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." o
r UDR, while at low temperatures/high frequencies they show "nearly constan
t loss," or NCL behavior, which persists down to cryogenic temperatures. Th
r: present paper seeks to examine the corresponding behaviors of "simple" s
ystems, i.e., dilute systems of the classical type in which a relatively sm
all number of defects are involved. Three systems studied here are oxygen-i
on conductors: CeO2 doped with Gd3+ and with Y3+, as well as CaTiO3 doped w
ith Al3+. In each case. we proceed from dilute to concentrated doping level
s. Also studied in very dilute concentrations are NaCl:Sm3+ (a Na- conducto
r) and KTaO3:Cu2+,H+ (a protonic conductor). It is found that in the UDR re
gime, the simple materials show very much the same behavior as the complex,
suggesting that UDR relaxation is intrinsic to the hopping process. A stri
king result is that the onset frequency of dispersive conductivity correspo
nds to the mean jump frequency of all carriers, both bound and free. In con
trast to the UDR regime, NCL behavior is only shown by complex materials, s
imple materials show discrete (Debye-type) relaxations that are due to off-
center configurations that relax by small rocking-type motions. As the conc
entrations increase, these relaxations smear out into a broad distribution
that gives rise to NCL behavior.