Recent advances in relating macroscopic electrical relaxation data to microscopic movements of the ions in ionically conducting materials

Abstract

The question of how to relate the macroscopic conductivity relaxation measurement (ε∗(ω), σ∗(ω) or M∗(ω)) to the microscopic movement of the ions is a problem that must be resolved. Comparing with the results of a stochastic transport theory of charged carriers, we find that among the other choices the electric modulus, M∗(ω), is the most appropriate representation of the macroscopic data to describe the microscopic movement of the ions. It is found that M∗(ω) faithfully reproduces the shape of the dispersion of the microscopic ionic movement except that the entire electric modulus relaxation time spectrum is shifted uniformly away from the microscopic ionic hopping relaxation time spectrum by a calculable frequency-independent factor. Nuclear spin relaxation is a microscopic probe of ionic movement. A combined study of ionic motion using electrical relaxation and nuclear spin relaxation in a crystalline ionic conductor provides the means to verify the theoretical relation between the macroscopic electric modulus spectrum and the microscopic ionic hopping relaxation spectrum. Finally, we present some recent advances in our understanding of the experimental data that indicate the importance of ion– ion interactions in many ionically conducting crystals, glasses and melts.