Tài liệu Handbook of Micro and Nano Tribology P3 pptx

Surface Theory • Friction Fundamentals3.4 Experimental Determinations of Surface Structure Low-Energy Electron Diffraction • High-Resolution Electron Microscopy • Field Ion Microscopy 3.

Ferrante, J et al “Surface Physics in Tribology”

Handbook of Micro/Nanotribology

Ed Bharat Bhushan

Boca Raton: CRC Press LLC, 1999

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 RemarksReferences

3.1 Introduction

Tribology, the study of the interaction between surfaces in contact, spans many disciplines from physicsand chemistry to mechanical engineering and material science Besides the many opportunities forinteresting 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 microscopicconsiderations to the macroscopic experiments used to examine the surface interactions We will approachthis problem in steps, first considering the fundamental idea of a surface and next recognizing its atomiccharacter and the expectations of a ball model of the atomic structures present, viewed as a terminatedbulk We will then consider a more realistic description of a relaxed surface and then consider how theclass of surface, i.e., metal, semiconductor, or insulator affects these considerations Finally, we will presentwhat 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 imental techniques used to determine surface properties and their limitations The primary objectivehere will be to provide a source for more thorough examination by the interested reader

exper-Finally, we will examine the relationship of tribological experiments to these more fundamentalatomistic considerations The primary goals of this section will be to again provide sources for furtherstudy of tribological experiments and to raise critical issues concerning the relationship between basicsurface properties with regard to tribology and the ability of certain classes of experiments to reveal theunderlying interactions We will attempt to avoid overlapping the material that we present with thatpresented 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 morethorough treatment Instead, we concentrate on techniques and issues of importance to tribology on thenanoscale

3.2 Geometry of Surfaces

We will now discuss simply from a geometric standpoint what occurs when you create two surfaces bydividing a solid along a given plane We limit the discussion to single crystals, since the same argumentsapply 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 ing crystals given in many solid-state texts (Ashcroft and Mermin, 1976; Kittel, 1986) It is meant to bedidactic in nature and because of length limitations will not attempt to be comprehensive To establishnotation and concepts we will limit our discussion to two of the possible Bravais lattices, face-centeredcubic (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 Theother descriptions that are frequently used are the primitive cells, which show the simplest structuresthat 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

describ-(3.1)

where n1, n2, and n3 are integers, and→a1,→a2, and→a3 are the unit basis vectors

Since we are interested in describing surface properties, we want to present the standard nomenclaturefor 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 n a n a n a= 1 + 2 2+ 3 3

convenient since these vectors are used to describe the band structure and diffraction effects in the solid.They are usually given in the form

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 rathernice NASA publication by Bacigalupi (1964) which gives diagrams of many surfaces and subsurfacestructures 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.

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 mostprominent cases of surface reconstruction are the Au(110) surface (Good and Banerjea, 1992) for metalsand the Si(111) surface (Zangwill, 1988) for semiconductors In addition, adsorbates often form structureswith symmetries different from the substrate, with the classic example the adsorption of oxygen onW(110) (Zangwill, 1988) Wood (1963) in a classic publication gives the nomenclature for describingsuch 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 arealso defined by Wood (1963)

The next consideration is that the interplanar spacing can vary, and slight shifts in atomic positionscan occur several planes from the free surface A recent paper by Bozzolo et al (1994) presents the resultsfor 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 theequilibrium 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 asthe 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 thesurface 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 spacingbetween the first two layers This construction causes an electron density increase between layers 2 and

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.)

to this behavior where the interplanar spacing increases between the first two layers due to bondingeffects (Needs, 1987; Feibelman, 1992) However, the pattern shown in Figure 3.4 is the usual behaviorfor most metallic surfaces There can be similar changes in position within the planes; however, theseare usually small effects (Rodriguez et al., 1993; Foiles, 1987) In Figure 3.5, we show a side view of agold (110) surface (Good and Banerjea, 1992) Figure 3.5a shows the unreconstructed surface and Figure3.5b shows a side view of the (2 × 1) missing row reconstruction Such behavior indicates the complexitythat can arise even for metal surfaces and the danger of using ideas which are too simplistic, since moredetails 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 crystallographicsteps For a gold (111) face tilted one half degree toward the (011) direction, evenly spaced single atomicheight steps would be only 27 nm apart Other surface-breaking crystal defects such as screw and edgedislocations may also be present, in addition to whatever surface scratches, grooves, and other polishingdamage 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 metalsurfaces, one expects incorporation into or loss from the crystal lattice preferentially at step edges Moregenerally 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 eveninterfaces become mobile, consolidation of steps may be observed Alternating strips of two low-indexcrystal faces can then develop from one high-index crystal plane, with lower total surface energy butwith a rougher, faceted topography Much theoretical and experimental work has been done over the lastdecade 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 electrongas to some degree can be considered to behave like a fluid, semiconductors have strong directionalbonding Consequently, the loss of neighbors leaves dangling bonds which are satisfied in ultrahighvacuum 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 thestructural and bonding states of the clean surface Surface segregation often occurs to metal surfaces andinterfaces (Faulkner, 1996, and other reviews cited therein) For example, trace quantities of sulfur oftensegregate 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 similargeometric surface reconstructions occur (Kobistek et al., 1994) Again, alloy surface composition can varydramatically 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 compositionwith both a large number of experimental results and some theoretical predictions for the composition

FIGURE 3.5 Side view of gold (110) surface: (a) 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.)

unrecon-(Good et al., 1993) In addition, nascent surfaces typically react with the ambient, giving monolayer filmsand 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 situationcan 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 theenergetics of surfaces from first-principles considerations For a long time, calculations of the electronicstructure and energetics of the surface had proven to be a difficult task The nature of theoreticalapproximations and the need for high-speed computers limited the problem to some fairly simpleapproaches (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) culties arise because in the creation of the surface, periodicity in the direction perpendicular to the surface

Diffi-is lost Periodicity simplifies many problems in solid-state theory by limiting the calculation to a singleunit cell with periodic boundary conditions With a surface present the wave vector perpendicular to thesurface,→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.)

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 ofall of the other electrons The LDA represents the mean field in terms of the local electron density at agiven location The Kohn–Sham equations are written in the form (using atomic units where the constantsappearing in the Schroedinger equation along with the electron charge and the speed of light,  = m e =

r)] is the exchange and correlation potential,ρ(→

r) is the electron density (the bracketsindicate that it is a functional of the density), andΦ(→

r) is the electrostatic potential given by

ι (k→) give the surface band structure and surface states, localized electronic states created because ofthe presence of the surface

The second piece of information given is the total energy in terms of the electron density, as obtainedfrom density functional theory This is represented schematically by the expression

(3.8)

where Eke is the kinetic energy contribution to the energy, Ees is the electrostatic contribution, Exc is theexchange 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 fromsuch calculations can be quite difficult since the surface energy, or indeed any of the energies of variousstructures of interest, are obtained as the difference of big numbers For example, for the surface theenergy would be given by

The initial and classic solutions of the Kohn–Sham equations for surfaces and interfaces were plished by Lang and Kohn (1970) for the free surface and Ferrante and Smith for interfaces (Ferranteand Smith, 1985; Smith and Ferrante, 1986) The calculations were simplified by using the jellium model

accom-to represent the ionic charge In the jellium model the ionic charge is smeared inaccom-to a uniform distribution.Both sets of authors introduced the effects of discreteness on the ionic contribution through perturbationtheory for the electron–ion interaction and through lattice sums for the ion–ion interaction The jelliummodel 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 anAl(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 seethe change in electron density in going from one material to another This characteristic tailing is anindication 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-dimensionalcalculations 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 thesurface density characteristic of metals For the adsorption we can see that there are localized chargetransfers and bonding effects indicating that it is necessary to perform three-dimensional calculations inorder to determine bonding effects Hong et al (1995) have also examined metal–ceramic interfaces andthe 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 theinterfacial strength In Figure 3.11 we show Ferrante and Smith’s results for a number of interfaces ofjellium 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 resultapplied to many other bonding situations including results of fully three-dimensional calculations Weshow the scaled curves from Figure 3.11 in Figure 3.12 Somewhat surprisingly because of large chargetransfer, 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 structurescan 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 manyatoms to represent a defect Instead, in order to model a defect and take advantage of the simplicities ofperiodicities, a cell is created selected at a size which will mimic the main energetics of the defects Inconclusion, 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 theenergy loss mechanism in sliding processes In spite of its importance, after many centuries frictionsurprisingly 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 somerecent 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

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.)

Historically, Coulomb (Bowden and Tabor, 1964; Dowson, 1979), realizing that surfaces were notideally flat and were formed by asperities (a hill-and-valley structure), proposed that interlocking asper-ities could be a source of the friction force This model has many limitations For example, if we picture

a perfectly sinusoidal interface there is no energy dissipation mechanism, since once the top of the firstasperity is attained the system will slide down the other side, thus needing no additional force once set

in motion Bowden and Tabor (1964), recognizing the existence of interfacial forces, proposed anothermechanism based on adhesion at interfaces Again, recognizing the existence of asperities, they proposethat adhesion occurs at asperity surfaces and that shearing occurs on translational motion This modelexplains a number of effects such as the disparity between true area of contact and apparent area ofcontact and the tracking of friction force with load, since the asperities and thus the true area of contactchange with asperity deformation (load) The actual arguments are more complex than indicated hereand require reading of the primary text for completeness These considerations also emphasize the basictopic of this chapter, i.e., the important effect of the state of the surface and interface on the frictionprocess Clearly, adsorbates, the differences of materials in contact, and lubricants greatly affect theinteraction

We now proceed to briefly outline some models of both the friction force and frictional energydissipation As addressed elsewhere in this book, there have recently been a number of attempts to modeltheoretically the friction interaction at the atomic level The general approaches have involved assuming

a two-body interaction potential at an interface, which in some cases may only be one dimensional, and

FIGURE 3.8 Electron number density n and jellium ion charge density for an aluminum (111)–magnesium (0001) interface (From Ferrante, J and Smith, J R (1985), Phys Rev B 31, 3427–3434 With permission.)

allowing the particles to interact across an interface, allowing motion of internal degrees of freedom ineither one or both surfaces Hirano and Shinjo (1990) examine a quasi-static model where one solid isconstrained to be rigid and the second is allowed to adapt to the structure of the first, interacting through

a two-body potential as translation occurs No energy dissipation mechanism is included They concludethat two processes occur, atomic locking where the readjusting atoms change their positions duringsliding, and dynamic locking where the configuration of the surface changes abruptly due to the dynamicprocess if the interatomic potential is stronger than a threshold value The latter process they conclude

is unlikely to happen in real systems They also conclude that the adhesive force is not related to the

FIGURE 3.9 (a) Electronic charge density contours at a nickel (100) surface (From Arlinghaus, F J et al (1980),

Phys Rev B 21, 2055–2059 With permission.) (b) Charge transfer of the palladium [100] slab upon silver adsorption (From Smith, J R and Ferrante, J (1985), Mater Sci Forum, 4, 21–38 With permission.)

friction phenomena, and discuss the possibility of a frictionless “superlubric” state (Shinjo and Hirano,1993; Hirano et al., 1997) Matsukawa and Fukuyama (1994) carry the process further in that they allowboth surfaces to adjust and examine the effects of velocity with attention to the three rules of frictionstated above They argue, not based on their calculations, that the Bowden and Tabor argument is notconsistent with flat interfaces having no asperities Since an adhesive force exists, there is a normal force

on the interfaces with no external normal load Consequently, rules of friction 1 and 2 break down Withrespect to rule 3, they find it restricted to certain circumstances They found that the dynamic frictionforce, in general, is sliding velocity dependent, but with a decreasing velocity dependence with increasingmaximum static friction force Hence, for systems with large static friction forces, the kinetic frictionforce shows behavior similar to classical rule 3, above Finally, Zhong and Tomanek (1990) performed afirst-principles calculation of the force to slide a monolayer of Pd in registry with the graphite surface

FIGURE 3.10 Example of a binding energy curve: (a) energy vs separation; (b) force vs separation (From Banerjea,

A et al (1991), in Fundamentals of Adhesion (Liang-Huang Lee, ed.), Plenum Press, New York With permission.)

FIGURE 3.11 Adhesive energy vs separation: (a) commensurate adhesion is assumed; (b) incommensurate sion is assumed (From Rose, J.H et al (1983), Phys Rev B 28, 1835–1845 With permission.)

adhe-Assuming some energy dissipation mechanism to be present, they calculated tangential force as a function

of load and sliding position

Sokoloff (1990, 1992, and references therein) addresses both the friction force and frictional energy

dissipation He represents the atoms in the solids as connected by springs, thus enabling an energy

dissipation mechanism by way of lattice vibrations He also looks at such issues as the energy to create

and move defects in the sliding process and examines the velocity dependence of kinetic friction based

on the possible processes present, including electronic excitations (Sokoloff, 1995) Persson (1991) also

proposes a model for energy dissipation due to electronic excitations induced within a metallic surface

Persson (1993, 1994, 1995) addresses in addition the effect of a boundary lubricant between macroscopic

bodies, modeling fluid pinning to give the experimentally observed logarithmic time dependence of

various relaxation processes Finally, as more fully covered in other chapters of this book, much recent

effort has gone into modeling specifically the lateral force component of the probe tip interaction with

a sample surface in scanning probe microscopy (e.g., Hölscher et al., 1997; Diestler et al., 1997, and

references therein; Lantz et al., 1997)

In conclusion, while these types of simulations may not reflect the fully complexity of real materials,

they are necessary and useful Although limited in scope, it is necessary to break down such complex

problems into isolated phenomena which it is hoped can result in the eventual unification to the larger

picture It simply is difficult to isolate the various components contributing to friction experimentally

3.4 Experimental Determinations of Surface Structure

In this section we will discuss three techniques for determining the structure of a crystal surface,

low-energy electron diffraction (LEED), high-resolution electron microscopy (HREM), and field ion

micros-copy (FIM) The first, LEED, is a diffraction method for determining structure and the latter two are

methods to view the lattices directly There are other methods for determining structure such as ion

FIGURE 3.12 Scaled adhesive binding energy as a function of scaled separation for systems in Figure 3.11 (From

Rose, J.H et al (1983), Phys Rev B 28, 1835–1845 With permission.)

scattering (Niehus et al., 1993), low-energy backscattered electrons (De Crescenzi, 1995), and even

sec-ondary electron holography (Chambers, 1992), which we will not discuss Other contributors to this

book address scanning probe microscopy and tribology, which are also nicely covered in an extensive

review article by Carpick and Salmeron (1997)

3.4.1 Low-Energy Electron Diffraction

Since LEED is a diffraction technique, when viewing a LEED pattern, you are viewing the reciprocal

lattice structure and not the atomic locations on the surface A LEED pattern typically is obtained by

scattering a low-energy electron beam (0 to 300 eV) from a single-crystal surface in ultrahigh vacuum

In Figure 3.13 we show the LEED pattern for the W(110) surface with a half monolayer of oxygen adsorbed

on it (Ferrante et al., 1973) We can first notice in Figure 3.13a that the pattern looks like the direct lattice

W(110) surface, but this only means that the diffraction pattern reflects the symmetry of the lattice

Notice that in Figure 3.13b extra spots appear at ½ order positions upon adsorption of oxygen Since

this is the reciprocal lattice, this means that the spacings of the rows of the chemisorbed oxygen actually

are at double the spacing of the underlying substrate In fact, the interpretation of this pattern is more

complicated since the structure shown would not imply a ½ monolayer coverage, but is interpreted as

an overlapping of domains at 90° from one another In this simple case the coverage is estimated by

adsorption experiments, where saturation is interpreted as a monolayer coverage The interpretation of

patterns is further complicated, since with complex structures such as the silicon 7 × 7 pattern, the direct

lattice producing this reciprocal lattice is not unique Therefore, it is necessary to have a method to select

between possible structures (Rous and Pendry, 1989)

We now digress for a moment in order to discuss the diffraction process The most familiar reference

work is X-ray diffraction (Kittel, 1986) We know that for X rays the diffraction pattern of the bulk would

produce what is known as a Laue pattern where the spots represent reflections from different planes

The standard diffraction condition for constructive interference of a wave reflected from successive planes

is given by the Bragg equation

(3.10)

where d is an interplanar spacing, θ is the diffraction angle, λ is the wavelength of the incident radiation,

and n is an integer indicating the order of diffraction Only certain values of θ are allowed where

diffractions from different sets of parallel planes add up constructively There is another simple method

for picturing the diffraction process known as the Ewald sphere construction (Kittel, 1986), where it can

be easily shown that the Bragg condition is equivalent to the relationship

FIGURE 3.13 LEED pattern for (a) clean and (b) oxidized tungsten (110) with one half monolayer of oxygen The

incident electron beam energy for both patterns is 119 eV (From Ferrante, J et al (1973), in Microanalysis Tools and

Techniques (McCall, J L and Mueller, W M., eds.), Plenum Press, New York With permission.)

2dsinθ=nλ

where→k is the wave vector (2π/λ) of the incident beam,→k′ is the wave vector of the diffracted beam, and

→

G is a reciprocal lattice vector The magnitude of the wave vectors k = k′ are equal since momentum is

conserved; i.e., we are only considering elastic scattering Therefore, a sphere of radius k can be

con-structed, which when intersecting a reciprocal lattice point indicates a diffracted beam This is equivalent

to the wave vector difference being equal to a reciprocal lattice vector, with that reciprocal lattice vectornormal to the set of planes of interest, and θ the angle between the wave vectors In complex patterns,spot intensities are used to distinguish between possible structures The equivalent Ewald constructionfor LEED is shown in Figure 3.14 We note that the reciprocal lattice for a true two-dimensional surfacewould be a set of rods instead of a set of points Consequently, the Ewald sphere will always intersect therods and give diffraction spots resulting from interferences due to scattering between rows of surfaceatoms, with the number of spots changing with electron wavelength and incident angle However, forLEED complexity results from spot intensity modulation by the three-dimensional lattice structure, anddetermining that direct lattice from the spot intensities In X-ray diffraction the scattering is described

as kinematic, which means that only single scattering events are considered With LEED, multiplescattering occurs because of the low energy of the incident electrons; thus structure determination involvessolving a difficult quantum mechanics problem Generally, various possible structures are constructedand the multiple scattering problem is solved for each proposed structure The structure that minimizesthe difference between the experimental intensity curves and the theoretical calculations is the probablestructure There are a number of parameters involved with atomic positions and electronic properties,and the best fit parameter is denoted as the “R-factor.” In spite of the seeming complexity, considerableprogress has been made and computer programs for performing the analysis are available (Van Hove

FIGURE 3.14 Ewald sphere construction for LEED (From Ferrante, J et al (1973), in Microanalysis Tools and

Techniques (McCall, J L., and Mueller, W M., eds.), Plenum Press, New York With permission.)

r r r

k k− ′ =G

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 down to the level

of the atomic ordering in alloys To understand fully the behavior of materials as a function of theircomposition, processing history, and structural characteristics, the highest resolution examination toolsare needed In this section we will limit the discussion to electron microscopy techniques using commonlyavailable equipment and capable or achieving atomic-scale resolution Traditional scanning electronmicroscopy (SEM), therefore, will not be discussed, although in tribology SEM has been and shouldcontinue to prove very useful, particularly when combined with X-ray spectroscopy Many modern Augerelectron spectrometers (discussed in the next section on surface chemical analysis) also have high-resolution scanning capabilities, and thus can perform imaging functions similar to a traditional SEM.Another technique not discussed here is photoelectron emission microscopy (PEEM) While PEEM canroutinely image photoelectron yield (related to the work function) differences due to single atomic layers,lateral resolution typically suffers in comparison to SEM PEEM has been applied to tribological materials,however, with interesting results (Montei and Kordesch, 1996)

Both transmission electron microscopy (TEM) and scanning transmission electron microscopy(STEM) make use of an electron beam accelerated through a potential of, typically, up to a few hundredthousand volts Generically, the parts of a S/TEM consist of an electron source such as a hot filament orfield 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 forimmediate viewing combined with a film transport and exposure mechanism for recording images Thesample is inserted directly into the beam column and must be electron transparent, both of which severelylimit sample size There are numerous good texts available about just TEM and STEM (e.g., Hirsch et al.,1977; Thomas and Goringe, 1979)

An advantage to probing a sample with high-energy electrons lies in the De Broglie formula relatingthe motion of a particle to its wavelength

(3.12)

where λ is the electron wavelength, h is the Planck constant, m is the particle mass, and E k is the kineticenergy of the particle An electron accelerated through a 100-kV potential then has a wavelength of0.04 Å, well below any diffraction limitation on atomic resolution imaging This is in contrast with LEED,for which electron wavelengths are typically of the same order as interatomic spacings As the electronbeam energy increases in S/TEM, greater sample thickness can be penetrated with a usable signal reachingthe detector Mitchell (1973) discusses the advantages of using very high accelerating voltages, which atthe time included TEM voltages up to 3 MV

As the electron beam traverses a sample, any crystalline regions illuminated will diffract the beam,forming patterns characteristic of the crystal type Apertures in the microscope column allow the dif-fraction patterns of selected sample areas to be observed Electron diffraction patterns combined with

an ability to tilt the sample make determination of crystal type and orientation relatively easy, as discussed

in Section 4.1 above for X-ray Ewald sphere construction Electrons traversing the sample can alsoundergo an inelastic collision (losing energy), followed by coherent rescattering This gives rise to cones

of radiation which reveal the symmetry of the reflecting crystal planes, showing up in diffraction images

as “Kikuchi lines,” named after the discoverer of the phenomenon The geometry of the Kikuchi linesprovides a convenient way of determining crystal orientation with fairly high accuracy Another technique

λ =

( )2mE h k 1 2

for illuminating sample orientation uses an aperture to select one of the diffracted beams to form theimage, 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 variousdislocations, stacking faults, or even strain around a small inclusion How that contrast changes withmicroscope settings can reveal information about the defect For example, screw dislocations may “dis-appear” (lose contrast) for specific relative orientations of crystal and electron beam An additional tool

in examining the three-dimensional structures within a sample is stereomicroscopy, where two images

of the same area are captured tilted from one another, typically by around 10° The two views are thensimultaneously shown each to one eye to reveal image feature depth

For sample elemental composition, both an X-ray spectrometer and/or an electron energy-loss trometer can be added to the S/TEM Particularly for STEM, due to minimal beam spreading duringpassage through the sample the analyzed volume for either spectrometer can be as small as tens ofnanometers in diameter X-ray and electron energy-loss spectrometers are somewhat complementary intheir ranges of easily detected elements Characteristic X rays are more probable when exciting the heavierelements, while electron energy losses due to light element K-shell excitations are easily resolvable.Both TEM and STEM rely on transmission of an electron beam through the sample, placing an upperlimit on specimen thickness which depends on the accelerating voltage available and on specimencomposition Samples are often thinned to less than a micrometer in thickness, with lateral dimensionslimited to a few millimeters An inherent difficulty in S/TEM sample preparation thus is locating a givenregion of interest within the region of visibility in the microscope, without altering sample characteristicsduring any thinning process needed For resolution at an atomic scale, columns of lighter element atomsare needed for image contrast, so individual atoms are not “seen.” Samples also need to be somewhatvacuum compatible, or at least stable enough in vacuum to allow examination The electron beam itselfmay alter the specimen by heating, by breaking down compounds within the sample, or by depositingcarbon on the sample surface if there are residual hydrocarbons in the microscope vacuum In short,S/TEM specimens should be robust under high-energy electron bombardment in vacuum

spec-3.4.3 Field Ion Microscopy

For many decades, FIM has provided direct lattice images from sharp metal tips Some early efforts toexamine contact adhesion used the FIM tip as a model asperity, which was brought into contact withvarious surfaces (Mueller and Nishikawa, 1968; Nishikawa and Mueller, 1968; Brainard and Buckley,

1971, 1973; Ferrante et al., 1973) As well, FIM has been applied to the study of friction (Tsukizoe et al.,1985), the effect of adsorbed oxygen on adhesion (Ohmae et al., 1987), and even direct examination ofsolid 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 atomimpinging on the tip experiences a high electric field due to the small tip radius This field polarizes theatom and creates a reasonable probability that an electron will tunnel from the atom to the metal tipleaving behind a helium ion Ionization is most probable directly over atoms in the tip where the localradius of curvature is highest Often, only 10 to 15% of the atoms on the tip located at the zone edgesand at kink sites are visible The helium ions are then accelerated to a phosphorescent screen at somedistance from the tip, giving a large geometric magnification Uncertainty in surface atom positions isoften reduced by cooling the tip to liquid helium temperature Figure 3.15 is an FIM pattern for a cleantungsten tip oriented in the (110) direction The small rings are various crystallographic planes thatappear on a hemispherical single-crystal surface A classic discussion of FIM pattern interpretation can

be found in Mueller (1969), a recent review has been published by Kellogg (1994), and a more extensivediscussion of FIM in tribology can be found in Ohmae (1993)

3.5 Chemical Analysis of Surfaces

In this section we will discuss four of the many surface chemical analytic tools which we feel have hadthe widest application in tribology, Auger electron spectroscopy (AES), X-ray photo-electron spectros-copy (XPS), secondary ion mass spectroscopy (SIMS), and infrared spectroscopy (IRS) AES gives ele-mental analysis of surfaces, but in some cases will give chemical compound information XPS can givecompound information as well as elemental SIMS can exhibit extreme elemental sensitivity as well as

“fingerprint” lubricant molecules IR can identify hydrocarbons on surfaces, which is relevant becausemost lubricants are hydrocarbon based Hantsche (1989) gives a basic comparison of some surface analytictechniques Before launching into this discussion we wish to present a general discussion of surfaceanalyses We use a process diagram to describe them given as

FIGURE 3.15 Field ion microscope pattern of a clean tungsten tip oriented in the (110) direction (From Ferrante,

J et al (1973), in Microanalysis Tools and Techniques ( McCall, J L and Mueller, W M., eds.), Plenum, Press New

York With permission.)

3.5.1 Auger Electron Spectroscopy

The physics of the Auger emission process is shown in Figure 3.16 An electron is accelerated to an energysufficient to ionize an inner level of an atom In the relaxation process an electron drops into the ionizedenergy level The energy that is released from this de-excitation is absorbed by an electron in a higherenergy level, and if the energy is sufficient it will escape from the solid The process shown is called aKLM transition, i.e., a level in the K-shell is ionized, an electron decays from an L-shell, and the finalelectron is emitted from an M-shell Similarly, a process involving different levels will have correspondingnomenclature The energy of the emitted electron has a simple relationship to the energies of the levelsinvolved, depending only on differences between these levels The relationships for the process shown are

is shown schematically in Figure 3.17 The dispersion of the emitted electrons is usually accomplished

by any of a number of electrostatic analyzers, e.g., cylindrical mirror or hemispherical analyzers Althoughthe operational details of the analyzers differ somewhat, the net result is the same

An example spectrum is shown in Figure 3.18 for a wear scar on a pure iron pin worn with dibutyladipate with 1 wt % zinc-dialkyl-dithiophosphate (ZDDP) This spectrum corresponds to the firstderivative of the actual spectral lines (peaks) in the spectrum (Brainard and Ferrante, 1979)

FIGURE 3.16 Auger transition diagram for an atom (From Ferrante, J et al (1973), in Microanalysis Tools and

Techniques ( McCall J L and Mueller W M., eds.), Plenum Press, New York With permission.)

∆Efinal=∆Einitial

EAuger=E K−E L−E M