11.1 Conductors and insulators

In a crystalline solid, electrons and ions are possible charge carriers. However, the conductance is the product of charge concentration and mobility. Electrons, because of their low mass are much more mobile and conducting materials are most often electronic conductors. The majority of this section will therefore be dedicated to the electronic properties of the solid, whilst ionic conductivity will be more specifically dealt with in section 11.1.6.

The distinction between insulators and conductors comes naturally within the framework of the band theory developed by Bloch and Wilson (1929). Please refer to other works for a detailed presentation, [ ^{[KIT 98]}] for example, as only the basic elements will be mentioned here.

A solid is an assembly of charged particles, electrons and atomic nuclei. Because of the difference in mass, atomic nuclei are very slow when compared to electrons and their positions can be considered merely as parameters and not as unknown functions of time, solutions of the Schr dinger equation. Furthermore, Coulomb repulsive interactions of one electron with others are averaged over the electronic population. These are the two basic assumptions of the band theory, assumptions which are often not entirely justified in the case of ceramic materials (this will be discussed later on). It is therefore sufficient to consider the motion of a single electron placed in an effective potential and to determine its energy levels and states by applying the equations of quantum mechanics. Despite the approximations made, it remains a...