Ferrante, J. et. al. “Surface Physics in Tribology” Handbook of Micro/Nanotribology. Ed. Bharat Bhushan Boca Raton: CRC Press LLC, 1999 © 1999 by CRC Press LLC © 1999 by CRC Press LLC 3 Surface Physics in Tribology John Ferrante and Phillip B. Abel 3.1 Introduction 3.2 Geometry of Surfaces 3.3 Theoretical Considerations Surface Theory • Friction Fundamentals 3.4 Experimental Determinations of Surface Structure Low-Energy Electron Diffraction • High-Resolution Electron Microscopy • Field Ion Microscopy 3.5 Chemical Analysis of Surfaces Auger Electron Spectroscopy • X-Ray Photoelectron Spectroscopy • Secondary Ion Mass Spectroscopy • Infrared Spectroscopy • Thermal Desorption 3.6 Surface Effects in Tribology Monolayer Effects in Adhesion and Friction • Atomic Effects Due to Adsorption of Hydrocarbons • Atomic Effects in Metal–Insulator Contacts 3.7 Concluding Remarks References 3.1 Introduction Tribology, the study of the interaction between surfaces in contact, spans many disciplines from physics and chemistry to mechanical engineering and material science. Besides the many opportunities for interesting research, it is of extreme technological importance. The key word in this chapter is surface. The chapter will be rather ambitious in scope in that we will attempt to cover the range from microscopic considerations to the macroscopic experiments used to examine the surface interactions. We will approach this problem in steps, first considering the fundamental idea of a surface and next recognizing its atomic character and the expectations of a ball model of the atomic structures present, viewed as a terminated bulk. We will then consider a more realistic description of a relaxed surface and then consider how the class of surface, i.e., metal, semiconductor, or insulator affects these considerations. Finally, we will present what is expected when a pure material is alloyed, as well as the effects of adsorbates. Following these more fundamental descriptions, we will give brief descriptions of some of the exper- imental techniques used to determine surface properties and their limitations. The primary objective here will be to provide a source for more thorough examination by the interested reader. © 1999 by CRC Press LLC Finally, we will examine the relationship of tribological experiments to these more fundamental atomistic considerations. The primary goals of this section will be to again provide sources for further study of tribological experiments and to raise critical issues concerning the relationship between basic surface properties with regard to tribology and the ability of certain classes of experiments to reveal the underlying interactions. We will attempt to avoid overlapping the material that we present with that presented by other authors in this publication. This chapter cannot be a complete treatment of the physics of surfaces due to space limitations. We recommend an excellent text by Zangwill (1988) for a more thorough treatment. Instead, we concentrate on techniques and issues of importance to tribology on the nanoscale. 3.2 Geometry of Surfaces We will now discuss simply from a geometric standpoint what occurs when you create two surfaces by dividing a solid along a given plane. We limit the discussion to single crystals, since the same arguments apply to polycrystalline samples except for the existence of many grains, each of which could be described by a corresponding argument. This discussion will start by introducing the standard notation for describ- ing crystals given in many solid-state texts (Ashcroft and Mermin, 1976; Kittel, 1986). It is meant to be didactic in nature and because of length limitations will not attempt to be comprehensive. To establish notation and concepts we will limit our discussion to two of the possible Bravais lattices, face-centered cubic (fcc) and body-centered cubic (bcc), which are the structures often found in metals. The unit cells, i.e., the structures which most easily display the symmetries of the crystals, are shown in Figure 3.1. The other descriptions that are frequently used are the primitive cells, which show the simplest structures that can be repeated to create a given structure. In Figure 3.1 we also show the primitive cell basis vectors, which can be used to generate the entire structure by the relation (3.1) where n 1 , n 2 , and n 3 are integers, and → a 1 , → a 2 , and → a 3 are the unit basis vectors. Since we are interested in describing surface properties, we want to present the standard nomenclature for specifying a surface. The algebraic description of a surface is usually given in terms of a vector normal to the surface. This is conveniently accomplished in terms of vectors that arise naturally in solids, namely, the reciprocal lattice vectors of the Bravais lattice (Ashcroft and Mermin, 1976; Kittel, 1986). This is FIGURE 3.1 (a) Unit cube of fcc crystal structure with primative cell basis vectors indicated. (b) Unit cube of bcc crystal structure, with primative cell basis vectors indicated. r rr r Rnana na=+ + 12233 © 1999 by CRC Press LLC convenient since these vectors are used to describe the band structure and diffraction effects in the solid. They are usually given in the form (3.2) where h, k, and l are integers. The reciprocal lattice vectors are related to the basis vectors of the direct lattice by (3.3) where a cyclic permutation of i, j, k are used in the definition. Typically, parentheses are used in the definition of the plane, e.g., ( h,k,l ). The (100) planes for fcc and bcc lattices are shown in Figure 3.2 where dots are used to show the location of the atoms in the next plane down. This provides the simplest description of the surface in terms of terminating the bulk. There is a rather nice NASA publication by Bacigalupi (1964) which gives diagrams of many surfaces and subsurface structures for fcc, bcc, and diamond lattices, in addition to a great deal of other useful information such FIGURE 3.2 Projection of cubic face (100) plane for (a) fcc and (b) bcc crystal structures. In both cases, smaller dots represent atomic positions in the next layer below the surface. r rrr Khbkb lb=++ 123 r rr rr r b aa aa a i jk =π × × () 2 12 3 © 1999 by CRC Press LLC as surface density and interplanar spacings. A modern reprinting of this NASA publication is called for. In many cases, this simple description is not adequate since the surface can reconstruct. The two most prominent cases of surface reconstruction are the Au(110) surface (Good and Banerjea, 1992) for metals and the Si(111) surface (Zangwill, 1988) for semiconductors. In addition, adsorbates often form structures with symmetries different from the substrate, with the classic example the adsorption of oxygen on W(110) (Zangwill, 1988). Wood (1963) in a classic publication gives the nomenclature for describing such structures. In Figure 3.3 we show an example of 2 × 2 structure, where the terminology describes a surface that has a layer with twice the spacings of the substrate. There are many other possibilities, such as structures rotated with respect to the substrate and centered differently from the substrate. These are also defined by Wood (1963). The next consideration is that the interplanar spacing can vary, and slight shifts in atomic positions can occur several planes from the free surface. A recent paper by Bozzolo et al. (1994) presents the results for a large number of metallic systems and serves as a good review of available publications. Figure 3.4 shows some typical results for Ni(100). The percent change given represents the deviation from the equilibrium interplanar spacing. The drawing in Figure 3.4 exaggerates these typically small differences to elucidate the behavior. Typically, this pattern of alternating contraction and expansion diminishing as the bulk is approached is found in most metals. It can be understood in a simple manner (Bozzolo et al., 1994). The energy for the bulk metal is a minimum at the bulk metallic density. The formation of the surface represents a loss of electron density because of the missing neighbors for the surface atoms. Therefore, this loss of electron density can be partially offset by a contraction of the interplanar spacing between the first two layers. This construction causes an electron density increase between layers 2 and 3, and thus the energy is lowered by a slight increase in the interplanar spacing. There are some exceptions FIGURE 3.3 Representation of fcc (110) face with an additional “2 × 2” layer, in which the species above the surface atoms have twice the spacing of the surface. Atomic positions in the next layer below the surface are presented by smaller dots. FIGURE 3.4 Side view of nickel (100) surface. On the left, the atoms are positioned as if still within a bulk fcc lattice (“unrelaxed”). On the right, the surface planes have been moved to minimize system energy. The percent change in lattice spacing is indicated, with the spacing in the image exaggerated to illustrate the effect. (From Bozzolo, G. et al. (1994), Surf. Sci. 315, 204–214. With permission.) © 1999 by CRC Press LLC to this behavior where the interplanar spacing increases between the first two layers due to bonding effects (Needs, 1987; Feibelman, 1992). However, the pattern shown in Figure 3.4 is the usual behavior for most metallic surfaces. There can be similar changes in position within the planes; however, these are usually small effects (Rodriguez et al., 1993; Foiles, 1987). In Figure 3.5, we show a side view of a gold (110) surface (Good and Banerjea, 1992). Figure 3.5a shows the unreconstructed surface and Figure 3.5b shows a side view of the (2 × 1) missing row reconstruction. Such behavior indicates the complexity that can arise even for metal surfaces and the danger of using ideas which are too simplistic, since more details of the bonding interactions are needed in this case and those of Needs (1987) and Feibelman (1992). Crystal surfaces encountered typically are not perfectly oriented nor atomically flat. Even “on-axis” (i.e., within a fraction of a degree) single-crystal low-index faces exhibit some density of crystallographic steps. For a gold (111) face tilted one half degree toward the (011) direction, evenly spaced single atomic height steps would be only 27 nm apart. Other surface-breaking crystal defects such as screw and edge dislocations may also be present, in addition to whatever surface scratches, grooves, and other polishing damage which remain in a typical single-crystal surface. Surface steps and step kinks would be expected to show greater reactivity than low-index surface planes. During either deposition or erosion of metal surfaces, one expects incorporation into or loss from the crystal lattice preferentially at step edges. More generally on simple metal surfaces, lone atoms on a low-index crystal face are expected to be most mobile (i.e., have the lowest activation energy to move). Atoms at steps would be somewhat more tightly bound, and atoms making up a low-index face would be least likely to move. High-index crystal faces can often be thought of as an ordered collection of steps on a low-index face. When surface species and even interfaces become mobile, consolidation of steps may be observed. Alternating strips of two low-index crystal faces can then develop from one high-index crystal plane, with lower total surface energy but with a rougher, faceted topography. Much theoretical and experimental work has been done over the last decade on nonequilibrium as well as equilibrium surface morphology (e.g., Redfield and Zangwill, 1992; Vlachos et al., 1993; Conrad and Engel, 1994; Bartelt et al., 1994; Williams, 1994; Kaxiras, 1996). Semiconductors and insulators generally behave differently. Unlike most metals for which the electron gas to some degree can be considered to behave like a fluid, semiconductors have strong directional bonding. Consequently, the loss of neighbors leaves dangling bonds which are satisfied in ultrahigh vacuum by reconstruction of the surface. The classic example of this is the silicon (111) 7 × 7 structure, where rebonding and the creation of surface states gives a complex structure. Until STM provided real- space images of this reconstruction (Binnig et al., 1983) much speculation surrounded this surface. Zangwill (1988) shows both the terminated bulk structure of Si(111) and the relaxed 7 × 7 structure. It is clear that viewing a surface as a simple terminated bulk can lead to severely erroneous conclusions. The relevance to tribology is clear since the nature of chemical reactions between surfaces, lubricants, and additives can be greatly affected by such radical surface alterations. There are other surface chemical state phenomena, even in ultrahigh vacuum, just as important as the structural and bonding states of the clean surface. Surface segregation often occurs to metal surfaces and interfaces (Faulkner, 1996, and other reviews cited therein). For example, trace quantities of sulfur often segregate to iron and steel surfaces or to grain boundaries in polycrystalline samples (Jennings et al., 1988). This can greatly affect results since sulfur, known to be a strong poisoning contaminant in catalysis, can affect interfacial bond strength. Sulfur is often a component in many lubricants. For alloys similar geometric surface reconstructions occur (Kobistek et al., 1994). Again, alloy surface composition can vary dramatically from the bulk, with segregation causing one of the elements to be the only component on a surface. In Figure 3.6 we show the surface composition for a CuNi alloy as a function of bulk composition with both a large number of experimental results and some theoretical predictions for the composition FIGURE 3.5 Side view of gold (110) surface: (a) unrecon- structed; (b) 1 × 2 missing row surface reconstruction. (From Good, B. S. and Banerjea, A. (1992), Mater. Res. Soc. Symp. Proc., 278, 211–216. With permission.) © 1999 by CRC Press LLC (Good et al., 1993). In addition, nascent surfaces typically react with the ambient, giving monolayer films and oxidation even in ultrahigh vacuum, producing even more pronounced surface composition effects. In conclusion, we see that even in the most simple circumstances, i.e., single-crystal surfaces, the situation can be very complicated. 3.3 Theoretical Considerations 3.3.1 Surface Theory We have shown how the formation of a surface can affect geometry. We now present some aspects of the energetics of surfaces from first-principles considerations. For a long time, calculations of the electronic structure and energetics of the surface had proven to be a difficult task. The nature of theoretical approximations and the need for high-speed computers limited the problem to some fairly simple approaches (Ashcroft and Mermin, 1976). The advent of better approximations for the many body effects, namely, for exchange and correlation, and the improvements in computers have changed this situation in the not too distant past. One aspect of the improvements was density functional theory and the use of the local density approximation (LDA) (Kohn and Sham, 1965; Lundqvist and March, 1983). Diffi- culties arise because in the creation of the surface, periodicity in the direction perpendicular to the surface is lost. Periodicity simplifies many problems in solid-state theory by limiting the calculation to a single unit cell with periodic boundary conditions. With a surface present the wave vector perpendicular to the surface, → k ⊥ , is not periodic, although the wave vector parallel to the surface, → k , still is. FIGURE 3.6 Copper (111) surface composition vs. copper-nickel alloy bulk composition: comparison between the experimental and theoretical results for the first and second planes. (See Good et al., 1993, and references therein.) © 1999 by CRC Press LLC The process usually proceeds by solving the one-electron Kohn–Sham equations (Kohn and Sham, 1965; Lundqvist and March, 1983), where a given electron is treated as though it is in the mean field of all of the other electrons. The LDA represents the mean field in terms of the local electron density at a given location. The Kohn–Sham equations are written in the form (using atomic units where the constants appearing in the Schroedinger equation along with the electron charge and the speed of light, ប = m e = e = c = 1). (3.4) where Ψ i and ⑀ ι are the one-electron wave function and energy, respectively, and (3.5) where V xc [ ρ ( → r )] is the exchange and correlation potential, ρ ( → r ) is the electron density (the brackets indicate that it is a functional of the density), and Φ ( → r ) is the electrostatic potential given by (3.6) in which the first term is the electron–electron interaction and the second term is the electron–ion interaction, Z j is the ion charge, and the electron density is given by (3.7) where occ refers to occupied states. The calculation proceeds by using some representation for the wave functions such as the linear muffin tin orbital approximation (LMTO), and iterating self-consistently. Self-consistency is obtained when either the output density or potential agree to within some specified criterion with the input. These calculations are not generally performed for the semi-infinite solid. Instead, they are performed for slabs of increasing thickness to the point where the interior atoms have essentially bulk properties. Usually, five planes are sufficient to give the surface properties. The values of ⑀ ι ( → k ) give the surface band structure and surface states, localized electronic states created because of the presence of the surface. The second piece of information given is the total energy in terms of the electron density, as obtained from density functional theory. This is represented schematically by the expression (3.8) where E ke is the kinetic energy contribution to the energy, E es is the electrostatic contribution, E xc is the exchange correlation contribution, and the brackets indicate that the energy is a functional of the density. Thus, the energy is an extremum of the correct density. Determining the surface energy accurately from such calculations can be quite difficult since the surface energy, or indeed any of the energies of various structures of interest, are obtained as the difference of big numbers. For example, for the surface the energy would be given by (3.9) where a is the distance between the surfaces (a = 0 to get the surface energy) and A is the cross-sectional area. −∇+ () [] () = () ( ) 12 2 Vr k r k k r iii r r r rr r ΨΨ ,,⑀ Vr r V r xc rr r () = () + () [] Φρ Φ rr r rr r r rdr r rr Z rR j j j () = ′ () − ′ −∑ − ∫ ρ ρ r r r rkr i () = () ΣΨ occ , 2 EE E Eρρρρ [] = [] + [] + [] ke es xc E Ea E A surface = () −∞ () 2 © 1999 by CRC Press LLC The initial and classic solutions of the Kohn–Sham equations for surfaces and interfaces were accom- plished by Lang and Kohn (1970) for the free surface and Ferrante and Smith for interfaces (Ferrante and Smith, 1985; Smith and Ferrante, 1986). The calculations were simplified by using the jellium model to represent the ionic charge. In the jellium model the ionic charge is smeared into a uniform distribution. Both sets of authors introduced the effects of discreteness on the ionic contribution through perturbation theory for the electron–ion interaction and through lattice sums for the ion–ion interaction. The jellium model is only expected to give reasonable results for the densest packed planes of simple metals. In Figures 3.7 and 3.8 we show the electron distribution at a jellium surface for Na and for an Al(111)–Mg(0001) interface (Ferrante and Smith, 1985) that is separated a small distance. In Figure 3.7 we can see the characteristic decay of the electron density away from the surface. In Figure 3.8 we see the change in electron density in going from one material to another. This characteristic tailing is an indication of the reactivity of the metal surface. In Figure 3.9 we show the electron distribution for a nickel (100) surface for the fully three-dimensional calculations performed by Arlinghouse et al. (1980) and that for a silver layer adsorbed on a palladium (100) interface (Smith and Ferrante, 1985) using self-consistent localized orbitals (SCLO) for approxi- mations to the wave functions. First, we note that for the Ni surface we see there is a smoothing of the surface density characteristic of metals. For the adsorption we can see that there are localized charge transfers and bonding effects indicating that it is necessary to perform three-dimensional calculations in order to determine bonding effects. Hong et al. (1995) have also examined metal–ceramic interfaces and the effects of impurities at the interface on the interfacial strength. In Figure 3.10 we schematically show the results of determining the interfacial energies as a function of separation between the surfaces with the energy in Figure 3.10a and the derivative curves giving the interfacial strength. In Figure 3.11 we show Ferrante and Smith’s results for a number of interfaces of jellium metals (Ferrante and Smith, 1985; Smith and Ferrante, 1986; Banerjea et al., 1991). Rose et al. (1981, 1983) found that these curves would scale onto one universal curve and indeed that this result applied to many other bonding situations including results of fully three-dimensional calculations. We show the scaled curves from Figure 3.11 in Figure 3.12. Somewhat surprisingly because of large charge transfer, Hong et al. (1995) found that this same behavior is applicable to metal–ceramic interfaces. Finnis (1996) gives a review of metal–ceramic interface theory. The complexities that we described earlier with regard to surface relaxations and complex structures can also be treated now by modern theoretical techniques. Often in these cases it is necessary to use “supercells” (Lambrecht and Segall, 1989). Since these structures are extended, it would require many atoms to represent a defect. Instead, in order to model a defect and take advantage of the simplicities of periodicities, a cell is created selected at a size which will mimic the main energetics of the defects. In conclusion, we can see that theoretical techniques have advanced substantially and are continuing to do so. They have and will shed light on many problems of interest experimentally. 3.3.2 Friction Fundamentals Friction, as commonly used, refers to a force resisting sliding. It is of obvious importance since it is the energy loss mechanism in sliding processes. In spite of its importance, after many centuries friction surprisingly has still avoided a complete physical explanation. An excellent history of the subject is given in a text by Dowson (1979). In this section we will outline some of the basic observations and give some recent relevant references treating the subject at the atomic level, in keeping with the theme of this chapter, and since the topic is much too complicated to treat in such a small space. There are two basic issues, the nature of the friction force and the energy dissipation mechanism. There are several commonplace observations, often considered general rules, regarding the friction force as outlined in the classic discussions of the subject by Bowden and Tabor (1964): 1. The friction force does not depend on the apparent area of contact. 2. The friction force is proportional to the normal load. 3. The kinetic friction force does not depend on the velocity and is less than the static friction force. © 1999 by CRC Press LLC FIGURE 3.7 Electron density at a jellium surface vs. position for a Na(011)–Na(011) contact for separations of 0.25, 3.0, and 15.0 au. (From Ferrante, J. and Smith, J. R. (1985), Phys. Rev. B 31, 3427–3434. With permission.) [...]... apparatus and in the materials involved that make measurement of the force distribution at the interface difficult Materials can change mechanical properties as a result of the forces applied For example, such properties as hardness, ductility, defect formation, plasticity, strain hardening, and creep must be considered Surface properties may be altered just by contact with the counterface material (Carpick... translation The values of the coefficient were of comparable magnitude to those of Gellman 3.6.2 Atomic Effects Due to Adsorption of Hydrocarbons Our primary objective in this and following sections is to explore the evidence for atomic effects on friction Again, we start by referring to recent publications by Gellman et al (Gellman, 1992; McFadden and Gellman, 1995a,b; Meyers et al., 1996) describing a number... diffracted beams to form the image, which nicely highlights sample area from which that diffracted beam originates (“darkfield” imaging technique) One source of TEM image contrast is the electron beam interacting with crystal defects such as various dislocations, stacking faults, or even strain around a small inclusion How that contrast changes with microscope settings can reveal information about the defect... sensitivity using small incident ion currents (“static” SIMS) Higher ion beam currents, often rastered, give species information as a function of sputter depth (“dynamic” SIMS or SIMS depth profiling) SIMS instrumentation can be roughly categorized by the type of ion detector used, e.g., quadrupole, magnetic sector, or time-of-flight, with their inherent differences in sensitivity and lateral and mass resolution... such as a hot filament or field emission tip, a vacuum column down which the accelerated and collimated electrons are focused by usually magnetic lenses, and an image collection section, often comprising a fluorescent screen for immediate viewing combined with a film transport and exposure mechanism for recording images The sample is inserted directly into the beam column and must be electron transparent,... Friction The bulk of the discussion in this section will be based on the recent high-quality experiments of Gellman and collaborators (Gellman, 1992; McFadden and Gellman, 1995a,b), while we acknowledge the pioneering contributions of Buckley and the members of his group (Buckley, 1981) Gellman has performed a number of adhesion and friction experiments on single crystals in contact, both for clean and... considerable progress has been made and computer programs for performing the analysis are available (Van Hove © 1999 by CRC Press LLC et al., 1993) The LEED structures give valuable information about adsorbate binding which can be used in the energy calculations described previously 3.4.2 High-Resolution Electron Microscopy Fundamentally, materials derive their properties from their makeup and structure, even... Diagram of UHV tribometer by Gellman (1992) The sample mounted to the tribometer is ≈1 cm in diameter The support bar is mounted onto a liquid nitrogen reservoir (From Gellman, A.J (1992), J Vac Sci Techol A 10, 180–187 With permission.) FIGURE 3.28 Adhesion coefficient vs sulfur coverage by McFadden and Gellman (1995a) Experimental conditions: temperature = 300 K; normal force = 40–60 mN; contact time... adsorbed oxygen on adhesion (Ohmae et al., 1987), and even direct examination of solid lubricants (Ohmae et al., 1990) In FIM a sharp metal tip is biased to a high negative potential relative to a phosphor-coated screen in an evacuated chamber backfilled to about a millitorr with helium or other noble gas A helium atom impinging on the tip experiences a high electric field due to the small tip radius This field... application in tribology, Auger electron spectroscopy (AES), X-ray photo-electron spectroscopy (XPS), secondary ion mass spectroscopy (SIMS), and infrared spectroscopy (IRS) AES gives elemental analysis of surfaces, but in some cases will give chemical compound information XPS can give compound information as well as elemental SIMS can exhibit extreme elemental sensitivity as well as “fingerprint” lubricant . Remarks References 3.1 Introduction Tribology, the study of the interaction between surfaces in contact, spans many disciplines from physics and chemistry to mechanical engineering and material. defects such as screw and edge dislocations may also be present, in addition to whatever surface scratches, grooves, and other polishing damage which remain in a typical single-crystal surface theoretical approximations and the need for high-speed computers limited the problem to some fairly simple approaches (Ashcroft and Mermin, 1976). The advent of better approximations for the many body