The ionic radius

The ions thus behave as almost hard, slightly compressible spheres which will assume a close packing under the influence 

The existence of constant ionic radii is also seen on examining the lattice spacings a of the alkali halides, in fact the pairs with the same alkali atom or halogen atom show about constant differences for the two different halogens or alkali respectively. 

2 For free ions the concept loses its significance. According to wave mechanics the charge density only approaches zero at large distances. For a K+ ion about 0.35 or 1.95 % of the total electron charge falls outside a sphere with an ionic radius r — 1.33 A. 

Since the ionic radius is an empirical concept and furthermore its value is only constant to a rough approximation (p. 39) these differences of a few 0.01 A are without significance. 

In Table 3 are collected the values of the ionic radii as deduced mainly by V. M. Goldschmidt from numerous X-ray crystal structure determinations, supplemented with numerous newer data, especially those of W. H. Zachariasen3. In this table in contrast to those of Goldschmidt the value 1.45 A has been attributed to the O2- ion instead of 1.35 A. These values are valid for a coordination number 6 (p. 39). 

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The reason why lanthanides of high atomic number emerge first is that the stability of a lanthanide ion-citrate ion complex increases with the atomic number. Since these complexes are formed by ions, this must mean that the ion-ligand attraction also increases with atomic number, i.e. that the ionic radius decreases (inverse square law). It is a characteristic of the lanthanides that the ionic radius... 

Shannon and Prewitt base their effective ionic radii on the assumption that the ionic radius of (CN 6) is 140 pm and that of (CN 6) is 133 pm. Also taken into consideration is the coordination number (CN) and electronic spin state (HS and LS, high spin and low spin) of first-row transition metal ions. These radii are empirical and include effects of covalence in specific metal-oxygen or metal-fiuorine bonds. Older crystal ionic radii were based on the radius of (CN 6) equal to 119 pm these radii are 14-18 percent larger than the effective ionic radii. 

Only body-centered cubic crystals, lattice constant 428.2 pm at 20°C, are reported for sodium (4). The atomic radius is 185 pm, the ionic radius 97 pm, and electronic configuration is lE2E2 3T (5). Physical properties of sodium are given ia Table 2. Greater detail and other properties are also available... 

The viscosities of liquid metals vaty by a factor of about 10 between the empty metals, and the full metals, and typical values are 0.54 x 10 poise for liquid potassium, and 4.1 x 10 poise for liquid copper, at dreir respective melting points. Empty metals are those in which the ionic radius is small compared to the metallic radius, and full metals are those in which the ionic radius is approximately the same as tire metallic radius. The process was described by Andrade as an activated process following an AiThenius expression... 

Table 5.1 lists some of the atomic properties of the Group 2 elements. Comparison with the data for Group 1 elements (p. 75) shows the substantial increase in the ionization energies this is related to their smaller size and higher nuclear charge, and is particularly notable for Be. Indeed, the ionic radius of Be is purely a notional figure since no compounds are known in which uncoordinated Be has a 2- - charge. In aqueous solutions the reduction potential of... 

By contrast, the ionic radius in a given oxidation state falls steadily and, though the available data are less extensive, it is clear that an actinide contraction exists, especially for the -f3 state, which is closely similar to the lanthanide contraction (see p. 1232). 

The conclusions are evidently relevant to the amount of entropy lost by ions in methanol solution—see Table 29. If, however, the expression (170) is used for an atomic ion, we know that it is applicable only for values of R that are large compared with the ionic radius—that is to say, it will give quantitative results only when applied to the solvent dipoles in the outer parts of the co-sphere. The extent to which it applies also to the dipoles in the inner parts of the co-sphere must depend on the degree to which the behavior of these molecules simulates that of the more distant molecules. This can be determined only by experiment. In Table 29 we have seen that for the ion pair (K+ + Br ) and for the ion pair (K+ + Cl-) in methanol the unitary part of ASa amounts to a loss of 26.8 e.u. and 30.5 e.u., respectively, in contrast to the values for the same ions in aqueous solution, where the loss of entropy in the outer parts of the co-sphere is more than counterbalanced by a gain in entropy that has been attributed to the disorder produced by the ionic field. 

Fixing attention on this difference between ions in methanol and ions in water, we may next ask whether the difference should be greater for an atomic ion of large or of small radius. The answer is clearly that, according to (18), if we take R equal to or proportional to the ionic radius a, between any two solvents the difference should be greater for the smaller ion greater for Ii+ than for K+ or Cs+, for example. If and 2 denote the dielectric constants of the two solvents, the difference, according to (18), would amount to... 

In the LiCl structure shown in Figure 9.18, the chloride ions form a face-centered cubic unit cell 0.513 nm on an edge. The ionic radius of Cl- is 0.181 nm. 

Since hydrofluoride synthesis is based on thermal treatment at relatively high temperatures, the possibility of obtaining certain fluorotantalates can be predicted according to thermal stability of the compounds. In the case of compounds whose crystal structure is made up of an octahedral complex of ions, the most important parameter is the anion-cation ratio. Therefore, it is very important to take in to account the ionic radius of the second cation in relation to the ionic radius of tantalum. Large cations, are not included in the... 

The formulated principals correlating crystal structure features with the X Nb(Ta) ratio do not take into account the impact of the second cation. Nevertheless, substitution of a second cation in compounds of similar types can change the character of the bonds within complex ions. Specifically, the decrease in the ionic radius of the second (outer-sphere) cation leads not only to a decrease in its coordination number but also to a decrease in the ionic bond component of the complex [277]. 

Calculations of the actual dependence of the activation barrier, Ag, on the metal size in the active site of SNase are summarized in Fig. 8.10. The results reflect mainly the energetics of i//2 and ij/3, since the dependence on the ionic radius in is found to be rather small. 

The ionic radius of an element is its share of the distance between neighboring ions in an ionic solid (12). The distance between the centers of a neighboring cation and anion is the sum of the two ionic radii. In practice, we take the radius of the oxide ion to he 140. pm and calculate the radii of other ions on the basis of that value. For example, because the distance between the centers of neighboring Mg2+ and O2 ions in magnesium oxide is 212 pm, the radius of the Mg21 ion is reported as 212 pm - 140 pm = 72 pm. 

Although the rule the reactivity of tight ion-pairs increases with increasing interionic distance still holds, the above results show that the ionic radius is not the only factor that determines the reactivity of tight ion-pairs. 

However, consideration in terms of the ionic radius or the LFSE shows that both factors predict that the maximum stabilities will be associated with nickel(ii) complexes, as opposed to the observed maxima at copper(ii). Can we give a satisfactory explanation for this The data presented above involve Ki values and if we consider the case of 1,2-diaminoethane, these refer to the process in Eq. (8.13). 

A hard Lewis acid has an acceptor atom with low polarizability. Most metal atoms and ions are hard acids. In general, the smaller the ionic radius and the larger the charge, the harder the acid. The ion, with an ionic... 

A soft Lewis acid has a relatively high polarizability. Large atoms and low oxidation states often convey softness. Contrast with Hg , a typical soft acid. The ionic radius of Hg is 116 pm, almost twice the size of... 

In such systems as (M, Mj (i/2))X (M, monovalent cation Mj, divalent cation X, common anion), the much stronger interaction of M2 with X leads to restricted internal mobility of Mi. This is called the tranquilization effect by M2 on the internal mobility of Mi. This effect is clear when Mj is a divalent or trivalent cation. However, it also occurs in binary alkali systems such as (Na, K)OH. The isotherms belong to type II (Fig. 2) % decreases with increasing concentration of Na. Since the ionic radius of OH-is as small as F", the Coulombic attraction of Na-OH is considerably stronger than that of K-OH. 

This result suggests that the sintering resistance of samples are enhanced as the ionic radius of A becomes large. It is, therefore, apparent that La is superior as the large cation in the mirror plane of the hexaaluminate in achieving both high thermal resistance and high activity to other tri-valent A cations with small ionic radii. 

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