Free-Electron Model of Metals

Abstract

The first volume of this series was primarily concerned with the structure of condensed matter. We studied whether an order is present in the arrangement of the atoms or ions that determine the overall structure of the solid, and then analyzed the dynamics of crystal lattices in the ordered (crystalline) phase. Next, we treated a very similar problem presented by magnetically ordered materials, determining the possible ordered arrangements of localized atomic magnetic moments and the elementary excitations arising from the dynamics of the moments. Various thermodynamic and magnetic properties of solids could be explained in terms of these. A second constituent of solids, which is perhaps even more important than the ion cores, is the system of electrons that are not tightly bound in the inner shells of the ions and that form metallic bonds or valence bonds between ion cores. In this volume we shall be concerned with the behavior of such electrons-which participate in bonding, and thus affect substantially the properties of solids. Throughout, we shall employ the one-particle approximation; the analysis of the role of electron-electron interactions will be the subject of the third volume. Soon after the discovery of the electron, 1 a straightforward explanation was suggested for the most characteristic properties of metals (good electrical and thermal conductivity) in terms of conduction electrons, i.e., electrons moving freely in metals. The successful description of the behavior of nearly ideal gases at the end of the 19th century, due primarily to L. Boltzmann's contributions to classical statistical mechanics, enabled P. Drude (1900) to apply a simple formulation of the kinetic theory of gases to a gas of electrons. This model was developed further by H. A. Lorentz (1905) to give a more detailed account of conduction phenomena. This model of the classical gas of free electrons is called the Drude model or Drude-Lorentz model. Despite its initial success, the inadequacies of the model soon transpired. These were rooted in the fact that the gas of electrons-if it can be consid-1 J. J. Thomson, 1897.