An Example of Electronic Disorder. Electrons and Electron Defects in α-Ag₂S

Abstract

An instructive example to discuss electronic disorder in solid compounds is α-Ag₂S, the cubic high-temperature modification of silver sulfide being stable above 179°C; this compound has been studied by Wagner [5.1], Miyatani [5.2], the author, Wedde and Sattler [5.3] and more recently by Bonnecaze, Lichanot and Gromb [5.9]. In 1931, Tubandt and Reinhold [5.4] found that the conductivity of α-silver sulfide being in equilibrium with metallic silver is about 20 times higher than that of α-Ag₂S which has been equilibrated with sulfur. This behaviour has been substantiated by more recent measurements, which show that the concentration of the free electrons varies also by a factor of about 20. However, for a rigorous thermodynamic treatment, which will be given below, it is essential to note that the thermodynamic activity of the electrons changes by a factor of about 100 concomitant to the concentration change stated above. This means that the thermodynamic behaviour of the electrons in α-Ag₂S cannot be understood on the basis of the Boltzmann approximation. It is, however, possible to explain their behaviour quantitatively if the electrons are assumed to be degenerate thus making the use of Fermi-Dirac statistics necessary. Proceeding in this way theory and experiment come together, i.e. quantitative agreement will be established.