Electrical relaxations: Simple versus complex ionic systems

Abstract

Complex materials are known to show two regions of ac electrical behavior. In the high-temperature/low-frequency domain, they show power-law frequency dependence of the conductivity known as ``universal dielectric response,'' or UDR, while at low temperatures/high frequencies they show ``nearly constant loss,'' or NCL behavior, which persists down to cryogenic temperatures. The present paper seeks to examine the corresponding behaviors of ``simple'' systems, i.e., dilute systems of the classical type in which a relatively small number of defects are involved. Three systems studied here are oxygen-ion conductors: ${\mathrm{CeO}}_{2}$ doped with ${\mathrm{Gd}}^{3+}$ and with ${\mathrm{Y}}^{3+},$ as well as ${\mathrm{CaTiO}}_{3}$ doped with ${\mathrm{Al}}^{3+}.$ In each case, we proceed from dilute to concentrated doping levels. Also studied in very dilute concentrations are ${\mathrm{N}\mathrm{a}\mathrm{C}\mathrm{l}:\mathrm{S}\mathrm{m}}^{3+}$ (a ${\mathrm{Na}}^{+}$ conductor) and ${\mathrm{KTaO}}_{3}{:\mathrm{C}\mathrm{u}}^{2+}{,\mathrm{H}}^{+}$ (a protonic conductor). It is found that in the UDR regime, the simple materials show very much the same behavior as the complex, suggesting that UDR relaxation is intrinsic to the hopping process. A striking result is that the onset frequency of dispersive conductivity corresponds to the mean jump frequency of all carriers, both bound and free. In contrast to the UDR regime, NCL behavior is only shown by complex materials; simple materials show discrete (Debye-type) relaxations that are due to off-center configurations that relax by small rocking-type motions. As the concentrations increase, these relaxations smear out into a broad distribution that gives rise to NCL behavior.