FREE-ELECTRON MODEL OF METALS

in solid-state physics, representation of a metallic solid as a container filled with a gas composed of free electrons (i.e., those responsible for high electrical and thermal conductivity) that move in a virtually uniform potential arising largely from metal ions in the crystal lattice. The free electrons, considered identical to the valence electrons of free metal atoms, are presumed to be moving independently of one another throughout the entire crystal. The free-electron model was first proposed by the Dutch physicist Hendrik A. Lorentz shortly after 1900 and was refined in 1928 by Arnold Sommerfeld of Germany. Sommerfeld introduced quantum-mechanical concepts, most notably the Pauli exclusion principle (q.v.). Although the model provided a satisfactory explanation for certain properties (e.g., conductivity and electronic specific heat) of simple monovalent metals, it had some serious shortcomings. It did not, for example, take into account the interaction of free electrons with the metal ions. Researchers soon recognized that a broader system was needed to explain the behaviour of complex metals and semiconductors. By the mid-1930s the free-electron model was largely superseded by the band theory (q.v.) of solids.