Che Zhng,Cheng Lu,＊,Linqing Pei,Jiqing Li,Rui Wng

a School of Mechanical,Materials,Mechatronic and Biomedical Engineering,University of Wollongong,Wollongong,NSW,2522,Australia

b College of Mechanical Engineering,Chongqing University,Chongqing,400044,China

Keywords:

ABSTRACT The three-dimensional(3D)graphene-based materials have raised significant interest due to excellent catalytic performance and unique electronic properties,while the preparation of uniform and stable 3D graphene structures remains a challenge.In this paper,using molecular dynamics simulations,we found that the nanotwinned copper(nt-Cu)matrix with small twin spacing can induce the wave-shaped wrinkling and sawtooth-shaped buckling graphene structures under uniaxial compression.The nt-Cu matrix possesses a symmetrical lattice structure for the lattice rotation with the dislocation annihilation,resulting in the transition of sandwiched graphene from 2D to 3D structures with good uniformity.The newly formed twin boundaries(TBs)in the nt-Cu matrix improve the resistance of graphene against the out-of-plane deformation so that graphene can maintain a stable wrinkling or buckling morphology in a wide strain range.These 3D texturing structures show great flexibility and their micro parameters can be controlled by applying different compressive strains.Furthermore,we propose a simple sliding method for decoupling graphene from the nt-Cu matrix without any damage.This work provides a novel strategy to induce and transfer the uniform wrinkling and buckling of graphene,which may expand the application of graphene in energy storage and catalysts.

1.Introduction

Transforming two-dimensional(2D)graphene sheets into threedimensional(3D)structures has attracted growing interest in recent years[1].Graphene can be easily warped in the out-of-plane direction because of low bending stiffness,exhibiting wrinkling,buckling and folding structures[2,3].The 3D graphene structures show distinct catalytic and electrical properties.For instance,a 3D honeycomb-like graphene sheet exhibits high catalytic performance as a counter electrode and it can achieve a high energy conversion efficiency(7.8%)in dye-sensitized solar cells[4].Pt-decorated 3D graphene-based nanoparticles are used as efficient methanol oxidation catalysts due to excellent catalytic activity[5].Furthermore,a simple operation of 3D texturing may lead to extraordinary changes of electronic properties.Unconventional superconductivity is realized in a superlattice structure created by stacking two sheets of graphene with a small‘magic’angle of about 1.1°[6].Trilayer graphene with ABA stacking has a massless Dirac-like band near the Fermi level[7],and the periodic wrinkles in graphene allow spin-polarized transport at low magnetic fields because of an enhanced spin-orbit interaction[8].The 3D graphene structures have a wide range of applications in energy storage[9],strain sensing[10],wettability surfaces[11],and catalysts[12].

A variety of efforts have been undertaken to induce the 3D texturing of graphene.Precisely folded graphene nanostructures are obtained by custom-design nanoscale origami[13].Suspended graphene sheets fold freely under intense mechanic stimulation[14].The formation of folded structures in graphene can be controlled by introducing curved templates during synthesis or transfer processes[15].A modified Cu(111)substrate and solvent-driven graphene-polymer bilayers have also been used to produce the wrinkling of graphene[16].However,most methods require harsh conditions.For example,graphene origami is achieved by using a tip of the scanning tunneling microscope(STM),which needs an extremely accurate operation at the atomic scale[6].Other methods require intense external stimulation[14],surface functionalization of graphene[17],artificially modified substrates[18],or complex solvent conditions[19].The uniformity and precision in the 3D geometries of graphene should also be further improved in functional electronic devices.

Copper is widely used metal for the synthesis and application of graphene.Due to the low solubility of carbon in copper and ease of graphene transfer,copper is an excellent choice as a substrate for the growth of graphene sheets by chemical vapor deposition(CVD)[20].Graphene/Cu nanocomposites also show excellent mechanical and thermal properties[21,22].However,a single-crystal Cu matrix is used in the CVD process and the orientation effect of Cu is not taken into consideration in some graphene/Cu nanocomposites[23,24].Recently,nanotwinned copper(nt-Cu)has attracted much attention because it exhibits ultrahigh strength,high ductility and electrical conductivity simultaneously[25,26].An attempt to synthesize graphene/nt-Cu composites with ultrahigh hardness was first undertaken by electrochemical deposition in 2017[27],while the other properties and potential applications of graphene/nt-Cu composites remain unknown so far.

There is an interesting softening phenomenon in the nt-Cu,known as the reverse Hall-Petch effect[28].As the twin spacing decreases,the strength of nt-Cu gradually increases to a maximum when the twin spacing is about 15 nm[29],while the strength drops with the further decreasing of twin spacing.The softening mechanism is explained by a large amount of orderly dislocation nucleation and movement in the twins[30].In this study,we found that nt-Cu with softening behavior can be a very suitable matrix to induce uniform wrinkling and buckling of graphene under uniaxial compression.These unique 3D graphene morphologies are firstly formed inside the nt-Cu matrix.After a simple sliding operation,they can be exposed to the surface of substrates for transfer and application.

2.Simulation methodology

The configurations of graphene/nt-Cu nanolayered composites are shown in Fig.1.An original Cu matrix is established in the X[1-1-2],Y[-1 1-1]and Z[1 1 0]directions respectively.Keeping the original crystal unchanged,successive atomic displacements on(111)planes are applied to generate the symmetric twin crystal along the X[1-1-2],Y[1-1 1]and Z[-1-1 0]directions[31].Different atomic displacements lead to different twin spacings.Then,single-layer or multilayer graphene is introduced into the nt-Cu matrix.The distance between graphene and the closest copper atoms is 3.1Åat equilibrium state,therefore the thickness of the vacuum layer for single-layer graphene is set as 6.2Å.The chirality of graphene is set as armchair along the X-axis and zigzag along the Z-axis.Fig.1(a)and(b)show one graphene sheet sandwiched in the nt-Cu matrix with twin spacing of 1.88 nm.For comparison,a composite with twin spacing of 3.94 nm and a composite without twin boundaries are designed as shown in Fig.1(c)and(d),respectively.In addition,an alternating composite is also constructed by introducing multilayer graphene into the nt-Cu matrix in Fig.1(e).Considering of the lattice mismatch and lattice distortion[32],an integer number of periodic units are required in the design of graphene and the nt-Cu matrix.The dimension of all models is about 440Åand 200Åin the X and Z direction respectively.The thickness in the Y-direction varies slightly because of different layers of graphene sheets.Every simulation model encapsulates more than 1.1 million atoms.More simulation details are shown in Table S1.

MD simulations were conducted by the open-source code Large-scale Atomic/Molecular Massively Parallel Simulator(LAMMPS)[33].A second-generation reactive empirical bond-order potential was employed to describe the carbon-carbon interaction in graphene[34].The interaction between Cu atoms was described by the embedded-atom method(EAM)[35].The interaction between carbon and Cu was described by a Lennard-Jones potential(potential depth 0.02578 eV,size parameter 3.0825Å)[36].After an energy minimization process,all models were relaxed in an isothermal-isobaric(NPT)ensemble at 10 K for a duration of 100 ps until the pressures in three directions were set to zero[37].The uniaxial compression was then applied along the X-axis with a strain rate of 5×108s-1.The zero pressure in the Y and Z directions is maintained by the NPT ensemble during the compressive loading.We applied periodic boundary conditions in all three directions.The open visualization tool(OVITO)were used to obtain structural information.The crystal structure is identified by common neighbor analysis(CNA).The copper atoms can be classified into face-centered cubic(FCC),hexagonal close-packed(HCP),or other types[38].The dislocation extraction algorithm(DXA)was applied to reveal the dislocation movement and identify the Burgers vectors[39].The stress component along X-direction(Sxx)is recorded for stress-strain curves and the stress component along the Y-direction(Syy)is also exported for further analysis.

Fig.2.The formation of wrinkling graphene structures in CTS1.(a)The stress-strain curve of CTS1.(b)The atomic CNA results at points A(ε=0.0825),B(ε=0.0855),C(ε=0.0862),D(ε=0.0871),E(ε=0.1075),and F(ε=0.1281).

3.Results and discussion

3.1.Wrinkling structures of single-layer graphene

Fig.2(a)shows the stress-strain curve of the graphene/nt-Cu composite with twin spacing of 1.88 nm(CTS1)under uniaxial compression.An obvious feature of the curve is that there are two linear increasing parts of stress.The first linear increasing stage corresponds to the elastic deformation of the composite.The primitive wrinkles of graphene are observed with local lattice disturbance at point A in Fig.2(b),which trigger the nucleation of a small amount of dislocations.Then stress starts to decrease after point A with the plastic deformation in the nt-Cu matrix.It can be seen from point B in Fig.2(b)that numerous dislocations generate and propagate near the graphene surface.The intersections between dislocations and twin boundaries(TBs)result in the gradual disappearance of original TBs.It is worth noting that there is a small fluctuation of stress at point B in Fig.2(b),indicating the movement of these dislocations can be restricted to some extent by the nt-Cu substrate with dense original TBs.The stress decreases sharply when nearly all original TBs collapse at point C.

However,the stress of CTS1 increases linearly again from point D until reaching a maximum at 14.1 GPa.The recovery of elasticity can be explained by the annihilation of dislocations due to the rotation of lattice orientation.With the continuous dislocation propagation from point A to point D under compressive loading in Fig.2(b),the angle between the symmetrical twin structures is gradually decreased after the disappearance of original TBs(Fig.S1).The dislocation density evolution indicates that there isan obvious annihilation of moststackingfaults from point D to point E(Fig.S2).Once the annihilation process is completed,a large number of newly formed TBs are vertical to the compression direction at point E in Fig.2(b).Finally,point F shows the second plastic deformation behavior with a sharp drop in stress.Small wrinkles in graphene are observed from point B to the second yield point,which is marked as point Y in Fig.2(a).Fig.3(a)shows that a wave-shaped morphology of graphene is initially formed at point B,in which the distance between adjacent wave crests is about 1.25 nm.These wrinkles exhibit a uniform distribution and can exist stably in a wide strain range from 0.0855(point B)to 0.1247(point Y).Fig.3(b)shows that the distance between adjacent wave crests is decreased to about 1.19 nm at point Y,while their thickness increases slightly from 0.23 nm to 0.32 nm with the increase of compressive strain.The relationship between the compressive strain and the morphology of graphene is shown in Fig.3(c).The distance and thickness have decreasing and increasing trends respectively under compressive loading.These micro parameters of wrinkling structures can be controlled by applying different compressive strains,which may induce variable mechanical and electronic properties.

Fig.3.Two representative wave-shaped morphologies of graphene during compression:(a)point B(ε=0.0855)and(b)point Y(0.1247).Copper atoms have been omitted for clarity.(c)The relationship between the compressive strain and the morphology of graphene.

3.2.The formation mechanism of wrinkling structures

The compression simulations of the other two composites have been performed for comparison.Fig.4(a)shows the stress-strain curves of a composite with twin spacing of 3.94 nm(CTS3)and a composite without twinboundaries(CWTB).There isonlyone linear increasing part of stressin both curves and then followed by a sharp drop.The primitive wrinkles of grapheneinCTS3areobservedatpointAandtheyresultinthenucleationof some dislocations in the inset of point A in Fig.4(b).However,when these wrinkles-induced dislocations generate,many other dislocations have alreadyexistedinCTS3.Forthesepre-existingdislocationsinCTS3,theyare first nucleated from the nt-Cu matrix(Fig.S3).In contrast,as we have discussed in Fig.2(b),the nucleation of all initial dislocations is from the wrinkles/copper interface in CTS1.Two dislocation nucleation modes are attributed to their difference in twin density,as dense TBs can act as effective stress concentrators to affect the yielding behavior[40].Our results are similar to the heterogeneous-to-homogeneous dislocation nucleation in ultra-twinned Au nanowires below a critical twin size(2.8 nm)[41].Theprimitive wrinklesinCTS3arefurther compressedtoformfoldsat point B in Fig.4(b).The original TBs do not collapse in the plastic deformation.Similar folding structures in CWTB are observed at point C and point D in Fig.4(b).Such a deformation of graphene from wrinkles to folds inasingle-crystal metalmatrixisconsistent withthe previouswork[36,42].

In order to investigate why the wrinkles in CTS1 can maintain a uniform wave-shaped morphology rather than forming folds,the Sxxand Syystress components of graphene in CTS1 and CWTB are obtained for further analysis.As shown in Fig.5(a),when the primitive wrinkles of graphene generate in CTS1,the Sxxof carbon atoms shows a homogeneous distribution at about-35 to-25 GPa,which indicates that the compressive loading is well distributed in all parts of graphene sheet.Meanwhile,the Syyshows that the graphene surface is under tensile stress along Y-direction at about 7 GPa.The banded distribution of Syyis in oneto-one correspondence with these wrinkles in graphene.This result evidently reveals that the movement of wrinkles along Y-direction is strongly hindered by the nt-Cu matrix.More importantly,the annihilation process leads to the formation of newly formed TBs that are perpendicular to the compression direction.These vertical TBs are evenly distributed on the surface of graphene and they can serve as barriers for large local deformation of graphene.In this case,the resistance of graphene against the out-of-plane deformation is enhanced so that the external loading can be well distributed throughout the whole surface of graphene,which is beneficial for the formation of uniform wrinkles.In contrast,the Sxxand Syyof graphene in CWTB both show an inhomogeneous distribution in Fig.5(b).For the carbon atoms located at the wrinkles,their Sxxis nearly zero with compressive Syy,indicating there is a rapid stress release caused by the formation from wrinkles to folds.Since the compressive loading is released in the central region,the other parts of graphene surface still maintain a flat morphology.Due to a lack of sufficient resistance for the out-of-plane deformation,the primitive wrinkles in CWTB can be easily compressed to form folds.

3.3.Buckling structures of multilayer graphene

By the incorporation of multilayer graphene while keeping the twin spacing constant,marked as ASTB in Fig.6(a),we found the uniform buckling structures can be observed in the nt-Cu matrix.Fig.6(b)shows that the primitive wrinkles of multilayer graphene provide preferential sites for dislocation nucleation.The nucleation of all initial dislocations is from the wrinkles/copper interface rather than from the nt-Cu matrix.At a strain of 0.0602,the stress distribution shows that the average compressive Sxxof carbon atoms is 40.2 GPa,while the value of Cu is only 9.5 GPa(See Fig.S4).These results indicate that multilayer graphene sheets play a similar role to dense TBs in CTS1,which can serve as stress concentrators to affect yielding behaviors.The subsequent plastic deformation of ASTB also involves the lattice rotation and dislocation annihilation.Fig.6(c)shows that the original TBs of ASTB have collapsed due to the lattice rotation.Graphene surfaces are crumpled with some wrinkles.Then,the lattice rotation occurs with the annihilation of most dislocations from Fig.6(c)-6(f).Such a process in nt-Cu matrix also leads to the transition of sandwiched graphene from disorder to order.Fig.6(f)shows that ASTB has a uniform grid structure.The perfect FCC Cu atoms are distributed adjacent to the flat parts of graphene,while newly formed TBs are located at every turning point in the sawtooth-shaped graphene sheets.

We note that such a structural change of ASTB from Fig.6(b)-6(f)is very fast.It occurs in a small strain range from 0.0692(point A)to 0.0731(point B)(see Fig.7(a)).Once the lattice rotation is completed with the annihilation of all dislocations,the stress increases linearly again until reaching the strain of 0.1214(point C).Fig.7(b)shows that the distance‘W’is about 5.06 nm at point B and it decreases continuously to about 4.79 nm at point C.The bending angleαalso decreases from 138.1°to 129.8°,while the thickness‘T’increases from 0.82 nm to 1.15 nm from point B to point C.These results indicate that the multilayer graphene sheets can maintain a stable buckling morphology in a wide strain range.Such flexibility may enhance the fault tolerance in experimental preparation and broaden its application prospects[43].The corresponding Syyin Fig.7(d)indicates that the turning areas of graphene sheets bear high tensile stress at 7.5 GPa.Considering that the newly formed TBs are located precisely at these turning areas in Fig.6(f),the regular distribution of Syyindicates that these new TBs in the nt-Cu matrix provide intensive support for the maintenance of a sawtooth-shaped graphene morphology.

Fig.4.The deformation from wrinkles to folds in CTS3 and CWTB.(a)The stress-strain curves of CTS3 and CWTB.(b)The atomic CNA results at points A(ε=0.0845),B(ε=0.0995),C(ε=0.0803),and D(ε=0.0995).The inserts in the lower right corner are to enlarge the wrinkling or folding regions of graphene for a clearer observation.

Fig.5.The comparison of stress distribution in graphene surface between CTS1 and CWTB.(a)The wrinkling of graphene in CTS1 with homogeneous distribution of Sxx and banded distribution of Syy.(b)The folds in CWTB with a rapid stress release.

Fig.6.The formation of buckling graphene structures in ASTB under compressive loading.The atomic CNA results at(a)ε=0,(b)ε=0.0692,(c)ε=0.0703,(d)ε=0.0713,(e)ε=0.0725,and(f)ε=0.0731.

Fig.7.The stability and flexibility of buckling structures in multilayer graphene/nt-Cu composites.(a)The stress-strain curve of ASTB.(b)The schematic illustration for distance‘W’,bending angleαand thickness‘T’.(c)The sawtooth-shaped morphology of multilayer graphene sheets at strain of 0.10 and(d)the corresponding Syy stress distribution,where the nt-Cu matrix has been hidden for clarity.

3.4.The synergistic movement of graphene and nt-Cu matrix

To examine the importance of the nt-Cu matrix in the formation of uniform buckling structures,we constructed another model based on ASTB,in which a single-crystal Cu matrix is used to replace the nt-Cu matrix while keeping the other conditions unchanged.It can be seen from Fig.8(a)that the primitive wrinkles of graphene lead to the nucleation of initial dislocations(Burgers vectors b=(1/6)[2 1-1]).After further compression,high density and tilted TBs were formed at the graphene/Cu interfaces,which is consistent with the previous study[22].The graphene morphology has an inhomogeneous distribution and shows a certain degree of inclination with respect to the compressive direction.Some residual dislocations still exist in the marked areas in Fig.8(a),resulting in a weak work hardening compared to that in ASTB(Fig.S5).The result of this comparison reveals the superiority of the nt-Cu matrix for the uniformity of buckling structures,as the nt-Cu matrix possesses a symmetrical lattice structure.When the twin spacing is small enough,the nt-Cu matrix becomes so soft that lattice rotation may occur with the dislocation annihilation.This process provides a driving force for the evolution of sandwiched graphene morphology from disorder to order as discussed in Fig.6.In addition,after the annihilation,newly formed TBs that are perpendicular to the compression direction can provide a supporting skeleton for graphene sheets.In contrast,for the graphene sheets in the single-crystal Cu matrix,they cannot form uniform buckling structures due to the residual dislocation movement without dislocation annihilation.

The incorporation of graphene is also an indispensable condition for the lattice rotation.To prove it,the compression simulation of pure nt-Cu has been conducted in Fig.8(b).Its plastic deformation is dominated by dislocation processes on different slip planes,leaving plenty of zigzag stacking faults.These structures are hardly destroyed even after being deformed by 20%strain.However,it can be seen from Fig.6 that these zigzag stacking faults can be easily changed in the presence of graphene.The synergistic movement of graphene and the nt-Cu matrix may be driven by two factors.First,it is well known that decoupling of graphene from the Cu matrix is very easy because of weak interfacial bonding.In this work,even if the decoupling movement is limited in a nanolayered structure,it is still easy for copper atoms to slip or rotate on the graphene surfaces under compressive loading.Second,the incorporation of multilayer graphene sheets can split a large thickness of the nt-Cu matrix into several thin films.In this case,each separated Cu film has a free space for the lattice rotation,which promotes the evolution of graphene morphology.

3.5.The decoupling of graphene from nt-Cu matrix

The uniform wrinkling and buckling of graphene are obtained under certain conditions and it is expected that they can be used in various applications.Previous studies indicate that graphene transfer is a key for its applications[44].The graphene sheets should be isolated from original substrates and then transferred to the target materials.The‘wet transfer method’is a widely used approach for chemical vapor deposition(CVD)-grown graphene transfer,in which polymeric polydimethylsiloxane(PDMS)or poly(methyl methacrylate)(PMMA)is used as a protective layer on the surface of graphene to minimize the transfer damage,followed by etching of the underneath substrate[45].However,as shown in Fig.9(a)and(d),thegraphenesheetswithuniquemorphologiesareembeddedinthe nt-Cu matrix,which makes it difficult for direct transfer.Thus,a necessary stepistoexposegraphene tothe surface ofthe nt-Cumatrix.Toachievethis,we first try to move the upper substrate along the Y-direction while keeping the lower substrate unchanged in Fig.9(b)and(e),but the results are unsatisfactory.The original wrinkling and buckling of graphene would be damaged in the decoupling process in Fig.S6.As shown in Fig.9(c)and(f),withtheincreaseofthedistancebetweenupperandlowerCusubstrates,the graphene-Cu interaction becomes weaker.Most carbon atoms in graphene are suspended in the gap rather than clinging to the substrate.Therefore,graphene loses its original morphology due to the lack of enough support from the nt-Cu matrix.

Fig.8.The compressive behavior of the graphene/single-crystal Cu composite and pure nt-Cu.(a)The inhomogeneous distribution of graphene sheets in the singlecrystal Cu matrix.(b)Atomic configurations of pure nt-Cu under uniaxial compression.

We propose another method by forcing the nt-Cu matrix to slide along the Z-direction,which is proved as a better choice for decoupling graphene.The sliding operation in CST1 is represented in Fig.10(a).The single-layer graphene with wrinkling structures is sandwiched by two nt-Cu substrates and only one substrate is given an initial velocity in the Zdirection.When this substrate slides,graphene also moves slightly along the Z-direction because of a weak Cu/graphene interaction[46].It can be seen from Fig.10(b)that region B is embedded in two substrates.A and C regions are exposed to the surface after the sliding process along the Z-direction.Fig.10(a)and(b)show graphene can maintain a uniform wrinkling morphology in the sliding process without any damage,as the carbon atoms in all regions are still supported by one-side substrate at least to avoid suspension.The buckling structures in ASTB can also be retained to the greatest extent by using this sliding method as shown from Fig.10(c)and(d).Due to a good blocking effect of four-layer graphene sheets,the whole nt-Cu matrix is divided into five thin Cu substrates.These films are independent of each other and they can slide freely along the Z-direction.Setting the gradient sliding speed for each layer of the substrate is an efficient method for decoupling multilayer graphene sheets in Fig.10(e).Once graphene sheets are exposed to the surface of substrates,they are similar to CVD-grown graphene sheets,which can be transferred for target applications by various advanced approaches[47,48].

4.Conclusions

In summary,we used MD simulations to investigate the formation of unique 3D graphene structures in the nt-Cu matrix under uniaxial compression.The single-layer graphene shows a uniform wrinkling morphology rather than forming folds,as new vertical TBs are evenly distributed on the surface of graphene,providing strong support to avoid large local deformation of graphene.The buckling structures are also obtained in the multilayer graphene/nt-Cu nanocomposites.The lattice rotation and the annihilation of dislocations during compression promote obvious changes of the graphene morphology from disorder to order.Both wrinkling and buckling structures show good stability in a wide strain range with small changes of micro parameters.Furthermore,a simple sliding method was proposed for the decoupling of graphene from the nt-Cu matrix.The unique 3D graphene morphology can be exposed to the surface of the nt-Cu matrix for the subsequent transfer process.Our findings are promising because they provide an effective approach to transform flat graphene sheets into uniform wrinkling and buckling structures,thereby promoting the application of 3D graphene structures in various fields such as energy storage and catalysts.

Fig.10.Satisfactory decoupling performance in the sliding process along the Z-direction.(a)Schematic illustration for the sliding operation in CST1.(b)The intact wrinkling morphology when the distance of the sliding is 13.3 nm,where A,B and C regions are marked by dotted lines.(c)A representative sliding operation in ASTB.(d)The intact buckling structures when the distance of the sliding is 19.1 nm.(e)Decoupling multilayer graphene sheets by setting the gradient sliding speed for each layer of the nt-Cu matrix.

Declaration of competing interest

None.

Acknowledgments

This work is supported by Australia Research Council Discovery Project(DP170103092)and National Natural Science Foundation of China(NSFC51701030).Simulations were performed using computing facilities provided by National Computational Infrastructure(NCI),which is supported by the Australian Government.J.L.and R.W.greatly acknowledge financial support from China Scholarship Council(CSC).

Appendix A.Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.nanoms.2020.06.002.