Atom-Surface Interaction

As mentioned in Chapter 1, simple models for atom/molecule-surface interaction were already suggested by Lennard-Jones and London [111]. Starting with the Lennard-Jones 12-6 potential for atom-atom interaction 

Extensive information on weakly bound, physisorbed atoms on solids is available from bound state resonance data obtained from beam scattering experiments. Strong changes in the scattering intensities are observed when selective adsorption in the physisorption well occurs (see, for instance, ref. [113]). The resonance positions yield the eigenvalues E of the potential V(z). These satiesfies to a good approximation the Bohr-Sommerfeld quantization condition 

TABLE 4.1 Atom-Surface Parameters for Rare Gas Atoms Interacting with Graphite and Ag(111) Surfaces 

We note that the long-range part varies as z, which may be rationalized by a dipole image-dipole interaction, or from an atom-atom dispersion interaction r summed over the lattice atoms (see exercise 4.1). Often the potential is modeled by an expression of the type 

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]. 

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Atom-surface interactions are intrinsically many-body problems which are known to have no analytical solutions. Due to the shorter de Broglie wavelengdi of an energetic ion than solid interatomic spacings, the energetic atom-surface interaction problem can be treated by classical mechanics. In the classical mechanical... 

Although the first quantal studies of atom-surface interactions occurred... 

One formalism which has been extensively used with classical trajectory methods to study gas-phase reactions has been the London-Eyring-Polanyi-Sato (LEPS) method . This is a semiempirical technique for generating potential energy surfaces which incorporates two-body interactions into a valence bond scheme. The combination of interactions for diatomic molecules in this formalism results in a many-body potential which displays correct asymptotic behavior, and which contains barriers for reaction. For the case of a diatomic molecule reacting with a surface, the surface is treated as one body of a three-body reaction, and so the two-body terms are composed of two atom-surface interactions and a gas-phase atom-atom potential. The LEPS formalism then introduces adjustable potential energy barriers into molecule-surface reactions. 

In efforts to improve upon the LEPS scheme outline above, other prescriptions for the single atom-surface interaction have been formulated. The initial studies using the LEPS approach modeled the atom-surface interaction as a two-body term where the parameters used in the function are... 

When an atom hits a surface, the initial kinetic energy of the atom can not only be transfered to the substrate. If the surface is corrugated, i.e. if the atom-surface interaction varies as a function of lateral coordinates of the atom, then the impinging atom can also change its lateral component of the initial velocity upon the collision. In the case of molecules, there are also the internal degrees of molecular vibration and rotation that can be excited (or de-excited) during the collision with the surface. 

The model described below is that previously given by White and Lassettre 22). The adsorbent is regarded as a plane-surfaced semiinfinite solid. The forces between the solid adsorbent and the adsorbed diatomic molecules are assumed to be centered at the positions of the component atoms of the molecule. The total interaction between the molecule and the surface is simply the sum of the atom-surface interactions (16, 22). The interaction potential for each atom of the adsorbed molecule is given by f zi) where Z is the distance of the i-th atom measured normal to the surface. Let the distance from the center of mass to the atoms of mass mi and m2, respectively be b and 2, as shown in Figure 1. The potential energy, V, of the adsorbed diatomic molecule is then... 

The model system comprising the reaction sequence from initial 0-atom attack to steady-state erosion of a hydrocarbon surface can serve as a benchmark for fundamental atom-surface interactions at hyperthermal collision energies and for etching mechanisms of materials. Within this model system, there is still much to learn. It is likely that when a hyperthermal oxygen atom strikes a saturated hydrocarbon surface, it will either abstract a hydrogen atom or it will scatter inelastically. The subsequent reaction sequence becomes murky. Very little is known about the mechanisms of oxidation, surface roughening, or material loss. In fact, even the sticking... 

A full theoretical treatment of the scattering problem would involve solution of the Schrodinger equation for the system, with the potential energy expressed in terms of equation (8). This approach, however, is impossible at present since the atom-surface interaction is too strong for treatment to be reliable within the Born or other weak-scattering approximations but considerable progress has been made using both... 

Consider a diatomic, AB, interacting with a surface, S. The basic idea is to utilize valence bond theory for the atom-surface interactions, AB and BS> along with AB to construct AB,S For each atom of the diatomic, we associate a single electron. Since association of one electron with each body in a three-body system allows only one bond, and since the solid can bind both atoms simultaneously, two valence electrons are associated with the solid. Physically, this reflects the ability of the infinite solid to donate and receive many electrons. The use of two electrons for the solid body and two for the diatomic leads to a four-body LEPS potential (Eyring et al. 1944) that is convenient mathematically, but contains nonphysical bonds between the two electrons in the solid. These are eliminated, based upon the rule that each electron can only interact with an electron on a different body, yielding the modified four-body LEPS form. One may also view this as an empirical parametrized form with a few parameters that have well-controlled effects on the global PES. 

These parameters must be determined from information on the atom-surface interaction potential, which may come from either sufficient experimental or theoretical information, such as the binding energy, height, and frequency for different sites of adsorption, or the full binding curves above each site. 

Zhang, Z., Metiu, H. Adsorbate migration on a solid surface The connection between hopping dynamics and the atom-surface interaction energy, J. Chem. Phys. 1990, 93, 2087. 

Various theoretical models have been proposed to describe the atom-surface interactions for the noble gases [91V1]. In the simplest approach, holding potential is obtained as the pairwise sum of atomic... 

The problem of lattice vibrations, which is one of the major task of solid state physics, has recently become of interest in order to obtain information on the dynamics and the electronic properties of solid surfaces. The rapid development of experimental techniques makes it possible to obtain information on surface phonons, surface structure and atom-surface interaction potentials. 

In these lectures we will focus on the determination of surface phonons over the entire Brillouin zone and on the study of the atom-surface interaction potential. We will compare our... 

Owing to the short-range nature of the interatomic pair potential, the non-stationary part of the atom-surface interaction is 2tssumed to be maunly contributed by the first layer of surface atoms. The instant configuration of this layer is described by the displacement Uk of kth atom from its equihbrium position Rk. It is convenient to express Uk through the amplitudes at of phonon modes I = (q,j) with wave vectors g and polarizations j (the system of units with ft = 1 is used throughout this review) ... 

The concept of a superlattice can also be applied to regular overlayers of foreign adsorbed atoms (see Section 2.2). If the coupling forces between atoms exceed the atom-surface interaction forces, they can form a structure which is not related to the symmetry of the substrate surface incommensurate structure or incoherent lattice). In such a case det C is an irrational number (Fig. 2.2c). 

The sub-Doppler structure of the SR spectrum provides an opportunity to determine the frequency shift caused by the atom-surface interaction with high resolution. This singularity can be isolated if one applies a low-frequency modulation to the incident light. By detecting the amplitude-modulated reflected signal one obtains for the reflectivity at the modulation frequency, cOm,... 

In order to fit the SR spectrum one has to take into accoimt the 2-dependence of the atomic transition frequency due to the atom-surface interaction (Section 2.2.1). It can be approximated as... 

The latter situation was observed in SR from the interface between a sapphire surface and Cs vapor (Failache et al. 1999). The SR spectrum was registered at the 6Pi/2 —> 6D3/2 transition while the transition 6S1/2 —> 6P1/2 was pumped by another laser (Fig. 7.6). An important feature of this gas-solid system is that the wavelength of the transition 7Pi/2 6D3/2 (12.15 pm) is close to the wavelength of surface optical phonons ( 12 pm) which leads to a large positive contribution to the energy of the 6D3/2 state. As a consequence, the atom-surface interaction in this state is repulsive (Fichet et al. 1995) and the SR spectrum at the transition 6P1/2 -> 6D3/2 is blue-shifted and can be fitted with C —160 kHz-pm. ... 

M. Ducloy and M. Fichet, General theory of frequency modulated selective reflection. Influence of atom surface interactions. /. Phys. II (France) 1991,1, 1429. 

A-B Morse parameters, and the A-surface and B-surface interaction. The above scheme could be extended to three atom-surface interaction by having five centers instead of four [133]. For a recent attempt to use an LEPS-like functional form for obtaining an analytical expression for the hydrogen-Cu(lll) surface, see ref. [134]. 

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