Confined-gas model for ion flow in a superionic conductor

Abstract

The diffusive motion of ions in a solid differs from ordinary vibrative motion in a very significant way. Although Coulomb forces play an important role, the diffusion of the ions is determined predominantly by the very short-range repulsion between ion cores. Owing to these forces, the ions are constrained to flow through a confining network of voids and narrow channels. We propose a model for superionic conduction in which these constraints are included realistically from the outset. This requires an extreme simplification of other aspects of the problem. To this end, the momentum and energy distributions of the conducting ions are taken to be those of charged particles in a Boltzmann gas of heavy molecules. An effective one-ion potential is imposed upon this system. The appropriate three-dimensional potential is determined from diffraction and extended x-ray absorption fine-structure measurements. We calculate the probabilities for the classical transit of the ions within this potential field. This leads directly to an a priori estimate of the temperature-dependent dc conductivity in the superionic phase. The resultant conductivities compare well with measurements on AgI and on the copper halides in both the superionic and normal phases.