Bhushan B. Handbook of Micro/Nano Tribology, Second Edition

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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 allow

both surfaces to adjust and examine the effects of velocity with attention to the three rules of friction

stated above. They argue, not based on their calculations, that the Bowden and Tabor argument is not

consistent 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. With

respect to rule 3, they ﬁnd it restricted to certain circumstances. They found that the dynamic friction

force, in general, is sliding velocity dependent, but with a decreasing velocity dependence with increasing

maximum static friction force. Hence, for systems with large static friction forces, the kinetic friction

force shows behavior similar to classical rule 3, above. Finally, Zhong and Tomanek (1990) performed a

ﬁrst-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 adhe-

sion is assumed. (From Rose, J.H. et al. (1983),

Phys. Rev. B

28, 1835–1845. With permission.)

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

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

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

is an interplanar spacing,

is the diffraction angle,

is the wavelength of the incident radiation,

and

is an integer indicating the order of diffraction. Only certain values of

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.)

2dnsin θλ=

(3.11)

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 vector

normal 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 construction

for LEED is shown in Figure 3.14. We note that the reciprocal lattice for a true two-dimensional surface

would be a set of rods instead of a set of points. Consequently, the Ewald sphere will always intersect the

rods and give diffraction spots resulting from interferences due to scattering between rows of surface

atoms, with the number of spots changing with electron wavelength and incident angle. However, for

LEED complexity results from spot intensity modulation by the three-dimensional lattice structure, and

determining 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, multiple

scattering occurs because of the low energy of the incident electrons; thus structure determination involves

solving a difﬁcult quantum mechanics problem. Generally, various possible structures are constructed

and the multiple scattering problem is solved for each proposed structure. The structure that minimizes

the difference between the experimental intensity curves and the theoretical calculations is the probable

structure. 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, considerable

progress 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.)

kk 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 their

composition, processing history, and structural characteristics, the highest resolution examination tools

are needed. In this section we will limit the discussion to electron microscopy techniques using commonly

available equipment and capable or achieving atomic-scale resolution. Traditional scanning electron

microscopy (SEM), therefore, will not be discussed, although in tribology SEM has been and should

continue to prove very useful, particularly when combined with X-ray spectroscopy. Many modern Auger

electron 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 can

routinely 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 hundred

thousand volts. Generically, the parts of a S/TEM consist of an electron source 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, both of which severely

limit 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 relating

the 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

is the kinetic

energy of the particle. An electron accelerated through a 100-kV potential then has a wavelength of

0.04 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 electron

beam energy increases in S/TEM, greater sample thickness can be penetrated with a usable signal reaching

the detector. Mitchell (1973) discusses the advantages of using very high accelerating voltages, which at

the 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 also

undergo 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 lines

provides a convenient way of determining crystal orientation with fairly high accuracy. Another technique

λ=

()

for illuminating sample orientation uses an aperture to select one of the 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. 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 then

simultaneously 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 spec-

trometer can be added to the S/TEM. Particularly for STEM, due to minimal beam spreading during

passage through the sample the analyzed volume for either spectrometer can be as small as tens of

nanometers in diameter. X-ray and electron energy-loss spectrometers are somewhat complementary in

their ranges of easily detected elements. Characteristic X rays are more probable when exciting the heavier

elements, 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 upper

limit on specimen thickness which depends on the accelerating voltage available and on specimen

composition. Samples are often thinned to less than a micrometer in thickness, with lateral dimensions

limited to a few millimeters. An inherent difﬁculty in S/TEM sample preparation thus is locating a given

region of interest within the region of visibility in the microscope, without altering sample characteristics

during any thinning process needed. For resolution at an atomic scale, columns of lighter element atoms

are needed for image contrast, so individual atoms are not “seen.” Samples also need to be somewhat

vacuum compatible, or at least stable enough in vacuum to allow examination. The electron beam itself

may alter the specimen by heating, by breaking down compounds within the sample, or by depositing

carbon 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.

3.4.3 Field Ion Microscopy

For many decades, FIM has provided direct lattice images from sharp metal tips. Some early efforts to

examine contact adhesion used the FIM tip as a model asperity, which was brought into contact with

various 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 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 polarizes the

atom and creates a reasonable probability that an electron will tunnel from the atom to the metal tip

leaving behind a helium ion. Ionization is most probable directly over atoms in the tip where the local

radius of curvature is highest. Often, only 10 to 15% of the atoms on the tip located at the zone edges

and at kink sites are visible. The helium ions are then accelerated to a phosphorescent screen at some

distance from the tip, giving a large geometric magniﬁcation. Uncertainty in surface atom positions is

often reduced by cooling the tip to liquid helium temperature. Figure 3.15 is an FIM pattern for a clean

tungsten tip oriented in the (110) direction. The small rings are various crystallographic planes that

appear 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 extensive

discussion 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 had

the 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 give

compound 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 because

most lubricants are hydrocarbon based. Hantsche (1989) gives a basic comparison of some surface analytic

techniques. Before launching into this discussion we wish to present a general discussion of surface

analyses. We use a process diagram to describe them given as

EXCITATION (INTERACTION)

⇓

DISPERSION

⇓

DETECTION

⇓

SPECTROGRAM

The ﬁrst step, excitation in interaction, represents production of the particles or radiation to be

analyzed. In light or photon emission spectroscopy a spark causes the excitation of atoms to higher energy

states, thus emitting characteristic photons. The dispersion stage could be thought of as a ﬁltering process

where the selected information is allowed to pass and other information is rejected. In light spectroscopy

this would correspond to the use of a grating or prism, for an ion or electron it might be an electrostatic

analyzer. Next is detection of the particle which could be a photographic plate for light or an electron

multiplier for ions or electrons. And, ﬁnally, the spectrogram tells what materials are present and, it is

hoped, how much is there.

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 energy

sufﬁcient to ionize an inner level of an atom. In the relaxation process an electron drops into the ionized

energy level. The energy that is released from this de-excitation is absorbed by an electron in a higher

energy level, and if the energy is sufﬁcient it will escape from the solid. The process shown is called a

KLM transition, i.e., a level in the K-shell is ionized, an electron decays from an L-shell, and the ﬁnal

electron is emitted from an M-shell. Similarly, a process involving different levels will have corresponding

nomenclature. The energy of the emitted electron has a simple relationship to the energies of the levels

involved, depending only on differences between these levels. The relationships for the process shown are

(3.13)

giving

(3.14)

Consequently, since the energy levels of the atoms are generally known, the element can be identiﬁed.

There are surprisingly few overlaps for materials of interest. When peaks do overlap, other peaks peculiar

to the given element along with data manipulation can be used to deconvolute peaks close in energy.

AES will not detect hydrogen, helium, or atomic lithium because there are not enough electrons for the

process to occur. AES is surface sensitive because the energy of the escaping electrons is low enough they

cannot originate from very deep within the solid without detectable inelastic energy losses. The equipment

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. Although

the 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 dibutyl

adipate with 1 wt. % zinc-dialkyl-dithiophosphate (ZDDP). This spectrum corresponds to the ﬁrst

derivative 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.)

∆∆EE

final initial

EEEE

KLMAuger

=−−

Historically, ﬁrst-derivative spectra were taken because the actual peaks were very small compared

with the slowly varying background, posing signal-to-noise problems when ampliﬁcation was sufﬁcient

to bring out the peak. The derivative emphasized the more rapidly changing peak, but made quantiﬁcation

more difﬁcult, since the AES peaks are not a simple shape such as Gaussian, where a quantitative

relationship exists between the derivative peak-to-peak height and the area under the original peak. The

advent of dedicated microprocessors and the ability to digitize the results enable more-sophisticated

treatment of the data. The signal-to-background problem can now be handled by modeling the back-

ground and subtracting it, leaving an enhanced AES peak. Thus, the number of particles present can be

obtained by ﬁnding the area under the peak, enhancing the quantitative capability of AES. AES can be

chemically sensitive in that energy levels may shift when chemical reactions occur. Large shifts can be

detected in the AES spectrum, or alternatively peak shapes may change with chemical reaction. Some

examples of these effects will be given later in the chapter.

There are two other techniques that are used in conjunction with AES that should be mentioned,

scanning Auger microscopy (SAM) and depth proﬁling. SAM is simply “tuning” to a particular AES peak

and rastering the electron beam in order to obtain an elemental map of a surface. This can be particularly

FIGURE 3.17 Schematic diagram of AES apparatus. (From Ferrante, J. (1982), J. Am. Soc. Lubr. Eng. 38, 223–236.

With permission.)

FIGURE 3.18 Auger spectrum of wear scar on pure iron pin run against M2 tool steel disk in dibutyl adipate

containing 1 wt% ZDPP. Sliding speed, 2.5 cm/s; load, 4.9 N; atmosphere, dry air. (From Brainard, W. A. and Ferrante,

J. (1979), NASA TP-1544, Washington, D.C.)