19Friction, Scratching/Wear,

Indentation, andLubrication Using

Scanning Probe Microscopy

19.1 Introduction 19.2 Description of AFM/FFM and Various Measurement

TechniquesSurface Roughness and Friction Force Measurements • Adhesion Measurements • Scratching, Wear, and Fabrication/Machining • Surface Potential Measurements • Nanoindentation Measurements • Boundary Lubrication Measurements

19.3 Friction and AdhesionAtomic-Scale Friction • Microscale Friction • Comparison of Microscale and Macroscale Friction Data • Effect of Tip Radii and Humidity on Adhesion and Friction

19.4 Scratching, Wear, and Fabrication/MachiningNanoscale Wear • Microscale Scratching • Microscale Wear • Nanofabrication/Nanomachining

19.5 IndentationPicoindentation • Nanoscale Indentation

19.6 Boundary Lubrication19.7 Closure

19.1 Introduction

The atomistic mechanisms and dynamics of the interactions of two materials during relative motionneed to be understood in order to develop a fundamental understanding of adhesion, friction, wear,indentation, and lubrication processes. At most solid–solid interfaces of technological relevance, contactoccurs at many asperities. Consequently, the importance of investigating single asperity contacts in studiesof the fundamental micromechanical and tribological properties of surfaces and interfaces has long beenrecognized. The recent emergence and proliferation of proximal probes, in particular scanning probemicroscopies (the scanning tunneling microscope and the atomic force microscope) and the surface forceapparatus, and of computational techniques for simulating tip–surface interactions and interfacial prop-erties, has allowed systematic investigations of interfacial problems with high resolution as well as waysand means for modifying and manipulating nanoscale structures. These advances have led to the appear-ance of the new field of micro/nanotribology, which pertains to experimental and theoretical investiga-tions of interfacial processes on scales ranging from the atomic- and molecular- to the microscale,occurring during adhesion, friction, scratching, wear, nanoindentation, and thin-film lubrication at

Bharat BhushanThe Ohio State University

sliding surfaces (Singer and Pollock, 1992; Persson and Tosatti, 1996; Bhushan, 1995, 1997, 1998a,b,1999a,b,c; Bhushan et al., 1995a; Guntherodt et al., 1995).

The micro/nanotribological studies are needed to develop fundamental understanding of interfacialphenomena on a small scale and to study interfacial phenomena in micro- and nanostructures used inmagnetic storage systems, microelectromechanical systems (MEMS), and other applications (Bhushan,1996, 1997, 1998a). Friction and wear of lightly loaded micro/nanocomponents are highly dependent onsurface interactions (few atomic layers). These structures are generally lubricated with molecularly thinfilms. Micro/nanotribological studies are also valuable in a fundamental understanding of interfacialphenomena in macrostructures to provide a bridge between science and engineering.

The surface force apparatus (SFA), the scanning tunneling microscope (STM), and atomic force andfriction force microscopes (AFM and FFM) are widely used in micro/nanotribological studies. Typicaloperating parameters are compared in Table 19.1. The SFA was developed in 1968 and is commonlyemployed to study both static and dynamic properties of molecularly thin films sandwiched between twomolecularly smooth surfaces. The STM, developed in 1981, allows imaging of electrically conductingsurfaces with atomic resolution, and has been used for imaging clean surfaces as well as lubricantmolecules. The introduction of the atomic force microscope in 1985 provided a method for measuringultra-small forces between a probe tip and an engineering (electrically conducting or insulating) surface,and has been used for topographical measurements of surfaces on the nanoscale, as well as for adhesionand electrostatic force measurements. Subsequent modifications of the AFM led to the development ofthe friction force microscope (FFM), designed for atomic-scale and microscale studies of friction. Thisinstrument measures forces transverse to the surface. The AFM is also being used for investigations ofscratching, wear, indentation, detection of transfer of material, boundary lubrication, and fabricationand machining. Meanwhile, significant progress in understanding the fundamental nature of bondingand interactions in materials, combined with advances in computer-based modeling and simulationmethods, has allowed theoretical studies of complex interfacial phenomena with high resolution in spaceand time. Such simulations provide insights into atomic-scale energetics, structure, dynamics, thermo-dynamics, transport, and rheological aspects of tribological processes.

The nature of interactions between two surfaces brought close together, and those between two surfacesin contact as they are separated, have been studied experimentally with the surface force apparatus. Thishas led to a basic understanding of the normal forces between surfaces and the way in which these aremodified by the presence of a thin liquid or polymer film. The frictional properties of such systems havebeen studied by moving the surfaces laterally, and such experiments have provided insights into themolecular-scale operation of lubricants such as thin liquid or polymer films. Complementary to thesestudies are those in which the AFM or FFM is used to provide a model asperity in contact with a solidor lubricated surface. These experiments have demonstrated that the relationship between friction and

TABLE 19.1 Comparison of Typical Operating Parameters in SFA, STM, and AFM/FFM Used for Micro/Nanotribological Studies

Operating Parameter SFA STM* AFM/FFM

Radius of mating surface/tipRadius of contact areaNormal loadSliding velocity

Sample limitations

~10 mm10–40 µm10–100 mN0.001–100 µm/s

Typically atomically smooth, optically transparent mica; opaque ceramic, smooth surfaces can also be used

5–100 nmN/AN/A0.02–2 µm/s

(scan size ~1 nm × 1 nm to 125 µm x 125 µm; scan rate <1–122 Hz)

Electrically conducting samples

5–100 nm0.05–0.5 nm<0.1 nN–500 nN0.02–2 µm/s

(scan size ~1 nm × 1 nm to 125 µm × 125 µm; scan rate <1–122 Hz)

None

* Can only be used for atomic-scale imaging

surface roughness is not always simple or obvious. AFM studies have also revealed much about thenanoscale nature of intimate contact during wear and indentation.

In this chapter, we present a review of significant aspects of micro/nanotribological studies conductedusing AFM/FFM.

19.2 Description of AFM/FFM and Various Measurement Techniques

An atomic force microscope (AFM), developed by Gerd Binnig and his colleagues in 1985, is capable ofinvestigating surfaces of scientific and engineering interest on an atomic scale (Binnig et al., 1986, 1987).The AFM relies on a scanning technique to produce very high-resolution, three-dimensional images ofsample surfaces. AFM measures ultrasmall forces (less than 1 nN) present between the AFM tip surfacemounted on a flexible cantilever beam and a sample surface. These small forces are measured by mea-suring the motion of a very flexible cantilever beam having an ultrasmall mass, by a variety of measure-ment techniques including optical deflection, optical interference, capacitance, and tunneling current.The deflection can be measured to within 0.02 nm, so for a typical cantilever force constant of 10 N/m,a force as low as 0.2 nN can be detected. In the operation of high-resolution AFM, the sample is generallyscanned rather than the tip because any cantilever movement would add vibrations. AFMs are nowavailable for measurement of large samples, where the tip is scanned and the sample is stationary. Toobtain atomic resolution with AFM, the spring constant of the cantilever should be weaker than theequivalent spring between atoms. A cantilever beam with a spring constant of about 1 N/m or lower isdesirable. Tips have to be as sharp as possible. Tips with a radius ranging from 10 to 100 nm are commonlyavailable.

Subsequent modifications to AFM led to the development of the friction force microscope (FFM) orthe lateral force microscope (LFM), designed for atomic-scale and microscale studies of friction (Mateet al., 1987; Bhushan and Ruan, 1994; Ruan and Bhushan, 1994a,b,c; Bhushan et al., 1994; Bhushan et al.,1995a; Scherer et al., 1999) and lubrication (Bhushan et al., 1995b; Koinkar and Bhushan, 1996a,b). Thisinstrument measures lateral or friction forces (in the plane of sample surface and in the direction ofsliding). By using a standard or a sharp diamond tip mounted on a stiff cantilever beam, AFM is alsoused in investigations of scratching and wear (Bhushan et al., 1994; Bhushan and Koinkar, 1994a; Koinkarand Bhushan, 1997a; Bhushan, 1999c; Sundararajan and Bhushan, 2000a), indentation (Bhushan et al.,1994; Bhushan and Koinkar, 1994a; Bhushan et al., 1996; Bhushan 1999c), and fabrication/machining(Bhushan et al., 1994).

Surface roughness, including atomic-scale imaging, is routinely measured using the AFM (Figure 19.1).Adhesion, friction, wear, and boundary lubrication at the interface between two solids with and withoutliquid films have been studied using AFM and FFM. Nanomechanical properties are also measured usingan AFM.

19.2.1 Surface Roughness and Friction Force Measurements

Simultaneous measurements of surface roughness and friction force can be made with commercialAFM/FFM. These instruments are available for measurements of small and large samples. In a smallsample AFM shown in Figure 19.1a, the sample is mounted on a PZT tube scanner, which consists ofseparate electrodes to scan precisely the sample in the x-y plane in a raster pattern and to move thesample in the vertical (z) direction. A sharp tip at the end of a flexible cantilever is brought in contactwith the sample. Normal and frictional forces being applied at the tip–sample interface are measuredusing a laser beam deflection technique. A laser beam from a diode laser is directed by a prism onto theback of a cantilever near its free end, tilted downward at about 10 degrees with respect to the horizontalplane. The reflected beam from the vertex of the cantilever is directed through a mirror onto a quadphotodetector (split photodetector with four quadrants). The differential signal from the top and bottomphotodiodes provides the AFM signal which is a sensitive measure of the cantilever vertical deflection.

Topographic features of the sample cause the tip to deflect in the vertical direction as the sample isscanned under the tip. This tip deflection will change the direction of the reflected laser beam, changingthe intensity difference between the top and bottom sets of photodetectors (AFM signal). In the AFMoperating mode called the height mode, for topographic imaging or for any other operation in whichthe applied normal force is to be kept constant, a feedback circuit is used to modulate the voltage appliedto the PZT scanner to adjust the height of the PZT, so that the cantilever vertical deflection (given bythe intensity difference between the top and bottom detector) will remain constant during scanning. ThePZT height variation is thus a direct measure of the surface roughness of the sample.

FIGURE 19.1 Schematics (a) of a commercial small sample atomic force microscope/friction force microscope(AFM/FFM), (b) of tapping mode used for surface topography measurements, and (c) of a large sample AFM/FFM.

Many multimode AFMs can be used for topography measurements in the so-called tapping mode,also referred to as dynamic force microscopy. In the tapping mode, during scanning over the surface, thecantilever is vibrated by a piezo mounted above it, and the oscillating tip slightly taps the surface at theresonant frequency of the cantilever (70 to 400 Hz) with a 20- to 100-nm oscillating amplitude introducedin the vertical direction with a feedback loop keeping the average normal force constant (Figure 19.1b).The oscillating amplitude is kept large enough so that the tip does not get stuck to the sample becauseof adhesive attractions. The tapping mode is used in topography measurements to minimize effects offriction and other lateral forces and to measure topography of soft surfaces.

For measurement of friction force being applied at the tip surface during sliding, left-hand and right-hand sets of quadrants of the photodetector are used. In the so-called friction mode, the sample is scannedback and forth in a direction orthogonal to the long axis of the cantilever beam. A friction force betweenthe sample and the tip will produce a twisting of the cantilever. As a result, the laser beam will be reflectedout of the plane defined by the incident beam and the beam reflected vertically from an untwistedcantilever. This produces an intensity difference of the laser beam received in the left-hand and right-hand sets of quadrants of the photodetector. The intensity difference between the two sets of detectors(FFM signal) is directly related to the degree of twisting and hence to the magnitude of the friction force.One problem associated with this method is that any misalignment between the laser beam and thephotodetector axis would introduce error in the measurement. However, by following the proceduresdeveloped by Ruan and Bhushan (1994a), in which the average FFM signal for the sample scanned intwo opposite directions is subtracted from the friction profiles of each of the two scans, the misalignmenteffect is eliminated. This method provides three-dimensional maps of friction force. By following thefriction force calibration procedures developed by Ruan and Bhushan (1994a), voltages correspondingto friction forces can be converted to force units. Coefficient of friction is obtained from the slope of

FIGURE 19.1 (continued)

friction force data measured as a function of normal loads typically ranging from 10 to 150 nN. Thisapproach eliminates any contributions due to the adhesive forces. For calculation of coefficient of frictionbased on a single point measurement, friction force should be divided by the sum of applied normalload and intrinsic adhesive force. Furthermore, it should be pointed out that for a single asperity contact,the coefficient of friction is not independent of load (see discussion later).

In a large-sample AFM, both force sensors using the optical deflection method and scanning unit aremounted on the microscope head (Figure 19.1c). Lateral resolution of this design is somewhat poorerthan the design in Figure 19.1a in which the sample is scanned instead of the cantilever beam. Theadvantage of the large-sample AFM is that large samples can be measured readily.

Topographic measurements in the contact mode are typically made using a sharp, microfabricatedsquare pyramidal Si3N4 tip on a cantilever beam (Figure 19.2a) with normal stiffness of about 0.5 N/mat a normal load of about 10 nN, and friction measurements are carried out in the load range of 10 to150 nN. Topography measurements in the tapping mode utilize a stiff cantilever with high resonantfrequency; typically a square-pyramidal etched single-crystal silicon tip, with a tip radius ranging from10 to 50 nm, mounted on a stiff rectangular silicon cantilever beam with a normal stiffness of about50 N/m, is used. To study the effect of radius of a single asperity (tip) on adhesion and friction, micro-spheres of silica with radii ranging from about 4 to 15 µm are attached with epoxy at the ends of tips ofSi3N4 cantilever beams. Optical micrographs of two of the microspheres mounted at the ends of triangularcantilever beams are shown in Figure 19.2b.

The tip is scanned in such a way that its trajectory on the sample forms a triangular pattern(Figure 19.3). Scanning speeds in the fast and slow scan directions depend on the scan area and scan

FIGURE 19.2 (a) SEM micrographs of a PECVD Si3N4 cantilever beam with tip and a stainless steel cantilever beamwith diamond tip, and (b) optical micrographs of commercial Si3N4 tip and two modified tips showing SiO2 spheresmounted over the sharp tip, at the end of the triangular Si3N4 cantilever beams (radii of the tips are given in the figure).

frequency. Scan sizes ranging from less than 1 nm × 1 nm to 125 µm × 125 µm and scan rates from lessthan 0.5 to 122 Hz can typically be used. Higher scan rates are used for smaller scan lengths. For example,scan rates in the fast and slow scan directions for an area of 10 µm × 10 µm scanned at 0.5 Hz are 10 µm/sand 20 nm/s, respectively.

19.2.2 Adhesion Measurements

Adhesive force measurements are performed in the so-called force calibration mode. In this mode, forcedistance curves are obtained (Figure 19.4). The horizontal axis gives the distance the piezo (and hence

(b)

FIGURE 19.2 (continued)

the sample) travels, and the vertical axis gives the tip deflection. As the piezo extends, it approaches thetip, which is at this point in free air and hence shows no deflection. This is indicated by the flat portionof the curve. As the tip approaches the sample within a few nanometers (point A), an attractive forceexists between the atoms of the tip surface and the atoms of the sample surface. The tip is pulled towardthe sample, and contact occurs at point B on the graph. From this point on, the tip is in contact withthe surface, and as the piezo extends further, the tip is further deflected. This is represented by the slopedportion of the curve. As the piezo retracts, the tip goes beyond the zero deflection (flat) line, because ofattractive forces (van der Waals forces and long-range meniscus forces), into the adhesive regime. Atpoint C in the graph, the tip snaps free of the adhesive forces and is again in free air. The horizontaldistance between points B and C along the retrace line gives the distance moved by the tip in the adhesiveregime. This distance multiplied by the stiffness of the cantilever gives the adhesive force. Incidentally,the horizontal shift between the loading and unloading curves results from the hysteresis in the PZT tube.

19.2.3 Scratching, Wear, and Fabrication/Machining

For microscale scratching, microscale wear, nanofabrication/nanomachining, and nanoindentation hard-ness measurements, an extremely hard tip is required. A three-sided pyramidal single-crystal naturaldiamond tip with an apex angle of 80° and a radius of about 100 nm mounted on a stainless steel cantileverbeam with normal stiffness of about 25 N/m is used at relatively higher loads (1 µN to 150 µN)(Figure 19.2a). For scratching and wear studies, the sample is generally scanned in a direction orthogonal

FIGURE 19.3 Schematic of triangular pattern trajectory of the tip as the sample (or the tip) is scanned in twodimensions. During scanning, data are recorded only during scans along the solid scan lines.

FIGURE 19.4 Typical force–distance curve for a contact between Si3N4 tip and single-crystal silicon surface inmeasurements made in the ambient environment. Contact between the tip and silicon occurs at point B; tip breaksfree of adhesive forces at point C as the sample moves away from the tip.

to the long axis of the cantilever beam (typically at a rate of 0.5 Hz) so that friction can be measuredduring scratching and wear. The tip is mounted on the beam such that one of its edges is orthogonal tothe long axis of the beam; therefore, wear during scanning along the beam axis is higher (about 2× to3×) than that during scanning orthogonal to the beam axis. For wear studies, typically an area of 2 µm ×2 µm is scanned at various normal loads (ranging from 1 to 100 µN) for a selected number of cycles.

Scratching can also be performed at ramped loads, and the coefficient of friction can be measuredduring scratching (Sundararajan and Bhushan, 2000a). A linear increase in the normal load approximatedby a large number of normal load increments of small magnitude is applied using a software interface(lithography module in Nanoscope III) that allows the user to generate controlled movement of the tipwith respect to the sample. The friction signal is tapped out of the AFM and is recorded on a computer.For most experiments, a scratch length of 25 µm and a velocity of 0.5 µm/s are used, and the number ofloading steps is usually taken to be 50.

Nanofabrication/nanomachining is conducted by scratching the sample surface with a diamond tip atspecified locations and scratching angles. The normal load used for scratching (writing) is on the orderof 1 to 100 µN with a writing speed on the order of 0.1 to 200 µm/s (Bhushan, 1995, 1998b, 1999a,b;Bhushan et al., 1994, 1995a).

19.2.4 Surface Potential Measurements

To detect wear precursors and to study the early stages of localized wear, the multimode AFM can beused to measure the potential difference between the tip and the sample by applying a DC bias potentialand an oscillating (AC) potential to a conducting tip over a grounded substrate in a Kelvin probemicroscopy or so-called nano-Kelvin probe technique (DeVecchio and Bhushan, 1998; Bhushan andGoldade, 2000a,b).

Mapping of the surface potential is made in the so-called lift mode (Figure 19.5). These measurementsare made simultaneously with the topography scan in the tapping mode, using an electrically conducting(nickel-coated single-crystal silicon) tip. After each line of the topography scan is completed, the feedbackloop controlling the vertical piezo is turned off, and the tip is lifted from the surface and traced over thesame topography at a constant distance of 100 nm. During the lift mode, a DC bias potential and anoscillating potential (3 to 7 Volts) is applied to the tip. The frequency of oscillation is chosen to be equalto the resonant frequency of the cantilever (~80 kHz). When a DC bias potential equal to the negativevalue of surface potential of the sample (on the order of ±2 Volts) is applied to the tip, it does not vibrate.During scanning, a difference between the DC bias potential applied to the tip and the potential of thesurface will create DC electric fields that interact with the oscillating charges (as a result of the ACpotential), causing the cantilever to oscillate at its resonant frequency, as in the tapping mode. However,a feedback loop is used to adjust the DC bias on the tip to exactly nullify the electric field, and thus thevibrations of the cantilever. The required bias voltage follows the localized potential of the surface. Thesurface potential was obtained by reversing the sign of the bias potential provided by the electronics(Bhushan and Goldade, 2000a,b). Surface and subsurface changes of structure and/or chemistry cancause changes in the measured potential of a surface. Thus, mapping of the surface potential after slidingcan be used for detecting wear precursors and studying the early stages of localized wear.

19.2.5 Nanoindentation Measurements

For nanoindentation hardness measurements, the scan size is set to zero and then a normal load is appliedto make the indents using the diamond tip. During this procedure, the tip is continuously pressed againstthe sample surface for about 2 seconds at various indentation loads. The sample surface is scanned beforeand after the scratching, wear, or indentation to obtain the initial and the final surface topography, at alow normal load of about 0.3 µN using the same diamond tip. An area larger than the indentation regionis scanned to observe the indentation marks. Nanohardness is calculated by dividing the indentation loadby the projected residual area of the indents.

Direct imaging of the indent allows one to quantify the piling up of ductile material around theindenter. However, it becomes difficult to identify the boundary of the indentation mark with greataccuracy. This makes the direct measurement of contact area somewhat inaccurate. A technique with thedual capability of depth-sensing and in situ imaging, which is most appropriate in nanomechanicalproperty studies, is used for accurate measurement of hardness with shallow depths (Bhushan, 1999a;Bhushan et al., 1996). This indentation system is used to make load-displacement measurement andsubsequently carry out in situ imaging of the indent, if required. The indentation system consists of athree-plate transducer with electrostatic actuation hardware used for direct application of normal loadand a capacitive sensor used for measurement of vertical displacement. The AFM head is replaced withthis transducer assembly while the specimen is mounted on the PZT scanner, which remains stationaryduring indentation experiments. Indent area and, consequently, hardness value can be obtained fromthe load-displacement data. The Young’s modulus of elasticity is obtained from the slope of the unloadingcurve.

Indentation experiments provide a single-point measurement of the Young’s modulus of elasticitycalculated from the slope of the indentation curve during unloading. Localized surface elasticity mapscan be obtained using a force modulation technique (Maivald et al., 1991; DeVecchio and Bhushan, 1997;Scherer et al., 1997). An oscillating tip is scanned over the sample surface in contact under steady andoscillating load. The oscillations are applied to the cantilever substrate with a bimorph (Figure 19.6a).For measurements, an etched silicon tip is first brought in contact with a sample under a static load of

FIGURE 19.5 Schematic of lift mode used to make surface potential measurement. The topography is collected intapping mode in the primary scan. The cantilever piezo is deactivated. Using topography information of the primaryscan, the cantilever is scanned across the surface at a constant height above the sample. An oscillating voltage at theresonant frequency is applied to the tip, and a feedback loop adjusts the DC bias of tip to maintain the cantileveramplitude at zero. The output of the feedback loop is recorded by the computer and becomes the surface potential map.(From Bhushan, B. (1999a), Handbook of Micro/Nanotribology, 2nd ed., CRC Press, Boca Raton, FL. With permission.)

50 to 300 nN. In addition to the static load applied by the sample piezo, a small oscillating (modulating)load is applied by a bimorph, generally at a frequency (about 8 kHz) far below that of the naturalresonance of the cantilever (70 to 400 kHz). When the tip is brought in contact with the sample, thesurface resists the oscillations of the tip, and the cantilever deflects. Under the same applied load, a stiffarea on the sample would deform less than a soft one; i.e., stiffer surfaces cause greater deflectionamplitudes of the cantilever (Figure 19.6b). The variations in the deflection amplitudes provide a measureof the relative stiffness of the surface. Contact analyses can be used to obtain a quantitative measure oflocalized elasticity of soft surfaces (DeVecchio and Bhushan, 1997). The elasticity data are collectedsimultaneously with the surface height data using a so-called negative lift mode technique. In this modeeach scan line of each topography image (obtained in tapping mode) is replaced with the tapping actiondisabled and with the tip lowered into steady contact with the surface.

FIGURE 19.6 Schematics (a) of the bimorph assembly, and (b) of the motion of the cantilever and tip as a resultof the oscillations of the bimorph for an infinitely stiff sample, an infinitely compliant sample, and an intermediatesample. The thin line represents the cantilever at the top cycle, and the thick line corresponds to the bottom of thecycle. The dashed line represents the position of the tip if the sample were not present or were infinitely compliant.dc, ds, and db are the oscillating (ac) deflection amplitude of the cantilever, penetration depth and oscillating (ac)amplitude of the bimorph, respectively. (From DeVecchio, D. and Bhushan, B. (1997), Localized surface elasticitymeasurements using an atomic force microscope, Rev. Sci. Instrum., 68, 4498-4505. With permission.)

19.2.6 Boundary Lubrication Measurements

For nanoscale boundary lubrication studies, the samples are typically scanned using a Si3N4 tip over anarea of 1 µm × 1 µm at a normal load of about 300 nN, in a direction orthogonal to the long axis of thecantilever beam. The samples are generally scanned with a scan rate of 1 Hz and a scanning speed of2 µm/s. Coefficient of friction is monitored during scanning for a desired number of cycles. After ascanning test, a larger area of 2 µm × 2 µm is scanned at a normal load of 40 nN to observe any wear scar.

19.3 Friction and Adhesion

19.3.1 Atomic-Scale Friction

To study friction mechanisms on an atomic scale, a well-characterized freshly cleaved surface of highlyoriented pyrolytic graphite (HOPG) has been studied by Mate et al. (1984) and Ruan and Bhushan(1994b). The atomic-scale friction force of HOPG exhibited the same periodicity as that of the corre-sponding topography (Figure 19.7a), but the peaks in friction and those in topography were displacedrelative to each other (Figure 19.7b). A Fourier expansion of the interatomic potential was used tocalculate the conservative interatomic forces between atoms of the FFM tip and those of the graphitesurface. Maxima in the interatomic forces in the normal and lateral directions do not occur at the samelocation, which explains the observed shift between the peaks in the lateral force and those in thecorresponding topography. Furthermore, the observed local variations in friction force were explainedby variation in the intrinsic lateral force between the sample and the FFM tip (Ruan and Bhushan, 1994b).These variations may not necessarily occur as a result of an atomic-scale stick-slip process (Mate et al.,1984), but can be due to variation in the intrinsic lateral force between the sample and the FFM tip.

19.3.2 Microscale Friction

Local variations in the microscale friction of cleaved graphite are observed. These arise from structuralchanges that occur during the cleaving process (Ruan and Bhushan, 1994c). The cleaved HOPG surfaceis largely atomically smooth but exhibits line-shaped regions in which the coefficient of friction is morethan an order of magnitude larger (Figure 19.8). Transmission electron microscopy indicates that theline-shaped regions consist of graphite planes of different orientation, as well as of amorphous carbon.Differences in friction have also been observed for multiphase ceramic materials (Koinkar and Bhushan,1996c). Figure 19.9 shows the surface roughness and friction force maps of Al2O3–TiC (70 to 30 wt%).TiC grains have a Knoop hardness of about 2800 kg/mm2; therefore, they do not polish as much andresult in a slightly higher elevation (about 2 to 3 nm higher than that of Al2O3 grains). TiC grains exhibithigher friction force than Al2O3 grains. The coefficients of friction of TiC and Al2O3 grains are 0.034 and0.026, respectively, and the coefficient of friction of Al2O3–TiC composite is 0.03. Local variation infriction force also arises from the scratches present on the Al2O3–TiC surface. Meyer et al. (1992) alsoused FFM to measure structural variations of organic mono- and multilayer films. All of these measure-ments suggest that the FFM can be used for structural mapping of the surfaces. FFM measurements canbe used to map chemical variations, as indicated by the use of the FFM with a modified probe tip tomap the spatial arrangement of chemical functional groups in mixed organic monolayer films (Frisbieet al., 1994). Here, sample regions that had stronger interactions with the functionalized probe tipexhibited larger friction.

Local variations in the microscale friction of nominally rough, homogeneous surfaces can be signifi-cant, and are seen to depend on the local surface slope rather than the surface height distribution(Figure 19.10). This dependence was first reported by Bhushan and Ruan (1994) and Bhushan et al.(1994) and later discussed in more detail by Koinkar and Bhushan (1997b) and Sundararajan andBhushan (2000b). In order to show elegantly any correlation between local values of friction and surfaceroughness, surface roughness and friction force maps of a gold-coated ruling with somewhat rectangular

grids and a silicon grid with square pits were obtained (Figure 19.11) (Sundararajan and Bhushan (2000b).Figures 19.10 and 19.11 show the surface roughness map, the slopes of the roughness map taken along thesliding direction (surface slope map) and the friction force map for various samples. There is a strongcorrelation between the surface slopes and friction forces. For example, in Figure 19.11, friction force ishigh locally at the edge of the grids and pits with a positive slope, and is low at the edges with a negative slope.

We now examine the mechanism of microscale friction, which may explain the resemblance betweenthe slope of surface roughness maps and the corresponding friction force maps (Ruan and Bhushan,1994b,c; Bhushan and Ruan, 1994; Bhushan et al., 1994; Bhushan, 1999a,b; Sundararajan and Bhushan,2000b). There are three dominant mechanisms of friction; adhesive, adhesive and roughness (ratchet),and plowing. As a first order, we may assume these to be additive. The adhesive mechanism alone cannot

FIGURE 19.7 (a) Gray-scale plots of surface topography and friction force maps of a 1 nm × 1 nm area of freshlycleaved HOPG, showing the atomic-scale variation of topography and friction, and (b) schematic of superimposedtopography and friction maps from (a); the symbols correspond to maxima. Note the spatial shift between the twoplots. (From Ruan, J. and Bhushan, B. (1994b), Atomic-scale and microscale friction of graphite and diamond usingfriction force microscopy, J. Appl. Phys., 76, 5022-5035. With permission.)

explain the local variation in friction. Let us consider the ratchet mechanism (Makinson, 1948). Weconsider a small tip sliding over an asperity making an angle θ with the horizontal plane (Figure 19.12).The normal force W (normal to the general surface) applied by the tip to the sample surface is constant.The friction force F on the sample would be a constant µoW for a smooth surface if the friction mechanismdoes not change. For a rough surface shown in Figure 19.12, if the adhesive mechanism does not changeduring sliding, the local value of coefficient of friction would remain constant,

(19.1)

where S is the local friction force and N is the local normal force. However, the friction and normalforces are measured with respect to global horizontal and normal axes, respectively. The measured localcoefficient of friction µ1 in the ascending part is

(19.2)

FIGURE 19.8 (a) Surface roughness and (b) friction force maps at a normal load of 42 nN of freshly cleaved HOPGsurface against a Si3N4 FFM tip. Friction in the line-shaped region is over an order of magnitude larger than in thesmooth areas. (From Ruan, J. and Bhushan, B. (1994b), Atomic-scale and microscale friction of graphite and diamondusing friction force microscopy, J. Appl. Phys., 76, 5022-5035. With permission.)

µ =0 S N

µ = = µ +( ) − µ( ) µ + µ1 0 0 0 01F W tan tan ~ tan ,θ θ θ θfor small tan

indicating that in the ascending part of the asperity one may simply add the friction force and the asperityslope to one another. Similarly, on the right-hand side (descending part) of the asperity,

(19.3)

For a symmetrical asperity, the average coefficient of friction experienced by the FFM tip traveling acrossthe whole asperity is

(19.4)

FIGURE 19.9 Gray-scale surface roughness (σ = 0.80 nm) and friction force maps (mean = 7.0 nN, σ = 0.90 nN)for Al2O3-TiC (70 to 30 wt%) at a normal load of 138 nN. (From Koinkar, V.N. and Bhushan, B. (1996c), Micro-tribological studies of Al2O3-TiC, polycrystalline and single-crystal Mn–Zn ferrite and SiC head slider materials,Wear, 202, 110-122. With permission.)

µ = µ −( ) + µ( ) µ − µ2 0 0 01tan tan ~ tan ,θ θ θ θ for small tan 0

µ = µ + µ( )= µ +( ) − µ( ) µ +( ) µ

ave 1 2

02

02 2

02

2

1 1 1tan tan ~ tanθ θ θ θ, for small tan 0

Next we consider, the plowing component of friction with the tip sliding in either direction, which is

(19.5)

Because in the FFM measurements we notice little damage to the sample surface, the contribution byplowing is expected to be small, and the ratchet mechanism is believed to be the dominant mechanismfor the local variations in the friction force map. With the tip sliding over the leading (ascending) edgeof an asperity, the surface slope is positive; it is negative during sliding over the trailing (descending)edge of an asperity. Thus, measured friction is high at the leading edge of asperities and low at the trailing

FIGURE 19.10 Surface roughness map (σ = 4.4 nm), surface slope map taken in the sample sliding direction (thehorizontal axis; mean = 0.023, σ = 0.197), and friction force map (mean = 6.2 nN, σ = 2.1 nN) for a lubricated thin-film magnetic rigid disk for a normal load of 160 nN. (From Bhushan, B., Koinkar, V.N., and Ruan, J. (1994),Microtribology of magnetic media, Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol., 208, 17-29. With permission.)

µp ~ tanθ

edge. In addition to the slope effect, the collision of tip when encountering an asperity with a positiveslope produces additional torsion of the cantilever beam leading to higher measured friction force. Whenencountering an asperity with the same negative slope, however, there is no collision effect and henceno effect on torsion. This effect also contributes to the difference in friction forces when the tip scansup and down on the same topography feature. The ratchet mechanism and the collision effects thussemiquantitatively explain the correlation between the slopes of the roughness maps and friction mapsobserved in Figures 19.10 and 19.11. We note that in the ratchet mechanism, the FFM tip is assumed tobe small compared to the size of asperities. This is valid since the typical radius of curvature of the tips

FIGURE 19.11 Surface roughness map, surface slope map taken in the sample sliding direction (the horizontalaxis), and friction force map for (a) a gold-coated ruling (with somewhat rectangular grids with a pitch of 1 µm anda ruling step height of about 70 nm) at a normal load of 25 nN, and (b) a silicon grid (with 5 µm square pits ofdepth 180 nm and a pitch of 10 µm). (From Sundararajan, S. and Bhushan, B. (2000b), Topography-inducedcontributions to friction forces measured using an atomic force/friction force microscope, J. Appl. Phys., 88, in press.With permission.)

is about 10 to 50 nm. The radii of curvature of the asperities of the samples measured here (the asperitiesthat produce most of the friction variation) are found to be typically about 100 to 200 nm, which islarger than that of the FFM tip (Bhushan and Blackman, 1991). It is important to note that the measuredlocal values of friction and normal forces are measured with respect to global (and not local) horizontaland vertical axes, which are believed to be relevant in applications.

Next, we study the directionality effect on friction. During friction measurements, the friction forcedata from both the forward (trace) and backward (retrace) scans are useful in understanding the originsof the observed friction forces. Magnitudes of material-induced effects are independent of the scandirection, whereas topography-induced effects are different between forward and backward scanningdirections. Since the sign of the friction force changes as the scanning direction is reversed (because ofthe reversal of torque applied to the end of the tip), addition of the friction force data of the forwardand backward scan eliminates the material-induced effects while topography-induced effects remain.Subtraction of the data between forward and backward scans does not eliminate either effects(Figure 19.13) (Sundararajan and Bhushan, 2000b).

Due to the reversal of the sign of the retrace (R) friction force with respect to the trace (T) data; thefriction force variations due to topography are in the same direction (peaks in trace correspond to peaks

FIGURE 19.11 (continued)

in retrace). However, the magnitudes of the peaks in trace and retrace at a given location are different.An increase in the friction force experienced by the tip when scanning up a sharp change in topographyis more than the decrease in the friction force experienced when scanning down the same topographychange, partly because of collision effects discussed earlier. Asperities on engineering surfaces are asym-metrical, which also affects the magnitude of friction force in the two directions. Asymmetry in tip shapemay also have an effect on the directionality effect of friction. We notice from Figure 19.15 that sincemagnitude of surface slopes is virtually identical, the tip shape asymmetry should not have much effect.Because of the differences in the magnitude of friction forces in the two directions, subtracting the twofriction data yields a residual peak (Figure 19.14). From Figure 19.14a, we note that this effect occurs atall locations of significant topography changes.

In order to facilitate comparison of the directionality effect on friction, it is important to take intoaccount the sign change of the surface slope and friction force in the trace and retrace directions.Figure 19.15 shows topography, slope, and friction force data for the gold ruler and silicon grid in thetrace and retrace directions. The correlation between surface slope and friction forces is clear. The thirdcolumn in the figures shows retrace slope and friction data with an inverted sign (-retrace). Now we cancompare trace data with -retrace data. It is clear the friction experienced by the tip is dependent uponthe scanning direction because of surface topography. In addition to the effect of topographical changesdiscussed earlier, during surface finishing processes, material can be transferred preferentially onto oneside of the asperities, which also causes asymmetry and direction dependence. Reduction in local varia-tions and in directionality of friction properties requires careful optimization of surface roughnessdistributions and of surface finishing processes.

The directionality as a result of the surface asperities effect will also be manifested in macroscopicfriction data; that is, the coefficient of friction may be different in one sliding direction than in the otherdirection. Asymmetrical asperities accentuate this effect. The frictional directionality can also exist inmaterials with particles having a preferred orientation. The directionality effect in friction on a macroscaleis observed in some magnetic tapes. In a macroscale test, a 12.7-mm-wide polymeric magnetic tape waswrapped over an aluminum drum and slid in a reciprocating motion with a normal load of 0.5 N anda sliding speed of about 60 mm/s (Bhushan, 1997). The coefficient of friction as a function of slidingdistance in either direction is shown in Figure 19.16. We note that the coefficient of friction on amacroscale for this tape is different in different directions. Directionality in friction is sometimes observedon the macroscale; on the microscale this is the norm (Bhushan 1996, 1999a). On the macroscale, theeffect of surface asperities normally is averaged over a large number of contacting asperities.

FIGURE 19.12 Schematic illustration showing the effect of an asperity (making an angle θ with the horizontalplane) on the surface in contact with the tip on local friction in the presence of adhesive friction mechanism. W andF are the normal and friction forces, respectively, and S and N are the force components along and perpendicularto the local surface of the sample at the contact point, respectively.

AFM/FFM experiments are generally conducted at relative velocities as high as a few tens of µm/s. Tosimulate applications, it is of interest to conduct friction experiments at higher velocities. High velocitiescan be achieved by mounting either the sample or the cantilever beam on a shear wave transducer(ultrasonic transducer) to produce surface oscillations at MHz frequencies (Scherer et al., 1998, 1999).Velocities on the order of a few mm/s can thus be achieved. The effect of in-plane and out-of-planesample vibration amplitude on the coefficient of friction is shown in Figure 19.17. Vibration of a sampleat ultrasonic frequencies (>20 kHz) can substantially reduce the coefficient of friction, known as ultra-sonic lubrication or sonolubrication. When the surface is vibrated in-plane, classical hydrodynamiclubrication develops hydrodynamic pressure, which supports the tip and reduces friction. When the

FIGURE 19.13 Schematic of friction forces expected when a tip traverses a sample that is composed of differentmaterials and sharp changes in topography. A schematic of surface slope is also shown.

surface is vibrated out-of-plane, a lift-off caused by the squeeze-film lubrication (a form of hydrodynamiclubrication) reduces friction.

19.3.3 Comparison of Microscale and Macroscale Friction Data

Table 19.2 shows the coefficient of friction measured for single-crystal silicon surfaces on micro- andmacroscales. To study the effect of sample material, data for virgin and ion-implanted silicon are pre-sented. The values on the microscale are much lower than those on the macroscale. There can be thefollowing four and possibly more differences in the operating conditions responsible for these differences.First, the contact stresses at AFM conditions generally do not exceed the sample hardness, which mini-mizes plastic deformation. Second, when measured for the small contact areas and very low loads usedin microscale studies, indentation hardness and modulus of elasticity are higher than at the macroscale,as will be discussed later (Bhushan et al., 1995a, 1996). Lack of plastic deformation and improvedmechanical properties reduce the degree of wear and friction. Next, the small apparent areas of contactreduce the number of particles trapped at the interface, and thus minimize the plowing contribution tothe friction force (Bhushan et al., 1995a). As a fourth and final difference, we will note in the next sectionthat coefficient of friction increases with an increase in the AFM tip radius. AFM data presented so far

FIGURE 19.14 (a) Gray-scale images and two-dimensional profiles of surface height and friction forces across asingle ruling of the gold-coated ruling, and (b) two-dimensional profiles of surface height and friction forces acrossa silicon grid pit. Friction force data in trace and retrace directions, and substrated force data are presented.

were taken with a sharp tip, whereas asperities coming in contact in macroscale tests, range fromnanoasperities to much larger asperities, which may be responsible for larger values of friction force onthe macroscale.

To demonstrate the load dependence on the coefficient of friction, stiff cantilevers were used to conductfriction experiments at high loads (Figure 19.18) (Bhushan and Kulkarni, 1996). At higher loads (withcontact stresses exceeding the hardness of the softer material), as anticipated, the coefficient of frictionfor microscale measurements increases toward values comparable with those obtained from macroscalemeasurements, and surface damage also increases. Thus Amontons’ law of friction, which states that thecoefficient of friction is independent of apparent contact area and normal load, does not hold formicroscale measurements. These findings suggest that microcomponents sliding under lightly loadedconditions should experience ultra low friction and near-zero wear (Bhushan et al., 1995a).

19.3.4 Effect of Tip Radii and Humidity on Adhesion and Friction

The tip radius and relative humidity affect adhesion and friction for dry and lubricated surfaces (Bhushanand Sundararajan, 1998; Bhushan and Dandavate, 2000). Figure 19.18 shows the variation of single pointadhesive force measurements as a function of tip radius on a Si(100) sample for a given humidity forseveral humidities. The adhesive force data are also plotted as a function of relative humidity for a giventip radius for several tip radii. The general trend at humidities up to the ambient is that a 50-nm-radius

FIGURE 19.14 (continued)

FIGURE 19.15 (a) Gray-scale images of surface heights, surface slopes, and friction forces for scans across a gold-coated ruling, and (b) two-dimensional profiles of surface heights, surface slopes, and friction forces for scans acrossthe silicon grid pit. (From Sundararajan, S. and Bhushan, B. (2000b), Topography-induced contributions to frictionforces measured using an atomic force/friction force microscope, J. Appl. Phys., 88, in press. With permission.)

Si3N4 tip exhibits a slightly lower adhesive force as compared to the other microtips of larger radii; inthe latter case, values are similar. Thus for the microtips there is no appreciable variation in adhesiveforce with tip radius at a given humidity up to the ambient. The adhesive force increases as relativehumidity increases for all tips. The trend in adhesive forces as a function of tip radii and relative humiditycan be explained by the presence of meniscus forces, which arise from capillary condensation of watervapor from the environment forming meniscus bridges. If enough liquid is present to form a meniscus

FIGURE 19.16 Coefficient of macroscale friction as a function of drum passes for a polymeric magnetic tape slidingover an aluminum drum in a reciprocating mode in both directions. Normal load = 0.5 N over 12.7-mm-wide tape,sliding speed = 60 mm/s. (From Bhushan, B. (1995), Micro/Nanotribology and its applications to magnetic storagedevices and MEMS, Tribol. Int., 28, 85-95. With permission.)

FIGURE 19.17 Reduction of coefficient of friction, measured at a normal load of 100 nN and average tip separationas a function of surface amplitude on a single-crystal silicon subjected to (a) in-plane and (b) out-of-plane vibrationsat about 1 MHz against a silicon nitride tip. (From Scherer, V., Arnold W., and Bhushan, B. (1998), Active frictioncontrol using ultrasonic vibration, in Tribology Issues and Opportunities in MEMS, Bhushan, B. (Ed.), KluwerAcademic Pub., Dordrecht, Netherlands, 463. With permission.)

TABLE 19.2 Surface Roughness (Standard Deviation of Surface Heights or σ) and Coefficients of Friction on Micro- and Macroscales of Single-Crystal Silicon Samples in Air

Material σ (nm)Coefficient of Microscale

Friction vs. Si3N4 tipa

Coefficient of Macroscale Friction vs. Alumina Ballb

Si (111)C+-implanted Si (111)

0.110.33

0.030.02

0.180.18

a Tip radius of about 50 nm in the load range of 10–150 nN (2.5–6.1 GPa), a scanning speed of5 µm/s and scan area of 1 µm × 1 µm.

b Ball radius of 3 mm at a normal load of 0.1 N (0.3 GPa) and average sliding speed of 0.8 mm/s.

bridge, the meniscus force should increase with an increase in tip radius (proportional to tip radius fora spherical tip) and should be independent of the relative humidity or water film thickness. In addition,an increase in tip radius in a dry environment results in increased contact area, leading to higher valuesof van der Waals forces. However, if nanoasperities on the tip and the sample are considered, then thenumber of contacting and near-contacting asperities forming meniscus bridges increases with an increaseof humidity, leading to an increase in meniscus forces. This explains the trends observed in Figure 19.19.From the data, the tip radius has little effect on the adhesive forces at low humidities but increases withtip radius at high humidity. Adhesive force also increases with an increase in humidity for all tips. Thisobservation suggests that thickness of the liquid film at low humidities is insufficient to form continuousmeniscus bridges to affect adhesive forces in the case of all tips.

Figure 19.19 also shows the variation in coefficient of friction as a function of tip radius at a givenhumidity, and as a function of relative humidity for a given tip radius for Si(100). It can be seen that for0% RH, the coefficient of friction is about the same for the tip radii except for the largest tip, whichshows a higher value. At all other humidities, the trend consistently shows that the coefficient of friction

FIGURE 19.18 (a) Coefficient of friction as a function of normal load and (b) corresponding wear depth as afunction of normal load for silicon, SiO2 coating, and natural diamond. Inflections in the curves for silicon and SiO2

correspond to the contact stresses equal to the hardnesses of these materials. (From Bhushan, B. and Kulkarni, A.V.(1996), Effect of normal load on microscale friction measurements, Thin Solid Films, 278, 49-56; 293, 333. Withpermission.)

increases with tip radius. An increase in friction with tip radius at low to moderate humidities arisesfrom increased contact area (higher van der Waals forces) and higher values of shear forces required forlarger contact area. At high humidities, similar to adhesive force data, an increase with tip radius occursbecause of both contact area and meniscus effects. Although AFM/FFM measurements are able to measurethe combined effect of the contribution of van der Waals and meniscus forces to friction force or adhesiveforce, it is difficult to measure their individual contributions separately. It can be seen that for all tips,the coefficient of friction increases with humidity to about ambient, beyond which it starts to decrease.The initial increase in the coefficient of friction with humidity arises from the fact that the thickness ofthe water film increases with an increase in the humidity, which results in a larger number of nanoas-perities forming meniscus bridges and leads to higher friction (larger shear force). The same trend isexpected with the microtips beyond 65% RH. This is attributed to the fact that at higher humidities, theadsorbed water film on the surface acts as a lubricant between the two surfaces. Thus the interface ischanged at higher humidities, resulting in lower shear strength and hence lower friction force andcoefficient of friction.

19.3.4.1 Adhesion and Friction Expressions for a Single Asperity Contact

We now obtain the expressions for the adhesive force and coefficient of friction for a single asperitycontact with a meniscus formed at the interface. For a spherical asperity of radius R in contact with aflat and smooth surface with the composite modulus of elasticity E* and with a concave meniscus, theattractive meniscus force (adhesive force) Wad is given as,

(19.6)

FIGURE 19.19 Adhesive force and coefficient of friction as a function of tip radius at several humidities and as afunction of relative humidity at several tip radii on Si(100). (From Bhushan, B. and Sundararajan, S. (1998),Micro/nanoscale friction and wear mechanisms of thin films using atomic force and friction force microscopy, ActaMater., 46, 3793-3804. With permission.)

W Rad = π +( )2 1 1 2γ θ θcos cos

For an elastic contact, the friction force is given as,

(19.7)

where γl is the surface tension of the liquid in air, θ1 and θ2 are the contact angles between the liquid andthe two surfaces, W is the external load, and τ is the average shear strength of the contacts (surface energyeffects are not considered here). Note that adhesive force increases linearly with an increase in the tipradius, and the friction force increases with an increase in tip radius as R2/3 and with normal load as(W + Wad)2/3. The experimental data in support of W2/3 dependence on the friction force can be foundin various references (see e.g., Schwarz et al., 1997). The coefficient of friction µe is obtained fromEquation 19.7 as

(19.8)

In the plastic contact regime (Bhushan, 1999d), the coefficient of friction µp is obtained as

(19.9)

where Hs is the hardness of the softer material. Note that in the plastic contact regime, the coefficient offriction is independent of external load, adhesive contributions, and surface geometry.

For comparisons, for multiple asperity contacts in the elastic contact regime the total adhesive forceWad is the summation of adhesive forces at n individual contacts,

(19.10)

and

where σp and Rp are the standard deviation of summit heights and average summit radius, respectively.Note that the coefficient of friction is independent of external and adhesive forces and depends only onthe surface roughness. In the plastic contact regime, the expression for µp in Equation 19.9 does notchange.

The source of the adhesive force, in a wet contact in the AFM experiments being performed in anambient environment, includes mainly attractive meniscus forces due to capillary condensation of watervapor from the environment. The meniscus force for a single contact increases with an increase in tipradius. A sharp AFM tip in contact with a smooth surface at low loads (on the order of a few nN) formost materials can be simulated as a single asperity contact. At higher loads, for rough surfaces and forsoft surfaces, multiple contacts will occur. Furthermore, at low loads (nN range) for most materials, thelocal deformation will be primarily elastic. Assuming that shear strength of contacts does not change,the adhesive force for smooth and hard surfaces at low normal load (on the order of a few nN) (for a

FW W R

Ee

ad= π+( )

τ3

4

2 3

*

µ =+( ) = π

+( )ee

ad ad

F

W W

R

E W Wτ 3

4

12 3

1 3*

µ =+( ) =p

p

ad S

F

W W H

τ

W Wad ad ii

n

= ( )=

∑1

µ ≈( )e

p pE R

3 21 2

.

*

τ

σ

single asperity contact in the elastic contact regime) will increase with an increase in tip radius, and thecoefficient of friction will decrease with an increase in total normal load as (W + Wad)–1/3 and will increasewith an increase of tip radius as R2/3. In this case, Amontons’ law of friction, which states that coefficientof friction is independent of normal load and is independent of apparent area of contact, does not hold.For a single asperity plastic contact and multiple asperity plastic contacts, neither the normal load or tipradius come into play in calculation of coefficient of friction. In the case of multiple asperity contacts,the number of contacts increases with an increase of normal load; therefore adhesive force increases withan increase in load.

In the data presented earlier in this section, the effect of tip radius and humidity on the adhesive forcesand coefficient of friction is investigated for experiments with a Si(100) surface at loads in the range of10 to 100 nN. The multiple asperity elastic-contact regime is relevant for this study. An increase inhumidity generally results in an increase in the number of meniscus bridges, which would increase theadhesive force. As was suggested earlier, that increase in humidity also may decrease the shear strengthof contacts. A combination of an increase in adhesive force and a decrease in shear strength will affectthe coefficient of friction. An increase in tip radius will increase the meniscus force (adhesive force). Asubstantial increase in the tip radius may also increase interatomic forces. These effects influence thecoefficient of friction with an increase in the tip radius.

19.4 Scratching, Wear, and Fabrication/Machining

19.4.1 Nanoscale Wear

Bhushan and Ruan (1994) conducted nanoscale wear tests on polymeric magnetic tapes using conven-tional silicon nitride tips at two different loads of 10 and 100 nN (Figure 19.20). For a low normal loadof 10 nN, measurements were made twice. There was no discernible difference between consecutivemeasurements for this load. However, as the load was increased from 10 nN to 100 nN, topographicalchanges were observed during subsequent scanning at a normal load of 10 nN; material was pushed inthe sliding direction of the AFM tip relative to the sample. The material movement is believed to occuras a result of plastic deformation of the tape surface. Thus, deformation and movement of the softmaterials on a nanoscale can be observed.

19.4.2 Microscale Scratching

The AFM can be used to investigate how surface materials can be moved or removed on micro- tonanoscales, for example, in scratching and wear (Bhushan, 1999a) (where these things are undesirable),and nanofabrication/nanomachining (where they are desirable). Figure 19.21a shows microscratchesmade on Si(111) at various loads and scanning velocity of 2 µm/s after 10 cycles (Bhushan et al., 1994).As expected, the scratch depth increases linearly with load. Such microscratching measurements can beused to study failure mechanisms on the microscale and to evaluate the mechanical integrity (scratchresistance) of ultra-thin films at low loads.

To study the effect of scanning velocity, unidirectional scratches, 5 µm in length, were generated atscanning velocities ranging from 1 to 100 µm/s at various normal loads ranging from 40 to 140 µN. Thereis no effect of scanning velocity obtained at a given normal load. For representative scratch profiles at80 µN, see Figure 19.21b. This may be because of a small effect of frictional heating with the change inscanning velocity used here. Furthermore, for a small change in interface temperature, there is a largeunderlying volume to dissipate the heat generated during scratching (Bhushan and Sundararajan, 1998).

Scratching can be performed at random loads to determine the scratch resistance of materials andcoatings. The coefficient of friction is measured during scratching and the load at which the coefficientof friction increases rapidly is known as the “critical load,” which is a measure of scratch resistance. Inaddition, the post-scratch imaging can be performed in situ with the AFM in tapping mode to studyfailure mechanisms. Figure 19.22 shows data from a scratch test on Si(100) with a scratch length of 25 µm

and a scratching velocity of 0.5 µm/s. At the beginning of the scratch, the coefficient of friction is 0.04,which is a typical value for silicon. At about 35 µN (indicated by the arrow in the figure), there is a sharpincrease in the coefficient of friction, which is the critical load. Beyond the critical load, the coefficientof friction continues to increase steadily. In the post-scratch image, we note that at the critical load, aclear groove starts to form. This implies that Si(100) was damaged by plowing at the critical load,associated with the plastic flow of the material. At and after the critical load, small and uniform debrisis observed, and the amount of debris increases with increasing normal load. Sundararajan and Bhushan(2000a) have also used this technique to measure scratch resistance of diamond-like carbon coatingsranging in thickness from 3.5 to 20 nm.

19.4.3 Microscale Wear

By scanning the sample in two dimensions with the AFM, wear scars are generated on the surface.Figure 19.23 shows the effect of normal load on the wear depth. We note that wear rate is very smallbelow 20 µN of normal load (Koinkar and Bhushan, 1997c; Zhao and Bhushan, 1998). A normal loadof 20 µN corresponds to contact stresses comparable to the hardness of the silicon. Primarily, elasticdeformation at loads below 20 µN is responsible for low wear (Bhushan and Kulkarni, 1996).

A typical wear mark, of the size 2 µm × 2 µm, generated at a normal load of 40 µN for one scan cycleand imaged using AFM with scan size of 4 µm × 4 µm at 300 nN load, is shown in Figure 19.24a (Koinkarand Bhushan, 1997c). The inverted map of wear marks shown in Figure 19.24b indicates the uniformmaterial removal at the bottom of the wear mark. An AFM image of the wear mark shows small debris

FIGURE 19.20 Surface roughness maps of a polymeric magnetic tape at the applied normal load of (a) 10 nN and(b) 100 nN. Location of the change in surface topography as a result of nanowear is indicated by arrows. (FromBhushan, B. and Ruan, J. (1994), Atomic-scale friction measurements using friction force microscopy: part II —application to magnetic media, ASME J. Tribol., 116, 389-396. With permission.)

at the edges, swiped during AFM scanning. Thus the debris is loose (not sticky) and can be removedduring the AFM scanning.

Next we examine the mechanism of material removal on a microscale in AFM wear experiments(Koinkar and Bhushan, 1997c; Bhushan and Sundararajan, 1998; Zhao and Bhushan, 1998). Figure 19.25shows a secondary electron image of the wear mark and associated wear particles. The specimen usedfor the scanning electron microscope (SEM) was not scanned with the AFM after initial wear, in orderto retain wear debris in the wear region. Wear debris is clearly observed. In the SEM micrographs, thewear debris appears to be agglomerated because of high surface energy of the fine particles. Particlesappear to be a mixture of rounded and so-called cutting type (feather-like or ribbon-like). Zhao andBhushan (1998) reported an increase in the number and size of cutting-type particles with the normalload. The presence of cutting-type particles indicates that the material is removed primarily by plasticdeformation.

To better understand the material removal mechanisms, transmission electron microscopy (TEM) hasbeen used. The TEM micrograph of the worn region and associated TEM diffraction pattern are shownin Figures 19.26a and b. The bend contours are observed to pass through the wear mark in the micrograph.The bend contours around and inside the wear mark are indicative of a strain field, which in the absenceof applied stresses, can be interpreted as plastic deformation and/or residual stresses. Often, localizedplastic deformation during loading would lead to residual stresses during unloading; therefore, bendcontours reflect a mix of elastic and plastic strains. The wear debris is observed outside the wear mark.The enlarged view of the wear debris in Figure 19.24c shows that much of the debris is ribbon-like,

FIGURE 19.21 Surface plots of (a) Si(111) scratched for ten cycles at various loads and a scanning velocity of2 µm/s. Note that x and y axes are in µm and z axis is in nm, and (b) Si(100) scratched in one unidirectional scancycle at a normal force of 80 µN and different scanning velocities.

FIGURE 19.22 (a) Applied normal load and friction signal measured during the microscratch experiment onSi(100) as a function of scratch distance, (b) friction data plotted in the form of coefficient of friction as a functionof normal load, and (c) AFM surface height image of scratch obtained in tapping mode. (From Sundararajan, S. andBhushan, B. (2000a), Development of a continuous microscratch technique in an atomic force microscope and itsapplication to study scratch resistance of ultra-thin hard amorphous carbon coatings, J. Mater. Res., in press. Withpermission.)

FIGURE 19.23 Wear depth as a function of normal load for Si(100) after one cycle. (From Zhao, X. and Bhushan,B. (1998), Material removal mechanism of single-crystal silicon on nanoscale and at ultralow loads, Wear, 223, 66-78.With permission.)

FIGURE 19.24 (a) Typical gray-scale, and (b) inverted AFM images of wear mark created using a diamond tip ata normal load of 40 µN and one scan cycle on Si(100) surface.

FIGURE 19.25 Secondary electron image of wear mark and debris for Si(100) produced at a normal load of 40 µNand one scan cycle.

indicating that material is removed by a cutting process via plastic deformation, which is consistent withthe SEM observations. The diffraction pattern from inside the wear mark is similar to that of virginsilicon, showing no evidence of any phase transformation (amorphization) during wear. A selected areadiffraction pattern of the wear debris shows some diffuse rings, which indicates the existence of amor-phous material in the wear debris, confirmed as silicon oxide products by chemical analysis. It is knownthat plastic deformation occurs by generation and propagation of dislocations. No dislocation activityor cracking was observed at 40 µN. However, dislocation arrays could be observed at 80 µN. Figure 19.27shows the TEM micrographs of the worn region at 80 µN; for better observation of the worn surface,wear debris was moved out of the wear mark by using AFM with a large area scan at 300 nN after thewear test. The existence of dislocation arrays confirms that material removal occurs by plastic deforma-tion. It is concluded that the material on microscale at high loads is removed by plastic deformation witha small contribution from elastic fracture (Zhao and Bhushan, 1998).

To understand wear mechanisms, evolution of wear can be studied using AFM. Figure 19.28 showsevolution of wear marks of a DLC-coated disk sample. The data illustrate how the microwear profile fora load of 20 µN develops as a function of the number of scanning cycles (Bhushan et al., 1994). Wear isnot uniform, but is initiated at the nanoscratches. Surface defects (with high surface energy) present atnanoscratches act as initiation sites for wear. Coating deposition also may not be uniform on and nearnanoscratches, which may lead to coating delamination. Thus, scratch-free surfaces will be relativelyresistant to wear.

Wear precursors (precursors to measurable wear) can be studied by making surface potential measure-ments (DeVecchio and Bhushan, 1998; Bhushan and Goldade, 2000a,b). The contact potential difference

FIGURE 19.26 Bright-field TEM micrographs (left) and diffraction patterns (right) of wear mark (a, b) and weardebris (c, d) in Si(100) produced at a normal load of 40 µN and one scan cycle. Bend contours around and insidewear mark are observed.

or simply surface potential between two surfaces depends on a variety of parameters such as electronicwork function, adsorption, and oxide layers. The surface potential map of an interface gives a measureof changes in the work function which is sensitive to both the physical and chemical conditions of thesurfaces, including structural and chemical changes. Before material is actually removed in a wear process,the surface experiences stresses that result in surface and subsurface changes of structure and/or chemistry.These can cause changes in the measured potential of a surface. An AFM tip allows mapping of surfacepotential with nanoscale resolution. Surface height and change in surface potential maps of a polishedsingle-crystal aluminum(100) sample, abraded using a diamond tip at two loads of approximately 1 µNand 9 µN, are shown in Figure 19.29a. [Note that the sign of the change in surface potential is reversedhere from that in DeVecchio and Bhushan (1998)]. It is evident that both abraded regions show a largepotential contrast (~0.17 Volts), with respect to the nonabraded area. The black region in the lower right-hand part of the topography scan shows a step that was created during the polishing phase. There is nopotential contrast between the high region and the low region of the sample, indicating that the techniqueis independent of surface height. Figure 19.29b shows a closeup scan of the upper (low load) wear regionin Figure 19.29a. Notice that while there is no detectable change in the surface topography, there isnonetheless a large change in the potential of the surface in the worn region. Indeed the wear mark ofFigure 19.29b might not be visible at all were it not for the noted absence of wear debris generated nearbyand then swept off during the low load scan. Thus, even in the case of zero wear (no measurabledeformation of the surface using AFM), there can be a significant change in the surface potential inside

FIGURE 19.27 (a) Bright-field and (b) weak-beam TEM micrographs of wear mark in Si(100) produced at a normalload of 80 µN and one scan cycle showing bend contours and dislocations. (From Zhao, X. and Bhushan, B. (1998),Material removal mechanism of single-crystal silicon on nanoscale and at ultralow loads, Wear, 223, 66-78. Withpermission.)

the wear mark, which is useful for study of wear precursors. It is believed that the removal of a thincontaminant layer, including the natural oxide layer, gives rise to the initial change in surface potential.The structural changes, which precede generation of wear debris and/or measurable wear scars, occur

FIGURE 19.28 Surface plots of diamond-like carbon-coated thin-film disk showing the worn region; the normalload and number of test cycles are indicated. (From Bhushan, B., Koinkar, V.N., and Ruan, J. (1994), Microtribologyof magnetic media, Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol., 208, 17-29. With permission.)

under ultra-low loads in the top few nanometers of the sample, and are primarily responsible for thesubsequent changes in surface potential.

19.4.4 Nanofabrication/Nanomachining

An AFM can be used for nanofabrication/nanomachining by extending the microscale scratching operation(Bhushan, 1995, 1998b, 1999a; Bhushan et al., 1994, 1995a). Figure 19.30 shows two examples of nanofab-rication. The patterns were created on a single-crystal silicon(100) wafer by scratching the sample surfacewith a diamond tip at specified locations and scratching angles. Each line is scribed manually at a normalload of 15 µN and a writing speed of 0.5 µm/s. The separation between lines is about 50 nm, and thevariation in line width is due to the tip asymmetry. Nanofabrication parameters such as normal load,scanning speed, and tip geometry can be controlled precisely to control depth and length of the devices.

Nanofabrication using mechanical scratching has several advantages over other techniques. Bettercontrol over the applied normal load, scan size, and scanning speed can be used for nanofabrication ofdevices. Using the technique, nanofabrication can be performed on any engineering surface. Use ofchemical etching or reactions is not required, and this dry nanofabrication process can be used whereuse of chemicals and electric field is prohibited. One disadvantage of this technique is the formation of

FIGURE 19.29 (a) Surface height and change in surface potential maps of wear regions generated at 1 µN (top)and 9 µN (bottom) on a single-crystal aluminum sample showing bright contrast in the surface potential map onthe worn regions. (b) Closeup of upper (low load) wear region. (From DeVecchio, D. and Bhushan, B. (1998), Useof a nanoscale Kelvin probe for detecting wear precursors, Rev. Sci. Instrum., 69, 3618-3624. With permission.)

debris during scratching. At light loads, debris formation is not a problem compared to high-loadscratching. However, debris can be removed easily out of the scan area at light loads during scanning.

19.5 Indentation

Mechanical properties, such as hardness and Young’s modulus of elasticity can be determined on themicro- to picoscales using the AFM (Bhushan and Ruan, 1994; Bhushan et al., 1994; Bhushan and Koinkar,1994a,b) and a depth-sensing indentation system used in conjunction with an AFM (Bhushan et al.,1996; Kulkarni and Bhushan, 1996a,b, 1997).

19.5.1 Picoindentation

Indentability on the scale of subnanometers of soft samples can be studied in the force calibration mode(Figure 19.4) by monitoring the slope of cantilever deflection as a function of sample traveling distanceafter the tip is engaged and the sample is pushed against the tip. For a rigid sample, cantilever deflectionequals the sample traveling distance, but the former quantity is smaller if the tip indents the sample. Inan example for a polymeric magnetic tape shown in Figure 19.31, the line in the left portion of the figureis curved with a slope of less than 1 shortly after the sample touches the tip, which suggests that the tip

FIGURE 19.30 (a) Trim and (b) spiral patterns generated by scratching a Si(100) surface using a diamond tip at anormal load of 15 µN and writing speed of 0.5 µm/s.

has indented the sample (Bhushan and Ruan, 1994). Later, the slope is equal to 1, suggesting that the tipno longer indents the sample. This observation indicates that the tape surface is soft locally (polymer rich)but hard (as a result of magnetic particles) underneath. Since the curves in extending and retracting modesare identical, the indentation is elastic up to a maximum load of about 22 nN used in the measurements.

Detection of transfer of material on a nanoscale is possible with the AFM. Indentation of C60-richfullerene films with an AFM tip has been shown (Ruan and Bhushan, 1993) to result in the transfer offullerene molecules to the AFM tip, as indicated by discontinuities in the cantilever deflection as a functionof sample traveling distance in subsequent indentation studies.

19.5.2 Nanoscale Indentation

The indentation hardness of surface films with an indentation depth of as small as about 1 nm can bemeasured using AFM (Bhushan and Koinkar, 1994b; Bhushan et al., 1996). Figure 19.32 shows the gray-scale plots of indentation marks made on Si(111) at normal loads of 60, 65, 70, and 100 µN. Triangularindents can be clearly observed with very shallow depths. At a normal load of 60 µN, indents are observedand the depth of penetration is about 1 nm. As the normal load is increased, the indents become clearerand indentation depth increases. For the case of hardness measurements at shallow depths on the sameorder as variations in surface roughness, it is desirable to subtract the original (unindented) map fromthe indent map for accurate measurement of the indentation size and depth (Bhushan et al., 1994).

To make accurate measurements of hardness at shallow depths, a depth-sensing indentation system isused. Figure 19.33 shows the load-displacement curves at different peak loads for Si(100). Load-displace-ment data at residual depths as low as about 1 nm can be obtained. Loading/unloading curves are notsmooth but exhibit sharp discontinuities, particularly at high loads. Any discontinuities in the loadingpart of the curve probably results from slip of the tip. The sharp discontinuities in the unloading partof the curves are believed to be due to formation of lateral cracks that form at the base of the mediancrack, which results in the surface of the specimen being thrust upward. The indentation hardness ofsurface films with an indentation depth of as small as about 1 nm has been measured for Si(100) (Bhushanet al., 1996; Kulkarni and Bhushan, 1996a,b, 1997). The hardness of silicon on a nanoscale is found tobe higher than on a microscale (Figure 19.34). This decrease in hardness with an increase in indentationdepth can be rationalized on the basis that as the volume of deformed material increases, there is a higherprobability of encountering material defects. Thus mechanical properties show size effect.

Bhushan and Koinkar (1994a) have used AFM measurements to show that ion implantation of siliconsurfaces increases their hardness and thus their wear resistance. Formation of surface alloy films withimproved mechanical properties by ion implantation is of growing technological importance as a meansof improving the mechanical properties of materials. Hardness of 20-nm-thick diamond-like carbonfilms have been measured by Kulkarni and Bhushan (1997).

FIGURE 19.31 Tip deflection (normal load) as a function of the Z (separation distance) curve for a polymericmagnetic tape. (From Bhushan, B. and Ruan, J. (1994), Atomic-scale friction measurements using friction forcemicroscopy: part II — application to magnetic media, ASME J. Tribol., 116, 389-396. With permission.)

The creep and strain-rate effects (viscoelastic effects) of ceramics can be studied using a depth-sensingindentation system. Bhushan et al. (1996) and Kulkarni et al. (1996a,b, 1997) have reported that ceramicsexhibit significant plasticity and creep on a nanoscale. Figure 19.35a shows the load-displacement curves

FIGURE 19.32 Gray-scale plots of indentation marks on the Si(111) sample at various indentation loads. Loads,indentation depths, and hardness values are listed in the figure. (From Bhushan, B. and Koinkar V.N. (1994b),Nanoindentation hardness measurements using atomic force microscopy, Appl. Phys. Lett., 64, 1653-1655. Withpermission.)

for single-crystal silicon at various peak loads held at 180 s. To demonstrate the creep effects, the load-displacement curves for a 500 µN peak load held at 0 and 30 s are also shown as an inset. Note thatsignificant creep occurs at room temperature. Nanoindenter experiments conducted by Li et al. (1991)exhibited significant creep only at high temperatures (greater than or equal to 0.25 times the meltingpoint of silicon). The mechanism of dislocation glide plasticity is believed to dominate the indentationcreep process on the macroscale. To study strain-rate sensitivity of silicon, data at two different (constant)rates of loading are presented in Figure 19.35b. Note that a change in the loading rate by a factor of aboutfive results in a significant change in the load-displacement data. The viscoelastic effects observed herefor silicon at ambient temperature could arise from the size effects mentioned earlier. Most likely, creep

FIGURE 19.33 Load-displacement curves at various peak loads for Si(100). (From Bhushan, B., Kulkarni, A.V.,Bonin, W., and Wyrobek, J.T. (1996), Nano/picoindentation measurement using a capacitance transducer system inatomic force microscopy, Philos. Mag., 74, 1117-1128. With permission.)

FIGURE 19.34 Indentation hardness as a function of residual indentation depth for Si(100). (From Bhushan, B.,Kulkarni, A.V., Bonin, W., and Wyrobek, J.T. (1996), Nano/picoindentation measurement using a capacitance trans-ducer system in atomic force microscopy, Philos. Mag., 74, 1117-1128. With permission.)

and strain-rate experiments are being conducted on the hydrated films present on the silicon surface inambient environment, and these films are expected to be viscoelastic.

The Young’s modulus of elasticity is calculated from the slope of the indentation curve during unload-ing. However, these measurements provide a single-point measurement. By using the force modulation

FIGURE 19.35 (a) Creep behavior and (b) strain-rate sensitivity of Si(100). (From Bhushan, B., Kulkarni, A.V.,Bonin, W., and Wyrobek, J.T. (1996), Nano/picoindentation measurement using a capacitance transducer system inatomic force microscopy, Philos. Mag., 74, 1117-1128. With permission.)

technique, it is possible to get localized elasticity maps of soft and compliant materials with penetrationdepths of less than 100 nm. This technique has been used successfully for polymeric magnetic tapes,which consist of magnetic and nonmagnetic ceramic particles in a polymeric matrix. Elasticity maps ofa tape can be used to identify relative distribution of hard magnetic and nonmagnetic ceramic particleson the tape surface, which has an effect on friction and stiction at the head-tape interface (Bhushan,1996). Figure 19.36 shows surface height and elasticity maps on a polymeric magnetic tape. The elasticityimage reveals sharp variations in surface elasticity due to the composite nature of the film. As can beclearly seen, regions of high elasticity do not always correspond to high or low topography. Based on aHertzian elastic-contact analysis, the static indentation depth of these samples during the force modu-lation scan is estimated to be about 1 nm. We conclude that the contrast seen is influenced most stronglyby material properties in the top few nanometers, independent of the composite structure beneath thesurface layer.

19.6 Boundary Lubrication

The classical approach to lubrication uses freely supported multimolecular layers of liquid lubricants(Bowden and Tabor, 1950; Bhushan, 1996, 1999d). The liquid lubricants are sometimes chemicallybonded to improve their wear resistance (Bhushan, 1996, 1999d). To study depletion of boundary layers,the microscale friction measurements are made as a function of number of cycles. For an example ofexperiments with virgin Si(100) surfaces and silicon surfaces lubricated with Z-15 and Z-Dol a PFPElubricants, see Figure 19.37 (Koinkar and Bhushan, 1996a,b). Z-Dol is PFPE lubricant with hydroxyl endgroups. Its film was thermally bonded at 150°C for 30 min (BUW-bonded, unwashed) and, in some casesthe unbonded fraction was washed off with a solvent to provide a chemically bonded layer of the lubricant(BW) film. In Figure 19.37a, the unlubricated silicon sample shows a slight increase in friction forcefollowed by a drop to a lower steady-state value after 20 cycles. Depletion of native oxide and possibleroughening of the silicon sample are believed to be responsible for the decrease in friction force after

FIGURE 19.36 Surface height and elasticity maps on a polymeric magnetic tape (σ = 6.72 nm and P-V = 31.7 nm;σ and P-V refer to standard deviation of surface heights and peak-to-valley distance, respectively). The gray-scaleon the elasticity map is arbitrary. (From DeVecchio, D. and Bhushan, B. (1997), Localized surface elasticity measure-ments using an atomic force microscope, Rev. Sci. Instrum., 68, 4498-4505. With permission.)

20 cycles. The initial friction force for the Z-15 lubricated sample is lower than that of unlubricatedsilicon and increases gradually to a friction force value comparable to that of the silicon after 20 cycles.This suggests the depletion of the Z-15 lubricant in the wear track. In the case of the Z-Dol coated siliconsample, the friction force starts out very low and remains low during the 100 cycles test. This suggeststhat Z-Dol does not become displaced/depleted as readily as Z-15. The nanowear results for BW andBUW/Z-Dol samples with different film thicknesses are shown in Figure 19.37b. The BW with thicknessof 2.3 nm exhibits an initial decrease in the friction force in the first few cycles and then remains steadyfor more than 100 cycles. The decrease in friction force possibly arises from the alignment of any freeliquid lubricant present over the bonded lubricant layer. BUW with a thickness of 4.0 nm exhibits behaviorsimilar to BW (2.3 nm). Lubricated BW and BUW samples with thinner films exhibit a higher value ofcoefficient of friction. Among the BW and BUW samples, BUW samples show the lower friction becauseof an extra unbonded fraction of the lubricant.

The effect of the operating environment on coefficient of friction of unlubricated and lubricatedsamples is shown in Figure 19.38. Silicon(100) samples were lubricated with 2.9-nm-thick Z-15 and2.3-nm-thick Z-Dol bonded and washed (BW) lubricants. The coefficient of friction in a dry environment

FIGURE 19.37 Friction force as a function of number of cycles using Si3N4 tip at a normal load of 300 nN for(a) unlubricated Si(100), Z-15 and bonded washed (BW) Z-Dol, and (b) bonded Z-Dol before washing (BUW) andafter washing (BW) with different film thicknesses. (From Koinkar, V.N. and Bhushan, B. (1996a), Micro/nanoscalestudies of boundary layers of liquid lubricants for magnetic disks, J. Appl. Phys., 79, 8071-8075. With permission.)

is lower than that in a high humidity environment. We believe that in the humid environment, thecondensed water from the humid environment competes with the liquid film present on the samplesurface, and interaction of the liquid film (water for the unlubricated sample and polymer lubricant forthe lubricated sample) with the substrate is weakened and a boundary layer of the liquid forms puddles.This dewetting results in poorer lubrication performance and high friction. Since Z-Dol is a bondedlubricant with superior frictional properties, the dewetting effect in a humid environment for Z-Dol ismore pronounced than for Z-15.

The effect of scanning speed on the coefficient of friction of unlubricated and lubricated samples isshown in Figure 19.39. The coefficient of friction for an unlubricated silicon sample and a lubricatedsample with Z-15 decreases with an increase in scanning velocity in the ambient environment. These

FIGURE 19.38 Coefficient of friction for unlubricated and lubricated Si(100) samples in ambient (~50% RH), drynitrogen (~5% RH), and dry air (~5 RH). (From Koinkar, V.N. and Bhushan, B. (1996b), Microtribological studies ofunlubricated and lubricated surfaces using atomic force/friction force microscopy, J. Vac. Sci. Technol. A, 14, 2378-2391.With permission.)

FIGURE 19.39 Coefficient of friction as a function of scanning velocity for unlubricated and lubricated Si(100)samples in ambient (~50% RH), dry nitrogen (~5% RH), and dry air (~5% RH). (From Koinkar, V.N. and Bhushan,B. (1996b), Microtribological studies of unlubricated and lubricated surfaces using atomic force/friction force micro-scopy, J. Vac. Sci. Technol. A, 14, 2378-2391. With permission.)

samples are insensitive to scanning velocity in dry environments. Samples lubricated with Z-Dol do notshow any effect of scanning velocity on the friction. Alignment of liquid molecules (shear thinning) isbelieved to be responsible for the drop in friction with an increase in scanning velocity for samples withmobile films and exposed to ambient environment.

For lubrication of microdevices, a more effective approach involves the deposition of organized, densemolecular layers of long-chain molecules on the surface contact. Such monolayers and thin films arecommonly produced by Langmuir–Blodgett (L–B) deposition and by chemical grafting of molecules intoself-assembled monolayers (SAMs). Based on the measurements, SAMs of octodecyl (C18) compoundsbased on methyl-terminated octadecyldimethylchlorosilane on an oxidized silicon exhibited lower coef-ficient of friction (0.018) and greater durability than LB films of zinc arachidate adsorbed on a goldsurface coated with octadecylthiol (ODT; coefficient of friction of 0.03; Figure 19.40) (Bhushan et al.,1995b). LB films are bonded to the substrate by weak van der Waals attraction, whereas SAMs arechemically bound via covalent bonds. Because of the choice of chain length and terminal linking groupthat SAMs offer, they hold great promise for boundary lubrication of microdevices.

Liquid film thickness measurement of thin lubricant films (on the order of 10 nm or thicker) withnanometer lateral resolution can be made with the AFM (Bhushan and Blackman, 1991; Bhushan, 1999a).The lubricant thickness is obtained by measuring the force on the tip as it approaches, contacts, andpushes through the liquid film and ultimately contacts the substrate. The distance between the sharpsnap-in (owing to the formation of a liquid meniscus between the film and the tip) at the liquid surfaceand the hard repulsion at the substrate surface is a measure of the liquid film thickness.

Lubricant film thickness mapping of ultra-thin films (on the order of a couple of 2 nm) can be obtainedusing friction force microscopy (Koinkar and Bhushan, 1996a) and adhesive force mapping (Bhushanand Dandavate, 2000). Figure 19.41 shows gray-scale plots of the surface topography and friction forceobtained simultaneously for unbonded Demnum-type PFPE lubricant film on silicon. The friction forceplot shows well-distinguished low and high friction regions roughly corresponding to high and lowregions in surface topography (thick and thin lubricant regions). A uniformly lubricated sample doesnot show such a variation in the friction. Friction force imaging can thus be used to measure the lubricantuniformity on the sample surface, which cannot be identified by surface topography alone. Figure 19.42shows the gray-scale plots of the adhesive force distribution for silicon samples coated uniformly andnonuniformly with Z-DOL-type PFPE lubricant. It can be clearly seen that there exists a region whichhas an adhesive force distinctly different from the other region for the nonuniformly coated sample. Thisimplies that the liquid film thickness is nonuniform, giving rise to a difference in the meniscus forces.

FIGURE 19.40 Surface plots showing the worn region after one scan cycle for self-assembled monolayers of methyl-terminated, octadecyldimethylchlorosilane (C18), and zinc arachidate (ZnA). Normal loads and wear depths areindicated. Note that wear of ZnA occurs at only 200 nN as compared to 40 µN for C18 film.

19.7 Closure

At most solid–solid interfaces of technological relevance, contact occurs at many asperities. A sharpAFM/FFM tip sliding on a surface simulates just one such contact. However, asperities come in all shapesand sizes. The effect of the radius of a single asperity (tip) on the friction/adhesion performance can bestudied using tips of different radii. AFM/FFM are used to study various tribological phenomena, whichinclude surface roughness, adhesion, friction, scratching, wear, indentation, detection of material transfer,and boundary lubrication. Measurement of atomic-scale friction of a freshly cleaved, highly orientedpyrolytic graphite exhibits the same periodicity as that of the corresponding topography. However, thepeaks in friction and those in the corresponding topography are displaced relative to each other. Variationsin atomic-scale friction and the observed displacement can be explained by the variation in interatomicforces in the normal and lateral directions. Local variations in microscale friction occur and are foundto correspond to the local slopes, suggesting that a ratchet mechanism and collision effects are responsiblefor this variation. Directionality in the friction is observed on both micro- and macroscales, which resultsfrom the surface roughness and surface preparation. Anisotropy in surface roughness accentuates thiseffect. Microscale friction is generally found to be smaller than the macrofriction because there is lessplowing contribution in microscale measurements. Microscale friction is load dependent and frictionvalues increase with an increase in the normal load, approaching the macrofriction at contact stresseshigher than the hardness of the softer material. The tip radius also has an effect on the adhesion andfriction.

Mechanism of material removal on the microscale is studied. Wear precursors can be detected at earlystages of wear using a surface potential measurement. Wear rate for single-crystal silicon is negligiblebelow 20 µN and is much higher and remains approximately constant at higher loads. Elastic deformationat low loads is responsible for negligible wear. Most of the wear debris is loose. SEM and TEM studiesof the wear region suggest that the material on the microscale is removed by plastic deformation with asmall contribution from elastic fracture; this observation is corroborated with the scratch data. Evolutionof wear has also been studied using AFM. Wear is found to be initiated at nanoscratches. For a slidinginterface requiring near-zero friction and wear, contact stresses should be below the hardness of the softermaterial to minimize plastic deformation, and surfaces should be free of nanoscratches. Further, wearprecursors can be studied by making surface potential measurements. It is found that even in the case

FIGURE 19.41 Gray-scale plots of the surface topography and friction force obtained simultaneously for unbondedperfluoropolyether lubricant film on silicon. (From Koinkar, V.N. and Bhushan, B. (1996a), Micro/nanoscale studiesof boundary layers of liquid lubricants for magnetic disks, J. Appl. Phys., 79, 8071-8075. With permission.)

of zero wear (no measurable deformation of the surface using AFM), there can be a significant changein the surface potential inside the wear mark, which is useful for studying wear precursors.

By using the force modulation technique, localized surface elasticity maps of composite materials withpenetrating depths of less than 100 nm, can be obtained. Modified AFM can be used to obtain load-displacement curves and for measurement of nanoindentation hardness and Young’s modulus of elasticity,

FIGURE 19.42 Gray-scale plots of the adhesive force distribution of a uniformly-coated, 3.5-nm-thick unbondedperfluoropolyether lubricant film on silicon and 3- to 10-nm-thick unbonded perfluoropolyether lubricant film onsilicon that was deliberately coated nonuniformly by vibrating the sample during the coating process. (From Bhushan,B. and Dandavate, C. (2000), Thin-film friction and adhesion studies using atomic force microscopy J. Appl. Phys.,87, 1201-1210. With permission.)

with depth of indentation as low as 1 nm. Hardness of ceramics on nanoscales is found to be higher thanthat on the microscale. Ceramics exhibit significant plasticity and creep on a nanoscale. Scratching andindentation on nanoscales are powerful ways to screen for adhesion and resistance to deformation ofultrathin films. Detection of material transfer on a nanoscale is possible with AFM.

Boundary lubrication studies and measurement of lubricant film thickness with a lateral resolutionon a nanoscale can be conducted using AFM. Self-assembled monolayers and chemically bonded lubricantfilms with a mobile fraction are superior in wear resistance.

Investigations of wear, scratching, and indentation on nanoscales using the AFM can provide insightsinto failure mechanisms of materials. Coefficients of friction, wear rates, and mechanical properties suchas hardness have been found to be different on the nanoscale than on the macroscale; generally, coeffi-cients of friction and wear rates on micro- and nanoscales are smaller, whereas hardness is greater.Therefore, micro/nanotribological studies may help define the regimes for ultra-low friction and near-zero wear.

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