Cationic radius

Yttrium, on the otlrer hand, which has a larger cation radius than Cr +, appears to affect the grain boundary cation diffusion and not the volume diffusion of Ni +. The effects of the addition of small amounts of yttrium to nickel is to decrease dre rate of tire low temperamre grain-boundary dominated oxidation kinetics. 

Fig. 5.20. The shock-induced polarization of a range of ionic crystals is shown at a compression of about 30%. This maximum value is well correlated with cation radius, dielectric constant, and a factor thought to represent dielectric strength. A mechanically induced point defect generation and migration model is preferred for the effect (after Davison and Graham [79D01]).

However, solubility, depending as it does on the rather small difference between solvation energy and lattice energy (both large quantities which themselves increase as cation size decreases) and on entropy effects, cannot be simply related to cation radius. No consistent trends are apparent in aqueous, or for that matter nonaqueous, solutions but an empirical distinction can often be made between the lighter cerium lanthanides and the heavier yttrium lanthanides. Thus oxalates, double sulfates and double nitrates of the former are rather less soluble and basic nitrates more soluble than those of the latter. The differences are by no means sharp, but classical separation procedures depended on them. 

The coordination chemistry of the large, electropositive Ln ions is complicated, especially in solution, by ill-defined stereochemistries and uncertain coordination numbers. This is well illustrated by the aquo ions themselves.These are known for all the lanthanides, providing the solutions are moderately acidic to prevent hydrolysis, with hydration numbers probably about 8 or 9 but with reported values depending on the methods used to measure them. It is likely that the primary hydration number decreases as the cationic radius falls across the series. However, confusion arises because the polarization of the H2O molecules attached directly to the cation facilitates hydrogen bonding to other H2O molecules. As this tendency will be the greater, the smaller the cation, it is quite reasonable that the secondary hydration number increases across the series. 

Various crown ethers (p. 96) with differing cavity diameters provide a range of coordination numbers and stoichiometries, although crystallographic data are sparse. An interesting series, illustrating the dependence of coordination number on cationic radius and ligand cavity diameter, is provided by the complexes formed by the lanthanide nitrates and the 18-crown-6 ether (i.e. 1,4,7,10,13,16-... 

The uncertainty of the proper coordination number of any particular plutonium species in solution leads to a corresponding uncertainty in the correct cationic radius. Shannon has evaluated much of the available data and obtained sets of "effective ionic radii" for metal ions in different oxidation states and coordination numbers (6). Unfortunately, the data for plutonium is quite sparse. By using Shannon s radii for other actinides (e.g., Th(iv), U(Vl)) and for Ln(III) ions, the values listed in Table I have been obtained for plutonium. These radii are estimated to have an uncertainty of 0.02 X ... 

The stability of a certain structure type depends essentially on the relative sizes of cations and anions. Even with a larger Madelung constant a structure type can be less stable than another structure type in which cations and anions can approach each other more closely this is so because the lattice energy also depends on the interionic distances [cf. equation (5.4), p. 44], The relative size of the ions is quantified by the radius ratio rm/rx rM being the cation radius and rx the anion radius. In the following the ions are taken to be hard spheres having specific radii. 

Silver(I) /3-diketonate derivatives have received significant attention due to the ease with which they can be converted to the elemental metal by thermal decomposition techniques such as metal organic chemical vapor deposition (MOCVD).59 The larger cationic radius of silver(I) with respect to copper(I) has caused problems in achieving both good volatility and adequate stability of silver(I) complexes for the use in CVD apparatus. These problems have been overcome with the new techniques such as super critical fluid transport CVD (SFTCVD), aerosol-assisted CVD (AACVD), and spray pyrolysis, where the requirements for volatile precursors are less stringent. 

In summary, although the metal-ion selectivity of the cryptands is normally largely enthalpy-controlled, entropic terms may also be quite important. Once again, the factors underlying these respective terms may be quite variable and, as a consequence, a criterion for preferred complexation based solely on a match of the cavity for the cation radius may not always be appropriate. 

The L M in the complexes of lanthanide nitrates with TMSO decreases along the lanthanide series (264, 265). All these complexes contain both bidentate and mono-dentate nitrate groups (264), the monodentate nitrates giving way to bidentate nitrates as the cationic radius decreases. 

Fig. 7.5. Dependence of the stability constants of valinomycin complexes of alkali metal ions on the cation radius. (After A. Hofmanovd et al. [79].)...

To prevent misunderstanding (94), we emphasize that neither experimental hydration energies nor experimental coordination numbers are necessary for these calculations. Moreover, the coordination numbers obtained are generally not comparable to empirical hydration numbers. The only experimental quantities that enter the calculations are a) cationic radius and charge b) van der Waals radius of water c) dipole and quadrupole moment of water d) polarizabilities e) ionization potentials and f) Born repulsion exponents as well as fundamental constants (see Ref. (92)). 

A precise calculation of AGd as a function of the cationic radius would be very difficult because it would involve a complete conformational analysis of a large and complicated ligand system (82). Nevertheless, the dependency of the cation selectivity on steric interactions is capable of illustration. The term AGd can be estimated very crudely by using Hooke s law. As is shown in Fig. 16, ligands that are differentiated only by the radius of their equilibrium cavities can easily discriminate between cations of different size. This may explain why valinomycin and antamanide, two antibiotics with similar coordination spheres (54, 66), do not prefer the same cation (82). As it is no easy task to predict the exact dimensions of the cavity for a proposed ligand, the tailored synthesis of such ligands is conceivable yet problematic. 

In order to compute the AG -vaIues, all the contributions listed in Chap. 4 should be considered, but for the electrically neutral 1 1 complexes treated here the expressions for AGb and AGv vanish. Only those terms that depend on the cationic radius are relevant to the difference of the AG -values as defined in Eq. (34), so that ... 

Fig. 1. Plot of log K vs cation radius for the reaction in aqueous solution, Mn+ + L = MLn+ where L = dicyclohexyl- 18-crown-6, isomer A ( ), dicyclohexyl- 18-crown-6 isomer B ( ), or 15-crown-5 (A). T = 25°. (4, 14)...

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