Cation relative size

In the ceramics field many of the new advanced ceramic oxides have a specially prepared mixture of cations which determines the crystal structure, through the relative sizes of the cations and oxygen ions, and the physical properties through the choice of cations and tlreh oxidation states. These include, for example, solid electrolytes and electrodes for sensors and fuel cells, fenites and garnets for magnetic systems, zirconates and titanates for piezoelectric materials, as well as ceramic superconductors and a number of other substances... 

Many of the spinel-type compounds mentioned above do not have the normal structure in which A are in tetrahedral sites (t) and B are in octahedral sites (o) instead they adopt the inverse spinel structure in which half the B cations occupy the tetrahedral sites whilst the other half of the B cations and all the A cations are distributed on the octahedral sites, i.e. (B)t[AB]o04. The occupancy of the octahedral sites may be random or ordered. Several factors influence whether a given spinel will adopt the normal or inverse structure, including (a) the relative sizes of A and B, (b) the Madelung constants for the normal and inverse structures, (c) ligand-field stabilization energies (p. 1131) of cations on tetrahedral and octahedral sites, and (d) polarization or covalency effects. ... 

Next, examine the lowest-unoccupied molecular orbital (LUMO) for the cation. The components of the LUMO (its lobes ) identify locations where the cation might bond to a water molecule. How many lobes are associated with C 7 For each lobe, draw the alcohol that will be produced (show stereochemistry). How many alcohol enantiomers will form If more than one is expected, decide which wiU form more rapidly based on the relative sizes of the lobes. 

Figure 1.48 illustrates the trends in ionic radii, and Fig. 1.49 shows the relative sizes of some ions and their parent atoms. All cations are smaller than their parent... 

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 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,... 

FABMS has been used as a semiquantitative indication of the selectivity of receptors for particular guest metal cations (Johnstone and Rose, 1983). The FABMS competition experiment on [7] with equimolar amounts of the nitrates of sodium, potassium, rubidium and caesium gave gas-phase complex ions of ([7] + K)+ ion (m/z 809) and a minor peak ([7] + Rb)+ ion (m/z 855) exclusively. The relative peak intensities therefore suggested a selectivity order of K+ Rb+ Na+, Cs+, indicative of the bis-crown effect, the ability of bis-crown ether ligands to complex a metal cation of size larger than the cavity of a single crown ether unit, forming a sandwich structure. 

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. 

To explain this different fractionation behavior, Taube (1954) postulated different isotope effects between the isotopic properties of water in the hydration sphere of the cation and the remaining bulk water. The hydration sphere is highly ordered, whereas the outer layer is poorly ordered. The relative sizes of the two layers are dependent upon the magnitude of the electric field around the dissolved ions. The strength of the interaction between the dissolved ion and water molecules is also dependent upon the atomic mass of the atom to which the ion is bonded. 

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 1.37 illustrates some ionic radii, and Fig. 1.38 shows the relative sizes of some ions and their parent atoms. All cations are smaller than their parent atoms, because the atom loses one or more electrons to form the cation and exposes its core, which is generally much smaller than the parent atom. For example, the atomic radius of Li, with the configuration ls22s, is 157 pm, but the ionic radius of Li+, the bare heliumlike Is2 core of the parent atom, is only 58 pm. This size difference is comparable to that between a cherry and its pit. Like atomic radii, cation radii increase down each group because electrons are occupying shells with higher principal quantum numbers. 

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. 

These points are well illustrated by comparing Cu, Ag and Au with respect to the relative stabilities of their oxidation states. Although few compounds formed by these elements can properly be described as ionic, the model can quite successfully rationalise the basic facts. The copper Group 1 Id is perhaps the untidiest in the Periodic Table. For Cu, II is the most common oxidation state Cu(I) compounds are quite numerous but have some tendency towards oxidation or disproportionation, and Cu(III) compounds are rare, being easily reduced. With silver, I is the dominant oxidation state the II oxidation state tends to disproportionate to I and III. For gold, III is the dominant state I tends to disproportionate and II is very rare. No clear trend can be discerned. The relevant quantities are the ionization energies Iu l2 and A the atomisation enthalpies of the metallic substances and the relative sizes of the atoms and their cations. These are collected below / and the atomisation enthalpies AH%tom are in kJ mol-1 and r, the metallic radii, are in pm. 

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. 

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