the tensile process, as can be seen by the close-upbond stress map in Figure 9. The similarity of the failure of the

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Fig. 9. Close-up of failure in zigzag 4-BNyne; (a) just prior to failure, (b) moment offailure, (c) unraveling phenomenon. Coloration follows the same stress-map scale asFigure 7.

M. Becton et al./Mechanical Properties of BNyne

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zigzag BNyne to the process shown in Figure 4 demonstratesthat, althoughzigzag-orientedBNyne is stiffer andweaker thanarmchair-oriented, they still undergo similar modes ofdeformation and failure, with the breaking of cross-linkerscausing an unraveling phenomenon in each case, although thedirectionality of the remaining chains creates a very cleardifference in strength, toughness, and stiffness, as shown in theprevious sections. This breaking of the cross-linkers is shown indetail in Figure 9a and b, and one can also clearly see thebulging-out-of-plane phenomenon occurring for the linearchains along the y direction which are highlighted in Figure 8.Carefully observing the failure process allows for betterexpectation and design when using this strong new materialin future applications.

4. Conclusions

Due to the recent meteoric rise in interest of hexagonal BNmaterials, it is therefore important to characterize the

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properties of its allotrope, BNynes, in order to betterunderstand how to utilize them in the nanodevices. Here,molecular dynamics simulations are performed to investigatethe mechanical properties and failure patterns of variousBNynes under the tensile loading. Simulation results indicatethat BNynes in both the armchair and zigzag directionsundergo two distinct phases of deformation leading up tofailure, and experience similar unraveling behavior afterfailure. It is shown that 1-BNyne is consistently much stiffer,stronger, and tougher than BNynes with higher numbers oftriple-single-bond linkers, while less distinction is madeamong other L. However, BNyne shows strong anisotropy forthe same number of acetylene-like linkers, stiffer yet weakerin the zigzag direction than the armchair direction. Lineartheoretical analyses are developed to relate the strength,stiffness, and toughness of the BNyne to its scaled latticespacing, enabling us to develop simple scaling laws for L-BNynes of any size. With these intriguing findings in mind, itcan be envisioned that BNynes can be considered a light buttough multi-responsive material in the nanodevices.

Article first published online: xxxxManuscript Revised: April 12, 2016

Manuscript Received: February 29, 2016

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