Friction and Degradation of Graphite: A Nanotribological Approach

We investigated the friction and wear of graphite by atomic force microscopy in sliding contact with SiOx, Pt, and diamond tips with contact forces up to several micronewtons. Graphite’s tribology strongly depends on the chemistry of the counter body. With a SiOx tip, friction is governed by puckering. Wear initiates at surface steps by mechanical destabilization of folds. With a Pt tip, the adhesive effects lead to the exfoliation of graphite. At higher loads, friction crosses over from exfoliation to puckering. For SiOx and Pt, the wear rate is low in ambient conditions. In the case of diamond tips, we measured a friction coefficient and a wear rate of an order of magnitude larger than with SiOx or Pt tips.


Introduction
For decades, graphite has been investigated regarding its lubricating mechanisms.Graphite has been used as a solidbased lubricant by coating moving parts operating under high/low pressure, a wide range of temperatures, and different gaseous atmospheres.Graphite is an important material for space applications to lubricate and protect parts from failure.Since graphite has sp 2 -hybridization in carbon layers stacked in an AB sequence and bonded by van der Waals interactions, graphite exhibits a low shear strength that has promoted its application as a solid lubricant [1].Several parameters have been found to alter the lubrication and structural/mechanical integrity of graphite: the sliding speed, the adsorbed surface films, water vapor, oxygen, chemical interactions with the counter material, and temperature.The friction coefficient of graphite is affected by the surrounding environment, such as water vapor, oxygen, and other gases, which easily adsorb onto graphite to form a thin surface film, and by the sliding speed [2].For example, the friction coefficient of graphite in a vacuum can be significantly reduced by introducing low pressures of water vapor, oxygen, and other gases or by increasing temperature.An alternative understanding is that molecules from the surrounding intercalate between the basal planes of graphite, making the interplanar distance larger and their van der Waals interactions weaker [3,4].Intercalation results in a smaller shear strength and makes the exfoliation of graphite easier in the presence of partial pressures of water vapor, oxygen, and other gases than in a vacuum [5,6].
The coefficient of friction of graphite is also affected by the counter materials, depending on their chemical interactions that may result in bonding and adhesion [7,8].When bonding and adhesion occur at the interface between graphite and a counter material, a larger coefficient of friction can be observed.Strong adhesion and friction can occur if the adsorbed films on graphite are removed from the surface by sliding counter materials.Under such conditions, the surface of graphite can break, leading to debris formation [5,6].
The pioneering works referred to above were limited to macroscopic investigations.Furthermore, the testing conditions were thus that severe wear of graphite was achieved and thus prevented detailed insights in the initial stages of its surface degradation.It is accepted that contacts initiate at nm-sized asperities and that the mechanisms governing friction and wear also take place at this length scale.With the development of atomic force microscopy, the investigation of nm-scale sliding contact has become readily possible in various environments, such as under ultrahigh vacuum conditions, in ambient, or in a liquid environment (water, corrosive solutions, or oil-based lubricants) [9][10][11][12][13].First nanotribological studies by AFM have investigated ideal surfaces in ultra-high vacuum (UHV) conditions, such as KF, KBr, mica, HOPG, and single-crystalline metallic or semiconducting surfaces [14][15][16][17][18][19].These early investigations yielded unpreceded insights into the structure's role in the friction of stiff surfaces.In the case of HOPG, atomic stick-slip was first reported by Mate et al. [10].Atomic stick-slip was later explained based on the Prandtl-Tomlinson model.In this case, a point mass asperity dragged on a corrugated surface potential operates thermally activated jumps from one local minimum to the next [20].Depending on the commensurability of sliding contacts with HOPG, a transition from atomic stick-slip to superlubricity has been observed [21,22].In Refs.[21,22], the authors investigated the atomicscale friction between graphite flakes transferred to a single nanoscopic asperity and the surface of HOPG for different mismatch angles.The authors experimentally verified that, for incommensurate contacts between two surfaces, atomic stick-slip vanishes, and friction becomes vanishingly small.Furthermore, the friction behavior of graphite at surface defects, such as step edges, has been investigated (see Refs. [23][24][25]).Friction on HOPG has been observed to increase at surface steps and depend on the step height and the sliding direction toward a step edge, e.g., upwards or downwards.Friction at the surface step edge of HOPG was observed to scale with the step height and to depend linearly on the normal force for the upward motion of the tip.In contrast, during the downward motion of the tip, the increased friction at a step edge was observed to be independent of the normal force and showed a weaker dependence on the step height.Moreover, the authors in Ref. [26] showed that friction at atomic step edges of graphite's surfaces significantly increases in the presence of a small amount of water molecules, while friction on the terraces is not strongly affected.Comparing the effect of adsorbed molecules of water and n-pentanol at the interface between a single silica asperity sliding on cleaved HOPG, adsorbed water has also been observed to increase friction [27].In Ref. [27], the authors explained this effect by the increase in commensurate interactions between surface and counter-sliding body.While friction on HOPG terraces increased with the relative humidity, friction at step edges decreased with the relative humidity, which was explained based on the structural transition of the adsorbed water layer from crystalline-like to amorphous.In contrast, friction on HOPG decreased with increased partial pressure of n-pentanol on terraces and at step edges.Recently, AFM measurements at the corners of single-layer graphene steps were performed for different edge angles and revealed that friction at the step edges largely depends on the edge structure [28].
These results have provided valuable insights into the dissipative mechanisms involved in the sliding contact with graphite.There is, however, still a gap to bridge between the early macroscopic investigations of graphite's tribology and Page 3 of 14 106 the more recent nanoscale experiments.Macroscopic investigations of graphite's tribology invariably involved its surface degradation, while nanoscale experiments have focused on its wear-less friction mechanism.In this work, we bridge this gap by investigating the friction and wear of graphite in ambient and underwater by atomic force microscopy in sliding single asperity contact with SiO x , Pt, and diamond tips over a wider range of contact forces up to several micronewtons.This approach allows us to distinguish between the effects of counter-sliding body interactions with graphite and the effect of the environment on the mechanisms of frictional dissipation and degradation of graphite.

Materials and Experimental Methods
We performed tribological tests on highly oriented pyrolytic graphite (HOPG) by atomic force microscopy (AFM) in ambient conditions and underwater.The relative humidity of the laboratory is controlled and kept below 20% by active dehumidifiers.Samples were prepared by exfoliation and transferred from a HOPG crystal (purchased by μMash, Estonia) onto adhesive tape.Figure 1 shows topography and lateral force images of a HOPG surface recorded in contact mode (c-)AFM with a soft single-crystalline silicon cantilever (type: contr, manufactured by NanoSensors, Switzerland).The topography image shows smooth terraces with a width of several hundreds of nanometers and a length of several micrometers.The corresponding lateral force map and its typical friction loop indicate that friction is higher at surface steps.
In this work, tribological testing was performed with a CoreAFM, manufactured by NanoSurf, Switzerland, and AFM cantilevers with tips of different chemistries: SiO x (type: NCHR), Pt-coated silicon (type: NCH-Pt), and polycrystalline diamond-coated silicon (type: CDT-NCLR); NanoSensors, Switzerland, manufactured all tips.Before measurements, we determined the cantilevers' bending stiffness C n by the Sader method [29].The calculated values were used to calculate the torsion stiffness C l of each cantilever [30].Subsequently, the sensitivity of the position-sensitive photodiode S was calibrated by recording a force-distance curve on a noncompliant nanocrystalline diamond thin film and determining the slope of the repulsive force signal V n as a function of the distance Z, where Tribological testing consisted of reciprocal sliding of nanometer-scale single asperity of three different chemistries under increasing load up to F n = 4500 nN or 15-fold scan repetitions at the same load.The scanning area and velocity were set to A s = 1.5 × 1.5 μm 2 and v s = 12 μm/s.During perpendicular scanning to the cantilevers' length axis, the following signals were recorded in both forward and backward directions: topography, normal force, and lateral force.The normal and lateral force signals V n and V l were converted into units of force by F n = C n SV n and F l = 3  2 C l S h l V l , where h is the tip height and l is the cantilever length [30].The friction force was calculated according to

2
, where F l,fwd and F l,bwd are the lateral forces in the forward and backward directions.We calculated each friction map's mean friction force and corresponding standard deviation.After tribological tests, we imaged the topography of the tested area with the same tip in tapping mode to characterize the amount of wear.

Friction and Wear of HOPG in Ambient Conditions
Figure 2 shows the normal force dependence of the friction force recorded on HOPG in ambient conditions with a SiO x tip, a Pt tip, and a diamond tip.

The Case of a SiO x Tip
For a SiO x tip in ambient conditions, the F f (F n ) plot is best fitted by a linear function of the type F f = F n + F ad (indicated as a red curve in Fig. 2 and the remainder of this work), whose slope corresponds to the coefficient of friction μ = 0.016.In this case, we find F ad = 0 nN.In the normal force values F n = 4 -460 nN, friction between HOPG and a SiO x tip increases from 0.6 to 3 nN.This increasing trend is punctuated by disparate events of sudden increases in friction, with a maximum friction force of F f = 7 nN for F n = 26 nN.
To better understand the origin of these sudden increases in the friction force at given normal force values, we present the topography and lateral force images corresponding to these events in Fig. 3.In Figs.2a and 3a, b, the colored symbols indicate the normal force values in the F f (F n ) plot.The first pair set of images in Fig. 3a, b correspond to F n = 4 nN (navy blue color).At this normal force value, the average friction force is F f = 0.6 ± 0.07 nN, constant over the terraces.At step edges, though, one can observe how friction increases.In Fig. 3a, b, the first topography and lateral force images exhibit two external steps corresponding to the brighter contrast in the lateral force image.These steps are mono-and bi-atomic with heights of 330-340 pm and 660-680 pm, respectively.Their friction corresponds to increases up to 5 nN and 8 nN, respectively.Increased friction at surface steps has been reported in Refs.[23][24][25].In Ref. [23], the authors investigated the effects of step height and sliding direction toward steps on the load dependence of friction.An increase in friction was observed during both the downward and upward motion of a Si 3 N 4 AFM-tip across atomic-scale steps of a HOPG surface.Regardless of the steps' height, the authors observed a linear increase of the friction force with the normal force for upward sliding.The corresponding F f (F n ) plots' slope increased in the order of mono-atomic, bi-atomic, and five-fold atomic steps.
In Ref. [23], friction increased at the same steps, but during the downward motion of the tip, it did not depend on the normal force; it remained constant over the whole domain of applied normal force values: F n = − 4 nN-17 nN.However, it showed a weak dependence on the step height.In the adhesive regime (F n = − 4 nN), the increase in friction was similar for both upward and downward motions.
The authors in Ref. [23] discussed these experimental observations based on a modified Prandtl-Tomlinson model considering an energy barrier at the surface steps, in analogy to surface diffusion and the motion of steps on crystal surfaces (see Refs. [31,32]).Figure 2a shows the first sudden increase in the friction force to F f = 1.9 nN at a normal force value F n = 11 nN (green color).The corresponding topography and friction images in Fig. 3a, b indicate constant friction over the graphitic terraces and the first signs of degradation along external surface steps.This local degradation occurs upward toward the external steps, where the tip is expected to exfoliate and destroy the upper terraces.With increasing the normal force value, such events are repeated at other locations along external steps, leading to dents along external steps (yellow color) and the complete exfoliation of basal planes (brown, purple, and okra color).For normal force values F n > 460 nN, friction between a SiO x tip and HOPG is accompanied by abrasion or dusting of the upper terrace in sliding contact with the tip.These degradation events are manifest in the friction signals as sudden bursts.Figure S1 illustrates this behavior by comparing a friction loop recorded without surface degradation with one recorded during degradation (see supplementary file).The friction loop corresponding to the line without degradation is narrow and smooth.In contrast, the one corresponding to surface degradation is significantly wider, i.e., it exhibits a larger friction force and is rougher, corresponding to a jerky lateral motion of the tip.
At this point, we shall ask: What is the rationale behind the linear dependence of friction on the normal force observed while sliding a single SiO x asperity on HOPG?At the macroscale, a linear dependence of the friction force on the applied normal force is commonly observed and rationalized based on the load independence of the contact pressure [33].This scenario does not apply to our experiments since the contact area between a spherical elastic body with a flat elastic counter body is known to grow with F 2∕3 n , according to the Hertzian theory of elastic contact [34].Another situation where a linear dependence of the friction force on the normal force is observed is when a single asperity plows through a surface [35].In Refs.[36,37], we have shown that for single diamond asperity sliding on surfaces of fcc metals and alloys, the coefficient of plowing scales inversely with the hardness of the material.Furthermore, plowing can be identified as the governing mechanism during sliding contact by imaging the area subjected to tribological measurements.Plowing is usually associated with pileups, which correspond to the material displaced ahead of the single sliding asperity.The authors want to mention the puckering mechanism as a third mechanism that yields a linear relationship between friction and normal forces.Puckering proceeds by forming a fold or wrinkle at the surface of a sample and its displacement ahead of a single sliding asperity.Puckering has been observed on layered and two-dimensional materials that exhibit a low out-of-plane stiffness, such as the basal plane of HOPG or graphene [38,39].The formation of a fold is mainly governed by elasticity and could thus be expected to be reversible.However, this would only be true when there were no interactions between graphitic basal planes.Puckering proceeds by local delamination of upper basal planes from lower ones, and the puckering force should scale with the delaminated area via the surface energy of graphite γ = 140 mJ/m 2 [40].It is reasonable to assume that the delamination area grows with the normal force.We suggest the following expression for the friction force: F f = 2 , where λ is the width of the fold.Using our experimental values, we obtain that λ increases from 0 to 150 nm over the whole range of investigated normal force values.Although simplistic, our approach provides a reasonable estimate for the length scale of the fold regarding its order of magnitude.A drawback of this approach is that we cannot estimate the height of the fold since we do not know the number of basal planes involved in the delamination.A plausible scenario is that a fold becomes mechanically unstable upon growing to a threshold height and fails by brittle fracture.
According to Ref. [41] and based on experimental results for atomically thin sheets of 2D materials exfoliated on a weak adherent silicon oxide substrate, the puckering mechanism becomes less prominent as the out-of-plane stiffness of the delaminated layer increases, i.e., as the thickness of the delaminated layer increases.In this experimental setup, due to the substrate's weak adherent properties, delamination occurred at the substrate/sheet interface, not within the sheet.Our experiments were conducted on bulk HOPG, and puckering could only involve the top basal planes of the HOPG sample.While we cannot determine the number of basal planes involved in the delamination, we suggest that the number of basal planes involved in the delamination is self-limited by the out-of-plane stiffness of the stack of basal planes.

The Case of a Pt Tip
In the case of a Pt tip sliding on HOPG in air, the F f (F n ) plot in Fig. 2b cannot satisfactorily be fitted by a linear curve over the entire domain of normal force values.Instead, in the normal force F n < 50 nN domain, we find that the equation F f = A F n best fits the load dependence of friction (indi- cated as a purple curve in Fig. 2 and the remainder of this work).This equation corresponds to the shearing of adhesive junctions between the tip and sample surface.The shear strength of such junctions is there, A(F n ) = πa 2 is the normal force-dependent contact area between tip and sample, and a is the contact radius.According to the JKR model of adhesive contact between elastic solids [42], the contact radius c a n b e e x p r e s s e d a s where R t is the tip radius, F ad is the adhesion force, and E * is the reduced modulus of elasticity that is given by , where E s,t and ν s,t are the Young's modulus and the Poisson's ratio of the sample and tip, respectively.According to the manufacturer's data, the tip radius of Ptcoated tips is 25 nm, and the elastic properties of Pt are E Pt = 168 GPa and ν Pt = 0.38.For HOPG, Xiao et al. reported an indentation modulus of elasticity M HOPG = 15-20 GPa when measured in compression [43].With these values, we calculate E * = 16.5 GPa, and from the best fit shown in Fig. 2b, we obtain τ = 377.9MPa and F ad = 1.9 nN.
For normal force values F n > 50 nN, the load dependence of friction between HOPG and a Pt tip is best fitted by a linear function whose slope is μ = 0.0078.In contrast to the SiO x tip, for a Pt tip, Fig. 3c, d indicates that partial exfoliation of graphite at external steps occurs at the lowest normal force value applied in this work.We explain this observation based on the adhesion of Pt on HOPG, whose strength appears to be strong enough to exfoliate external steps during sliding.While Pt and carbon do not form thermodynamically stable compounds, several experimental investigations have characterized the chemical interactions between these two elements [44,45].For example, strong covalent bonds with very small charge transfer were found between fullerene clusters deposited on Pt(111) surface [44], and the existence of a surface PtC x , with x close to one, was reported for dc reactive sputtering deposited polycrystalline Pt films that contained up to 17 at.%C [45].These experimental findings have motivated theoretical simulations to calculate platinum and carbon atoms' bond length and energy.Reference [46] reported the bond length l b ~ 0.2 nm and energy E Pt-C = 5.3 eV.Assuming an atomic density of Pt atoms per unit area for a Pt(111) surface of 15 at./nm 2 , we obtain the interfacial energy between a Pt tip and HOPG to be γ Pt-C = 39.75 eV/nm 2 or γ Pt-C = 6.365J/m 2 .On the other hand, the work of adhesion derived from the adhesion force is Since the separation of a Pt tip from a HOPG surface generates a free Pt surface and a free HOPG surface, the interfacial energy between Pt and graphite can be estimated as W ad = γ Pt-C -γ Pt -γ HOPG .The surface energy of Pt has been experimentally determined to be close to γ = 2.5 J/m 2 , while for HOPG, the surface energy value has been reported to vary in the range γ = 140-150 mJ/m 2 .With these values and our estimate of γ Pt-C , we could expect W ad ≈ 3.7 J/m 2 .Of course, this value is overestimated since Pt and C atoms could only undergo bonding at graphitic surface step edges, where the carbon atoms have dangling bonds.However, these calculations highlight that at surface step edges of HOPG, the interactions with a Pt tip are stronger than reflected by our experimental adhesion force value.We suggest that interatomic bonds can form at the lowest contact force between a Pt tip and a HOPG surface at the step edges and are stronger than the required strength to exfoliate graphite locally.The interlayer strength of the materials primarily governs the mechanics of exfoliation.
Considering van der Waals interactions, the interlayer force can be expressed as F = − A 6 D 3 , where A is the Hamaker constant and D is the equilibrium interplanar distance [46].For graphite, this force is F = 3 × 10 9 N/m 2 , with A = 2.8 × 10 -19 J and D = 0.165 nm [40].This force is an upper bond corresponding to the case where both layers remain parallel, and exfoliation proceeds perpendicular to them.However, the force necessary for exfoliation can be significantly decreased if an upper layer is peeled over a distance d from a lower one.The peeling force has been expressed per unit area as F peel = F D 2d [47].With D < < d, the peeling force is significantly smaller than the cohesion force.The exfoliation energy of graphene has been reported to be 1.8 eV/nm 2 or 288 mJ/m 2 [48], i.e., twice the surface energy of graphite.Figure S2 shows that at the lowest applied normal force, graphite flakes with lateral dimensions of several tens tohundreds of nanometers are detached from step edges at the surface of HOPG upon sliding a Pt tip (see supplementary file).Inserting this d = 10 nm, we calculate F peel = 27 × 10 6 N/m 2 .The value we obtain for the shear strength lies between the cohesion force F per unit area and the peeling force F peel per unit area.
According to Bowden and Tabor, the shear strength measures the shear stress to be applied to shear an adhesive junction.With a Pt tip sliding on HOPG, we find the shear stress τ = 377.9MPa.This value is significantly lower than during single nanoscale asperity sliding contacts with metals.In Ref. [49], we found that the shear strength was significantly larger for the case of Si sliding on copper.Results in the same order of magnitude as in Ref. [49] were also reported for single diamond asperity sliding contact of metals (see Refs. [36,37]).In these works, the shear strength was close to the theoretical strength of the metal under investigation.From our experimental results with a Pt tip sliding on HOPG, we find that, considering the shear modulus of HOPG to be G = 5 GPa (see Ref. [50]), ≈ G 13 , thus also very close to the ideal strength of a crystal.
For normal force values F n > 50 nN, the load dependence of friction is best fitted by a linear function, as in the case of a SiO x tip.When a Pt tip slides on HOPG, the friction coefficient is twice as low as with a SiO x tip.This result also suggests that in this regime of normal force, friction is governed by puckering, i.e., the formation of a fold accompanied by local delamination.

The Case of a Diamond Tip
Furthermore, we find that, for a diamond tip sliding on HOPG in air, friction linearly increases with the normal force over the whole domain of F n values applied in this work (see Fig. 2c).Thereby, our experimental data were best fitted by a function of the type F f = F n + F ad .In this case, the coefficient of friction is μ = 0.125, and the adhesion force between HOPG and diamond is F ad = 197.92nN.This μ value is ten times higher than with a SiO x tip and twenty times higher than with a Pt tip, while the adhesion between HOPG and diamond is a hundred times stronger than with Pt.Furthermore, Fig. 3e, f shows that, in the case of diamond sliding on HOPG, wear sets in at the lowest applied normal force.In these images, it is difficult to distinguish the HOPG surface structure since material transfer most likely affected the sliding contact, as indicated by the SEM image of the diamond tip recorded after tribological measurements (see Fig. 4).The SEM micrograph of the diamond tip in Fig. 4 shows a substantial amount of transferred material.Unlike the SiO x tip imaged after tribological test on HOPG and showing transferred graphitic flakes, the material transferred onto the diamond tip seems rather amorphous.It may indicate an alteration of graphite during reciprocal sliding against diamond.
Amorphization of graphite has been reported in gray cast iron under tribological solicitation [51].There, the tribological test simulated the breaking conditions, and its induced disorder of graphite was compared with the effect of graphite's milling.Strain-induced graphite amorphization was also reported in the case of geological faults [52].Recently, shear-induced amorphization was simulated at the tribological interfaces between diamond or silicon crystals [53][54][55][56].In Ref. [53], the authors showed that an amorphous carbon adlayer forms at the interface between two diamond crystals under tribological conditions.The formation of this adlayer involves a sp3-sp2 order-disorder transition, and its growth rate was observed to be affected by the crystallographic orientation of the surface and the sliding direction.Analog to these results, we suggest that the interface between graphite and diamond undergoes a shear-induced amorphization.In this case, the friction force is likely dependent on the thickness of the amorphized layer and its viscous flow.In Ref. [54], the thickness of the interfacial layer between two diamond crystals has been discussed to depend on the contact pressure and the sliding distance.

Wear of HOPG During Sliding Contact with Different Counter Body Materials in Ambient Conditions
Figure 5 shows topography images recorded on graphite after 15-fold scanning repetition at constant normal force values with SiO x , Pt, and diamond tips in ambient.From these images, we determined the normal force dependence of the wear depth for the individual tips in ambient (see Fig. 6).In all cases, the wear depth d w increased almost linearly with the normal force.For each tip used in ambient, we determined the wear rate of HOPG according to Archard's law, in which case the wear volume is expressed as V w = kF n l s , and l s is the sliding distance, and k is the wear rate [57].
From the results presented in Fig. 5, we determined the slope of each d w (F n ) plot to calculate the wear rate k according to k = A s l s dd w dF n , with A s = 1.5 × 1.5 μm 2 and l s = 15 × 512 × 1.5 = 11,520 μm (see Table 1).
We find that the wear rate of graphite increases in the order with a Pt tip, a SiO x tip, and a diamond tip.With a diamond tip in ambient, the wear rate of HOPG is significantly larger than with SiO x and Pt tips.Recently, the lubrication of iron with graphite layers of different thicknesses has been investigated under a contact pressure of up to 1 GPa [58].There, the authors reported that the friction coefficient increased from 0.12 by a factor of 3.6 while increasing the thickness of the graphite layer from 0.2 to 17 μm.They attributed this effect to more pronounced plowing contributions as the layer thickness increased.
Furthermore, the authors observed that the substrate's roughness enhanced graphite's lubricating and wear-preventive performances.As the roughness of the substrate increased, a stable carbon film of several tens of nanometers formed at the tribological interface.Our wear rate values of HOPG for sliding contact in ambient with SiO x or Pt tips, shown in Table 1, are comparable with the values reported in Ref. [59] for a 0.2-mm-thick graphite layer.Regarding HOPG wear with a diamond tip, we determined a wear coefficient at least an order of magnitude larger than with SiO x or Pt tips.As discussed above, this high wear rate is accompanied by significantly larger friction force values and material transfer to the tip, which we attribute to the shearinduced amorphization of the interface between diamond and graphite.In this scope, the amorphous interfacial is expected to thicken with increasing normal force and to lead the tip to sink in and to displace the amorphous layer ahead, thus forming pileups, as observed in Fig. 5g, h, and i.This explanation is an analogy to the simulation results of the shear-induced amorphization at the interfaces between two diamond or two silicon crystals.There, the authors observed a growth of the amorphous interfacial layer as a function of the applied pressure.A major difference between the theoretical model and our experiments lies in the geometry of our system: in Refs.[53,54,56], the contacting crystals had the same cross-sectional area and the sinking in was thus not part of the picture (Table 2).

Friction and Wear of HOPG Underwater
Our experimental results in water indicate slight changes in the friction behavior of HOPG (see Figs. 7, 8).Notably, we find that, for a SiO x tip, the F f (F n ) plot best fits the shearing model of adhesive junctions, as indicated by a purple curve in Fig. 7a.We obtained τ = 27.42MPa, F ad = 8.87 nN.For F n > 250 nN, we observe that several experimental data points deviate from the fitting curve.This may indicate a superposition of mechanisms (see Fig. 7a): shearing of adhesive junctions and puckering.It is, however, difficult to separate these two contributions based on our experimental data since no clear transition normal force value can be identified.For this reason, we prefer limiting our data analysis to fitting with a function for the shearing model of adhesive junctions only.
For a Pt tip sliding on HOPG in water, our experimental data best fit the shearing model of adhesive junctions.Thereby, τ = 87.43MPa and F ad = 0 nN.In contrast, for a diamond tip sliding on HOPG in water, the friction remained linearly dependent on the normal force over the entire domain of applied normal force values; in this case, the friction coefficient is μ = 0.133 and F ad = 48.68nN.
It is worth emphasizing that the shear strength values determined from our experimental results in water are significantly lower than in ambient conditions.This result confirms that the exfoliation of graphite is made easier by the intercalation of water molecules between the basal planes.Interestingly, puckering does not appear to be significantly affected by the environment.
The intercalation of water between wet-transferred MoS2 and graphite has recently been experimentally observed by Hong et al. [60], and the effect of water intercalation on the friction of multilayer graphene and graphene oxide was also validated by Arif et al. [61].
Figure 9 shows topography images recorded on graphite after 15-fold scanning repetition at constant normal force values with SiO x , Pt, and diamond tips in ambient and underwater.From these images, we determined the normal force dependence of the wear depth for the individual tips underwater (see Fig. 10).In all cases, the wear depth d w increased almost linearly with the normal force.
For SiO x and Pt tips, the wear rate evaluated in ambient conditions is almost an order of magnitude lower than underwater.In contrast, the wear of HOPG with diamond tips does not increase as steeply when measured underwater as with SiO x and Pt tips.

Conclusions
The friction and wear performances of graphite strongly depend on the chemistry of the counter-sliding body.In chemically inert sliding contact, such as with a SiO x tip, friction is governed by puckering.Wear initiates at surface step edges by mechanical destabilization of folds, leading to fracture.In the case of an adhesive sliding contact such as with a Pt tip, the adhesive strength of Pt with surface step edges of HOPG is large enough to partially exfoliate HOPG basal planes even at the lowest contact forces.The leading friction mechanism crosses over at higher load values from adhesion-mediated exfoliation to puckering.In both cases, the wear rate is low.With both tip materials, we observe a friction decrease and an increase in the wear rate when changing the measurement conditions from ambient to underwater.This effect can be explained by the intercalation of water molecules between the basal planes of HOPG that results in weaker interactions between basal planes.In the case of diamond as a counter body material, we measured a friction coefficient and a wear rate of an order of magnitude larger than with SiO x or Pt tips.We explain the occurrence of severe friction and wear based on a shear-induced order-disorder reaction.

Fig. 1 (
Fig. 1 (Left) Topography and (Right) lateral force images recorded with a soft singlecrystalline silicon cantilever on HOPG.Below each image, typical line profiles are also shown; the different colors for the lateral force Fl line profiles correspond to (blue) the forward and (orange) the backward scan directions (Color figure online)

Fig. 2
Fig. 2 Dependence of friction on the normal force for HOPG in ambient versus a SiO x , b Pt, and c diamond.The colored dot symbols correspond to the AFM topography images shown in Fig. 3.For better readability, the friction force is plotted versus the logarithm of the normal force.In this figure, we plotted our experimental friction data

106 Page 8 of 14 Fig. 4
Fig. 4 Postmortem SEM images of a SiO x , b Pt, and c diamond tips used for tribological testing of HOPG in ambient conditions

Fig. 5
Fig. 5 AFM topography images of HOPG after 15-fold scanning repetition in ambient at constant normal force values (indicated in Fig. 6) with a-c SiO x , d-f Pt, and g-i diamond tips.For each topography image, we also indicate the wear depth d w

Fig. 7 Fig. 9
Fig. 7 Dependence of friction on the normal force for HOPG underwater versus a SiO x , b Pt, and c diamond.The colored dot symbols correspond to the AFM topography images shown in Fig. 8.For better readability, the friction force is plotted versus the logarithm of the normal force.In (a, b), we also show the best fit of our experimental

Table 1
Wear rate values of HOPG for different tip materials used in ambient

Table 2
Wear rate values of HOPG for different tip materials used underwater