Crystals homopolar

Figure 5.12 Glide activation energies from high temperature data vs. energy band gaps. Note that the data for the homopolar crystals (C, SiC, Si, and Ge) lie quite close to the correlation line, while the data for The heteropolar crystals show some scatter. The reason why GaP Is an exception is not known. Also, note that the slope of the correlation line is two. 

Crystal Types. Crystals can, therefore, be classified in four groups, as follows (A) Ionic Crystals, (B) Homopolar Crystals, (C) Metallic Crystals and (D) Kesidual Force Crystals these are typified respectively by crystals of sodium chloride, diamond, iron and paraffin wax. We shall, in the present work, naturally be concerned mainly with metallic crystals and will have to deal in some detail with their individual structures. It might not, however, be out of place to include here the following brief summary of the properties which characterise the different crystal types. This may be done as follows ... 

B) Homopolar Crystals. Such crystals also are transparent and tend to have high melting-points. They do not conduct electricity. They are extremely hard—the diamond, tor example, being the hardest substance known—and are extremely brittle. They cannot undergo plastic deformation. 

In a homopolar crystal, such as Ge, the strong electric dipoles created in a displacement of bare core-charges +4]ej are completely cancelled by the electronic charge density, which readily relaxes, l.e. adapts its distribution to the displacement. In a polar crystal, however, this cancellation is not complete, and we are interested in the resulting electric moment, which the phenomenological theories traditionally represent as a displaced effective charge. 

Table 1.3 Equilibrium forms of homopolar crystals (after (1.90]).

If the wave function for a localized state is such that the probability of encountering the electron on the foreign atom is the same as that of encountering it in the crystal then, when such a state is doubly occupied, we have a purely homopolar surface bond. The quantity R, defined in terms of the wave-function coefficients by the equation... 

Figure 2b depicts a strong acceptor bond for a Na atom. It is formed from the weak bond depicted in Fig. 2a, for example, as a result of the capture and localization of a free electron, that is, as a result of the transformation of a Na+ ion of the lattice serving as an adsorption center, into a neutral Na atom. We obtain a bond of the same type as in the molecules H2 or Na2. This is a typically homopolar two-electron bond formed by a valence electron of the adsorbed Na atom and an electron of the crystal lattice borrowed from the free electron population. The quantum-mechanical treatment of the problem 2, 8) shows that these two electrons are bound by exchange forces which in the given case are the forces keeping the adsorbed Na atom at the surface and at the same time holding the free electron of the lattice near the adsorbed atom. 

These functions of the free electrons and holes follow from the very concept of a free electron or a free hole. We shall illustrate this on the two limiting cases of a purely homopolar and a purely ionic crystal. 

Some metals crystallize in more than one structural type, which means that there are two alio tropic modifications. The metals marked do not conform precisely to the closest-packed structure, but deviate slightly from it. Uranium, manganese, gallium and indium have very abnormal structures, and the last two are transitional between metallic and non-metallic elements of the carbon group. The picture presented by the metallic structures is utterly different from that of elements of the four last groups of the periodic system. The homopolar bonds of these latter strive to produce a state in which the number of neighbours of each atom is determined by its valency. In the other elements, however, forces appear to be acting that tend to surround each atom with as many other atoms as possible. 

In the homopolar bond, a pair of atoms are coupled together by two electrons while, in a metal, all the electrons hold all the ions together in the crystal. The theory of the metallic bond is even more complicated than that of the homopolar bond, as the subsequent discussion will show. In this section we shall only discuss how metallic properties are distributed in the periodic system. 

InSe and GaSe crystals are characterized with a weak interaction of 3D Wannier excitons with homopolar optical A -phonons [18, 19]. Therefore, when calculating the exciton absorption spectra, we took into consideration effects of broadening the exciton states using the standard convolution procedure (see in [18]) for theoretical values of a(7jco) the absorption coefficient in the Elliott s model [20] with y /io>) — 77 [n(E 2+/ 2)] the Lorentzian function in the Toyozawa s model [21], where r is the half-width at half-maximum which is usually associated with the lifetime tl/2r. 

Molecular Crystals.—The molecules which we have been discussing in this chapter are tightly bound structures, held together by strong homopolar forces. Mathematically, these forces can be described approximately by Morse curves, as discussed in Sec. 1, Chap. IX. On the other hand, the forces holding one molecule to another are simply the Van der Waals forces, which we have spoken about in Chap. XXII, and which are very much weaker than homopolar forces, as we saw from Table XXIV-3. It thus comes about that the crystals of these materials consist of compact molecules, spaced rather widely apart. Since the forces between molecules are so weak, the crystals melt at low tempera-... 

The other complicated structures come at the ends of the groups in the periodic table, and as we have said they correspond to something more like homopolar bonds than metallic bonds. We have already commented on germanium and tin (the so-called gray modification of tin), which crystallize in the diamond structure, corresponding to the four homopolar bonds which they could form. They are of course very different from diamond in their properties, though silicon is between a... 

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... 

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