In ionic crystals

N. F. Mott and R. W. Gurney, Electronic Processes in Ionic Crystals, Clarendon Press, Oxford, 1940. 

Fig. 17.1. (a) Dislocation motion is intrinsically easy in pure metals - though alloying to give solid solutions or precipitates con moke it more difficult. (b) Dislocation motion in covalent solids is intrinsically difficult because the interatomic bonds must be broken and reformed. ( ) Dislocation motion in ionic crystals is easy on some planes, but hard on others. The hard systems usually dominate. 

It is perhaps not too fanciful to compare the stormy history of liquid crystals to that of colour centres in ionic crystals resolute empiricism followed by fierce strife between rival theoretical schools, until at last a systematic theoretical approach led to understanding and then to widespread practical application. In neither of these domains would it be true to say that the empirical approach sufficed to generate practical uses such uses in fact had to await the advent of good theory. 

Numerous observations of the effect in ionic crystals were carried out by Mineev and Ivanov in the Soviet Union [76M01]. This is a class of crystals in which a number of materials factors can be confidently varied. By choice of crystallographic orientation, various slip directions can be invoked. By choice of various crystals other physical factors such as dielectric constant, ionic radius, and an electronic factor thought to be representative of dielec-... 

Lanthanides Elements 57 (La) through 70 (Yb) in the periodic table, 146 Lanthanum, 147 Laser fusion, 528 Lattices in ionic crystals, 249 Lavoisier, Antoine, 14 Law of conservation of energy A natural law stating that energy can neither be created nor destroyed it can only be converted from one form to another, 214... 

The Niccolite Structure. The substances which crystallize with the niccolite structure (B8) are compounds of transition elements with S, Se, Te, As, Sb, Bi, or Sn. The physical properties of the substances indicate that the crystals are not ionic, and this is substantiated by the lack of agreement with the structural rules for ionic crystals. Thus each metal atom is surrounded by an octahedron of non-metal atoms but these octahedra share faces, and the edges of the shared faces are longer than other edges (rather than shorter, as in ionic crystals). Hence we conclude that the bonds are covalent, with probably some metallic character also. 

In deriving theoretical values for inter-ionic distances in ionic crystals the sum of the univalent crystal radii for the two ions should be taken, and corrected by means of Equation 13, with z given a value dependent on the ratio of the Coulomb energy of the crystal to that of a univalent sodium chloride type crystal. Thus, for fluorite the sum of the univalent crystal radii of calcium ion and fluoride ion would be used, corrected by Equation 13 with z placed equal to y/2, for the Coulomb energy of the fluorite crystal (per ion) is just twice that of the univalent sodium chloride structure. This procedure leads to the result 1.34 A. (the experimental distance is 1.36 A.). However, usually it is permissible to use the sodium chloride crystal radius for each ion, that is, to put z = 2 for the calcium... 

A similar procedure can be used in predicting interatomic distances in ionic crystals, by evaluating the potential energy of a three-dimensional array of... 

The packing in ionic crystals requires that ions of opposite charges alternate with one another to maximize attractions among ions. A second important feature of ionic crystals is that the cations and anions usually are of different sizes. Usually the cations are smaller than the anions. Consequently, ionic compounds adopt a variety of structures that depend on the charges and sizes of the ions. One way to discuss ionic structures is to identify a crystal lattice for one set of ions, and then describe how the other ions pack within the lattice of the first set. 

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). 

In addition to the thermal vacancies, impurity-related vacancies will develop in ionic crystals. When impurity ions have a charge different from ions of like charge which are the crystal s main constituents, part of the lattice sites must remain vacant in order to preserve electroneutrality. Such impurity-type defects depend little on temperature, and their major effects are apparent at low temperatures when few thermal vacancies exist. 

In ionic crystals with d = nearest neighbor distance, the ions repulse each other strongly when d becomes smaller than the equilibrium value d0. This can be described by an inverse power function, +l/dn, where n is a power of order, 9. As for the electrostatic attractions, these repulsions must be summed over the N molecules of the crystal structure, yielding another constant, D. The energy, < > per molecule (ion pair) is then ... 

Inelastic shearing of atoms relative to one another is the mechanism that determines hardness. The shearing is localized at dislocation lines and at kinks along these lines. The kinks are very sharp in covalent crystals where they encompass only individual chemical bonds. On the other hand, in metal crystals they are often very extended. In metallic glasses they are localized in configurations that have a variety of shapes. In ionic crystals the kinks are localized in order to minimize the electrostatic energy. 

Another special factor in ionic crystals is that dislocation cores in them acquire net charge. As a result, plastic bending of an ionic crystal causes the top and bottom regions to become charged relative to the middle. This is easily demonstrated because such specimens preferentially attract fine insulating powders. It has been studied in some detail by Li (2000). 

As mentioned earlier in this chapter dislocations in ionic crystal may carry a net electric charge. Therefore, their motion may be influenced by applied electric fields, and may generate observable fields external to a specimen during plastic flow. These effects have been studied by Li (2000) and others. 

J. C. M. Li, Charged Dislocations and Plasto-electric Effect in Ionic Crystals, Mater. Sci. Eng., A287,265 (2000). 

Although this is a small fraction, for 1 mole of lattice sites, this amounts to 5.6 X1018 Schottky defects. The ability of ions to move from their sites into vacancies and by so doing creating new vacancies is largely responsible for the conductivity in ionic crystals. 

When applied to the motion of ions in a crystal, the term drift applies to motion of ions under the influence of an electric field. Although movement of electrons in conduction bands determines conductivity in metals, in ionic compounds it is the motion of ions that determines the electrical condu-ctivity. There are no free or mobile electrons in ionic crystals. The mobility of an ion, ji, is defined as the velocity of the ion in an electric field of unit strength. Intuitively, it seems that the mobility of the ion in a crystal should be related to the diffusion coefficient. This is, in fact, the case, and the relationship is... 

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