Mean coordination number

N Mean-coordination number classifier-selectivity value ... 

Changing the size of metal particles leads to a change in the atom s mean coordination number, as in smaller particles the number ratio of surface atoms to bulk atoms increases. As a result, the metal s valence band becomes... 

The behaviour of lanthanum in dimethyl formamide (DMF) is quite different from that in methanol and acetonitrile. While perchlorate forms inner sphere complexes with lanthanides in acetonitrile [31], no such complexes are formed in DMF [32]. The coordination properties in DMF solutions were studied by NMR and UV-Vis spectroscopy techniques [33,34], The rate of DMF exchange in the system ytterbium perchlorate-DMF-CD2CI2 was slow enough that 1H NMR resonances permitted the determination of the mean coordination number to be 7.8 0.2. Similar determination in the case of thulium(III) gave a mean coordination number of 7.7 0.2. Thus it was concluded that the predominant species in heavy lanthanides is Ln(DMF)g+ in DMF solutions. In the case of lighter lanthanides, the following equilibrium exists... 

A = Alkali metal AE = Alkaline-earth metal a-P = Amorphous phosphorus CN = Mean coordination number (i(M-P) = Distance between M and P atom Distances between P atoms E = Element = Band gap M = Metal PBO = Pauling bond order (P) = Formal charge of a P atom (M) = Formal charge of a M atom R = Zr, Ftf, rare earth metal or actinoid metal RE = Rare earth element / cov = Covalent radius ... 

These AIMD results - Fig. 8.19 - are roughly consistent with the inferences formulated upon neutron scattering from 4.6 M NaOD aqueous solutions (Both et al, 2003) which report a mean coordination number of 3.7 0.3. This... 

Let the total number of their connecting necks be equal to Nt(rp). Then the mean coordination number for voids with r > rp is determined as... 

Taking into account the fact that the mean coordination number for all the voids is defined by Eq. (21), we can rewrite Eq. (30) as... 

It is of interest to note that in the case under consideration (i.e., when the pore volume is concentrated in necks) the desorption process is described [Eqs. (38) or (39)] by employing only the neck-size distribution and the mean coordination number for voids. The neck-size distribution can be calculated from the adsorption branch of the isotherm. Thus, the analysis of the desorption branch of the isotherm allows one to obtain the mean coordination number. In fact, Zo can be obtained from the position of the desorption knee. In addition, using Eq. (39) and the scaling expression for 9 b2 [Eq. (12)], it is possible to estimate the average linear dimension L of the microparticles in porous solids 34). 

Figure 29B shows the influence of the mean void radius on the deactivation process. An increase in the mean void radius results in a sharper threshold, below which the network loses its global connectivity. The effect of the mean coordination number on the deactivation kinetics is shown in... 

Fig. 30. Relative activity as a function of time at various values of the mean coordination number (A) and at various values of dispersion of pore-size distribution (B). The time dependence of the critical radius is described by Eq. (49). 

Two transformations are applied to the data of fig 4. First, the abscissa is transformed to the mean coordination number z (= mean number of nearest neighbours). The interpolation formula proposed by Bhatt and Rice, ... 

Fig. 13. The difference between the experimental ionisation potentials and the behaviour expected for the two classical scaling laws [see eqn (12)] is plotted as a function of the mean coordination number z, which increases to the left. The zero of the two curves has been shifted by 1 eV. The open circles joined by the straight, dashed line are from the tight-binding calculation of rdf. (8). The experimental results show a much more rapid decrease than calculate in the independent electron theory. This suggests that the transition at z 10.6 is indeed driven by electronic correlation, as in a Mott transition in bulk material. The insert shows the bandgap e expected for an independent electron theory (a) and one with enough correlation (b) to induce the discontinuous Mott transition as discussed in the text. The similarity to the theoretical and experimental data near z = 10.6 is obvious.

The simplest static property is the mean coordination number, , which is loosely defined as the average number of pore throats per pore body (Dullien, 1991). For spatially periodic systems, such as cubic packing of uniform spheres, it is relatively easy to determine . Methods of estimating for more heterogeneous porous media are reviewed by Sahimi (1995). 

In the case of very small metallic particles (a few nm) the coordination number of the shells can be used to determine the size of the metallic particles with an assumption of their shape (Zhang et al. 1995). This analysis is based on the fact that surface atoms have lower coordination numbers than bulk atoms. The mean coordination number can be calculated from the model of metallic particles and compared with the experiment. 

To gain an initial, qualitative insight into the relationships that exist in crystals formed from chain molecules, we use a simple model with roughly the same rationale as that of the Lennard-Jones and Devonshire model. Let us regard a bundle of N parallel, stretched chain-molecules as the ideal crystal and let its structure be characterized by a mean coordination number q (Fig. 2.4). This model embraces both, extended chain crystals and lamellae formed by folded-chain molecules. Naturally, in the latter ca the chain molecule is merely a segm t of the real chain. It is assumed that all defeats can be built-up from ener ticalfy non-degenerate units with... 

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