Surface structure notation

More complicated surface structures that contain steps or even kinks may also be described in this notation as n(ht,kt,lt)x hs,ksh), which indicates that the surface contains n rows of atoms forming a terrace, and one step of (hsfsk) structure. 

The Wood notation, as this way of describing surface structures is called, is adequate for simple geometries. However, for more complicated structures it fails, and one uses a 2x2 matrix which expresses how the vectors al and a2 of the substrate unit cell transform into those of the overlayer. 

In the majority of cases where adsorbates form ordered surface structures, the unit cells of those structures are larger than the unit cell of the substrate the surface lattice is then called a super lattice. The surface unit cell is the basic quantity in the description of the ordering of surfaces. It is necessary therefore to have a notation that allows the unique characterization of superlattices relative to the substrate lattice. 

Figure 5a shows the diffraction pattern associated with the clean (100) platinum surface. There are extra diffraction features in addition to those expected for this surface structure from the X-ray unit cell. This surface exhibits a so-called (5x1) surface structure (8). There are two perpendicular domains of this structure and there are 3, , f, and f order spots between the (00) and (10) diffraction beams. The surface structure is not quite as simple as the shorthand notation indicates, as shown by the splitting of the fractional order beams. The surface structure appears to be stable at all temperatures... 

Let us start with the simple case of an ideal crystal with one atom per unit cell that is cut along a plane, and assume that the surface does not change. The resulting surface structure can then be described by specifying the bulk crystal structure and the relative orientation of the cutting plane. This ideal surface structure is called the substrate structure. The orientation of the cutting plane and thus of the surface is commonly notated by use of the so-called Miller indices. 

We first discuss some basic aspects of surface structures, including ordering principles and notations, followed by an overview of the number and types of surface structures that have been investigated. Finally we shall highlight a few major trends emerging from the structural results. 

A complete discussion of surface structure includes the use of a shorthand notation describing the location of surface atoms. This abbreviated representation of the surface is based upon a projection of the bnlk structure on to the surface plane. From this projection the surface stmcture is described in terms of the unit cell vectors of the bulk material (a, b) ... 

Fig. 3.2. Surface structure of platinum single crystal catalysts with the corresponding Miller index notations given in brackets. (Reproduced, with permission, from Ref. 14.)...

Different spot patterns can be interpreted in terms of different surface structures in a fairly straightforward manner. There is a standard notation for describing the structures and their corresponding patterns (110, 111, 118), but it is beyond our scope to delve into it here. 

Confusion can arise if the Park-Madden symbol is made to refer to an ad-layer mesh alone, rather than to the proper combined mesh of the surface structure which by definition inclvdes the substrate mesh (Section IIA). The temptation to describe just the adlayer structure arises because the symmetry of the combination mesh is commonly lower, and the combination mesh can be awkwardly large. In such a situation LEED patterns can be very complicated even though structure is basically simple. Suitable conventional notation to handle this has not been formulated, and in such cases it is appropriate and desirable to describe the overlayer mesh separately, in addition to describing the combination mesh. This is particularly useful for coincidence lattices (Section IVE). 

Many surfaces exhibit a different periodicity than expected from the bulk lattice, as is most readily seen in the diffraction patterns of LEED often additional diffraction features appear which are indicative of a superlattice. This corresponds to the formation of a new two-dimensional lattice on the surface, usually with some simple relationship to the expected ideal lattice [5]. For instance, a layer of adsorbate atoms may occupy only every other equivalent adsorption site on the surface, in both surface dimensions. Such a lattice can be labelled (2x2) in each surface dimension the repeat distance is doubled relative to the ideal substrate. In this example, the unit cell of the original bulk-like surface is magnified by a factor of two in both directions, so that the new surface unit cell has dimensions (2 x 2) relative to the original unit cell. For instance, an oxygen overlayer on Pt (111), at a quarter-monolayer coverage, is observed to adopt an ordered (2 X 2) superlattice this can be denoted as Pt (111) -i- (2 x 2)-0, which provides a compact description of the main crystallographic characteristics of this surface. This particular notation is that of the Surface Structure Database [141 other equivalent notations are also common in the literature, such as Pt (111)-(2 x 2)-0 or Pt... 

The scattering intensity is, in principle, non-zero at any point along the CTRs, and the bulk Bragg peaks are located along each surface rod, notated by surface Bragg indices H and K, at Qz values dictated by the bulk crystal structure. The CTR structure is shown schematically in Figure 6B, where the thin vertical lines are the CTRs, and the spots on these rods correspond to bulk Bragg conditions. 

The simplest LEED patterns are most frequently characterized by a shorthand notation in which the unit cell of the surface structure is designated with respect to the bulk unit cell. An arrangement of surface atoms (the surface net ) identical to that in the bulk unit cell is called the substrate structure and is designated (1 x 1). For example, the substrate structure of platinum on the (111) surface is designated Pt(lll)-(1 X 1). If the surface structure that forms in the presence of an adsorbed gas is characterized by a unit cell identical to the primitive unit cell of the substrate, the surface structure is denoted (1 x 1)-S, where S is the chemical symbol or formula for the adsorbate. For example, a monolayer of oxygen adsorbed on the (111) face of silicon is denoted Si(l 11)-(1 X l)-0. 

A notation for these surfaces, the compact-step notation, devised by Lang and Somoijai [3], gives the surface structure in the general form w h,k,l,) X (h kj,), where hjc,l,) and h kj,) are the Miller indices of the terrace plane and the step plane, respectively, while w is the number of atoms that are counted in the width of the terrace, including the step-edge atom and the in-step atom. Thus, the fcc(755) surface is denoted by 7(111) x 1(100), or also by 7(111) x (100) for simplicity. A stepped surface with steps that are themselves high-Miller-index faces is termed a kinked surface. For example, the fcc(10, 8, 7) = 7(111) X (310) surface is a kinked surface. The step notation is, of course, equally applicable to surfaces of bcc, hep, and other ciystals, in addition to surfaces of fee crystals. Stepped surfaces of several orientations are listed in Table 2.2 (p. 88). Here the crystal faces are denoted both by their Miller indices and by their stepped-surface notation. 

For very small metallic particles, or clusters, crystal faces have no meaning. It is better to define surface structure with the notation introduced by Van Hardeveld and Hartog. They consider the coordination number i of a surface atom and the coordination number j of a surface active site, which was called as coordination model. Surface atom is denoted by Cj when it has i nearest neighbors. The active site is denoted by By when it has j nearest neighbors. Examples of C4, Ce and C7 atoms are shown in Fig. 2.8. Several active sites, B4, B5, Be and B7 are shown in Fig. 2.9. 

The individual structures listed in the tables are named using standard notations, particularly for superlattices we use Wood, rect (rectangular) or occasionally matrix notations for the superlattices, which are defined in many books and reviews [86V, 99W] they appear in the exact form used in the Surface Structure Database [99W]. 

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