are still unanswered. Since we focus in this chapter on the analysis of wearless friction on atomically flat surfaces without defects, it is reasonable to expect that the origin for the different friction observed on the different materials can be found in the local arrangement of the atoms at the tip–sample contact area. If this expectation holds, it should be possible to distinguish areas of different chemical composition by lateral force microscopy. This ability is sometimes called “chemical imaging”; examples for such investigations will be discussed in Section 18.5.1. Another interesting consequence of the above expec- tation is that the friction should depend on the direction with which the tip profiles the sample surface. This frictional anisotropy is especially easy to verify experimentally if a material exhibiting an asymmetric surface potential is used as a sample, as presented in Section 18.5.3. Finally, we will see in Section 18.5.2 that even small conformational (i.e., purely geometrical) changes within a surface unit cell give rise to different friction in lateral force maps. 18.5.1 Frictional Contrast Caused by Local Changes in the Chemical Composition The ability of the FFM to provide a contrast between surfaces of different chemical composition is not only important for tribologists, but also of considerable general interest for users from the whole field of scanning force microscopy, where contrast mechanisms are needed which provide information in addition to the pure topography. Since the lateral forces acting on the FFM tip are not independent of the topography,* atomically or molecularly flat terraces give the most unambiguous results. Consequently, chemical contrast has first been demonstrated for Langmuir–Blodgett films, which can easily be prepared and investigated under atmospheric conditions and exhibit large, molecularly flat surfaces. See, for example, Overney et al. (1992), or Meyer et al. (1992). However, in this chapter we will restrict the discussion to the atomic-scale frictional effects at crystalline surfaces. In order to check the frictional behavior for such systems, Lüthi et al. (1995) partially covered the surface of an NaCl(001) single crystal with 1 to 6 monolayers of AgBr (Figure 18.6a), which has the same crystalline structure as NaCl. In the corresponding FFM investigations (Figure 18.6b), they found a strong frictional contrast between the AgBr islands and the NaCl substrate due to the different chemical composition of the two materials. FIGURE 18.6 (a) Topography and (b) lateral force map of an AgBr thin film deposited on NaCl(001) at room temperature (image size: 1.4 µm × 1.4 µm). The AgBr islands are 1 to 6 monolayers high and partially cover the NaCl substrate. In the lateral force map, the AgBr islands are revealed as areas with about ten times higher friction than the corresponding friction observed on the NaCl surface. (From Meyer, E., Lüthi, R., Howald, L., and Güntherodt, H J., 1995. Friction force microscopy, in Forces in Scanning Probe Methods, Güntherodt, H J., Ansel- metti, D., and E. Meyer (Eds.), Kluwer Academic Publishers, Dordrecht, The Netherlands, 285. With permission.) *Scanning “up hill” causes more torsion of the cantilever than scanning “down hill”; see, for example, Grafström et al. (1993), Fujisawa et al. (1993b), Ruan and Bhushan (1994a), or Aimé et al. (1995). © 2001 by CRC Press LLC are still unanswered. Since we focus in this chapter on the analysis of wearless friction on atomically flat surfaces without defects, it is reasonable to expect that the origin for the different friction observed on the different materials can be found in the local arrangement of the atoms at the tip–sample contact area. If this expectation holds, it should be possible to distinguish areas of different chemical composition by lateral force microscopy. This ability is sometimes called “chemical imaging”; examples for such investigations will be discussed in Section 18.5.1. Another interesting consequence of the above expec- tation is that the friction should depend on the direction with which the tip profiles the sample surface. This frictional anisotropy is especially easy to verify experimentally if a material exhibiting an asymmetric surface potential is used as a sample, as presented in Section 18.5.3. Finally, we will see in Section 18.5.2 that even small conformational (i.e., purely geometrical) changes within a surface unit cell give rise to different friction in lateral force maps. 18.5.1 Frictional Contrast Caused by Local Changes in the Chemical Composition The ability of the FFM to provide a contrast between surfaces of different chemical composition is not only important for tribologists, but also of considerable general interest for users from the whole field of scanning force microscopy, where contrast mechanisms are needed which provide information in addition to the pure topography. Since the lateral forces acting on the FFM tip are not independent of the topography,* atomically or molecularly flat terraces give the most unambiguous results. Consequently, chemical contrast has first been demonstrated for Langmuir–Blodgett films, which can easily be prepared and investigated under atmospheric conditions and exhibit large, molecularly flat surfaces. See, for example, Overney et al. (1992), or Meyer et al. (1992). However, in this chapter we will restrict the discussion to the atomic-scale frictional effects at crystalline surfaces. In order to check the frictional behavior for such systems, Lüthi et al. (1995) partially covered the surface of an NaCl(001) single crystal with 1 to 6 monolayers of AgBr (Figure 18.6a), which has the same crystalline structure as NaCl. In the corresponding FFM investigations (Figure 18.6b), they found a strong frictional contrast between the AgBr islands and the NaCl substrate due to the different chemical composition of the two materials. FIGURE 18.6 (a) Topography and (b) lateral force map of an AgBr thin film deposited on NaCl(001) at room temperature (image size: 1.4 µm × 1.4 µm). The AgBr islands are 1 to 6 monolayers high and partially cover the NaCl substrate. In the lateral force map, the AgBr islands are revealed as areas with about ten times higher friction than the corresponding friction observed on the NaCl surface. (From Meyer, E., Lüthi, R., Howald, L., and Güntherodt, H J., 1995. Friction force microscopy, in Forces in Scanning Probe Methods, Güntherodt, H J., Ansel- metti, D., and E. Meyer (Eds.), Kluwer Academic Publishers, Dordrecht, The Netherlands, 285. With permission.) *Scanning “up hill” causes more torsion of the cantilever than scanning “down hill”; see, for example, Grafström et al. (1993), Fujisawa et al. (1993b), Ruan and Bhushan (1994a), or Aimé et al. (1995). © 2001 by CRC Press LLC are still unanswered. Since we focus in this chapter on the analysis of wearless friction on atomically flat surfaces without defects, it is reasonable to expect that the origin for the different friction observed on the different materials can be found in the local arrangement of the atoms at the tip–sample contact area. If this expectation holds, it should be possible to distinguish areas of different chemical composition by lateral force microscopy. This ability is sometimes called “chemical imaging”; examples for such investigations will be discussed in Section 18.5.1. Another interesting consequence of the above expec- tation is that the friction should depend on the direction with which the tip profiles the sample surface. This frictional anisotropy is especially easy to verify experimentally if a material exhibiting an asymmetric surface potential is used as a sample, as presented in Section 18.5.3. Finally, we will see in Section 18.5.2 that even small conformational (i.e., purely geometrical) changes within a surface unit cell give rise to different friction in lateral force maps. 18.5.1 Frictional Contrast Caused by Local Changes in the Chemical Composition The ability of the FFM to provide a contrast between surfaces of different chemical composition is not only important for tribologists, but also of considerable general interest for users from the whole field of scanning force microscopy, where contrast mechanisms are needed which provide information in addition to the pure topography. Since the lateral forces acting on the FFM tip are not independent of the topography,* atomically or molecularly flat terraces give the most unambiguous results. Consequently, chemical contrast has first been demonstrated for Langmuir–Blodgett films, which can easily be prepared and investigated under atmospheric conditions and exhibit large, molecularly flat surfaces. See, for example, Overney et al. (1992), or Meyer et al. (1992). However, in this chapter we will restrict the discussion to the atomic-scale frictional effects at crystalline surfaces. In order to check the frictional behavior for such systems, Lüthi et al. (1995) partially covered the surface of an NaCl(001) single crystal with 1 to 6 monolayers of AgBr (Figure 18.6a), which has the same crystalline structure as NaCl. In the corresponding FFM investigations (Figure 18.6b), they found a strong frictional contrast between the AgBr islands and the NaCl substrate due to the different chemical composition of the two materials. FIGURE 18.6 (a) Topography and (b) lateral force map of an AgBr thin film deposited on NaCl(001) at room temperature (image size: 1.4 µm × 1.4 µm). The AgBr islands are 1 to 6 monolayers high and partially cover the NaCl substrate. In the lateral force map, the AgBr islands are revealed as areas with about ten times higher friction than the corresponding friction observed on the NaCl surface. (From Meyer, E., Lüthi, R., Howald, L., and Güntherodt, H J., 1995. Friction force microscopy, in Forces in Scanning Probe Methods, Güntherodt, H J., Ansel- metti, D., and E. Meyer (Eds.), Kluwer Academic Publishers, Dordrecht, The Netherlands, 285. With permission.) *Scanning “up hill” causes more torsion of the cantilever than scanning “down hill”; see, for example, Grafström et al. (1993), Fujisawa et al. (1993b), Ruan and Bhushan (1994a), or Aimé et al. (1995). © 2001 by CRC Press LLC 19 Friction, Scratching/Wear, Indentation, and Lubrication Using Scanning Probe Microscopy 19.1 Introduction 19.2 Description of AFM/FFM and Various Measurement Techniques Surface Roughness and Friction Force Measurements • Adhesion Measurements • Scratching, Wear, and Fabrication/Machining • Surface Potential Measurements • Nanoindentation Measurements • Boundary Lubrication Measurements 19.3 Friction and Adhesion Atomic-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/Machining Nanoscale Wear • Microscale Scratching • Microscale Wear • Nanofabrication/Nanomachining 19.5 Indentation Picoindentation • Nanoscale Indentation 19.6 Boundary Lubrication 19.7 Closure 19.1 Introduction The atomistic mechanisms and dynamics of the interactions of two materials during relative motion need 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, contact occurs at many asperities. Consequently, the importance of investigating single asperity contacts in studies of the fundamental micromechanical and tribological properties of surfaces and interfaces has long been recognized. The recent emergence and proliferation of proximal probes, in particular scanning probe microscopies (the scanning tunneling microscope and the atomic force microscope) and the surface force apparatus, 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 ways and 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 Bhushan The Ohio State University © 2001 by CRC Press LLC 20 Computer Simulations of Friction, Lubrication, and Wear 20.1 Introduction 20.2 Atomistic Computer Simulations Model Potentials • Maintaining Constant Temperature • Imposing Load and Shear 20.3 Wearless Friction in Low-Dimensional Systems Two Simple Models of Crystalline Surfaces in Direct Contact • Metastability and Static Friction in One Dimension • Metastability and Kinetic Friction • Tomlinson Model in Two Dimensions: Atomic Force Microscopy • Frenkel–Kontorova Model in Two Dimensions: Adsorbed Monolayers 20.4 Dry Sliding of Crystalline Surfaces Effect of Commensurability • Chemically Passivated Surfaces • Single Asperity Contacts 20.5 Lubricated Surfaces Flow Boundary Conditions • Phase Transitions and Viscosity Changes in Molecularly Thin Films • Submonolayer Lubrication • Corrugated Surfaces 20.6 Stick-Slip Dynamics 20.7 Strongly Irreversible Tribological Processes Plastic Deformation • Wear • Tribochemistry 20.1 Introduction Computer simulations have played an important role in advancing our understanding of tribological processes. They allow controlled numerical experiments where the geometry, sliding conditions, and interactions between atoms can be varied at will to explore their effects on friction, lubrication, and wear. Unlike laboratory experiments, computer simulations enable scientists to follow and analyze the full dynamics of all atoms. Moreover, theorists have no other general approach to analyze processes like friction and wear, because there is no known principle like minimization of free energy that determines the steady state of nonequilibrium systems. Even if there were, simulations would be needed to address the complex systems of interest, just as in many equilibrium problems. Tremendous advances in computing hardware and methodology have dramatically increased the ability of theorists to simulate tribological processes. This has led to an explosion in the number of computational studies over the last decade, and allowed increasingly sophisticated modeling of sliding contacts. Although it is not yet possible to treat all the length scales and time scales that enter the friction coefficient of Mark O. Robbins The Johns Hopkins University Martin H. Müser Johannes Gutenberg-Universität © 2001 by CRC Press LLC . crystalline surfaces. In order to check the frictional behavior for such systems, Lüthi et al. (1995) partially covered the surface of an NaCl(001) single crystal with 1 to 6 monolayers of AgBr (Figure. room temperature (image size: 1.4 µm × 1.4 µm). The AgBr islands are 1 to 6 monolayers high and partially cover the NaCl substrate. In the lateral force map, the AgBr islands are revealed as areas. crystalline surfaces. In order to check the frictional behavior for such systems, Lüthi et al. (1995) partially covered the surface of an NaCl(001) single crystal with 1 to 6 monolayers of AgBr (Figure