Interactions between surface atoms

If chemisorbed species are polar, or dipole moments are induced by adatom-substrate interactions, there will be a dipole-dipole interaction between two adatoms. The interaction is given by 

Two adatoms will always interact with each other weakly via the van der Waals interaction. This interaction, while important in physisorption, is a relatively minor factor in chemisorption. The leading term is 

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. 

Ed is the activation energy of surface diffusion. The adatom cohesive energies of various adatom pairs on various planes of tungsten range from 0.1 to 0.6 eV. They show strong chemical specificity. On the W (110), 

Kinetic experiments, while useful in estimating the adatom cohesive energy of a cluster, become very complicated if pair energies at more than one bond state, or information on the inter-adatom potential, are desirable. The distance dependence of pair interaction can be more easily derived by an equilibrium experiment.173 The principle is very simple. At equilibrium, the relative frequencies of observing the two adatoms at various bond states or bond separations at a given temperature are related to their pair energies according to the Boltzmann factors. Thus 

---

Catalyst characterization by the relative value of slopes, a , is most useful when parallel trends in the properties of the catalysts, measured by other probes, chemical or physical, are discovered. Examples are the estimation of acid strength of the surface sites or the estimation of energy of interaction between surface atoms on the basis of shifts in spectra. All of the quantities used for comparison must be intensive, that is, they must express some form of energy or be proportional to energy. 

In this appendix we report the analytical expressions of the forces relative to the (100) surface of an FCC crystal. In these expressions the force constants in the surface region are taken to be different from those of the bulk. The superscript "S" means that all the atoms involved in the interaction (two atoms for central and three for angular forces) are on the surface plane. The superscript "P" refers to interactions involving a surface atom and atoms that are on the first plane below the surface. The superscript "T" refers to interactions between surface atoms and atoms on the second internal plane. Finally the superscript "B" refers to bulklike forces, u., v. and w. are the cartesian components of the ni ni ni... 

Molecular dynamics simulations were conducted in order to study effects of mono-atomic scale steps on sliding surfaces on the dynamic behaviour of lubricant molecules under high pressure and shear. Hydrocarbons, including n-hexane, cyclohexane and n-hexadecane, were assumed as lubricants. Simulations were made such that two layers of lubricant molecules were formed. It was found that steps on the surfaces had dramatic effects on interactions between surface atoms and lubricant molecules. Movements of lubricant molecules, and thus traction between the surfaces, were affected by interactions between the molecules and those between the molecules and the roughness structure, both of which depended on the molecular structure of the lubricant. 

The Lennard-Jones type potential is used for the interaction between Fe atoms and lubricant molecules. The parameter c in the Leonard-Jones potential was changed in order to investigate the effect of the interaction between lubricants and the sur ces. There are oxide or any other contaminants present on actual solid sur ces, ndiich may make interaction between surface atoms and lubricant molecules weaker. The calculations are conducted by using the original value e, and the half value of E, denoted by E0.5. 

To investigate the effect of interaction between surface atoms and lubricants on the velocity profiles, simulation was made with the half L-J parameter 80.5. Figure 9 shows the results. Weak interaction between lubricant molecules and surface atoms allows slip at both the upper and lower surfaces except for the case of the lower surface with cyclohexane. The weak interaction also allows the molecules to move more fi ly, resulting m rather straight density profiles. Figure 10 shows the profiles in the case when both upper and lower surface have steps and the L-J parameter S0.5 is employed. No slip is seen at the surfaces, and the velocity profiles are continuous in all cases. Motions of admolecules on the stepped surfaces are examined. Figure 11 shows top views of trajectories of n-hexane molecules adsorbed on the upper surface with/without steps for the L-J parameter 80.5-... 

Molecular dynamics simulations have been conducted in order to investigate effects of mono-atomic steps on sliding surfaces on dynamic behaviour of lubricant molecules under high pressure and shear. The steps on the surfaces have a dramatic effect of increasing interactions between surface atoms and lubricant molecules. Movement of lubricant molecules on sliding... 

Surfaces can be characterized using scaiming probe microscopies (see section B1.19). In addition, by attaching a colloidal particle to tire tip of an atomic force microscope, colloidal interactions can be probed as well [27]. Interactions between surfaces can be studied using tire surface force apparatus (see section B1.20). This also helps one to understand tire interactions between colloidal particles. 

The autliors analyse tliese results in considerable detail, demonstrating tliat botli tlie stmcture of tlie surface and steric interactions between F atoms on neighbouring SiF groups influence the reaction progress. 

The interaction between particle and surface and the interaction among atoms in the particle are modeled by the Leimard-Jones potential [26]. The parameters of the Leimard-Jones potential are set as follows pp = 0.86 eV, o-pp =2.27 A, eps = 0.43 eV, o-ps=3.0 A. The Tersoff potential [27], a classical model capable of describing a wide range of silicon structure, is employed for the interaction between silicon atoms of the surface. The particle prepared by annealing simulation from 5,000 K to 50 K, is composed of 864 atoms with cohesive energy of 5.77 eV/atom and diameter of 24 A. The silicon surface consists of 45,760 silicon atoms. The crystal orientations of [ 100], [010], [001 ] are set asx,y,z coordinate axes, respectively. So there are 40 atom layers in the z direction with a thickness of 54.3 A. Before collision, the whole system undergoes a relaxation of 5,000 fsat300 K. 

The diversity of EEP reactions on a solid surface can be illustrated by the survey if interaction between excited atoms of mercury and zinc oxide [186]. When atoms of Hg get to an oxidized surface of ZnO at room temperature, an increase in the semiconductor electrical conductivity take place (Fig. 5.3, curve 2). The electrical conductivity change signal is irreversible, and in case of an increase in the temperature, after the Hg flux is disabled, an additional increase in the electrical conductivity (curves 3 and 4) takes place. One can logically suppose that we are dealing here with partial reduction of zinc oxide according to the scheme... 

Interaction between Metastable Atoms of Rare Gases and Surface of Oxide Semiconductors... 

The presence of adsorbed layers also affects the other parameters of the interaction between metastable atoms and a metal surface. Titley et al. [136] have shown that the presence of an adsorbed layer of oxygen on a W( 110) surface increases the reflection coefficient of helium metastable atoms. The reflection is of irregular nature and grows higher when the incidence angle of the initial beam increases. A series of publications [132, 136, 137] indicate that the presence of adsorbed layers causes an increase in the quantum yield of electron emission from a metal under the action of rare gas metastable atoms. 

The pattern of interaction between metastable atoms of rare gases and a semiconductor or dielectric surface is not yet clear, the literature data in this field are incomplete and uncoordinated, a fact that is primarily associated with the lack of convenient techniques suitable for studying these systems. 

The most critical aspect of atomistic simulations is thus the representation of the interactions between atoms by an algebraic function. If covalency is important, a part of the expression should contain details of how the interaction changes with angle, to mimic directional covalent bonds. In cases where a simulation is used to predict the location of a cluster of atoms within or at the surface of a solid, interactions between the atoms in the cluster, interactions between the atoms in the solid, and interactions between the atoms in the cluster and those in the solid must all be included. 

The above 1-dimensional model may be extended to 3-dimensions, in a straightforward manner, and yields a substrate whose surface is completely covered by adatoms. The TBA again leads to a difference equation and boundary conditions which can be solved directly (Grimley 1960). We do not intend to discuss the 3-dimensional case here and, instead, direct the reader to the loc. sit. articles. However, in passing, we note that, even when there is no direct interaction between the atoms in the adlayer, an important indirect interaction occurs between them via the substrate by a delocalization of the bonding electrons in directions parallel to the surface (Koutecky 1957, Grimley 1960). This topic is discussed in Chapter 8. 

The role of instabilities involving confined impurity atoms has been investigated by Mtiser using a model in which two one-dimensional (1-D) or 2-D surfaces were separated by a very low concentration of confined atoms and slid past one another.25 The motion of the confined atoms was simulated with Langevin dynamics where the interactions between these atoms were neglected and the atom-wall interactions were described by... 

For the actual Pt3Sn compound, the surface enrichment of (111) and (100) planes has been computed (45) by assuming that it only takes place by inversion between surface atoms and neighboring atoms. Since in this calculation only interaction between nearest neighbors was taken into account, this assumption was justified. However, if interactions are of longer range, the layers that interchange atoms with atoms from the surface can extend deeper into the solid. 

It is also interesting to consider charge-transfer models developed primarily for metal surfaces. There are clear parallels to the metal oxide case in that there is an interaction between discrete molecular orbitals on one side, and electronic bands on the other side of the interface. The Newns-Anderson model [118] qualitatively accounts for the interactions between adsorbed atoms and metal surfaces. The model is based on resonance of adatom levels with a substrate band. In particular, the model considers an energy shift in the adatom level, as well as a broadening of that level. The width of the level is taken as a measure of the interaction strength with the substrate bands [118]. Also femtosecond electron dynamics have been studied at electrode interfaces, see e.g. [119]. It needs to be established, however, to what extent metal surface models are valid also for organic adsorbates on metal oxides in view of the differences between the metal an the metal oxide band structures. The significance of the band gap, as well as of surface states in it, must in any case be considered [102]. 

---