Boron doping effect on the interface interaction and mechanical properties of graphene reinforced copper matrix composite

Accepted Manuscript Title: Boron doping effect on the interface interaction and mechanical properties of graphene reinforced copper matrix composite Authors: Bingcheng Fang, Jiajun Li, Naiqin Zhao, Chunsheng Shi, Liying Ma, Chunnian He, Fang He, Enzuo Liu PII: DOI: Reference:

S0169-4332(17)32074-3 http://dx.doi.org/doi:10.1016/j.apsusc.2017.07.084 APSUSC 36618

To appear in:

APSUSC

Received date: Revised date: Accepted date:

5-5-2017 27-6-2017 11-7-2017

Please cite this article as: Bingcheng Fang, Jiajun Li, Naiqin Zhao, Chunsheng Shi, Liying Ma, Chunnian He, Fang He, Enzuo Liu, Boron doping effect on the interface interaction and mechanical properties of graphene reinforced copper matrix composite, Applied Surface Sciencehttp://dx.doi.org/10.1016/j.apsusc.2017.07.084 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Boron doping effect on the interface interaction and mechanical properties of graphene reinforced copper matrix composite Bingcheng Fang,a Jiajun Li,a Naiqin Zhao,*,a,b Chunsheng Shi,a Liying Ma,a Chunnian He,a Fang He,a Enzuo Liu,*,a,b a

School of Materials Science and Engineering and Tianjin Key Laboratory of

Composites and Functional Materials, Tianjin University, Weijin Road, No. 92, Tianjin 300072, China b

Collaborative Innovation Center of Chemical Science and Engineering, Weijin Road,

No. 92, Tianjin 300072, China *Corresponding author. Tel. & Fax. : +86 22 27891371. E-mail address: [email protected] (E. Z. Liu), [email protected] (N. Q. Zhao).

Graphical abstract”:

Highlights: 

The chemical role of the intermediate O between Cu and graphene is revealed.



Interaction between Cu and B- and N-doped graphene with integrity are studied.



B doping effect is comparable to or even better than the intermediate oxygen.



B doping enhances the mechanical properties of graphene/Cu composite.

1

Abstract In order to explore an efficient way of modifying graphene to improve the Cu/graphene interfacial bonding and remain the excellent mechanical and physical properties of graphene, the interaction between Cu and the pristine, atomic oxygen functionalized and boron- or nitrogen-doped graphene with and without defects was systematically investigated by density functional theory calculation. The electronic structure analysis revealed that the chemically active oxygen can enhance the binding energy Eb of Cu with graphene by forming strong covalent bonds, supporting the experimental study suggesting an vital role of intermediate oxygen in the improvement of the mechanical properties of graphene/Cu composites. Due to the strong hybridization between Cu-3d electron states and the 2p states of both boron and carbon atoms, the boron-doping effect is comparable to or even better than the chemical bridging role of oxygen in the reduced graphene oxide reinforced Cu matrix composite. Furthermore, we evidenced an enhancement of mechanical properties including bulk modulus, shear modulus and Young modulus of graphene/Cu composite after boron doping, which closely relates to the increased interfacial binding energy between boron-doped graphene and Cu surfaces.

Keywords Density functional calculations; Intermediate oxygen; Boron (nitrogen)-doped; Interfacial bonding; Mechanical modulus

1. Introduction In the past decade, extensive experiments have been carried out on using carbonaceous nanomaterials as reinforcement in metal matrices in order to obtain 2

lightweight metal matrix composites (MMCs) with excellent mechanical properties [1-5]. Graphene, a two-dimensional (2-D) single atomic layer of strong sp2 hybridized carbon atoms [6], has recently gained considerable interest as a reinforcement material for MMCs owing to its extraordinary mechanical, electrical and thermal properties [7-9]. As compared to its 0-D and 1-D counterparts, the planar structure and the larger specific surface area of graphene is expected to improve the load transfer capacity in the MMCs more significantly [10, 11]. Moreover, the production cost of graphene in large quantities is much more cost-effective [12, 13]. Therefore, graphene is more suitable relative to other carbon materials as an effective and economical reinforcement material for the manufacture of MMCs. Copper (Cu) is a ductile metal with excellent electrical and thermal conductivity but poor mechanical strength. Thereby, graphene is expected to be a promising reinforcing material for Cu. To make the most efficient use of the reinforcing function of graphene, a homogeneous dispersion of graphene in the Cu matrix and a robust interfacial bonding between graphene and Cu are of fundamental importance [14-20]. The approach of in-situ growth of graphene on flaky Cu powder surface [21] and the technique of fabricating Cu/graphene composites by high-ratio differential speed rolling [22] are effective to achieve uniform-dispersed graphene in the Cu matrix. As for the interfacial bonding between graphene and Cu, both experimental and theoretical studies demonstrate that the adhesion between pristine graphene (P-GR) and Cu surface is weak [23-28]. The obtained mechanical measurements were obviously below the theoretical predictions. On the other hand, the interface bonding 3

between Cu and graphene could be improved by chemical bridging role of oxygen originated from the graphene oxide as the precursor using a molecular-level mixing process, which results in the enhancement of the modulus and strength of Cu matrix [29, 30]. However, this method is not suitable for bulk production, and the residual oxygen functional groups would enormously reduce the electrical conductivity and mechanical properties of graphene [17, 31]. Thus, it is necessary to provide a new strategy to improve the interfacial bonding between Cu and graphene to meet the demand of the integration of structure and function. It is well known that the boron- or nitrogen- doping effect can modulate the electronic structure and change the chemical properties of graphene [32-35], which will eventually affect the Cu/graphene interface. Moreover, it has been reported that boron or nitrogen doped graphene exhibits higher electrical conductivity than P-GR [36], and the elastic modulus of boron or nitrogen doped graphene is of the similar magnitude as that of P-GR [37, 38].Therefore, it is imperative to evaluate the boron or nitrogen doping effects on the interaction between Cu and graphene through the comparison with the chemical bridging role of oxygen in a reduced graphene oxide (RGO) reinforced copper matrix composite with theoretical calculations. For this reason, the effects of intermediate oxygen, boron and nitrogen doping on the interaction behavior of a single Cu atom adsorbed on the surface of graphene with and without defects are systematically studied through first-principles total energy calculations. The present calculations reveal that both boron and nitrogen doped graphene have a positive effect on the Cu surface adsorption, and it is worth noting 4

that the improved binding energy induced by doping boron is comparable to or even better than that by the mediate oxygen bridging Cu and graphene in the experiments. Furthermore, to evaluate the boron-doping effect on the mechanical property of Cu/graphene composites, the elastic properties calculation of graphene/Cu composites with and without doping boron was performed subsequently.

2. Computational details All results reported here were calculated using the projector augmented wave (PAW) formalism [39, 40] of density functional theory as implemented in the Vienna ab initio simulation package [41, 42]. A kinetic energy cutoff of 400 eV was used with a plane-wave basis set. In order to model a Cu atom adsorbed on single graphene layer with defects, we chose a 5×5 hexagonal supercell of graphene as the simulation cell. In the direction perpendicular to the graphene plane, a vacuum region of 20 Å was used to eliminate the interactions between the neighboring images. Spin polarization is considered and the exchange–correlation interactions between electrons were treated within the generalized gradient approximation (GGA) refined by Perdew, Burke and Ernzerhof (PBE) [43]. The stable geometries of defective graphene and the energy-minimized structures of pristine and defective graphene with atomic oxygen, boron or nitrogen were obtained firstly by allowing both the atomic positions and the cell shape to vary. Then, the combined configurations with Cu adsorbed were optimized until the maximum force acting on each atom converged to 0.01 eV/Å or less. All internal coordinates were fully relaxed with a Gaussian smearing width of 0.05 eV, while the lattice constants were kept fixed. The Brillouin 5

zone was sampled using  -centered scheme with 3×3×1 k-point grid for the structural optimization. For the converged structures, subsequent energy and electronic properties calculations with a larger 7×7×1 k mesh were performed. The tetrahedron method together with Blöchl corrections [44] was used, and the convergence criterion was set to 10-5 eV. In the elastic property calculations, a hexagonal supercell consisting of 48 atoms (40 Cu atoms and 8 carbon atoms of P-GR) was considered on account of the executable amount of computational effort, and the exchange-correlation functional is approximated with the local density approximation (LDA) [45] because it is established that LDA predicts graphene/metal interfacial geometries in closer agreement with experiment than does the GGA [27, 46, 47]. All the structures are fully relaxed with respect to cell shape, volume, and atomic coordinates. Since structural resemblance of Cu(111) to graphene, the supercell system of 2×2 graphene cells accommodated on the

3  3 Cu(111) surface was used to construct interface

model with the pre-strains in graphene are 1.76% in the framework of LDA.

3. Results and discussion 3.1. Doping effect on the interaction between Cu and P-GR As a benchmark, the adsorption of Cu on the P-GR was performed in the first place so as to reveal the effects of mediate oxygen and boron or nitrogen doping on the interaction between Cu and graphene. Because of the hexagonal symmetry of the P-GR lattice, three high symmetry adsorption sites (T, B, and M) for a single adatom were studied as shown in Fig. 1(a). Site B (Fig. 1(c)) is the most stable adsorption site 6

for Cu atom with the Cu-C bond length of 2.16 Å, in agreement with the previous results [48]. In order to reveal the chemical role of the intermediate oxygen, and evaluate the boron and nitrogen doping effects on the interaction between Cu and graphene, the binding energy Eb of a Cu atom on various graphene is defined as (1) where ECu, Egraphene, and ECu/graphene are the energies of a Cu atom in its ground state, various graphene and the corresponding complexes after relaxation, respectively. The Eb and the related bond length are summarized in Table 1. Eb is 0.25eV on P-GR, which is consistent with the weak adsorption obtained in other theoretical studies [49, 50]. The partial density of states (PDOS) analysis of Fig. 2(a) showed a negligible interaction between the Cu and the carbon atoms, which can be seen further from limited electron accumulation in the region between Cu and carbon atoms in the differential charge density contours shown in Fig. 3(a). The most stable configurations of P-GR-O with and without Cu were shown in Fig. 1(b) and (d), respectively. The favored adsorption position for oxygen atom is also the “B” site with two C-O bond lengths are 1.47 Å. When the atomic Cu was attached around the oxygen of the graphene, Cu still sat above the C-C bond and the oxygen atom was dragged to the T site with a Cu-O bond length of 1.87 Å as shown in Fig. 1(d). The Eb of Cu on the P-GR-O markedly increases to 1.53 eV and the strong interaction can be corroborated by the electronic structure analysis. In Fig. 2(b), the 2p electron states of the oxygen atom has extensive overlap with Cu-3d states in the energy interval from -3 eV to 1.5 eV across the Fermi level, which 7

is consistent with covalent bond characteristic between Cu and oxygen atoms shown in Fig. 3(b). On the other hand, the increasing 2p electron states of the C1 atom in the vicinity of the Fermi level induced by oxygen strongly hybridize with Cu-3d states, also there are two superimposed DOS peaks between the 2p states of oxygen and the C3 atoms at -6 and -3 eV. Consequently, these superimposed peaks of the oxygen 2p states with the states of the Cu and carbon atoms at the Fermi level account for the enhanced Eb between Cu and P-GR. After revealing the chemical role of oxygen in the RGO reinforced Cu matrix composites, a comparative study of boron- and nitrogen-doping effects on the Eb between Cu and P-GR is discussed in some detail. The boron and nitrogen doped P-GR models are built in which one carbon atom is substituted by one boron or nitrogen atom. Fig. 1(e) shows that the energetically favorable adsorption site for Cu atom is on the top of the boron-carbon bond with the Cu-B and Cu-C bond lengths of 2.06 Å and 2.12 Å, respectively. Compared with P-GR, boron-doping enhances Eb with the Cu atom adsorbed on the similar site from 0.25 to 1.43 eV. From the PDOS analysis in Fig. 2(c), it is apparent that Cu-3d states are more delocalized than the case in Fig. 2(a) and it can be strongly hybridized with both 2p states of the boron and carbon atoms from -4.5 to 0.5 eV across the Fermi level. The stronger interaction between the Cu atom and P-GRB can be seen further from more electron accumulation between Cu and boron or carbon in the different charge density contours shown in Fig. 3(c). Therefore, the enhanced Eb can be ascribed to the pronounced hybridization between a 8

more delocalized Cu-3d states and the 2p states of both boron and carbon atoms. As for the adsorption of a Cu atom on the P-GRN surface, the most stable position for the Cu atom is above the carbon atom neighboring the nitrogen dopant with a Cu-C bond length of 2.03 Å. The marginal increase of Eb is 0.18 eV, which is associated with a greater degree of electron density accumulation along Cu-C bond observed from the differential charge density contours shown in Fig. 3(d). The further insight into the superimposed DOS peaks between the 2p states of the carbon atom and Cu-3d states at the Fermi level shown in Fig. 2(d) is in good accordance with the results mentioned above. More specifically, the electron localization around nitrogen at the expense of weakening the π-π interactions of the neighboring carbon atoms due to the larger electron affinity of nitrogen, resulting in the enhanced interaction between Cu and the carbon atom neighboring the nitrogen dopant. Given that defects inevitably exist in graphene during the practical preparation process, the most common types of native point defects such as Stone-Wales (SW) and monovacancy (MV) defects are taken into account in our work. 3.2 Doping effect on the interaction between Cu and SW-GR As for the boron and nitrogen doping in SW-GR, six inequivalent carbon atoms marked as 0 to 5 shown in Fig. 4(a) are considered to be substituted by one boron or nitrogen atom. The boron and nitrogen dopants in SW-GR energetically prefer to occur at the carbon sites marked as 4 and 3, respectively. (detailed data are listed in the Supporting Information, Table. S1) On the SW-GR surface (Fig. 4(c)), the Cu atom bonded to the carbon atom 9

marked as 1 with a Cu-C bond length of 1.99 Å. Eb is larger than that of P-GR case, which is associated with the overlap between 2p states of the carbon atom and Cu-3d states at about -3.2 and -2 eV. As shown in Fig. 4(b), the most stable position of oxygen on the SW-GR surface is above the C-C bond between the two pentagons with two C-O bond lengths of 1.45 Å. However, the oxygen atom moved to the top site of the C3 atom (Fig. 4(d)) as the Cu atom approached the SW-GR-O, and the stable position for Cu atom is above the C-C bond. The serious deformation of the SW-GR observed in the side view significantly enhanced the Eb from 0.57 to 1.65 eV. PDOS analysis in Fig. 5(b) shows that the 2p states of oxygen has extensive overlap with Cu-3d states between -4 and 0.5 eV in addition to the 2p states of the carbon atoms in the energy interval from -6 to 0.5 eV across the Fermi level. The mechanism for the enhancement in Cu adsorption on SW-GR-O is virtually identical to the P-GR-O/Cu case. According to the combined configuration shown in Fig. 4(e), Cu atom prefers to bind with the boron atom and the carbon atom marked as 2 with the Cu-B and Cu-C bond lengths of 2.01 and 2.10 Å, respectively. The extensive overlap between Cu-3d states and the 2p states of both boron and carbon atoms in the region between -4.7 and -2.4 eV shown in Fig. 5(c) is responsible for the enhanced interaction (1.50 eV of Eb) between the Cu atom and SW-GRB. On the other hand, the most energetically favorable site for a Cu atom on SW-GRN is found to be located above the carbon atom marked as 1’ shown in Fig. 4(a). The resulting Eb and the equilibrium Cu-C distance are 0.48 eV larger and 0.02 Å 10

shorter than those in the SW-GR case without nitrogen, respectively. Because the Cu-N distance (4.55 Å) is too long to contribute the interaction between Cu and the SW-GRN, the hybridization between the 2p states of the carbon atom and Cu-3d states near the Fermi level shown in Fig. 5(d) is supposed to be the central reason for the improvement of Eb. The theoretical explanation for the increase of the reactivity of the carbon atoms marked as 1’ after nitrogen doping is given in the Supporting Information, Fig. S1. As outlined above ， we have evidenced that the oxygen functional group dramatically strengthens the interaction between Cu and graphene with and without Stone-Wales defect. On the other hand, the boron- and nitrogen-doping enhance the Eb between Cu and graphene under different degree, and the boron-doping effect is comparable to the chemical bridging role of oxygen in RGO reinforced Cu matrix composites in the light of our results. 3.3 Doping effect on the interaction between Cu and MV-GR As can be seen in Fig. 6(a), the MV undergoes a Jahn-Teller distortion leading to the rearrangement of the three dangling bonds to form the pentagon-enneagon structure, which leaves one active dangling carbon marked as 1. Compared with the SW-GR, there are eight inequivalent carbon atoms marked as 0 to 7 in the MV-GR shown in Fig. 6(a) and the carbon atoms marked as 5 and 1 are the most favorable substitution sites for boron and nitrogen atoms according to our calculations. (detailed data are listed in the Supporting Information, Table. S2) As expected, the MV substantially improved the interaction between Cu and 11

graphene with three short Cu-C bonds of about 1.88 Å as shown in Fig. 6(c), and then the Eb increased to 3.31 eV. The significant enhancement in the Eb is caused by the extensive overlap between Cu-3d states and the 2p states of the carbons at the MV defect, especially the strong hybridization between them around the Fermi level displayed in Fig. 7(a). The stable configuration of adsorbing atomic oxygen in the MV-GR is consistent with the geometry of oxygen doped graphene with three C-O bond lengths of 1.49 Å as shown in Fig. 6(b). The oxygen thus passivated the active dangling carbon in the MV-GR and the Eb reduced to 1.54 eV as a result of forming one Cu-C bond after the Cu adsorption. It is evident that the superimposed DOS peaks between the Cu atom and the carbon atoms around the vacancy in the vicinity of the Fermi level in Fig. 7(a) was not observed in Fig. 7(b), even though the simultaneous hybridization of oxygen with the states of the Cu and carbon atoms occurs as they do in the P-GR and SW-GR cases. In contrast to the conspicuous decrease of Eb derived from the passivation of oxygen, we found the Eb of Cu on the MV-GRB decreases somewhat to 3.17 eV whereas the equilibrium distances between Cu and the three atoms at the vacancy increase slightly in terms of the data listed in Table 1. Specifically, the optimized structure in Fig. 6(e) showed that the boron atom moves towards to the C1 and C2 atoms and the distances between C1-B and C2-B are confirmed to be 0.17 and 0.35 Å shorter than those of C1-C3 and C2-C3 depicted in Fig. 6(c), respectively. The closer interatomic distance would result in higher electron density around the vacancy and thus contributes the short-range electron repulsion to the Cu atom so that a reduced 12

interaction between Cu and MV-GRB. Compared with PDOS analysis in Fig. 7(a), the lesser hybridization between Cu-3d states and the 2p states of both boron and carbon atoms around the Fermi level was observed in Fig. 7(c). In addition, the Eb of Cu on the MV-GRN declines to 2.50 eV. As shown in Fig. 7(d), for Cu, the fully occupied 3d electron states form a narrow high peak at about -0.8 eV, indicating an increase of electron localization. In the same vein, the 2p states of the nitrogen atom are very local around the Fermi level, which is derived from the large electron affinity of itself with respect to the surrounding carbon atoms. Accordingly, the more localized behavior of their electron states is in fair agreement with the longer Cu-N bond length than the respective Cu-C bonds listed in Table 1, so that the interaction between the Cu atom and MV-GRN decreases inevitably. As opposed to the cases of P-GR and SW-GR, the atomic oxygen at the vacancy and boron- (nitrogen-) doping are all disadvantageous to the interaction between Cu and MV-GR. It is apparent that the reduced Eb caused by the passivation of the active dangling bond by oxygen is much more than that induced by boron doping. 3.4. The mechanical properties of graphene/Cu composites When looking at the whole set of systems studied above, we found the boron-doping effect in the respect of the enhancement of Eb between Cu and graphene is comparable with or even better than the covalent oxygen bridging Cu and carbon atoms in the RGO reinforced Cu matrix composite. Accordingly, to further evaluate the boron-doping effect on the interfacial binding and mechanical properties of Cu/graphene composite, a sandwich-like layered composite (Fig.8) was modeled to 13

investigate the boron-doping effect on the bulk modulus, shear modulus, and Young modulus of a Cu(111)/P-GR/Cu(111) layered composite, which has great potential as excellent building blocks for assembling graphene/Cu bulk materials [51]. The mechanical properties of the layered composites are also compared with those of pure Cu matrix. The interfacial binding energy Eib between P-GR and the Cu(111) surfaces in layered composite, listed in Table 3, is defined as Eib  EP-GR  ECu(111)  Ecomposite ,

(2)

where EP-GR, ECu(111), and Ecomposite are the energies of free-standing P-GR, 10 atomic layers Cu(111) with a vacuum region of 15 Å, and their layered complexes after relaxation, respectively. Two substitution positions of the boron atoms in P-GR, i.e., two inequivalent carbon atoms sketched as C1, C2 in Fig.8(b) were both studied, and the optimized models were shown in Fig.8(c) and (d), respectively. The Eib of the layered composites in Fig.8(b)-(d) are 0.73, 2.42, and 2.75 eV, respectively. It is obvious that the effect of boron-doping is beneficial to the improvement of Eib, and the more stable boron-doping model in Fig.8(d) was used for the subsequent elastic properties calculation. After the energy-minimized structures of the Cu(111)/P-GR/Cu(111) layered composites with and without doping boron have been determined by our DFT optimization calculations, five independent elastic constants ( c11 , c12 , c13 , c33 , and c44 ) [52] of hexagonal structure were calculated according to the method of strain vs. strain energy (by applying small strains to the equilibrium lattice and determining the 14

resulting changes in the total energy) [53-55]. The elastic strain energy of a solid under small strain is given by

E 

V0 2

6

6

 C e e

ij i j

(3)

i =1 j =1

Where V0 is the equilibrium volume of the undistorted lattice cell, ΔE is the energy increment from the strain with strain tensor

 (e1, e2, e3, e4, e5, e6) . The five

independent elastic constants for hexagonal composites were determined by selectively imposing five different deformations given in Table 2 on the equilibrium lattice of hexagonal unit cell and determining the dependence of the resulting change in energy on the deformation. The three distortions involving (c11  c12 ) ,

1 c33 , and 2

1 (c11  c12  2c13  c33 ) are accompanied by a volume change but retain the hexagonal 2 symmetry. Conversely, the lattice parameters a1, a2, and c take different values after the deformation of

1 (c11  c12 ) and c44 , thereby making the distorted lattice belong 4

to a monoclinic and a triclinic system, respectively. Up to six strain parameters δ of -2%, -1%, -0.5%, 0.5%, 1%, and 2% were applied to determine each elastic constant. Fig.9(a)-(e) illustrate the plots of change in total energy as a function of strain for the five distortions imposing on Cu/GRB/Cu composite, and the elastic constants were then calculated using equations in Table 2. The energy-strain graph of Cu/GR/Cu composite was plotted in Fig.S2 in the Supporting Information. Table 3 lists the values of the elastic constants of the layered composites calculated in the present study. In terms of elastic constants, the mechanical stability criteria for hexagonal structure [56] C11  | C12 | 0，C44  0， (C11  C12 )C33  2C132  0 15

(4)

can be analyzed explicitly. Our results confirm that mechanical stability criteria of the layered composites in Fig. 8(b) and (d) are satisfied. The bulk modulus (K) was determined by calculating the total energy of the system as a function of volume and by fitting it to Murnaghan’s equation of state [57]. The shear modulus (G) was calculated using Voigt’s approximation [58], that is,

G

1 (7c11  5c12  12c44  2c33  4c13 ) 30

(5)

The directional dependence of the Young modulus (E) for hexagonal symmetry can be calculated using the following relationship [59, 60]:

1  (1  l32 )2 s11  l34 s33  l32 (1  l32 )(2s13  s44 ) E

(6)

where s11 , s13 , s33 and s44 are compliance constants, and l3 is the cosine of the two directions of loading-axis and z-axis shown in Fig.8(a). The Young modulus in xy plane and z-axis direction were calculated according to the compliance constants

s11 and s33 , as well as the conversion formulas between compliance constants and elastic constants for hexagonal symmetry (details can be found in the Supporting Information, formulas S1 – S4). The mechanical properties of the layered composites summarized in Table 3 are compared with those of pure Cu so as to obtain more insights into the strengthening effect of P-GR and P-GRB. The face-centered-cubic (fcc) copper unit cell including 4 Cu atoms was used to perform the elastic property calculation. For cubic symmetry, there are three independent elastic constants c11 , c12 , and c44 . The three different deformations imposing on the equilibrium lattice of fcc Cu unit cell is given in Table.S3 in the Supporting Information, and the energy-strain graphs were plotted in 16

Fig.9(f)-(h). The elastic constants c11 , c12 , and c44 are 223.8, 167.7, and 93.7 GPa, respectively, and the effective elastic modulus of pure Cu are evaluated from the elastic constants by using the Voight-Reuss-Hill averaging scheme [61]. The theoretical values for bulk modulus, shear modulus, and Young modulus of pure Cu in the present study are 181, 57.9, and 157 GPa, respectively, which are 27.5%, 20.8%, and 22.7% higher than the experimental results [62, 63] due to the overestimation of elastic constants within the LDA [64, 65]. Compared with the elastic properties of pure Cu matrix, the strengthening effect of P-GR only reflects in the enhancement of G and E in xy plane on account of the superhigh in-plane Young modulus of P-GR. Significantly, the increased Eib and the decreased values of d1 and d2 in the Cu/GRB/Cu system not only correlate directly with the dramatic increase of B and Ez, but also contribute to the enhancement of Exy due to the promotion of load transfer mechanism, albeit it has been reported that the in-plane Young modulus of graphene decline slightly after doping boron [37]. The efficiency of stress transfer from Cu matrix to boron doped graphene in our simulation is similar to the experimental verifications of modifying interface by another metal [13, 66, 67] and oxygen mediated chemical bonding between RGO and Cu matrix [29, 68].

4. Conclusions In summary, the adsorption of a single Cu atom on the surface of the pristine and defective graphene with and without decorating atomic oxygen as well as doping boron or nitrogen have been investigated by density functional theory method. The 17

calculation results revealed that the remnant oxygen atoms on the surface of graphene enhance the Cu/graphene binding through forming covalent bonds with the Cu atom directly, manifesting the experimental studies that suggested a vital role of the oxygen at the interface in the RGO reinforced Cu matrix composite. In terms of the binding energy Eb of a Cu atom with oxygen functionalized and boron or nitrogen doped graphene with and without defects, we evidenced that boron-doping effect is comparable to or even better than the chemical bridging role of oxygen between Cu and graphene, providing a promising scheme of introducing boron doped graphene instead of RGO to prepare Cu matrix composites with excellent mechanical and electronic properties. Furthermore, our calculation results showed that the boron-doping effect not only improves the bulk modulus, shear modulus, and Young modulus

in

the

direction

normal

to

the

graphene

surface

of

a

Cu(111)/graphene/Cu(111) layered composite based upon the prominent increase of interfacial binding energy dramatically, but also enhances the Young modulus in the directions parallel to graphene surface, which have the potential application in the establishment of quantitative relationship between interface effects and mechanical properties from the standpoint of experimental design.

Acknowledgement The authors acknowledge the financial support by the State Key Program of National Natural Science of China (Grant No. 51531004). The work was carried out at National Supercomputer Center in Tianjin, and the calculations were performed on TianHe-1(A). 18

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nanolaminated

composite

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Fabricated

by

a

Preform

Impregnation

Process:

Bioinspired

Strategy

Strengthening-Toughening of Metal Matrix Composite, Acs Nano 9 (2015) 6934-6943.

22

for

Fig. 1. Energy minimized structures of (a) P-GR, (b) P-GR-O, (c) P-GR/Cu, (d) P-GR-O/Cu, (e) P-GRB/Cu, and (f) P-GRN/Cu. T, B, and M in (a) are the three adsorption sites standing for the position of adatom above a carbon atom, above a carbon-carbon bond, and above the center of a hexagon, respectively. The upper panels and the lower panels in (c)-(f) give the top and side views, respectively.

23

Fig. 2. The partial density of states for particular atoms in (a) P-GR/Cu, (b) P-GR-O/Cu, (c) P-GRB/Cu, and (d) P-GRN/Cu. The carbon atom indices correspond to those in Fig. 1(c)-(d). The energy of the Fermi level is set to zero.

24

Fig. 3. The 2D differential charge density contours of the optimized structures in Fig.1(c)-(f), respectively. For each figure, the isosurface contours are drawn with an increment of 0.0021 e/Å3 from -0.1 to 0.1 e/Å3, and the green solid and black dashed curves denote the electron gain and electron depleted regions, respectively.

25

Fig. 4. Energy minimized structures of (a) SW-GR, (b) SW-GR-O, (c) SW-GR/Cu, (d) SW-GR-O/Cu, (e) SW-GRB/Cu, and (f) SW-GRN/Cu. The inequivalent sites for carbon atom in SW defect region are labeled by nonzero numbers, while carbon atom labeled with zero stands for the site far from the defect region. The upper panels and the lower panels in (c)-(f) give the top and side views, respectively.

26

Fig. 5. The partial density of states for particular atoms in (a) SW-GR/Cu, (b) SW-GR-O/Cu, (c) SW-GRB/Cu, and (d) SW-GRN/Cu. The carbon atom indices correspond to those in Fig. 4(d). The energy of the Fermi level is set to zero.

27

Fig. 6. Energy minimized structures of (a) MV-GR, (b) MV-GR-O, (c) MV-GR/Cu, (d) MV-GR-O/Cu, (e) MV-GRB/Cu, and (f) MV-GRN/Cu. The inequivalent sites for carbon atom in MV defect region are labeled by nonzero numbers, while carbon atom labeled with zero stands for the site far from the defect region. The upper panels and the lower panels in (c)-(f) give the top and side views, respectively.

28

Fig. 7. The partial density of states for particular atoms in (a) MV-GR/Cu, (b) MV-GR-O/Cu, (c) MV-GRB/Cu, and (d) MV-GRN/Cu. The carbon atom indices correspond to those in Fig. 6(c)-(f). The energy of the Fermi level is set to zero.

Fig. 8. Fully relaxed Cu(111)/P-GR/Cu(111) model and two possible Cu(111)/P-GRB/Cu(111) models with the top view in (a) and the side views in (b)-(d). The two nonequivalent carbon atoms C1 and C2 are indicated in model (b). For the values of the distances d1 and d2 labelled in (d), see Table 3. 29

Fig. 9. Strain energy as a function of strain parameter for five different deformations of hexagonal Cu/GRB/Cu layered composite (a)-(e) and for three different deformations of cubic pure Cu (f)-(h).

30

Table 1 Nearest-neighbor distances between Cu and carbon(s) (dCu-C), the equilibrium Cu-O distance (dCu-O), Cu-B distance (dCu-B), and Cu-N distance (dCu-N) for graphene, oxygen decorated, boron and nitrogen doped graphene, respectively. Eb represents the binding energies of the atomic Cu adsorbed on different graphene surfaces. SW-GR and MV-GR represent graphene with Stone-Wales and monovacancy defects, respectively. GR-O, GRB, and GRN represent atomic oxygen decorated, boron and nitrogen doped graphene, respectively.

System

dCu-C (Å)

dCu-O (Å)

dCu-B (Å)

dCu-N (Å)

Eb (eV)

P-GR/Cu P-GR-O/Cu

2.16/2.16 2.16/2.24

1.87

-

-

0.25 1.53

P-GRB/Cu

2.12

-

2.06

-

1.43

P-GRN/Cu

2.03

-

-

2.80

0.43

SW-GR/Cu

1.99

-

-

-

0.57

SW-GR-O/Cu

2.09/2.17

1.89

-

-

1.65

SW-GRB/Cu

2.01

-

2.10

-

1.50

SW-GRN/Cu

1.97

-

-

4.55

1.05

MV-GR/Cu

1.87/1.88/1.88

-

-

-

3.31

MV-GR-O/Cu

1.88/2.85/2.85

2.78

-

-

1.54

MV-GRB/Cu

1.88/2.06

-

2.04

-

3.17

MV-GRN/Cu

1.84/1.85

-

-

1.92

2.50

31

Table 2 Distortion matrix and energy-strain relations for layered composites.

Distortion matrix

0 1+   0 1+  0 0 

0  0 1 

0.5 1

0  0 1 

 1   0.5  0 

0

Composites structure after deformation

Energy-strain relations

Hexagonal

ΔE/V0 = (C11+C12)δ2

Monoclinic

ΔE/V0 =

1 0 0    0 1 0   0 0 1+     1   0  0.5 

0.5

ΔE/V0 =

Hexagonal

0.5   0.5  1 

0 1

1 C33δ2 2

ΔE/V0 = C44δ2

Triclinic

0 0  1+   0   0 1+  0 0 1+  

1 (C11-C12)δ2 4

ΔE/V0 = (C11+C12+2C13+C33/2)δ2

Hexagonal

Table 3 Present work DFT estimations of the interfacial binding energies (Eib, in eV), the distances between Cu(111) surfaces and graphene (d1 and d2 depicted in Fig.8(d), in Å) and the elastic properties (cij, bulk modulus K, shear modulus G, and Young modulus E in xy plane and z-axis direction, all in GPa) of Cu(111)/P-GR/Cu(111) (abbreviated as Cu/GR/Cu) and Cu(111)/P-GRB/Cu(111) (abbreviated as Cu/GRB/Cu) layered composites.

Eib

d1

d2

C11

C12

C13

C33

C44

K

G

Exy

Ez

Cu/GR/Cu

0.73

2.60

2.40

389.9

140.2

85.7

68.2

37.5

109.1

75.6

278.7

41.7

Cu/GRB/Cu

2.75

2.26

2.24

380.2

135.8

107.7

260.6

47.9

200.3

88.2

310.8

216.3

32