9960
J. Phys. Chem. 1995,99, 9960-9965
Universal Aspects of the Atomic-Scale Friction of Diamond Surfaces Martin D. Perry and Judith A. Harrison* Department of Chemistry, US.Naval Academy, Annapolis, Maryland 21402 Received: January 12, 1995; In Final Form: April 17, 1995@
Several facets are observed when diamond films are produced by chemical vapor deposition methods. It is unknown, however, if all of these facets exhibit the same atomic-scale frictional behavior. In an effort to determine whether a facet or surface topological dependence of the atomic-scale friction of diamond exists, we have used molecular dynamics simulations to examine the friction which occurs when the (100)-(2 x 1) reconstructed surfaces of two diamond lattices are placed in sliding contact. Calculations are performed as a function of applied load, crystallographic sliding direction, and sliding velocity. Results from these calculations are compared with previous computations performed on a diamond (1 11) surface. We find that the general dependence of the friction coefficient, p , on the applied load is similar, regardless of the facet. Indeed, this conclusion is supported by atomic force microscope experiments which have examined the friction of diamond (100) and (111) surfaces [Germann et al., J. Appl. Phys. 1993, 73, 1631. While the friction coefficients, and therefore the amount of energy dissipation, are similar regardless of facet, the atomic-scale motions which lead to energy dissipation differ slightly depending on the facet.
I. Introduction
consists of two diamond lattices oriented so that their (100)-(2 x 1) reconstructed surfaces are in close proximity to one another Recent developments in chemical vapor deposition (CVD) (Figure la). A single reconstructed diamond (100)-(2 x 1) techniques for diamond growth have instigated a flurry of surface consists of 12 layers of atoms; 11 layers of carbon atoms experimental and theoretical investigations aimed at understandcontaining 16 atoms each and one layer of hydrogen atoms also ing the microscopic properties of diamond films and their containing 16 atoms. Both surfaces are terminated with formation. A majority of the interest has concentrated on hydrogen atoms at the interface. Thus, each individual surface unveiling the mechanisms responsible for the growth process;'-I0 contains 192 atoms. however, very little computational effort has focused on the To properly simulate the heat-transfer effects of the bulk unique properties of diamond and diamond films such as its crystal, the lattice atoms were partitioned into three subsets. low friction and extreme resistance to wear. The atoms of the two outermost layers (along the Z axis) of While much is currently understood about diamond and each surface were held rigid (boxed atoms in Figure la). A diamond films on the macroscopic level,"-13 very little is known thermostat43was applied to the atoms of the next five layers of about the microscopic processes which cause friction and wear both the upper and lower surface to control the temperature of of diamond. Recent advances in scientific instrumentation, such the system. The atoms of the five innermost layers of each as the surface force a p ~ a r a t u s , ' ~ the - ' ~ quartz crystal microbalsurface, Le., layers closest to the interface, had no physical a n ~ e , ' * .and ' ~ the atomic force microscope (AFM),20-25have constraints placed upon them. In order to correctly simulate allowed for the study of atomic-scale friction and wear. In an infinite (100)-(2 x 1) sliding interface, periodic boundary addition, these experimental achievements have stimulated conditions were applied in the plane that contains the (100)-(2 theoretical studies of atomic-scale friction using analytical x 1) surface of the lattice (the X Y plane depicted in Figure lb). model^,*^-^^ first principles c a l c ~ l a t i o n s , ~and ~ - ~molecular ~ dynamic^.^^-^' Molecular dynamics simulations were performed by integratIn our previous ~ o r k , ~ we ~ -investigated ~' the atomic-scale ing Newton's equations of motion with a Nordsieck predictor friction and wear between two diamond (111) surfaces in sliding corre~tor"~ and a constant time step of 0.5 fs. The empirical contact using molecular dynamics simulations. Diamond films hydrocarbon potential developed by BrenneP5 was employed produced using CVD techniques contain (100)- and (1 10)in all of the calculations. This potential is based on Tersoff's oriented facets, as well as the (1 11) substrate ~ r i e n t a t i o n . ~ ~ covalent bonding formalism46with additional terms that correct Therefore, any comprehensive understanding of the atomic-scale for overbinding of radicals and nonlocal environmental effects. frictional behavior of diamond films must include knowledge Nonlocal effects are included using an analytical function that of the behavior of all facets. In the present study, we focus defines conjugation in terms of the coordination of carbon atoms our attention on the frictional behavior of (100)-(2 x 1) that neighbor carbon-carbon bonds. This potential is unique reconstructed diamond surfaces. The (2 x 1) reconstruction is in that it allows for the formation and breaking of chemical chosen due to its thermodynamic stability over the (1 x 1) bonds along with the associated changes in hybridization. reconstructed surface.42 Friction was investigated by sliding the rigid layers of the upper surface at a constant velocity of 1.0 k p s (100 m/s) in the chosen 11. Methods and Procedures crystallographic sliding direction while maintaining a constant separation between the rigid layers. The normal force, F,, and Atomic-scale friction was investigated by placing two diathe frictional force, F, or F,, on the upper (sliding) surface were mond (100)-(2 x l ) reconstructed surfaces in contact and sliding calculated by summing the forces on each rigid layer atom. them in a given crystallographic direction. The present study These forces were averaged every 20 time steps and normalized by the number of atoms in the rigid layer to obtain the force * To whom correspondence should be addressed. 'Abstract published in Advance ACS Abstracts, June 1, 1995. per atom. The simulations were performed for 30 ps at average This article not subject to U.S. Copyright. Published 1995 by the American Chemical Society
Atomic-Scale Friction of Diamond Surfaces
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Figure 2. Average friction coefficient a: a function of average normal load, ( F J , per atom for sliding at 1.0 A/ps and 300 K. (a, b) Open squares and open triangles represent sliding in the [Oll] and [Oll] directions on a reconstructed diamond (100)-(2 x 1)-surface, respectively. (c) Filled squares represent sliding in the [112] direction on a hydrogen-terminated diamond (1 11) surface.
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(b) Figure 1. (a) Initial configurations for th_ereconstructed diamond (100)(2 x 1) surfaces viewed along the [Oll] direction. White spheres represent carbon atoms, and gray spheres represent hydrogen atoms. Reconstruction of the surfaces is evidenced in the second layer of carbon atoms to which the hydrogen atoms are bonded. The second layer carbon atoms and their reconstructed bonds have been cross-hatched for clarity. (b) The lower surface viewed along the [loo] direction. The unit cell spacingjn the [Oll] direction ks 5.030 A, while the unit cell spacing in the [Oll] direction is 2.515 A. The Z direction is out of the plane of the paper.
normal loads between 0 and 20 GPa. These pressures are consistent with those which are achieved experimentally using an AFM.22 The friction coefficient, p, for individual sliding runs was taken to b e the average frictional force (average force in the sliding direction) on the rigid layers of the upper surface divided by the average normal force on those same rigid layers. Average friction coefficients were obtained by averaging the individual friction coefficients from sliding simulations whose starting configurations differed only in horizontal position of the upper surface. The horizontal position of the upper lattice was altered by translation of the upper surface in a direction perpendicular to the sliding direction prior to the start of the sliding simulation (Figure lb). In this way, friction coefficients were averaged over the unit cell perpendicular to the sliding direction.
Molecular dynamics simulations have been utilized to examine friction on the reconstructed (100)-(2 x 1) face of diamond (shown in Figure 1) at 300 K as a function of crystallographic sliding direction, normal load, starting configuration, and sliding velocity. It was previously demonstrated that, for moderate to high temperatures, the lattice temperature had only a small effect on p of diamond (111) surfaces;37 therefore, we have not performed any computations as a function of this variable. A. Behavior of p with Load: Surface Topological Effects. The friction coefficients as a function of the average normal load for sliding in the [Oll], Le., parallel to the dimer bonds, and [Oil] directions, Le., perpendicular to the dimer bonds, on a reconstructed diamond (100)-(2 x 1) surface are shown in Figure 2, a and b, respectively. All data points were computed from sliding runs at 300 K for sliding velocities of 1.0 k p s . The qualitative behavior of p with load observed here is strikingly similar to the dependence of p with load observed in the diamond (1 11) system when sliding in the [ 1121 direction (Figure 2c).39 However, there are some small differences among these three sets of data. These differences are discussed below. The value of normal load where a nonzero friction coefficient is fist observed, i.e., the threshold, is slightly lower when sliding on the (1 11) surface (Figure 2c) compared to sliding on the reconstructed diamond (100)-(2 x 1) surface (Figure 2a,b). One possible explanation for this behavior is the orientation of the terminal hydrogen atoms on the (1 11) surface versus the (100)( 2 x 1) reconstructed surface. The terminal C-H bond on a (111) hydrogen-terminated, diamond surface is approximately perpendicular to the plane which contains the opposing diamond surface. For convenience, we refer to this geometry as axiallike positioning of the terminal hydrogen atoms. In contrast, due to the dimer reconstruction, the terminal C-H bonds on the diamond (100)-(2 x 1) surface are not perpendicular to the plane which contains the opposing diamond surface (XY plane in Figure lb). We refer to this geometry of the terminal hydrogen atoms as equitorial-like. The axial-like positioning of the hydrogen atoms on the (1 11) surface results in larger repulsive interactions between opposing surfaces than the
9962 J. Phys. Chem., Vol. 99, No. 24, 1995 I
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Figure 3. Average vibrational energy of oscillators between layers as a function of sliding distance at 300 K for the diamond (1 1 1) system. The average normal load and friction coefficient are 0.72 nN/atom and 0.42, respectively. The vibrational energy between the first and second layer of the lower diamond surface is shown in the lower panel, between the second and third layers in the middle panel, and between the third and fourth layers in the upper panel.
Figure 4. Average vibrational energy of oscillators between layers as a function of sliding distance at 300 K for the diamond (100) system. The average normal load and friction coefficient are 0.75 nNlatom and 0.48, respectively. The vibrational energy between the first and second layers of the lower diamond surface is shown in the lower panel, between the second and third layers in the middle panel, and between the third and fourth layers in the upper panel.
equitorial-like positioning for a given surface separation; thus, the threshold to friction is lower. At intermediate loads, between approximately 0.3 and 0.5 nN/atom, quantitative agreement among all sets of data is observed. When the lattices are compressed at higher loads, larger than 0.5 nN/atom, the friction coefficients for sliding perpendicular to the dimer bonds on the (100) surface appear to be lower than when sliding parallel to the dimer bonds. The values of p for sliding in the [ 1121 direction of diamond (1 11) are approximately the same as they are when sliding parallel to the dimer bonds on the (100) surface. While we note the differences among friction coefficients when sliding on the (100) surface are small due to the length of the error bars, there is a physical explanation for this behavior. For the (1 11) surface, previous studies have shown that at high loads the sliding is dominated by the stick-slip phenomenon. This behavior causes mechanical excitation of the interface. This energy is ultimately transferred to the rest of the lattice and dissipated as heat. The dissipation of energy was shown to be the essence of atomicscale friction.40 The diamond surfaces examined here exhibit stick-slip behavior when sliding parallel to the dimer bonds (Figure 2a) but not when sliding perpendicular to the dimer bonds (Figure 2b). Therefore, the friction coefficients are slightly higher when sliding in the former direction compared to the latter, because more energy is dissipated when stickslip i s observed. The mechanical excitation of the interface when sliding can be quantified by calculating the vibrational energy between the layers of the diamond lattice during sliding.40 (The vibrational energy between pairs of atoms in adjacent layers is calculated using the equation appropriate for an harmonic oscillator and averaged over the number of pairs within the layer.) The vibrational energy between layers of the diamond lattice as a function of sliding distance for both the (1 11)40and the (100) diamond systems is shown in Figures 3 and 4,respectively. It is apparent from comparison of these two figures that, at comparable loads, the amount of vibrational excitation in both systems is approximately equal. That is, the heights of the maxima in these data are approximately the same. The decay of these peaks back to their base line value prior to the next
encounter with hydrogen atoms on the opposing surface demonstrates the efficient dissipation of energy to the bath. Because the amount of excitation and hence the amount of energy dissipation are similar in both systems, the friction coefficients are approximately equal. We note that recent atomic force microscope experiments, which have used a CVD diamond tip to examine the friction of diamond (100) and (1 11) surfaces, have also shown that the average frictional forces observed in both these systems are the same.** Increasing the normal load results in more mechanical excitation of the lattice when sliding and ultimately in stickslip. Increased mechanical excitation results in larger values of p . The vibrational energy as a function of sliding distance at a fairly large normal load, 1.10 nN/atom, is shown in Figure 5. Comparison of these data with the vibrational energy data obtained at a lower normal load, shown in Figure 4,confirms the conclusion stated above. B. Atomic-Scale Sliding Mechanisms. With the surfaces configured as in Figure 1, the upper surface was slid perpendicular to the dimer bonds at 1.0 k p s . The force normal to the sliding interface, F:, and the shear force, F,, in the sliding direction on the rigid layers of the upper surface are shown as function of unit cell distance in Figure 6a. In this crystallographic direction, the unit cell distance, or the distance between hydrogen atoms (or dimer bonds), is 2.515 A. The average normal load, (F:), on the upper surface for this simulation is 0.20 nNlatom, and the friction coefficient, p , is 0.002. The normal and shear forces are both periodic functions of sliding distance, exhibiting one symmetric maximum for each unit cell with the maxima in these F, data consistently occurring prior to the maxima in these F- data. This type of oscillatory behavior was also observed in the diamond (111) ~ y s t e m . ~ 'In . ~that ~ work, the shapes of the peaks in the F, and F: data, the periodic structure of these data, and the displacement of the F , maxima with respect to the F: maxima were all explained in terms of specific atomic-scale motions of the interface atoms during sliding. This type of analysis can also be done for the (100) diamond system. For instance, as the upper surface slides perpendicular to the dimer bonds, the hydrogen atoms of the upper surface, which were
Atomic-Scale Friction of Diamond Surfaces
J. Phys. Chem., Vol. 99, No. 24, 1995 9963 (c)
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Sliding Distance/Unit Cell Figure 5. Average vibrational energy of oscillators between layers as a function of sliding distance at 300 K for the diamond (100) system. This data corresponds to the simulation shown in Figure 8c. The vibrational energy between the first and second layers of the lower diamond surface is shown in the lower panel, between the second and third layers in the middle panel, and between the third and fourth layers in the upper panel.
directly positioned over hydrogen atoms on the lower surface at the start of the simulation, pass over the valley above the carbon atoms in the fourth layer of the lower surface before encountering the next carbon-hydrogen pair on the lower surface. Both F- and F, increase as the hydrogen atoms on opposing surfaces begin to interact repulsively. Because the hydrogen atoms are allowed to move freely, they do not pass directly over each other. Instead, their repulsive forces cause them to revolve around each other in the XY plane. These maxima in the frictional force data occur just prior to this revolution of the hydrogen atoms. Because this motion decreases some of the shear force in the sliding direction, F, begins to decrease. Once the revolution of the hydrogen atoms is complete, the repulsive interaction between the hydrogen atoms pushes the upper surface in the sliding direction. This corresponds to the negative minima in these F, data shown in Figure 6a. The maxima in the normal force data occur when the hydrogen atoms of the upper surface pass by the hydrogen atoms of the lower surface. Thus, F, has already begun to decrease when F- is at a maximum. It was previously shown37 that increasing the applied load increased p but did not significantly affect the sliding mechanisms. This is also true when sliding perpendicular to the dimer bonds on the (100) surface. When the applied load on the lattices is increased and the sliding simulations repeated, data shown in Figure 6b,c are obtained. For these data shown in Figure 6b, the applied load and friction coefficient are 0.50 nN/ atom and 0.37, respectively. Doubling the normal load to 1.02 nN/atom (Figure 6c) only increased ,M slightly to 0.41. The qualitative shape of the frictional and normal force curves as a function of sliding distance remains virtually unchanged regardless of the normal load, implying that the sliding mechanism is unchanged. It is important to note that the stick-slip phenomenon is not observed for the highest load simulations in this direction. When the lattice is compressed at higher loads, the terminal hydrogen atoms at the interface are no longer positioned directly above each other as seen in Figure 7 . With the hydrogen atoms in these positions and the upper surface sliding perpendicular to the dimer bonds (into the paper in Figure 7 ) , interaction between the hydrogen atoms is reduced. This
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Figure 7. Initial configurations for the reconstructed diamond (100)( 2 x 1) surfaces at high loads. Carbon and hydrogen atoms are designated as in Figure 1.
prevents the upper surface interface from becoming stuck as it slides over the lower surface. There is some experimental evidence for frictional anisotropy of diam0nd.4~ Indeed, previous simulations regarding the frictional behavior of diamond (1 11) surfaces show that when the surfaces are atomically flat, some anisotropy can exist between friction coefficients calculated for different sliding direction^.^^ It is worth noting that no such pronounced frictional anisotropy for sliding perpendicular to the dimer bonds versus parallel to them has been observed here. This is apparent from plots of p versus average normal load for both sliding directions shown in Figure 2a,b. The slightly larger values of the average friction coefficient for sliding in the direction parallel to the dimer bonds at higher loads are most likely a result of the stick-slip phenomena. Even at the highest loads examined when sliding perpendicular to the dimer bonds, stick-slip is not observed.
Perry and Harrison
9964 J. Phys. Chem., Vol. 99, No. 24, 1995 1.5
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1 2 3 4 5 Sliding Distance/Unit Cell Figure 9. Variation of the frictional force and normal force per atom as a function of sliding velocity for sliding the rigid layers of the upper surface in the [Ol 11 direction at 300 K. Dashed lines represent F, and solid lines represent F,. 0
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Sliding Distance/Unit Cell Figure 8. Frictional force and normal force per atom as a function of unit cell distance for sliding the rigid layers of the upper surface in the [Oll] direction at 1.0 Nps and 300 K for three different values of applied load. Dashed lines represent F; and solid lines represent F,. (a) (F,) = 0.19 nN/atom andp = 0.003. (b) (F,) = 0.58 nN/atom and p = 0.264. (c) (F,) = 1.10 nN/atom and p = 0.405. Beginning with the lattice configured in the same initial positions as shown in Figure 1, the upper surface is now slid in the direction parallel to the dimer bonds at 1.0 &ps. The resulting forces on the rigid layer of the upper surface, F- and FA,are shown as a function of unit cell distance in Figure 8a. For this simulation, the values of the average normal load and friction coefficient are 0.19 nN/atom and 0.003, respectively. The shapes of these curves are qualitatively similar to the curves obtained when sliding perpendicular to the dimer bonds. For example, the position of the frictional force maxima still consistently occur prior to these maxima in the normal force data. Because the surface is reconstructed in this direction, the unit cell distance is twice what is was in the direction perpendicular to the dimer bonds, or 5.030 A. This difference in atomic arrangement in the direction parallel to the dimer bonds produces two maxima in both the FLand F , data for each unit cell instead of one maximum as observed when perpendicular to the dimers. At the beginning of the simulation, the hydrogen atoms of the upper surface are positioned directly over the hydrogen atoms of the lower surface. As the upper lattice slides parallel to the dimer bonds, the hydrogen atoms pass over the reconstructed bond between second layer carbon atoms on the lower surface before encountering the next hydrogen atom. Repulsive interactions between hydrogen atoms on the upper surface and those on the lower surface again lead to increases in F: and F,,. Here again, the hydrogen atoms do not pass directly over each other, but revolve around each other in order to reduce repulsive interactions. Once the hydrogen atoms of the upper surface have slid by the hydrogens on the end of the reconstructed carbon-carbon bond, they pass over a deep valley created by third and fourth layer carbon atoms of the lower surface, corresponding to the minima in the Fs data. As the upper surface hydrogen atoms approach the next group of lower surface hydrogen atoms, F- and F, begin to increase again due to the repulsive interaction between hydrogen atoms. The maxima in both sets of data occur as previously mentioned. When the normal loads are increased and the upper surface is slid parallel to dimer bonds, distinct changes in the shapes of the frictional and normal forces versus sliding distance are observed as illustrated in Figure 8b,c. In these sliding runs,
the loads have been increased to 0.58 and 1.10 nN/atom, resulting in friction coefficients of 0.264 and 0.405, respectively. The values of p increase with applied load as was the case when sliding perpendicular to the dimers; however, the atomistic sliding mechanisms when sliding parallel to the dimers are not load independent. As the load is increased, instead of two symmetric peaks for each unit cell, two asymmetric peaks for each unit cell in the F, data and one broadened peak for each unit cell in the Fs data are observed (Figure 8b). Most worthy of note is the behavior occurring between the first and second unit cell distance. Because the compression of the two surfaces is greater, the hydrogen atoms no longer pass over one another as easily as in the lower load simulations. The first peak in the F, data occurs as the upper surface hydrogen atoms approach the hydrogen atoms on the lower surface as before. Unlike the lower load simulations, the hydrogen atoms have more difficulty revolving around each other due to the compression of the lattice. Thus, they momentarily become stuck as the upper surface continues to slide. As this motion continues, the stress at the interface increases until it becomes great enough to overcome the "sticking" force. Then hydrogen atoms on the upper surface slip past the lower surface hydrogen atoms on one end of the reconstructed carbon-carbon surface bond and quickly encounter the hydrogen atoms on the other end of the bond. The position of the upper surface is such that the interaction between these hydrogen atoms is almost missed. Also, the second hydrogen atom is tilted in the sliding direction which reduces the chance of interaction. Consequently, the second peak in the F, data is not usually as large as the first peak. As the upper surface continues to slide, the stick-slip behavior3' again takes place, and a sharp decrease in these F , data is observed. The minima in these F , data occur when the hydrogen atoms are positioned above the deep valley created by the third and fourth layer carbon atoms of the lower surface. The broadening of these F, data is also due to the closer proximity of the two surfaces at this load, resulting in two peaks becoming resolved into one. This broadening effect is further evidenced at higher load simulations as depicted in Figure 8c. Due to a more pronounced stick-slip behavior, the second peak is no longer resolved in either set of data, resulting in a single peak for each unit cell. Reducing the sliding speed to 0.1 h p s and repeating a simulation for sliding parallel to the dimers yields the F- and F , data as a function of sliding distance shown in Figure 9b.
Atomic-Scale Friction of Diamond Surfaces While the qualitative shape of these data at the two speeds differs, the average values of the frictional force, (Fx),and the normal force, (F:), are comparable; therefore, the friction coefficients obtained from each run are approximately the same. For the 1.O k p s simulation, p = 0.43 compared with p = 0.45 for the 0.1 k p s simulation. Differences in the atomic-scale motions while sliding give rise to the different shapes of F, and F; when sliding at differing speeds. For instance, when the sliding velocity is 1.O k p s (Figure 9a), the second peak in the frictional force data is almost always not resolved. This is a result of the upper surface slipping past the lower surface to quickly to allow the second set of hydrogen atoms to interact. When the velocity is reduced to 0.1 k p s (Figure 9b), this surface feature is resolved as evidenced by the smaller second peak for each unit cell. It is important to note that while the atomic-scale mechanism of friction is changing as the velocity is reduced, the friction coefficient remains essentially unaffected.
IV. Summary We have used molecular dynamics simulations to study the atomic-scale friction which occurs when two reconstructed diamond (100)-(2 x 1) surfaces were placed in sliding contact at 300 K. Calculations have been performed as a function of applied load, crystallographic sliding direction, and sliding velocity. Results from the present calculations have been compared with previous computations on a diamond (1 11) s ~ r f a c e ~ to ’ , ~determine ~ whether the atomic-scale friction of diamond was dependent on the surface topology. We found that the general dependence of p on the applied load was similar, regardless of the facet in agreement with recent atomic force microscope findings.22 Thus, the topology of the surface cannot be determined solely by examining the friction coefficient as a function of applied load. At low applied loads, the atomistic sliding mechanisms possessed some similar characteristics for all directions studied on all facets. That is, each time the hydrogen atoms of an upper surface passed over lower surface hydrogen atoms, peaks in the shear and normal forces were observed. At higher applied loads, the atomistic sliding mechanisms began to vary depending mainly on whether or not the stick-slip phenomena occurred. For sliding in the [ 1121 direction on the (111) surface and sliding in the [Oll] direction on the (100)-(2 x 1) surface, stick-slip was observed, resulting in slightly higher friction coefficients than those calculated for sliding in the [Oil] direction on the (100)-(2 x 1) surface at the same loads. Stick-slip was not observed for this direction due to the fact that the hydrogen atoms were no longer positioned directly over one another, thus reducing the chances for the upper surface to become stuck as it slid over the lower surface. Decreasing the sliding velocity by an order of magnitude did not significantly affect the value of p ; however, the atomicscale friction mechanism was altered for sliding in the [Oll] direction on the (100)-(2 x 1) surface. At slower speeds, the second set of hydrogen atoms on the reconstructed carboncarbon bond had more time to interact, resulting in the resolution of the smaller second peak in the shear force data. Thus, appropriate experimental sliding velocities must be carefully chosen to avoid overlooking important structural features of shear or frictional force data.
Acknowledgment, This work was supported by the US. Office of Naval Research (ONR) under contract N00014-95WR-20014. The authors also thank Donald W. Brenner, Susan B. Sinnott, Frederick H. Streitz, James J. C. Barrett, and Carter T. White for many helpful discussions. Some of the figures
J. Phys. Chem., Vol. 99, No. 24, 1995 9965 were generated with the program XMol (XMol, version 1.3.1, Minnesota, Supercomputer Center, Inc., Minneapolis, MN, 1993).
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