Nantribology: Rubbing on a Small Scale - Journal of Chemical

Symposium: Chemistry at the Nanometer Scale edited by

Symposium: Chemistry at the Nanometer Scale

K. W. Hipps Washington State University Pullman, WA 99163

Nanotribology: Rubbing on a Small Scale J. Thomas Dickinson Department of Physics, Washington State University, Pullman, WA 99164-2814; [email protected]

Nanoscale science is driven by two major efforts. The first is to use new tools that allow nanometer-scale measurements to be performed. This allows us to probe matter, structures, and surfaces on the nanometer-size scale in order to understand how things fundamentally work at these dimensions. The second effort, fed by the first, deals with developing new technology, namely nanotechnology, in general. The activity has focused on building and developing at the atomic-, molecular-, or macromolecular-level devices and structures involving length scales of approximately one to several hundred nanometers. Scanning probes such as STM, AFM, and SNOM deserve an enormous portion of the credit for the push to both understand and exploit nanometer-scale phenomena (1). One area that has greatly benefited from these efforts is tribology. Tribology is derived from the Greek root “tribo-” that means to rub, grind, or wear away; in general, tribology is the science and investigation of friction, wear, and lubrication. Wherever two surfaces undergo relative, sliding motion, usually in contact (but not always), the interactions between these surfaces generally lead to friction and material modification. Today’s machines and even our joints are central topics of study in this rich and important field. Since the days of Leonardo da Vinci (1452–1519), with important early contributions from Guillaume Amontons (1663–1705), Leonard Euler (1707–1783), and Charles Coulomb (1736– 1806), studies of macroscopic friction, wear, and lubrication have progressed and given us considerable phenomenological understanding of very complex systems. For a wide variety of conditions (e.g., contact area, sliding velocity, surface roughness, and temperature), the force of friction, f, is given in term of the kinetic coefficient of friction (µk ) and the load or normal force (FN) by f = µk F N

(1)

This equation is known as Amonton’s law of friction when µk is treated as a constant. It is derived from the classical treat-

ment of friction and has served engineers well for many decades. Examining materials at the nanometer scale provides insight into tribological processes. If one examines two rubbing surfaces with higher and higher magnification, one soon reaches a description of typical surfaces in terms of their protusions or asperities. No two surfaces are totally flat, particularly at the scale of a few tenths to a few nanometers. These surface “bumps”, represented schematically in Figure 1A, interact strongly with each other, perhaps with a layer of fluid between the bumps (e.g., a lubricant) or perhaps in contact. In contact, these microscopic irregularities of surfaces often touch, crash into, and pull and push one another as materials slide. The forces and stresses (stress equals an applied force divided by the contact area) that asperities experience can be much higher than what one would calculate from a gross applied force per total area. An example that illustrates the gross applied force versus the force experienced by a single asperity is instructive; the bedof-nails demonstration, which physicists love to do. An instructor weighing 80 kg lies down on the bed of nails with ∼200 nails supporting his or her body. The gross area of contact is 0.8 m2. The gross stress is the person’s weight per contact area; that is, (m g)A, which is [(80 kg)(10 ms2)]0.8 m2 or 1000 Nm2 or ∼1000 Pa (1 Newtonmeter2 is a unit of pressure or stress, called a Pascal, Pa). Now if we look at a single nail, it supports 1200th of the total force, which equals 4 N. We estimate the contact of the instructor’s body with the nail to be a circle of 1 mm in radius, which yields an A ∼3 × 10᎑6 m2. Thus, the stress applied by the nail to the instructor’s body is ∼1 × 106 Pa or 1 MPa, over three orders of magnitude higher than the gross stress. Speaking from experience (as the instructor) this demonstration hurts! A wimpy way out is to use thick clothing that greatly reduces the discomfort by increasing the area of contact with your skin and thereby reducing the stress. The point being made is that asperities often support the major loads between surfaces in contact.

Figure 1. Schematic representation of contacting surfaces for (A) two rough surfaces in shear involving multi-asperity contact and (B) a “single” asperity, namely an AFM tip, in contact with a surface.

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In the case of sliding contacts, these high stresses generated by contacting asperities dominate the interacting asperities and can lead to extreme temperatures, deformation, and for some materials even welding and subsequent tearing of asperities. In the case of polished metals, ceramics, and smooth plastics, these asperities are frequently submicrometer in dimension. Thus, approaching tribology from the nanometer size scale, using, for example, an AFM tip to model a single asperity, offers us the opportunity to make measurements on a much simpler system than two sliding macroscopic surfaces. Krim at North Carolina State University coined the term “nanotribology” in 1991 (2). One important consequence from studies of single-asperity, nanometerscale friction is that Amonton’s Law frequently breaks down so that there is interesting physics yet to be revealed (3). In addition, this scale lends itself to intimate connection with multiscale simulation and modeling efforts, for example, using molecular-dynamics techniques. There is a time-scale problem (simulations frequently cover nanoseconds, experiments milliseconds to seconds). Intense efforts are currently being made to close this gap (4). Nanometer-scale investigations thus offer the potential of providing first-principles understanding of tribo-systems in terms of fundamental intermolecular forces. Furthermore, our understanding of other technologies are greatly aided by a nanoscience approach. The physics and chemistry of combined mechanical and chemical polishing (known as chemical mechanical planarization, CMP) (5) are not well understood in spite of the fact that the entire microelectronics industry uses these techniques repeatedly in silicon-integrated-circuit fabrication (e.g., computer chips). The need for planarization of interlayered dielectrics and metal films arises from the repeated lithographic steps that require extremely flat surfaces to achieve the high resolution needed for high-density electronic structures. CMP involves slightly aggressive solutions in combination of abrasive particles and a polishing pad; through a combination of mechanical and chemical processes, very smooth surfaces can be generated. A model system to reveal the mechanisms underlying CMP is the use of an AFM tip to simulate a single abrasive particle (or a single asperity) translated along the substrate in the solution (Figure 1B). As we will see below, we gain considerable control of the applied stresses and parameters such as solution chemistry and temperature and often use the tip itself to image on a nanometer scale the changes in the substrate that result from the tip–surface interaction.

Examples of Fundamental Studies One of the most common experiences involving frictional effects in sliding is the so-called stick-slip phenomenon. The squeaking door hinge, squealing and chattering brakes, squeaking rubber-soled shoes on a basketball court, and even in the sliding of faults in the earth viewed over long times are all examples of stick-slip behavior. Loosely holding a pencil in your hand with the eraser on a clean hard surface (table or desk), and translating it sideways, tipping the pencil ∼30⬚ away from direction of sliding can easily be made to stickslip. The macroscopic explanation is basically a dynamic oscillation between static contact (no slip) followed by a jump owing to an instability into sliding (slip). This normally repeats itself as long as the surfaces continue to move; a large difference between the static and dynamic coefficients of friction promotes this type of motion.

quadrant photodetector

Lateral Force Measurements with an AFM The general principles of the AFM have been presented previously. In the case of laser-beam reflection from the top of the cantilever and detection of cantilever deflection with a quadrant-position-sensitive detector one can measure two cantilever displacement modes simultaneously (6). As seen in Figure 2, if the quadrants are labeled a, b, c, and d as shown, then a deflection of the cantilever normal to the surface would deflect the laser beam on the photodetector in the vertical direction. Thus, if we take the voltages generated by light hitting these quadrants and add and subtract them as follows: (Va + Vb) − (Vc + Vd) we will be most sensitive to normal deflection. With suitable calibration, this signal tells www.JCE.DivCHED.org

us how hard the tip is pushing on the substrate. Using this signal with electronic feedback to maintain constant normal force, one is operating the AFM in the usual contact mode for topographical imaging of surfaces. Similarly, as we drag the tip in a direction perpendicular to the cantilever as shown by the trace on the substrate, a frictional or lateral force on the tip will cause the cantilever to rock or twist (torsional mode) and the laser beam will therefore move horizontally on the photodetector. Thus if we take the detector voltages and add and subtract them as follows: (Va + Vc) − (Vb + Vd) we will be most sensitive to the twisting or torsional motion of the cantilever. Again, with suitable calibration, we can then relate this derived voltage to the lateral or frictional force. Commercial instruments make this signal available (uncalibrated) during typical scanning measurements. When the signal is plotted versus position of the tip, it provides a frictional or lateral force map that can be useful for understanding heterogeneous surfaces. This type of imaging is often called frictional force microscopy (FFM). This image is often called the lateral force image; lateral force images often provide substantial improvement in the definition of images of soft samples such as polymers (7). In nanotribology, lateral force measurements are an important tool for studying friction.

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a c

b d

laser beam

cantilever tip

substrate

Figure 2. A schematic of the detection scheme for a laser reflection AFM to monitor both normal and lateral deflection of the cantilever.

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Figure 3. (A) A lateral force image (2 x 2 nm) (tungsten wire tip on basal plane of graphite) where the intensity of the image is scaled to the frictional force (bright areas indicate higher forces). The period seen in this scan is 0.25 nm. (B) The lateral deflection of the wire cantilever and the corresponding frictional force as a function of sample position for three normal forces. The circles indicate where double-slip events occurred. (Reprinted Figure 2 with permission from Mate, C. M; McClelland, G. M.; Erlandsson, R.; Chiang, S. Phys. Rev. Lett. 1987, 59, 1942–1945. Copyright 1987 by the American Physical Society.)

B

Mate, McCelland, et al. showed in 1987 that stick-slip behavior could be observed on an incredibly small-size scale (8). Under ultrahigh vacuum conditions, they constructed an AFM capable of measuring lateral forces with a tiny tip estimated to produce contact areas on the order of 104 nm2. A 2 × 2-nm lateral force image of a tungsten wire tip sliding on the basal plane of graphite is shown in Figure 3A . This image exhibits a periodicity of 0.25 nm, which is the same period as the honeycomb unit-cell structure on the graphite cleavage plane. Figure 3B shows single back and forth traces (the tip is moving with a speed of 40 nms) of the lateral force versus displacement for three different normal forces. These traces show first that there is hysteresis, which means that there are energy losses in the motion consistent with friction, and second, with increasing normal force, stick-slip motion sets in, which generates the triangular waveform in the lateral force. (The area enclosed by the two curves represents the energy dissipated in one cycle). The apparent coefficient of friction ( fFN) was quite low. It varied from tip to tip but values were all in the range of 0.005 to 0.015. The traces indicated that there were two components of the lateral force: the con736


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servative, oscillatory force responsible for the stick-slip and a nonconservative component responsible for the observed hysteresis, which Mate et al. attributed to phonon generation, viscous dissipation, or plastic deformation and wear. Pinpointing the dominant mechanisms for friction is still a major effort of the nanotribology community. A good description of a number of these observations was presented by Tomának et al. using the Tomlinson model for molecular friction (9). A recent study on a completely different tip–substrate system also shows frictional behavior strongly dependent on the normal force. Ernst Meyer and his group in Basel, Switzerland have routinely achieved atomic dimension tips and seen numerous examples of atomic resolution, for example, on alkali halides using silicon tips and cantilevers. Socoliuc, et al. found—at normal contact forces of a few nano-Newtons—that stick-slip sliding was seen as shown in Figure 4a– c (10). The scan direction was along the [100] direction of the NaCl surface and the period seen here equals what would be equivalent to the Cl−Cl− (or Na+Na+) spacing along a row of Na+Cl− Na+Cl−… ions. Note for Figure 4c, FN is reported as ᎑0.47 nN, which means the cantilever is bent with the

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Figure 4. (a–c) Measurements of the lateral force acting on the tip sliding forward and backward in [100] direction over the NaCl(001) surface. The lines are typical cross sections through a two-dimensional scan along the strongest force amplitude. The externally applied load was (a) FN = 4.7 nN, (b) FN = 3.3 nN, and (c) FN = -0.47 nN. (d–f) Corresponding numerical results from the Tomlinson model. (Reprinted Figure 1 with permission from Socoliuc, A.; Bennewitz, R.; Gnecco, E.; Meyer, E. Phys. Rev. Lett. 2004, 92, 134301. Copyright 2004 by the American Physical Society.)

opposite curvature from compressive loading of the tip against the surface. Nevertheless, there is still a small normal force applied to the surface associated with the adhesion of the tip on the surface. For positive values the lateral force for two sliding directions show strong, jumpy stick-slip motion and hysteresis, that is, a dissipative, frictional force. Whereas under small negative FN values (but still in contact), modulated lateral forces are seen but with no hysteresis. Thus, within the sensitivity of the experiment, below some critical load, dissipation disappears. During this type of sliding, the tip moves smoothly from minimum to minimum with no jumping. Figure 4(d–f ) are simulated lateral force versus displacement curves based again on the Tomlinson model that show good agreement. The authors suggest that below this critical load there probably continues to be some small degree of dissipation and more sensitive measurements are necessary to detect it. Closely related studies on atomic-level friction have shown that other aspects of friction differ from classical, macroscopic behavior. In many cases the frictional force, f, deviates substantially from a simple linear dependence on FN. Likewise, the velocity dependence of f at constant FN has been shown to be significant (i.e., µ is not constant but increases slowly with changing sliding velocity). Closely tied to these careful AFM and FFM experiments are a number of atomic-level computer simulations of sliding surfaces. With small areas of contact, large computer models can be constructed to further our understanding of www.JCE.DivCHED.org

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nanometer-scale tribological processes. A number of studies have been reported that offered insight into friction, wear, and lubrication at the atomic and molecular level (11–15). The ability to arrange nanometer structures with controlled layers of interesting molecular structure (including dangling bonds, chemisorbed atoms and molecules, and mobile but confined molecules) allows a rich set of tribological problems to be addressed. One example of such a study, by Judith Harrison et al. at the U.S. Navy Academy, models hydrogen-terminated amorphous diamond-like carbon in sliding contact with a (111) surface of single crystal diamond (16). [The (111) surface of diamond is parallel to a plane that intersects the cubic crystal axes at one unit each of a, b, c]. Such surfaces are relevant to a number of technologies including protective coatings for hard disks used for memory storage and in microelectromechanical systems (MEMS) to lower friction and stiction (troublesome static friction that arises when two surfaces are first in contact at rest and then sliding is attempted; this can be a major source of failure of read–write heads resting on a hard disk during on–off cycles). Through the use of potentials that can model chemical bonds, these researchers showed that by varying the degree of hydrogen termination (saturated surfaces would be less chemically interactive; unsaturated surfaces would be stronger interactive leading to formation of carbon–carbon bonds across the interface), they could watch in time the tribochemistry that results as surfaces slide past each other. The observed formation and breaking of C⫺C bonds during a single slide are

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Figure 5. (A) Number of carbon–-carbon bonds formed (solid line) and broken (dashed line) at the interface as a function of sliding distance. The difference between the two is the net increase in the number of bonds during a single slide. (B) Friction curves for an amorphous film sliding on a counterface that is fully or 100% hydrogen terminated (squares), 90% hydrogen terminated (circles), and 80% hydrogen terminated (triangles). (Reprinted Figures 9 and 10 with permission from Gao, G. T.; Mikulski, P. T.; Harrison, J. A. J. Am. Chem. Soc. 2002, 124, 7202–7209. Copyright 2002 by the American Chemical Society.)

B

shown in Figure 5A. The difference between these two curves represents the net increase in the number of C⫺C bonds. Sliding resulted in tribochemistry changing the nature of the interface and presumably the friction. The f versus FN curves (friction vs. load) for a diamond counterface that is 100%, 90%, or 80% hydrogen terminated are shown in Figure 5B. As the percent termination is reduced, the degree of passivation decreases, allowing more frequent C⫺C bonds to be formed. This raises the frictional forces due to the dissipation of distorting and breaking these bonds, plus restructuring of the amorphous film during sliding. Any energy dissipation during displacement shows up as a dissipative frictional force. An Example of Stress-Enhanced Dissolution Combined chemical and mechanical attack is most effective for material and particle removal in a wide variety of contexts; we already mentioned the importance of CMP in the semiconductor industry. Together, they provide an especially effective “one-two punch” to surfaces that can be exploited to produce desired structural features or, conversely, atomically-flat surfaces. Scanning probes are particularly valuable tools for the study of this synergism, being able to both localize the tribological stimulation and to image the resulting wear with nanometer-scale resolution (17–19). In many respects, the AFM tip can simulate a single asperity or abrasive particle interacting with nearly ideal substrates. Some 738


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work in our laboratory allows us to examine a model system involving stress-enhanced dissolution of steps on a single crystal of CaCO3. Calcite is readily imaged by AFM in aqueous solutions (20). The dissolution and growth of calcite crystals in aqueous solution has been previously studied by AFM (21–28) and by other means (29–33). The basic phenomena where ions are removed from a typical crystal surface are shown in Figure 6. The removal of a cluster of ions from a terrace to nucleate a pit is the hardest in terms of overcoming a substantial activation-energy barrier. The presence of a dislocation at or near the surface greatly lowers this barrier; thus, etch pits often nucleate at dislocations. The formation of a double kink (basically a tiny “chunk” out of a perfect step edge) requires less energy and is the necessary precursor for dissolving a perfect step. Finally, removal of ions from a single kink is the easiest (lowest activation energy). Under aggressive solution chemistry, we therefore see that the rate-limiting step for step dissolution is the formation of double kinks. We have shown that dramatic corrosive wear can be induced by scanning the AFM tip back and forth across the edge of a naturally-occurring etch pit at high contact forces (18). Indenting the surface with an AFM tip near the edge of a etch pit also locally enhanced dissolution along steps near the tip. We attribute these effects to increased rates of doublekink nucleation in the strain field of the AFM tip (18). Spontaneously-nucleated etch pits on calcite, often one atomic layer deep, typically form parallelograms bounded by

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kink propagation (easy!)

single kink pit nucleation (hard!)

double kink nucleation (medium) double kink

Figure 6. Schematic representation of a single crystal surface with one atomic step undergoing dissolution. The removal of ions from a perfect terrace (pit nucleation) is shown on the left. Double-kink nucleation is shown occurring on the step edge in the lower position and single-kink propagation (removal of ions at a single-kink site) is shown in the higher position.

Figure 7. AFM image of a slow step on calcite after 3800 linear scans at a normal force of FN = 160 nN along the white line.

A

in flowing 60 µM solution

under "no flow" conditions (more saturated)

B

1.4

1.2

1.2

Growth Rate / (nm sⴚ1)

Growth Rate / (nm sⴚ1)

two pairs of crystallographically distinct steps. During steadystate dissolution, one pair moves much more rapidly than the other (25). We designate these steps “fast steps” and “slow steps,” respectively. Physically, the difference between fast and slow steps is related to the inclination of the plane of the carbonate ions relative to the sample surface, a steric effect. The rate-limiting step in pit growth is believed to be doublekink nucleation along the pit edges (25); the weakly-bound ions at the resulting kinks are readily incorporated into solution, resulting in rapid kink motion to the corners of the pit. Fast steps are more vulnerable to dissolution than slow steps because the CO32− ions along fast steps are more exposed to the surrounding water. This lowers the activation energy for double-kink nucleation (ion removal) on fast steps. A similar model was employed by Hirth and Pound to describe evaporation from crystal surfaces (34). Drawing the AFM tip back and forth across the edge of a one-monolayer-deep etch pit creates a wear pattern that can be directly interpreted in terms of double-kink nucleation. The geometry of the experiment and resulting features are shown in Figure 7. The path of the AFM tip during wear is marked by the white line. The maximum step displacement in the scanned region, ∆x, was measured from the end of the “wear track” to the line defined by the unperturbed portions of the original step (as far as possible from the wear track). Similar treatments on flat terraces (away from steps) had no detectable effect on the surface. Likewise, repeated linear scans across cleavage steps on dry calcite surfaces (in ambient air) had no effect when imaged on this scale. This synergism between the corrosive environment and mechanical loading clearly marks this as an example of corrosive tribology. The geometry of the “wear track” in Figure 7 illustrates two important features of molecular-scale dissolution. The jogs along the edges of the wear track reflect the tendency of atomic-scale kinks to aggregate into larger structures. Further, the two edges of the wear track show significantly different patterns of jogs, reflecting the different propagation behavior of crystallographically-distinct kinks along these steps. These differences are also responsible for the marked contrast in dissolution along the two halves of the original step. Dissolution along the portion of the original step to the left of the wear track (accomplished by kinks moving in the +[100] direction) has been much more rapid than dissolution along the portion of the original step to the right of the wear track (accomplished by kinks moving in the ᎑[100] direction). Analysis of material dissolution after wear track formation suggests that the jogs produced by wear are especially vulnerable to dissolution and play an important role in the planarization of stepped material. This experimental geometry was chosen because the length of the wear track (∆x in Figure 7) is quantitatively related to the rate of double-kink nucleation where the AFM tip crosses the step. Further, the wear track growth rate (∆x∆t) is a strong function of contact force. Plots of growth rate versus contact force for two solution concentrations are shown in Figure 8. These measurements employed 500 × 500-nm2 scans acquired at a scan rate of 24 Hz (tip velocity of 12 µms). The dark lines in Figure 8 represent a least squares fit of the data to a model function described below (an exponential function of the surface stress). Growth-rate measurements taken with different cantilevers show a high degree of consis-

1.0 0.8 0.6

slow steps

0.4 0.2 0.0

1.0

0.8

fast steps

0.6

0.4

slow steps

0.2

0.0 0

20

40

60

80

100 120

Contact Force / nN

150

200

240

Contact Force / nN

Figure 8. Wear track growth rate versus contact force (A) under flowing, 60 µM solution and (B) in more saturated solution (obtained by turning off flow) The data points represented by different symbols were made on different calcite samples with different cantilevers. The dark line is a least squares fit of eq 2 to the data.

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tency, as indicated by the data points represented by different symbols in Figure 8A. Each symbol represents measurements made on different days, with different calcite samples (from the same block) and cantilevers (from the same wafer). Wear tracks across fast steps grow much faster than wear tracks across slow steps. At the low solution concentration employed in Figure 8A (60 µM solution flowing at ∼10 µLs), wear tracks across fast steps grew too quickly for practical measurements. We therefore reduced the growth velocity by providing a more saturated solution, where a certain fraction of the nucleated double kinks are annihilated by redeposition of material from solution. Even at these higher solution concentrations, the AFM tip effectively mixes the nearby solution, preventing the development of concentration gradients that would complicate analysis. The resulting wear track growth rates are shown in Figure 8B, where a high degree of saturation was provided by stopping the flow of solution for about 30 minutes. Under these conditions, a contact force of 270 nN is required to produce growth rates on slow steps comparable to 70 nN in flowing solution. Nevertheless, the strong dependence of growth rate on contact force confirms that reaction-limited conditions prevail; that is, wear track growth is not limited by concentration gradients. Over most of the range of contact forces probed in Figure 8B, wear tracks across fast steps grew at least twice as fast as wear tracks across slow steps. Thus fast steps are considerably more vulnerable to tribologicallyenhanced dissolution than slow steps. We have observed similar, strong enhancements in dissolution during 2D AFM imaging (18). However, 2D scanning nucleates kinks at many points along the step; mutual annihilation of kinks nucleated at different points along the step make it difficult to infer the rate of kink nucleation from the step velocity. In contrast, kinks nucleated by linear scanning are formed along a narrow portion of the step and propagate away from this point in opposite directions. At the highest contact forces employed in this work, the average number of double kinks nucleated per scan is about 0.2, which corresponds to about 5 per second. This allows sufficient time for kinks nucleated along one row of ions to propagate away from the line scan before the next kink is nucleated, so that the next kink is nucleated along a new row. Then the total number of nucleated kinks can be estimated by dividing the length of the wear track, ∆x, by the distance between ionic rows (0.32 nm). Despite the high stresses applied by the AFM tip, we see no evidence for plastic deformation in this work or in AFM tip indentation experiments (18). The lowest contact forces employed in this work (15 nN) correspond to average compressive stresses of about 2 GPa; Vickers indentation (which employs millimeter-sized tips) at these stresses would produce an indent some tens of micrometers across (35). We attribute the absence of AFM-induced deformation to the small size of the AFM tip (tip radius ∼40 nm). Deformation is strongly hindered when the indentor is smaller than a typical slip band (usually ∼1 µm) (36). Deformation is also hindered at high strain rates (37), such as those associated with the motion of the tip across the surface. The absence of a threshold stress for the onset of enhanced dissolution also argues against dislocation emission and twinning as possible sources of double kinks. We conclude that plastic deforma740


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tion does not contribute to mechanically enhanced dissolution under these conditions. In terms of the available mechanical energy, the operation of mechanical effects is striking. At the highest contact forces employed (assuming elastic interactions only), the total work done by the tip on the substrate is less than 200 eV, and this mechanical energy is distributed over thousands of bonds. Further, double-kink nucleation is not likely under the center of the tip, where the stresses are highest, because the compressive stresses there hinder the escape of solvated ions. The (albeit weaker) tensile stresses along the surface surrounding the AFM tip are much more likely to promote dissolution. Stress effects are strongly enhanced along steps, where surface ions are less constrained by surrounding ions. Ion displacement can play a key role in volume-activated processes, where the work done (force × displacement) can directly reduce the binding energy. The magnitude of the stresses adjacent to the AFM tip can be estimated for the case of isotropic, elastic behavior. The maximum tensile stress involves the radial component, σr, along the circle where the AFM tip contacts the substrate. Double-kink nucleation will be enhanced over a modest range of distances from edge of tip contact (a few tip radii, from Saint Venant’s principle), so that the relevant average stress will be somewhat lower. This suggests that mechanical enhancements are insensitive to variations in the geometry of the AFM tip itself, but also introduces some uncertainty in the value of the (average) stress responsible for enhanced dissolution. The peak tensile stress given by the Hertz relation for an infinitely stiff, spherical tip is (38) 1

σr

1 − 2ν 2FN E = π 9 1 − ν2

(

3

2

)

(2)

2 2

r

where E and ν are Young’s modulus and Poisson’s ratio, respectively, for the substrate; FN is normal force between the sphere and substrate; and r is the sphere radius. σr is relatively insensitive to errors in the contact force (FN13 dependence) and is somewhat more sensitive to errors in the tip radius (r –2/3). To avoid the complications of material anisotropy, we use technical moduli (directionally averaged values) appropriate for CaCO3: E = 81 GPa, ν = 0.32 (39). For example, a tip radius of curvature r = 40 nm and an applied normal force of 100 nN yields a maximum radial stress of about 560 MPa. The dependence of the wear track growth rate (expressed as a velocity, V ) on contact force is readily modeled with a Zhurkov–Arrhenius expression (40) V = Vo exp −

E act − v * σ kBT

= Vo ′ exp

v* σ kBT

(3)

where Vo is the appropriate pre-exponential, Eact is the zerostress activation energy for double-kink nucleation, and v* is an activation volume. The best-fit curve of eq 3 to the data of Figure 8A (flowing solution), using the stresses given by eq 1, is shown by the dark lines in Figure 8. The best-fit values of the parameters correspond to Vo´ ≈ 6 ± 3 pm/s [where

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Figure 9. A sequence of AFM images of a pit in calcite with two atomic layer deep features at different times: (a) 0 s, (b) 343 s, and (c) 690 s. Six continuous scans filled in the pit in a solution concentration of σ = 1.5. Normal scanning force is 7 nN and scan rate was 7 mm/s. Figure b shows that the bottom pit layer filled in almost twice as fast as the top layer.

Vo´ = Vo exp(᎑EactkBT )] and v* ≈ 3.7 ± 0.3 × 10᎑29 m3, respectively. This activation volume is slightly larger than the average volume per ion in the CaCO3 lattice (3.3 × 10᎑29 m3), making it reasonable to suppose that this activation volume corresponds to the displacement of one or perhaps two ions from a step site. (The CO32− ion is considerably larger than the Ca2+ ion.) We note that the displacement of ions in flat terrace sites is limited by the surrounding ions; this may explain why scratching does not nucleate new etch pits over the range of contact forces used here. The large size of the CO32− ion and the fact that a component C⫺O bond is directed into the solution would make it especially vulnerable to combined mechanical and chemical effects. A similar analysis of the wear track growth rates at slow steps under “no flow” conditions (Figure 8B) yields v* ≈ 3.9 ± 0.5 × 10᎑29 m3. The agreement with v* under flowing solution is well within the numerical uncertainty of the curve fitting procedure. This agreement is consistent with the expectation that the degree of saturation controls the lifetime of nucleated kinks and not the (stress-enhanced) nucleation rate. The best-fit value for v* for dissolution along fast steps is somewhat larger, v* ≈ 6.0 ± 0.5 × 10᎑29 m3. A higher activation volume is consistent with the reduced steric constraint experienced by CO32− ions along fast steps, which would allow for larger displacements at a given stress and render them more vulnerable to water attack. An estimate of the activation energy for double-kink nucleation at zero stress can be derived from eq 3 assuming that Vo corresponds to a typical “attempt frequency,” fo, multiplied by the step displacement per successful attempt (one lattice spacing: 0.32 nm). Setting fo equal to typical vibrational frequencies (1013 s᎑1), the measured pre-exponential (Vo´ in eq 3) at T = 293 K corresponds to an activation energy of 0.8 ± 0.2 eV; a plausible value based on a simple calculation of the energy to remove a neutral CaCO3 molecule from a one dimensional chain of Ca2+ and CO32− ions and taken to fully solvated Ca2+ and CO32− ions. At the highest stresses employed in this work (corresponding to a normal force of 270 nN), this activation energy for double-kink nucleation is reduced by about 0.2 eV. Thus, it is reasonable to interpret the observed step dissolution in terms of a thermally-activated process. In addition, the Zhurkov–Arrhenius description of the observed stress www.JCE.DivCHED.org

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dependence of the wear track growth also appears to be valid. We point out that crack velocities in environmental crack growth (41) often display a similar dependence on stress intensity, although in this case the relation between stress intensity and stress at the crack tip can be very difficult to deduce. We have been able to reverse this tip-induced dissolution process in calcite, that is, to generate tip-induced deposition. This can be achieved by continuously scanning at low normal force (FN < 50 nN) in supersaturated solutions. Scanning over entire etch pits causes the pit to be filled. The images in Figure 9 show a sequence of such tip-induced growth produced in six continuous scans at FN = 7 nN in a solution concentration of σ = 1.5. Under these conditions, the etch pits gradually disappear, eventually yielding an atomicallysmooth surface with no signs of defects. Images of nearby areas acquired before and after the images in Figure 9 show adjacent rhombehedral pits that were essentially unchanged during the acquisition of the images in Figure 9. At lower superaturations, scanning-induced deposition was minimal or absent. At higher supersaturations, deposition (in the form of continuous step motion) was also observed a few nanometers to each side of the scanned regions, however at a rate much slower than that induced directly under the tip. These observations indicated that the combination of scanning and chemistry can locally deposit material at preexisting etch pits to produce a high quality, smooth surface on the nanometer scale. The carbonate ions along the calcite cleavage steps partially overlap one another, somewhat like shingles on a roof. It is relatively easy to add shingles to a partially shingled roof working from bottom to top; each new shingle goes on top of previously shingled material. Conversely, adding shingles to the bottom of a previously shingled patch of roof is quite difficult, if the same overlap is required. New shingles must slide under the old ones. Similarly, carbonate ions are relatively easy to add to (or remove from) on the fast steps, but relatively difficult to add to the slow steps. The overall model for this tip-induced growth is that the tip acts as a broom, sweeping ions sorbed on the terraces above the step edge, raising the degree of supersaturation right where the growth occurs. Experimental evidence of this model has been presented for another study of tip-induced growth by Hariadi et al. (42).

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Conclusion We have presented some of the basic issues and motivation for use of scanning probes in this exciting area of nanotribology. Only a few examples of recent results were presented. There still remain numerous fundamental studies to be made and a wide range of applications to technology to explore. For those interested in further reading, review articles and texts on nanotribology can be found in refs 43–49. Acknowledgements The author would like to thank Forrest Stevens, Ann McEvoy, Steve Langford, and Rizal Hariadi for helpful discussions. Part of this work was supported by the National Science Foundation under Grant CMS-0409861. Literature Cited 1. Scanning Probe Microscopy and Spectroscopy: Theory, Techniques, and Applications; Bonnell, D., Ed.; Wiley VCH: New York, 2000. 2. Krim, J.; Solina, D.; Chiarello, R. Phys. Rev. Lett. 1991, 66, 181–184. 3. Ringlein, J.; Robbins, M. O. Am. J. Phys. 2004, 72, 884–891. 4. Beyond the Molecular Frontier: Challenges for Chemistry and Chemical Engineering Committee on Challenges for the Chemical Sciences in the 21st Century; National Research Council; National Academies Press: Washington, DC, 2003. 5. Roberts, B. Advanced Semiconductor Manufacturing Conference and Workshop, 1992. ASMC 92 Proceedings. IEEE/ SEMI 1992; pp 206–210 6. Meyer, G.; Amer, N. M. Appl. Phys. Lett. 1990, 57, 2089– 2091. 7. Nie, H. Y.; Walzak, M. J.; McIntyre, N. S.; El-Sherik, A. M. Appl. Surf. Sci. 1999, 144–145, 633–637. 8. Mate, C. M.; McClelland, G. M.; Erlandsson, R.; Chiang, S. Phys. Rev. Lett. 1987, 59, 1942–1945. 9. Tománek, D.; Zhong, W.; Thomas, H. Europhys. Lett. 1991, 15, 887. 10. Socoliuc, A.; Bennewitz, R.; Gnecco, E.; Meyer, E. Phys. Rev. Lett. 2004, 92, 134301. 11. Harrison, J. A.; Stuart, S. J.; Brenner, D. W. In Handbook of Micro/NanoTribology; Bhushan, B., Ed.; CRC Press; Boca Raton, FL, 1999. 12. Perry, M. D.; Harrison, J. A. Langmuir 1996, 12, 4552–4556. 13. Shimizuy, J.; Eday, H.; Yoritsunez, M.; Ohmurax, E. Nanotechnology 1998, 9, 118–123. 14. Zhang, L. C.; Johnson, K. L.; Cheong, W. C. D. Tribology Lett. 2001, 10, 23–28. 15. Gao, J.; Luedtke, W. D.; Gourdon, D.; Ruths, M.; Israelachvili, J. N.; Landman, U. J. Phys. Chem. B 2004, 108, 3410–3425. 16. Gao, G. T.; Mikulski, P. T.; Harrison, J. A. J. Am. Chem. Soc. 2002, 124, 7202–7209. 17. Nakahara, S.; Langford, S. C.; Dickinson, J. T. Tribology Lett. 1995, 1, 277–300.

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