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.

In this chapter we introduce the methods conventionally used to explore friction on the nanoscale. The leading position among the instrumental setups is held by the atomic force microscope. Here we will briefly illustrate the type of forces sensed by this instrument and its basic modes of application. Other experimental techniques in nanotribology are the surface force apparatus, the quartz crystal microbalance and also, to some extent, scanning tunneling microscopy and transmission electron microscopy. Virtual experiments rely on molecular dynamics simulations. A short introduction to this method will be followed by a series of numerical results reproducing friction and wear measurements at the atomic level.

Atomic force microscopy

In a typical atomic force microscope (AFM) [24] a sharp micro-fabricated tip is scanned over a surface. Standard AFM tips are made of silicon or silicon nitride, but tips can be also coated to allow a large variety of material combinations. The probing tip is attached to a cantilever force sensor, the sensitivity of which can be well below 1 nN. Images of the surface topography are recorded by controlling the tip–sample distance in order to maintain a constant (normal) force. This is made possible by using piezoresistive cantilevers, or, most commonly, by a light beam reflected from the back side of the cantilever into a photodetector, which allows one to monitor the cantilever bending (Fig. 17.1). The lateral force between tip and surface is responsible for the cantilever torsion and can be measured if the photodetector is equipped with four quadrants. If this is the case the AFM can be used as a friction force microscope (FFM), see Appendix A. The design of a home-built AFM, optimized for friction measurements in ultra-high vacuum (UHV), is shown in Fig. 17.2.

The tip–sample force can be related not only to the static bending or torsion of the cantilever.