Surfaces Miller indices

Figure Bl.21.1 shows a number of other clean umeconstnicted low-Miller-index surfaces. Most surfaces studied in surface science have low Miller indices, like (111), (110) and (100). These planes correspond to relatively close-packed surfaces that are atomically rather smooth. With fee materials, the (111) surface is the densest and smoothest, followed by the (100) surface the (110) surface is somewhat more open , in the sense that an additional atom with the same or smaller diameter can bond directly to an atom in the second substrate layer. For the hexagonal close-packed (licp) materials, the (0001) surface is very similar to the fee (111) surface the difference only occurs deeper into the surface, namely in the fashion of stacking of the hexagonal close-packed monolayers onto each other (ABABAB.. . versus ABCABC.. ., in the convenient layerstacking notation). The hep (1010) surface resembles the fee (110) surface to some extent, in that it also...

A superlattice can be caused by adsorbates adopting a different periodicity than the substrate surface, or also by a reconstmction of the clean surface. In figure B 1.21.3 several superlattices that are conmionly detected on low-Miller-index surfaces are shown with their Wood notation. 

Figure 1.5 The surface structures of (i) several high-Miller index stepped surfaces with different terrace widths and step orientations (ii) several high Miller-index surfaces with differing kink concentrations in the steps. From G.A. Somorjai, Chemistry in Two Dimensions, Cornell University Press. London, 1981, pp. 160and 161. Used by permission ofCornell University Press.

This surface is therefore the (111) surface. This surface is an important one because it has the highest possible density of atoms in the surface layer of any possible Miller index surface of an fee material. Surfaces with the highest surface atom densities for a particular crystal structure are typically the most stable, and thus they play an important role in real crystals at equilibrium. This qualitative argument indicates that on a real polycrystal of Cu, the Cu(l 11) surface should represent a significant fraction of the crystal s surface total area. 

In some cases, the step sites have different chemistry, i.e., they break chemical bonds, thereby producing new chemical species on the surface. This happens for example during NO adsorption on a stepped platinum surface l In this circumstance the step effect on ordering is through the new types of chemistry introduced by the presence of steps. Hydrocarbons for example dissociate readily at stepped surfaces of platinum or nickel while this occurs much more slowly on the low Miller-Index surfaces in the absence of a large concentration of steps As a result ordered hydrocarbon surface structures cannot be formed on the stepped surfaces of these metals while they can be produced on the low Miller-Index surfaces. 

We should mention here a special notation used for describing high-Miller-index surfaces. Such surfaces can often be more usefully described as stepped surfaces involving relatively close-packed terraces of low-Miller-index orientation separated by steps whose faces have also a low-Miller-index orientation. For example, the fcc(755) surface can be more easily visualized with the notation fcc(S)-[6(l 11)X (100)], where (S) means stepped , since this indicates that the surface is composed of terraces of (111) orientation and 6 atoms wide, separated by steps of (100) orientation and 1 atom high. A list of such correspondences of notation for stepped fee surfaces is included in Sect. V. 

Low Miller index surfaces of metallic single crystals are the most commonly used substrates in LEED investigations. The reasons for their widespread use are that they have the lowest surface free energy and therefore are the most stable, have the highest rotational symmetry and are the most densely packed. Also, in the case of transition metals and semiconductors they are chemically less reactive than the higher Miller index crystal faces. 

The metal substrates used in the LEED experiments have either face centered cubic (fee), body centered cubic (bcc) or hexagonal closed packed (hep) crystal structures. For the cubic metals the (111), (100) and (110) planes are the low Miller index surfaces and they have threefold, fourfold and twofold rotational symmetry, respectively. 

In the last few years LEED studies of high Miller index or stepped surfaces have become more frequent. Almost all of these studies have been on fee metals, where the atomic structure of these surfaces consists of periodic arrays of terraces and steps. A nomenclature which is more descriptive of the actual surface configuration has been developed for these surfaces, as described in Section III. In Table 5.5 the stepped surface nomenclature for several high Miller index surfaces of fee crystals has been tabulated. In Fig. 5.1 the location of these high Miller index surfaces are shown on the... 

By the use of mainly LEED and lately ion scattering techniques the location of many atomic adsorbates, their bond distances and bond angles from their nearest neighbor atoms have been determined. The substrates utilized in these investigations were low Miller Index surfaces of fee, hep and bcc metals in most cases, and low Miller Index surfaces of semiconductors that crystallize in the diamond, zincblende and wurtzite structures in some cases that could be cleaned and ordered with good reproducibility. 

D. The Atomic Surface Structure of High Miller Index Surfaces.. 12... 

IV. Chemisorption of Hydrocarbons on Low and High Miller Index Surfaces of... 

We call this Pt(100) surface reconstructed. Surface reconstruction is defined as the state of the clean surface when its LEED pattern indicates the presence of a surface unit mesh different from the bulklike (1 x 1) unit mesh that is expected from the projection of the bulk X-ray unit cell. Conversely, an unreconstructed surface has a surface structure and a so-called (1 x 1) diffraction pattern that is expected from the projection of the X-ray unit cell for that particular surface. Such a definition of surface reconstruction does not tell us anything about possible changes in the interlayer distances between the first and the second layers of atoms at the surface. Contraction or expansion in the direction perpendicular to the surface can take place without changing the (1 x 1) two-dimensional surface unit cell size or orientation. Indeed, several low Miller index surfaces of clean monatomic and diatomic solids exhibit unreconstructed surfaces, but the surface structure also exhibits contraction or expansion perpendicular to the surface plane in the first layer of atoms (9b). 

Fig. 6. A stereographic triangle of a platinum crystal depicting the various high Miller index surfaces of platinum that were studied.

One of the most exciting observations of LEED studies of adsorbed monolayers on low Miller index crystal surfaces is the predominance of ordering within these layers (18). These studies have detected a large number of surface structures formed upon adsorption of different atoms and molecules on a variety of solid surfaces. Conditions range from low temperature, inert gas physisorption to the chemisorption of reactive diatomic gas molecules and hydrocarbons at room temperature and above. A listing of over 200 adsorbed surface structures, mostly of small molecules, adsorbed on low Miller index surfaces can be found in a recent review (/). 

The chemisorption of over 25 hydrocarbons has been studied by LEED on four different stepped-crystal faces of platinum (5), the Pt(S)-[9(l 11) x (100)], Pt(S)-[6(l 11) x (100)], Pt(S)-[7(lll) x (310)], and Pt(S)-[4(l 11 x (100)] structures. These surface structures are shown in Fig. 7. The chemisorption of hydrocarbons produces carbonaceous deposits with characteristics that depend on the substrate structure, the type of hydrocarbon chemisorbed, the rate of adsorption, and the surface temperature. Thus, in contrast with the chemisorption behavior on low Miller index surfaces, breaking of C-H and C-C bonds can readily take place at stepped surfaces of platinum even at 300 K and at low adsorbate pressures (10 9-10-6 Torr). Hydrocarbons on the [9(100) x (100)] and [6(111) x (100)] crystal faces form mostly ordered, partially dehydrogenated carbonaceous deposits, while disordered carbonaceous layers are formed on the [7(111) x (310)] surface, which has a high concentration of kinks in the steps. The distinctly different chemisorption characteristics of these stepped-platinum surfaces can be explained by... 

In a series of studies, the dehydrogenation and hydrogenolysis of cyclohexane was studied on both the stepped and low Miller index (111) crystal faces of platinum at a surface temperature of 300°C and a hydrogen to cyclohexane ratio of 20 1. While the rates on the stepped and low Miller index surfaces were not very different for the formation of benzene and hexane, the formation of cyclohexene was very structure sensitive, its rate being 100 times greater on the stepped surface than on the (111) crystal face. In Table III mrnnare the initial turnover numbers for the various reactions at low... 

There are still a number of surface systems where the structure cannot be determined by LEED for theoretical and experimental reasons. High Miller-index surfaces, such as stepped or kinked surfaces, have layers separated by very small distances normal to the surface. The calculational tools normally used for LEED break down in this case, and no new approach has yet been developed to solve this problem. Experimental difficulties restrict the study of insulator surfaces, because of charging problems, and of molecular crystal surfaces, because of beam damage problems. 

The theories of surface structure and bonding have been reviewed. It should be clear to the reader that surface structural chemistry is indeed a frontier area for both theorists and experimental researchers. From an experimentalists viewpoint the data base of atomic and molecular surface structures is very small at present. Most investigations have been carried out on flat, low Miller index surfaces of monatomic solids, either clean or with atomic or small molecules as adsorbates. 

Fig. 14. Idealized low Miller index surface planes of 7-alumina and nature of the different hydroxyl groups, (a) A layer, parallel to the (111) plane (b) B layer, parallel to the (111) plane (c) C layer, parallel to the (110) plane (d) D layer, parallel to the (110) plane [reprinted with permission from Lewis and Kydd (44) copyright 1991 Academic Press],... 

In contrast, other low Miller index surfaces of Ti02 have not attracted so much attention in terms of adsorbate structure determinations. Only two such studies have been reported, both involving Ti02( 100). Fig. 11 shows simple schematic diagrams of the (1x1) and (1x3) phases of this surface, both of which will be mentioned below. The (1x3) reconstruction is known to consist of (110) microfacets from previous work (see Ref. 79 and Refs, therein), whereas the displayed (1x1) structure is merely that expected on the basis of Tasker s rule [80]. 

Cr203 has the same bulk crystal structure as a-Al203, namely corundum. Of its several low Miller index surfaces only one, (0001), has been employed for adsorbate structural determinations so far. To overcome sample charging problems a thin film has been utilised for these studies, rather than a single crystal. The surface structure of this (0001) oriented thin film has been investigated by LEED-IV [112]. Simulations of the experimental data evidence a chromium terminated surface with large vertical interlayer relaxations, reaching down five or six layers. 

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