Similarly to standard AFM (Fig. 17.1), friction force microscopy (FFM) is based on the relative motion of a sharp tip on a solid surface. This motion is realized by a scanner formed by piezoelectric elements, which moves the surface perpendicularly to the tip with a certain time periodicity. The scanner can be also extended or retracted in order to vary the normal force FN between tip and surface. This force is responsible for the deflection of the microcantilever supporting the tip. If FN increases while scanning due to local variations of the surface height, the scanner is retracted by a feedback loop. If FN decreases, the surface is brought closer to the tip by extending the scanner. In such a way, the surface topography can be reconstructed line by line from the vertical deformation of the scanner. An accurate control of the imaging process is made possible by a light beam, which is reflected from the rear of the cantilever into a photodetector. When the bending of the cantilever changes, the light spot on the detector moves up or down. This causes a variation of the photocurrent corresponding to the value of FN to be controlled.

The scan motion is also accompanied by friction. A tangential force F with the opposite direction to the scan velocity v hinders the sliding motion. The force F causes the torsion of the cantilever, and can be recorded simultaneously with the topography if the photodetector can measure not only the normal deflection but also the torsion of the lever while scanning. In practice this is made possible by a four-quadrants photodetector, which converts the photocurrent corresponding to the lateral force into a voltage VL. Note that the friction also causes lateral bending of the cantilever, but this effect is modest if the thickness of the lever is much less than its width.

The first atomic friction measurements by Mate et al. [206] were actually based on the deflection of a tungsten wire.

The study of friction, wear and lubrication between two surfaces in relative motion is called tribology. This term is derived from the Greek verb ‘tribos’, which means ‘to rub’. On one hand tribology aims at a scientific foundation of these phenomena. On the other hand it aims at a better design, manufacture and maintenance of devices which are affected by these ‘annoyances’. Tribology has a very important economical outcome. According to one of the first reports on this issue, tribological problems accounted for 6% of the Gross Domestic Product in industrialized countries in the 1960s [160]. This percentage may have increased by now. Tri-bological problems are found in pinions, pulleys, rollers and continuous tracks, in pin joints and electric connectors, and may cause more failure than fracture, fatigue and plastic deformation. On the other hand, friction is highly desirable, or even essential, in power transmission systems like belt drives, automobile brakes and clutches. Friction can also reduce road slipperiness and increase rail adhesion. Before starting our rather theoretical description of tribology, it is important to recall the milestones that have marked the progress in this subject from the dawn of civilization.

Historical notes

More than 40 000 years ago a complex process such as the generation of frictional heat from the lighting of fire was already well known. Nowadays the same process is studied by a branch of tribology, which is known as ‘tribochemistry’ and is focusing, more generally, on friction-induced chemical reactions. The early use of surface lubricants to reduce friction is unambiguously proven by a famous painting from ancient Egypt, in which a ‘prototribologist’ supports the work of a few dozen slaves by pouring oil in front of the heavy sled that they are pulling (Fig. 1.1). More than four thousand years later Leonardo da Vinci (1452–1519) started a systematic investigation of tribology, as documented by his drawings (Fig. 1.2). Leonardo's intuition and perseverance resulted in the formulation of the first friction law, which states the proportionality between friction and normal force.

Friction permeates every aspect of our life. It accompanies us when we walk and our fingers when they slide on the display of a tablet. Friction produces very annoying results when a chalk is rubbed against a blackboard and may cause tremendous damage when it fails to hold two tectonic plates together and a powerful earthquake is suddenly generated. Friction can also be very useful, when a cat suddenly jumps in front of our car and the brake pedal avoids serious consequences; and even pleasant, when a talented violinist takes up a bow and starts playing his Stradivarius. In any case, friction is certainly not a boring subject, and writing a book about friction is definitely not an easy task.

In spite of an immense amount of experimental data, a general theory of sliding friction between two solid surfaces is still missing. The simple Amontons' law, stating that the friction is proportional to the normal force, has been found to work exceptionally well in a variety of situations. Based on this law, theoretical models with different degrees of complexity have been derived and successfully applied to reproduce real situations. Even if Amontons' law is universally accepted as empirical evidence rather than as a consequence of first principles, the attitude is rapidly changing and it is now possible to prove by analytical means that the friction between two rough elastic surfaces has to be almost proportional to the loading force. A different situation is encountered when studying the drag force accompanying the motion of a solid object in a viscous liquid. Here, the Navier–Stokes law works usually quite well, which made hydrodynamic lubrication an established subject a long time ago. Still, problems arise when the lubricants are confined and the friction can only be investigated, theoretically, using atomic-scale models.

In the past 25 years, significant progress has been achieved in the understanding of the basic principles of sliding friction.

In this chapter we will discuss a selection of experimental observations of friction on the nanoscale, obtained by atomic force microscopy and related techniques. After presenting high resolution friction maps on different materials, we will compare the load, velocity and temperature dependence of friction detected in the experiments to the predictions of the Prandtl–Tomlinson model. The comparison will be extended to simple experiments showing the effect of contact vibrations and friction anisotropy on crystalline samples.

Friction measurements on the atomic scale

The first lattice resolved maps of stick–slip were acquired by Mate et al. [206] just one year after the atomic force microscope was invented [24]. In their experiment, Mate et al. used a tungsten wire as a probing tip and detected lateral forces on a graphite surface using non-fiber interferometry. Since graphite is stable, chemically inert and easy to cleave along atomic planes, it is an ideal material for this kind of measurement. The pioneer work by Mate et al. was followed by experiments on ionic crystals (NaCl, KBr etc.), metals (Cu, Au, Al, W, Pt, Pd and Ag) and covalent materials: semiconductors, carbon-based materials (e.g. graphite, diamond, and diamondlike carbon), organic materials and many oxides.

The ultra-high vacuum (UHV) environment reduces the influence of contaminants on the sample surfaces and results in more precise and reproducible results. An atomic-scale friction map, acquired with a silicon tip sliding on a NaCl(001) cleavage surface in UHV (lattice constant a = 0. 564 nm), is shown in Fig. 18.1(a). The spring force F grows up to a maximum value, corresponding to the static friction Fs ≈ 0.4 nN at which the tip suddenly slips. After that, the tip quickly rebinds to a neighboring unit cell on the crystal surface. The process is repeated several times along each scan line, reproducing the structure of the surface lattice.

In this chapter we consider the transition from elastic to plastic behavior (the yield point). This transition implies that the material undergoes irreversible shape changes in response to external forces. A simple example is a piece of metal permanently bent into a new shape. Several physical mechanisms can cause plastic deformation. Plasticity in metals is usually associated with the motion of dislocations, while in brittle materials it is caused predominantly by slip at microcracks. After introducing the most important criteria for yielding, the concept of plastic flow and the definition of hardness, we will consider various examples of indentation, sliding and rolling involving plastically deformed objects. These processes are severely affected by the friction at the contact interfaces, which is also discussed in the chapter. We will also mention the importance of plasticity in geotechnics, where it determines the safety of a structure founded on a soil. In this context, a peculiar role is played by the angle of internal friction of the materials.

Plasticity

A typical stress–strain curve for a material in simple tension is shown in Fig. 12.1. The initial part of the curve is a straight line with a slope equal to the Young's modulus E of the material. The linear relationship between σ and ε ends at a certain point, corresponding to the yield strength Y. At this point plastic deformation occurs. The value of Y depends on the manufacturing process and on the purity of the material. For metals, it is typically in the range of 10–100 MPa. If the material is stressed further in the plastic range and the load is released, the recovery is elastic, with the same value of E as in the first loading. This key assumption was carefully verified by Tabor in a series of measurements on soft metals using spherical and conical indenters [327, 321]. A subsequent loading of the material results in an increased value of the yield strength, as seen in Fig. 12.1. This effect is known as work hardening or strain hardening.