Bulk atoms

Much surface work is concerned with the local atomic structure associated with a single domain. Some surfaces are essentially bulk-temiinated, i.e. the atomic positions are basically unchanged from those of the bulk as if the atomic bonds in the crystal were simply cut. More coimnon, however, are deviations from the bulk atomic structure. These structural adjustments can be classified as either relaxations or reconstructions. To illustrate the various classifications of surface structures, figure A1.7.3(a ) shows a side-view of a bulk-temiinated surface, figure A1.7.3(b) shows an oscillatory relaxation and figure A1.7.3(c) shows a reconstructed surface. 

Note that in core-level photoelectron spectroscopy, it is often found that the surface atoms have a different binding energy than the bulk atoms. These are called surface core-level shifts (SCLS), and should not be confiised with intrinsic surface states. Au SCLS is observed because the atom is in a chemically different enviromuent than the bulk atoms, but the core-level state that is being monitored is one that is present in all of the atoms in the material. A surface state, on the other hand, exists only at the particular surface. 

If the lattices are viewed as close-packed spheres, the fee and the hep lattices have the highest density, possessing about 26% empty space. Each atom in the interior has 12 nearest neighbors, or in other words, an atom in the interior has a coordination number of 12. The bcc lattice is slightly more open and contains about 32% empty space. The coordination number of a bulk atom inside the bcc lattice is 8. 

The valence band structure of very small metal crystallites is expected to differ from that of an infinite crystal for a number of reasons (a) with a ratio of surface to bulk atoms approaching unity (ca. 2 nm diameter), the potential seen by the nearly free valence electrons will be very different from the periodic potential of an infinite crystal (b) surface states, if they exist, would be expected to dominate the electronic density of states (DOS) (c) the electronic DOS of very small metal crystallites on a support surface will be affected by the metal-support interactions. It is essential to determine at what crystallite size (or number of atoms per crystallite) the electronic density of sates begins to depart from that of the infinite crystal, as the material state of the catalyst particle can affect changes in the surface thermodynamics which may control the catalysis and electro-catalysis of heterogeneous reactions as well as the physical properties of the catalyst particle [26]. 

The effects of adsorbate coverage (film thickness) on the Pd 3d5/2 XPS peak positions of the Pd/W(l 1 0), Pd/ Re(0001), and Pd/Mo(l 10) systems were systematically investigated [63]. The peak positions reported for Pd coverage in excess of 1 ML represent a product of electrons emitted from surface and subsurface atoms. For the case of Pd(lOO), theoretical calculation suggest that the Pd 3d5/2 XPS BE of the surface atoms is 0.4 eV lower than that of bulk Pd. A similar difference has been observed experimentally for Ni and Pt surfaces. These shifts in BE are a consequence of variations in the coordination number of the surface atoms compared to bulk atom. If we reference the combined peak of bulk and surface atoms in 40 ML of Pd on W(1 1 0) to that of Pd(l 00) a difference of —0.8 eV is obtained between the Pd 3ds/2 BE of a pseudomorphic monolayer of Pd on W(110) and that of the surface atoms of Pd(l 00). The corresponding shifts... 

Changing the size of metal particles leads to a change in the atom s mean coordination number, as in smaller particles the number ratio of surface atoms to bulk atoms increases. As a result, the metal s valence band becomes... 

Both vanadium and niobium metals form dihydrides only at high pressures(27), and numerous phases with hydrogen compositions less than one(28). Experiments were performed to saturate vanadium clusters with deuterium. Figure 4 is a plot of the number of deuteri urn molecules found in the products. The solid straight lines are for D V ratios of 1 and 2. The corresponding curved dashed lines include corrections for some bulk atoms(2c). The best fit to the data including only surface atoms indicate a stoichiometry of 1.5. It is likely that this high surface stoichiometry is an indication of bulk i ncorporation of deuterium. 

The term atomic layer is used here to indicate, in general, a layer of atoms on the surface, where all the atoms are in contact with the surface. The term atomic layer does not specify a coverage, just that the layer is no more then one atom thick, probably less then a ML, relative to the number of substrate surface atoms. There can be several structures formed at different coverages, all under a ML, but all are one atom thick, and all would correspond to an atomic layer. Thus a statement that an atomic layer was formed suggests only that no bulk atoms were deposited. Where as, the statement that a monolayer was formed suggests a coverage, dependent on the ML definition in use. 

The distinctive feature of a surface atom is that it has fewer neighbors than an atom in the interior. This unsaturated coordination forms the reason why the electronic and vibrational properties and sometimes the crystallographic positions of surface atoms differ from those of the bulk atoms. 

Zs is the number of missing nearest neighbors of a surface atom Z is the coordination number of a bulk atom iVs is the density of atoms in the surface. 

Atoms at the surface lack neighbors on the vacuum side. Hence, in the direction perpendicular to the surface the atoms have more freedom to vibrate than bulk atoms ... 

Vibrations in the surface plane, however, will be rather similar to those in the bulk because the coordination in this plane is complete, at least for fee (111) and (100), hep (001) and bcc (110) surfaces. Thus the Debye temperature of a surface is lower than that of the bulk, because the perpendicular lattice vibrations are softer at the surface. A rule of thumb is that the surface Debye temperature varies between about 1/3 and 2/3 of the bulk value (see Table A.2). Also included in this table is the displacement ratio, the ratio of the mean squared displacements of surface and bulk atoms due to the lattice vibrations [1]. 

In addition to the acoustical modes and MSo, we observe in the first half of the Brillouin zone a weak optical mode MS7 at 19-20 me V. This particular mode has also been observed by Stroscio et with electron energy loss spectrocopy. According to Persson et the surface phonon density of states along the FX-direction is a region of depleted density of states, which they call pseudo band gap, inside which the resonance mode MS7 peals of. This behavior is explained in Fig. 16 (a) top view of a (110) surface (b) and (c) schematic plot of Ae structure of the layers in a plane normal to the (110) surface and containing the (110) and (100) directions, respectively. Along the (110) direction each bulk atom has six nearest neighbors in a lattice plane, while in the (100) direction it has only four. As exemplified in Fig. 17, where inelastic... 

Figure 3.16. Some simple defects found on a low-index crystal face 1, the perfect flat face, a terrace 2, an emerging screw dislocation 3, the intersection of an edge dislocation with the terrace 4, an impurity adsorbed atom 5, a monatomic step in the surface, a ledge 6, a vacancy in the ledge 7, a kink, a step in the ledge 8 an adatom of the same type as the bulk atoms 9, a vacancy in the terrace 10, an adatom on the terrace. (From Ref. 12, with permission from Oxford University Press.)...

Fig. 8a and b. First neighbour bonds of a central atom which is a bulk atom of a fee crystal. It has 12 first-neighbour bonds, b A cobalt atom in a monolayer of cobalt on copper (111). In this case the three upper bond force constants are reduced to zero (surface effect) while the effect of the copper substrate is to reduce the values of the three lower bonf force constants by about 15%... 

Figure 2.27 Schematic representation of surface and bulk atoms in a condensed phase. From W. D. Kingery, H. K. Bowen, and D. R. Uhhnann, Introduction to Ceramics. Copyright 1976 by John Wiley Sons, Inc. This material is used by permission of John Wiley Sons, Inc.

In surface studies, one is confronted with the difficulty of detecting a small number of surface atoms in the presence of a large number of bulk atoms a typical solid surface has 10 atoms/cm as compared with 10 atoms/cm in the bulk. In order to be able to probe the properties of solid surfaces using conventional methods, one needs the use of powders with very high surface-to-volume ratio so that surface effects become dominant. However, this technique suffers from the distinct disadvantage of an entirely uncontrolled surface structure and composition which are known to play an important role in surface chemical reactions. It is thus desirable to use specimens with well-defined surfaces which generally means small surface area, of the order of 1 cm, and examine them with tools that are surface sensitive. 

In a molecular dynamic simulation147 of bulk atomic diffusion by a vacancy mechanism, two atoms may occasionally jump together as a pair. The temperature of the simulation is close to the melting point of the crystal. In FTM studies of single atom and atomic cluster diffusion, the temperature is only about one tenth the melting point of the substrate. All cluster diffusion, except that in the (1 x 1) to (1 x 2) surface reconstruction of Pt and Ir (110) surfaces already discussed in Section 4.1.2(b), are consistent with mechanisms based on jumps of individual atoms.148,149 In fact, jumps of individual atoms in the coupled motion of adatoms in the adjacent channel of the W (112) surface can be directly seen in the FTM if the temperature of the tip is raised to near 270 K.150... 

As is seen from the behaviour of the more sophisticated Heine-Abarenkov pseudopotential in Fig. 5.12, the first node q0 in aluminium lies just to the left of (2 / ) / and g = (2n/a)2, the magnitude of the reciprocal lattice vectors that determine the band gaps at L and X respectively. This explains both the positive value and the smallness of the Fourier component of the potential, which we deduced from the observed band gap in eqn (5.45). Taking the equilibrium lattice constant of aluminium to be a = 7.7 au and reading off from Fig. 5.12 that q0 at 0.8(4 / ), we find from eqn (5.57) that the Ashcroft empty core radius for aluminium is Re = 1.2 au. Thus, the ion core occupies only 6% of the bulk atomic volume. Nevertheless, we will find that its strong repulsive influence has a marked effect not only on the equilibrium bond length but also on the crystal structure adopted. 

Figure 1.3. Plan view of the Ni(100)c(2 x 2)-0 and Ni(100)(2 x 2)-C p4g surface structures. In each case the full lines show the primitive unit mesh while in the -induced structure the dashed lines show the centred (2 x 2) mesh. In the case of the C-induced structure the outermost Ni atoms are shown as smaller more-darkly shaded spheres than those of the underlying substrate to see more clearly the relationship of this reconstructed layer to the substrate. Notice that this reconstruction also leads to some reduced Ni-Ni nearest-neighbour distances in the surface, so using the bulk atomic radii for these atoms would lead to some overlapping spheres.

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