The nature of edge pinning and vanishing friction in microscale structural superlubric graphite contact

doi:10.21203/rs.3.rs-3140084/v1

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The nature of edge pinning and vanishing friction in microscale structural superlubric graphite contact

https://doi.org/10.21203/rs.3.rs-3140084/v1

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Structural superlubricity (SSL), a state of ultralow friction and no wear between two solid surfaces in contact, offers a fundamental solution for reducing friction and wear. Recent studies find that the edge pinning of SSL contact dominates the friction. However, its nature remains mysterious due to the lack of direct characterizations on atomic scale, especially for graphite, one of the most widely used materials for SSL. Here, for microscale graphite mesa, with detailed characterizations using atomic force microscopy, friction force microscopy, focused ion beam, high-resolution transmission electron microscope, and X-ray photoelectron spectroscopy, we unambiguously reveal the atomic structure and chemical composition of the disordered edge. The friction stress for each contact condition, namely, edge/edge, edge/surface, and surface/surface contacts are quantified, with the ratio being 10⁴:10³:1. The mechanism is revealed by full-atomic molecular dynamic simulations, which reproduce the measured friction quantitatively. Inspired by such understanding, through fabricating Si_xN_y caps with tensile stress, we further eliminate the friction caused by the edges through disengaging the edges from the substrate. As a result, an SSL contact with ultralow friction stress of 0.1 kPa or lower is achieved directly. Such a vanishing friction is 1-2 orders lower than all the values ever reported and approaches the theoretical limit of friction for structural superlubric contact.

Physical sciences/Materials science/Condensed-matter physics/Surfaces, interfaces and thin films

Physical sciences/Engineering/Mechanical engineering

structural superlubricity

graphite

edge pinning

vanishing friction

Structural superlubricity (SSL) holds the promise of zero static friction and vanishing kinetic friction as sliding speed approaches zero [1–6]. As first realized between crystalline surfaces such as graphite [7–9], friction anisotropy and sublinear scaling relation are regarded as typical features for SSL. Based on such criteria, besides graphite, SSL has been found in various junctions composed of either pure van der Waals layered materials [3], or van der Waal layered material and non-layered materials, such as diamond like carbon, sapphire, silicon et al [10]. The corresponding environmental conditions include vacuum, inert, ambient, and liquid [8, 11, 12]. While ultralow friction coefficient and the absence of wear have been reported by many groups [1–4, 13–16], however, the vanishing kinetic friction predicted theoretically has never been observed, in fact all above 1 kPa [8, 17, 18], albeit the sliding speed is rather low, e.g., of µm/s.

Such an apparent contradiction is attributed to the edge pinning effect as firstly pointed out in theoretical studies [19–23], then later confirmed by experimental measurements [18, 24]. For example, Guo et al reveal that thermal-induced edge barriers and forces can govern the interlayer interaction of double walled carbon nanotubes [19]. van Wijk et al point out the importance of the pinning caused by vertical distortions of edge atoms for the sliding of graphite flakes [20]. Based on Frenkel-Kontorova model, Ma et al find that the energy dissipation density of the edges can be 1–2 orders higher than the interior region [21]. Koren and Duerig show that the relaxation of the edge atoms for graphite flake lead to an increase in friction, and play an important role in the scaling law of friction [22]. Gigli et al show the key role played by the edge of graphene nanoribbons for its superlubric sliding [23]. These pioneering theoretical studies were later confirmed in the experimental systems including microscale graphite mesa [24], MoS₂/graphite and MoS₂/h-BN van der Waals heterostructures [18].

While the importance of the edge pinning has been acknowledged and their contribution to friction have been studied [18–24], the nature of the edge pinning effect, i.e., the atomic structure and chemical compositions of the edges and the corresponding mechanisms for their effects on friction, remains mysterious, especially for graphite, one of the most widely used materials for SSL [1–4, 13–15]. Besides, a more crucial question is how to realize an edge-free SSL contact in experiment. This is of particular importance not only for practical application of SSL, but also for the validation of SSL theories.

Here, we report, for the first time, the atomic structure, and chemical compositions of the edge for SSL graphite contacts. The contributions of three different contact conditions (edge/edge contact, edge/face contact, face/face contact) to friction is quantitatively estimated to be in the order of 10⁴:10³:1. Nanoscale characterization by atomic force microscope (AFM), transmission electron microscope (TEM) and X-ray photoelectron spectroscopy (XPS) reveal that there is a disordered region about 30 nm wide at the edge of the graphite mesas containing C-C sp³ bond and different oxygen-containing groups. With full atomic molecular dynamic simulations, we show that it is this disordered region which accounts for the differences of friction for the three kinds contact conditions. Through fabricating Si_xN_y caps with tensile stress, we further eliminate the friction caused by the edges through disengaging the edges from the substrate, achieve a contact with friction stress of 0.1 kPa.

We first fabricated square graphite mesas in different sizes capped with SiO₂ by reactive ion etching (RIE) as in previous work [8, 9]. Graphite mesas showing self-retracting motion [9], i.e. the extruded part of the mesa will automatically retract back to its initial position, were selected for the friction measurement as they are structural superlubric due to the single crystalline sliding interface[25]. During the friction measurement, the upper graphite flake was directly sheared relative to the bottom graphite mesa (i.e., substrate) in forward and backward directions using a visual AFM tip (VIT_P/IR, NT-MDT&TipsNano) under ambient conditions, as shown in Fig. 1a. The normal force applied by the AFM tip onto the SiO₂ cap at the top of the graphite flake was typically 30 µN. Figure 1b shows a typical shear force loop measured for such a reciprocating sliding, the corresponding shear force in forward and backward directions are denoted as ${F}_{+}$ and ${F}_{-}$ respectively. There is an obvious peak for the shear force during both forward and backward sliding with the peak values being ${F}_{peak\_f}$ and ${F}_{peak\_b}$ respectively. The width of the peaks is about 30 nm. Interestingly, we noticed that the states corresponding to the peak shear force happened when the flake coincided with the substrate during sliding (inset ii in Fig. 1b). For such states, the contact area of the sliding interface reaches maximum, meanwhile the edges of the flake and substrate perpendicular to the sliding direction are just in contact with each other instantaneously. It is worth noting that the edges parallel to the sliding directions are either in contact with the surface of the counterpart or suspended due to the slight shift perpendicular to the sliding direction, ${d}_{\perp }$, which is induced by the AFM tip (see section 1 in SI for more details).

We further measured the peak friction force (defined as ${F}_{peak}=({F}_{peak\_f}-{F}_{peak\_b})/2$) for rectangular graphite mesas with the side length L being 2 µm, 3 µm, 4 µm, and 8 µm. For each size, 5 graphite mesas were measured, and each graphite mesa was repeatedly measured 50 times, then averaged. Note that ${F}_{peak}$ remains stable during the whole 50 scans. As shown in Fig. 2a, ${F}_{peak}$ scales linearly with $L$, which indicates that the peak friction is due to the overlap of edges.

To understand the origin of the peak friction, we notice that at the peak of the shear force (inset ii in Fig. 1b), the total friction force can be expressed as

$$\begin{array}{c}{{F}_{peak}={2f}_{ee}L+2{f}_{es}L+\tau }_{ss}{L}^{2}\#\left(1\right)\end{array}$$

where ${f}_{ee}$, ${f}_{es}$ are the contributions of friction per unit length for edge/edge contact and edge/surface contact respectively, and ${\tau }_{ss}$ is the contribution of friction per unit area for surface/surface contact. Since ${d}_{\perp }$ (labeled in inset ii in Fig. 1b, about 80 nm) is much smaller than L (≥ 2 µm), we neglected the effect of ${d}_{\perp }$in Eq. 1. The linear relation between ${F}_{peak}$ and $L$ (Fig. 2a) indicates ${\tau }_{ss}L$ is much smaller than ${f}_{ee}$ or ${f}_{es}$. However, ${\tau }_{ss}$ can be estimated by rewriting Eq. 1 as

$$\begin{array}{c}{{F}_{peak}/L={2(f}_{ee}+{f}_{es})+\tau }_{ss}L.\#\left(2\right)\end{array}$$

By fitting ${F}_{peak}/L$ to $L$ according to Eq. 2, the slope and intercept are estimated to be ${\tau }_{ss}=0.69\pm 0.85 \text{k}\text{P}\text{a}$ and ${f}_{ee}+{f}_{es}=b/2=0.120\pm 0.003\text{N}/\text{m}$. The value of ${\tau }_{ss}$ is consistent with the shear stress of the graphite/graphite superlubric interface (− 2±2 kPa by Qu et al [24]).

To further decouple ${f}_{ee}$ and ${f}_{es}$, we noticed that during sliding, when the edges perpendicular to the sliding direction are not in contact (insets i and iii in Fig. 1b), the total friction force ${F}_{fri}=({F}_{+}-{F}_{-})/2$ can be expressed as

$$\begin{array}{c}{{F}_{fri}\left(d\right)={2f}_{es}\left(L-d\right)+2{f}_{es}L+\tau }_{ss}L\left(L-d\right)={4{f}_{es}L+\tau }_{ss}{L}^{2}-\left(2{f}_{es}+{\tau }_{ss}L\right)d,\#\left(3\right)\end{array}$$

where $d$ is the relative displacement of the flake with respect to substrate along the sliding direction as shown in inset i or iii in Fig. 1b. One example fitting of ${F}_{fri}$ to Eq. 3 is shown in inset i in Fig. 2c, delivers a fitted value of ${f}_{es}$. For 4 µm square mesas, we totally measured 7 samples, the result is shown in the inset ii of Fig. 2c. For these 7 samples, the average result is ${f}_{es}=0.006\pm 0.001 \text{N}/\text{m}$. With the estimated ${f}_{es}$, finally we can calculate ${f}_{ee}$ from the fitted result of Eq. (2) which delivers ${f}_{ee}=0.114\pm 0.004$ N/m.

The estimated values of ${f}_{es}$ and ${f}_{ee}$ immediately show an interesting observation. While in both cases the edge contributes to the friction, the edge/edge friction ${f}_{ee}$ is 1 to 2 orders larger than the edge/surface friction ${f}_{es}$. To understand this observation, we first sheared the graphite flake away, then used AFM (NT-MDT, NTEGRA Prima) to characterize the morphology of the regions near and include the edges of the graphite substrate in contact mode as illustrated in Fig. 3a. The corresponding friction force map between the silicon AFM tip with tip curvature radius of 6 nm and these regions on substrate is shown in Fig. 3b. Clearly, the sidewall of the substrate still shows a step-like layered structure. As shown in Fig. 3g, close to the nominal edge of the substrate, there is a region with a width of about 30 nm where the sliding friction of the AFM tip is 1 order larger than that in the graphite basal plane. Furthermore, we scanned the atomic-scale morphology at the junction of this region and the basal plane by AFM, as shown in Fig. 3c. The graphite basal plane shows periodic crystal lattice, but the 30 nm wide region does not. From the above characterization, we could conclude that the real edge has a certain width, which will be referred to as edge in the subsequent text. It is worth noting that the edge width is in good agreement with the width of the peak in the shear force loop in Fig. 1b which is also about 30 nm.

To understand the structure of the edge on atomic level, we further transferred the upper graphite flake to the surface of the silicon substrate with a tungsten tip, then cut the graphite flake by focused ion beam (FIB) and analyzed the cross section using a high-resolution transmission electron microscope (HRTEM) as illustrated in Fig. 3d. The HRTEM (JEOL, JEM-2010) image (Fig. 3e) clearly shows a perfect laminar lattice structure for the inner graphite region. The edge region (Fig. 3f), however, is filled with discontinuous and distorted layered structure, with the edge width $w$ being about 30 nm. These HRTEM observations agrees with those of AFM. The cause of the structure within the edge is easy to understand, since during the micro-fabrication process of graphite mesas, the graphite was etched by oxygen RIE process. In addition to reacting with oxygen (chemical etching), graphite was also bombarded by oxygen ions (physical etching, the energy of oxygen ions is 400 eV), thus became amorphous as suggested by previous studies [26–30].

The AFM and HRTEM characterization results demonstrate that the width for the edge of the graphite mesa composed of the (upper) flake and substrate is about 30 nm, which enable us calculate the friction stress for the three contact conditions: ${\tau }_{ee}={f}_{ee}/\omega =3.80\pm 0.13 \text{M}\text{P}\text{a}$, ${\tau }_{es}={f}_{es}/\omega =0.20\pm 0.03 \text{M}\text{P}\text{a}$, ${\tau }_{ss}=0.0007\pm 0.0009 \text{M}\text{P}\text{a}$, the ratio of the friction stress in these three contact conditions is in the order of 10⁴:10³:1.

Having revealed the atomic structure of the edge region, next we focused on analyzing the chemical states of the edge using X-ray photoelectron spectroscopy (XPS; Ulvac-PHI, Quantera II) with details shown in section 3 in SI. Considering that the edge shows nano-sized layered structure, it is reasonable to believe that carbon atoms still account for the majority at the edge. The C1s peak (Fig. 3h) shows that the carbon atoms at the edge have five chemical states, namely C-C sp² bond (binding energy of 284.5 eV), C-C sp³ bond (binding energy of 285.1 eV), and C-OH bond (binding energy of 286.1 eV), C = O bond (binding energy of 286.9 eV), C-O-C bond (binding energy of 288.1 eV) [31–36]. By calculating the area of each peak, the relative proportions of the above chemical bonds are 53.11%, 27.37%, 12.74%, 6.05%, 0.73%, respectively, which indicates that most of the carbon atoms at the edge are in C-C sp² and sp³ states. These oxygen-containing groups, which should be mainly introduced by oxygen RIE process, have also been found in carbon materials (namely, graphene, graphite, and carbon nanotube) after oxygen plasma treatment [34–36]. The information depth of XPS in carbon materials is calculated to be about 9 nm [32], thus the XPS C1s spectrum represents the average signal of carbon atoms in the edges. Besides the carbon atoms, the chemical state of oxygen is also revealed by the XPS O1s spectrum (see section 4 in SI for more details). For the three main chemical states of the oxygen element: C-O bond, C = O bond, and O-H bond, the corresponding contents are 39.76%, 31.79%, 28.45% respectively. This is consistent with the XPS C1s spectrum of the graphite mesa edges.

The characterization provides us the atomic-scale structure and chemical states of these edges at an unprecedented level. This information allows molecular dynamics (MD) simulations, which mimics experimental set-ups and have atomic-scale dynamics, to be used to understand the origin of the different contributions to friction as measured in our experiments, namely surface/surface (${\tau }_{\text{s}\text{s}}$), edge/surface (${\tau }_{\text{e}\text{s}}$) and edge/edge (${\tau }_{\text{e}\text{e}}$). To this end, three full atomic models (Fig. 4a-c) were established, and the kinetic friction was calculated by non-equilibrium MD simulations. Diamond-like carbon (DLC) was used to represent the amorphous carbon as found in experiment. The friction pairs in the simulation models consist of graphene/graphene, DLC/graphene, and DLC/DLC respectively. Considering that graphene is in interior contact region while DLC is at the edge, we adopted periodic boundary conditions (PBC) and open boundary conditions (OBC) for the models respectively as labeled in Fig. 4a-c. We decorated the hydroxyl groups at the edge of the simulation model (with linear density 0.5 nm^− 1) to represent the C-O bond, C = O bond, and O-H bond groups at the edge as characterized in experiments. Detailed simulation set-ups are shown in Methods section.

The values of friction stress estimated with MD simulations for the surface/surface ${\tau }_{ss}^{MD}$, edge/surface ${\tau }_{es}^{MD}$ and edge/edge ${\tau }_{\text{e}\text{e}}^{\text{M}\text{D}}$ are 1.6 ± 0.8 kPa, 28 ± 5.1 kPa and 65 ± 27 MPa respectively. The magnitude of${\tau }_{ss}^{MD}$ agrees well with previous studies [24, 25], and the value of ${\tau }_{\text{e}\text{e}}^{\text{M}\text{D}}$ is consistent with the reported results for classical DLC-based lubrication systems [37, 38]. The relatively large friction stress observed in MD than that measured in experiments is due to the inevitably larger sliding velocity in simulations. Importantly, the ratio between ${\tau }_{ss}^{MD}$, ${\tau }_{es}^{MD}$, and ${\tau }_{ee}^{MD}$ agrees with our experimental observations (Fig. 4d), indicating that the MD simulations capture the physical essence of the experiments.

As revealed in MD simulations, the interaction of edge/face and edge/edge contacts is purely van der Waals (vdW) force. There is no bond breaking or atom transfer during the whole sliding process, in agreement with the wearless friction measurement observed in experiments. The large roughness of DLC, compared to the atomically smooth graphene surface, is the main reason for the boost of ${\tau }_{ee}^{MD}$ and ${\tau }_{es}^{MD}$. In addition, according to our simulation, the electrostatic interaction between the functional groups terminated at the DLC edge, e.g., hydrogen bond between hydroxyls, which is much stronger than the vdW interaction, causes a sudden increase in friction when the upper and lower flakes overlap (Fig. 4c), which is also observed in experiments. Therefore, the different magnitudes of friction contributions are due to the different roughness and nature of interactions.

Since the amorphous edges of the graphite mesas account for most of the friction, disengaging the edges from the substrate can ensure a full crystalline incommensurate contact. An intuitive method is to bend the graphite flake by introducing tensile stress in the cap of the flake through micro fabrication. Specifically, through the synergistic effect of proper tensile stress in the cap together with the van der Waals force between the graphite flake and the substrate, the graphite flake may take on the shape of a pan, thus disengaging the amorphous edges from the substrate. Many studies have shown that silicon nitride (Si_xN_y) films deposited by plasma enhanced chemical vapor deposition (PECVD) method generally exhibit tensile stress, which can be further increased by annealing or ultraviolet light irradiation through breaking Si-H and N-H bonds to reduce hydrogen content [39, 40]. Thus, we used PECVD Si_xN_y film as the cap material to bend the graphite. The micro fabrication process of graphite mesas with Si_xN_y caps is detailed in Methods section.

For the graphite mesas with Si_xN_y cap before thermal annealing, we directly measured the shear force for the graphite interface by AFM (NT-MDT, NTEGRA Prima) with a scanning speed of 2 µm/s, and the experimental set-up is the same as Fig. 1a. The middle section of the lateral force shows a peak value in both the forward and backward directions (Fig. 5a), the same characteristic as the graphite mesas with SiO₂ cap. During the following annealing process, the temperature was increased from room temperature to 500°C at a rate of 10°C/min, kept at 500°C for 60 minutes, and then reduced to room temperature at a rate of 10°C/min. A typical lateral force loop after annealing is shown in Fig. 5b. Compared with samples before annealing, the most obvious difference is the disappearance of the peak when the upper flake and lower mesa overlapped. With comparative experiment for graphite mesas with SiO₂ caps instead (see section 7 in SI), we found that this is due to the warp of the upper graphite flake caused by the tensile stress within the Si_xN_y cap, thus disengaging the edges from the substrate, forming an edge-free graphite contact. As a result, the friction force is greatly decreased, which can be inferred from the overlap between the shear force curves corresponding to forward and backward scans (Fig. 5b).

To get a statistical estimation on the reduced friction, we measured the shear force for 5 different mesas with Si_xN_y caps after thermal annealing. With the warp width of the upper flake measured to be about 40 nm from Fig. 5b, the corresponding friction stress are found to be on the order of 0.1 kPa or smaller, which already reaches the measurement accuracy of the AFM used here (see sections 8 and 9 in SI for details). This value agrees well with the friction stress decoupled for the graphite/graphite contact before annealing (${\tau }_{ss}=0.7\pm 0.9 \text{k}\text{P}\text{a}$), verifying the accuracy of the decoupled values. It is worth noting that this is the smallest friction stress ever realized experimentally in solid contacts, the first direct experimental value below 1 kPa, which is one to two orders lower that the reported values across all the structural superlubric systems [1–4, 10, 13–15, 18].

In summary, we characterized the atomic structure and chemical states of SSL graphite mesa edges, which shows 30 nm wide amorphous region, based on which we simultaneously decoupled the friction stress of three types of contacts (edge/edge, edge/face, face/face) in the structural superlubric graphite mesa interface, the ratio of which is on the order of 10⁴:10³:1. With full atomic MD simulations, we produce such ratio quantitatively and reveal the mechanism to be the different roughness and nature of interactions caused by the disordered edges. By fabricating Si_xN_y caps with large tensile stress, we disengaged the edges of the graphite flakes from the substrate thereby eliminating the friction force contributed by the edges as well as the corresponding abrupt increase in friction. Graphite mesa with friction stress on the order of 0.1 kPa or lower is obtained. Such an ultralow friction is 1 to 2 orders of magnitude lower than the reported values across all the SSL contacts.

For fundamental research, our results provide the first direct experimental evidence for the long-assumed vanishing kinetic friction. In future, using AFM with improved measurement accuracy, the exact value of kinetic friction would be our next step as it will serve as a touchstone for theories such as the rich family of Frenkel-Kontorova model. Heterojunctions composed of edge-free graphite mesa and ultraflat surfaces such as hBN, diamond like carbon will also be of great interest. For practical application, our results show a clear avenue towards devices with moving interfaces of ultralow dissipation and provide a definite value of friction for the design of devices based on SSL, a frictionless interface one can ever imagine.

Fabrication of graphite flake. Rectangular graphite mesas were fabricated on the surface of a freshly cleaved HOPG (Veeco ZYB grade) sample, using fabrication procedures described previously [9]. The height of the mesas is typically around 700 nm, with their side length denoted by L. 200-nm thick SiO₂ caps were fabricated on the top of the mesas for facile manipulation using a tip. Rectangular mesas of 4 different sizes were used, i.e., L=2, 3, 4, and 8 μm. The mesas were first sheared laterally either by a tungsten tip attached to a nano-manipulator (Kleindiek MM3A) or by an AFM tip pressed on the SiO₂ cap. Upon shearing, the graphite mesa cleaved into the upper and lower sections due to the presumed existence of a weak (i.e., incommensurate) interface within the layered structure of HOPG, such as a twist boundary. Such a process creates new graphite surfaces. When the tip was released, about 30-70% of the upper parts of these sheared graphite mesas self-retracted to their original positions to minimize the free energy. Previous publications have shown that this self-retraction motion is a direct manifestation of microscale superlubricity, and that self-retractable mesas provide atomically smooth single crystalline contact interfaces [25].

Measurement of friction force. The frictional measurements of the graphite mesa composed of (upper) graphite flake and (graphite) substrate were performed under an ambient condition (temperature of 24 ± 1 °C and relative humidity of 31 ± 3%). The experimental set-up included a commercial AFM (NT-MDT, NTEGRA Prima), a 100 μm XYZ piezoelectric tube scanner, a high numerical aperture objective lens (× 100 (Mitutoyu)) equipped with a top visual AFM probe (VIT-P tip (NT-MDT)). Figure 1a shows a sketch of the set-up. The AFM tip was within the sight of the optical microscope when it was in contact with the SiO₂ cap of the graphitic mesas. The electric signal corresponding to the torsional deformation of the cantilever is recorded, and converted to the lateral force by a constant calibration factor which is obtained by the diamagnetic lateral force calibration method [41]. The absolute value of the lateral force could be shifted due to the crosstalk effect of AFM, but the subtraction of the lateral forces during forward and backward scanning yields the friction force accurately [17, 41].

Simulation models and set-ups. The slider (orange in Fig. S5 in SI) and the substrate (blue in Fig. S5 in SI) of three simulation models consist of graphene/graphene, DLC/graphene, and DLC/DLC respectively. In order to model the edge effects observed in our experiments which is due to the amorphous carbon structures, we apply the quench protocol [42] to generate amorphous carbon structures: thermostats are attached to the cabon sources with temperature 5000 K. After the melting of the carbon structure, the system is thermostatically equilibrated for 100 ps and then cooled down to 300 K at a rate of ~100 K/ps which allows proper relaxation of the amorphous structure [43]. Hydrogen atoms and hydroxyls (with linear density 0.5 nm⁻¹) are then saturated to the surface and edge of DLC respectively, following a 1-ns-thermal relaxation. For all simulation models, the bottom and top layer (or region with thickness of 3 Å) atoms are tethered by z-direction springs (k_z=0.3 N/m) to restrict its out-of-plane motion (and to mimic the z-direction elasticity of graphite). A pulling spring with spring constant K_p=100 N/m is coupled to the center of mass of the slider. The other end of the pulling spring moves with a constant velocity v₀ along x direction (and also −x direction to get a complete friction loop). All MD simulations are performed using LAMMPS code[44]. The interlayer interaction between the graphene and DLC is described by the Lennard-Jones potential. It is well acknowledged that registry dependent force field[45] should be used to describe interlayer interaction among grapehen layers. However, given that we know the incommensurate contacted graphene has extremely low friction (compared to the friction between DLC/graphene and DLC/DLC), we did not choose the ILP force field for better computing efficiency. The intralayer interactions of C-C and C-H are described by the REBO force field [46]. The interaction among hydroxyls and carbon atoms is described by the OPLS force field [47]. All simulations are conducted at room temperature with Langevin thermostat applied to the bottom layer/region to correctly describe the energy dissipation [48]. For graphene/graphene and graphene/dlc systems, the kinetic friction is calculated from the time-averaged lateral force of the pulling spring, F_L. For DLC/DLC system, the friction is calculated from the enclosed region of the friction loop. The friction stress is then estimated from the per-area kinetic friction force.

Fabrication process of graphite mesas with Si_xN_y caps. The micro fabrication process of the graphite mesas with Si_xN_y caps is illustrated in Figure S6 in SI, 250 nm thick Si_xN_y film was first deposited on highly oriented pyrolytic graphite (HOPG) by PECVD. Second, 10 nm thick Al film was magnetron sputtered onto the Si_xN_y surface. Third, negative photoresist was spin-coated on the Al film. Fourth, the photoresist was patterned into squares by electron beam lithography (EBL). Fifth, the portion of the Al film unprotected by the photoresist was etched away by ion beam etching (IBE). Sixth, the portion of the Si_xN_y film unprotected by Al was etched away by oxygen reactive ion etching (RIE). Seventh, the remaining portion of the Al film was used as a mask in the following RIE process of the graphite. Then, Al film was wet etched. This led to the graphite mesas with Si_xN_y cap. The 10 nm Al film acts as a protective layer to prevent the Si_xN_y surface from being oxidized during the graphite RIE etching process.

DATA AVAILABILITY

The data supporting the findings of this study are available within the paper and the Supplementary Information. Source data are provided with this paper.

ACKNOWLEDGMENTS

The authors wish to acknowledge the financial support by National Natural Science Foundation of China (11890673, 11890671), the Shenzhen Fundamental Research Key Project (JCYJ20200109150608043), and Shenzhen Science and Technology Program (JCYJ20210324100600001).

O. Hod, E. Meyer, Q. Zheng, M. Urbakh, Structural superlubricity and ultralow friction across the length scales, Nature, 563 (2018) 485–492.
A. Vanossi, C. Bechinger, M. Urbakh, Structural lubricity in soft and hard matter systems, Nat. Commun., 11 (2020) 4657.
Y. Song, C. Qu, M. Ma, Q. Zheng, Structural Superlubricity Based on Crystalline Materials, Small, 16 (2020) 1903018.
J.M. Martin, A. Erdemir, SUPERLUBRICITY: Friction's vanishing act, Physics Today, 71 (2018) 40–46.
D. Berman, A. Erdemir, A.V. Sumant, Approaches for Achieving Superlubricity in Two-Dimensional Materials, Acs Nano, 12 (2018) 2122–2137.
M.Z. Baykara, M.R. Vazirisereshk, A. Martini, Emerging superlubricity: A review of the state of the art and perspectives on future research, Appl. Phys. Rev., 5 (2018) 041102.
M. Dienwiebel, G.S. Verhoeven, N. Pradeep, J.W.M. Frenken, J.A. Heimberg, H.W. Zandbergen, Superlubricity of graphite, Phys. Rev. Lett., 92 (2004) 126101.
Z. Liu, J. Yang, F. Grey, J.Z. Liu, Y. Liu, Y. Wang, Y. Yang, Y. Cheng, Q. Zheng, Observation of Microscale Superlubricity in Graphite, Phys. Rev. Lett., 108 (2012) 205503.
Q.S. Zheng, B. Jiang, S.P. Liu, Y.X. Weng, L. Lu, Q.K. Xue, J. Zhu, Q. Jiang, S. Wang, L.M. Peng, Self-retracting motion of graphite microflakes, Phys. Rev. Lett., 100 (2008) 067205.
D. Peng, J. Wang, H. Jiang, S. Zhao, Z. Wu, K. Tian, M. Ma, Q. Zheng, 100 km wear-free sliding achieved by microscale superlubric graphite/DLC heterojunctions under ambient conditions, National Science Review, 9 (2022) nwab109.
C.C. Vu, S.M. Zhang, M. Urbakh, Q.Y. Li, Q.C. He, Q.S. Zheng, Observation of normal-force-independent superlubricity in mesoscopic graphite contacts, Phys. Rev. B, 94 (2016) 081405(R).
C. Qu, W. Cao, B. Liu, A. Wang, F. Xie, M. Ma, W. Shan, M. Urbakh, Q. Zheng, Direct Measurement of Adhesions of Liquids on Graphite, J. Phys. Chem. C, 123 (2019) 11671–11676.
X. Chen, J. Li, Superlubricity of carbon nanostructures, Carbon, 158 (2020) 1–23.
S. Zhang, T. Ma, A. Erdemir, Q. Li, Tribology of two-dimensional materials: From mechanisms to modulating strategies, Materials Today, 26 (2019) 67–86.
W. Zhai, K. Zhou, Nanomaterials in Superlubricity, Adv. Funct. Mater., 29 (2019) 1806395.
J. Yuan, R. Yang, G. Zhang, Structural superlubricity in 2D van der Waals heterojunctions, Nanotechnology, 33 (2022) 102002.
Y. Song, D. Mandelli, O. Hod, M. Urbakh, M. Ma, Q. Zheng, Robust microscale superlubricity in graphite/hexagonal boron nitride layered heterojunctions, Nature Mater., 17 (2018) 894–899.
M. Liao, P. Nicolini, L. Du, J. Yuan, S. Wang, H. Yu, J. Tang, P. Cheng, K. Watanabe, T. Taniguchi, L. Gu, V.E.P. Claerbout, A. Silva, D. Kramer, T. Polcar, R. Yang, D. Shi, G. Zhang, UItra-low friction and edge-pinning effect in large-lattice-mismatch van der Waals heterostructures, Nature Mater., 21 (2022) 47-+.
Z.R. Guo, T.C. Chang, X.M. Guo, H.J. Gao, Thermal-Induced Edge Barriers and Forces in Interlayer Interaction of Concentric Carbon Nanotubes, Phys. Rev. Lett., 107 (2011) 105502.
M.M. van Wijk, M. Dienwiebel, J.W.M. Frenken, A. Fasolino, Superlubric to stick-slip sliding of incommensurate graphene flakes on graphite, Phys. Rev. B, 88 (2013) 235423.
M. Ma, A. Benassi, A. Vanossi, M. Urbakh, Critical Length Limiting Superlow Friction, Phys. Rev. Lett., 114 (2015) 055501.
E. Koren, U. Duerig, Moire scaling of the sliding force in twisted bilayer graphene, Phys. Rev. B, 94 (2016) 045401.
L. Gigli, N. Manini, A. Benassi, E. Tosatti, A. Vanossi, R. Guerra, Graphene nanoribbons on gold: understanding superlubricity and edge effects, 2D Mater., 4 (2017) 045003.
C. Qu, K. Wang, J. Wang, Y. Gongyang, R.W. Carpick, M. Urbakh, Q. Zheng, Origin of Friction in Superlubric Graphite Contacts, Phys. Rev. Lett., 125 (2020) 126102.
K. Wang, C. Qu, J. Wang, B. Quan, Q. Zheng, Characterization of a Microscale Superlubric Graphite Interface, Phys. Rev. Lett., 125 (2020) 026101.
A. Ito, Y. Wang, S. Irle, K. Morokuma, H. Nakamura, Molecular dynamics simulation of hydrogen atom sputtering on the surface of graphite with defect and edge, Journal of Nuclear Materials, 390 – 91 (2009) 183–187.
K. Nakai, C. Kinoshita, A. Matsunaga, A study of amorphization and microstructural evolution of graphite under electron or ion irradiation, Ultramicroscopy, 39 (1991) 361–368.
H. Fredriksson, D. Chakarov, B. Kasemo, Patterning of highly oriented pyrolytic graphite and glassy carbon surfaces by nanolithography and oxygen plasma etching, Carbon, 47 (2009) 1335–1342.
B. Peng, M. Locascio, P. Zapol, S. Li, S.L. Mielke, G.C. Schatz, H.D. Espinosa, Measurements of near-ultimate strength for multiwalled carbon nanotubes and irradiation-induced crosslinking improvements, Nature Nanotech., 3 (2008) 626–631.
R. Coratger, A. Claverie, A. Chahboun, V. Landry, F. Ajustron, J. Beauvillain, Effects of ion mass and energy on the damage induced by an ion beam on graphite surfaces: a scanning tunneling microscopy study, Surf. Sci., 262 (1992) 208–218.
C. Pirlot, I. Willems, A. Fonseca, J.B. Nagy, J. Delhalle, Preparation and characterization of carbon nanotube/polyacrylonitrile composites, Advanced Engineering Materials, 4 (2002) 109–114.
B. Lesiak, L. Kover, J. Toth, J. Zemek, P. Jiricek, A. Kromka, N. Rangam, C sp(2)/sp(3) hybridisations in carbon nanomaterials - XPS and (X)AES study, Appl. Surf. Sci., 452 (2018) 223–231.
S. Drewniak, R. Muzyka, A. Stolarczyk, T. Pustelny, M. Kotyczka-Moranska, M. Setkiewicz, Studies of Reduced Graphene Oxide and Graphite Oxide in the Aspect of Their Possible Application in Gas Sensors, Sensors, 16 (2016) 103.
A. Felten, C. Bittencourt, J.J. Pireaux, G. Van Lier, J.C. Charlier, Radio-frequency plasma functionalization of carbon nanotubes surface O-2, NH3, and CF4 treatments, Journal of Applied Physics, 98 (2005) 074308.
Z. Wang, F.H. Yang, R.T. Yang, Enhanced Hydrogen Spillover on Carbon Surfaces Modified by Oxygen Plasma, J. Phys. Chem. C, 114 (2010) 1601–1609.
A. Nourbakhsh, M. Cantoro, A.V. Klekachev, G. Pourtois, T. Vosch, J. Hofkens, M.H. van der Veen, M.M. Heyns, S. De Gendt, B.F. Sels, Single Layer vs Bilayer Graphene: A Comparative Study of the Effects of Oxygen Plasma Treatment on Their Electronic and Optical Properties, J. Phys. Chem. C, 115 (2011) 16619–16624.
T. Kuwahara, P.A. Romero, S. Makowski, V. Weihnacht, G. Moras, M. Moseler, Mechano-chemical decomposition of organic friction modifiers with multiple reactive centres induces superlubricity of ta-C, Nat. Commun., 10 (2019) 151.
L. Bai, N. Srikanth, H. Wu, F. Liu, B. Liu, K. Zhou, Effect of environmental hydrogen atoms on the tribological behaviors of diamond-like carbon films, Tribol. Int., 99 (2016) 258–266.
R. Arghavani, L. Xia, H. M'Saad, M. Balseanu, G. Karunasiri, A. Mascarenhas, S.E. Thompson, A reliable and manufacturable method to induce a stress of > 1 GPa on a p-channel MOSFET in high volume manufacturing, Ieee Electron Device Letters, 27 (2006) 114–116.
M. Belyansky, M. Chace, O. Gluschenkov, J. Kempisty, N. Klymko, A. Madan, A. Mallikarjunan, S. Molis, P. Ronsheim, Y. Wang, D. Yang, Y. Li, Methods of producing plasma enhanced chemical vapor deposition silicon nitride thin films with high compressive and tensile stress, Journal of Vacuum Science & Technology A, 26 (2008) 517–521.
Q. Li, K.S. Kim, A. Rydberg, Lateral force calibration of an atomic force microscope with a diamagnetic levitation spring system, Rev. Sci. Instrum., 77 (2006) 065105.
L. Li, M. Xu, W. Song, A. Ovcharenko, G. Zhang, D. Jia, The effect of empirical potential functions on modeling of amorphous carbon using molecular dynamics method, Appl. Surf. Sci., 286 (2013) 287–297.
N.A. Marks, D.R. McKenzie, B.A. Pailthorpe, M. Bernasconi, M. Parrinello, Ab initio simulations of tetrahedral amorphous carbon, Phys. Rev. B, 54 (1996) 9703–9714.
A.P. Thompson, H.M. Aktulga, R. Berger, D.S. Bolintineanu, W.M. Brown, P.S. Crozier, P.J.i.t. Veld, A. Kohlmeyer, S.G. Moore, T.D. Nguyen, R. Shan, M.J. Stevens, J. Tranchida, C. Trott, S.J. Plimpton, LAMMPS-a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales, Comput. Phys. Commun., 271 (2022) 108171.
W.G. Ouyang, D. Mandelli, M. Urbakh, O. Hod, Nanoserpents: Graphene Nanoribbon Motion on Two-Dimensional Hexagonal Materials, Nano Lett., 18 (2018) 6009–6016.
D.W. Brenner, O.A. Shenderova, J.A. Harrison, S.J. Stuart, B. Ni, S.B. Sinnott, A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons, J. Phys.: Condens. Matter, 14 (2002) 783–802.
W.L. Jorgensen, D.S. Maxwell, J. TiradoRives, Development and testing of the OPLS all-atom force field on conformational energetics and properties of organic liquids, J. Am. Chem. Soc., 118 (1996) 11225–11236.
A. Benassi, A. Vanossi, G.E. Santoro, E. Tosatti, Parameter-free dissipation in simulated sliding friction, Phys. Rev. B, 82 (2010) 4.

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The nature of edge pinning and vanishing friction in microscale structural superlubric graphite contact

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