Effects of reduced dimensionality in the relaxation dynamics of ionic conductors (original) (raw)
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Journal of Non-crystalline Solids, 2006
We present Admittance Spectroscopy measurements on two different ionically conducting materials, Gd 2 Ti 2Ày Zr y O 7 and Li 0.5Àx Na x -La 0.5 TiO 3 . Electrical relaxation data have been found to be well described by stretched exponential functions of the form U(t) = exp(À(t/ s) 1Àn ). In Gd 2 Ti 2Ày Zr y O 7 the concentration of mobile ions in the whole series is very low, from 1% to 0.02 %, and we find that by strongly decreasing the density of mobile ions the value of the exponent n shows a significant decrease from 0.44 ± 0.01 to 0.16 ± 0.01. In Li 0.5Àx -Na x La 0.5 TiO 3 we have investigated changes in ion dynamics when approaching the percolation threshold for lithium diffusion by increasing the number of immoble sodium ions, and found that the exponent n increases towards a value of 0.81 ± 0.01 as the mobility of lithium ions becomes more and more constrained close to the percolation threshold. Both results are discussed in terms of the importance of ion-ion correlations in the dispersive behavior of the electrical conductivity.
Universal scaling of the conductivity relaxation in crystalline ionic conductors
Physical Review B, 1998
We present complex admittance measurements on single-crystal yttria-stabilized zirconia and polycrystalline Li 0.5 La 0.5 TiO 3 over the frequency range 5 Hz to 30 MHz and at temperatures ranging between 150 and 650 K. Electric-field relaxation in both fast ionic conductors can be described using Kohlrausch-Williams-Watts decay functions, but departures are observed at high frequencies and low temperatures. Electric modulus data obey the Dixon-Nagel scaling that has been proposed to be universal in describing the relaxation processes in supercooled liquids. Our data provide broader universality to the Dixon-Nagel scaling, and are interpreted in terms of the influence of mobile ions positional disorder on the relaxation dynamics.
Journal of Non-crystalline Solids, 2002
We have investigated the crossover in the ac conductivity of ionic conductors from the linear frequency dependence (near-constant loss) found at low temperatures, to the power law dependence characteristic of ionic hopping at higher temperatures. We have analyzed electrical conductivity measurements of the fast ionic conductor Li0.18La0.61TiO3 in the frequency range 20 Hz–5 MHz, and from room temperature down to 8 K. Our results show the failure of the so-called `augmented Jonscher's expression' to describe the ac conductivity in the whole frequency and temperature ranges, and give further support to the origin of the near-constant loss in the vibrational relaxation of ions within their cages.
Solid State Ionics, 1999
The question of how to relate the macroscopic conductivity relaxation measurement (´*(v), s*(v) or M*(v)) 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*(v), is the most appropriate representation of the macroscopic data to describe the microscopic movement of the ions. It is found that M*(v) 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.
Electrical conductivity relaxation and nuclear magnetic resonance of Li conducting Li0.5La0.5TiO3
Physical Review B, 1996
Lithium ionic conductivity of Li 0.5 La 0.5 TiO 3 has been studied using nuclear magnetic resonance ͑NMR͒ and admittance spectroscopy ͑AS͒ techniques. Spin-lattice relaxation and electrical conductivity relaxation are well described in terms of stretched-exponential correlation functions in the time domain of the form (t)ϭexp"Ϫ(t/)  …, but showing different relaxation times scales ( 0 ϭ1.4ϫ10 Ϫ11 s from NMR and 0 ϭ10 Ϫ14 s from AS͒, and activation energies ͑0.15 and 0.4 eV, respectively͒. Different  exponents, 1 from spin lattice relaxation and 0.4 from electric-field relaxation have been also deduced. A microscopic activation energy for lithium motion of 0.15 eV is deduced from both techniques. Discrepancies between both techniques are analyzed and discussed in terms of frequency-dependent correlation effects.
Small power-law dependence of ionic conductivity and diffusional dimensionality in β-alumina
Solid State Ionics, 2015
AC conductivity σ(ω) of single crystals of Ag β-alumina and Na β-alumina has been studied in the temperature range from approximately 100 K to room temperature. The DC regime of σ(ω), which had a close relation to the ion dynamics for the long-range diffusion, was found to have the small power-law dependence σ(ω) ∝ ω n with frequency exponent n = 0.11-0.15, not σ(ω) ∝ ω 0 = const. In higher frequencies, the σ(ω) was monotonically increasing with Log-frequency and was put into Jonscher's universal law (σ(ω) ∝ ω 0.6). The β-alumina is an ideal two-dimensional super ionic conductor. Its low-dimensionality and the scaling theory for a random walk enable us to understand the small power-law dependence of ionic conductivity. We suggested that a "scaleinvariance" would hold true behind the super ionic conduction in the self-similarity point of view.
Size Dependent Ion Diffusion in Na2Ti3O7 and Na2Ti6O13
Journal of Advances in Nanomaterials
Titanates are promising anode materials for the lithium-ion (LIBs) and sodium-ion (SIBs) secondary batteries due to their high discharge capacity and low voltage. By means of complex impedance spectroscopy (CIS), we investigated the ion dependence of diffusion dynamics in the same host framework, i.e., Na2Ti3O7 and Na2Ti6O13. In Na2Ti3O7 with a stepped layered framework, the diffusion constant (D Na = 2.07×10 −10 cm 2 /s) of Na + is comparable to that (D Li = 2.07×10 −10 cm 2 /s) of Li + at ca. 324 K. In Na2Ti6O13 with a tunneled structure, D Na (= 0.16×10 −10 cm 2 /s) is much lower than D Li (= 0.64×10 −10 cm 2 /s) at 298 K. We will discuss the size dependent ion diffusion in terms of the nanostructure of Na2Ti3O7 and Na2Ti6O13.