Anion relative size

FIGURE 1.49 The relative sizes of some cations and anions compared with their parent atoms. Note that cations (pink) are smaller than their parent atoms (gray), whereas anions (green) are larger. 

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. 

On the other hand, the crystal structures of ionic compounds with small molecular ions depend mainly on how space can be filled most efficiently by the ions, following the principle of cations around anions and anions around cations. Geometric factors such as the relative size of the ions and the shape of molecular ions are of prime importance. More details are given in Chapter 7. 

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. 

When three different kinds of spherical ions are present, their relative sizes are also an important factor that controls the stability of a structure. The PbFCl type is an example having anions packed with different densities according to their sizes. As shown in Fig. 7.5, the Cl- ions form a layer with a square pattern. On top of that there is a layer of F ions, also with a square pattern, but rotated through 45°. The F ions are situated above the edges of the squares of the Cl- layer (dotted line in Fig. 7.5). With this arrangement the F -F distances are smaller by a factor of 0.707 (= /2) than the CP-CP distances this matches the ionic radius ratio of rF-/rcl- = 0.73. An F layer contains twice as many ions as a CP layer. Every Pb2+ ion is located in an antiprism having as vertices four F and four... 

When spherical objects are stacked to produce a three-dimensional array (crystal lattice), the relative sizes of the spheres determine what types of arrangements are possible. It is the interaction of the cations and anions by electrostatic forces that leads to stability of any ionic structure. Therefore, it is essential that each cation be surrounded by several anions and each anion be surrounded by several cations. This local arrangement is largely determined by the relative sizes of the ions. The number of ions of opposite charge surrounding a given ion in a crystal is called the coordination number. This is actually not a very good term because the bonds are not coordinate bonds (see Chapter 16). For a specific cation, there will be a limit to the number of anions that can surround the cation because... 

Calculating the minimum size for the cation that can be in contact with the six anions as the anions are just touching each other is a simple problem. The critical factor is the relative sizes of the ions,... 

FIG. 16. Chemical structures and approximate relative sizes of the three pairs of molecules studied here. Note that the charges on the molecules of each pair are the same. Because the permeate solution was initially just pure water, the cationic molecules come across the membrane with their charge-balancing anions. 

The relative sizes of the cation and anion are not the only determinant of the coordination number the bonding strength of the anion also plays an important role and explains how the same cation can display different coordination numbers in different compounds. 

Figure 4.16 Effects of relative sizes of anions and cations in octahedral (six) coordination. Two additional anions, positioned above and below the plane, have been omitted for clarity.

FIGURE 1.38 The relative sizes of cations, anions, and their parent atoms for a selection of elements. Note that cations are smaller than their parent atoms whereas anions are larger. 

For ionic compounds the coordination number is the number of anions that are arfang d about the cation in a organized structure. For example, NaCl has a coordination number of 6. In otherwords, 6 CF atoms surround 1 Na+ atom. The number of anions that can surround a cation is dependent (but not entirely) on the relative sizes of the ions involved. Table 2.15 illustrates thtnmlios of the radii of the ions and their coordination number. 

For ionic crystals there is strong attraction between cations and anions, and strong repulsion between ions having the same charge. These interactions determine structures because ions must be shielded from those with the same charge. The relative sizes of the ions are important in determining the CN. Removal of electron(s) decreases the size of a cation relative to the atom and addition of electron(s) increases the size of an anion relative to the atom. Commonly, for an MX compound the anion is larger than the cation and the anions are close packed in crystals with cations in octahedral or tetrahedral sites. 

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. 

Pauling subsequently introduced three mles governing ionic sfructures (Pauling, 1928, 1929). The first is known as the radius ratio rule. The idea is that the relative sizes of the ions determine the sfructure adopted by an ionic compound. Pauling proposed specific values for the ratios of the cation radius to the anion radius as lower limits for different coordination types. These values are given in Table 3.5. 

For example, for C104 (rc17+ =0.22 A and r02 = 1.21 A), the calculated V,. is 675 A3 and the observed Vc is 673.7 A3 (T = 125 K). Concerning bond lengths within an anion, our use of effective radii is justified because the results are identical to those obtained from molecular orbital calculations (45,46). But the empirical effective anion volume, i.e., its contribution to Vc, is only about 50% of the calculated VA [65% (298 K) and 42% (125 K)] of calculated VA. Values of these volumes are given in Table I and we conclude that our approach provides a very good measure of the anion volumes, in particular their relative sizes. 

Various factors influence ionic size. We will first consider the relative sizes of an ion and its parent atom. Since a positive ion is formed by removing electrons from a neutral atom, the resulting cation is smaller than its parent atom. The opposite is true for negative ions the addition of electrons to a neutral atom produces an anion significantly larger than its parent atom. 

In fact, trigonal holes are so small that they are never occupied in binary ionic compounds. Whether the tetrahedral or octahedral holes in a given binary ionic solid are occupied depends mainly on the relative sizes of the anion and cation. Next, we will determine the sizes of the octahedral and tetrahedral holes and consider guidelines for their occupation by ions. 

In this section we will consider some specific binary ionic solids to show how these solids illustrate the ideas of ion packing. Because an ionic solid must be neutral overall, the stoichiometry of the compound (the ratio of the numbers of anions to cations) is determined by the ion charges. On the other hand, the structure of the compound (the placement of the ions in the solid) is determined, at least to a first approximation, by the relative sizes of the ions. 

The addition of tributylstannyllithium to the carbonyl group of various a-substituted aldehydes is accompanied by asymmetric a-induction8. The extent depends only on the relative sizes of a-substituents. The tributylstannyl anion exhibits much the same stereoselectivity as unhindered Grignard reagents (for 2,3-dimethylbutanal d.r. 3 1 and 2.5 1, respectively). Stereoselectivity is improved with aldehydes substituted at the /(-position by oxygen. For example, when a-methyl-/i-(benzyloxy)methoxypropanal is treated with tributylstannyllithium in tetrahydrofuran, a mixture of diastereomers is formed, the ratio of which varies from 5 1 at — 78°C to8 l at — 119"C8. 

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