Robust microscale structural superlubricity between graphite and nanostructured surface

Robust microscale structural superlubricity between graphite and nanostructured surface | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Robust microscale structural superlubricity between graphite and nanostructured surface Xuanyu Huang, Tengfei Li, Jin Wang, Kai Xia, Deli Peng, Xiaojian Xiang, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2273111/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 22 May, 2023 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Abstract Structural superlubricity (SSL), a state of nearly zero friction and no wear between two contacted solid surfaces, brought a dawn for the revolutionary solution of friction and wear problems. Recently, SSL was realized between microscale graphite flake with two dimensional single-crystalline surface and various non-van der Waals materials, which greatly broadens its application range. However, the SSL state has a certain probability of failure due to the edge defects of graphite flake. Here, we achieve robust SSL state between microscale graphite flakes and nanostructured silicon surfaces under ambient condition. We find that the friction is always less than 1 μN, the differential friction coefficient is on the order of 10 -4 , without observable wear. Detailed characterization and simulation show that this is attributed to the edge warping of graphite flake on the nanostructured surface under concentrated force, which eliminate the edge interaction between the graphite flake and the substrate. This study proves that a graphite flake with single crystal surface without edge contact with the substrate can universally realize robust SSL state with any non-van der Waals materials in the atmosphere, which reduce the roughness requirements of SSL technology and provides a new method for SSL technology to generally apply in the atmospheric environment. Physical sciences/Materials science/Structural materials/Mechanical properties Physical sciences/Nanoscience and technology/Graphene/Mechanical and structural properties and devices Physical sciences/Materials science/Nanoscale materials/Two-dimensional materials Physical sciences/Materials science/Nanoscale materials/Structural properties Physical sciences/Nanoscience and technology/Nanoscale materials/Structural properties Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Introduction Friction and wear are two fundamental physical phenomena coupled together in nature, which have caused huge energy waste, environmental pollution and component failure in mechanical system 1 , and made it difficult for a large number of key technologies such as novel design of micro-electromechanical system (MEMS) 2 . It is estimated that nearly one-third of the energy provided by fossil fuels in automobiles is dissipated by friction 3 . In the microscopic world, based on the scale effect, the interface friction and wear will become one of the most important problems compared to other effects, which cause the failure of the devices. Although liquid lubricants such as organic oils have a great inhibitory effect on friction and wear in practical applications, they will fail under strong constraints and extreme external conditions, such as high external loads, high temperatures, as well as in the presence of chemical contamination or in a vacuum environment 4 . Lubrication based on the shear within liquid will fail on nanoscale as the viscosity may greatly increase 5 , which is difficult to apply to micro-scale scenarios, such as MEMS, micro sensors, micro robots, etc 6 , 7 . Therefore, to solve the above problems, a new revolutionary technology is needed to reduce friction or even eliminate wear from the essential physical characteristics, instead of introducing other indirect substances as friction pairs. Structural superlubricity (SSL), a state of nearly zero friction and no wear between two contact solid surfaces 6 , 8 , 9 , that relies on the effective cancellation of lateral forces between rigid crystalline contacts provides a revolutionary solution to above challenge. Since the successful realization of micro-scale SSL in the atmospheric environment in 2012 10 , in addition to the realizations of high-speed SSL ( \(293 \text{m}/\text{s}\) ) 11 , SSL has attracted wide-ranging interest in not only academic studies 12 , but also practical applications, such as superlubric generators (SLGs) 13 , 14 and superlubric resonators 11 . More recently, SSL was realized between microscale graphite and many non-van der Waals materials such as diamond-like-carbon (DLC), Si, SiO 2 , Al 3 O 2 , Si 3 N 4 , etc 15 . It greatly broadens the application range of SSL technology. However, in this study, we unexpectedly discovered that when an atomic force microscope probe is pressed on a microscale graphite flake and dragged to slide on an atomic-level flat silicon surface, there is a certain probability of high friction ( \(>5 {\mu }\text{N}\) ) and corresponding wear will occur. On the contrary, the friction is always less than 1 \({\mu }\text{N}\) between graphite flake and nanostructured silicon surface, the differential friction coefficient is on the order of \(1{0}^{-4}\) , and there is no observable wear, indicating the presence of SSL. Through detailed characterization and simulation, we found that friction and wear between the graphite flake and atomic-level flat silicon surface mainly occur along the edge, and the dangling bonds along the edge will have a strong interaction with the substrate atoms 16 – 18 ; but the edge of graphite flake on the nanostructured surface will occur warping under concentrated force, thereby reducing the edge interaction between the graphite flake and the substrate. Results Ultralow friction between graphite flake and nanostructured surfaces The whole experiment process is divided into three steps. In the first step, we selected a graphite flake that was cleaved by shear from a square graphite mesa of \(4 \times 4 \times 0.9 {\mu }\text{m}\) with a self-retracting motion (SRM) property 19 (see the Methods section and Supplementary Section 3 for details). The graphite mesa was made of highly ordered pyrolytic graphite (HOPG) with an Au cap of 100 nm thickness (fabrication details are provided in Supplementary Section 1 and the Methods section). The SRM motion is a strong indication for the presence of SSL at the interface between the bottom of graphite flake and the surface of the lower part of the graphite mesa. The cleaved surface (or bottom surface) of an graphite flake is a single-crystalline graphene sheet 20 . In the second step, we transferred the graphite flake onto two types of silicon surfaces (see the Methods section and Supplementary Section 3 for details), one of which is a very clean and atomic-level flat silicon surface, and the other is a surface with nanostructures. Their surface topography is shown in Figs. 1 c and e, respectively. The selection and transfer process of graphite flake were performed under an ambient atmospheric environment in a thousand-class clean room with a temperature of 25 ± 1°C and a relative humidity of 25 ± 1%. In the third step, we used the lateral force module of the atomic force microscope (AFM, Cypher S-Oxford Instruments) to measure the friction between the graphite flake and two types of silicon surfaces, and the experimental setup is shown in Fig. 1 a, which includes the AFM tip, laser, optical lens, and PZT tube (see the Methods section and Supplementary Section 5 for details). We pressed on the top of the graphite flake using an AFM tip to induce relative sliding between the graphite flake and the two types of silicon surfaces through lateral motion of the piezoelectric displacement platform; Fig. 1 b shows the optical image of the experimental setup. The laser will be irradiated on the cantilever of the AFM tip, and the photodiode will receive the reflection laser signal to feel the deformation of the cantilever (See Methods section and Supplementary Section 5 for more details). The friction measurements were performed under an ambient atmosphere with a temperature of 25 ± 1°C and a relative humidity of 30 ± 4%. The measured lateral force signals when the graphite flake slides on the atomic-level smooth surface (Fig. 1 c) and the nanostructured surface (Fig. 1 e) are shown in Figs. 1 d and f, respectively. For a normal load of 20.04 \({\mu }\text{N}\) , we found that the friction of graphite flake sliding on the atomic-level smooth surface is ~ \(6 {\mu }\text{N}\) , which is much larger than that sliding on the nanostructured surface, which is ~ \( 0.2 {\mu }\text{N}\) . This high friction ~( \(6 {\mu }\text{N}\) ) is also orders larger than the typical value for graphite flake sliding on other surfaces showing SSL, which is on the order of 0.1 \({\mu }\text{N}\) 1 5 . To understand the phenomenon of the large friction between the graphite flake and the atomic-level flat silicon surface in Fig. 1 d, we performed detailed in-situ characterizations of the sliding interface as shown in Supplementary Section 7. We found a possible reason that the carbon atoms at the edge of the graphite flake are dragged by the substrate through the strong chemical interaction with silicon, resulting in the occurrence of large friction and wear (i.e., failure of SSL state). Robust SSL state at the graphite flake/nanostructured silicon interface In order to further verify the robust structural superlubric (SSL) state between the graphite flake and the nanostructured silicon surface, we conducted a series of tribological tests between a \(4 \times 4 {\mu }\text{m}\) graphite flake and the other silicon surface with prepared nanostructures (fabrication process is presented in the Supplementary Section 2 and Methods section) by the same experimental set-up as Fig. 1 a and under the same environmental conditions. Detailed testing procedures are detailed in the Methods section and Supplementary Section 6. Firstly, we selected a silicon area with nanostructures, the morphology of which is shown in Fig. 2 b. Then we measured the friction force of graphite flake/nanostructured silicon interface under various normal load in situ as shown in Fig. 2 d. An ultra-low differential friction coefficient of 0.00044 ± 0.00027 is found, with the friction force about \(0.7 {\mu }\text{N}\) . Secondly, we performed a 5120-cycle sliding experiment for graphite flake on the same area. The measured friction forces of the entire sliding process are shown in Fig. 2 a. The friction forces were stabilized in the range of \(0.6–0.7 {\mu }\text{N}\) . After the sliding experiment, we characterized the morphology of the nanostructured silicon surface in situ (Fig. 2 c), found no obvious wear debris or damage. Further, we performed Raman mapping characterization on the slid nanostructured silicon surface, the red frame in Fig. 2 e is the scan area, which includes the whole sliding region (yellow dash frame). The intensity distributions of D peak (1350 \(\text{c}{\text{m}}^{-1}\) ), G peak (1580 \(\text{c}{\text{m}}^{-1}\) ) and 2D peak (2700 \(\text{c}{\text{m}}^{-1}\) ) are displayed in Figs. 2 f-h, respectively, where Fig. 2 i shows the single-point Raman spectrum at the blue cross mark position in Fig. 2 e (illustration is an enlarged view of range \(1200-2800 \text{c}{\text{m}}^{-1}\) ). No observable D, G, 2D graphite peaks were found, indicates that there was no graphite wear debris on the slid nanostructured silicon surface. We also performed Raman characterization at different positions (points 1–9 in illustration) on the slid graphite flake surface, as shown in Fig. 2 j. The absence of D peak indicates that there was no visible wear of the graphite flake surface after 5120 sliding cycles. Altogether, the small friction (< 1 µN), ultralow differential friction coefficient (~ 10 − 4 ), and absence of wear indicate the presence of robust SSL state between graphite flake and nanostructured silicon surface. Mechanism of robust SSL state at graphite flake/nanostructured silicon interface To understand the mechanism of the SSL state at graphite/nanostructured silicon interface, we carried out simulations using finite element method (FEM) for the experimental process as shown in Fig. 3 a. The van der Waals interaction between the graphite flake and silicon surface is derived from Lennard-Jones (LJ) potential (see Supplementary Section 8.1 for details). The graphite flakes are \(4 {\mu }\text{m}\times 4 {\mu }\text{m}\) in size and \(200 \text{n}\text{m}\) in height, covered with \(100 \text{n}\text{m}\) thick Au caps and the normal load on its center is \(20 {\mu }\text{N}\) , which is within the range of the applied normal load in the experiments. For the nanostructured silicon surface, the spacing and height of the rough peak array are \(400 \text{n}\text{m}\) and \(7 \text{n}\text{m}\) respectively. The surface shape of each roughness peak is obtained by rotating and sweeping the function \(y=A\text{s}\text{i}\text{n}{\left(\frac{\pi x}{L}\right)}^{n}\) around the symmetry axis, where \(A=7 \text{n}\text{m}, L=350 \text{n}\text{m}\) and \(n=10\) , which are statistically obtained from actual measured topography from Fig. 2 b (see Supplementary Section 4 for details). The sliding displacement \({\Delta }x\) of the graphite flake is \(0\) in the initial state. When the graphite flake is pressed against nanostructured silicon surface, as shown in Fig. 3 b for the Mises stress distribution across the diagonal section, there is a concentrated normal stress around the rough peak near the loading center, while no normal stress between the peripheral region of the graphite flake and the nanostructured silicon is observed. We further plot the displacement in height (upper) and Mises stress (lower) distribution along the bottom of the graphite flake pressed on nanostructured silicon across the diagonal section, as shown in Fig. 3 c, which shows that the peripheral part of the graphite flake warps upon the original state (black dotted line) under the central force, where the warping height of the edge is \({\Delta }h\) . Together with the zero normal stress between the peripheral region of the graphite flake and the nanostructured silicon, it is evident that the graphite edges become out of contact upon loading (Supplementary Section 9 gives the overall pressure distribution between the bottom surface of the graphite flake and the nanostructured silicon substrate, indicating that only the rough peaks near the loading center are in contact with the bottom surface of the graphite flake, and the corresponding actual contact area is only \(6.23\times {10}^{-2}{{\mu }\text{m}}^{2}\) ). Such transition of the contact state, however, is absent for graphite flake pressed against a flat silicon surface (see Supplementary Section 8.2 for details). We then simulated the edge warpage of graphite flake during sliding on the nanostructured silicon surface through half rough peak period (i.e., 200 nm), and plotted the relationship between the minimum warpage height along the edge \({{\Delta }h}_{\text{m}\text{i}\text{n}}\) and sliding distance \({\Delta }x\) in Fig. 3 d. The minimum warpage height \({{\Delta }h}_{\text{m}\text{i}\text{n}}\) goes lower when the load point goes closer to the rough peak, but remains positive throughout, which indicates that the warping of the edge keeps stable during the continuous sliding. From mechanical point of view, the FEM simulation shows that the bending moment generated by the central load on the nanostructured silicon surface overcomes van der Waals adsorption between graphite and nanostructured silicon surfaces and results in the warping of the graphite flake edges during sliding. In addition, the maximum stress at the bottom surface of graphite flake shown in the lower image of Fig. 3 c is around \(0.6 \text{G}\text{P}\text{a}\) , which is lower than the critical withstand pressure to maintain the SSL state at the bottom surface of graphite flake (> 1 GPa) 21 , so stress concentration will not lead to the failure of the SSL state within the range of normal force applied in our experiments. Considering that finite element methods in a relatively large scale may underestimate or overestimate the van der Waals interaction between contact surfaces which acts at sub-nanometer scale, we performed additional molecular dynamics (MD) simulations to extract the maximum adhesion between one rough peak and the graphite. The MD simulation model, which was established according to the morphology of the rough peak in experiments (Figs. 3 e and f), is shown in Fig. 3 g where the simulation box has the size of \(60 \text{n}\text{m}\times 60 \text{n}\text{m}\times 7 \text{n}\text{m}\) (see Methods section and Supplementary Section 10 for details). The simulated adhesive force versus distance respect to the equilibrium interlayer spacing is shown in Fig. 3 h (blue solid line), where the maximum adhesion is \(46 \text{n}\text{N}\) (blue dotted line). The de-adhesion force of single rough peak due to the bending moment caused by the central load around is estimated to be about \(178 \text{n}\text{N}\) (the illustration and red dotted line in Fig. 3 h, see Supplementary Section 8.3 for details), which is larger than maximum adhesion force. Therefore, these MD results validate the de-adhesion process obtained by the FEM on atomic scale. Based on the above analysis, we can conclude that the mechanism of the robust SSL state at the graphite flake/nanostructure silicon interface is that the edge of the graphite flake on the nanostructure silicon surface will warp under the central normal force, thereby eliminate the interaction between the edge of graphite flake and substrate, which is proved to be the main source of friction 17 . On the contrary, due to the tight van der Waal adhesion between the graphite flake and atomic flat silicon surface, the edges of the graphite flakes interact with the silicon surface, which may eventually lead to large friction and induce wear. Experimental verification of edge warping mechanism We verified above proposed mechanism by conducting a series of experiments for graphite flake/nanostructured silicon interface. First of all, we measured the friction coefficient of graphite flake/nanostructured silicon interface for different loading positions, where the eccentricity, i.e., distance between the loading position and the center of the flake is δ , as shown in Fig. 4 a, where the optical observation of the different \(\delta =0, 0.4, 0.8, 1.2 {\mu }\text{m}\) are shown in Fig. 4 b. The measured friction force of different applied normal force under different \(\delta\) are shown in Fig. 4 f, which can be seen that the friction force and fitted friction coefficient increases rapidly with the increase of \(\delta\) , especially when \(\delta =1.2 {\mu }\text{m}\) , that is, when AFM tip pressed near the edge of graphite flake. We then simulated the warping of graphite flake on nanostructured silicon under different \(\delta\) through the same FEM method in the last section. The simulated height distribution of the graphite flake bottom surface under a normal loading of 20 \({\mu }\text{N}\) with \(\delta =0\) and \(\delta =1.2 {\mu }\text{m}\) are shown in Figs. 4 c and d, respectively. Under central normal loading ( \(\delta =0\) ) condition, all edges of the graphite flake are de-adhered and warped due to bending moment ( \({\Delta }{h}_{\text{m}\text{i}\text{n}}>0\) ). On the contrary, when the edges are loaded ( \(\delta =1.2 {\mu }\text{m}\) ), the edges near the loaded side ( \(X=2 {\mu }\text{m}\) ) cannot be warped due to insufficient bending moments and concentrated forces, resulting in downwards deformation ( \({\Delta }{h}_{\text{m}\text{i}\text{n}}<0\) ). The minimum warpage height \({{\Delta }h}_{\text{m}\text{i}\text{n}}\) under different loading positions ( \(\delta =0, 0.4, 0.8, \text{1.2,1.6} {\mu }\text{m}\) ) is shown in Fig. 4 e, where \({{\Delta }h}_{\text{m}\text{i}\text{n}}\) drops rapidly to negative when \(\delta \ge 1.2 {\mu }\text{m}\) , which explains the failure of the SSL state when \(\delta =1.2 {\mu }\text{m}\) in the experiment (high friction force and coefficient in Fig. 4 f when \(\delta =1.2 {\mu }\text{m}\) ). Therefore, above results indicates that the incretion of the interaction between the graphite flake edge and the substrate increases the friction force and friction coefficient (SSL state failure) 17 , which verify the edge warping under concentrated normal force in the center of the graphite flake is the mechanism of robust SSL state at graphite flake/nanostructured silicon interface. An intuitive deduction according to the mechanism as well as Fig. 4 is larger eccentricity will facilitate the failure of SSL. To this end, we conducted a series of tribological tests for \(\delta =1.8 {\mu }\text{m}\) . As shown in Fig. 5 a, the measured friction fluctuated and suddenly increased during the process of 3072-cycle sliding, which is probably caused by the collision between the edge of the graphite flake and the nanostructure. Meanwhile, wear debris is also observed on nanostructured silicon surface after sliding (Figs. 5 b, c). Further Raman spectroscopy map of the nanostructured silicon surface after sliding (Figs. 5 d-h) shows that the wear debris is composed of graphite. This is also supported by the direct Raman spectroscopy characterization for the bottom surface of graphite flake after sliding (Fig. 5 i). Conclusion To conclude, we achieve a robust structural superlubric (SSL) state with a microscale graphite flake/nanostructured silicon interface under ambient condition. The friction is always less than 1 \({\mu }\text{N}\) , the friction coefficient is measured to be the order of \(1{0}^{-4}\) , and there is no observable wear. The mechanism is revealed to be the edge warping of graphite flake on the nanostructured surface under concentrated force, which eliminates the high friction and wear caused by the strong interaction between the edge and the substrate 16 , 17 . This work not only proves that a graphite flake with single crystal surface can realize robust SSL state with nanostructured surface in the atmosphere, which reduce the roughness requirements of SSL technology, but also provides a general surface modification method to achieve robust SSL state between graphene flakes and non-vdW materials, which promotes the general application of SSL technology. Method Preparation of graphite mesa with Au cap. We fabricated square graphite mesa arrays with Au cap on highly ordered pyrolytic graphite (HOPG, ZYB grade (Brucker) 22 ). The fabrication process is shown in Supplementary Fig. 1a, we firstly spun on a double layer photoresist LOR 1A (100 nm)/ZEP (400 nm) on the freshly cleaved surface of the HOPG as shown in Supplementary Fig. 1a (i), and then remove the photoresist in the mesa pattern array region by electron beam lithography and development process as shown in Supplementary Fig. 1a (ii). Secondly, we grew the Au film with thickness of 100nm through electron beam evaporation as shown in Supplementary Fig. 1a (iii). Thirdly, we obtained the Au pattern array through lift-off process as shown in Supplementary Fig. 1a (iv). Lastly, we used Au pattern array as a mask to obtain graphite mesa with Au cap by oxygen reactive ion etching process as shown in Supplementary Fig. 1a (v), where the etching depth is \(0.8 {\mu }\text{m}\) . The characterizations of fabricated graphite mesa with Au film are shown in Supplementary Figs. 1b-e. Preparation of nanostructed silicon surface. Firstly, we ultrasonically cleaned the silicon surface with acetone, alcohol and deionized water for 5 minutes, and then performed the surface hydrophilic treatment by oxygen plasma, as shown in Supplementary Fig. 2a (i). Then we mixed 200 nm polystyrene (PS) microsphere solution (mass fraction 10%, produced by Huge Biotechnology Company) with alcohol and deionized water in a ratio of 1:2:2 and ultrasonic for 30 minutes to obtain the diluted solution. Further we immersed the silicon surface with deionized water and used the pipette to drop the diluted solution \(250 {\mu }\text{L}\) , and made it self-assemble on the liquid interface, as shown in Supplementary Fig. 2a (ii). Secondly, we evaporated the deionized water in atmospheric environment, and deposit the self-assembled PS microsphere array on the silicon surface, as shown in Supplementary Fig. 2a (iii). Then, we reduced the size of PS microspheres by oxygen plasma etching (power: 400 W, oxygen flow: 400 sccm, etching time: 4 min), as shown in Supplementary Fig. 2a (iv). Thirdly, we used PS microsphere array as mask to obtain the nanostructures by ion beam etching process (beam: \(1 \text{m}\text{A}/\text{c}{\text{m}}^{2}\) , energy: 500 eV, etching time: 15s), as shown in Supplementary Fig. 2a (v). Lastly, we removed the PS microsphere array by excessive oxygen plasma etching, as shown in Supplementary Fig. 2a (vi). Graphite flake/silicon interface formation . Firstly, we used a tungsten microtip controlled by a micromanipulator (Kleindiek MM3A) to attach the Au cap of graphite mesa fabricated in Supplementary Fig. 1, as shown in Supplementary Fig. 3a, and applied a shear stress by the micromanipulator to split the graphite mesa a distance of ~ \(2 {\mu }\text{m}\) from the vertical direction, as shown in Supplementary Fig. 3b. Secondly, we removed the microtip to observe whether the sheared graphite flake undergoes self-recovery motion (SRM) 19 to determine whether it has a single crystal structural superlubric bottom surface 20 , as shown in Supplementary Fig. 3c. Thirdly, we re-attached the graphite flake which has SRM property with a microtip and split it out completely, then picked up the dangling graphite flake dragged by the microtip as shown in Supplementary Figs. 3d and e. Lastly, we placed the dangling graphite flake slowly by micromanipulator on the fabricated silicon surface, since the adsorption force of the graphite flake and silicon is larger than that of the microtip and graphite flake, the graphite flake would remain on the silicon surface, as shown in Supplementary Fig. 3f, which formed the graphite flake/silicon interface shown in Fig. 1 a. Friction measurement of AFM system. The friction measurements of the graphite/n-Si heterostructures were performed under an ambient atmosphere with a temperature of 25 ± 1°C and a relative humidity of 30 ± 4%. The experimental set-up included a commercial NTEGRA upright AFM (Cypher S-Oxford Instruments), a XYZ piezoelectric displacement platform, a high numerical aperture objective lens ( \(\times\) 20) and visualized AFM tip (ACCESS-NC-GG(Appnano)). Figure 1 a shows the schematic of the experimental set-up. We accurately pressed the AFM tip on the Au cap of the graphite flake through the optical microscope and piezoelectric displacement platform. The AFM tip was calibrated in situ by the Sader method 23 , 24 for the normal direction force and the diamagnetic levitation spring system 25 for the lateral direction force, the specific results of the calibration process are shown in the Supplementary Fig. 6. Surface characterization method of tribological experiment. Here, we show the main process and method of the experiment in Fig. 2 , Fig. 5 and Supplementary Fig. 9. For details, please refer to Supplementary Section 6. Taking Fig. 5 as an example, the first step is to use the atomic force microscope (AFM, Cypher S-Oxford Instruments ) in tapping mode to characterize the morphology of the silicon surface before sliding (Fig. 5 b). For the second step, we used the AFM tip (ACCESS-NC-GG(Appnano)) to apply normal load on the graphite flake, and then moved it to the center of the previous morphological characterization region, as shown in Supplementary Fig. 7c, and then measured the friction force of 3,072 cycles sliding process (Fig. 5 a). For the third step, we used the AFM tip to move graphite flake out of the sliding region, as shown in Supplementary Fig. 7e, and then used AFM in tapping mode to characterize the morphology of sliding region in situ through the positioning function of AFM, to judge whether there is any observable damage (Fig. 5 c). For the fourth step, we performed a Raman characterization (WITec Raman spectra, Ulm, Germany equipped with an alpha 300RA microscope using ZEISS 100x/0.9 objective, a 532 nm laser, a 300 gr/mm grating and a charge-coupled device cooled down to -60℃. The laser power was set 6 mW and the Raman image of the sample was measured with a 200 nm step size and an acquisition time of 1-5s. The acquired images were analyzed using a WITec Control/Project 5.3.) on the slid silicon surface (Figs. 5 d-h), to determine whether there is any observable graphite wear debris from whether there are D (1350 \(\text{c}{\text{m}}^{-1}\) ), G (1580 \(\text{c}{\text{m}}^{-1}\) ) and 2D (2700 \(\text{c}{\text{m}}^{-1}\) ) graphite peaks. Lastly, we used the method shown in Supplementary Fig. 8 to lift the graphite flake by overcoming the van der Waals adsorption force between graphite flake and silicon surfaces, and flipped 180 degrees to perform the Raman characterization (LabRAM HR Evolution Raman spectrometer from HORIBA, with resolution of \(0.1 \text{c}{\text{m}}^{-1}\) , laser wavelength of \(532 \text{n}\text{m}\) , grating of 1800 gr/mm, acquisition time of 4s and spot diameter of \(1 {\mu }\text{m}\) ) on the slid graphite flake surface (Fig. 5 i), to determine whether there is any observable damage from whether there is a D peak (1350 \(\text{c}{\text{m}}^{-1}\) ). The setup of finite element simulation of edge warping mechanism. The FEM simulation model is consistent with the experiments in scale and consist of Au cap, graphite flake and nanostructured silicon substrates, which is shown in Fig. 3 a. The Au cap and graphite flake are both \(4\times 4 {\mu }\text{m}\) in size and are bonded together. The thickness of Au cap is \(100 \text{n}\text{m}\) , and graphite flake’s thickness is \(200 \text{n}\text{m}\) . The nanostructured silicon substrate is \(4.8 {\mu }\text{m}\times 4.8 {\mu }\text{m}\) in size and has a thickness of \(50 \text{n}\text{m}\) without rough peaks. The rough peaks on the nanostructured silicon surface are \(7 \text{n}\text{m}\) in height and the shape function for its cross section is \(y=A\text{s}\text{i}\text{n}{\left(\frac{\pi x}{L}\right)}^{n}\) , in which \(A=7 \text{n}\text{m}\) , \(L=350 \text{n}\text{m}\) and \(n=10\) . Distance between rough peaks is \(400 \text{n}\text{m}\) , so there’s \(12\times 12\) rough peaks in total and \(10\times 10\) of them are below the graphite mesa consisting of graphite flake and Au cap. The Young’s Modulus and Poisson’s ratio of Au and Si are \(79.5 \text{G}\text{P}\text{a}\) and \(0.42\) , \(190 \text{G}\text{p}\text{a}\) and \(0.278\) , respectively 26 . The graphite flake is set to be orthotropic with stress-strain relation 27–30 $$\begin{array}{c}\left(\begin{array}{c}{\sigma }_{x}\\ {\sigma }_{y}\\ {\sigma }_{z}\\ {\tau }_{\text{xy}}\\ {\tau }_{\text{yz}}\\ {\tau }_{\text{xz}}\end{array}\right)=\left[\begin{array}{cccccc}1060& 180& 15& 0& 0& 0\\ 180& 1060& 15& 0& 0& 0\\ 15& 15& 36.5& 0& 0& 0\\ 0& 0& 0& 440& 0& 0\\ 0& 0& 0& 0& 4& 0\\ 0& 0& 0& 0& 0& 4\end{array}\right]\left(\begin{array}{c}{\epsilon }_{x}\\ {\epsilon }_{y}\\ {\epsilon }_{z}\\ {\gamma }_{\text{xy}}\\ {\gamma }_{\text{yz}}\\ {\gamma }_{\text{xz}}\end{array}\right),\#\left(1\right)\end{array}$$ Where the elastic modulus is given in units of Gpa. The van der Waals interaction between the graphite flake and silicon surface is derived from Lennard-Jones (LJ) potential. Bottom surface of the substrate is fixed in all directions and the contact point with AFM tip, a circular area in the center of the graphite mesa’s top surface with diameter of \(50 \text{n}\text{m}\) , is fixed and can only move in the vertical direction to prevent the graphite mesa from rotating and sliding. During the simulation steps, negligible load is firstly applied to make graphite mesa and the substrate contact, then a normal load of \(20 {\mu }\text{N}\) is applied on the graphite flake’s central area gradually. The setup of molecular dynamics simulation of single rough peak adhesive force. The MD simulation model consists of the silicon substrate and AB-stacking bilayer graphene. The morphology of the substrate is based on the experimental characterization (Figs. 3 e and f are characterized by AFM, Cypher S-Oxford Instruments). Since the equilibrium distance of the vdW interaction between silicon and graphite is sub-nanometer and it decays with distance to the 6 powers, we used a miniature simulation model to ensure the simulation efficiency. The 2-nm-thick substrate used in our simulation is the tip of the realistic rough peak (usually with height 7 nm), and only bilayer graphene is used. The simulation box has the size of \(60 \text{n}\text{m}\times 60 \text{n}\text{m}\times 7 \text{n}\text{m}\) . There are \(4\times {10}^{5}\) atoms for the simulation system. Periodic boundary conditions are applied to \(x\) and \(y\) directions. The quasi-static MD simulations are performed using LAMMPS 31 . The interlayer interaction between graphene/graphene and graphene/silicon is described by Lennard-Jones potential 32 . The intralayer interaction of graphene and substrate is described by REBO force field 33 and the modified Tersoff force field 34 respectively. The bottom atomic layer of the substrate is fixed as a rigid body. Springs with spring constant \({k}_{\text{z}}=2.7 \text{N}/\text{m}\) are tethered to each carbon atom of the upper graphene layer to mimic the elastic behavior of bulk graphite 35 . To extract the maximum adhesion between the graphene and silicon substrate, we used the quasi-static simulation protocol 36 . At each step the rigid bottom atomic layer is displaced by -0.02 Å along z direction, followed by minimizing the total energy of the whole system with FIRE algorithm 37 until the forces acting on each atom reduces below the tolerance 10 -4 eV/Å. Declarations Acknowledgements Q.Z. wishes to acknowledge the financial support by National Natural Science Foundation of China No. 11572173, No. 11890671, No. 51961145304, No. 11921002. M.M. acknowledges the financial support from the NSFC (Grant no. 11890673 and 11772168) and the Shenzhen fundamental research key project JCYJ20200109150608043. X.J. acknowledges the financial support by National Natural Science Foundation of China No. 12002216 and the GuangDong Basic and Applied Basic Research Foundation 2020A1515110995. References 1 Holmberg, K., Andersson, P. & Erdemir, A. Global energy consumption due to friction in passenger cars. Tribology International 47 , 221-234, doi:10.1016/j.triboint.2011.11.022 (2012). 2 Long-Sheng, F., Yu-Chong, T. & Muller, R. S. IC-processed electrostatic micro-motors. International Electron Devices Meeting. Technical Digest (IEEE Cat. No.88CH2528-8) , 666-669, doi:10.1109/iedm.1988.32901 (1988). 3 Berman, D., Deshmukh, S. A., Sankaranarayanan, S. K. R. S., Erdemir, A. & Sumant, A. V. Macroscale superlubricity enabled by graphene nanoscroll formation. Science 348 , 1118-1122, doi:10.1126/science.1262024 (2015). 4 Granick, S., Zhu, Y. X. & Lee, H. Slippery questions about complex fluids flowing past solids. Nature Materials 2 , 221-227, doi:10.1038/nmat854 (2003). 5 Granick, S. 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W. et al. A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons. Journal of Physics-Condensed Matter 14 , 783-802, doi:10.1088/0953-8984/14/4/312 (2002). 34 Kumagai, T., Izumi, S., Hara, S. & Sakai, S. Development of bond-order potentials that can reproduce the elastic constants and melting point of silicon for classical molecular dynamics simulation. Computational Materials Science 39 , 457-464, doi:10.1016/j.commatsci.2006.07.013 (2007). 35 Guo, Z., Chang, T., Guo, X. & Gao, H. Mechanics of thermophoretic and thermally induced edge forces in carbon nanotube nanodevices. Journal of the Mechanics and Physics of Solids 60 , 1676-1687, doi:10.1016/j.jmps.2012.04.013 (2012). 36 Bonelli, F., Manini, N., Cadelano, E. & Colombo, L. Atomistic simulations of the sliding friction of graphene flakes. The European Physical Journal B 70 , 449-459 (2009). 37 Bitzek, E., Koskinen, P., Gahler, F., Moseler, M. & Gumbsch, P. Structural relaxation made simple. Physical Review Letters 97 , 4, doi:10.1103/PhysRevLett.97.170201 (2006). Additional Declarations There is NO Competing Interest. Supplementary Files SupplementaryInformation.docx Robust microscale structural superlubricity between graphite and nanostructured surface Cite Share Download PDF Status: Published Journal Publication published 22 May, 2023 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-2273111","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":154620685,"identity":"9512801e-340e-4ee5-a996-3fbab13bfa12","order_by":0,"name":"Xuanyu Huang","email":"","orcid":"https://orcid.org/0000-0003-3021-3405","institution":"Tsinghua University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Xuanyu","middleName":"","lastName":"Huang","suffix":""},{"id":154620686,"identity":"02682320-d30b-4bb9-9d42-6cb345b8a342","order_by":1,"name":"Tengfei Li","email":"","orcid":"","institution":"Tsinghua University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Tengfei","middleName":"","lastName":"Li","suffix":""},{"id":154620687,"identity":"e3842c50-a4b6-417d-830d-acb9d0995d7d","order_by":2,"name":"Jin Wang","email":"","orcid":"https://orcid.org/0000-0002-3924-2942","institution":"Scuola Internazionale Superiore di Studi Avanzati","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Jin","middleName":"","lastName":"Wang","suffix":""},{"id":154620688,"identity":"7944fd68-9f26-4c56-90d8-ec23bc9b9ce7","order_by":3,"name":"Kai Xia","email":"","orcid":"","institution":"Institute of Superlubricity Technology, Research Institute of Tsinghua University in Shenzhen","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Kai","middleName":"","lastName":"Xia","suffix":""},{"id":154620689,"identity":"cbd78c4a-91a8-4d4c-9682-2f4bd6ab65db","order_by":4,"name":"Deli Peng","email":"","orcid":"","institution":"Institute of Superlubricity Technology, Research Institute of Tsinghua University in Shenzhen","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Deli","middleName":"","lastName":"Peng","suffix":""},{"id":154620690,"identity":"620c24af-ca4b-4b16-bcac-4aa42525e06f","order_by":5,"name":"Xiaojian Xiang","email":"","orcid":"","institution":"Tsinghua University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Xiaojian","middleName":"","lastName":"Xiang","suffix":""},{"id":154620691,"identity":"4b65c4c7-6d73-45f1-a703-19e332f288e6","order_by":6,"name":"Ming Ma","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9klEQVRIiWNgGAWjYJCCAwwMEnL8EMYBsIgEEVosjCXbSNECBBWJBsdg2glp0W0/nXi44JdEgvH99odAxp3E/gbmg7d5GOzycGkxO5O74fDMPok8s2M8BkDGs8QZB9iSrXkYkotxajkA1MLbI1EM1MIAZBxObDjAYybNw3AgsQGXlvNvwVoSN7exPwBrmX+A/xt+LTeAtvD8kEjcwMZgAGQcTtxwgIeNgBaQLQ0SxhLHcgyAjMPGGw+zGVvOMUjG47DczZ95/tTJ8TcffwxkHJadd7z54Y03FXY4tYABYxsygxnEMsCnHgT+YDBGwSgYBaNgFCAAALEpZQ03VHQhAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0001-6016-286X","institution":"Tsinghua University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Ming","middleName":"","lastName":"Ma","suffix":""},{"id":154620692,"identity":"57415aaa-e53f-41ba-a66f-c83fe7267273","order_by":7,"name":"Quanshui Zheng","email":"","orcid":"https://orcid.org/0000-0002-4828-2751","institution":"Tsinghua University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Quanshui","middleName":"","lastName":"Zheng","suffix":""}],"badges":[],"createdAt":"2022-11-14 17:45:39","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2273111/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2273111/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41467-023-38680-6","type":"published","date":"2023-05-22T04:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":29687490,"identity":"da7051a2-7ef5-4b2f-a172-cd0065e0393d","added_by":"auto","created_at":"2022-11-29 23:05:06","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":122678,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFriction measurement of superlubric graphite flake and two types of silicon surfaces\u003c/strong\u003e.\u003cstrong\u003e a\u003c/strong\u003e Schematic diagram of the experimental set-up to measure the friction of graphite/silicon interface. The silicon substrate was rigidly fixed to the piezoelectric ceramic transducer (PZT) stage on top of which an Au capped graphite flake was placed. Normal force and lateral force are applied by pressing the AFM tip on the top of the Au cap. When the PZT stage reciprocates, the AFM tip will drag the graphite flake to relative slide on the silicon substrate. \u003cstrong\u003eb\u003c/strong\u003e Optical microscopic image of experimental set-up. \u003cstrong\u003ec\u003c/strong\u003e and\u003cstrong\u003e e \u003c/strong\u003eare the surface topography of atomic-level smooth surface and nanostructured surface, respectively. \u003cstrong\u003ed \u003c/strong\u003eand\u003cstrong\u003e f \u003c/strong\u003eare the\u003cstrong\u003e \u003c/strong\u003elateral force signal when graphite flake sliding on the atomic-level smooth surface and nanostructured surface respectively, with a displacement amplitude of 1 μm and a speed of 2 μm/s under a normal force of 20.04 μN.\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2273111/v1/c102363fa59fc6879a75e6b4.jpg"},{"id":29688139,"identity":"34b4f63a-86c3-4542-ab73-dd847dddbff6","added_by":"auto","created_at":"2022-11-29 23:13:07","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":186712,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eTribological tests between graphite flakes and nanostructured silicon surface. a\u003c/strong\u003e Measured friction force during 5120 continuous sliding cycles with a displacement amplitude of 1 μm and speed of 2 μm/s under a normal force of 14.65 μN. \u003cstrong\u003eb \u003c/strong\u003eand \u003cstrong\u003ec \u003c/strong\u003eare the topography of the nanostructured surface before and after 5120 sliding cycles, respectively, where the yellow dashed frame is the boundary of the sliding region.\u003cstrong\u003e d\u003c/strong\u003e Measured friction force of graphite flake/nanostructured silicon interface in situ under different normal load with a displacement amplitude of 1 μm and speed of 2 μm/s. \u003cstrong\u003ee-h\u003c/strong\u003e are the Raman characterization results of the sliding region on nanostructured silicon, where \u003cstrong\u003ee \u003c/strong\u003eis\u003cstrong\u003e \u003c/strong\u003ethe optical observation, the red frame is the scan area of 6 μm × 6 μm (including the whole sliding region), \u003cstrong\u003ef-h\u003c/strong\u003e are the intensity distributions of D peak (1350 cm\u003csup\u003e-1\u003c/sup\u003e), G peak (1580 cm\u003csup\u003e-1\u003c/sup\u003e) and 2D peak (2700 cm\u003csup\u003e-1\u003c/sup\u003e), respectively, there is no observable graphite composition. \u003cstrong\u003ei \u003c/strong\u003eSingle-point Raman spectrum at the blue cross mark position in \u003cstrong\u003ee\u003c/strong\u003e, the illustration is an enlarged view of the black dash frame region, there are no observable D, G and 2D graphite peaks. \u003cstrong\u003ej \u003c/strong\u003eRaman characterization of the bottom surface of graphite flake after 5120 sliding cycles; points 1–9 represent the test positions, there is no observable D peak, and the illustration is the optical observation of flipped graphite flake.\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2273111/v1/f5dabc6df98e76b91ecf1dab.jpg"},{"id":29687513,"identity":"b988994e-485c-4333-9e01-468104402952","added_by":"auto","created_at":"2022-11-29 23:05:07","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":143285,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eEdge warping of graphite flakes on nanostructured surface\u003c/strong\u003e. \u003cstrong\u003ea-d \u003c/strong\u003eare the finite element simulation results. \u003cstrong\u003ea\u003c/strong\u003e Schematic diagram of the finite element simulation model with nanostructured silicon/graphite flake heterojunction, where the concentrated normal load of 20 μn is applied to the center of the graphite flake. \u003cstrong\u003eb \u003c/strong\u003eMises stress distribution across the diagonal section under central normal loading when Δχ = 0. \u003cstrong\u003ec \u003c/strong\u003eDisplacement in height (upper) and Mises stress (lower) distribution along the bottom surface of graphite flake across diagonal section (see illustration in the lower image), where the inset in the upper image is a partial enlarged view of the green dashed frame, and the black dotted line in the upper image is the original position of the bottom surface of the graphite flake, the warping height of edge is Δh. \u003cstrong\u003ed \u003c/strong\u003eWarping height Δh under different displacement Δχ of graphite flake (simulation range is half the period of rough peak of 200 nm, and the dot pitch is 10 nm). \u003cstrong\u003ee-h \u003c/strong\u003eare the molecular simulation results.\u003cstrong\u003e e \u003c/strong\u003eand\u003cstrong\u003ef \u003c/strong\u003eare the morphology of a typical single rough peak, where\u003cstrong\u003e f \u003c/strong\u003eis the 250 nm × 250 nm two-dimensional morphology, and \u003cstrong\u003ee\u003c/strong\u003e is the height data of the blue section line in\u003cstrong\u003e f\u003c/strong\u003e. \u003cstrong\u003eg\u003c/strong\u003e Schematic diagram of the molecular dynamic simulation model of graphite/single-coarse peak interface, where the simulation box size is 60 nm × 60 nm × 7 nm. \u003cstrong\u003eh \u003c/strong\u003eSimulated adhesive force upon with the distance respect to the equilibrium interlayer spacing (blue solid line), where the maximum adhesion force is 46 nN (blue dotted line). The illustration is the FEMsimulation of the force needed to balance the bending moment caused by the central load around a single rough peak (i.e., de-adhesion force), where the de-adhesion force is about 178 nN (red dotted line), which is larger than maximum adhesion force.\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2273111/v1/35623f38cc86ee8f406b053c.jpg"},{"id":29687512,"identity":"b1981d1a-ea37-4628-8a73-2b3194fd4f04","added_by":"auto","created_at":"2022-11-29 23:05:07","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":111907,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFriction coefficient between graphite flake and nanostructured surface for different loading positions\u003c/strong\u003e.\u003cstrong\u003ea\u003c/strong\u003e Schematic diagram of the experimental set-up to measure the friction of graphite flake/nanostructured silicon interface under different loading positions, where the distance between the loading position of the AFM tip and the center is δ. \u003cstrong\u003eb \u003c/strong\u003eOptical microscope observation for different δ. \u003cstrong\u003ec \u003c/strong\u003eand \u003cstrong\u003ed\u003c/strong\u003e are simulated height distribution of the graphite flake bottom surface under the normal loading when δ=0 and δ=1.2 μm respectively with a normal load of 20 μN. \u003cstrong\u003ee \u003c/strong\u003eRelationship between minimum warpage height Δh\u003csub\u003emin\u003c/sub\u003e and loading position δ with a normal load of 20 μn. \u003cstrong\u003ef\u003c/strong\u003e Measured friction force of different applied normal load under different δ.\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2273111/v1/1ffbfbd285da83edc24f3069.jpg"},{"id":29687515,"identity":"bd0fc1ad-bd7a-4084-bd1b-b779b32966c7","added_by":"auto","created_at":"2022-11-29 23:05:07","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":166801,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eWear characterization of the graphite flake on the nanostructured surface under edge loading\u003c/strong\u003e.\u003cstrong\u003e a\u003c/strong\u003e Measured friction force during 3072 continuous sliding cycles with a displacement amplitude of 1 μm and speed of 2 μm/s under a normal force of 21.98 μN. \u003cstrong\u003eb \u003c/strong\u003eand \u003cstrong\u003ec \u003c/strong\u003eare the topography of the nanostructured surface before and after 3072 sliding cycles, respectively, where the newly-appearing highlighted region is the wear debris, and the yellow dashed frame is the boundary of the sliding region.\u003cstrong\u003e d-h\u003c/strong\u003e are the Raman characterization results of the sliding region on nanostructured silicon, where \u003cstrong\u003ed \u003c/strong\u003eis\u003cstrong\u003e \u003c/strong\u003ethe optical observation, the red frame is the scan area of 6 μm × 6 μm (including the whole sliding region), \u003cstrong\u003ee-g\u003c/strong\u003e are the intensity distributions of D peak (1350 cm\u003csup\u003e-1\u003c/sup\u003e), G peak (1580 cm\u003csup\u003e-1\u003c/sup\u003e) and 2D peak (2700 cm\u003csup\u003e-1\u003c/sup\u003e), respectively, it can be seen that there is large intensity at the location of the wear debris in three images. \u003cstrong\u003eh \u003c/strong\u003eSingle-point Raman spectrum at the wear debris position (blue cross mark in \u003cstrong\u003ed\u003c/strong\u003e), there are significant D, G and 2D graphite peaks. \u003cstrong\u003ei \u003c/strong\u003eRaman characterization of the graphite flake bottom surface at edge positions on the side close to the loading position after 3072 sliding cycles; points 1–3 represent the test positions, where significant D peaks appear.\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2273111/v1/8997599b39f1fde77f091b88.jpg"},{"id":37363185,"identity":"2b3202b9-45f1-4af3-a852-42170f6aa8be","added_by":"auto","created_at":"2023-05-23 07:13:20","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1295522,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2273111/v1/33f7d38d-92d8-429e-afb5-9a609bbf9c48.pdf"},{"id":29687516,"identity":"e1ccb3ec-d315-4994-a8ef-3473cdcb8807","added_by":"auto","created_at":"2022-11-29 23:05:08","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":24634560,"visible":true,"origin":"","legend":"\u003cp\u003eRobust microscale structural superlubricity between graphite and nanostructured surface\u003c/p\u003e","description":"","filename":"SupplementaryInformation.docx","url":"https://assets-eu.researchsquare.com/files/rs-2273111/v1/1274156a874d2fe98060f6f5.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Robust microscale structural superlubricity between graphite and nanostructured surface","fulltext":[{"header":"Introduction","content":"\u003cp\u003eFriction and wear are two fundamental physical phenomena coupled together in nature, which have caused huge energy waste, environmental pollution and component failure in mechanical system\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e, and made it difficult for a large number of key technologies such as novel design of micro-electromechanical system (MEMS)\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e. It is estimated that nearly one-third of the energy provided by fossil fuels in automobiles is dissipated by friction\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e. In the microscopic world, based on the scale effect, the interface friction and wear will become one of the most important problems compared to other effects, which cause the failure of the devices.\u003c/p\u003e \u003cp\u003eAlthough liquid lubricants such as organic oils have a great inhibitory effect on friction and wear in practical applications, they will fail under strong constraints and extreme external conditions, such as high external loads, high temperatures, as well as in the presence of chemical contamination or in a vacuum environment\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e. Lubrication based on the shear within liquid will fail on nanoscale as the viscosity may greatly increase\u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e, which is difficult to apply to micro-scale scenarios, such as MEMS, micro sensors, micro robots, etc\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e,\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e. Therefore, to solve the above problems, a new revolutionary technology is needed to reduce friction or even eliminate wear from the essential physical characteristics, instead of introducing other indirect substances as friction pairs.\u003c/p\u003e \u003cp\u003eStructural superlubricity (SSL), a state of nearly zero friction and no wear between two contact solid surfaces\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e,\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e,\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e, that relies on the effective cancellation of lateral forces between rigid crystalline contacts provides a revolutionary solution to above challenge. Since the successful realization of micro-scale SSL in the atmospheric environment in 2012\u003csup\u003e10\u003c/sup\u003e, in addition to the realizations of high-speed SSL (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(293 \\text{m}/\\text{s}\\)\u003c/span\u003e\u003c/span\u003e)\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e, SSL has attracted wide-ranging interest in not only academic studies\u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e, but also practical applications, such as superlubric generators (SLGs)\u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e,\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e and superlubric resonators\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e. More recently, SSL was realized between microscale graphite and many non-van der Waals materials such as diamond-like-carbon (DLC), Si, SiO\u003csub\u003e2\u003c/sub\u003e, Al\u003csub\u003e3\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e, Si\u003csub\u003e3\u003c/sub\u003eN\u003csub\u003e4\u003c/sub\u003e, etc\u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e. It greatly broadens the application range of SSL technology.\u003c/p\u003e \u003cp\u003eHowever, in this study, we unexpectedly discovered that when an atomic force microscope probe is pressed on a microscale graphite flake and dragged to slide on an atomic-level flat silicon surface, there is a certain probability of high friction (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\u0026gt;5 {\\mu }\\text{N}\\)\u003c/span\u003e\u003c/span\u003e) and corresponding wear will occur. On the contrary, the friction is always less than 1 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\mu }\\text{N}\\)\u003c/span\u003e\u003c/span\u003e between graphite flake and nanostructured silicon surface, the differential friction coefficient is on the order of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(1{0}^{-4}\\)\u003c/span\u003e\u003c/span\u003e, and there is no observable wear, indicating the presence of SSL. Through detailed characterization and simulation, we found that friction and wear between the graphite flake and atomic-level flat silicon surface mainly occur along the edge, and the dangling bonds along the edge will have a strong interaction with the substrate atoms\u003csup\u003e\u003cspan additionalcitationids=\"CR17\" citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e; but the edge of graphite flake on the nanostructured surface will occur warping under concentrated force, thereby reducing the edge interaction between the graphite flake and the substrate.\u003c/p\u003e"},{"header":"Results","content":"\u003cdiv class=\"Section2\" id=\"Sec3\"\u003e\n \u003ch2\u003eUltralow friction between graphite flake and nanostructured surfaces\u003c/h2\u003e\n \u003cp\u003eThe whole experiment process is divided into three steps. In the first step, we selected a graphite flake that was cleaved by shear from a square graphite mesa of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(4 \\times 4 \\times 0.9 {\\mu }\\text{m}\\)\u003c/span\u003e\u003c/span\u003e with a self-retracting motion (SRM) property\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e (see the Methods section and Supplementary Section 3 for details). The graphite mesa was made of highly ordered pyrolytic graphite (HOPG) with an Au cap of 100 nm thickness (fabrication details are provided in Supplementary Section 1 and the Methods section). The SRM motion is a strong indication for the presence of SSL at the interface between the bottom of graphite flake and the surface of the lower part of the graphite mesa. The cleaved surface (or bottom surface) of an graphite flake is a single-crystalline graphene sheet\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\n \u003cp\u003eIn the second step, we transferred the graphite flake onto two types of silicon surfaces (see the Methods section and Supplementary Section 3 for details), one of which is a very clean and atomic-level flat silicon surface, and the other is a surface with nanostructures. Their surface topography is shown in Figs. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ec and e, respectively. The selection and transfer process of graphite flake were performed under an ambient atmospheric environment in a thousand-class clean room with a temperature of 25\u0026thinsp;\u0026plusmn;\u0026thinsp;1\u0026deg;C and a relative humidity of 25\u0026thinsp;\u0026plusmn;\u0026thinsp;1%.\u003c/p\u003e\n \u003cp\u003eIn the third step, we used the lateral force module of the atomic force microscope (AFM, Cypher S-Oxford Instruments) to measure the friction between the graphite flake and two types of silicon surfaces, and the experimental setup is shown in Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ea, which includes the AFM tip, laser, optical lens, and PZT tube (see the Methods section and Supplementary Section 5 for details). We pressed on the top of the graphite flake using an AFM tip to induce relative sliding between the graphite flake and the two types of silicon surfaces through lateral motion of the piezoelectric displacement platform; Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003eb shows the optical image of the experimental setup. The laser will be irradiated on the cantilever of the AFM tip, and the photodiode will receive the reflection laser signal to feel the deformation of the cantilever (See Methods section and Supplementary Section 5 for more details). The friction measurements were performed under an ambient atmosphere with a temperature of 25\u0026thinsp;\u0026plusmn;\u0026thinsp;1\u0026deg;C and a relative humidity of 30\u0026thinsp;\u0026plusmn;\u0026thinsp;4%.\u003c/p\u003e\n \u003cp\u003eThe measured lateral force signals when the graphite flake slides on the atomic-level smooth surface (Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ec) and the nanostructured surface (Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ee) are shown in Figs. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ed and f, respectively. For a normal load of 20.04 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\mu }\\text{N}\\)\u003c/span\u003e\u003c/span\u003e, we found that the friction of graphite flake sliding on the atomic-level smooth surface is ~\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(6 {\\mu }\\text{N}\\)\u003c/span\u003e\u003c/span\u003e, which is much larger than that sliding on the nanostructured surface, which is ~\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\( 0.2 {\\mu }\\text{N}\\)\u003c/span\u003e\u003c/span\u003e. This high friction ~(\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(6 {\\mu }\\text{N}\\)\u003c/span\u003e\u003c/span\u003e) is also orders larger than the typical value for graphite flake sliding on other surfaces showing SSL, which is on the order of 0.1 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\mu }\\text{N}\\)\u003c/span\u003e\u003c/span\u003e\u003csup\u003e1\u003cspan class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. To understand the phenomenon of the large friction between the graphite flake and the atomic-level flat silicon surface in Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ed, we performed detailed in-situ characterizations of the sliding interface as shown in Supplementary Section 7. We found a possible reason that the carbon atoms at the edge of the graphite flake are dragged by the substrate through the strong chemical interaction with silicon, resulting in the occurrence of large friction and wear (i.e., failure of SSL state).\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv class=\"Section2\" id=\"Sec4\"\u003e\n \u003ch2\u003eRobust SSL state at the graphite flake/nanostructured silicon interface\u003c/h2\u003e\n \u003cp\u003eIn order to further verify the robust structural superlubric (SSL) state between the graphite flake and the nanostructured silicon surface, we conducted a series of tribological tests between a \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(4 \\times 4 {\\mu }\\text{m}\\)\u003c/span\u003e\u003c/span\u003e graphite flake and the other silicon surface with prepared nanostructures (fabrication process is presented in the Supplementary Section 2 and Methods section) by the same experimental set-up as Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ea and under the same environmental conditions. Detailed testing procedures are detailed in the Methods section and Supplementary Section 6. Firstly, we selected a silicon area with nanostructures, the morphology of which is shown in Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003eb. Then we measured the friction force of graphite flake/nanostructured silicon interface under various normal load in situ as shown in Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ed. An ultra-low differential friction coefficient of 0.00044\u0026thinsp;\u0026plusmn;\u0026thinsp;0.00027 is found, with the friction force about \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(0.7 {\\mu }\\text{N}\\)\u003c/span\u003e\u003c/span\u003e. Secondly, we performed a 5120-cycle sliding experiment for graphite flake on the same area. The measured friction forces of the entire sliding process are shown in Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ea. The friction forces were stabilized in the range of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(0.6\u0026ndash;0.7 {\\mu }\\text{N}\\)\u003c/span\u003e\u003c/span\u003e. After the sliding experiment, we characterized the morphology of the nanostructured silicon surface in situ (Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ec), found no obvious wear debris or damage.\u003c/p\u003e\n \u003cp\u003eFurther, we performed Raman mapping characterization on the slid nanostructured silicon surface, the red frame in Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ee is the scan area, which includes the whole sliding region (yellow dash frame). The intensity distributions of D peak (1350 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{c}{\\text{m}}^{-1}\\)\u003c/span\u003e\u003c/span\u003e), G peak (1580 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{c}{\\text{m}}^{-1}\\)\u003c/span\u003e\u003c/span\u003e) and 2D peak (2700 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{c}{\\text{m}}^{-1}\\)\u003c/span\u003e\u003c/span\u003e) are displayed in Figs. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ef-h, respectively, where Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ei shows the single-point Raman spectrum at the blue cross mark position in Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ee (illustration is an enlarged view of range \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(1200-2800 \\text{c}{\\text{m}}^{-1}\\)\u003c/span\u003e\u003c/span\u003e). No observable D, G, 2D graphite peaks were found, indicates that there was no graphite wear debris on the slid nanostructured silicon surface. We also performed Raman characterization at different positions (points 1\u0026ndash;9 in illustration) on the slid graphite flake surface, as shown in Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ej. The absence of D peak indicates that there was no visible wear of the graphite flake surface after 5120 sliding cycles. Altogether, the small friction (\u0026lt;\u0026thinsp;1 \u0026micro;N), ultralow differential friction coefficient (~\u0026thinsp;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e), and absence of wear indicate the presence of robust SSL state between graphite flake and nanostructured silicon surface.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv class=\"Section2\" id=\"Sec5\"\u003e\n \u003ch2\u003eMechanism of robust SSL state at graphite flake/nanostructured silicon interface\u003c/h2\u003e\n \u003cp\u003eTo understand the mechanism of the SSL state at graphite/nanostructured silicon interface, we carried out simulations using finite element method (FEM) for the experimental process as shown in Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ea. The van der Waals interaction between the graphite flake and silicon surface is derived from Lennard-Jones (LJ) potential (see Supplementary Section 8.1 for details). The graphite flakes are \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(4 {\\mu }\\text{m}\\times 4 {\\mu }\\text{m}\\)\u003c/span\u003e\u003c/span\u003e in size and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(200 \\text{n}\\text{m}\\)\u003c/span\u003e\u003c/span\u003e in height, covered with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(100 \\text{n}\\text{m}\\)\u003c/span\u003e\u003c/span\u003e thick Au caps and the normal load on its center is\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(20 {\\mu }\\text{N}\\)\u003c/span\u003e\u003c/span\u003e, which is within the range of the applied normal load in the experiments. For the nanostructured silicon surface, the spacing and height of the rough peak array are \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(400 \\text{n}\\text{m}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(7 \\text{n}\\text{m}\\)\u003c/span\u003e\u003c/span\u003e respectively. The surface shape of each roughness peak is obtained by rotating and sweeping the function \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(y=A\\text{s}\\text{i}\\text{n}{\\left(\\frac{\\pi x}{L}\\right)}^{n}\\)\u003c/span\u003e\u003c/span\u003e around the symmetry axis, where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(A=7 \\text{n}\\text{m}, L=350 \\text{n}\\text{m}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n=10\\)\u003c/span\u003e\u003c/span\u003e, which are statistically obtained from actual measured topography from Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003eb (see Supplementary Section 4 for details). The sliding displacement \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\Delta }x\\)\u003c/span\u003e\u003c/span\u003e of the graphite flake is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(0\\)\u003c/span\u003e\u003c/span\u003e in the initial state.\u003c/p\u003e\n \u003cp\u003eWhen the graphite flake is pressed against nanostructured silicon surface, as shown in Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003eb for the Mises stress distribution across the diagonal section, there is a concentrated normal stress around the rough peak near the loading center, while no normal stress between the peripheral region of the graphite flake and the nanostructured silicon is observed. We further plot the displacement in height (upper) and Mises stress (lower) distribution along the bottom of the graphite flake pressed on nanostructured silicon across the diagonal section, as shown in Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ec, which shows that the peripheral part of the graphite flake warps upon the original state (black dotted line) under the central force, where the warping height of the edge is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\Delta }h\\)\u003c/span\u003e\u003c/span\u003e. Together with the zero normal stress between the peripheral region of the graphite flake and the nanostructured silicon, it is evident that the graphite edges become out of contact upon loading (Supplementary Section 9 gives the overall pressure distribution between the bottom surface of the graphite flake and the nanostructured silicon substrate, indicating that only the rough peaks near the loading center are in contact with the bottom surface of the graphite flake, and the corresponding actual contact area is only \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(6.23\\times {10}^{-2}{{\\mu }\\text{m}}^{2}\\)\u003c/span\u003e\u003c/span\u003e). Such transition of the contact state, however, is absent for graphite flake pressed against a flat silicon surface (see Supplementary Section 8.2 for details).\u003c/p\u003e\n \u003cp\u003eWe then simulated the edge warpage of graphite flake during sliding on the nanostructured silicon surface through half rough peak period (i.e., 200 nm), and plotted the relationship between the minimum warpage height along the edge \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\Delta }h}_{\\text{m}\\text{i}\\text{n}}\\)\u003c/span\u003e\u003c/span\u003e and sliding distance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\Delta }x\\)\u003c/span\u003e\u003c/span\u003e in Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ed. The minimum warpage height \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\Delta }h}_{\\text{m}\\text{i}\\text{n}}\\)\u003c/span\u003e\u003c/span\u003e goes lower when the load point goes closer to the rough peak, but remains positive throughout, which indicates that the warping of the edge keeps stable during the continuous sliding. From mechanical point of view, the FEM simulation shows that the bending moment generated by the central load on the nanostructured silicon surface overcomes van der Waals adsorption between graphite and nanostructured silicon surfaces and results in the warping of the graphite flake edges during sliding. In addition, the maximum stress at the bottom surface of graphite flake shown in the lower image of Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ec is around \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(0.6 \\text{G}\\text{P}\\text{a}\\)\u003c/span\u003e\u003c/span\u003e, which is lower than the critical withstand pressure to maintain the SSL state at the bottom surface of graphite flake (\u0026gt;\u0026thinsp;1 GPa)\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e, so stress concentration will not lead to the failure of the SSL state within the range of normal force applied in our experiments.\u003c/p\u003e\n \u003cp\u003eConsidering that finite element methods in a relatively large scale may underestimate or overestimate the van der Waals interaction between contact surfaces which acts at sub-nanometer scale, we performed additional molecular dynamics (MD) simulations to extract the maximum adhesion between one rough peak and the graphite. The MD simulation model, which was established according to the morphology of the rough peak in experiments (Figs. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ee and f), is shown in Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003eg where the simulation box has the size of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(60 \\text{n}\\text{m}\\times 60 \\text{n}\\text{m}\\times 7 \\text{n}\\text{m}\\)\u003c/span\u003e\u003c/span\u003e (see Methods section and Supplementary Section 10 for details). The simulated adhesive force versus distance respect to the equilibrium interlayer spacing is shown in Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003eh (blue solid line), where the maximum adhesion is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(46 \\text{n}\\text{N}\\)\u003c/span\u003e\u003c/span\u003e (blue dotted line). The de-adhesion force of single rough peak due to the bending moment caused by the central load around is estimated to be about \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(178 \\text{n}\\text{N}\\)\u003c/span\u003e\u003c/span\u003e (the illustration and red dotted line in Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003eh, see Supplementary Section 8.3 for details), which is larger than maximum adhesion force. Therefore, these MD results validate the de-adhesion process obtained by the FEM on atomic scale.\u003c/p\u003e\n \u003cp\u003eBased on the above analysis, we can conclude that the mechanism of the robust SSL state at the graphite flake/nanostructure silicon interface is that the edge of the graphite flake on the nanostructure silicon surface will warp under the central normal force, thereby eliminate the interaction between the edge of graphite flake and substrate, which is proved to be the main source of friction\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e. On the contrary, due to the tight van der Waal adhesion between the graphite flake and atomic flat silicon surface, the edges of the graphite flakes interact with the silicon surface, which may eventually lead to large friction and induce wear.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv class=\"Section2\" id=\"Sec6\"\u003e\n \u003ch2\u003eExperimental verification of edge warping mechanism\u003c/h2\u003e\n \u003cp\u003eWe verified above proposed mechanism by conducting a series of experiments for graphite flake/nanostructured silicon interface. First of all, we measured the friction coefficient of graphite flake/nanostructured silicon interface for different loading positions, where the eccentricity, i.e., distance between the loading position and the center of the flake is \u003cem\u003e\u0026delta;\u003c/em\u003e, as shown in Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ea, where the optical observation of the different \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\delta =0, 0.4, 0.8, 1.2 {\\mu }\\text{m}\\)\u003c/span\u003e\u003c/span\u003e are shown in Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003eb. The measured friction force of different applied normal force under different \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\delta\\)\u003c/span\u003e\u003c/span\u003e are shown in Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ef, which can be seen that the friction force and fitted friction coefficient increases rapidly with the increase of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\delta\\)\u003c/span\u003e\u003c/span\u003e, especially when \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\delta =1.2 {\\mu }\\text{m}\\)\u003c/span\u003e\u003c/span\u003e, that is, when AFM tip pressed near the edge of graphite flake.\u003c/p\u003e\n \u003cp\u003eWe then simulated the warping of graphite flake on nanostructured silicon under different \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\delta\\)\u003c/span\u003e\u003c/span\u003e through the same FEM method in the last section. The simulated height distribution of the graphite flake bottom surface under a normal loading of 20 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\mu }\\text{N}\\)\u003c/span\u003e\u003c/span\u003e with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\delta =0\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\delta =1.2 {\\mu }\\text{m}\\)\u003c/span\u003e\u003c/span\u003e are shown in Figs. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ec and d, respectively. Under central normal loading (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\delta =0\\)\u003c/span\u003e\u003c/span\u003e) condition, all edges of the graphite flake are de-adhered and warped due to bending moment (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\Delta }{h}_{\\text{m}\\text{i}\\text{n}}\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e). On the contrary, when the edges are loaded (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\delta =1.2 {\\mu }\\text{m}\\)\u003c/span\u003e\u003c/span\u003e), the edges near the loaded side (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(X=2 {\\mu }\\text{m}\\)\u003c/span\u003e\u003c/span\u003e) cannot be warped due to insufficient bending moments and concentrated forces, resulting in downwards deformation (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\Delta }{h}_{\\text{m}\\text{i}\\text{n}}\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e). The minimum warpage height \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\Delta }h}_{\\text{m}\\text{i}\\text{n}}\\)\u003c/span\u003e\u003c/span\u003e under different loading positions (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\delta =0, 0.4, 0.8, \\text{1.2,1.6} {\\mu }\\text{m}\\)\u003c/span\u003e\u003c/span\u003e) is shown in Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ee, where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\Delta }h}_{\\text{m}\\text{i}\\text{n}}\\)\u003c/span\u003e\u003c/span\u003e drops rapidly to negative when \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\delta \\ge 1.2 {\\mu }\\text{m}\\)\u003c/span\u003e\u003c/span\u003e, which explains the failure of the SSL state when \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\delta =1.2 {\\mu }\\text{m}\\)\u003c/span\u003e\u003c/span\u003e in the experiment (high friction force and coefficient in Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ef when \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\delta =1.2 {\\mu }\\text{m}\\)\u003c/span\u003e\u003c/span\u003e). Therefore, above results indicates that the incretion of the interaction between the graphite flake edge and the substrate increases the friction force and friction coefficient (SSL state failure)\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e, which verify the edge warping under concentrated normal force in the center of the graphite flake is the mechanism of robust SSL state at graphite flake/nanostructured silicon interface.\u003c/p\u003e\n \u003cp\u003eAn intuitive deduction according to the mechanism as well as Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e is larger eccentricity will facilitate the failure of SSL. To this end, we conducted a series of tribological tests for \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\delta =1.8 {\\mu }\\text{m}\\)\u003c/span\u003e\u003c/span\u003e. As shown in Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ea, the measured friction fluctuated and suddenly increased during the process of 3072-cycle sliding, which is probably caused by the collision between the edge of the graphite flake and the nanostructure. Meanwhile, wear debris is also observed on nanostructured silicon surface after sliding (Figs. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003eb, c). Further Raman spectroscopy map of the nanostructured silicon surface after sliding (Figs. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ed-h) shows that the wear debris is composed of graphite. This is also supported by the direct Raman spectroscopy characterization for the bottom surface of graphite flake after sliding (Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ei).\u003c/p\u003e\n\u003c/div\u003e"},{"header":"Conclusion","content":"\u003cp\u003eTo conclude, we achieve a robust structural superlubric (SSL) state with a microscale graphite flake/nanostructured silicon interface under ambient condition. The friction is always less than 1 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\mu }\\text{N}\\)\u003c/span\u003e\u003c/span\u003e, the friction coefficient is measured to be the order of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(1{0}^{-4}\\)\u003c/span\u003e\u003c/span\u003e, and there is no observable wear. The mechanism is revealed to be the edge warping of graphite flake on the nanostructured surface under concentrated force, which eliminates the high friction and wear caused by the strong interaction between the edge and the substrate\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e,\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e. This work not only proves that a graphite flake with single crystal surface can realize robust SSL state with nanostructured surface in the atmosphere, which reduce the roughness requirements of SSL technology, but also provides a general surface modification method to achieve robust SSL state between graphene flakes and non-vdW materials, which promotes the general application of SSL technology.\u003c/p\u003e"},{"header":"Method","content":"\u003cp\u003e\u003cstrong\u003ePreparation of graphite mesa with Au cap.\u003c/strong\u003e We fabricated square graphite mesa arrays with Au cap on highly ordered pyrolytic graphite (HOPG, ZYB grade (Brucker) \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e). The fabrication process is shown in Supplementary Fig. 1a, we firstly spun on a double layer photoresist LOR 1A (100 nm)/ZEP (400 nm) on the freshly cleaved surface of the HOPG as shown in Supplementary Fig. 1a (i), and then remove the photoresist in the mesa pattern array region by electron beam lithography and development process as shown in Supplementary Fig. 1a (ii). Secondly, we grew the Au film with thickness of 100nm through electron beam evaporation as shown in Supplementary Fig. 1a (iii). Thirdly, we obtained the Au pattern array through lift-off process as shown in Supplementary Fig. 1a (iv). Lastly, we used Au pattern array as a mask to obtain graphite mesa with Au cap by oxygen reactive ion etching process as shown in Supplementary Fig. 1a (v), where the etching depth is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(0.8 {\\mu }\\text{m}\\)\u003c/span\u003e\u003c/span\u003e. The characterizations of fabricated graphite mesa with Au film are shown in Supplementary Figs.\u0026nbsp;1b-e.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ePreparation of nanostructed silicon surface.\u003c/strong\u003e Firstly, we ultrasonically cleaned the silicon surface with acetone, alcohol and deionized water for 5 minutes, and then performed the surface hydrophilic treatment by oxygen plasma, as shown in Supplementary Fig. 2a (i). Then we mixed 200 nm polystyrene (PS) microsphere solution (mass fraction 10%, produced by Huge Biotechnology Company) with alcohol and deionized water in a ratio of 1:2:2 and ultrasonic for 30 minutes to obtain the diluted solution. Further we immersed the silicon surface with deionized water and used the pipette to drop the diluted solution \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(250 {\\mu }\\text{L}\\)\u003c/span\u003e\u003c/span\u003e, and made it self-assemble on the liquid interface, as shown in Supplementary Fig. 2a (ii). Secondly, we evaporated the deionized water in atmospheric environment, and deposit the self-assembled PS microsphere array on the silicon surface, as shown in Supplementary Fig. 2a (iii). Then, we reduced the size of PS microspheres by oxygen plasma etching (power: 400 W, oxygen flow: 400 sccm, etching time: 4 min), as shown in Supplementary Fig. 2a (iv). Thirdly, we used PS microsphere array as mask to obtain the nanostructures by ion beam etching process (beam: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(1 \\text{m}\\text{A}/\\text{c}{\\text{m}}^{2}\\)\u003c/span\u003e\u003c/span\u003e, energy: 500 eV, etching time: 15s), as shown in Supplementary Fig.\u0026nbsp;2a (v). Lastly, we removed the PS microsphere array by excessive oxygen plasma etching, as shown in Supplementary Fig.\u0026nbsp;2a (vi).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eGraphite flake/silicon interface formation\u003c/strong\u003e. Firstly, we used a tungsten microtip controlled by a micromanipulator (Kleindiek MM3A) to attach the Au cap of graphite mesa fabricated in Supplementary Fig.\u0026nbsp;1, as shown in Supplementary Fig.\u0026nbsp;3a, and applied a shear stress by the micromanipulator to split the graphite mesa a distance of ~\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(2 {\\mu }\\text{m}\\)\u003c/span\u003e\u003c/span\u003e from the vertical direction, as shown in Supplementary Fig. 3b. Secondly, we removed the microtip to observe whether the sheared graphite flake undergoes self-recovery motion (SRM) \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e to determine whether it has a single crystal structural superlubric bottom surface \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e, as shown in Supplementary Fig. 3c. Thirdly, we re-attached the graphite flake which has SRM property with a microtip and split it out completely, then picked up the dangling graphite flake dragged by the microtip as shown in Supplementary Figs. 3d and e. Lastly, we placed the dangling graphite flake slowly by micromanipulator on the fabricated silicon surface, since the adsorption force of the graphite flake and silicon is larger than that of the microtip and graphite flake, the graphite flake would remain on the silicon surface, as shown in Supplementary Fig. 3f, which formed the graphite flake/silicon interface shown in Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ea.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFriction measurement of AFM system.\u003c/strong\u003e The friction measurements of the graphite/n-Si heterostructures were performed under an ambient atmosphere with a temperature of 25\u0026thinsp;\u0026plusmn;\u0026thinsp;1\u0026deg;C and a relative humidity of 30\u0026thinsp;\u0026plusmn;\u0026thinsp;4%. The experimental set-up included a commercial NTEGRA upright AFM (Cypher S-Oxford Instruments), a XYZ piezoelectric displacement platform, a high numerical aperture objective lens (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\times\\)\u003c/span\u003e\u003c/span\u003e20) and visualized AFM tip (ACCESS-NC-GG(Appnano)). Figure \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ea shows the schematic of the experimental set-up. We accurately pressed the AFM tip on the Au cap of the graphite flake through the optical microscope and piezoelectric displacement platform. The AFM tip was calibrated in situ by the Sader method \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e23\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e for the normal direction force and the diamagnetic levitation spring system \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e for the lateral direction force, the specific results of the calibration process are shown in the Supplementary Fig. 6.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSurface characterization method of tribological experiment.\u003c/strong\u003e Here, we show the main process and method of the experiment in Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e, Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e and Supplementary Fig. 9. For details, please refer to Supplementary Section 6. Taking Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e as an example, the first step is to use the atomic force microscope (AFM, Cypher S-Oxford Instruments\u003cstrong\u003e)\u003c/strong\u003e in tapping mode to characterize the morphology of the silicon surface before sliding (Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003eb). For the second step, we used the AFM tip (ACCESS-NC-GG(Appnano)) to apply normal load on the graphite flake, and then moved it to the center of the previous morphological characterization region, as shown in Supplementary Fig. 7c, and then measured the friction force of 3,072 cycles sliding process (Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ea). For the third step, we used the AFM tip to move graphite flake out of the sliding region, as shown in Supplementary Fig. 7e, and then used AFM in tapping mode to characterize the morphology of sliding region \u003cem\u003ein situ\u003c/em\u003e through the positioning function of AFM, to judge whether there is any observable damage (Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ec). For the fourth step, we performed a Raman characterization (WITec Raman spectra, Ulm, Germany equipped with an alpha 300RA microscope using ZEISS 100x/0.9 objective, a 532 nm laser, a 300 gr/mm grating and a charge-coupled device cooled down to -60℃. The laser power was set 6 mW and the Raman image of the sample was measured with a 200 nm step size and an acquisition time of 1-5s. The acquired images were analyzed using a WITec Control/Project 5.3.) on the slid silicon surface (Figs. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ed-h), to determine whether there is any observable graphite wear debris from whether there are D (1350 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{c}{\\text{m}}^{-1}\\)\u003c/span\u003e\u003c/span\u003e), G (1580 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{c}{\\text{m}}^{-1}\\)\u003c/span\u003e\u003c/span\u003e) and 2D (2700 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{c}{\\text{m}}^{-1}\\)\u003c/span\u003e\u003c/span\u003e) graphite peaks. Lastly, we used the method shown in Supplementary Fig. 8 to lift the graphite flake by overcoming the van der Waals adsorption force between graphite flake and silicon surfaces, and flipped 180 degrees to perform the Raman characterization (LabRAM HR Evolution Raman spectrometer from HORIBA, with resolution of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(0.1 \\text{c}{\\text{m}}^{-1}\\)\u003c/span\u003e\u003c/span\u003e, laser wavelength of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(532 \\text{n}\\text{m}\\)\u003c/span\u003e\u003c/span\u003e, grating of 1800 gr/mm, acquisition time of 4s and spot diameter of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(1 {\\mu }\\text{m}\\)\u003c/span\u003e\u003c/span\u003e) on the slid graphite flake surface (Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ei), to determine whether there is any observable damage from whether there is a D peak (1350 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{c}{\\text{m}}^{-1}\\)\u003c/span\u003e\u003c/span\u003e).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eThe setup of finite element simulation of edge warping mechanism.\u003c/strong\u003e The FEM simulation model is consistent with the experiments in scale and consist of Au cap, graphite flake and nanostructured silicon substrates, which is shown in Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ea. The Au cap and graphite flake are both \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(4\\times 4 {\\mu }\\text{m}\\)\u003c/span\u003e\u003c/span\u003e in size and are bonded together. The thickness of Au cap is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(100 \\text{n}\\text{m}\\)\u003c/span\u003e\u003c/span\u003e, and graphite flake\u0026rsquo;s thickness is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(200 \\text{n}\\text{m}\\)\u003c/span\u003e\u003c/span\u003e. The nanostructured silicon substrate is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(4.8 {\\mu }\\text{m}\\times 4.8 {\\mu }\\text{m}\\)\u003c/span\u003e\u003c/span\u003e in size and has a thickness of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(50 \\text{n}\\text{m}\\)\u003c/span\u003e\u003c/span\u003e without rough peaks. The rough peaks on the nanostructured silicon surface are \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(7 \\text{n}\\text{m}\\)\u003c/span\u003e\u003c/span\u003e in height and the shape function for its cross section is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(y=A\\text{s}\\text{i}\\text{n}{\\left(\\frac{\\pi x}{L}\\right)}^{n}\\)\u003c/span\u003e\u003c/span\u003e, in which \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(A=7 \\text{n}\\text{m}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(L=350 \\text{n}\\text{m}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n=10\\)\u003c/span\u003e\u003c/span\u003e. Distance between rough peaks is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(400 \\text{n}\\text{m}\\)\u003c/span\u003e\u003c/span\u003e, so there\u0026rsquo;s \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(12\\times 12\\)\u003c/span\u003e\u003c/span\u003e rough peaks in total and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(10\\times 10\\)\u003c/span\u003e\u003c/span\u003e of them are below the graphite mesa consisting of graphite flake and Au cap. The Young\u0026rsquo;s Modulus and Poisson\u0026rsquo;s ratio of Au and Si are \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(79.5 \\text{G}\\text{P}\\text{a}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(0.42\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(190 \\text{G}\\text{p}\\text{a}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(0.278\\)\u003c/span\u003e\u003c/span\u003e, respectively\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e. The graphite flake is set to be orthotropic with stress-strain relation\u003csup\u003e27\u0026ndash;30\u003c/sup\u003e\u003c/p\u003e\n\u003cdiv class=\"Equation\" id=\"Equa\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e$$\\begin{array}{c}\\left(\\begin{array}{c}{\\sigma }_{x}\\\\ {\\sigma }_{y}\\\\ {\\sigma }_{z}\\\\ {\\tau }_{\\text{xy}}\\\\ {\\tau }_{\\text{yz}}\\\\ {\\tau }_{\\text{xz}}\\end{array}\\right)=\\left[\\begin{array}{cccccc}1060\u0026amp; 180\u0026amp; 15\u0026amp; 0\u0026amp; 0\u0026amp; 0\\\\ 180\u0026amp; 1060\u0026amp; 15\u0026amp; 0\u0026amp; 0\u0026amp; 0\\\\ 15\u0026amp; 15\u0026amp; 36.5\u0026amp; 0\u0026amp; 0\u0026amp; 0\\\\ 0\u0026amp; 0\u0026amp; 0\u0026amp; 440\u0026amp; 0\u0026amp; 0\\\\ 0\u0026amp; 0\u0026amp; 0\u0026amp; 0\u0026amp; 4\u0026amp; 0\\\\ 0\u0026amp; 0\u0026amp; 0\u0026amp; 0\u0026amp; 0\u0026amp; 4\\end{array}\\right]\\left(\\begin{array}{c}{\\epsilon }_{x}\\\\ {\\epsilon }_{y}\\\\ {\\epsilon }_{z}\\\\ {\\gamma }_{\\text{xy}}\\\\ {\\gamma }_{\\text{yz}}\\\\ {\\gamma }_{\\text{xz}}\\end{array}\\right),\\#\\left(1\\right)\\end{array}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n\u003cp\u003eWhere the elastic modulus is given in units of Gpa. The van der Waals interaction between the graphite flake and silicon surface is derived from Lennard-Jones (LJ) potential. Bottom surface of the substrate is fixed in all directions and the contact point with AFM tip, a circular area in the center of the graphite mesa\u0026rsquo;s top surface with diameter of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(50 \\text{n}\\text{m}\\)\u003c/span\u003e\u003c/span\u003e, is fixed and can only move in the vertical direction to prevent the graphite mesa from rotating and sliding. During the simulation steps, negligible load is firstly applied to make graphite mesa and the substrate contact, then a normal load of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(20 {\\mu }\\text{N}\\)\u003c/span\u003e\u003c/span\u003e is applied on the graphite flake\u0026rsquo;s central area gradually.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eThe setup of molecular dynamics simulation of single rough peak adhesive force.\u003c/strong\u003e The MD simulation model consists of the silicon substrate and AB-stacking bilayer graphene. The morphology of the substrate is based on the experimental characterization (Figs. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ee and f are characterized by AFM, Cypher S-Oxford Instruments). Since the equilibrium distance of the vdW interaction between silicon and graphite is sub-nanometer and it decays with distance to the 6 powers, we used a miniature simulation model to ensure the simulation efficiency. The 2-nm-thick substrate used in our simulation is the tip of the realistic rough peak (usually with height 7 nm), and only bilayer graphene is used. The simulation box has the size of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(60 \\text{n}\\text{m}\\times 60 \\text{n}\\text{m}\\times 7 \\text{n}\\text{m}\\)\u003c/span\u003e\u003c/span\u003e. There are \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(4\\times {10}^{5}\\)\u003c/span\u003e\u003c/span\u003e atoms for the simulation system. Periodic boundary conditions are applied to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(x\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(y\\)\u003c/span\u003e\u003c/span\u003e directions. The quasi-static MD simulations are performed using LAMMPS\u003csup\u003e31\u003c/sup\u003e. The interlayer interaction between graphene/graphene and graphene/silicon is described by Lennard-Jones potential\u003csup\u003e32\u003c/sup\u003e. The intralayer interaction of graphene and substrate is described by REBO force field\u003csup\u003e33\u003c/sup\u003e and the modified Tersoff force field\u003csup\u003e34\u003c/sup\u003e respectively. The bottom atomic layer of the substrate is fixed as a rigid body. Springs with spring constant \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({k}_{\\text{z}}=2.7 \\text{N}/\\text{m}\\)\u003c/span\u003e\u003c/span\u003e are tethered to each carbon atom of the upper graphene layer to mimic the elastic behavior of bulk graphite\u003csup\u003e35\u003c/sup\u003e. To extract the maximum adhesion between the graphene and silicon substrate, we used the quasi-static simulation protocol\u003csup\u003e36\u003c/sup\u003e. At each step the rigid bottom atomic layer is displaced by -0.02 \u0026Aring; along \u003cem\u003ez\u003c/em\u003e direction, followed by minimizing the total energy of the whole system with FIRE algorithm\u003csup\u003e37\u003c/sup\u003e until the forces acting on each atom reduces below the tolerance 10\u003csup\u003e-4\u003c/sup\u003e eV/\u0026Aring;.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAcknowledgements\u003c/h2\u003e \u003cp\u003eQ.Z. wishes to acknowledge the financial support by National Natural Science Foundation of China No. 11572173, No. 11890671, No. 51961145304, No. 11921002. M.M. acknowledges the financial support from the NSFC (Grant no. 11890673 and 11772168) and the Shenzhen fundamental research key project JCYJ20200109150608043. X.J. acknowledges the financial support by National Natural Science Foundation of China No. 12002216 and the GuangDong Basic and Applied Basic Research Foundation 2020A1515110995.\u003c/p\u003e"},{"header":"References","content":"\u003cp\u003e1\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;Holmberg, K., Andersson, P. \u0026amp; Erdemir, A. Global energy consumption due to friction in passenger cars. \u003cem\u003eTribology International\u003c/em\u003e \u003cstrong\u003e47\u003c/strong\u003e, 221-234, doi:10.1016/j.triboint.2011.11.022 (2012).\u003c/p\u003e\n\u003cp\u003e2\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;Long-Sheng, F., Yu-Chong, T. \u0026amp; Muller, R. S. IC-processed electrostatic micro-motors. \u003cem\u003eInternational Electron Devices Meeting. Technical Digest (IEEE Cat. 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Structural relaxation made simple. \u003cem\u003ePhysical Review Letters\u003c/em\u003e \u003cstrong\u003e97\u003c/strong\u003e, 4, doi:10.1103/PhysRevLett.97.170201 (2006).\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-2273111/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2273111/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cstrong\u003eStructural superlubricity (SSL), a state of nearly zero friction and no wear between two contacted solid surfaces, brought a dawn for the revolutionary solution of friction and wear problems. Recently, SSL was realized between microscale graphite flake with two dimensional single-crystalline surface and various non-van der Waals materials, which greatly broadens its application range. However, the SSL state has a certain probability of failure due to the edge defects of graphite flake. Here, we achieve robust SSL state between microscale graphite flakes and nanostructured silicon surfaces under ambient condition. We find that the friction is always less than 1 μN, the differential friction coefficient is on the order of 10\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003e-4\u003c/strong\u003e\u003c/sup\u003e\u003cstrong\u003e, without observable wear. Detailed characterization and simulation show that this is attributed to the edge warping of graphite flake on the nanostructured surface under concentrated force, which eliminate the edge interaction between the graphite flake and the substrate. This study proves that a graphite flake with single crystal surface without edge contact with the substrate can universally realize robust SSL state with any non-van der Waals materials in the atmosphere, which reduce the roughness requirements of SSL technology and provides a new method for SSL technology to generally apply in the atmospheric environment.\u003c/strong\u003e\u003c/p\u003e","manuscriptTitle":"Robust microscale structural superlubricity between graphite and nanostructured surface","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2022-11-29 23:05:02","doi":"10.21203/rs.3.rs-2273111/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nature-communications","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"NCOMMS","sideBox":"Learn more about [Nature Communications](http://www.nature.com/ncomms/)","snPcode":"","submissionUrl":"https://mts-ncomms.nature.com/","title":"Nature Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Communications","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"0202a836-c203-46fb-8f93-b423cd73333c","owner":[],"postedDate":"November 29th, 2022","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":17203051,"name":"Physical sciences/Materials science/Structural materials/Mechanical properties"},{"id":17203052,"name":"Physical sciences/Nanoscience and technology/Graphene/Mechanical and structural properties and devices"},{"id":17203053,"name":"Physical sciences/Materials science/Nanoscale materials/Two-dimensional materials"},{"id":17203054,"name":"Physical sciences/Materials science/Nanoscale materials/Structural properties"},{"id":17203055,"name":"Physical sciences/Nanoscience and technology/Nanoscale materials/Structural properties"}],"tags":[],"updatedAt":"2023-05-23T07:13:13+00:00","versionOfRecord":{"articleIdentity":"rs-2273111","link":"https://doi.org/10.1038/s41467-023-38680-6","journal":{"identity":"nature-communications","isVorOnly":false,"title":"Nature Communications"},"publishedOn":"2023-05-22 04:00:00","publishedOnDateReadable":"May 22nd, 2023"},"versionCreatedAt":"2022-11-29 23:05:02","video":"","vorDoi":"10.1038/s41467-023-38680-6","vorDoiUrl":"https://doi.org/10.1038/s41467-023-38680-6","workflowStages":[]},"version":"v1","identity":"rs-2273111","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-2273111","identity":"rs-2273111","version":["v1"]},"buildId":"rHA-KDH7Qsr4HCuvH75dn","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}