Radius of ions

Table 42. Cbystallogbaphic Radii of Ions in Angstroms And in parentheses the reciprocals of the radii...

If S[ is a weak base (low DN) and S2 is a strong base, cations are selectively solvated by S2 conversely, if Sj is a good acceptor (high AN) it will preferentially solvate the anion. As a consequence, the Stokes radii of ions generally change with the composition of a binary solvent. 

Crystal Radii and Univalent Crystal Radii of Ions... 

TABLE 3 Charge Numbers and Radii of Ions and Their Hydration Numbers and Hydrated Radii in NB at 25° C... 

FIGURE 1.11 Radii of ions having the neon configuration. 

Yatsimirskii, K.B. "Thermochemical Radii of Ions and Heats of Formation of Salts, "Izvest. Akad. Nauk. S.S.S.R., Otdel. 

The radii of ions within a Group of the Periodic Table, such as the alkali metals, increase with atomic number, Z as you go down a Group, more electrons are present, and the outer ones are further from the nucleus. 

As we end this section, let us reconsider ionic radii briefly. Many ionic compounds contain complex or polyatomic ions. Clearly, it is going to be extremely difficult to measure the radii of ions such as ammonium, NH4, or carbonate, COs, for instance. However, Yatsimirskii has devised a method which determines a value of the radius of a polyatomic ion by applying the Kapustinskii equation to lattice energies determined from thermochemical cycles. Such values are called thermochemical radii, and Table 1.17 lists some values. 

Since the electron distribution function for an ion extends indefi-finitely, it is evident that no single characteristic size can be assigned to it. Instead, the apparent ionic radius will depend upon the physical property under discussion and will differ for different properties. We are interested in ionic radii such that the sum of two radii (with certain corrections when necessary) is equal to the equilibrium distance between the corresponding ions in contact in a crystal. It will be shown later that the equilibrium interionic distance for two ions is determined not only by the nature of the electron distributions for the ions, as shown in Figure 13-1, but also by the structure of the crystal and the ratio of radii of cation and anion. We take as our standard crystals those with the sodium chloride arrangement, with the ratio of radii of cation and anion about 0.75 and with the amount of ionic character of the bonds about the same as in the alkali halogenides, and calculate crystal radii of ions such that the sum of two radii gives the equilibrium interionic distance in a standard crystal. 

The ionic radii of the M3+ and M4+ ions of the actinides decrease with increasing positive charge of the nucleus (the actinide contraction) (Fig. 15.15). This contraction is due to the successive addition of electrons in an inner f shell where the incomplete screening of the nuclear charge by the added f electron leads to a contraction of the outer valence orbital. Because the ionic radii of ions of the same oxidation state are generally similar (Fig. 15.15), the ionic compounds of the actinides are isostructural. 

TW is the relaxation rate for water protons in the absence of the metal ion, u is the paramagnetic moment of the ion and y and (i are conventional constants. We can now examine m.r.e. values in a series of complexes, in terms of p, and calculating r from known radii of ions. This will reveal changes in ts or/and x0/w. We commenced such a study using the Ln(III) complexes of dipicolinic acid. 

Similar substantially constant differences are obtained with other pairs of alkali halides of B 1 structure, having either a cation or an anion in common. As a result, the conclusion was reached that each ion makes a specific contribution toward an experimentally observed r0, well-nigh irrespective of the nature of the other ion with which it is associated in the lattice. In other words, characteristic radii should be attributable to the ions (1,2). However, a knowledge of the internuclear distances in the crystals is not sufficient by itself to determine absolute values for crystal radii of ions, and various criteria have been used to assign the size of a particular ion or the relative sizes of a pair of alkali and halide ions. 

If we assume that the radii of ions in an iso-electronic series are inversely proportional to effective nuclear charges (p. 175), we may use our values of the radii of Na+ and F and calculate the radii of the Mg2+ and... 

The radii of the atoms of the inert gases (in the condensed state) are not directly comparable with the radii of ions (in crystals) because of the much lower cohesion energy in the former case. 

The physics of electrostatics in aqueous solution has attracted scientists notice for centuries. At present, the solvation of ions, volumes and radii of ions in solution, and ionic interactions are still hotly debated research fields. Recently, thermodynamic, transport and structural data were mutually employed for gaining fruitful physicochemical insights into electrolyte solutions [2]. This chapter recapitulates the essential... 

Wasastjerna, J. A. On the radii of ions. Societas Scientiarum Fennica Commen-tationes Physico-Mathematicae I. 38, 1-25 (1923). 

Radii of ions capable of substituting in apatite in small amounts (Shannon and Prewitt, 1969)... 

Since in all calculations the value n = 1 was chosen, the number of lattice sites per unit area M/A was calculated from the crystal radii of ions, assuming an hexagonal lattice structure. The bulk activity of the ions a] was approximated by the mean activity of the salt calculated from the Debye Huckel equation. Finally, an estimation of the magnitude of B/( a) shows that this parameter ranges from -3 to 0. Indeed if we assume that Ps = 6 10 °Cm, 1 = 5- 10 °m, M/A = 6 10 sites m and a = 2, then ... 

Figure 8.9 shows the radii of ions derived from the familiar elements, arranged according to elements positions in the periodic table. We can see parallel trends between atomic radii and ionic radii. For example, from top to bottom both the atomic radius and the ionic radius increase within a group. For ions derived from elements in different groups, a size comparison is meaningful only if the ions are isoelectronic. If we examine isoelectronic ions, we find that cations are smaller than anions. For example, Na is smaller than F . Both ions have the same number of electrons, but Na... 

Fig. 10 presents the fragment of a lattice of a solid Ceo (f.c.c. structure) and the sites into which the atoms of alkaline metals can be placed. For each Cfio molecule there are two tetrahedral and one octahedral position for the interstitial atom, with radii of 1.12 A and 2.06 A, respectively [76]. The radii of ions of alkaline metals (0.97 for Na, 1.33 for K, and 1.47 A for Rb) approximately coincide with the sizes of these sites and, when completely filled, result in the A3C60 structure. The AiCgo high temperature structure is similar to A3C60, but only the octahedral sites are occupied. 

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