Characterization of Mechanical Properties

     Viewing topography by itself is very informative in the studies of in-situ crystal growth [118, 826], monitoring deformations in various materials [149, 208, 658, 930, 1225] and especially in viewing ordering of structural units at nanoscale [7, 58, 59, 61, 518, 721, 777 812, 1350] (browse also thematic reference lists in Reference collections section). Of these, surface reconstruction phenomenon is studied very well because observation of atomically resolved surfaces of silicon become in a way a benchmark for SPM apparatus as well as for quality of a scanning tip (Fig. 1). During the decade a great progress has been made in improvement of SPM resolution and surface reconstruction of many substances was resolved at nanoscale. The most commonly used SPM methods to resolve atomic structures are Scanning Tunneling Microscopy for investigations of conductive materials and Non-Contact AFM (NC-AFM) for both conductive and nonconductive materials which exploit the shift in resonant frequency of a cantilever as a measure of tip-surface interactions.

Fig. 1 AFM image of Si(111) 7x7 surface reconstruction taken by JEOL JSPM-4500A microscope in tapping mode. Scan size 4 x 4 nm, height 0.4 nm.

     Topographical and frictional (tribological) investigations by means of Scanning Force Microscopy allows for measuring various geometries on the sample surfaces, as well as a number of related parameters such as surface roughness (as a rule, root-mean-square or RMS-roughness is considered), homogeneity etc. Also, such measurements can provide indirect information on mechanical properties of the surfaces or their fragments such as wear resistance, elasticity (stiffness) and so on [593, 1035]. Atomic Force Microscopy for surface topography measurements and Lateral Force Microscopy [1308] are often used in a couple yielding more fruitful, reliable and correct results.

     Scanning Tunneling and Scanning Force Microscopy are very attractive techniques for the characterization of nanostructures prepared by various methods. Augustin et al. [891] investigated the shape and appearance of quite different nanostructures: regular gold particles deposited through the latex particles on glass; tube-like tracks in mica with aspect ratio of 10⁵, made by heavy ion irradiation; atomic-scale modifications made by STM tip on TaNi₂Te₂ atomically flat surface and on blue bronze Rb_0,3MoO₃. Analysis of scanned images can provide insight to the formation mechanisms of such nanostructures and help to vary technological process to attain the desired result.

     Scanning Probe Microscopy is a method of choice for studying of sputtered and evaporated thin films. These films, as a rule, are amorphous or polycrystalline and their structure are found to be predominantly columnar. Many thin film properties are affected by this columnar microstructure. These are thin optical coatings such as MgF₂ and LaF₃ [387, 688, 1209], a number of various metal films deposited using systems from different suppliers [765]. SFM helps to verify and extend so-called structure zone model describing the effect of deposition conditions on the columnar microstructure of thin films.

     Surface roughness is an important factor that influences optical scattering. Diminishing surface roughness is a major means for improvement of optical systems performance. Ion-beam sputtering deposition (IBSD) has been shown to be an excellent method for making low scattering coatings. Lee et al. [626] used Atomic Force Microscopy to determine the quality of dual beam ion sputtered (DBSD) TiO₂ films for optical applications in order to reveal the influence of various sputtering parameters such as deposition energy and oxygen concentration. Authors found conditions result in the best smoothness and minimal surface roughness of the final films.

     Characterization of the particle size, shape and surface morphology is critical for quality control and assurance of the physicochemical properties of final products such as pharmaceutical solid particles including powders and granules. Surface roughness is known to play an important role in the manufacturing process and to affect the physicochemical properties of the drug products. Li and Park [505] performed fractal analysis of pharmaceutical particles by Atomic Force Microscopy. Characterization of surface roughness involves two steps: instrumental measurement and quantification of the surface roughness. The latter includes two attributes: roughness heights and lateral dimensions. Commonly used parameters such as arithmetic mean surface roughness, root-mean-square roughness, average peak to valley height between five highest peaks and five deepest valleys within the sampling length, and skewness, in effect have been found to be poor representations of surface roughness. One should take into consideration another attribute of surface roughness, namely lateral dimension that describes how frequently the surface height changes. It is known that the surface/interface topographies of all materials are fractals at the molecular level and can be represented by decimal number between 2 and 3. Thus, surface roughness characterization can be built on AFM measurements and subsequent fractal analysis approach, which takes into account both roughness heights and lateral dimensions. The results of fractal analysis of four wet granule samples, raw powder materials and freeze-dried mannitol powders revealed an intrinsic relationship between fractal dimension and underlying processes which produced the material and formed the surface morphology.

     Growing interest to fractal approach for the quantitative characterization of surface roughness can also be deduced from a number of earlier and latest works [29, 689, 938]. Here we would emphasize complementary usage of several methods, such as X-ray scattering and AFM which provides more adequate and accurate description of surface roughness allowing to imagine the evolution of the surface topography during various chemical and physical processes as described by Arnault et al. [29]. For instance, the knowledge and the control of the oxidation mechanisms at high temperature is a great challenge for aerospace and metallurgical industries. Numerous questions are still not resolved concerning the early stages of the oxidation kinetics, their temperature dependence, surface and metal/oxide interface morphology. In this way, the study of the fractal surface parameters is valuable to follow the oxidation processes because the surface roughness evolution is in strong relation with the oxide growth mode.

     The authors of the previous paper denote a substantial drawback of SFM, i.e. the small scan area available for fractal analysis. Today's SPM apparatus can image areas spreading over several millimeters as described in [156] by Hosaka et al. The method of "Digital Probing" or "Recession Mode" AFM presented in this work was developed to measure high aspect ratio microelectronic structures without any damage to the measured wafer. In contrast to other well-known methods and techniques a high aspect ratio probe (such as "wisker" or even nanotube) returns far back (up to 2,1 µm) at every measured point of the scan after touching the surface at this point (with contact force within 2-20 nN). This technique allows for measuring steep walls and deep trenches (90-160 nm in width and 600 nm in depth with angles of about 85° as depicted for the typical structure) and effectively suppresses the probe wearing. A pay for this as yet is a very long scan time measures 45 minutes to acquire 256x256 pixels array. This is an example of using AFM in Critical Dimension Metrology (CDM) since proximal probing techniques are the only nondestructive control means applicable at nanoscale.

     Determining of structural accuracy of critical parts within optical spectrometers made by LIGA-process (involves deep X-ray lithography, electroforming and moulding) has been successfully made by AFM [1009]. The "heart" of the spectrometer is self-focusing blazed diffraction grating which structural accuracy and sidewall roughness determine transmission, signal-to-noise ratio, peak intensity and partitioning of the intensity into the different optical orders of the spectrometer. The demanded measurement accuracy of the grating having 1.2 µm step height and 6 µm step width exceeds the resolution of optical microscopes as well as of profilometers. Thus AFM by itself become the method of choice.

     The increasing significance of SPM in tribological investigations at micro- and nanoscale is the consequence of restrictions in performance for other methods, their lack of resolution power or insufficiency of descriptive potential. For instance, several conventional techniques can be applied for calculation of the amount of material loss in tribological experiments such as stylus profilometry or laser profilometry. However, due to ongoing reduction of tribologically stressed components and because the amount of wear often reaches values beyond the detection limit for this techniques Atomic Force Microscopy becomes the method of choice in wear investigations at nanoscale. Among known problems of AFM itself is complexity of multiple measurements on the same sample area after processing the sample, say, using tribometer. Schofer and Santner [681] used specially designed stage on which both stand-alone AFM and tribometer can be mounted in alternate way with high accuracy. This setup allows imaging the same surface section of a sample with an atomic force microscope before and after tribological stressing. Authors performed measurements of hardness indentations on a Si wafer with ultra-high precision and studied wear events due to sliding motion on an AuNi coating and filled polymers for electrical contact systems. Also, means for accuracy improvement of quantitative wear analysis and possible error correction were considered in details.

     The typical procedure of friction force measurements is described in the paper of Bhushan and Sundararajan 600. The tip was scanned along the cantilever axis to obtain coefficient of friction and it was scanned orthogonal to the cantilever axis to obtain friction force maps. Coefficient of friction was obtained from the slope of friction force data measured as a function of normal loads typically ranging from 50 to 250 nN. This approach eliminates any differences in contributions due to the adhesive forces.

     Measuring topography, characterization of friction and wear of amorphous carbon thin films for hard disk data storage applications is of great concern in the development of better overcoats (see also SPM in Data Storage section). Scanning Force Microscopy is an increasingly popular technique to assess film roughness, fractal dimension, or power spectral density. To reveal more subtle features, like topographic anisotropy, image processing is required. Schouterden and Lairson [1006] used digital Wiener filtering to reveal anisotropy in the AFM topography of supersmooth surfaces. Topography and frictional properties (contact forces between tip and sample was of 1-10 nN) of unworn surface and the surfaces worn for 240 and 1500 sec. with sliding diamond counterbody (contact load of 2,4 mN was applied) was measured, and the dependence of local friction force of the z-height and the crosscorrelation between friction and z-height was calculated. It was shown that wear introduces anisotropy on two different levels: directional (in-plane) and z-height anisotropy. Second derivative distributions of unworn surfaces with different wear tracks showed that wear makes the surface preferentially smoother in the wear direction. The local friction force as measured by LFM indicated a change in local surface topography or chemistry upon wear. Assuming the macroscopic friction force is proportional to the real area of contact authors proposed a simple wear model.

     An attempt to apply Atomic Force Microscopy to a quantitative description of profiles and fracture surfaces of hard materials such as carbides was made by Cwajna and Roskosz [330]. Authors agreed that preparation of topography maps enables the determination of not only selected profiles but the whole surface of the investigated fracture and that high resolution is a beneficial feature of atomic microscopy. But one can argue with the conclusion that no possibility of registration, analysis, and quantitative description of phases occurring on fracture surfaces, overlaps, and secondary cracks are possible with AFM because there is a number of additional modes and techniques such as Nanoindentation (it, though, does not belong to AFM family but could be used in a couple) which are capable of providing all necessary information beyond topographical one. The paper of Randall et al. [1450] gives the best example for this.

     There is a vast class of crystals named ferroics. In general, it includes ferroelectrics, ferromagnetics and ferroelastics. Structural and/or physical properties of these crystals change strongly below the specific temperature. It is well known also that they exhibit similar structure as bulk material divided into domains having different electric, magnetic or mechanical properties. Investigation of the surface structure of ferroelectric and ferroelastic crystals are interesting because of some expectations that the surface structure can be correlated with the domain and/or domain boundary structures. Also, due to high resolution of SPM atomic level corrugations can be monitored at their surfaces.

     Ferroelastic crystals represent a relatively new class of ferroics which history amounts a little more than 30 years. Czajka et al. [335] explored topography and frictional properties of freshly cleaved surfaces of K₃Na(SeO₄)₂ (KNSe), NH₄LiH₃(SO₄)₄ (ALHS) and Gd₂(MoO₄)₃ (GMO) in ambient and UHV conditions. Terraces separated by c/2 (KNSe) and c/4 (ALHS) where c is the biggest lattice constant before structural transformation were observed indicating that transition had place. Friction (Lateral) Force Microscopy measurements revealed substantially different friction properties of the terraces separated with half of lattice period in the c-axis direction. Authors suggest that this contrast is due to different molecular orientation invoked by transition. The lateral force image of GMO shows very distinct domain structure and the angle of 2,35° of a surface bend at the domain boundary was observed.

     Earlier, stripes and needle-shaped domains were observed on the lead vanadate ferroelastic crystal surface by Bhalla et al. [151]. It suggested that the domain wall height gradually decreases and than vanishes approaching the tip of the needle shaped domain. These features can be most undesirable for some devices based on acousto-optic properties. Authors believe that the surface morphological differences on unit cell scale in the two domain regions, which finally resulted as a contrast in the AFM scans of the surface, may provide a unique insight in understanding the ferroelastic distortions of the lattice in ferroic crystals.

     In some cases topographic as well as mechanical modes and techniques of Scanning Probe Microscopy allows for revealing properties even magnetically or electrically active objects.

     For example, Morais et al. [336] used contact AFM to estimate size distribution of magnetic nanoparticles in a magnetite-based magnetic fluid (MF) sample. It is known that the physical, chemical, and physico-chemical properties of such fluids are strongly influenced by the details of the distribution in size and shape of the dispersed colloidal nanomagnetic particles. The average particle size obtained from the AFM data is very close to that of obtained from the direct magnetization experiments. The authors suppose that the higher standard deviation for the latter could be explained by the presence of agglomerates. Lacava et al. [632] explored AFM, transmission electron microscopy (TEM), and ferromagnetic resonance (FMR) methods for the same measurements. Compared to TEM, the AFM method showed a nanoparticle diameter reduction of 20% and increase in standard deviation of 15%. These differences were associated with the AFM tip and the magnetic nanoparticles concentration on the substrate.

     Another example is an AFM study of the surface topography and domain structures of triglycin sulfate (TGS, (NH₃CH₂OO)₃·H₂SO₄) by Tolstikhina et al. [1352]. This ferroelectric crystal has been intensively studied on a macroscale. The crystals grown old, after annealing and g-irradiated under various doses were studied. Images were obtained in contact, resonant, and lateral force modes. A classical lens-like domain oriented with the long axis of the lens parallel to the crystallographic a-axis was clearly seen on LFM images. The domain contrasted with the surrounding matrix having the opposite polarization. An interesting substructure was observed within the domain: a number of round-shaped formations of opposite polarity of about 100-150 nm in diameter were arranged like beads along the whole perimeter of the domain wall. These formations can serve as nuclei for subsequent repolarization. Authors state that imaging in all modes, especially in contact one, tends to alter the pattern of the specimen polarization. Moreover, if optimum scanning conditions are found provided that the samples undergo specific treatment, a predetermined domain structure can be written on the ferroelectric surface.

     A couple of AFM and LFM with a net constant force of about 80 nN was used by Ankudinov et al. [1342] to investigate cross-sections of ZnMgSSe- and BeMgZnSe-based laser diodes. Topographic singularities located in the vicinity of a quantum well active region was found and attributed to relaxation of relatively stressed layers after cleavage. Analysis of data obtained allowed to stress on the following observations: (1) an inequality in the surface morphology of the cladding layers of the studied S- and Be-containing heterostructures and (2) a dependence of the shape and height of the singularity at the waveguide position on the active region design. Thus, in contrast to SEM and TEM, using AFM and LFM the stress distribution across the structure as subnanometer-scale relief modulation at the structure cleavage plane can be successfully observed. It provides the basis for estimation of the influence of the material hardness on the cleavage surface morphology.

     In numerous cases when specimen cannot be fragmented in order to be put onto SPM stage, the techniques of surface replication are available which are widely used for SEM and TEM studies. Campbell and Lankford [421] performed systematic investigation of AFM applicability for imaging replicated samples. It has been shown that AFM of replicas offers higher resolution than that obtainable from replicas imaged by conventional (non-field emission) SEM. Direct measurement of vertical and lateral dimensions, and their angular relationships, are quickly available, and the AFM images are free of electron optical and interaction artifacts. However, any dimensional measurement, taken below some critical scan size on a replica, has a large probability of being inaccurate since the replica is not a perfect "negative" copy of the surface from which it was taken. Thus, resolution limit of the AFM when applied to replicas is defined by the fidelity of the replica itself, rather than by the resolving ability of the AFM and superior replication technology must be developed if replicas are to be useful in work that requires the higher resolution AFM modes.

     The properties of metal-metal oxide interfaces are of major importance in the field of supported metal heterogeneous catalysis, even in those cases where there is no strong chemical interaction between the two phases. Of these, metal-alumina systems are in widespread use, in both academic and technological applications. By means of Atomic Force Microscopy Bird et al. [439] explored the genesis of realistic Ag-a-alumina model catalysts from an aqueous precursor (AgNO₃), using conditions identical to those used in the synthesis of practical dispersed catalysts. Authors selected the alumina substrates of two orientations. It was found that on the smooth (0001) surface, precursor decomposition leads to formation of a quasi-2D Ag network that undergoes rapid sintering in oxygen at 780 K to yield large isolated metal particles. Surprisingly, the same process on the step-kinked (11-20) surface leads to formation of quasi-1D Ag nanowires that decorate the step edges. Most interestingly, these nanowires were relatively stable against sintering in 1 bar oxygen at 780 K having 50-70 nm in width and many hundreds of nanometers in length, suggesting a particularly favourable interaction between Ag and the (1-102) plane of a-alumina. Thus, Atomic Force Microscopy provided a viable method for investigating the genesis of realistic model metal-on-insulator catalysts from solution precursors.

     Proximal probe techniques could serve as an excellent supplement to another commonly used surface analysis methods such as Scanning Electron Microscopy, Transmission Electron Microscopy, Electron Spectroscopy (AES and XPS), Secondary Ion Mass Spectrometry (SIMS) and others.

     An excellent example of complementary usage of AFM and XPS inelastic peak shape analysis in a study of germanium deposited on Si(001) by electron beam evaporation is presented in the work of Simonsen et al. [274]. It was found that combining the two techniques gives much more detailed information on the nanostructure of the surface of semiconductor/semiconductor systems than AFM alone. XPS peak shape analysis provides chemical and in-depth information and an average island shape, while AFM gives detailed, local information on the island distribution, but no chemical information. In this sense, the two techniques have a complementary nature.

     Another example is the paper of Malherbe and Odendaal [1030] who used Auger Electron Spectroscopy and X-ray Photoelectron Spectroscopy in a couple with AFM to assess the influence of ion bombardment on the structural and topographic characteristics of electronic materials especially compound semiconductors. It was found, for instance, that the extent of bombardment-induced topography depends primarily on the substrate material while the ion beam characteristics play only a secondary role. The work gives a survey of surface modification of many semiconductor materials (see the references therein).

     Development of powerful enhancements such as Phase Imaging™ (trademark registered by Digital Instruments) [32, 665], Force Modulation Mode and others make Scanning Force Microscopy quite sensitive to a number of another material properties. These enhancements allow for estimation and quantitative description of elasticity (or stiffness), hardness, adhesion, viscosity and other properties. Let us formulate the most general definitions of the properties mentioned.

     Hardness is the measure of locally loaded region of material to withstand external force keeping the structure and form unchanged.

     Elasticity (stiffness) determines the material's relative measure to deform reversibly under applied loading.

     Adhesion is the sticking ability of the species on the surface being investigated. Attractive forces may be of various nature such as those caused by electrostatic charges, capillary forces etc.

     Viscosity defines dynamics of material's deformation (often flow), i.e. rheological properties.

     As in the case of LFM, acquisition of data relating to these properties can often be performed simultaneously with topography allowing for striking breakthrough in improvement of contrast and resolution of conventional AFM modes. The problems of simultaneous acquisition of topography and material's properties have been analyzed by Burnham et al. [1410].

     In the experiments for hardness determination AFM is usually used in a couple with technique named Nanoindentation [4, 634, 815, 872, 1035, 1219, 1450]. A typical nanoscopic indenter (so-called Berkovich indenter) is a three-sided pyramidal single-crystal natural diamond tip mounted on the beam such that one sharp edge is parallel to the long axis of the beam (though, this is taken into consideration only for wear and scratching experiments, which are often planned to be performed along with nanoindentation as well). Indenter stresses the surface of material studied at various exactly maintained forces for about 1-2 s. The indentation pit has a distinct geometry, which can be characterized using AFM with high precision. Moreover, AFM is the only method capable of exact geometry determination of such tiny areas. Nanohardness is calculated by dividing the loading force by the projected residual area of the indentation.

     AFM/nanoindentation is the only method for hardness determination of ultrathin coatings such as hard disk protective carbon films. To exclude influence of film support layer the depth of nanoindentation should be several times (5-10) less than the film thickness. Indenters are able to leave pits as small as 1 nm in depth, so the above condition as a rule is observed well. In order to obtain an accurate relationship between the indentation depth and the projected contact area, indenter tip shape calibration needs to be carried out especially for ultrasmall penetration depths. The problem of determination of area function of the indenters is discussed in details by Herrmann et al. [1452] since geometry of the indenter tip is the most significant source of uncertainty in nanoindentation measurements. Authors draw attention to a number of other problems related to accuracy of this method.

     Nanohardness has been found to vary upon indentation depth (and, consequently, loading) especially for hard and fragile materials such as monocrystalline silicon. It tends to decrease along the rising of loading applied. For example, for (111)-oriented silicon it falls down by 5GPa after loading rise of about 35 mN according to Bhushan and Koinkar [1279]. Changing in hardness for (100)-oriented silicon is not so dramatic [1280]. The comparison is presented in Fig. 2.

Fig. 2 Nanohardness of a-(111) and b-(100) oriented silicon as a dependence of indentation loading (a - [1279], b - [1280])

     Decrease in hardness can be explained by formation of multiple defects in the local area suffered from loading that lead to degradation of the local structure. This degradation, perhaps, goes much more readily in the case when the symmetries of the surface and the indenter coincide in the contact direction, as can be seen in the case of (111)-oriented silicon.

     Nonetheless, inducing defects may substantially extend the sample's hardness and corresponding tribological properties such as wear resistance. Ion implantation is the most commonly used method for this purpose especially in application to polymers.

     An ideal solution for AFM/nanoindentation apparatus would be obviously the system, which exploit the only indenter for both indenting and imaging of the indentation produced. Unfortunately, it is impossible in practice to join advantages of nanosensing AFM cantilever tip capability with extraordinary hardness of the indenter. Therefore, solutions have to be found in combination of both indentation and AFM imaging apparatus into the single device, as, for example, presented by Randall et al. [1450].

     Besides hardness, the Young's modulus of elasticity can be obtained from the slope of the unloading curve [1035]. A typical loading(unloading)-displacement curves for relatively hard materials are depicted in Fig. 3.

Fig. 3 A typical loading-displacement curve.

      Their hysteretic appearance means that deformation is not fully elastic and partially destructive. One can diminish inelastic deformation using specially flattened tips but in this case morfology of the surface and flat portion of the tip become another factors influencing accuracy of the final result [2623, 2624]. For compliant materials such as polymer blends, magnetic tapes etc. both loading and unloading curves are closely identical.

     In application to polymers nanoindentation is used mainly for determination of elasticity and viscoelasticity [1219] since deformation has manly reversible elastic character. Because nanoindentation is local point technique it does not suite for mapping variations of hardness, elasticity and other properties on the sample surface. Localized surface elasticity maps can be obtained using a force-modulation or phase imaging techniques [502, 1221, 1222, 2802, 2803].

     The systematic analysis of Force Modulation AFM (FM-AFM) is presented in the paper of Li et al. [502]. FM-AFM reveals the major topographic features of Contact Mode AFM (CM-AFM) but affords greater resolution for sample features that are difficult in CM-AFM, and allows for continuous two-dimensional mapping of local mechanical properties on a scale of nanometers that the CM-AFM, Tapping Mode AFM (TM-AFM) and any other techniques, are not capable of sensing. This information can be used to elucidate other properties of the investigated surface, such as crystallinity variation, phase separation and distribution, and mechanisms of formation of deposited films.

     Variations in amplitude of oscillations (usually sinusoidal) introduced by special bimorph well below the resonant frequency of the cantilever are used for measuring local variations of hardness or stiffness of the samples. (In the case of qualitative measurements it is hardly to distinguish between hardness and stiffness). Very soft samples do not affect greatly oscillation amplitude since tip penetrates relatively deep the surface. The changes in oscillation amplitude for hard samples are more significant showing anharmonic distortions. Along with amplitude and height (topography) imaging, phase detection channel can also be used to measure some other characteristics such as viscosity.

     For electrodeposited cerium oxide considered in this paper, FM-AFM provides very distinct grain boundaries while many grains, up to a few hundred nanometers diameter were not resolved in the height images. Some of the grains appear monolithic, but others are further composed of a number of aggregated fine grains as could not be observed in corresponding height images. The overall grain structure suggests that the film is deposited through a nucleation mechanism, rather than a "general growth" process in which the deposit is added to the substrate surface uniformity to produce an even, continuous film.

     The nature of adhesive interactions between the tip and the sample surface is very multicomponent and complicated [251, 407, 436, 443]. There is no ubiquitous measure for adhesion as well as it is too difficult to give comprehensive and at the same time exact definition of this "property".

     Ouyang et al. [569] considered three main driving forces of adhesive interactions such as van der Waals force, electrostatic force, and capillary force of water film on solid surface. The authors aimed to distinguish quantitatively among contributions of each force to the total adhesion for various materials and ambient conditions by regarding AFM tip as a standard. The adhesive forces were determined by measuring the pull-off forces between the tip and sample surface in "so-called" force calibration mode of AFM. Typical shapes of curves for this mode are shown in Fig. 4.

Fig. 4 Typical curves of tip deflection as a functions of Z-piezo travel.

     A small negative bending of the cantilever just before the beginning of positive deflection, depicted as a little pit in the loading curve, is attributed to electrostatic and van der Waals forces which cause attraction of the tip as it closely approaches to the sample surface. Adhesiveness is proportional to the amount of Z-piezo travel DZ on the unloading curve from the point of zero deflection (A) to the point of final release of the cantilever after pull-off from the surface (B).

     The differences in contributions of the forces mentioned above have been shown to vary depending upon the material in a great extent. Three lamellar materials were taken for the study: mica, graphite and MoS₂. It was found that capillary forces at relative humidity of about 50% play significant role for mica and graphite, whereas for MoS₂ they are the smallest. Electrostatic forces are dominates for MoS₂ and it is known that this material usually studied while immersed in liquid to remove unwanted electrostatic and capillary forces. Intensity of capillary forces strongly depends on the hydrophilicity of the surface studied as was investigated, for example, by Moon et al. (see [1489] in SPM-based nanotechnology section). Graphite showed the minimum overall adhesiveness and minimum electrostatic and van der Waals forces contributions in particular. When selection is necessary among the lamellar materials according to their lubricating properties one should choose in favour of graphite since great contribution of electrostatic forces in the case of MoS₂ during friction introduce a hazard for applications critical to electrostatic discharges such as oil and gas mining. In contrast to graphite mica showed the most pronounced adhesive properties for its high van der Waals force that is not changeable by atmosphere. Authors conclude that the conditions for low adhesions are both the low van der Waals interaction and the proper atmosphere.

     Examining the slight changes in the slope of loading and unloading curves in Fig 4. one can in principle assess an indentation measure of the tip into the surface of compliant materials such as polymers, as was performed by Bhushan et al. [1224]. Later Vanlandingham et al. [686] examined in details this repulsive region of the force curves. In this paper the technique is developed that (1) relates the elastic modulus of the sample to the sample response measured using AFM force curves, and (2) emphasizes the importance of the relative stiffness of the cantilever probe and the sample to the determination of elastic modulus. The authors used two separate cantilevers having spring constants of 1 and 60 N/m respectively for measuring indentations on a number of polymer samples. These were polyurethanes, visible-light-cured acrylated epoxies, thermally cured epoxies and polyetheretherketone (PEEK).

     The elastic moduli of these polymer samples were determined independently using dynamic mechanical analysis, and range from 0.02 to 3.0 GPa. In order to provide a calibration reference, titanium (E>100GPa) was used as an "infinitely stiff" material for the determination of conversion and amplification factors of registration system (in effect, cantilever bending which put along the ordinate axis in Fig. 3 is measured in terms of voltage generated in photodiode by light reflected by backside of the cantilever, so conversion parameters from V to nm should be taken into account). The ratio of the real slope to the maximum possible one is called reduction factor f. This factor was observed to increase as the stiffness of the sample increased. The response of polymers with moduli greater than 0,5 and 0,1 GPa for 60 N/m and 1N/m probes respectively, approaches that of the "infinitely stiff" titanium sample. Therefore, above these modulus values, samples of differing moduli become indistinguishable. The use of the reduction factor, however, does not take into account the actual indentation process. It has been shown that when the amount of probe tip displacement D_t exceeds the indentation displacement D_i, their relation D_i/D_t become insensitive to modulus changes. In other words, the force applied by the probe to the sample surface is insufficient to produce adequate deformation of the stiffer samples. Because the 60 N/m probe applies higher forces to the sample than does the 1 N/m probe for a given tip displacement, it is sensitive up to higher modulus values and thus can be used to evaluate higher modulus samples. Thus, using very stiff cantilevers (~500 N/m) one can measure modulus changes in polymers commonly used in engineering applications. Authors suppose that these calibration curves will allow for the study of modulus changes in heterogeneous regions typically found in polymer blends, adhesive systems, coatings, and in the vicinity of fibers of composite materials.