Volume 18 - Friction, Lubrication, and Wear Technology Part 12 ppt

The emission of secondary ions depends on the chemical and physical characteristics of the target surface, the primary beam characteristics, and the matrix characteristics of the target

Fig 27 Time-of-flight data for species composing the 1.9 eV ESDIED peak

Fig 28 Time-of-flight data for species composing the 3.5 eV ESDIED peak

It has been shown (Ref 55) that the time-of-flight of an ion is proportional to its mass The relationship is time-of-flight = 4.2 , where m is the mass of the ion Hence, flight times of 4.2, 16.4, and 16.9 s are expected for H+, O+, and OH+, respectively Time-of-flight data for the 3.5 eV ESDIED peak also shows that H+ is being desorbed, but that O+ and/or

OH+ are probably not

ESD Applications. The data acquired for the polycrystalline tin oxide sample discussed in the previous section is discussed further here Consider the ESDIED and time-of-flight data shown in Fig 29 The data were acquired after annealing for 30 min at 600 °C (1110 °F) and 9.3 × 10-7 Pa (7.0 × 10-9 torr) Note that the 1.9 eV ESDIED peak is very small relative to the higher-energy peak around 4.3 eV The time-of-flight data of Fig 30 and 31 show that O+ and OH+are both desorbed, and the 4.3 eV peak has more O+ than OH+, relative to the 1.9 eV peak

Fig 29 ESDIED spectrum for polycrystalline tin oxide sample following annealing in vacuum for 30 min at 600

°C (1110 °F)

Fig 30 Time-of-flight data for species composing the 1.9 eV ESDIED peak following annealing in vacuum for 30

min at 600 °C (1110 °F)

Fig 31 Time-of-flight data for species composing the 4.3 eV ESDIED peak following annealing in vacuum for 30

min at 600 °C (1110 °F)

The ESD data can be explained by the following considerations First, it is necessary to realize that tin oxide undergoes dehydration for the annealing conditions used This has been shown by Cox (Ref 57) using valence band ESCA If it is noted that the O+ and OH+ desorption signal is very small prior to annealing, but significantly larger following annealing,

it is clear that the surface O+ and OH+ for the clean sample, prior to annealing, are not active with regard to desorption by electron stimulation However, the O+ and OH+ that remain after dehydration are amenable to desorption by electron stimulation Therefore, oxygen and hydrogen not associated with water of hydration have been distinguished because these bonding states are active with respect to ESD, whereas those associated with water of hydration are not

It is possible to test this interpretation by exposing the sample to an oxidizing atmosphere This was accomplished by annealing the sample in oxygen for 1.5 h at 400 °C (750 °F) at 1.3 × 10-4 Pa (10-6 torr.) The ESDIED and time-of-flight data are shown in Fig 32 33 34 The 1.9 eV ESDIED peak has increased in size relative to that observed for the previous

600 °C (1110 °F) annealing treatment The relative amounts of O+ and OH+ being desorbed have also decreased again, compared with data collected following the 600 °C (1110 °F) annealing treatment

Fig 32 ESDIED spectrum for polycrystalline tin oxide sample following annealing in oxygen for 90 min at 400

°C (750 °F)

Fig 33 Time-of-flight data for species composing the 4.3 eV ESDIED peak following annealing in oxygen for 90

min at 400 °C (750 °F)

Fig 34 Time-of-flight data for species composing the 4.3 eV ESDIED peak following annealing in oxygen for 90

min at 400 °C (750 °F)

It is reasonable to expect oxygen supplied to the sample during the oxidation treatment to become associated with vacancies generated during the dehydration process Therefore, it can be concluded that the 1.9 eV ESDIED peak is associated with water of hydration, and the higher-energy ESDIED peak is associated with other species, such as oxygen bound to tin, in the lattice structure

Thus, oxygen and hydroxyl groups associated with water of hydration are not active with regard to desorption by electron stimulation, relative to oxygen and hydroxyl groups associated with other bonding situations ESD has been used to distinguish these oxygen and hydrogen types

ESD is a valuable technique because it enables hydrogen detection and it can be used with minimum modifications to existing AES equipment The major drawback is that data interpretation beyond identification of desorbing species is often difficult An alternative to ESD is discussed next

Secondary Ion Mass Spectrometry (SIMS)

SIMS is an analytical technique that has become very popular over the past few years Enhanced element sensitivity and hydrogen detection capability (order of ppm) are two advantages of SIMS that AES and XPS techniques do not offer Its primary disadvantages are that it is inherently a destructive technique and quantitation is more difficult, relative to techniques such as AES and XPS

Specific examples of the application of SIMS to studies of wear, lubrication, and friction are somewhat limited, when compared with techniques such as AES An excellent example of the application of SIMS to study material transfer

resulting from abrasive contact between a ceramic and several metals is described in Ref 58 SIMS is particularly suited

to such studies if the amounts of material transferred are expected to be very small

SIMS Fundamentals. The SIMS process is performed by bombarding the surface of a solid target material of interest with a beam of energetic ions The ions composing the bombarding beam are referred to as primary ions These ions can

be delivered to the target surface at energies up to approximately 40 keV The result of collision processes between primary ions and the target surface of interest is the emission of negative, positive, and neutral species The term

"species" is employed to indicate that ions or agglomerations of atoms bearing a net charge can be emitted from the surface The species emitted from the surface are analyzed in terms of their mass-to-charge ratios (m/e) Therefore, only charged species can be analyzed Neutral species that have been sputtered from the surface must first be ionized before analysis is possible

It is important to point out that charged species leaving the target surface as a result of sputtering constitute only a small portion of all sputtered atoms leaving the surface This typically ranges from a few hundredths of a percent, up to approximately 1% Discussions of analytical descriptions of secondary ion yield and parameters that influence the overall yield, such as ionization probability, are discussed in Ref 46 and 47

SIMS can be performed in two modes In one case, the primary ion beam is rastered over the surface covering an area of approximately 50 × 50 m (2 × 2 mils) (Ref 46) This mode of analysis is referred to as static SIMS and is characterized

by a relatively slow removal rate of atoms from the surface of the target material

Alternatively, the primary ion beam can be focused on an area of submicron dimension and material removed at very high rates relative to static SIMS This mode of operation is referred to as dynamic SIMS Its sampling depth is on the order of

103 nm, whereas static SIMS is characterized by sampling depths of only a couple of atomic layers (Ref 46)

SIMS is often employed to obtain chemical depth profile information Dynamic SIMS can achieve practical sputter rates,

as well as maximum sensitivity (Ref 46) Therefore, this section focuses on this mode

In most cases, the primary ion beam employed with SIMS is an inert gas However, primary beam systems should be capable of generating both negatively and positively charged ions of reactive gases Negatively charged ions, such as O-, can be used as a primary beam source when sample charging is expected to be a problem With versatility in the primary beam source, electrically insulating materials can be analyzed with a minimum of difficulties

An additional advantage of the ability to implement several types of primary ion beam gases is the effect of secondary ion yield This is because secondary ion yields are influenced by the charge characteristics at the surface Ion yields are maximized when neutralization probabilities are low Therefore, positively charged secondary species are less likely to be neutralized when electronegative atoms are present in surface and near-surface regions of the material from which secondary ions are being sputtered For this reason, if oxygen is used as a primary beam source, rather than an inert gas, the emission of positively charged secondary ions can be expected to be enhanced This point is discussed in Ref 47

The SIMS spectrum consists of a representation of the signal intensity, or count rate, as a function of mass-to-charge ratio (m/e) Consider the SIMS data presented in Fig 35 These data represent a SIMS survey scan for the surface and near-surface regions of a BiOx-Au-glass thin-film system, such as that discussed in the AES section (see Fig 17) The SIMS data in Fig 35 contain several elements that do not appear in the film data in Fig 17 (that is, elements in addition to

Bi, O, Au, and Si) These additional elements are the result of trace contamination of the deposition chamber from previous deposition processes This is an excellent example of the increased sensitivity of SIMS relative to AES

Fig 35 SIMS survey of bismuth layer of BiOx-Au-glass specimen

The reader should be aware that quantitation of SIMS data is a very complicated issue The basis problem is the fact that the secondary ion yield can be significantly influenced by several phenomena that can be very complex in nature The emission of secondary ions depends on the chemical and physical characteristics of the target surface, the primary beam characteristics, and the matrix characteristics of the target material

The most direct method of quantitation is to compare SIMS results with a reference material of known composition for a given set of conditions for data acquisition Of course, this involves the availability of reference materials for all anticipated matrix configurations that might be encountered At best, this is inconvenient It would therefore be helpful if

a myriad of matrix configurations could be evaluated by simply extending data required for a minimum number of reference samples

In principle, this could be accomplished by the ability to extend relative sensitivity factors obtained for a few reference materials to any arbitrary matrix configuration This has been achieved by defining a parameter that characterizes the electronic properties of the surface of the target material (Ref 59)

It is of interest to note that data from internal standards have been employed to specify parameters of a model to predict relative atomic fraction values from secondary ion intensities (Ref 60) The model referenced here has been applied with a reasonable degree of success when one considers that it has been applied to a variety of materials

SIMS equipment includes an ion source (ion gun), a UHV environment, and a detection system that consists of components such that energy and mass selection of the sputtered species occurs prior to the detector References 47 and

59 provide a more detailed equipment description

SIMS Applications. As previously mentioned, SIMS is a valuable technique in terms of detecting elements present in relatively small concentrations, as well as detecting hydrogen These capabilities can be particularly useful in friction, lubrication, and wear problems involving materials that contain hydrogen and/or where small amounts of material transfer occur

Material transfer examples include that which results when materials are in tribocontact and that which results from diffusion processes Material transfer by diffusion is often difficult to substantiate, especially if the amount of mass transfer is relatively small

For the purpose of demonstration, the interdiffusion of constituents composing a layered BiOx-Al-glass system is discussed This system is analogous to the BiOx-Au-glass thin-film system previously discussed and is used here because the amount of interdiffusion associated with high-temperature oxidation of the BiAl-glass-layered structure is substantial and can be clearly identified

Consider the SIMS depth profile data shown in Fig 36 and 37 These data respectively represent results for a layered structure that was not subjected to high-temperature oxidation, and a layered structure that was The secondary ions monitored are Al+, Bi+, O+, and Si+ The data clearly demonstrate that interdiffusion occurs among constituents of the bismuth layer, the metal layer, and the glass substrate It is interesting to note that interdiffusion processes for this system were, in general, not nearly as observable with AES depth profiling as with SIMS Again, this demonstrates the advantage

of the increased sensitivity of SIMS, relative to other surface analytical techniques

Fig 36 SIMS depth profile of layered Bi-Au-glass specimen

Fig 37 SIMS depth profile of layered BiOx-Au-glass specimen

It is important at this point to emphasize that care must be taken when evaluating data acquired near interfacial regions This consideration is often applicable when mass transport by diffusion is of interest The important point is that the sputtering process can produce mixing of constituents across the interface, which results in peak broadening in the composition profile Such broadening can be interpreted as diffusion effects if sufficient care is not taken The most practical way to avoid difficulty is to evaluate reference materials for comparison, as was done here by comparing a sample not subjected to high-temperature oxidation to a sample that was

The capability to detect hydrogen can be very useful in friction, lubrication, and wear studies because such studies often involve systems that contain hydrogen For instance, Sugita and Ueda (Ref 61) studied the wear characteristics of silicon nitride in water with respect to the material produced at the specimen-counterface interface SIMS analysis showed that the worn surface contained silicon bonded to oxygen and hydrogen Therefore, silicon was oxidized as a result of the tribocontact The presence of hydrogen suggests that the oxidized silicon is hydrated to some extent X-ray diffraction data were used in conjunction with the SIMS data to propose a mechanism of material removal for this system of silicon nitride rubbing against silicon nitride in a water environment The mechanism proposed is one in which the silicon in silicon nitride is first oxidized and then converted to an amorphous form of silica hydrate, which is then removed by frictional forces associated with the rubbing of the two silicon nitride faces

Thus, SIMS provides a means by which hydrogen can be detected and a means by which elements can be observed at very low concentrations Its primary disadvantages are that it is inherently a destructive technique and chemical bonding information such as that obtained with XPS and AES is not available

Infrared (IR) Spectroscopy

The IR spectroscopy technique should be mentioned because it is becoming more important in the study of the chemistry

of solid surfaces; however, it will not be treated in detail in this article Infrared spectroscopy has been employed for some time as a routine technique for determining the molecular structure of organic compounds, and therefore it is not a new technique

IR spectroscopy is performed by subjecting the sample to a source of IR radiation This source is sometimes referred to as

an emitter For practical purposes, the IR range is taken to be electromagnetic radiation within the energy range for 200 to 4000/cm In practice, more than one type of emitter is required to cover the entire IR range The electric field of the electromagnetic radiation can couple with oscillating dipoles of vibrating molecules The result of this interaction, or coupling, of the electromagnetic radiation with vibrational energy modes of molecules is absorption of the radiation

The IR absorption spectrum appears in the form of the percent of radiation transmitted through the sample (that is, not absorbed) as a function of IR radiation energy Structures that are expected to be active with regard to IR absorption are those that exhibit a net dipole moment Symmetric molecules, such as N2 and O2, are not expected to exhibit an absorption species for any relative position of the atoms (bond length) On the other hand, molecules such as HCl, NO, and CO are expected to exhibit characteristic absorption frequencies

Problems in friction, lubrication, and wear can involve analysis of surface components that are present in coverages of considerably less than one monolayer This is possible with IR spectroscopy, but most investigators employ the technique

of multiple internal reflectance (MIR) spectroscopy for such studies This technique offers increased sensitivity for surface components, allowing detailed studies of adsorbate-surface interactions In fact, MIR spectroscopy can be used to determine the orientation of adsorbate molecules on solid surfaces Both IR and MIR spectroscopy are discussed further

in Ref 62 and 63

References

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X-Ray Characterization of Surface Wear

C.R Houska, Virginia Polytechnic Institute and State University

Introduction

X-RAY DIFFRACTION and spectroscopy provide a variable-depth probe of the atomic arrangements and composition of near-surface material Depending on the sample, x-ray wavelength, and experimental arrangement, quantitative data from about 10 nm to a number of m can be provided This range of penetration depth can be used to examine wear-modified and unmodified regions Deeper penetrations allow unmodified material to be sampled as a reference for those changes taking place near the surface

The first consideration is to examine the conditions that determine penetration depths for both x-ray diffraction (XRD) and x-ray fluorescence (XRF) Both kinds of data can be obtained using either commercially available equipment or specialized beamlines at synchrotron radiation facilities Synchrotron beamlines allow more flexibility in the choice of wavelengths and provide highly collimated and intense beams that add to the capability to alter the penetration distance

by adjusting the optical arrangement Small glancing angles between the specimen surface and either the incident or diffracted beams are effective in probing closer to the surface

X-rays can become totally reflected from locally flat surfaces at extremely low angles of incidence (<0.25°) Under these conditions, beam penetration becomes anomalous and limited to less than 8 nm Penetration distance, , depends on the angle of incidence, i, relative to the critical angle, c; that is,

(Eq 1)

where = x-ray wavelength (Ref 1)

An uncertainty or divergence in the angle of the incident beam, i, can introduce a large uncertainty in penetration distance A wavy or rough surface and an ideally parallel beam also leads to quantitative uncertainties because i takes on

a range of values Because of these difficulties in determining penetration distance with total reflection, the subsequent discussion involves glancing angles that are greater than the critical angle Above the critical angle, one can define penetration distances more simply using a large data file of absorption coefficients (Ref 2) and more conventional equipment

Surface roughness introduces an additional complication Near the surface, signal-producing material is removed Where

it exist, the beam paths differ from point to point at a fixed distance below the mean surface A fluctuation in path length produces a net decrease in the measured signal (Ref 3) This problem has been studied using severely ground samples and

a correction given in terms of a Gaussian distribution of asperities with correlation (Ref 4)

X-Ray Diffraction and Fluorescence from Flat Surfaces

Analyses of penetration distances are typically based on flat surfaces The surface need only be flat over a distance that allows the incident and outgoing signal beams to see a locally flat region of the surface Under these conditions, beam paths enter and leave near-surface material only once Both diffraction and fluorescence signals are treated together with a common absorption term XRF has one more absorption term, because of a difference in the incident and fluorescence wavelengths

The following discussion refers to a differential element of irradiated area

Fig 1 X-ray optics illustrating: i = angle of incidence, s = signal angle, = angle of tilt from symmetrical

arrangement, and 2 = angle between signal and incident beam Other quantities include A0 = cross-sectional

area of incident beam, and total volume of signal element is A0/sin( + ) multiplied by its thickness, dZ, located at a depth - Z The detector is located at a distance R from the sample

For a diffracting element, QD differs, depending on whether the volume dV contains a single crystal or a polycrystalline

substance Only a polycrystalline substance with a flat surface, which gives (Ref 6, 7)

(Eq 6)

will be considered Here, is the Bragg angle for the sample, VC is the volume of the unit cell, ' is the Bragg angle of the

monochromator, if used, j is the multiplicity, and F is the structure factor If the thermal factor is known, it can be included as an additional term in QD

The exponential term in Eq 2 is of primary interest because it determines beam penetration With a fluorescence signal, two linear absorption coefficients are required; that is, one for the incident beam, i, and another for the signal as it leaves the sample, s For diffraction, the incident and signal wavelength are the same with i = s = The absorption coefficient depends on the material and wavelength

With a homogeneous sample, the contributions from all layers are obtained by integrating Eq 3 One normally integrates

to infinity for a thick sample, giving the effective penetration distance

which is written so as to isolate the effective volume term on the right The term on the left is the reduced integrated

intensity, where P is determined by the total area under a peak

If one considers a pair of rays entering and leaving the sample, penetrating to a distance equal to the effective penetration distance, Z0, the beam is reduced by e-1 purely from sample absorption The accumulated signal from all elements between the surface and Z0 relative to an infinitely thick sample is 1 - e-1, or 0.63 As increases, the trend is for the penetration distance to decrease as the absorption coefficient usually increases However, crossing an absorption edge causes a sudden change in the penetration distance (Ref 8) Another common way of decreasing the penetration distance

is to decrease the angle of incidence below the Bragg angle, , with a fixed 2 This decreases S-1 for a particular Bragg peak as one goes toward smaller glancing angles In fact, one can tilt the sample so that the glancing angle is one the signal side and obtain a similar decrease The direction of tilt does influence the area of beam as it intersects with the sample and gives a higher effective volume at low angles of incidence and, therefore, more intensity

Figure 2 illustrates changes in the effective penetration for a large in angles with CuK ( = 0.1542 nm), CrK ( = 0.2291 nm), a partially stabilized zirconia sample (PSZ), and the (111) and (400) Bragg reflections (Ref 9) A wavelength

of 0.4 nm is also shown with the (111) set to illustrate an extreme wavelength that is only available at a synchrotron radiation beamline Here, it can be seen that when the angle of incidence equals the signal angle, the effective penetration

is a maximum at 0.42 m, and can be further reduced to 0.02 m for ± tilts of 40° This would give glancing angles below 2.9° for a Bragg angle of 42.9° In other words, 63% of the Bragg peak would come from the region between the

surface and 0.02 m Changing from CrK to CuK , radiation increase the maximum penetration from 1.05 to 2.08

m

Fig 2 Examples of effective flat sample penetration depths for (111) and (400) peaks with various wavelengths

(0.4 nm, CrK ) and CuK and tilt angle All are based on the absorption in partially stabilized zirconia and its lattice constant The maximum tilt is limited by and the critical angle for total reflection

One would have to go to even lower glancing angles to attain 0.02 m, which may not be practical with commercial x-ray systems The relatively high absorption coefficient of zirconia tends to give limited penetration A similar family of curves is found for the (400), but with larger penetration distance, because of the larger Bragg angle for the reflection

At a larger , larger tilts are required to attain glancing angle conditions This larger range in is visible when the (111) family is compared with the (400)

X-Ray Diffraction and Fluorescence from Rough Surfaces

The Gaussian distribution is commonly used to describe the distribution of excursions (Ref 9, 10) It is also convenient to

use for x-ray problems With this distribution, the density of excursions from the mean surface plane between locations Z1

and Z1 + dZ1 is

(Eq 10)

where is the standard deviation of the excursions

The area fraction of sample at a distance Z1 from the mean plane is

(Eq 11)

This is the well-known error function complement shown at the right of Fig 3 It is 0.5 at the mean plane, 0 for large positive excursions beyond about +2 , and 1 for those deeper than -2 into the sample

Fig 3 Location of signal-producing elements about the mean plane of a surface with a Gaussian distribution of

asperities Area fraction, Af, of occupied sampling plane is shown to right

X-ray diffraction from polycrystalline samples requires that crystallites be oriented to satisfy Bragg's law For polycrystalline samples, this usually turns out to be a small fraction of the sampling plane, unless one is using an oriented single crystal Consequently, the statistical signal fluctuation from XRD can be large for material near the mean plane, unless the material has very small grains This is not the case for x-ray fluorescence analysis, where all atoms near the surface have a finite probability to contribute a measurable signal

With a real surface, the signal-producing elements are likely to be correlated with absorbing elements in either the entrance path or along an exit path out of the sample This surface roughness problem has been treated using numerical calculations based on a Gaussian distribution with correlation (Ref 4) There is no simple analytical answer to this problem Some general conclusions allow one to establish conditions where surface roughness calculations become unimportant The x-ray theory contains a correlation parameter, c, which indicates how quickly a surface excursion loses correlation with increasing distance, , from a neighboring point A large c causes neighboring points along the surface

to look alike, whereas a small c causes nearby points to be unrelated

An estimate for the value, giving the maximum integrated intensity correction for roughness, can be obtained from

(Eq 12)

Likewise, if one is not to exceed a maximum intensity correction of 15%, the following condition should be satisfied:

The roughness correction has been shown to go to zero at the extremes of 90° and 0° under symmetrical conditions (Ref 3) At these limits, the paths are either completely correlated or are uncorrelated The statistical model previously cited (Ref 4) does not treat the case when an incident or signal ray is likely to see more than one asperity

Experience with the examination of rough surfaces using x-rays is very limited At this time, x-rays do not appear to give results as good as those obtained using profilometer data in order to determine the statistical parameters that describe real surfaces At low glancing angles, either with the incident or the signal beam, one can lose quantitative accuracy of

intensity data when Z0 approaches the mean surface excursion distance However, this need not be a problem for either qualitative chemical or phase identification Routine approaches for identification problems are described in Ref 8

Near-Surface Gradients

Equation 2 defines the reduced intensity in terms of a thin slab element having an irradiated area Ae = A0/sin( + ) For

a single-phase homogeneous material free of strain, all elements can be treated as identical and either summed or integrated to obtain the full signal This led to the integral result for the effective volume, Eq 9 If the surface has been disturbed mechanically, thermally, or chemically, and this produces a change in the spacing of diffracting planes that extends over those probe distances already discussed, the Bragg peaks become distributed over a range of 2 angles Peaks are no longer superimposed at the same position and can be treated as differential behavior Both integral and

differential gradients have been described in terms of a continuous distribution function, Hi(Z), which describes the gradient of i with distance Z below the surface (Ref 11, 12) The subscript designates the kind of distribution; that is,

residual strain, atom type, a particular phase, texture, grain size, or other structural disturbances distributed along a gradient These can be defined as integral or differential gradients with respect to the signal elements, depending on whether the intensity is unshifted or shifted in 2

A feature that exhibits a differential behavior displays a change in the d-spacing with position along the gradient zone

Under these conditions, the diffraction angle 2 between the incident and signals beams changes according to Bragg's law:

A change in d causes a distribution of intensity over a range in 2 angles The most often leads to an asymmetrical

broadening of the Bragg peak, which can be produced by chemical or residual strain gradients The intensity of the diffracted signal is again proportional to the effective volume or the area of sampling plane multiplied by its thickness, which is given by (Ref 13, 14):

(Eq 15)

This depends on the d-spacing gradient, dd/dZ, over each element and leads to a redistribution of the Bragg intensity, along with 2 axis or differential behavior Equation 15 indicates that a small d-spacing gradient tends to give higher

intensity

A fluorescence signal "i" of a fixed wavelength at each position Z gives integral behavior over a gradient zone When

analyzed by a crystal or energy-dispersive detector, one finds that signals at different depths with a common superimpose Therefore, the total signal is obtained by summing all measurable signals to some effective distance below

the surface Here, the signal is not dispersed at each depth -Z Integral behavior is expected from a gradient in the volume

fraction of crystal phases having fixed compositions Here, the diffraction signals accumulate from the entire zone at fixed

2 positions, giving relatively sharp peaks The positions are simply determined from Bragg's law and the published lattice parameters and structures (Ref 8) of the various phases along a zone

Texture can also be treated as an integral quantity because fixed lattice parameters produce an accumulation of diffracted signals from all parts of a zone If a texture gradient exists over the probe distance considered, the variation in relative integrated intensity from one Bragg peak to another will vary, depending on the pole density gradient of the diffracting planes and the probe depth A severe thermal-mechanical disturbance at the surface could produce crystallite reorientation and a measurable texture gradient This problem has not been examined quantitatively

A grain-size gradient in the range that produces x-ray diffraction line broadening (<100 nm) could give different line widths, again, depending on the gradient, probe depth, and instrument resolution Because each diffraction peak occurs at the same 2 position from different portions of the zone, it is considered to be integral behavior A similar argument can

be given for nonuniform strain, but without a uniform strain component This might be produced by a gradient in the dislocation density At high dislocation densities, the diffraction peaks become broadened at fixed 2 positions This leads to an integral behavior, with either line width or shape changing with probe depth

There are normally inherent differences in our ability to accurately detect changes in differential and integral measurements Conventional x-ray diffraction sources are typically of low intensity and require long counting times to attain statistical accuracies better than 5% when polycrystalline samples are used Integral behavior is examined largely from changes in relative intensity measurements as they vary with different probe depths Differential behavior further depends on changes in the intensity distribution with 2 which is usually very sensitive to the gradient profile The accuracy of the 2 scale can easily be 1 in 10,000, making an XRD measurement of differential behavior highly accurate The following sections provide examples of both integral and differential behavior using XRD

Integral Gradient

The examination of phase gradients along a wear track of a partially stabilized zirconia disk by XRD provides an example

of integral behavior Three distinct crystal phases can be present in this material: cubic, tetragonal, and monoclinic Linear, exponential, and stepped distributions have been considered (Ref 11, 12) The exponential distribution can be written as (Ref 11):

and the subscript i refers to the Miller indices (hkl) reflecting at an angle The linear absorption coefficient averaged

over all phases is < > For the exponential distribution given by Eq 11, this simplified to

(Eq 20)

for a flat sample

Fig 4 Experimental near-surface area fraction distribution showing: undisturbed substrate limit, H 0i; surface

area fraction, H si , and location e-1 point in terms of -b i

The quantity S is the path length factor given in Eq 8 with s = i S becomes very large as ± Two cases are considered below

In the first case, the beam samples only a small fraction of the exponential distribution This condition requires that (bi<

>S) 1 A large value for any one of these terms could limit the overall view of the gradient Therefore, it is reasonable

that the effective volume for phase i should be

(Eq 21)

That is, only the phase distributions at the surface are seen

In the second case, if (bi< >S) 1, due to any one or any combination of these terms, the near-surface gradient is too small to be observable Therefore, the effective volume is determined by the volume fraction in the substrate

(Eq 22)

In order to evaluate bi , at least one measurement should be made in the range (b i< >S 1, and additional measurements

are required to solve for H Oi and Hsi These are obtained at different values or with different values, because of a

traveling at 0.3 m/s (1 ft/s) at the point of contact The total time of testing was 61 h XRD patterns from both the worn track and the back side of the disk were obtained with synchrotron radiation of wavelength = 0.24797 nm Two paths were obtained using a typical symmetrical arrangement ( = 0°) and an asymmetrical arrangement having the sample normal tilted toward the incident beam, giving a 6° angle with the diffracted beam The XRD patterns include the (111) and (11 ) reflections of the monoclinic phase [M(111), M(11 )] and the overlapping (111) reflections of the cubic and tetragonal phases [C(111)] and [T(111)], respectively

Figures 5 and 6 show the general features of the symmetrical and asymmetrical diffraction patterns The peak separation was carried out using a Pearson VII least squares fitting procedure Although wear testing introduces a detectable amount

of the tetragonal phase, the combined intensity of C(111) and T(111) are used, along with M(111) and M(11 ) These will be used later to determine the phase distributions of the combined cubic and tetragonal phases The combined C(111) and T(111) reflections are denoted by CT(111)

Fig 5 X-ray diffraction data points for unworn side of a PSZ disk obtained using symmetrical optics and =

0.24797 nm Individual profiles are shown as solid lines Source: Ref 11

Fig 6 X-ray diffraction data points for worn side of PSZ disk obtained with asymmetrical optics and =

0.24797 nm Individual profiles are shown as solid lines Source: Ref 11

A constant volume fraction of the undisturbed bulk region was obtained from the back side of the PSZ disk with CuKradiation and symmetrical diffraction geometry The linear absorption coefficient of PSZ for CuK radiation is of that for the obtained with synchrotron radiation This combination results in deeper penetration of the x-ray beam, which gives an XRD pattern that better represents the phase distribution in the bulk material These intensities gave an

upper limit of 0.445 for the volume fraction of cubic and tetragonal phases (Hoct) Profiles for both the worn track and the polished back side of the disk are shown in Fig 7

Fig 7 Distribution of high-temperature cubic and tetragonal phases for unworn polished sample and worn track

region Source: Ref 11

Different probe lengths are obtained by adjusting S< > The ratio of the reduced intensity of one phase to another is

directly related to the effective volume ratio

(Eq 23)

The notation is defined as follows: i and i' designate any two phases in a sample with n phases The summations over j and j' indicate that more that one peak can be selected from each of the phases Because i and i' can be any two of the n phases, Eq 23 represents a set containing up to (n - 1) independent intensity ratios for a fixed and In the multiple-wavelength technique (Ref 12), one normally uses = 0° in Eq 23 to get 2 (n - 1) intensity ratios in terms of n effective

volumes With the integrated intensity ratios measured from the XRD patterns, the unknown parameters contained in the effective volumes can be determined because varies with Similarly, with multiple-beam paths, one can use a fixed and several tilt angles, , to obtain the intensity ratios in terms of n effective volumes The unknown parameters, located

in the effective volumes, can be obtained from the measured integrated intensities and other data that are normally available

= 6.2 m and a correlation distance ( c) of 81 m For the polished sample, the beam penetration distance was always much larger than , whereas for the ground sample, was always at least a factor of 3 larger

The (111) peak profiles of the polished and the ground FSZ samples were obtained using Cuk radiation and symmetrical diffraction optics The optics The CuK component was obtained using a diffracted beam quartz monochromator and a fine-focus Cu tube Results from the polished and ground samples are shown in Fig 8 Profiles extend asymmetrically toward the low-angle side, because of a state of compression near the surface The (111) profiles

of the polished and the ground samples were also measured, using synchrotron radiation of 0.24794 nm with both symmetrical and asymmetrical optics, at the Oak Ridge National Laboratory beamline (National Synchrotron Light Source), before annealing The polished and ground sample profiles measured with symmetric diffraction optics are shown in Fig 8(a) through (d) Intensity bands are observed from ground and polished samples using two radiations The longer synchrotron wavelength is less penetrating and better emphasizes the distribution near the surface zone

Fig 8 (111) intensity bands from polished and ground samples of partially stabilized zirconia showing

experimental data points and computer simulations (solid lines) for and symmetrical optics with CuK radiation ( - 0.15406 nm), (a) and (b); synchrotron radiation with = 0.24797 nm, (c) and (d); and 3° asymmetric optics with = 0.24797 nm, (e) and (f)

To further emphasize the near-surface regions, (111) profiles of both samples were measured with asymmetrical diffraction optics, as shown in Fig 8(e) and 8(f) Asymmetric diffraction optics were obtained by tilting the sample normal toward the diffracted beam by an amount such that the incident angle is 3° The small incident angle results in less penetration, and, as expected, influences the peak profile for the polished sample The peak profile of the polished sample obtained with asymmetrical diffraction optics enhances the low-angle side of the pattern compared to that found with the symmetrical optics For the ground sample, no change was observed between the profiles obtained with symmetrical and asymmetrical optics This result will be discussed later

After both samples were subsequently annealed at 1200 °C (2190 °F) for 1 h and furnace cooled, the profiles were indistinguishable However, considerable sharpening was observed To check these findings, the samples were repolished

using alumina powder No peak shift was observed, but the profile was extended asymmetrically toward the low-angle side This reconfirms the conclusion that the polishing process introduces a low-level intensity band, and the main peak remains unshifted The peak shift between the profiles of the ground and polished samples before annealing is real, and is due to the extended range of the strain gradient in the severely ground sample

With depth measured from a load surface asperity, the sample can be treated as a system of thin curved layers located at

various depths The d-spacing of each layer is treated as a constant, and the corresponding intensity is calculated using a

theory that includes roughness Figure 9 illustrates two strain profiles obtained from two radiations for the severely ground sample The polished sample is essentially flat, with the layers parallel to the sample surface, whereas the ground sample is rough, and consists of layers of constant strain that follow the same fluctuation as the surface profile The diffraction theory treats the intensity from each layer under both the symmetrical and asymmetrical diffraction conditions

The strain profiles for the polished sample are shown in Fig 10 Because the d-spacing changes continuously from one

layer to another, the intensities are spread over a 2 range according to Bragg's law

Fig 9 Depth profiles of strain for ground sample obtained with symmetrical optics A, CuK radiation; B, =

0.24797 nm (synchrotron radiation) Source: Ref 15

Fig 10 Depth profiles of strain for polished sample obtained under the following conditions: A, symmetrical

optics using CuK ( = 0.15406 nm and = 0.24797 nm) (synchrotron radiation); B, asymmetrical optics with = 0.24797 nm (synchrotron radiation) Source: Ref 15

Computer-simulated intensity bands are compared with the fitted experimental data in Fig 8(a) through (f) Both the measured and simulated (solid lines) profiles are expanded vertically by 10 times at the low-angle side to better show the final fit The redistribution of intensity, in this case, is weak and could be overlooked in routine XRD It could be completely missed in complex powder patterns having many overlapping diffraction peaks

A reexamination of Fig 9 and 10 shows that the maximum compressive strain near the surface is large, giving 4% for the ground surface and 5% for the polished Although polishing gives the highest strain, the overall zone thickness is about the size found after severe grinding

Analysis of Debris Particles

At one instant of time during a wear test, a small fraction of the asperities of a surface become separated as debris particles It would be very instructive to be able to focus only on the characteristics of these regions, that is, to determine the crystal phases, dislocation density, and a statistical description of their arrangement However, these features are lost

in an examination of the overall near-surface region because of their small volume fraction

An alternative is to device efficient methods of collecting the debris particles that break away from these special asperities An analysis of debris particles could be useful in establishing wear mechanisms This collection need not require the dismantling of a machine, but rather, a concentrate of wear fragments could be collected at filter locations Ideally, one would like to look back and relate the structural parameters of debris to the conditions present in the asperities prior to breakaway, and to correlate these findings with machine operational conditions The previous discussion of substrate structure relates to wear conditioning processes Both substrate and debris should be examined in a comparative approach

For material that contain more than one crystal phase, or a material that can undergo further phase transformation, the first question one might ask is: What phases are present? By knowing the stability of these phases from either the equilibrium diagrams or the temperature range of metastable, phases, one can relate back to thermal and chemical conditions prior to the breakaway point This is particularly true if the particles are small and have a high surface/volume ratio, allowing

rapid cooling from the local temperature at an asperity during separation An example of a debris analysis is given later for zirconia

X-ray diffraction profile analysis has been used to examine highly deformed metals since the 1950s More recently, this has been described in Ref 6 and 7 The results provide a mean subgrain size and root mean square strain as a function of distance and crystal direction Early investigations were carried out on "cold-work" filings In other words, powder samples were obtained by filing a solid sample whose average temperature was close to room temperature Any local heating associated with the breakaway process was overlooked in what was considered to be a cold-working process The most reliable data of this type have been reexamined (Ref 15, 16) The process of producing filings can be treated as one form of wear process A major concern of line-shape techniques is the need to examine the full profile as pairs of first- and second-order Bragg peaks When profiles overlap for one reason or another, one must make procedural compromises Recent advances allow a least squares fitting procedure to be used on overlapping data sets (Ref 16) It gives the mean particle size and two strain parameters, < >, < > The mean square strain varies according to

where n gives distance between two points in the crystal in units of the average d-spacing, d, for the first order of a set of reflections (h1k1l1) and (h2k2l2) Strain is determined along columns perpendicular to the reflecting planes Knowing the two strain parameters given above allows < > to be evaluated A pair of fitted profiles obtained from zirconia debris are shown in Fig 11 (Ref 17)

Fig 11 Least squares fitting of (200) (left) and (400) (right) profiles using procedures described in Ref 18

Equation 24 presents the results in a purely statistical form, and does not provide a basic connection with dislocation

theory It has been shown that the two strain parameters noted above, as well as <L>, the average subgrain size, determine

the dislocation density according to (Ref 18, 19):

(Eq 25)

where b is the Burger's vector

This varies directly with < >, and inversely with subgrain size, L A second parameter, obtained from the more-recent line-shape analysis, contains the correlation distance, Rc, for unlike dislocation relative to L This is given by (Ref 17, 18):

For the most part, the dislocation density is high and in the 1011/cm2 range Dislocations are highly correlated, with Rc

close to the average diameter of the subgrain for metallic filings and ZrO2 debris

Table 1 Results for body-centered cubic materials, face-centered cubic aluminum, and partially stabilized cubic zirconia

The results given in Table 1 for body- and face-centered cubic material allow a simple explanation to be given for the

structure of cold-worked fragments Filings show a high degree of correlation (small Rc/<L>) and high dislocation

densities This is related to sample conditions, such as the temperature and local conditions at which a high-density dislocation structure is produced Fragments produced by filing or grinding at room temperature, or even at liquid nitrogen temperature, cannot be "cold." Instead, they are rapidly heated to a high temperature during fracture, and rapidly quenched, because of their high surface-to-volume ratio Dislocations are mobile for short periods of time over short distances and can cluster

Table 1 includes results from cubic debris particles obtained from a worn PSZ The substrate contains three phases, as already discussed It should be noted that the cubic phase is stable at high temperatures, making it reasonable that only the cubic form should be found in the debris The dislocation density for zirconia is the highest entry, whereas the correlation distance is close to the mean diameter One can present the same arguments for zirconia debris as for cold-worked metal filings Prior to breakaway, material at the asperity has a very high dislocation density A high separation temperature allows some dislocation movement to form subgrain clusters

The question of how much debris one must collect for an ideal line-shape analysis needs to be considered Typically, for quantitative work, one would like to be able to fill a cavity of at least 15 mm (0.6 in.) in diameter to a depth of 2 mm (0.08 in.) The sample thickness should be several times the penetration depths already discussed Quantitative diffractometer studies require much more sample than what is required for an x-ray powder camera, but also offer the opportunity for more extensive data analysis

Conclusions and Future Trends

Both the wear-modified phase distribution and the debris indicate that at least a fraction of the surface material has been subjected to high temperatures during wear testing Zirconia debris has an even higher dislocation density than metal filings, indicating severe deformation before breakaway from the surface High correlation between dislocations is likely

to result from a time-restricted, thermally activated process taking place at an elevated temperature immediately after fracture It was found that large residual compressive strains build up in the ground surface region of the zirconia substrate A state of dynamic equilibrium is likely to be present between the production of regions of high defect density-residual strain and relaxations produced by annealing The annealing processes within near-surface bulk substrate material

is likely to offer a spectrum of possibilities

Data from a ground PSZ sample revealed the formation of a place gradient extending over a distance of several microns This represents another form of conditioning that could influence subsequent wear testing Depths from a few tenths to the micron range are typical x-ray probe distances for many commercial materials

Future research will require a careful selection of samples and radiation Quantitative diffractometer data will give the greatest amount of information A part from local surface asperities, the mean surface should be flat Typically, it also should have surface dimensions ranging from 10 to 30 mm (0.4 to 1.2 in.) to fit into commercial systems XRD data should be inter-related with XRF or other near-surface analyses revealing chemical changes Variable penetration depths often allow the condition near a surface to be compared with deeper regions that are relatively unaffected by wear processes

A detailed analysis of diffraction patterns from concentrated industrial wear debris under different conditions may establish trends that predict malfunctions Similarities or differences between the wear from a given machine and testers, which are used to simulate machine conditions, could also be examined

Thin-film attachments are available for most commercial diffractometers, allowing low glancing angles to be attained This can greatly reduce the beam penetration These attachments should be considered for examinations of worn surfaces,

as well as for thin layers of debris

Perhaps the most severe restriction in an x-ray analysis using conventional x-ray sources is the limited area of disturbed surface available for examination using routine pin-on-disk testing One would rather examine square cross sections of at least 15 mm (0.6 in.) Although synchrotron radiation would allow one to examine a small fraction of this size, it is often not readily available A smaller-sized sample used with conventional sources would force compromises in the data analysis and lessen the opportunity to obtain quantitative results Any use of x-rays must begin with a consideration of sample size

References

1 G.H Vineyard, Phys Rev B: Condens Matter, Vol 26, 1982, p 416

2 W.C McMaster, N Kerr Del Grande, J.H Mallett, and J.H Hubbell, "Compilation of X-ray Cross Sections," Report UCRL-50174, Sec I, 1970; Sec II, Rev I, 1969; Sec III, 1969; Sec IV, Lawrence Radiation Laboratory (Livermore), 1969

3 R.J Harrison and A Paskin, Acta Cryst., Vol 17, 1964, p 325

4 B Hwang and C.R Houska, J Appl Phys., Vol 63, 1988, p 5346

5 C.J Sparks, Synchrotron Radiation Research, H Winick and S Doniach, Ed., Plenum Publishing, 1980

6 B.E Warren, X-Ray Diffraction, Addison-Wesley, 1969

7 L.H Schwartz and J.B Cohen, Diffraction from Materials, Springer-Verlag, 1987

8 B.D Cullity, Elements of X-Ray Diffraction, Addison-Wesley, 1978

9 B Hwang, "Near Surface Structure of Ceramic Components," Ph D thesis, Virginia Polytechnic Institute and State University, May 1987

10 T.R Thomas, Rough Surfaces, Longman, London, 1982

11 B Hwang, C.R Houska, G.E Ice, and A Habenschuss, Adv Ceram Mater., Vol 3, 1988, p 189 V

12 R.C Garvie, R.H.K Hannink, and N.V Swain, J Mater Sci Lett., Vol 1, 1982, p 437

13 C.R Houska, J Appl Phys., Vol 41, 1970, p 69

14 C.R Houska, Treatise on Materials Science, Vol 19A, H Herman, Ed., Academic Press Inc., 1980

15 B Hwang, C.R Houska, G.E Ice, and A Habenschuss, J Appl Phys., Vol 63, 1988, p 5351

16 C.R Houska, J Appl Phys., Vol 52, 1981, p 748

17 S Rao and C.R Houska, Acta Cryst., Vol A42, 1986, p 14

18 S Rao and C.R Houska, Matter Res Soc Symp Proc., Vol 138, 1989, p 93

19 S Rao and C.R Houska, Acta Cryst., Vol A44, 1988, p 1021

Basic Tribological Parameters

Horst Czichos, BAM (Germany)

Introduction

TRIBOLOGICAL PARAMETERS are characteristics of mechanical systems with "interacting surfaces in relative motion," including the initiation of motion The tribological processes of interacting surfaces have a dual character They are on one hand necessary for the functional performance of "tribosystems" or "tribocomponents" (see the "Glossary of Terms" in this Volume), but are on the other hand inevitably connected with friction and wear In engineering applications, the functional purpose of trobosystems can be broadly classified into the following categories (Ref 1):

• The guidance, transmission, coupling, control, stop, and annihilation of motion, force, mechanical energy, and power (bearings, joints, gears, clutches, cams and tappets, bolts and nuts, fasteners, and brakes)

• The transportation and control of flow of matter (pipelines, wheel/rail, tire/road, valves, and seals)

• The forming, machining, and tearing of materials (drawing, pressing, cutting, shaping, quarrying, and dredging)

• The generation and transmission of information (printing heads and magnetic recording interfaces)

The diagnosis of friction and wear data of such tribosystems or corresponding laboratory test configurations and test specimens requires special attention because numerous characteristics, parameters, and factors must be taken into consideration This is due to the fact that friction and wear are not intrinsic materials properties, but must be related to the entire system of interacting components, namely materials pairs and interfacial lubricants This is obvious from a comparison between the test conditions to obtain strength data or friction and wear data (Fig 1)

Fig 1 Characteristics and parameters of (a) strength tests and (b) friction and wear tests

In strength tests (Fig 1a), the deformation or fracture resistance of a material specimen in a given environment is determined under the action of a certain stress mode, such as tension, compression, shear, bending, or torsion The

resulting strength data (in terms of force per cross section, or energy) are considered as intrinsic materials properties depending basically on the following groups of parameters:

• Materials parameters, such as composition, microstructure, and specimen geometry

• Operational parameters, such as stress type, load, deformation velocity, and temperature

In a friction or wear test (Fig 1b), the resistance against motion (friction) or the resistance against surface damage (wear)

of a material/material pair (dry system) or a material/lubricant/material combination (lubricated system) in a given environment is determined under the action of a certain type of motion, such as sliding or rolling The resulting tribometric characteristics in particular the friction or wear data must understood as tribological systems characteristics associated with the following group of parameters:

• Structural parameters, which characterize the components (materials, lubricant, and environment)

involved in the friction and wear process and their physical, chemical, and technological properties

• Operational parameters, that is, the loading, kinematic, and temperature conditions and their functional

duration

• Interaction parameters, which characterize, in particular, the action of the operating parameters on the

structural components of the tribological system and define its contact and lubrication modes

Structural Parameters

The analysis of structural parameters must identify first the components involved in a given friction and wear problem Figure 2 shows typical examples of tribosystems subject to friction and wear together with corresponding simplified test configurations and their elementary structure This figure illustrates that in any friction and wear situation, four tribocomponents are involved (Ref 2):

• Triboelement (1)

• Triboelement (2)

• Interfacial element (3), for example, lubricant or dust particles

• Environmental medium (4), for example, air or corrosive atmosphere

Table 1 lists examples of the tribocomponents that make up various tribosystems

Table 1 Structural components of common tribosystems

Tribosystem Triboelement (1) Triboelement (2) Interfacial

Gear box Gear 1 Gear 2 Gear oil Air Closed

Wheel/rail Wheel Rail Moisture Air Open

Sliding guide Slider Support Grease Air Closed

Bearing Bushing Shaft Lubricant Oil mist Closed

Milling system Milling wheel Milling jaw Minerals Air Open

Fig 2 Examples of engineering tribosystems, test configurations, and their elementary structure

In analyzing the structure of tribosystems, a distinction can be made between "closed systems," in which all components are continuously involved in the friction and wear process, and "open systems," in which a materials flow in and out of the system occurs

The friction and wear data of tribosystems depend on various properties of their structural components (tribocomponents) Structural parameters of closed tribosystems can be classified in most cases into two groups

Group A consists of triboelements (1) and (2) and involves:

• Chemical parameters such as volume composition and surface composition

• Physical parameters such as thermal conductivity

• Mechanical parameters such as elastic modulus, hardness, and fracture toughness

• Geometric parameters such as geometry dimensions, and surface topography

• Microstructural parameters such as grain size, dislocation density, and stacking fault energy

Group B consists of interfacial (fluid) element (3) and environmental (gaseous) medium (4) and involves:

• Chemical parameters such as composition, additive content, acidity, and humidity

• Physical parameters such as density, thermal conductivity, and flash and fire point

• Mechanical parameters such as viscosity, and viscosity-temperature and viscosity-pressure

characteristics

For open systems, for example, manufacturing systems such as machining and molding, or quarrying and dredging systems, the structural parameters characterizing the materials flow in and out of the system are often difficult to specify

In addition to the structural elements necessary to fulfill the functional purpose of the tribosystem, detrimental elements such as dirt, dust, and moisture may also be present and must be recognized in the analysis of structural parameters To assist in the compilation of the various parameters relevant to a given friction and wear problem, a data sheet of basic tribological parameters is described later in this article (see the section entitled "Data Sheet of Basic Tribological Parameters" )

Operational Parameters

Operational parameters characterize the functional conditions of a tribosystem They can be considered (with the exception of friction-induced temperatures) as independent variables that can be varied during tribological testing to obtain friction and wear data experimentally The basic operational parameters in tribology are:

• Type of motion, that is, the kinematics of triboelements (1) and (2), to be classified in terms of sliding,

rolling, spin, and impact and their possible superpositions (Fig 3) The kinematics can be continuous, intermittent, reverse, or oscillating

• Load (FN), defined as the total force (including weight) that acts perpendicular to the contact area between triboelement (1) and (2), as shown in Fig 3

• Velocity (v), to be specified with respect to the vector components and the absolute values of the

individual motions of triboelements (1) ad (2) According to the Table 2, distinctions must be made

among the relative velocity vr (relevant to friction-induced temperature rises), the sum velocity vs

(relevant, in lubricated tribosystems, to the formation of an elastohydrodynamic film), and the roll ratios

slide-to-• Temperature (T) of the structural components at stated location and time, that is, the initial

(steady-state) temperature and the friction-induced temperature rise (average temperature rise and flash temperatures) to be estimated on the basis of friction heating calculations (see the following article in this Section on "Design of Friction and Wear Experiments")

• Time dependence of the set of operational parameters (FN, v, T, for example, load cycles and heating or cooling intervals

• Duration (t) of operation, performance, or test

In addition to these functional operational parameters, disturbances such as external vibrations or radiation might need to

be taken into consideration as well

Table 2 Type of motion and velocities of the components of a tribosystem for sliding and sliding and rolling

Fig 3 Kinematics of tribosystems

Interaction Parameters

Interaction parameters characterize the action of the operational parameters on the structural components of tribosystems These parameters define in particular the contact mode and the lubrication mode of a tribosystem with a given material/material or material/lubricant/material structure The contact mode of two touching solid bodies is characterized microscopically by materials interactions, which are described by contact stresses and stress distributions The materials and stress interactions cause a resistance against motion (friction) and may lead to surface damage (wear) Therefore, the materials and stress interactions in tribosystems are also called friction and wear mechanisms, or generally tribological processes, and specified in terms such as adhesion, abrasion, tribochemical reactions, surface fatigue, and so forth

Interface Forces and Energies. Theoretically, the microscopic interaction forces between contacting solids include,

at least in principle, all those types of atomic and molecular interaction that contribute to the cohesion of solids, such as metallic, covalent, and ionic, that is, primary chemical bonds (short-range forces), as well as secondary van der Waals bonds (long-range forces) (Ref 3, 4) These surface forces depend in a complicated manner on the physicochemical nature

of the materials and the structure and composition of the outermost surface layers and contaminants It should also be noted that the chemical composition, the electronic nature, and the microstructure of surfaces may be quite different from that of the subsurface (volume) of a material

Experimentally, the only macroscopic way to characterize adhesive interactions between two solid bodies contacting

under a normal load, FN, is to destroy the bonding and to measure in the opposite direction to FN the force, FA, necessary

for the separation of the surfaces The ratio a = FA/FN is termed the coefficient of adhesion On the microscopic level, it is possible to determine with an atomic force microscope (noise level 2 × 10-11 N) the interface forces (including friction forces) between single atoms of contacting surface tips (Ref 5)

In energetic terms, the formation of a solid/solid contact results in a net release of surface energy resulting from the replacement of two surfaces by one solid/solid interface of lower surface energy The change in surface energy per unit area of contact, , can be written as: