Atomic beams Waals interactions

In atomic force microscopy (AFM), the sharp tip of a microscopic probe attached to a flexible cantilever is drawn across an uneven surface such as a membrane (Fig. 1). Electrostatic and van der Waals interactions between the tip and the sample produce a force that moves the probe up and down (in the z dimension) as it encounters hills and valleys in the sample. A laser beam reflected from the cantilever detects motions of as little as 1 A. In one type of atomic force microscope, the force on the probe is held constant (relative to a standard force, on the order of piconewtons) by a feedback circuit that causes the platform holding the sample to rise or fall to keep the force constant. A series of scans in the x and y dimensions (the plane of the membrane) yields a three-dimensional contour map of the surface with resolution near the atomic scale—0.1 nm in the vertical dimension, 0.5 to 1.0 nm in the lateral dimensions. The membrane rafts shown in Figure ll-20b were visualized by this technique. 

Differential scattering experiments with Ne and other beams state selected with a tuneable dye laser are near realization. Differences in the potential-energy curves and reaction probabilities for the iP2 and iP0 states will provide valuable insight into the role of the core ion on the collision dynamics and electronic structure as well as clarify the relative importance of the two states in macroscopic processes. Experiments using a metal-atom crossed beam, also currently in progress at Freiburg, promise a revealing contrast to the weak van der Waals interactions thus far studied. 

A thermal energy atomic beam (20-200 meV) has a wavelength on the order of inter-atomic distances. The atomic beam diffracts from a contour of the surface potential corresponding to the beam energy. This contour is located 3-4 A above the ion cores in the outermost layer of the surface. Atomic beam diffraction patterns are normally interpreted using model surface scattering calculations, where the scattering is described as a Van der Waals interaction. 

For atomic ground states the expression above is only an approximation since a metal cannot be a perfect reflector for the virtual photons exchanged between the atom and surface in the optical region. Indeed even for an ideal, perfect conductor the expression ceases to be valid when the atom-surface distance is greater than a few wavelengths. At large distance the van der Waals force is modified by retardation effects and becomes asymptotically proportional to d . Unfortunately since the interaction is then itself very small, retardation effects are very difficult to demonstrate by atomic beam deflection. 

The application of refractions to the study of structures is based on comparing the experimental values with those calculated on various structural assumptions, of which the most important is additivity (Landolt, 1862) in the first approximation (within ca 10 %), the refraction of a compound is the sum of constant increments of different atoms, ions and bonds. Refractions of some isolated atoms can be measured by the deviation of an atomic beam in an inhomogeneous electric field or by spectroscopic methods. In other cases electronic polarizabilities of free atoms were calculated by ab initio methods. All available experimental and the best of the computed refractions of free atoms are presented in Table 11.5. These values can be used to calculate the energy of van der Waals interactions, magnetic susceptibility, or to establish correlations with atomic and molecular-physical properties. The formation of covalent bonds changes the refractions of isolated atoms and their values transform into the covalent refractions, which are different for isolated molecules and for crystals. Direct measurements of RI of A2 molecules or elemental solids give the most accurate information on the covalent refractions, in other cases the latter have to be calculated from molecular refractions by the additive method. 

Binnig et al. [48] invented the atomic force microscope in 1985. Their original model of the AFM consisted of a diamond shard attached to a strip of gold foil. The diamond tip contacted the surface directly, with the inter-atomic van der Waals forces providing the interaction mechanism. Detection of the cantilever s vertical movement was done with a second tip—an STM placed above the cantilever. Today, most AFMs use a laser beam deflection system, introduced by Meyer and Amer [49], where a laser is reflected from the back of the reflective AFM lever and onto a position-sensitive detector. 

An elegant technique for studying van der Waals complexes at low temperatures was developed by Toennies and coworkers [442]. A beam of large He clusters (lO -lO He atoms) passes through a region with a sufficient vapor pressure of atoms or molecules. The He droplets pick up a molecule which either sticks to the surface or diffuses into the central part of the droplet, where it is cooled down to a low temperature of 100 mK up to a few Kelvin (see Fig. 4.22). Since the interaction with the He atoms is very small, the spectrum of this trapped molecule does not differ much from that of a free cold molecule. However, unlike cooling during the adiabatic expansion of a supersonic jet, where Tyib > Trot > Ttrans in this case Trot = Tyib = Thc [443 45]. This implies that all molecules are at their lowest vibration-rotational levels and the absorption spectrum becomes considerably simplified. 

Van der Waals diatomics formed through the weak interaction between a noble gas atom and an alkali atom have also been studied in noble gas beams seeded with alkali vapor [452]. 

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