We report direct force measurements of the formation of a chemical bond. The experiments were performed using a low-temperature atomic force microscope, a silicon tip, and a silicon (111) 7x7 surface. The measured site-dependent attractive short-range force, which attains a maximum value of 2.1 nanonewtons, is in good agreement with first-principles calculations of an incipient covalent bond in an analogous model system. The resolution was sufficient to distinguish differences in the interaction potential between inequivalent adatoms, demonstrating the ability of atomic force microscopy to provide quantitative, atomic-scale information on surface chemical reactivity.

We present a transfer-function approach to calculate the force on a magnetic force microscope tip and the stray field due to a perpendicularly magnetized medium having an arbitrary magnetization pattern. Under certain conditions, it is possible to calculate the magnetization pattern from the measured force data. We apply this transfer function theory to quantitatively simulate magnetic force microscopy data acquired on a CoNi/Pt multilayer and on an epitaxially grown Cu/Ni/Cu/Si͑001͒ magnetic thin film. The method described here serves as an excellent basis for ͑i͒ the definition of the condition for achieving maximum resolution in a specific experiment, ͑ii͒ the differences of force and force z-derivative imaging, ͑iii͒ the artificial distinction between domain and domain wall contrast, and finally ͑iv͒ the influence of various tip shapes on image content.

A low temperature scanning force microscope (SFM) operating in a dynamic mode in ultrahigh vacuum was used to study the Si(111)- (7x7) surface at 7.2 K. Not only the twelve adatoms but also the six rest atoms of the unit cell are clearly resolved for the first time with SFM. In addition, the first measurements of the short range chemical bonding forces above specific atomic sites are presented. The data are in good agreement with first principles computations and indicate that the nearest atoms in the tip and sample relax significantly when the tip is within a few A of the surface.

A method is presented for the analysis of magnetic force microscopy ͑MFM͒ measurements that allows the quantitative determination of the sample stray field. It is shown how measurements on an easily obtainable calibration sample can be used to calibrate the MFM measurement as a function of the wavelength of the sample stray field at the tip apex. It is demonstrated that the thus obtained MFM calibration can be used to determine the stray field distribution of the tip. Furthermore, the effect of the tip on the MFM imaging mechanism is analyzed by comparing it to some simple tip models. From the analysis, it is shown that the point-monopole and dipole models do not accurately describe the MFM imaging mechanism.

Piezoelectric quartz tuning forks are investigated for use as force sensors in dynamic mode scanning probe microscopy at temperatures down to 1.5 K and in magnetic fields up to 8 T. The mechanical properties of the forks are extracted from the frequency dependent admittance and simultaneous interferometric measurements. The performance of the forks in a cryogenic environment is investigated. Force-distance studies performed with these sensors at low temperatures are presented.