Number of surface atoms

Since solids do not exist as truly infinite systems, there are issues related to their temiination (i.e. surfaces). However, in most cases, the existence of a surface does not strongly affect the properties of the crystal as a whole. The number of atoms in the interior of a cluster scale as the cube of the size of the specimen while the number of surface atoms scale as the square of the size of the specimen. For a sample of macroscopic size, the number of interior atoms vastly exceeds the number of atoms at the surface. On the other hand, there are interesting properties of the surface of condensed matter systems that have no analogue in atomic or molecular systems. For example, electronic states can exist that trap electrons at the interface between a solid and the vacuum [1]. 

Xps spectra also bear a relationship between photoelectron intensity and number of surface atoms sampled (19,27). Quantitation of these data can be achieved with a precision to within ca 20%. For a homogeneous sample analy2ed in a fixed geometry, the relationship between xps intensity and number of atoms is given by... 

A dispersion factor, defined as the ratio of the number of surface atoms to the total number of atoms ia the particle, is commonly used to describe highly dispersed systems that do not exhibit a particularly high surface-area-to-volume ratio (22). Representative values for 10-, 100-, and 1000-nm particles are, respectively, on the order of 0.15—0.30, 0.40, and 0.003—0.02, depending on the specific dimensions of the atoms or molecules that comprise the particles. Other quantities can be used to describe the degree of dispersion (6,7), but these tend to assume, at least, quasi-equUibrium conditions that are not always met (7,23). 

The number of surface atoms can be determined by chemisorption of probe molecules (H2, O2...), knowing the stoichiometry of the adsorbed species. As an example, in the case of Pt, the stoichiometry of irreversibly adsorbed hydrogen (H/Pts) and oxygen (0/Pts) at room temperature are both close to 1/1 [108-111]. Knowing the total number of atoms (elemental analysis) and the number of irreversibly adsorbed H and O, the dispersion of the particles (D = Pts/Pt) is then easily obtained. Note that the dispersion of these particles decreases when their size increases (Fig. 5). 

The quantity of AsPha fixed and Ce evolved after 3 h of reaction at 303,373, and 443 K, related to the amount of total Ni (As xed/Nit) or to the number of surface atoms (Asfixed/Nis) as reported in Table 6 indicates that the reaction of AsPha with Ni under H2 proceeds through a stepwise process, with a progressive hydrogenolysis of the As - Ph bonds. Moreover, after reaction at 443 K, the diffraction pattern of the sohd presents clear lines at 33.6 and 50.5 26 assigned to the NiAs phase (nickeUne), thus showing that an alloy has been formed. 

At smooth metal electrodes that have been subjected to annealing, the number of different crystallographic defects (dislocations, kinks, etc.) emerging at the surface is between 10 and lO cm. This number is small relative to the total number of surface atoms (which is on the order of 10 cm ). In the literature, attempts have been described to determine the catalytic activity of electrodes having an artihcially boosted number of surface defects. These experiments gave no unambiguous results in some cases some increase, in other cases some decrease in activity was observed. 

Normalized to the number of surface atoms determined by total H2-O2 titration. 

Figure 3.4. The influence of the cry.stallographic plane on the number of surface atoms and the structure of the metallic surface, as illustrated for nickel The co-ordination numbers of the atoms in the three crystal surfaces are 8, 7 and 9 for the (100), (110) and (111) plane, respectively. Because bulk Ni has 12 neighbours, the surface atoms are unsaturated (after Le Page, 1987).

Metals are widely u.sed in catalysis. In some specific cases they are applied in the form of gauzes, but usually a higher dispersion (even up to 90%) is aimed for. A major reason for this is the price of the metals (very often noble metals are used), in combination with an optimized use of the reactor volume. The ratio of number of surface atoms (ns) to the total number of atoms (nr) is called the dispersion , also known as D ... 

In some specific cases one would like to convert the chemisorption data into an averaged particle size. In that case, the number of surface atoms per unit surface area (density of surface atoms) is an essential parameter. Since this number depends on the type of the crystallographic plane, (see Table 3.7), one also needs information on the types of crystallographic planes exposed to the gas phase. This is also important for another reason the adsorption stoichiometry may depend on the crystallographic plane. 

The number of surface atoms per unit area for some transition... 

Although (15.1) and (15.2) hold strictly only for a liquid in equilibrium with its vapor, they have been commonly apphed also to solid materials, in particular for describing nanoparticle sintering (see the discussion in [Campbell et al., 2002]). However, a number of comphcations must be considered for solid materials. First of all, y cr, since for a sohd a change in the surface area A can be reahzed either by increasing the number of surface atoms without changing the interatomic distances between them (this is related to the first term in (15.3)) or by introducing a strain (this is related to the second term in (15.3)) ... 

FIGURE 1.2 Estimation of particle size from the fraction exposed (FE). Dispersion (D) = percentage of atoms exposed, i.e., number of surface atoms/total number of atoms. Usually designated by %D, but sometimes by FE or %FE. 

Up to now only individual surface atoms have been considered. In many cases, however, a sorptive process or a catalytic reaction requires the combined action of a number of surface atoms. In these cases it is the number of sites active in the process under consideration that is of paramount importance. In dealing with reactions requiring the presence of B5 sites, we are in the fortunate circumstance that the number of these sites... 

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. 

One can estimate this excessive energy using a ratio of the number of surface atoms Ns to the total number, A v. of atoms in a considered object as Ns/NvxA/Ithat is, the ratio of the surface area, A, of the object to its volume, V. The ratio A/V is known as dispersion, and (A/Vy1 expresses the characteristic size of the object [3],... 

Figure 23 Cancellation of lateral forces between two surfaces. The atoms in the top layer, represented by circles, experience forces that are dependent on the position of the atom with respect to the periodic substrate. The arrows on the atoms indicate the magnitude and direction of these forces. For contacts lacking commensurability that are contain a sufficiently large number of surface atoms or irregularities, these forces will cancel in a statistical sense.

Anderson that at this level the mechanistic details are a matter of opinion (7). There is, however, a difference as far as the number of surface atoms participating in the reaction is concerned. Mechanism A requires more than one Mechanism C, however, requires only one metal atom. Van Schaik et al. 89) reported skeletal isomerization according to Mechanism A over platinum-rich platinum-gold alloys, whereas over gold-rich catalysts, isolated platinum atoms could promote Mechanism C only. Garin and Gault (82) assumed the formation of a C4 cyclic intermediate with the insertion of a platinum atom as the fourth member of the ring. This concept of Mechanism B would also involve one metal atom. 

For these particles, the number of surface atoms (N ) and total atoms (N,) for... 

The simulation is performed on the (111) surface of a face-centered-cubic crystal. Figure 6 shows the top three layers of an ideal surface. We say an atom is a surface atom if there is no atom sitting right, above it along the (111 ) direction. The number of surface atoms (or better to say, surface sites) is thus conserved. We demand in... 

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