Coordination number, of surface atoms

Surfaces are regions of high energy due to the asymmetry in the interface region and the lowered coordination number of surface atoms. In order to make such interfaces, work has to be done, as shown in tig. 4, to break bonds in the bulk of the material. 

The structure of a surface which is formed is strongly related to the thermodynamics. Because of the high energy of the interface, surfaces attempt to minimise this energy by increasing the coordination number of surface atoms and this is achieved in several ways, as follows ... 

Table 6.127 shows the variation of the total number of atoms (N), the fraction of surface atoms (FE), and the average coordination number of surface atoms, as a function of crystallite size d. It is now thought that the properties of Pt crystallites differ from those of the bulk metal for... 

Length of crystal edge Fraction of atoms on surface Total number of atoms in crystal Average coordination number of surface atoms... 

It is important to distinguish first-sheU coordination of the adsorbate and second-shell coordination number of surface atoms with surrounding metal atoms, as is shown in Table 10.1. 

Local surface structure and coordination numbers of neighbouring atoms can be extracted from the analysis of extended X-ray absorption fine structures (EXAFS). The essential feature of the method22 is the excitation of a core-hole by monoenergetic photons modulation of the absorption cross-section with energy above the excitation threshold provides information on the distances between neighbouring atoms. A more surface-sensitive version (SEXAFS) monitors the photoemitted or Auger electrons, where the electron escape depth is small ( 1 nm) and discriminates in favour of surface atoms over those within the bulk solid. Model compounds, where bond distances and atomic environments are known, are required as standards. 

Adsorption of carbon monoxide takes place all over the surface and there is distinct evidence that, at least on nickel, the CO stretching frequency depends upon the coordination number of the nickel atom to which it is attached. Hence, the adsorption of carbon monoxide yields information about the relative numbers of surface atoms with different coordination numbers. This information, howrever, is at best merely of a semiquantitative nature. Steric effects also play a role, as is evidenced by the fact that the subcarbonyl species can be formed only on nickel atoms with a lowr coordination number. 

In general one can say that those parts of the band that correspond to bonds which have been broken in order to create the surface are narrower. A similar effect can be expected for small particles the average coordination number of the atom decreases and the bands are narrower. This effect can be observed in photoemission experiments an example is shown in Fig. 3.18. 

After Werner 76b and more recently Iiundle 17K one is led to suggest that the maximum coordination number of an atom may be considered as having reference to the space around the surface of the kernel of the atom 78),... 

Steps at metal surfaces were argued to be good candidates for an increased reactivity because of the lower coordination number of the atoms [8]. In a seminal work Davis and Somoijai [9] concluded, e.g. that the ability of Pt to break C-H bonds during hydrocarbon dehydrogenation is enhanced at kinked Pt surfaces pre-dosed with oxygen, while Gland and coworkers demonstrated that CO adsorbs preferentially on the atomically rough steps of Pt(3 21) [10] and that some 02 dissociation [11] may occur at the same surface. 

When the d valence electron band is nearly completely filled, interaction with the doubly occupied CO 5o orbital, leading to a significant fraction of occupied antibonding orbital fragments a between adsorbate and surface atoms, will be repulsive. This Pauli repulsion is proportional to the number of surface atom neighbours and hence is a minimum in atop coordination. This counteracts the... 

Changes in bond strength with variation of coordinative unsaturation of surface atoms are very similar to the effects of coadsorption [11]. When two adsorbate atoms share a bond with the same surface atoms, the surface atom effectively has an increased coordination number. Therefore the adatom bond strength is weaker than when there is no sharing between metal surface atoms. The heat of adsorption generally decreases at high adsorbate surface coverage as a result of this effect. 

We finally arrive at a point where we can relate what we have learned to the principal theme of the text. Recall that small clusters essentially consist of surface whereas band theory applies to situations where the number of surface atoms is so small with respect to atoms in the bulk they can be ignored. In the Al77 cluster we have a shell-like structure of All A1i2 A144 (A1R)2o or a ratio of 20/57 = 0.35 surface to bulk. In addition, each of the 20 surface atoms is coordinated to... 

Figure 2. The most common type of imperfection site on a (111) crystal plane is steps. This illustration shows the perspective of regularly placed steps on the (111) surface. Every ninth row is a step (the step atoms are shaded) and this may be indexed as 9(111) X (111). The coordination number of step atoms is seven.

Figure 4. This (110) low Miller index plane is like a super-stepped surface—every other row is a step. The coordination numbers of surface metal atoms in the crests and troughs of this stepped or ruffled surface are seven and eleven, respectively.

Surface atoms on real catalysts reside in a variety of coordination environments depending on the exposed crystal plane (see Figure 5.1.3) and may exhibit different catalytic activities in a given reaction. Thus, a turnover frequency based on [ ]q will be an average value of the catalytic activity. In fact, the calculated turnover frequency is a lower bound to the true activity because only a fraction of the total number of surface atoms may contribute to the reaction rate. Nevertheless, the concept of a turnover frequency on a uniform surface has proven to be very useful in relating reaction rates determined on metal single crystals, metal foils, and supported metal particles. 

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