Coordination number in solids

Lu3+) and this relatively large size for 3+ ions (cf. Al3+ 53 pm) is associated with correspondingly high coordination numbers in solid compounds. 

A. Diebold, K. S. Hagen, Iron(II) polyamine chemistry Variation of spin state and coordination number in solid state and solution with iron(II) tris(2-pyridylmethyl)amine complexes, Inorg. Chem. 37 (1998) 215. 

Table 1.8. First Coordination Numbers in Solid and Liquids ...

Crystallographic ionic radii (A), typical coordination number in solid and hydration enthalpies (kjrnol ) of the rare earth and... 

These are common coordination numbers in solids, not hydration numbers in solution. They have been used to provide a conventional size parameter for calculation of hydration enthalpies. It is recognized that in many coordination compounds the 3 + ions are coordinated to eight or even more ligands, and that in aqueous solution the primary coordination sphere has nine water molecules for light 3 + ions and eight for heavy 3+ ions. 

The dominant features which control the stoichiometry of transition-metal complexes relate to the relative sizes of the metal ions and the ligands, rather than the niceties of electronic configuration. You will recall that the structures of simple ionic solids may be predicted with reasonable accuracy on the basis of radius-ratio rules in which the relative ionic sizes of the cations and anions in the lattice determine the structure adopted. Similar effects are important in determining coordination numbers in transition-metal compounds. In short, it is possible to pack more small ligands than large ligands about a metal ion of a given size. 

A diverse coordination chemistry is emerging for bismuth(III) made possible by a spacious and flexible coordination environment, allowing for coordination numbers in excess of 9. Although the available data are still limited, distinct trends are evident, and the polymeric solid-state features that may be assumed on the basis of high coordination numbers can be mediated by appropriate selection of organic-based ligands. The unusual structural arrangements observed for many types of complex may prove to be representative as the number of examples of such systems increases. 

Generally, however, Mn(II) in the interior of the solid can also have low coordination number in the neighborhood of vacancy or any similar structural defects. The signal I, on the other hand, is from the fully coordinated Mn(II), i.e., with coordination number 4. Decrease in the relative intensity of signal II by AA addition is obviously the result of capping of sulfur defects by AA. 

Spatial constraints can also influence the coordination number and can often explain, for example, why the same cation can occur with more than one coordination number in the same crystal. However, a full treatment of spatial constraints requires an understanding of crystallographic symmetry, so further discussion is deferred to Part III which deals with the chemistry of extended three-dimensional solids. 

The coordination number can sometimes be established by coordinated physical measurements such as conductance, molecular weight measurement, infrared, UV-VIS-near IR, and emission spectroscopy [16]. The coordination numbers of solid complexes can be obtained by X-ray diffraction methods. Infrared spectroscopy and the conductance methods were used in the determination of the coordination numbers of Nd(NCh)3 4DMSO and Dy(N03>3 3DMSO complexes [17]. 

The question of coordination in aqueous solutions is not as clear as in solid state. Sped-ding s work [53] on the partial molar volumes of aquo ions of lanthanides and the irregular trends of these quantities in the lanthanides has been taken as evidence for change in coordination number in the lanthanide series [54]. The change in coordination from 9 to 8 in the lanthanide series has been confirmed by X-ray and neutron diffraction studies of LnCb solutions [55], The coordination numbers of lanthanides determined in aqueous solutions by various techniques along with the coordination numbers obtained are given below ... 

Arrays of ions tend to maximize the net electrostatic attraction between ions, while minimizing the repulsive interactions. The former ensures that cations are surrounded by anions, and anions by cations, with the highest possible coordination numbers. In order to reduce repulsive forces, ionic solids maximize the distance between like charges. At the same time, unlike charges cannot be allowed to get too close, or short-range repulsive forces will destabUize the stmcmre. The balance between these competing requirements means that ionic sohds are highly symmetric stmctures with maximized coordination numbers and volumes. 

An important use of high mechanical pressiues is to force solids to assume crystal structures and coordination numbers in which they are normally unstable. Thus, four-coordinate Si in Si02, typified by quartz or try dimite, can be forced to assume the six-coordinate rutile stracture under very high pressures. Once formed, these structures are kinetically stable. The high-pressure polymorph of silica, called stishovite is found terrestrially as the result of meteor impact. 

Overall, then, the existence of the three scandium-containing ions [Sc(H20)x] + (x = 6,7,8) in five different solid salts indicates that in itself X-ray diffraction data on solids cannot be relied upon to indicate the coordination number in aqueous solution. Ultimately, it is the solubihty of a particular salt that determines which compound crystalhses out from aqueous solution. 

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 41. Square scheme illustrating the principle of operation for the threaded compounds CU.29+, CU.30+ or Cu.31", reported in Figure 42. The subscripts 4 and 5 indicate the copper coordination number in each complex. The stable Cu (4) complex is oxidized to an intermediate tetrahedral divalent species Cu"(4) which undergoes a rearrangement to afford the stable Cu"(5) complex. Upon reduction, a Cu (5) species is formed as a transient which finally reorganizes to regenerate the starting complex. The solid circle represents Cu, and the open circle represents Cu".

Mix, Phase jj parameter corresponding to the ratio of the coordination number in the surface to that in the bulk considering the surface relaxation. " In particular, for the solid solutions, here we use the value 0.75 as by assuming that the coordi-... 

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