Ionic radius tabulation

Rate of water loss from metal cations as a function of the ratio of the charge to the radius of the metal ion. Rate constants from Margerum et al. (1978). 2Jx ratios calculated from ionic radii tabulated in the CRC Handbook of Chemistry and Physics. 

Ahrens (1952) proposed the first extended tabulation of ionic radii, partially modifying the univalent radii in the Vl-fold coordination of Pauling (1927a) on the basis of the observed correlation between ionic radius (r) and ionization potential (/), which can be expressed in the forms... 

Note Using the tabulated ionic radius of Ca (i.e. that of Ca2+) would be less valid than using the atomic radius of a neighboring monovalent ion, for the problem asks about a hypothetical compound of monovalent calcium. Predictions with the smaller Ca2+ radius (100 pm) differ substantially from those listed above the expected structure changes to rock-salt, the lattice enthalpy to 758 kJmol-1, Af// (CaCl) to —446kJ mol-1 and the final reaction enthalpy to +96 kJ mol-1. 

We focus attention on the fact that the crystal radii (CRs) for the various cations listed in table 1.11 are simply equivalent to the effective ionic radii (IRs) augmented by 0.14 A. Wittaker and Muntus (1970) observed that the CR radii of Shannon and Prewitt (1969) conform better than IR radii to the radius ratio principle and proposed a tabulation with intermediate values, consistent with the above principle (defined by the authors as ionic radii for geochemistry ), as particularly useful for sihcates. It was not considered necessary to reproduce the... 

It was inferred from simple geometrical considerations (condition for contact between neighbouring X anions) that this structure could only be formed if the ratio of the cation radius to the anion radius is between 0.41 and 0.73. It is not easy to check this condition for the AnX compounds because there is some difficulty to define the radius to be used for this comparison. If the tabulated ionic radii are used, many of the AnX compounds are in the range mentioned, but some of them me outside, e.g. the monocarbides. 

It is, of course, impossible to measure the absolute size of an isolated atom its electron cloud extends to infinity. It is possible to calculate the radius within which (say) 95% of its total electron cloud is confined but most measures of atomic/ionic size are based upon experimental measurements of internuclear distances in molecules and crystals. This means that the measurement is dependent on the nature of the bonding in the species concerned, and is a property of the atom or ion under scrutiny in a particular substance or group of substances. This must always be borne in mind in making use of tabulated radii of atoms or ions. The most important dictum to remember is that radii are significant only insofar as they reproduce experimental internuclear distances when added together. The absolute significance of a radius is highly suspect,... 

The sizes of atoms and ions influence how they interact in chemical compounds. Although atomic radius is not a precisely defined concept, these sizes can be estimated in several ways. If the electron density is known from theory or experiment, a contour surface of fixed electron density can be drawn, as demonstrated in Section 5.1 for one-electron atoms. Alternatively, if the atoms or ions in a crystal are assumed to be in contact with one another, a size can be defined from the measured distances between their centers (this approach is explored in greater detail in Chapter 21). These and other measures of size are reasonably consistent with each other and allow for the tabulation of sets of atomic and ionic radii, many of which are listed in Appendix F. 

We should mention that in the few cases in which the variation in electron density in a crystal has been accurately determined (e.g. NaCl), the minimum electron density does not in fact occur at distances from the nuclei indicated by the ionic radii in general use e.g. in LiF and NaCl, the minima are found at 92 and 118 pm from the nucleus of the cation, whereas tabulated values of / l + and rj4a+ are 76 and 102 pm, respectively. Such data make it clear that discussing lattice structures in terms of the ratio of the ionic radii is, at best, only a rough guide. For this reason, we restrict our discussion of radius ratio rules to that in Box 5.4. 

In the derivation of these ionic radii, it has been assumed that the repulsion coefficient B depends only on the coordination number that is, on the number of anion-cation contacts, but if the radius ratio is close to or less than the lower limit, anion-anion contact occurs and the additional Bom repulsion will lead to equilibrium with the attractive Coulomb forces at a larger distance than that given by the sum of the ionic radii. This phenomenon of double repulsion is shown (see tabulation) by the lithium halides especially. In a more detailed treatment, Pauling 112, 114) has... 

As has been shown in the preceding section, it is this distance criterion that has been used in defining self-consistent sets of ionic radii of which the tabulation of Shannon is the most complete one. With respect to the radius ratio, the quantitative significance is low, at best (see Section 1.1), and a materials scientist is better off in interpreting this part of the first rule as being mostly qualitative in nature. 

T = Xc,zf being the ionic concentration and s, the viscosity and the dielectric constant of the solvent, respectively , the reciprocal average radius of the ionic atmosphere a, the mean distance of closest approach of ions

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