Valence crystals bonding

The binding of valence crystals can also be explained from the standpoint of energy bands. In Fig. XXIX-12 we show energy bands for diamond, a typical crystal held by homopolar bonds. We see that the... 

Crystalline substances may be classified into five major types (Sll). They vary in the kind and strength of the bond between the constituent atoms or ions, and in their electrical, magnetic, and mechanical properties. These types are metal crystals, ionic crystals, valence crystals, semiconductor crystals, and molecular crystals. 

Valence crystals are formed by combinations of atoms of the lighter elements in the middle column of the periodic table, such as diamond and silicon carbide. These crystals conform to valence rules, and the interatomic bonds are due to the sharing of electron pairs. Valence crystals are characterized by very great hardness, poor cleavage, and poor electrical conductivity. 

Figure 2 The relation between bond valence and bond length for Ca-0 bonds. The line shows equation (1). The points are electrostatic fluxes calculated using Coulomb s law for several different Ca-bearing crystals. (Figure 3.1 from The Chemical Bond in Inorganic Chemistry by Brown, David (2001)). (Ref. 3. Reproduced by permission of Oxford University Press)...

The strong bonding in valence crystals results in the failure of these crystals to demonstrate, on irradiation, quasichemical changes such as depolymerization. Unlike metals, however, valence crystals have no conduction electrons. This permits them to retain electronic dislocations as well as atomic displacement. The trapping of dislocated electrons in the crystal by potential wells such as those created by atomic vacancies results in coloration of the normally transparent valence crystals. 

The correlation of bond valence and bond length as applied above can be extended further according to the concept of Dunitz and Burgi of mapping a series of crystal structures as pathways of chemical reacions (Section 122.1). Hush derived the expression pm + Pmh = 1, and Grundemann et al.112 extended it to give Eqs. (4.12H4.14). 

The discussion so far has focussed on the calculation of valences (and bond lengths) in periodic crystals, but the bond valence method is equally plicable to aperiodic structures and is potentially very useful for predicting relaxations around defects in crystals (Brown, 1988) and at surfaces and interfaces (O Keeffe, 1991b). 

Exactly the same procedure as outlined above is used in appUcations to crystals. Bonds between pairs of different atoms are considered to have separate valences to be determined by valence sums. Atoms are considered different if they are distinct in the crystallographic sense. A difficulty that often arises in practice is that bonds between pairs of atoms that are related by symmetry are not necessarily themselves related by symmetry a familiar example is that of the corundum (a-Al203) structure in which there is only one kind of A1 atom and one kind of O atom but two different Al-0 bonds that are of unequal lengths. The method of analysis used above would ascribe equal bond valences to these two bonds, but, because they are of unequal lengths, different apparent bond valences would be ascribed to them. 

Detailed comparison with observed crystal structures requires both accurate structures and the development of parameters appropriate for bonds to nitrides, neither of which are generally available at present. However the important point is to recognize that the expected bond valences predict bond lengths which are different fi-om those predicted by the ionic radius approach. Thus using ionic radii for four-coordinated Li and O the predicted Li-O bond length would be that for valence 1/4 rather than 7/24, etc. 

Calculations of the electronic structure of crystals Ti02 and Ti20s and corresponding cluster show that numerical results for local properties of the electronic structure of crystals (atomic charges, covalences, free and total valences, and bond... 

Metals are extreme examples of delocalized bonding. A sodium metal crystal, for example, can be regarded as an array of Na ions surrounded by a sea of electrons (Figure 9.18). The valence, or bonding, electrons are delocalized over the entire metal crystal. The freedom of these electrons to move throughout the crystal is responsible for the electrical conductivity of a metal. 

Figure IV.7 Crystal structure and characterisation of valence band bonds in WSe2 ...

Bochicchio, R. C., Reale, H. F., Medrano, J. (1989). Extension of the quantum theory of valence and bonding to molecular and crystal systems with translation symmetry. Phys. Rev. B 40, 7186-7190. 

For screening purposes, bond valence or bond valence site energy (BVSE) pathway models derived from static structure models appear to be the most straightforward approach. In a range of earlier studies, it has been discussed how the bond valence method can be used to analyze ion transport pathways statistically, yielding predictions of ionic conductivity from crystal structure data and RMC- or MD-generated structure models [4, 8-10]. 

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