Bonding in ionic crystals

FIGURE 7.21 Unit Cell of Orthorhombic YBa GUjO. The yttrium atom in the middle is in a reflection plane. 

Hoffmann has also shown that the contributions to the density of states of specific orbitals can be calculated. In rutile, Ti02, a clear separation of the d orbital contribution into t2g and parts can be seen, as predicted by ligand field theory (Chapter 10). 

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The energy of a single bond in ionic crystals is often described by... 

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. 

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. 

Throughout our discussion the crystals will be referred to as composed of ions. This does not signify that the chemical bonds in the crystal are necessarily ionic in the sense of the quantum mechanics they should not, however, be of the extreme non-polar or shared electron pair type.13 Thus compounds of copper14 and many other eighteen-shell atoms cannot be... 

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. 

Chemical structures may be well explained and predicted by means of a set of differently applied constant atomic radii roughly constant for the many cases of a few main types of bond. Thus Pauling (1) used covalent, metallic, van der Waals and ionic radii, aU Structural Radii r chosen to add up to observed Structural Distances D where identical atoms are nearest neighbours D = 2r. But in ionic crystals identical ions are never nearest neighbours hence a special problem arises which forty years ago seemed to have been definitively solved by Goldschmidt (2) and Pauling (/). 

The values of Tq are the result of ai/the various types of bonding in the crystal, not just of the ionic bonding, and so are rather shorter than one would expect for purely ionic bonding. 

A large number of binary AB compounds formed by elements of groups IIIA and VA or IIA and VIA (the so-called III-V and II-VI compounds) also fcrystallize in diamond-like structures. Among the I-VII compounds, copper (I) halides and Agl crystallize in this structure. Unlike in diamond, the bonds in such binary compounds are not entirely covalent because of the difference in electronegativity between the constituent atoms. This can be understood in terms of the fractional ionic character or ionicity of bonds in these crystals. 

Since an a priori definition of the effective region is hardly possible, each atomic region is usually approximated by a spherical region around the atom, where the radius is taken as its ionic, atomic, or covalent bond radius. The radial distribution of electron density around an atom is also useful to estimate the effective radius of an atom, particularly in ionic crystals. In an ionic crystal, the distance from the metal nucleus to the minimum in the radial distribution curve generally corresponds to the ionic radius. As an example, the radial distribution curves around K in o-KvCrO., (85) are shown in Fig. 19a. The radial distributions of valence electrons (2p electrons) exhibit a minimum at 1.60 A for K(l) and 1.52 A for K(2), respectively. These distances correspond to the ionic radii in crystals (1.52-1.65 A)... 

Figure 7.3 Sodium chloride crystals. The lines are drawn only to show the orientation one to another and do not imply that the bonds in ionic compounds are directional or stick-like...

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