Adatoms interaction

The essential properties of incommensurate modulated structures can be studied within a simple one-dimensional model, the well-known Frenkel-Kontorova model . The competing interactions between the substrate potential and the lateral adatom interactions are modeled by a chain of adatoms, coupled with harmonic springs of force constant K, placed in a cosine substrate potential of amplitude V and periodicity b (see Fig. 27). The microscopic energy of this model is ... 

A special case is when the electrochem-ically active components are attached to the metal or carbon (electrode) surface in the form of mono- or multilayers, for example, oxides, hydroxides, insoluble salts, metalloorganic compounds, transition-metal hexacyanides, clays, zeolites containing polyoxianions or cations, intercalative systems. The submonolayers of adatoms formed by underpotential deposition are neglected, since in this case, the peak potentials are determined by the substrate-adatom interactions (compound formation). From the ideal surface cyclic voltammetric responses, E° can also be calculated as... 

A physical model and a theory have been proposed [72], which might be helpful in comparative studies on electrocompres-sive behavior of electrodeposited chloride, bromide, and iodide monolayers on the Au(lll) electrode. The theoretical results were in good agreement with the experimental data, which evidence that the adatom-adatom interactions (especially repulsive ones) and electrosorption valency of halide anions determine the compressibility within halide adlayers. Also, Lipkowski et al. have discussed various aspects of adsorption of halide anions on Au(lll) in a review paper [36]. From this paper, we have taken quantitative data concerning adsorption of halide anions on Au(lll) (cf Fig. 3). 

Waszczuk et al. [329] have carried out radiometric studies of UPD of thallium on single-crystal Ag electrode from perchloric acid solutions. Deposition of Tl on Ag(lOO) to obtain monolayer, bilayer, and bulk crystallites has been studied by Wang et al. [330]. These studies have shown that apart from the substrate geometry, the nature of the substrate-adatom interactions also influence the structure of the UPD metal adlayers. This is because of the fact that, contrary to Au and Pt electrodes, Tl forms a well-ordered bilayer phase before bulk deposition on Ag(lOO) surface occurs. 

A further question regarding the adsorption registry is whether it depends on adsorption coverage, i.e., on density of adatoms this is relevant to the effects of adatom-adatom interactions. The situation is illustrated by a limited set of results, namely those for quarter-monolayer and half-monolayer adsorption of 0, S, Se and Te on Ni(lOO) in p(2 X 2) and c(2 X 2) periodicities the adsorption site is found not to depend on coverage in these cases (the nearest adatom-adatom distances are 4.90 and 3.46 A for the two coverages, respectively, compared with the largest adatom diameter of about 2.7 A for Te). 

Experimental studies of adatom interactions focus on two quantities, namely the binding energy and the interatomic force, or the distance dependence of the potential energy. These are two different quantities, although in the past they have been occasionally mixed up in some studies. In many FIM studies where the term force is used, concern is in reality only with binding energy at a certain bond distance or a certain site. We will describe briefly here some FIM studies of adatom interactions with metallic substrates. In Section 4.2.5 adatom-adatom and adatom-substitutional impurity atom interactions will be discussed. 

The tungsten (110) surface is one of the best studied of all surfaces, especially in field emission and field ion microscopy for many reasons. It is a very stable surface without surface reconstruction or phase transformation. It is also inert to contaminations. For the study of adatom-adatom interactions, it is a very smooth plane with the largest density of adsorption sites available of any W surface. Lesser restrictions are imposed on the adatom-adatom separation. As the surface is structurally very smooth, wave mechanical interference effects are least affected by the surface atomic structure. 

Table 4.4 Adatom-adatom interaction derived from pair distribution functions...

Many theories of adatom-adatom interactions and other interactions are based on a model Hamiltonian developed by Anderson for dilute alloys. Such a Hamiltonian may also be used to explain adatom-impurity atom interactions. 

Fig. 4.36 Intraction potential between a W adatom and a substitutional Re atom inside the (110) surface layer. This interaction is almost identical to W-Re adatom-adatom interaction on the W (110) surface.

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