Coordination number ideal

Oxidation state Coordination number Idealized geometry Examples... 

Table 31.4 is a list of typical compounds of the actinides and demonstrates the wider range of oxidation states compared to lanthanide compounds. High coordination numbers are still evident, and distortions from the idealized stereochemistries which are quoted are again general. However, no doubt at least partly because the early actinides have received most attention, the widest range of stereochemistries is... 

First, the hydrogen bond is a bond by hydrogen between two atoms the coordination number of hydrogen does not exceed two.7 The positive hydrogen ion is a bare proton, with no electron shell about it. This vanishingly small cation would attract one anion (which we idealize here as a rigid sphere of finite radius—see Chap. 13) to the equilibrium intemuclear distance equal to the anion radius, and could then similarly attract a second anion, as shown in Figure 12-1, to form... 

In Fig. 1 are assembled the most important coordination polyhedra of tin(II) compounds omitting high coordination numbers which are difficult to illustrate. In Table 7 the corresponding bond angles characterizing the deviation from ideal... 

The structural element of two almost ideal tetrahedra which are connected to each other at their tops is completely unknown so far for Group 13 compounds nor can it be found in the elemental structures, although the central Ga2 unit is close to the a-phase. However, its coordination number of 4(1 + 3) does not reach the coordination number 7(1 + 6) of a-gallium. 

The rather low coordination in the (100) and (110) surfaces will clearly lead to some instability and it is perhaps not surprising that the ideal surface structures shown in Figure 1.2 are frequently found in a rather modified form in which the structure changes to increase the coordination number. Thus, the (100) surfaces of Ir, Pt and Au all show a topmost layer that is close-packed and buckled, as shown in Figure 1.3, and the (110) surfaces of these metals show a remarkable reconstruction in which one or more alternate rows in the <001 > direction are removed and the atoms used to build up small facets of the more stable (111) surface, as shown in Figure 1.4, These reconstructions have primarily been characterised on bare surfaces under high-vacuum conditions and it is of considerable interest and importance to note that chemisorption on such reconstructed surfaces can cause them to snap back to the unreconstructed form even at room temperature. Recently, it has also been shown that reconstructions at the liquid-solid interface also... 

A striking feature of the formulas (4.68a)-(4.68c) is that the coordination number (CN) of ligands bonded to Co is six (CN = 6) in each case. Werner conjectured that such six-fold coordination corresponds to idealized octahedral geometry about the central Co ion, which leads to unique structures for [Co(NH3)6]3+ and [Co(NH3)5C1]2+ but distinct cis and trans isomers for [Co(NH3)4Cl2]+, as observed. X-ray studies subsequently confirmed the accuracy of Werner s brilliant structural inferences. 

So far we have considered mixtures of atoms or species of similar size and shape. Now we will consider a mixture of a polymeric solute and a solvent of monomers [7, 8], The ideal entropy of mixing used until now cannot possibly hold for this polymer solution, in which the solute molecule may be thousands or more times the size of the solvent. The long chain polymer may be considered to consist of r chain segments, each of which is equal in size to the solvent molecule. Therefore r is also equal to the ratio of the molar volumes of the solute and the solvent. The solute and the solvent can be distributed in a lattice where each lattice site can contain one solvent molecule. The coordination number of a lattice site is z. 

Fig. 2. Ideal polyhedra for various high coordination numbers... 

Mossbauer spectroscopy involves the measurement of minute frequency shifts in the resonant gamma-ray absorption cross-section of a target nucleus (most commonly Fe occasionally Sn, Au, and a few others) embedded in a solid material. Because Mossbauer spectroscopy directly probes the chemical properties of the target nucleus, it is ideally suited to studies of complex materials and Fe-poor solid solutions. Mossbauer studies are commonly used to infer properties like oxidation states and coordination number at the site occupied by the target atom (Flawthome 1988). Mossbauer-based fractionation models are based on an extension of Equations (4) and (5) (Bigeleisen and Mayer 1947), which relate a to either sums of squares of vibrational frequencies or a sum of force constants. In the Polyakov (1997)... 

The adsorption site, i.e. the chemisorption position of the adatoms on (within, below) the substrate surface, thanks to the polarisation dependence of SEXAFS. Often a unique assignment can be derived from the analysis of both polarisation dependent bond lengths and relative coordination numbers. The relative, polarisation dependent, amplitudes of the EXAFS oscillations indicate without ambiguity the chemisorption position if such position is the same for all adsorbed atoms. More than one chemisorption site could be present at a time (surface defect sites or just several of the ideal surface sites). If the relative population of the chemisorption sites is of the same order of magnitude, then the analysis of the data becomes difficult, or just impossible. 

Ideal coordination numbers for anions can, in principle, be determined in a similar way but it is difficult to find many examples of an anion surrounded by only one kind of cation. In the alkali halides, CP is six coordinated by each of the smaller alkali metal atoms, but is eight coordinated by Cs" ". An ideal coordination number of 7 can therefore be chosen. The coordination numbers around 0 in stable compounds range between 2 and 6 with an average close to 4 and similar values are found for F . 

With a knowledge of the ideal coordination numbers expected for each of the ions, one can explore the crystal chemistry of a compound without prior knowledge of its structure or even its bond graph. It is not even necessary that the compound exist in order to explore its chemistry and to discover whether it is likely to be stable, and if so, what its properties might be. 

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