D. Wilmer

Concept of mismatch and relaxation derived from conductivity spectra of solid electrolytes

Abstract Below the microwave regime, conductivity spectra of crystalline ionic conductors like RbAg 4 I 5 and others display remarkably uniform characteristics. Depending on the ranges of temperature and frequency, these may be approximated in terms of UDR (universal dynamic response) and NCL (nearly constant loss) behaviour, while a plateau is observed at millimetre wave frequencies. All these features are consistently described by a new non-power-law, non-KWW master curve. Its formal structure is shown to be equivalent to a proportionality of the rates of relaxation via the single- and many-particle routes. This is the essence of the concept of mismatch and relaxation (CMR).

Ionic and polaronic glassy conductors: conductivity spectra and implications for ionic hopping in glass

Complete conductivity spectra have been taken of a lithium ion and a polaron conducting glass. The former exhibits high-frequency plateaux in its hopping conductivities and two different power-law exponents in the dispersive regime. This is readily explained if ions, contrary to polarons, have a pronounced site preference. At the same time, this view also explains the well known differences in the dependence of carrier mobility on carrier concentration in the two types of glasses.

Ionic and polaronic hopping in glass

Abstract In this paper we present conductivity spectra of the ion conducting glasses B 2 O 3 · 0.56Li 2 O · 0.45LiBr and Ag 2 S · GeS 2 and of the polaron conducting glass 0.2P 2 O 5 · 0.8 (0.89V 2 O 5 · 0.11V 2 O 4 ), covering a frequency range of more than 13 decades. At frequencies below the onset of the vibrational motion the spectra of both ion conducting glasses clearly differ from those of the polaronic glass. The dispersive conductivity of 0.2P 2 O 5 · 0.8 (0.89V 2 O 5 · 0.11V 2 O 4 ) follows a simple power-law behavior, the exponent being smaller than one. In contrast, the conductivities of both ion conducting glasses show the existence of two power-law exponents; one is the Jonscher exponent, the other is larger than unity. The data are interpreted in terms of the ‘unified site relaxation model’.

Dynamics of mobile ions in crystals, glasses and melts, described by the concept of mismatch and relaxation

Abstract The concept of mismatch and relaxation (CMR) provides a model description for the dynamics of the hopping motion of ions in ion-conducting materials. The following applications are discussed. (i) In the crystalline fast ion conductor RbAg 4 I 5 the CMR is employed to analyse the gradual transition from random to nonrandom hopping that is found to occur below 298 K. (ii) When used to describe the ion dynamics in fragile supercooled melts, the CMR yields a new equation for the temperature dependence of the dc conductivity. (iii) In interacting dipole systems, the nearly-constant-loss (NCL) behaviour is reproduced by the CMR. (iv) After introduction of a structure-sensitive parameter, the CMR is able to fit experimental conductivity spectra that display significant differences in shape.

Two-dimensional silver fast-ion conduction in (LaO)AgS

Abstract The silver fast-ion conductor (LaO)AgS was examined in temperature-dependent ac impedance and time-of-flight neutron diffraction experiments. Comparison of our conductivity data with those published earlier suggests that the presence of unreacted Ag2S resulting from different sample preparation methods is the possible reason for severe discrepancies in the conductivity data of other authors. Anisotropic temperature factors obtained by Rietveld analysis of our neutron diffraction data indicate enhanced silver ion mobility in the a–b plane of the tetragonal structure. The observed silver ion density shows that the preferred conduction path is via interstitial ( 1 2 1 2 1 2 ) sites, i.e. along 〈110〉. (LaO)AgS is a two-dimensional silver fast-ion conductor.

Dynamics of mobile ions in solid electrolytes: conductivity spectra and the concept of mismatch and relaxation

Abstract Experimental conductivity spectra σ(ν) of solid electrolytes with disordered structures, both crystalline and glassy, exhibit surprisingly similar overall characteristics. On closer inspection, however, differences become apparent as well. These include slightly different shapes of the frequency-dependent functions σ(ν) and, in the low-frequency limit, the observation of either Arrhenius or non-Arrhenius temperature dependences. The empirical features of conductivity spectra, both the common and the more specific ones, are now well reproduced with the help of two coupled rate equations describing the evolution of the ion dynamics with time in a very general fashion. The present treatment, which is based on the jump relaxation model, is called the concept of mismatch and relaxation (CMR). From the CMR, realistic spectra σ(ν) are derived for crystalline and glassy ion conductors at different temperatures. Characteristic features in the spectra are traced back to their dynamic origins.

Anion reorientation in Na3PO4

Abstract The reorientational motion of phosphate anions in the high-temperature phase of Na 3 PO 4 has been investigated with a coherent quasielastic neutron-scattering experiment. Our study aimed at clarifying the relevance of the so-called “paddle-wheel” mechanism, i.e., the influence of the anion motion on the translational Na + ion conduction. In the Q range between 0.3 and 2.3 A −1 , the data could be fitted by the sum of a δ function and a single Lorentzian whose width exhibits an Arrhenius behavior with an activation energy of 0.184 eV. We have calculated S q ( Q , ω ), the coherent quasielastic structure factor of the oxygen ions, based on several models. A comparison of the model predictions with our experimental data shows that only three oxygen atoms per anion are rotationally mobile. The experiment yields an additional small maximum around 1.5 A −1 , which appears more pronounced at higher temperatures. Its position on the Q scale suggests that sodium ions, further away from the center of rotation, are involved in the reorientational anion motion.

Ion dynamics in solid electrolytes described by the concept of mismatch and relaxation

Abstract Below the far-infrared frequency regime, conductivity spectra of crystalline ion conductors like RbAg4I5 and others display remarkably uniform characteristics. Well-known approximations include the universal dynamic response (UDR) and the nearly constant loss (NCL) behaviour. We now present a new non-power-law, non-KWW master curve. Its shape is shown to be equivalent to a proportionality between two particular functions of time. These functions are interpreted as rates of mismatch relaxation via the so-called single-particle and many-particle routes. The proportionality of relaxation rates is the central statement of the concept of mismatch and relaxation (CMR).