The conductivities of inorganic solids

Key points: A metallic conductor is a substance with an electric conductivity that decreases with increasing temperature; a semiconductor is a substance with an electric conductivity that increases with increasing temperature. The molecular orbital theory of small molecules can be extended to account for the prop erties of solids, which are aggregations of an almost infinite number of atoms. This ap proach is strikingly successful for the description of metals; it can be used to explain their characteristic lustre, their good electrical and thermal conductivity, and their malleability. All these properties arise from the ability of the atoms to contribute electrons to a common ‘sea’. The lustre and electrical conductivities stem from the mobility of these electrons in response to either the oscillating electric field of an incident ray of light or to a potential difference. The high thermal conductivity is also a consequence of electron mobility be cause an electron can collide with a vibrating atom, pick up its energy, and transfer it to another atom elsewhere in the solid. The ease with which metals can be mechanically de formed is another aspect of electron mobility because the electron sea can quickly readjust to a deformation of the solid and continue to bind the atoms together. Electronic conduction is also a characteristic of semiconductors. The criterion for dis tinguishing between a metallic conductor and a semiconductor is the temperature depend ence of the electric conductivity (Fig. 3.60): A metallic conductor is a substance with an electric conductivity that decreases with increasing temperature. A semiconductor is a substance with an electric conductivity that increases with increasing temperature. It is also generally the case (but not the criterion for distinguishing them) that the conductivities of metals at room temperature are higher than those of semiconductors. Typical values are given in Fig. 3.60. A solid insulator is a substance with a very low electrical conductivity. However, when that conductivity can be measured, it is found to increase with temperature, like that of a semiconductor. For some purposes, therefore, it is possible to disregard the classification ‘insulator’ and to treat all solids as either metals or semiconductors. Superconductors are a special class of materials that have zero electrical resistance below a critical temperature.

Fig. 3.60 The variation of the electrical conductivity of a substance with temperature is the basis of the classification of the substance as a metallic conductor, a semiconductor, or a superconductor.

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The Fermi level

Densities of states

Band formation by orbital overlap

Nonstoichiometry

Intrinsic point defects

Solubility

Thermal stabilities of ionic solids

The Born–Mayer equation

Structure maps

The radius ratio

Ionic radii

Characteristic structures of ionic solids