Ions, 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... 

The electron configuration or orbital diagram of an atom of an element can be deduced from its position in the periodic table. Beyond that, position in the table can be used to predict (Section 6.8) the relative sizes of atoms and ions (atomic radius, ionic radius) and the relative tendencies of atoms to give up or acquire electrons (ionization energy, electronegativity). 

In each set, the atomic volumes increase going from halogen to inert gas to alkali metal, as shown graphically in Figure 6-9c. Figure 6-10 shows models constructed on the same scale to show the relative sizes of atoms indicated by the atomic volumes and by the packing of the ions in the ionic solids. 

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... 

EXAMPLE 1.11 Sample exercise Deciding the relative sizes of ions... 

Bearing in mind that the relative sizes of the ions permit isomorphous replacement of OH by F but not by Cl, we write with considerable confidence the formula (Si, Al, Fe, P)18O20(OH, F)laCl, which agrees well with analyses 1, 2, and 3. Inasmuch as aluminium (as well as phosphorus) may replace silicon with coordination number 4, it is evident that there are at least five silicon atoms in the unit, corresponding to the chemical formula... 

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. 

The different hydration numbers can have important effects on the solution behaviour of ions. For example, the sodium ion in ionic crystals has a mean radius of 0 095 nm, whereas the potassium ion has a mean radius of 0133 nm. In aqueous solution, these relative sizes are reversed, since the three water molecules clustered around the Na ion give it a radius of 0-24 nm, while the two water molecules around give it a radius of only 017 nm (Moore, 1972). The presence of ions dissolved in water alters the translational freedom of certain molecules and has the effect of considerably modifying both the properties and structure of water in these solutions (Robinson Stokes, 1955). 

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. 

The zinc blende type is unknown for truly ionic compounds because there exists no pair of ions having the appropriate radius ratio. However, it is well known for compounds with considerable covalent bonding even when the zinc blende type is not to be expected according to the relative sizes of the atoms in the sense of the above-mentioned considerations. Examples are CuCl, Agl, ZnS, SiC, and GaAs. We focus in more detail on this structure type in Chapter 12. 

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... 

Further ternary compounds for which the relative sizes of the ions are an important factor for their stability are the perovskites and the spinels, which are discussed in Sections 17.4 and 17.6. 

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,... 

Figure 7.18 The two half-cells in a cell are joined with a salt bridge. Inset more ions leave the bridge ends than enter it the relative sizes of the arrows indicate the relative extents of diffusion...

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. 

Thirdly, there is the purely structural argument from Relative Size if ions of one type are much the largest, they will effectively fix the structure since the others can pack between them. This argument, which makes no assumption whatever about electron-clouds, is often referred only to lithium iodide, but much more evidence is available. Such questions of crystal-form and isomorphism are in fact the most important applications of ionic-radius systems in chemistry and mineralogy (cp. the classical work of V. M. Goldschmidt (2)). 

Moreover, the Relative Size argument also applies to those divalent iodides which are approximately close-packed arrays of iodide (cp. Wyckoff 24)). The following table shows for such compounds the gram-formula weights, the X-ray determined densities, and hence the volume Vanion (cc/gm/atom) occupied by the iodide gram/ion, which has a minimum value of about 28 cc. 

The crystal structures observed in ternary fluorides of the transition metals may be explained to a first approximation by reasons of geometry, i. e. by the relative sizes and charges of their constituent ions. The underlying hard sphere model of ions proves to be surprisingly useful. 

When we have an ordered assembly of atoms called a lattice, there is more than one bond per atom, and we must take into account interactions with adjacent atoms that result in an increased interionic spacing compared to an isolated atom. We do this with the Madelmg constant, ckm. This parameter depends on the structure of the ionic crystal, the charge on the ions, and the relative size of the ions. The Madelung constant fits directly into the energy expression (Eq. 1.25) ... 

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