On the metal-non-metal transition in sodium-ammonia solutions

Abstract

An analysis of the Knight shift, magnetic susceptibility and conductivity of ‘metallic’ solutions of sodium in ammonia shows that the metal-non-metal (MNM) transition takes place when the density of states N(E _F) at the Fermi level is about one-third of the free-electron value, and that it drops as the transition is approached. This supports a model put forward by Mott and Davis (1968) and Mott (1971) for the MNM transition in disordered systems; fixed magnetic moments, varying only with the frequency of ionic motion, are supposed to remain on the metal atoms, or on donors in a semi-conductor, on the metallic side of the transition, so that a splitting of the conduction band into two overlapping Hubbard bands occurs. For a non-crystalline array of centres, this leads to a minimum (a pseudogap) in the density of states, and the MNM transition takes place when states at the Fermi energy become localized in the Anderson sense, which occurs when the ratio g defined by eqn. (2) has a value of about ⅓.