Atom surface potential

Many results on surface phonon dispersions are obtained through atomic (mainly He) scattering. 

The interaction of an incident atom with a surface is described by the atont-surface potential (Fig. 5.2-59), which consists of a hard repulsive part at short distances and a weak van der Waals attraction at larger distances. 

In the potential well between the van der Waals potential and the hard repulsive potential, quantized energy levels n exist (see Fig. 5.2-59). Table 5.2-24 summarizes the parameters of the atom-surface potentials for a number of surfaces and impinging atoms (or molecules). A more extended discussion is given in [2.14,15]. 

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The next phase for the theorists in connection with this work lies in predictions of helium atom scattering intensities associated with surface phonon creation and annihilation for each variety of vibrational motion. In trying to understand why certain vibrational modes in these similar materials appear so much more prominently in some salts than others, one is always led back to the guiding principle that the vibrational motion has to perturb the surface electronic structure so that the static atom-surface potential is modulated by the vibration. Although the polarizabilities of the ions may contribute far less to the overall binding energies of alkali halide crystals than the Coulombic forces do, they seem to play a critical role in the vibrational dynamics of these materials. 

As indicated in Section III.B, the multiphonon scattering can also be investigated and interpreted in terms of the atom-surface potential. Most of this work has been carried out with alkali halides, but some experiments have also been done using metals. Figure 29 shows the typical behavior seen for... 

Fig. 5.2-59 Typical atom-surface potential, with definitions of the main interaction parameters. The surface unit ceU is shown in the inset. The numbers on the axes refer to He-Ag(llO) [2.92]. Vq surface averaged potential Vt potential at the top position Vb potential at the bottom position...

Table 5 2-2 Parameters of the atom-surface potential. Values of are given in the order n = 0, 1, 2, 3 References...

In these lectures we will present the theory of atomic scattering focusing in particular on the atom surface potential. This potential is separated in an attractive part of the Van der Waals type and in a repulsive part related to the surface charge which is approximate as a superposition of atomic charges. The lateral Fourier trasform of this potential, which enters in the cross sections, has a gaussian form which is essential in order to explain the falling off of the Rayleigh peaks at the zone boundary. 

In contrast to the van der Waals potential between two molecules, the atom-surface potential decreases as 1 /z with distance from the surface. 

If an atom is in an excited state, the character of the atom-surface potential (attractive versus repulsive) is determined by the sum of the van der Waals interaction (Eq. (2.100)) and the classical shift (Eq. (2.101)). The first term may be either positive or negative. The second term also may have either sign if one of the transition frequencies is close to the frequency of a surface excitation determined by the equation n (cp) + 1 = 0. As a result, the interaction constant C may be either positive or negative. 

The X-ray scattering explores the 3D-structure of matter but for molecule surface scattering the incoming molecule will see a surface which is periodic in the x-y plane only. Thus the atom-surface potentials are expanded in a Fourier series in 2-dimensional reciprocal lattice vectors as ... 

The physisorption wells are in the meV range and the atoms are physisorbed at some value of the distance z 2-4 A from the surface. For a discussion of the systematic trends in atom-surface potentials, see also ref. [120]. 

Atom-surface potential information from low-energy... 

K. L. Wolfe and J, H. Weare, Theoretical correlation of intensity features of selective adsorption with Fourier components of the atom-surface potential, Phys. Rev. Lett. 41 1663 (1978). 

ATOM-SURFACE POTENTIAL INFORMATION FROM LOW-ENERGY ATOM-SURFACE SCATTERING... 

By emphasizing certain resonance features in the elastic intensity, one may use beams of light inert atomic particles to directly measure properties of the atom surface potential. From highly developed experiments it has been possible to infer very precise forms for the atom-surface interaction. Potentials inferred this way may have wider application than just atom-surface scattering since for many systems the solid-state nature of the target system may be unimportant. For such systems information such as the two-body potential established from gas-surface scattering may provide information about the two-body potential governing gas phase interactions. 

The main advantage of diffraction studies is the direct relationship between the scattered intensity and the surface periodicity. Because of the extreme sensitivity of He scattering to the surface region, He-beam diffraction experiments have been able to unequivocally identify surface structures that have not been seen by other approaches. Unfortunately further interpretation of diffraction data in order to obtain atom-surface potential information requires the use of a fairly detailed theoretical model of the scattering. 

A more fruitful experimental approach to obtain atom-surface potential information appears to be the selective adsorption experiment. In these experiments certain resonance features in the scattering intensity corresponding to the formation of quasibound states of the atom surface potential are observed. This class of experiments has only been performed for the best characterized surfaces. A partial review of the data and theoretical results will be presented here. As we will show the experiments measure properties of the surface very directly. However, they are relatively difficult to perform. 

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