Average coordination number

Figure 2. Fhase adjusted Fourier transforms of Ft metal, 1% Ft/ Cabosil catalyst in H2 and 0.5% Ft/Cabosil catalyst in H2, all at 90 K. All are plotted to the same scale to emphasize the diminished magnitude because of the smaller average coordination numbers in the catalysts. The INSET shows the Ft-0 peak area retransformed with the appropriate Ft-0 phase shift. The artifact at low R is due to the EXAFS extraction procedure.

B.J.H. methods) (iii) the average diameter (T.E.M.) and/or the dispersion (chemisorption of probe molecule) of the metallic particle. EXAFS will also provide average coordination numbers, which decrease sharply as the particle size decreases. 

On the other hand, however, Sajeevkumar and Singh found the average coordination number to be 4.7 (141), whereas Megyes et al. found up to six acetonitrile molecules bound to the Li+ ion in the gas phase by means of mass spectrometry (142). Therefore, we reinvestigated the maximum coordination number of [Li(CH3CN)n]+ and also of [Li(NCH),J 1 purely by quantum chemical calculations, which resulted in [Li(NCH)4]+ and [Li(CH3CN)4]+ (93). 

Nj is the coordination number, equal to the number of neighbors in the fh coordination shell. For an fee metal such as rhodium we expect 12 neighbors in the first shell. If a particle becomes small, the average coordination number decreases. Note that unless the sample is that of a single element, TV is a fractional coordination number, i.e. the product of the real coordination number and the concentration of the... 

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. 

Further, one can calculate the distribution of the number and size of spheres intersections, but let us consider just an average number of crossings per sphere, which is n=— 81n(e) and corresponds to an average coordination number for the packing of spheres np. 

Note added in proof. Earlier in the text it was mentioned that the model used to describe the structure function of low density H20(as) does not describe that of high density H20(as). However, Narten, Venkatesh and Rice 27) do show than an ice I-like network with a near neighbor distance of 2.76 A has the density and distance spectrum of high density H20(as) if one permits 45% of the cavities characteristic of this structure to be occupied by water molecules. These are not ordinary unbonded interstitials. If the cavity molecules are located on the c axis at a distance of 2.76 A from the nearest network molecule each cavity molecule would have second neighbor network molecules at a distance of 3.25 A. Moreover, since occupancy of 45% of the cavities implies that 81% of the water molecules are part of the tetrahedral network and 19% in cavity positions, the average coordination number of nearest neighbors in this model is 4.3, as is found for H20(as) 10 K/10 K. Structure functions calculated for this interstitial variant of a randomized ice I model (the randomization is effected as in the simple ice I... 

The melting of the Si (100) surface has previously been investigated with classical molecular dynamics simulation. However, it is now known that these potentials fail to capture much of the this process. Upon melting. Si goes from a 4-fold coordinated semiconductor to a metallic liquid. The density of the liquid is about ten percent higher than in the solid. The average coordination number is between 6 and 7, which is rather low for a metal. This low coordination number is indicative of persistant remnants of covalent bonding. Moreover, recent ab initio simulations of the liquid show that spin effects play an important role. ... 

Borates can be viewed as complex salts in which the Lewis basicity of the structural unit must match the Lewis acidity of the interstitial complex to produce a stable structure. The relationship between basicity of the borate structural unit and its BO4/BO3 ratio was mentioned above, indicating that each specific structural unit has an associated basicity. It was recently shown that the Lewis basicity of borate structural units correlates with the average coordination number of the oxygen atoms they contain, counting H-bonds... 

Rule 11.2 (Corollary 1). The ratio of the average coordination number of the cations, Nf, to the average coordination number of the anions, Nf), is the same as the ratio of the number of anions, x, to the number of cations, a. 

Other properties of aqueous solutions where discontinuities were observed were molar volumes, heat capacities and viscosities.210-212 From all these pieces of evidence, the general opinion was that n in [M(H20) ]3+(aq) was nine for the lighter lanthanide ions, but eight for the heavier,213 though some workers were of the opinion that n did not change along the series.214 Solution X-ray studies have provided evidence for an average coordination number of 8.9 for Nd3+(aq),215 while neutron diffraction supports a value of 8.5 for the same ion.216... 

As the particle size decreases, the ratio between the number of atoms at the surface to those in the bulk increases with a parallel decrease in the average coordination number for the metal atom, which is also expected to be a factor of electrocatalysis. It has been calculated for Pt that the minimum size of a crystallite (cluster) for all atoms to be on the surface is 4 nm, corresponding to a specific surface area of 280 m2g-1 [322] (note that this is larger than the critical particle size where absorption of H atoms disappears on Pd) [333]. It is also interesting that dispersed catalysts can in turn influence the electronic properties of the support so that an interesting combination of sites with varied properties can result [330]. At low catalyst loadings, spillover of intermediates is also possible. 

A series of AB5 congruent-melting compounds (e.g., SnMgs, CaZn5, CeC 05, LaCu, SrAus ) are found at this stoichiometry. These compounds assume exclusively the D2d -type structure. This structure has two distinct B atomic sites with coordination numbers of 3 and 4 as shown in Fig. 22. Thus, the average coordination number for B is n = [(2x3) + (3x4)] = 18/5. Thus, the maximum of the liquidus line occurs at//m =n/(n + n )= 5/6... 

Fig. 9.18. Dependence of Zr02 film mass and the Zr average coordination number on the number of ALD cycles.

Based upon the theoretical maximum surface area (S01) and the measured surface area (SBEX, cfr. chapter 2), the average coordination number of the primary particles in the aggregate can be calculated as ... 

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