While metallic conduction has attracted considerable interest for a long time, a clear knowledge of the character of electron dynamics in metals has emerged surprisingly recently. In this chapter we shall follow the historical sequence in first examining simple free electron models, for which it was supposed that atoms in metals could liberate their outer electrons to produce an electron “gas” for random thermal motion and contributions to conduction. These models explained a number of important metallic properties, but raised a new set of questions, which remained unanswerable until it was realized that this electron gas moves through space also occupied by a periodic array of positively charged atomic cores.

The periodic nature of a crystal lattice has often been emphasized in the last two chapters. In this chapter we shall see that the periodicity of the ion core array produces an electrostatic field distribution which profoundly affects the relationship between energy and momentum for a mobile electron. We call this relationship the “band theory of solids.” In addition to permitting a more realistic picture of metallic conduction, band theory explains why many solids have insulating or semiconducting properties.

As a curious consequence, advances in the understanding of semiconducting and insulating solids were very rapid during the 1940's and 1950's, and we might well say that by the mid 1950's some simple semiconductors were better understood than any metals. The pendulum has started to swing back since that time, and with the development of highly sophisticated experimental techniques there has been a lively resurgence of interest in metals.