Nonlinear DC and Dispersive Conductivity of Ion Conducting Glasses and Glass Ceramics

Abstract

Ionic Motion / Nonlinear Ionic Conductivity / Glasses / Glass CeramicsFrequency-dependent third-order conductivity spectra σ 3 (ν) of various ion conducting glasses and glass ceramics were obtained by applying sinusoidal electric fields with high amplitudes and by analysing the resulting higher-harmonic currents. In the DC conductivity regime, the third-order conductivity σ 3, dc was found to be positive for all materials and at all temperatures. From the ratio of the third-order conductivity to the low-field conductivity, σ 3, dc /σ 1, dc , apparent jump distances were calculated. These apparent jump distances are much larger than jump distances between neighbouring sites in the glasses and decrease with increasing temperature. In (Li 2 O) 1−x · (Na 2 O) x · Al 2 O 3 · (SiO 2 ) 4 glasses, the mixed alkali effect leads to a minimum in the apparent jump distance, while partial crystallisation of Li 2 O · Al 2 O 3 · (SiO 2 ) 2 glasses leads to an increase of the apparent jump distance. In the dispersive regime, the third-order conductivity σ 3 (ν) of all glasses and glass ceramics is negative and exhibits an approximate power-law dependence, however with a larger exponent than the dispersive low-field conductivity σ 1 (ν). For a given material, the third-order conductivity spectra σ 3 (ν) obey the time-temperature superposition principle and can be superimposed by using the Summerfield scaling. Remarkably, the shift between the σ 3 (ν) master curves of different materials is much stronger than the shift between the σ 1 (ν) master curves. In order to rationalize this effect, we calculate the nonlinear dispersive hopping conductivity in a double minimum potential approximation.

Nonlinear ion transport in the supercooled ionic liquid 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide: Frequency dependence of third-order and fifth-order conductivity coefficients

“…At higher frequencies in the dispersive regime, the third-order conductivity decreases with increasing frequency and becomes negative. [15][16][17][18] This kind of frequency dependence was also found in a single-particle hopping model. 21 In this model, the dispersive third-order conductivity decreases with increasing frequency, goes through a minimum, and then increases with increasing frequency.…”

“…For instance, some models predict negative thirdorder dc conductivity coefficients, 19 whereas the third-order dc conductivity coefficients observed in experiment were always positive. [14][15][16][17][18] Other models predict positive third-order a) Email: laxminar@chemie.uni-marburg.de dc conductivity coefficients, which are, however, much smaller than those found in experiments. 19,20 The frequency dependence of the third-order conductivity spectra of solid ion conductors differs clearly from the universal dynamic response observed in the linear spectra.…”

“…However, when the ac electric fields applied to ionic conductors (solid and liquid) are increased to values beyond 50-100 kV/cm, the current response becomes nonlinear. [10][11][12][13][14][15][16][17][18] Nonlinear conductivity spectra provide additional information about the ion transport mechanisms. Unfortunately, a general nonlinear response theory relating nonlinear ion conductivity spectra to the equilibrium dynamics of the ions does not exist.…”

The frequency dependence of nonlinear conductivity in non-homogeneous systems: An analytically solvable model

“…Experimentally, nonlinear ac measurements have been carried out on alkali-ion conducting glasses as well as on the ionic liquid HMIM-TFSI [7,[9][10][11][12][13]. In both cases, the nonlinear conductivity σ 3 was positive in the dc regime and gradually decreased with increasing frequency.…”

Physical mechanisms of nonlinear conductivity: A model analysis

“…for j(w) ∝ sinh(w). Note that σ r can be directly obtained from the experiments and reaches values of the order of 100 4,30 . Note that nearest-neighbor hopping dynamics and the presence of discrete sites is by far the dominant transport mechanism in alkali silicate systems in the linear and nonlinear regime 15,31 .…”