Layer-dependent friction on the surface of alternately stacked graphene and h-BN

Abstract

Two-dimensional materials have great potential as lubricating coatings on metal surfaces. This work investigates the performance of alternately stacked graphene and h-BN as lubricating coatings via molecular dynamics (MD) simulations. Our results indicate that stacking with graphene enhances the lubrication of h-BN, and the alternately stacked graphene and h-BN with graphene as the surface (mGBN_G) exhibits better lubricating and anti-wear properties than graphene. The friction coefficient on the surface of mGBN_G changes non-monotonically with the layer number, mainly attributed to wrinkling, indentation, and differences in the elastic–plastic deformation of the Cu substrate caused by the pressure from the tip. The 6GBN_G is optimal with high out-of-plane stiffness, and its friction coefficient is as low as 0.002 under 180 nN normal load, even lower compared with graphene with the same layer number. Differential charge density calculations reveal that C/B/N electronegativity differences induce interface charge transfer, enhancing interlayer van der Waals interactions, and improve the overall shear strength and mechanical properties. Notably, 6GBN_G maintains an ultra-low friction (μ < 0.002) at temperature ≤300 K, normal loads of 170–200 nN, and sliding velocity <0.2 Å ps⁻¹. These findings provide crucial guidance for the design of high-performance lubricating coatings.

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1. Introduction

Since the revolutionary discovery of graphene in 2004,¹ two-dimensional (2D) materials have attracted extensive attention, and exhibited unique advantages in various fields, including energy storage and conversion,^2,3 and next-generation information techniques.⁴ Graphene, transition metal sulfide (MoS₂ and WS₂) and hexagonal boron nitride (h-BN) have been adopted as lubricating materials due to their ultra-high strength, weak interlayer interactions, and excellent chemical stability.^5–8 Metals play a crucial role in nano/microelectromechanical systems (NEMS/MEMS); however, their poor wear resistance often results in device functional failure under tribological stress. Significantly, coating 2D materials on the metal surface is effective in enhancing their anti-wear and lubricating performance, which enables further utilization of their novel properties and expansion of their application.

Great efforts have been devoted to enhance the anti-wear and lubricating performance of the metal surface. Wang et al.⁹ demonstrated that coating graphene nanosheets significantly improves the wear resistance and lubrication of copper based on the molecular dynamics (MD) simulation. Especially, superlubricity with ultra-low wear rates was obtained under ultra-high contact pressures by coating steel with 2D materials such as graphene family materials and transition metal dichalcogenides at room temperature.¹⁰ Although graphene boasts excellent lubricating properties, it facilitates electron transfer in galvanic cells, accelerating the reduction of oxygen around defects and the oxidation of the base metal (i.e., electrochemical corrosion). In contrast, the excellent insulating property of h-BN makes it a common choice for chemical protective films, though h-BN lags behind graphene in lubricity.^11–13 In this context, stacking graphene with h-BN may yield a promising coating film combining the advantages of them.

The layers of 2D materials are bound to each other by weak van der Waals forces. So the stacking structure, including the layer number and atomic coordination mode, as well as the physical and chemical properties, can be easily regulated.^14–17 Frictional properties on the surface of 2D materials are related to several factors,^{10,14–16,18–23} including the layer number,^18–20,24 stacking,^21–23 defects,^25,26 and the substrate.^27,28 Studies^18–20 have shown that increasing the layer number within a certain range can reduce the friction. Li et al.¹⁸ investigated the friction of MXenes against various 2D materials by employing an atomic force microscope (AFM), and found that the layer number has a smaller impact on friction. For different 2D materials, the dependence of surface friction on the layer number may vary.

Particularly, heterostructures formed by integrating two different 2D materials often yield remarkable properties, such as superconductivity, tunable optical and ferromagnetic behaviors and superlubricity.^29–33 Employing the AFM technique, Zhang et al.³⁴ studied the friction in the graphene/h-BN heterostructure, which displayed extraordinary Moiré-level stick–slip behavior. MJG Guimarey³⁵ sprayed 2D nanosheets of h-BN onto low-carbon steel and observed excellent anti-wear performance. Additionally, MD simulations show that Young's modulus and Poisson's ratio of few-layer alternately stacked graphene and h-BN strongly depend on the parity of the layer number.³⁰ The parity dependence of Poisson's ratio disappears as the layer number exceeds seven, and it exhibits the property of a negative Poisson's ratio.

In this study, we investigated the friction on the surfaces of variedly stacked graphene and h-BN via MD simulations. Our results demonstrate the advantages of alternate stacking in reducing friction under high loads. Additionally, we investigated the variation of friction coefficients and wear volume with the layer numbers for multilayer alternately stacked graphene and h-BN with graphene as the surface (mGBN_G) and graphene (mG) under normal loads. We also characterized the indentation depth, tip amplitude, and Young's modulus of the coatings. Our study shows that the friction on the surfaces of mGBN_G and mG is influenced by wrinkle, indentation effects and elastic–plastic deformation of the Cu substrate caused by the pressure from the tip. We also supplemented our MD simulations with first-principles calculations of charge density differences. The results confirmed that mGBN_G exhibits superiority in reducing friction and enhancing anti-wear properties compared with mG under high loads. Notably, 6GBN_G was identified as the optimal lubricating coating structure, and the effects of critical working conditions on its frictional performance were explored.

2. Simulation and calculation methods

Fig. 1 shows the model for MD simulation of tip nanoscratching the coating film on the Cu substrate. The dimensions of graphene and h-BN are 24.4 nm × 12.5 nm and 24.8 nm × 12.9 nm, respectively, both comprising 12 000 atoms. The armchair and zigzag directions are along the x-axis and y-axis, respectively. The Cu substrate consisting of 54 243 atoms has dimensions of 26.6 nm × 14.8 nm × 1.45 nm. It is divided into top and bottom parts with thicknesses of 1.05 and 0.4 nm. The bottom part is fixed. To isolate the impact of Cu substrate thickness, the thickness of the top part is greater than the cutoff distance of the Lennard-Jones (LJ) potential. A diamond tip is simulated by a spherical cap filled with carbon atoms. It has a radius of 4 nm and a height of 2.0 nm, consisting of 7850 atoms. For all simulations, the tip is assumed to be rigid and remains perpendicular to the surface of the coated 2D sheet. As demonstrated in Fig. S1, we further confirm that the rigid tip has negligible influence on the simulation results.

Fig. 1 Model for molecular dynamics simulation of tip nanoscratching the coating film on the Cu substrate.

The LJ potential was employed to describe the interactions in four specific scenarios: between the tip and the coated 2D sheet, between the coated 2D sheet and the substrate, between the tip and the substrate, and between layers of the 2D sheet. The LJ potential of two atoms is calculated according to the equation U(r) = 4ε[(σ/r)¹² − (σ/r)⁶], where r is the distance between two atoms, ε is the potential well depth, and σ is the distance at which the potential energy is zero when r = σ. The LJ potential parameters used for describing the interatomic interactions are listed in Table 1.⁹ The cutoff distance is set to be 10 Å as a good balance between computation consumption and accuracy.²¹ The second-generation reactive empirical bond order (AIREBO),³⁶ the Tersoff,³⁷ and the EAM/ALLPY³⁸ potentials were employed to describe the atomic interactions within graphene, h-BN, and the Cu substrate, respectively. These potentials have been widely adopted and shown good performance on describing the properties of the materials in the present study.^9,30,32

Table 1 The Lennard-Jones (LJ) potential parameters used for describing the interatomic interactions in molecular dynamics simulations

Atom pair	ε/(meV)	δ/(Å)
C–C	4.55	3.431
B–B	7.81	4.083
N–N	2.96	3.261
C–B	5.96	3.534
C–N	3.72	3.368
B–N	4.81	3.649
B–Cu	1.31	3.376
N–Cu	0.81	3.187
C–Cu	0.99	3.272

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The MD simulations were performed by using LAMMPS.³⁹ The velocity Verlet algorithm was used to solve the equations of motion, and the time step was set to 1 fs. The temperature of the coating film and the top part of the substrate was controlled by using a Nose–Hoover thermostat, which has been widely used for studying interfacial and frictional behavior.^40,41 The NVT ensemble has been adopted in the entire simulation. The damping factor was set to 0.1 ps, suitable for most systems.^42,43 Periodic boundary conditions were applied along the x-axis and y-axis directions. To avoid relative sliding between the 2D sheet and the Cu substrate as well as between the layers of the 2D sheet, both ends of the coated 2D sheet along the sliding direction (x-axis) are fixed. The effects of Moiré patterns and interfacial effects were not considered in this study.

The MD simulations of nanoscratching include three steps: (i) structural relaxation until the system reaches equilibrium, (ii) applying a normal force via the diamond tip and equilibrating for 50 ps, (iii) applying a constant velocity to the tip and dragging it to move along the x-axis. Unless otherwise stated, all the MD simulations of tip nanoscratching were performed under a normal force of 0.1 nN atom⁻¹, a temperature of 300 K, a sliding velocity of 0.2 Å ps⁻¹, and a sliding distance of 8 nm. The tensile MD simulations are performed via two steps: the structure is equilibrated, then the left end of the 2D sheet is fixed while the other end is displaced at a constant velocity of 1 Å ps⁻¹ along the x-axis.

Fig. 2 presents the structures of 2G and 2GBN_G. The C–C bond length in 2G is 1.425 Å, while both the C–C and B–N bond lengths in 2GBN_G are 1.435 Å; the interlayer spacings are 3.448 and 3.428 Å for 2G and 2GBN_G, respectively. These structures were adopted for first-principles calculations. The first-principles calculations were performed using the Vienna ab initio simulation package (VASP)^44,45 based on density functional theory (DFT). Specifically, DFT was employed to compute the potential energy surface and the charge density difference. The projector augmented wave (PAW) method was used to calculate the electron–ion interactions.⁴⁶ The generalized gradient approximation (GGA) in the form of the Perdew–Burke–Ernzerhof (PBE) functional was used to calculate the electronic exchange–correlation interaction.⁴⁷ The DFT-D3 correction of the Grimme method was used to describe the van der Waals interactions between the adjacent layers.⁴⁸ The cutoff energy for the plane-wave basis set was set to 550 eV. A 14 × 14 × 1 gamma-centered k-mesh based on the Monkhorst–Pack method was used to sample the Brillouin zone. To eliminate the interactions between the adjacent slabs, a vacuum layer of 20 Å was added. The atomic structures were fully relaxed until the force on each atom was less than 0.01 eV Å⁻¹, and the energy difference between two consecutive self-consistent calculations was less than 10⁻⁵ eV.

Fig. 2 Top and side views of 2-layer (a) graphene (2G) and (b) alternately stacked graphene and hexagonal boron nitride with graphene as the surface (2GBN_G). Brown, white, and green balls represent C, N, and B atoms, respectively. The unit cells are marked with the black dashed lines.

3. Results and discussion

3.1 The variation of friction on the five coating films with layer numbers

Fig. 3(a) shows the possible stackings of graphene and h-BN as the coating film. Five stackings are considered, multilayer graphene (mG), multilayer h-BN (mBN), multilayer graphene and h-BN (mG–nBN, m is the layer number of graphene, n is the layer number of h-BN), and multilayer alternately stacked graphene and h-BN with graphene or h-BN as the surface (mGBN_G or mGBN_BN). The simulations of diamond tip nanoscratching the surfaces of these five coating films were performed. The average friction coefficients on the surface of the five coating films with 1–6 layers were calculated. The results are shown in Fig. 3(b). As reference, the friction coefficient of the diamond tip nanoscratching the Cu surface was calculated to be 0.41.

Fig. 3 (a) Schematic diagram showing the stackings of multilayer graphene (mG), multilayer hexagonal boron nitride (mBN), m layers of graphene and n layers of hexagonal boron nitride (mG–nBN), multilayer alternately stacked graphene and hexagonal boron nitride with graphene as the surface (mGBN_G) and hexagonal boron nitride as the surface (mGBN_BN). (b) The variation of the average friction coefficients on mG, mBN, mG–nBN, mGBN_G and mGBN_BN with the layer numbers from 1 to 6.

Fig. 3(b) shows that the average friction coefficients on the surface of the five coating films all decrease monotonically with the increase of the layer number from 1 to 6. This can be explained by the thickness-dependent wrinkling effect. As the layer number increases, the out-of-plane bending stiffness of the 2D material increases.^49,50 Correspondingly, the formation of wrinkles in front of the tip is suppressed, and the bulge height of the wrinkles gradually decreases. Larger wrinkles usually increase the contact area between the tip and the surface, causing more energy dissipation and high friction. Additionally, our results indicate that all of the five coating films significantly reduce the friction coefficient on the Cu substrate.

Comparing mG and mBN films with the same layer number, mG exhibits lower average friction coefficients, consistent with previous results.⁵¹ Additionally, the average friction coefficient on the mG–nBN film is higher compared with the mG film but was lower compared with the mBN film with the same layer number. Our results show that stacking with graphene improves the lubrication of h-BN. Comparing the two ways of combining graphene and BN, the average friction coefficient on the surface of mGBN is lower compared with mG–nBN with the same layer number. It indicates that alternately stacking graphene and BN structure is more effective in reducing friction.

Further comparing mGBN_G with mGBN_BN with the same layer number, we find that the average friction coefficient on the surface of mGBN_G is lower. Importantly, the average friction coefficients on mGBN_G with layer numbers of 4–6 are not only lower than those on mBN, but also lower than those on mG with the same layer number. This trend is also clearly illustrated in the SI Fig. S2, where the variation of the average friction coefficients on mG and mGBN_G with layer numbers from 1 to 6 is presented, with error bars (representing standard deviation, n = 3) indicating the statistical significance. This demonstrates that the lubrication of graphene can be further enhanced via alternately stacking with h-BN. Hence, the following part of this study focuses on the frictional properties of mGBN_G.

3.2 Friction on the surface of alternately stacked graphene and h-BN under normal load

We studied the friction on the surface of mGBN_G under normal loads of 100, 200, 300, and 500 nN. The mGBN_G structures have been stacked with h-BN as the bottom layer, which provides insulation against electrochemical corrosion. Therefore, even-numbered layers of mGBN_G were studied and compared with mG. Fig. 3, 4 and 5 respectively show the changes in the average friction coefficient, indentation depth and tip amplitude on the surfaces of mG and mGBN_G with the layer numbers of 2–14 under normal loads. This indicates that the average friction coefficient and tip amplitude on the surfaces of mG and mGBN_G stabilize as the layer number reaches 10. This suggests that mG and mGBN_G with layers more than 10 can be considered as bulk materials. The “carpet effect”¹⁹ is not visibly evident, especially when the number of layers exceeds 4. This indicates that the evolution of the frictional performance of mG and mGBN_G with the layer number larger than 4 is no longer dominated by the “carpet effect”, and thus has little impact on friction in this study.

Fig. 4 The variation of the average friction coefficients on the surfaces of multilayer graphene (mG) and alternately stacked graphene and hexagonal boron nitride with graphene as the surface (mGBN_G) with respect to the layer number under normal loads of (a) 100 nN, (b) 200 nN, (c) 300 nN and (d) 500 nN.

Fig. 5 The variation of the indentation depth on the surfaces of multilayer graphene (mG) and multilayer alternately stacked graphene and hexagonal boron nitride with graphene as the surface (mGBN_G) with respect to the layer number under normal loads of (a) 100 nN, (b) 200 nN, (c) 300 nN and (d) 500 nN.

Under a load of 100 nN, the average friction coefficients on the surfaces of mG and mGBN_G both decrease with increasing layer number from 2 to 10, and stabilize at about 0.003 and 0.004, respectively. As shown in Fig. 5, the indentation depths on the surfaces of mG and mGBN_G under a load of 100 nN are both small and increase with the increasing layer number. The Cu substrate undergoes almost no plastic deformation. Fig. 6(a) shows that the tip amplitude on the surfaces of both mG and mGBN_G under a load of 100 nN hardly changes with the increase of the layer number. Additionally, the indentation depth on mGBN_G is slightly lower than that on mG with the same layer number, indicating that the contact area between tip and mG is larger during sliding. But, the friction coefficient on mGBN_G is higher than that on mG with the same layer number. By examining the output files, we find that the effect of wrinkling dominates over the indentation depth under a load of 100 nN, and the effect of the tip amplitude and indentation depth on the friction is not significant. As the layer number increases, the out-of-plane bending stiffness of the 2D sheet increases, suppressing the formation of wrinkles, leading to the reduction of friction on both surfaces. Taking 2-layer mG and mGBN_G as examples, we calculated the potential energy surfaces of a single carbon atom sliding on the two surfaces. As shown in Fig. 7, the potential energy of mG fluctuates slightly compared with mGBN_G. It further explains the lower average friction coefficient on mG.

Fig. 6 The variation in amplitude of the tip on the surfaces of multilayer graphene (mG) and multilayer alternately stacked graphene and hexagonal boron nitride with graphene as the surface (mGBN_G) with respect to the layer number under normal loads of (a) 100 nN, (b) 200 nN, (c) 300 nN and (d) 500 nN. The dashed line indicates a criterion for tip vibration: above the dashed line, the vibration is intense and has a significant impact on friction; below the dashed line, the tip sliding is relatively stable and has less impact on friction.

Fig. 7 The potential energy surface of 2-layer (a) graphene (mG) and (b) alternately stacked graphene and hexagonal boron nitride with graphene as the surface (mGBN_G) scanned by a single carbon atom, calculated via density functional theory (DFT). The atomic lattices are overlaid onto the respective PES maps for clarity.

Applying a load of 200 nN, as shown in Fig. 4(b), the average friction coefficients on the surface of mG and mGBN_G both decrease to the minimum values of 0.0018 and 0.0025 at a layer number of 6, then increase and stabilize at around 0.0036 and 0.0035, respectively. As shown in Fig. 5(b), the indentation depths on the two surfaces change with the layer number in a similar pattern. The Cu substrate coated with 2–6 layers of films undergoes plastic deformation. The coated film can disperse the stress from the tip, consequently, the indentation depth decreases with increasing layer number. As the layer number is larger than 6, the stress dispersion effect from the coating is no longer enhanced, and the supporting effect of the substrate is weakened. Correspondingly, the indentation depth increases with the increase of the layer number, resulting in the increase of contact area and friction. Notably, compared with mG, the average friction coefficient on the surface of mGBN_G with the layer number of 2–6 is larger. As the layer number is larger than 8, the average friction coefficient on the surface of mGBN_G is smaller. Fig. 5(b) shows that the difference of indentation depth between mG and mGBN_G gradually increases with layer numbers larger than 6. As shown in Fig. 6(b), the tip vibration amplitude on both mG and mGBN_G hardly changes with increasing layer number. Our results show that under a load of 200 nN, the indentation depth is more important in influencing friction. We performed additional calculations for 10-layer mG and mGBN_G under loads of 100–200 nN, and found that the average friction coefficient on mG remains consistently lower compared with mGBN_G under loads less than 170 nN.

Under a load of 300 nN, the Cu substrate undergoes noticeable but still small plastic deformation, and still provides support to the coated film. The variations in average friction coefficients with layer numbers are highly similar to those under 200 nN, except for that the friction on the 2-layer films under 300 nN is significantly higher. The tip amplitude on the surface of 2-layer films under 300 nN is about three times larger those under 200 nN. It indicates that increasing the layer number of the coated film will significantly reduce the tip amplitude during sliding under high load. Friction coefficients on mG and mGBN_G both reach their minimum values of 0.0055 and 0.0052 at the layer number of 6, respectively. The friction coefficient on mGBN_G is lower than that on mG as the layer number is larger than 6. This phenomenon starts at the layer number of 8 under a load of 200 nN. This suggests that the higher the load, the more pronounced the advantage of mGBN_G in reducing friction.

Fig. 8 shows the indentation morphology on mG and mGBN_G with layer numbers of 2–10 under a load of 300 nN. There are noticeable wrinkles in front of the tip on the 2-layer and 4-layer mG and mGBN_G, hindering tip sliding. Correspondingly, the friction force on the surface of 2-layer and 4-layer mG and mGBN_G increases significantly at the beginning of sliding as shown in Fig. 9. Differently, there are no obvious wrinkles in front of the tip on mG and mGBN_G with layer numbers of 6–10, and the friction force curves are relatively smooth at the beginning. Besides, Fig. S3 shows the dislocation snapshots of mG and mGBN_G with layer numbers of 2–10 under a load of 300 nN. This indicates that the number of dislocations around the tip decreases with increasing thickness of the 2D coating film. During tip sliding, dislocations in the substrate undergo motion under stress. Overcoming lattice resistance caused by these dislocations further intensifies the energy dissipation and the frictional effect. Thus, the greater the number of dislocations in the substrate, the larger the friction force tends to be. Notably, no dislocations remain on the substrate of mGBN_G when the layer number reaches six. Whereas, dislocations remain on the substrate of mG until eight layers. Our results indicate that increasing the layer number can effectively reduce the wrinkles and number of dislocations in the substrate, thereby reducing friction. It should be noted that the friction forces on 2-layer mG and mGBN_G remain relatively high during sliding because of the much larger tip amplitude. This means that the tip amplitude also significantly influences friction. Under a higher load, the tip is more likely to experience severe vibrations. Increasing the layer number of the lubricating film can effectively suppress tip vibrations, thereby reducing friction. It is also validated under a load of 500 nN.

Fig. 8 Indentation morphology on the surfaces of (a) multilayer graphene (mG, m = 2, 4, 6, 8, and 10) and (b) multilayer alternately stacked graphene and hexagonal boron nitride with graphene as the surface (mGBN_G, m = 2, 4, 6, 8, and 10) under 300 nN load. Atoms are colored based on the value of the Z-coordinate, which represents the difference between the Z-coordinate of each atom and the average Z-coordinate of all atoms in the uppermost layer in the unloaded state.

Fig. 9 The variation of the friction force on the surfaces of (a) multilayer graphene (mG, m = 2, 4, 6, 8, and 10) and (b) multilayer alternately stacked graphene and hexagonal boron nitride with graphene as the surface (mGBN_G, m = 2, 4, 6, 8, and 10) during sliding under 300 nN normal load.

Under a load of 500 nN, the Cu substrate undergoes obvious plastic deformation with a distinct bulge in front of the tip, which hinders the sliding. The indentation depth increases slightly, while the tip vibration amplitude increases significantly with the layer number increasing from 2 to 6, resulting in much higher friction. The minimum indentation depth and the lowest average friction coefficient both occur at a layer number of 8. This indicates that as the load increases, the optimal thickness of the lubricating film also increases.

3.3 Mechanical properties and wear analysis of alternately stacked graphene and h-BN

Fig. 6 shows that under a load ranging from 100 to 500 nN, the indentation depth on the surface of mG is greater compared with mGBN_G with the same layer number. To explain this, we performed tensile simulations for mG and mGBN_G with layer numbers of 2–10. Fig. 10 shows the resulting stress–strain curves. Under the strain of 0–20%, the stress–strain curves conform to the formula of σ = Eε + Dε², where σ is the symmetric second Piola–Kirchhoff stress, ε is the uniaxial Lagrangian strain, E is Young's modulus, and D is the third-order elastic modulus. Young's modulus of 2–10 layers mG and mGBN_G was obtained by fitting the stress–strain curves. As listed in Table 2, the Young's modulus of mGBN_G is slightly higher than that of mG with the same layer number, meaning that mGBN_G undergoes smaller elastic deformation. Correspondingly, the indentation depth and contact area on the surface of mGBN_G are smaller. Importantly, the minimum friction coefficient on the surface of mGBN_G under a normal load of 200 nN is approximately 0.002, much lower compared to the “3Gra + 3h-BN” heterostructure (0.018).⁴⁸ This highlights the advantage of the present design for enhancing lubricating performance.

Fig. 10 The stress–strain curves of multilayer graphene (mG, m = 2, 4, 6, 8, and 10) and multilayer alternately stacked graphene and hexagonal boron nitride with graphene as the surface (mGBN_G, m = 2, 4, 6, 8, and 10).

Table 2 Young's modulus of multilayer graphene (mG, m = 2, 4, 6, 8, and 10) and multilayer alternately stacked graphene and hexagonal boron nitride with graphene as the surface (mGBN_G, m = 2, 4, 6, 8, and 10) in tensile simulations

Young's modulus (Gpa)	2	4	6	8	10
mG	86.74	170.81	239.80	295.38	342.45
mGBN_G	88.85	173.38	244.37	302.86	352.82

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In addition, we also calculated the wear volume. The results are shown in Fig. 11(a) and Fig. S4. Fig. S4 shows the wear morphology of the copper substrate after being rubbed by a diamond tip under a load of 300 nN. As shown in Fig. 11(a), the wear volume of the copper substrate decreases rapidly with the increase in the layer number of coating, indicating that increasing the coating thickness can effectively reduce the wear on the substrate. Moreover, the mGBN_G coating exhibits better friction reduction compared with the mG coating with the same layer number. Fig. 11(b) shows that the contact area between the tip and the coating surface decreases with the increase in the layer number within the range of 2–6 layers. It also shows an upward trend when the layer number exceeds 6. In comparison with mG, the contact area of mGBN_G is smaller. This result is consistent with the trend of the indentation depth, as shown in Fig. 6(c), further indicating that mGBN_G has higher out-of-plane stiffness and undergoes less out-of-plane deformation under the same load.

Fig. 11 (a) The wear volume of the copper substrate coated with multilayer graphene (mG, m = 2, 4, 6, and 8) and multilayer alternately stacked graphene and hexagonal boron nitride with graphene as the surface (mGBN_G, m = 2, 4, 6, and 8) after friction by a diamond tip under a 300 nN normal load. (b) The contact area between the diamond tip and the surfaces of mG and mGBN_G under a 300 nN normal load.

Fig. S5 and Fig. 12 respectively display the surface wear morphologies and wear volumes of the copper substrates coated with 2GBN_G, 4GBN_G, and 6GBN_G after friction by a diamond tip under normal loads (fn = 100, 200, 300, and 500 nN). The results show that at a load of 100 nN, the substrates coated with the three coatings exhibit no plastic deformation, and the wear volume is zero. When the load increases to 200 nN, plastic deformation starts to occur on the substrates covered by 2GBN_G and 4GBN_G, while the substrate coated by 6GBN_G still maintains elastic deformation. This elastic state can persist until the load increases to 300 nN, indicating that the 6GBN_G coating has better wear-resistance. At a load of 300 nN, the wear volume of the substrate coated with 2GBN_G increases sharply, while the wear volume of the substrate coated with 4GBN_G is significantly lower than that of 2GBN_G under the same load. This demonstrates that a proper layer number can be selected according to the load conditions in practical applications to achieve the best friction–reduction effect.

Fig. 12 The wear volume of the copper substrate coated with multilayer alternately stacked graphene and hexagonal boron nitride with graphene as the surface (mGBN_G, m = 2, 4, and 6) after friction by a diamond tip under (a) 100 nN, (b) 200 nN, (c) 300 nN and (d) 500 nN normal loads.

We further calculated the differential charge density of 2-layer graphene (2G) and the graphene/h-BN (2GBN_G) heterojunction. The results are shown in Fig. 13. In the heterojunction structure, there are significant differences in the atomic arrangements and electron distributions. Meanwhile, due to the difference in electronegativity between C atoms and B, N atoms, a certain degree of charge transfer occurs, strengthening the interlayer van der Waals interaction. The enhanced interlayer force can effectively suppress interlayer sliding, improving the overall shear-resistance and mechanical properties of the material. It explains the advantages of the alternately stacked structure in mechanical properties and provides a theoretical basis for its excellent lubrication and friction–reduction properties.

Fig. 13 Side views for the charge density difference of 2-layer (a) graphene (2G) and (b) alternately stacked graphene and hexagonal boron nitride with graphene as the surface (2GBN_G), calculated via density functional theory (DFT). The isosurface value is ±0.00005 e Bohr⁻³. Blue and yellow colors indicate electron depletion and accumulation regions, respectively. Charge density difference at the mid-plane of (c) 2G and (d) 2GBN_G.

3.4 Friction on the surface of alternately stacked graphene and h-BN with the optimal layer number

In this section, we investigated the effects of load, sliding velocity, and temperature on the average friction coefficient on 6-layer mGBN_G. As shown in Fig. 14(a), the average friction coefficient first decreases and then increases with the load from 100 to 300 nN, reaching a minimum value of about 0.0024 at 180 nN. Under a load of 180 nN, the indentation depth and contact area are minimized. Our simulations show that under a load less than 180 nN, the surface of 6-layer mGBN_G remains relatively flat. Under a load larger than 180 nN, the support from the substrate weakens as the load increases, leading to an increase in indentation depth and contact area, and resulting in the increase of the average friction coefficient.

Fig. 14 The variation of the average friction coefficient on the surface of 6-layer alternately stacked graphene and hexagonal boron nitride with graphene as the surface (mGBN_G) with respect to (a) load and (b) sliding velocity.

Fig. 14(b) shows the variation in the average friction coefficient on 6-layer mGBN_G under a load of 200 nN with sliding velocity. As shown in Fig. 14(b), the average friction coefficient increases monotonically with sliding velocity. The tip vibrates more severely at higher sliding velocity, resulting in an increase of friction. As shown in Fig. 15, the friction force is relatively stable at 1 K but fluctuates at 300 K due to the thermal motion of atoms, leading to an increase of friction. According to our study, the friction on 6-layer mGBN_G is low (0.002) at 300 K and below, under loads of 170–200 nN, and at sliding velocity lower than 0.2 Å ps⁻¹.

Fig. 15 The variation in friction force on the surface of 6-layer alternately stacked graphene and hexagonal boron nitride with graphene as the surface (mGBN_G) along the sliding path at temperatures of 1 and 300 K.

4. Conclusions

To evaluate the lubricating and anti-wear performance as lubricating coatings on the metal surface, this study investigates the frictional behavior of diamond tip nanoscratching on the alternately stacked graphene and h-BN via MD simulations and first-principles calculations. Our investigation confirms that incorporating graphene into h-BN effectively enhances the latter's lubricating properties, and the alternately stacked structure with graphene as the surface (mGBN_G) outperforms graphene in both lubrication and anti-wear performance. The friction coefficient of mGBN_G exhibits a nonmonotonic variation with increasing layer number, which is primarily driven by the combined effects of wrinkling, indentation and differences in the elastic–plastic deformation of the Cu substrate caused by the pressure from the tip. Notably, the variation pattern of friction with the layer number differs under different loads, originating from discrepancies in the plastic deformation degree of the Cu substrate. 6GBN_G, which is identified as the optimal structure as a lubricating coating, not only minimizes friction but also exhibits excellent anti-wear performance. Importantly, 6GBN_G maintains ultra-low friction (μ < 0.002) under practical working conditions: temperature ≤300 K, normal loads of 170–200 nN, and sliding velocity <0.2 Å ps⁻¹. The optimal layer number shifts to 8 under higher loads (e.g., 500 nN), indicating that the coating thickness can be tailored according to specific load requirements to achieve the best performance. Overall, this study demonstrates the potential of mGBN_G as a high-performance lubricating coating and provides guidance for the design of solid lubricants balancing low friction, high anti-wear capability and corrosion resistance.

Author contributions

The study and methods were conceived by Hao Wang, Lu Chen, and Xiaoli Fan. Research was performed by Hao Wang. All authors discussed and collaborated to the formal analysis. All authors participated in the writing and revisions of this paper.

Conflicts of interest

The authors declare no competing interests.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Supplementary information (SI) is available. See DOI: https://doi.org/10.1039/d5cp03937a.

Acknowledgements

We acknowledge the Fundamental Research Funds of the Central Universities (G2025KY06202), the Research Fund of the State Key Laboratory of Solidification Processing (NPU) (2023-TZ-01), the Innovation Capability Support Program of Shaanxi Province (Program No. 2024RS-CXTD-30), and the Natural Science Basic Research Program of Shaanxi (Program No. 2025JC-YBQN-781).

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