Ionic crystals energy bands

Most metal oxides are ionic crystals and belong to either the class of semiconductors or insulators, in which the valence band mainly comprises the frontier orbitals of oxide ions and the conduction band contains the frontier orbitals of metal ions. In forming an ionic metal oxide ciTstal from metal ions and oxide ions, as shown in Fig. 2-21, the crystalline field shifts the frontier electron level of metal ions to higher energies to form an antibonding band (the conduction... 

In ionic crystals a polaron is the region round an electron in the conduction band in which the material is polarized by the electron, as first proposed by Landau (1933). Round the electron, the field with which it interacts has a potential-energy function... 

Fig. 2 Conceptual illustration of a energy band scheme and b an ionic crystal lattice consisting of M2+ and O2- ions...

For nonmetallic substances, the electrons cannot move as freely as in the case of metals because their energy bands are essentially completely full or empty. The electrical conductivity in nonmetallic materials is dominated by another mechanism, i.e., the defect mechanism, instead of electron conduction. In ionic crystals such as salts (e.g., sodium chloride), two types of ions, cations and anions, are driven to move by the electrical force qE once an electrical field is applied. The ions can move only by the defect mechanism that is, they exchange position with a vacancy of the same type. At the room temperature, the fraction of vacancies for salt is very small (of the order of 10-17) with low exchange frequency (of the order of 1 Hz) so that electrical conductivity is extremely low. Although impurities and high temperature can affect electrical conductivity by a large factor, nonmetallic materials generally have very low electrical conductivity and these substances are widely used as electrical insulators. 

In a more accurate picture of ionic crystals, the ions are held together in a three-dimensional lattice by a combination of electrostatic attraction and covalent bonding. Although there is a small amount of covalent character in even the most ionic compounds, there are no directional bonds, and each Li ion is surrounded by six F ions, each of which in turn is surrounded by six Li ions. The crystal molecular orbitals form energy bands, described in Chapter 7. 

The fact that compounds such as Mg2Si to MgjPb have such high resistances and crystallize with the antifluorite structure does not mean that they are ionic crystals. Wave-mechanical calculations show that in these crystals the number of energy states of an electron is equal to the ratio of valence electrons atoms (8/3) so that, as in other insulators, the electrons cannot become free (that is, reach the conduction band) and so conduct electricity. That the high resistance is characteristic only of the crystalline material and is not due to ionic bonds between the atoms is confirmed by the fact that the conductivity of molten MgjSn, for example, is about the same as that of molten tin. 

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