Woods notation

As a partieular ease, a surfaee may be given the Wood notation (1 x i) as in Ni (111)-(1 x i) this notation indieates that the two-dimensional unit eell of the surfaee has the same size as the two-dimensional unit eell of the bulk (111) layers. Thus, an ideally tenuinated bulk lattiee without overlayers or reoonstnietions will earry the label (1 x i). 

The Wood notation ean be generalized somewhat fiirther, by adding either the prefix e for eentred, or the prefix p for primitive. For instanee, one may have a e (2 x 2) unit eell or a p(2 x 2) unit eell, the latter often abbreviated to (2 x 2) beeause it is identieal to it. In a eentred unit eell, the eentre of the eell is an exaet eopy of the eomers of the eell this makes the eell non-primitive, i.e. it is no longer the smallest eell that, when repeated periodieally aeross the surfaee, generates the entire surfaee stnieture. Nonetheless, the eentred notation is often used beeause it ean be quite eonvenient, as the next example will illustrate. 

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. 

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 structures, the unit cells of these structures are longer than that of the substrate they are referred to as superlattices. Two notations are used to describe the superlattice, the Wood notation and a matrix notation.18 Some examples of overlayer structures at an fcc(llO) surface are as follows ... 

Figure 6.10 illustrates LEED patterns of the clean Rh(lll) surface, and the surface after adsorption of 0.25 monolayers (ML) of NH3 [22]. The latter forms the primitive (2x2) overlayer structure (see Appendix I for the Wood notation). In the (2x2) overlayer, a new unit cell exists on the surface with twice the dimensions of the substrate unit cell. Hence the reciprocal unit cell of the adsorbate has half the size of that of the substrate and the LEED pattern shows four times as many spots. 

Adsorbates may form ordered overlayers, which can have their own periodicity. The adsorbate structure is given with respect to that of the substrate metal. For simple arrangements the Wood notation is used some examples are given in Fig. A.3. The notation Pt (110) - c(2x2) O means that oxygen atoms form an ordered overlayer with a unit cell that has twice the dimensions of the Pt (110) unit cell, and an additional O in the middle. Note that this abbreviation does not specify where the O is with respect to the Pt atoms. It may be on top of the Pt atoms but also in bridged or fourfold sites, or in principle anywhere as long as the periodic... 

A non-matrix notation, called Wood notation can be used when the angles between the pairs of basis vectors are the same for the substrate and the superlattice, i.e., when the angle between and is the same as the angle between bj and b2-Then the unit cell relationship is given by, in general,... 

Fig. 3.4. Common superlattices on low Miller index crystal surfaces. The Wood notation is used...

Since the version represented by the solid square in Figure 9.17d best characterizes the adsorption, it is described as a c(2 x 2) net, the c reminding us that this is a centered structure. The full description of the LEED pattern in Figure 9.16c in the Wood notation is therefore written W( 100)—c(2 x 2)—hydrogen. 

In the adsorption studies we have discussed, the expansion of the unit mesh is the same in both directions, but this need not be the case. Examples in which the expansion along different axes of the mesh varies are p(4 x 2)—O for the adsorption of 02 on Mo(l 11), p(3 x 15)—O for 02 on Pt(l 11), c(4 x 2)—S for H2S on Au(100), and c(9 x 5)—CO for CO on W(110). Somorjai (1981, 1994) has assembled extensive tables of this sort of information. Note that many but not all adsorbates are dissociated on the metal surfaces. Finally, it is not necessary for the supernet and the substrate to show the same angles between sides of their respective meshes. The Wood notation does not apply in these cases, but an alternative notation exists... 

In order to describe the 2D crystal lattice periodicities of the adsorbate unit cell, two notations are used in the literature the Wood notation [10] and the matrix notation [11]. For the latter, the transformation matrix (mn ii2, i2i i22) hnks the adsorbate lattice vectors ( i, 2) to the substrate lattice vectors (a, a2) via ... 

Two sets of notation are commonly used to describe overlayer structures observed in diffraction experiments, the Wood notation [92] and a matrix notation. Although the latter is more flexible, the former is more widely used and we shall restrict ourselves to it in this review. The nomenclature is based on a comparison between the unit mesh of the topmost layer, the overlayer, and that of the second, unreconstructed, substrate layer. If a and b are the unit mesh vectors of the substrate layer and a, and bg the unit mesh vectors of the overlayer, then Wood s notation for an overlayer of adsorbed species A on the hkl plane of a crystal M is... 

Modem surface crystallographic studies have shown that on the atomic scale, most clean metals tend to minimize their surface energy by two kinds of surface atom rearrangements - relaxation and reconstmction [22-26]. In this review, the term surface reconstruction applies to the case in which there is lateral (i.e. in the surface plane) movement of surface atoms such that the surface layer has a symmetry that is different from that of the underlying bulk of the crystal. Hence, the surface layer has a two-dimensional unit cell that is different from the corresponding two-dimensional unit cell of a layer in the bulk. The periodicity of the surface can be defined by Woods notation for example, an unreconstructed surface would be termed as (1x1), whereas if the surface unit cell size was doubled in one of the primary vector directions, it would be termed as (2 x 1), and so on. On the other hand, surface relaxation apphes to the case in which the surface layer is in a (1 x 1) state but the layer is displaced along the surface normal direction from the position expected for bulk termination of the crystal lattice. In this section, both surface reconstruction and surface relaxation effects are described with specific examples chosen to illustrate the phenomena as they are observed in the electrochemical environment. 

Figure 5.2-3 shows a few examples of reconstruction for a layer of adatoms on top of a substrate. The matrix and Wood notations are compared. It can be seen from the figure that (i) the elementary cell is not uniquely... 

Fig. 5.2-3a-d Examples of reconstruction for a layer of adatoms (small shaded circles) on top of a square lattice substrate (large empty circles). Matrix and Wood notations are compared. Notice that (c) and (d) differ only for the choice of the unit cell... 

Figure 4.38. Surface reconstruction of Si planes. Shown are a) fcc-(100)-(2 x 2), also referred to as fcc-(100)-p(2 X 2) referring to a primitive unit, b) an STM image of a Si(lll) reconstructed surface, and c) the Woods notation of reconstructed fcc(lOO) surfaces.

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