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This chapter describes the design of modern AFM instruments in detail. It shows both how the instruments are built, and how they work. There are descriptions of the mechanical, electronic, and software design of the instrument, as well as a section on the design of AFM probes, one of the most important components in any AFM. For the instrument user, understanding how the instrument works can greatly improve the results obtained, and this chapter has all the information an AFM user could need about how AFMs work, and more importantly, why they work that way.

This chapter discusses atomic force microscopy (AFM), focusing on the methods for atomic force detection. Although the force detection always requires a cantilever, there are two types of modes: the static mode and the dynamic mode. The general design and the typical method of manufacturing of the cantilevers are discussed. Two popular methods of static force detection are presented. The popular dynamic-force detection method, the tapping mode is described, especially the methods in liquids. The non-contact AFM, which has achieved atomic resolution in the weak attractive force regime, is discussed in detail. An elementary and transparent analysis of the principles, including the frequency shift, the second harmonics, and the average tunneling current, is presented. It requires only Newton's equation and Fourier analysis, and the final results are analyzed over the entire range of vibrational amplitude. The implementation is briefly discussed.

This chapter describes sophisticated measurements reported on the archetypal SMM, which allows for a more detailed understanding of their properties. Firstly this chapter discusses the role of fourth order terms of the crystal field by using experimental data on single crystals of Mn12ac using micro Hall probes and cantilever torquemeter. The role of intercluster interactions is described in detail for Mn4. In a compound with a dimeric structure (Mn4)₂, the role of intercluster interactions on the magnetic tunnelling is described. The effects of the magnetic tunnelling on long range magnetic order are illustrated with experimental data from several SMM, but with more details in Mn4. Finally, experiments where the relaxation of the magnetization is monitored under applied electromagnetic radiation of ca. 115 GHz are reported.

This chapter starts chronologically with the first measurement, by means of a torsion pendulum, in the recent phase of Casimir force experiments. Then the main breakthroughs in the measurement of the Casimir force between metallic surfaces are presented. One of them was the first demonstration of corrections to the Casimir force due to the nonzero skin depth and surface roughness by means of an atomic force microscope. Another breakthrough was a series of precise indirect measurements of the Casimir pressure by means of a micromechanical torsional oscillator. These measurements allowed a definitive choice between different theoretical approaches to the thermal Casimir force for real metal surfaces. Many other experiments performed in the last few years are also presented, specifically one measurement using the configuration of two parallel plates. The chapter ends with a brief discussion of proposed experiments using metallic surfaces.

The meaning behind the mysterious Principle of Virtual Work is explained. Some worked examples in statics (equilibrium) are given, and the method of Virtual Work is compared and contrasted with the method of Newtonian Mechanics. The meaning of virtual displacements is explained very carefully. They must be ‘small’, happen simultaneously, and do not cause a force, result froma force, or take any time to occur. Counter to intuition, not all the actual displacements can be allowed as virtual displacements. Some examples worked through are: Feynman’s pivoting (cantilever) bar, a “black box,” a weighted spring, a ladder, a capacitor, a soap bubble, and Atwood’s machine. The links between mechanics and geometry are demonstrated, and it is shown how the reaction or constraint forces are always perpendicular to the virtual displacements. Lanczos’s Postulate A and its astounding universality are explained.

This chapter discusses atomic force microscopy (AFM), focusing on the methods for atomic force detection. Although the force detection always requires a cantilever, there are two types of modes: the static mode and the dynamic mode. The general design and the typical method of manufacturing of the cantilevers are discussed. Two popular methods of static force detection are presented. The popular dynamic-force detection method, the tapping mode is described, especially the methods in liquids. The non-contact AFM, which has achieved atomic resolution in the weak attractive force regime, is discussed in detail. An elementary and transparent analysis of the principles, including the frequency shift, the second harmonics, and the average tunneling current, is presented. It requires only Newton’s equation and Fourier analysis, and the final results are analyzed over the entire range of vibrational amplitude. The implementation is briefly discussed.