Concept Of Mismatch And Relaxation Research Articles

Analysis of ion conduction and relaxation in Na2NbCdP3O12 glass

The ac conductivity of ionic conducting Na2NbCdP3O12 is studied over the frequency range of 100Hz to 1MHz at different temperatures. The conduction mechanism of the material is studied using the concept of mismatch and relaxation (CMR) model and the length scale of the ion transport process is studied from the many particle displacement function <R(t)2> for various temperature. The non-Debye relaxation mechanism and ionic conduction is analysed through the anomalous relaxation function and it is compared with CMR.

Influence of SiO2 on conduction and relaxation mechanism of Li+ ions in binary network former lead silicate glasses

Ion conducting glasses having composition 30Li2O·(70−x)PbO·xSiO2 were prepared by the normal melt quench technique. The compositional variations in density, molar volume and glass transition temperature confirm the dual role of PbO acting as a network modifying oxide as well as a network forming oxide. Conduction and relaxation mechanisms in these glasses were studied using impedance spectroscopy in the frequency range from 1Hz to 7MHz and in a temperature range below glass transition temperature. The ac and dc conductivities, activation energy of the dc conductivity and relaxation frequency were extracted from the impedance spectra. Similar values of activation energy for dc conduction and for conductivity relaxation time indicate that the ions have to overcome the same energy barrier while conducting and relaxing. The increase in dc conductivity for silica rich compositions is attributed to the presence of mixed former effect in the studied glasses. The study of conductivity spectra reveals a transition from non-random to random hopping motion of lithium ions on successive replacement of PbO by SiO2 in glass matrix. The conduction and relaxation mechanism in the studied glasses are well explained with the concept of mismatch and relaxation (CMR) model.

On the physical interpretation of constant phase elements

Complex impedance spectra of ion-conducting lithium borate network glasses are used to study the deformed shape of impedance semicircles which are usually described by a parallel circuit of an ohmic resistor and a phenomenological Constant Phase Element (CPE). Based on the Concept of Mismatch and Relaxation (CMR) of Funke et al. which provides a theoretical treatment of the ion dynamics in disordered materials, a quantitative description of the experimental impedance spectra is presented. It takes into account the contribution of the static glass network by introducing an additional capacitor, and provides both, a physical interpretation of the CPE and an easy-to-handle mathematical formula to calculate the ’real’ capacity of a CPE.

A Mechanistic Approach to Conductivity Relaxation in Ionic Glasses

Abstract A mechanism is proposed for conductivity relaxation in ionic glasses, based on the operation of a memory effect (as postulated in the dynamic structure model) that provides the necessary synergy for ‘pair-wise’ coupling of ionic motions in single cation glasses. It is suggested that this mechanism (which resembles in some respects the older ‘interstitialcy’ process) constitutes an essential component of the single and many-particle reaction route’ in Funke’s concept of mismatch and relaxation (CMR). This coupling is also present in mixed cation glasses, but the appearance of a site mismatch effect and the consequent disappearance of synergy leads to anomalous behaviours typical of the mixed cation effect, including recently reported increases in activation volume.

Nearly constant loss behavior in γ-RbAg 4I 5: microwave conductivity plateau identified

A pronounced nearly constant loss (NCL) contribution to the frequency-dependent conductivity has been detected in the low-temperature γ-phase of the archetypal crystalline fast ion conductor, rubidium silver iodide. At 113 K, the conductivity spectrum, σ( ν), of γ-RbAg 4I 5 has been measured in a wide frequency range extending up to more than 100 GHz. In contrast to the phases α and β, the spectrum cannot be interpreted as a superposition of a high-frequency vibrational part plus a low-frequency dispersive component that reflects the ionic hopping dynamics responsible for macroscopic ionic transport. Rather, an additional NCL component is identified featuring a roughly linear σ( ν) ∝ ν behavior within about two decades of frequency. This component is found to merge into saturation at high frequencies and into a σ(ν)∝ ν 2 behavior at low frequencies. It is well reproduced in terms of a model describing highly correlated, strictly localized displacive movements of interacting ions. The model is based on the concept of mismatch and relaxation (CMR).

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

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 4I 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.

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

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.

Ion dynamics in mixed alkali glasses

To study the ion dynamics in an amorphous mixed alkali system, frequency-dependent conductivities of 0.3[xLi2O·(1 − x)Na2O]·0.7B2O3 glasses have been measured by impedance spectroscopy in a wide temperature range. The conductivities show a transition from their dc values into a dispersive regime where they increase continuously with frequency, tending towards a linear frequency dependence at sufficiently low temperatures. In addition to the “classical” mixed alkali effect, i.e. the occurrence of a minimum in the dc conductivity, we also observe the following new mixed alkali effect. In contrast to conductivity spectra of single cation glasses which follow the time-temperature superposition principle, featuring a temperature-invariant shape, the shapes of the conductivity spectra of the mixed alkali glasses studied here are found to change with temperature. To explain the effect, we suggest differently activated mobilities of the two different ionic species. The spectra are discussed in the framework of the concept of mismatch and relaxation (CMR).

Ionic motion in materials with disordered structures: conductivity spectra and the concept of mismatch and relaxation

Solid electrolytes with disordered structures, both crystalline and glassy, as well as supercooled ionic melts, exhibit surprisingly similar features in their conductivity spectra, σ(ν). This finding suggests that the dynamics of the mobile ions in the different systems should be governed by similar rules. Examples are given in this study, including new results on γ-RbAg4I5, β-AgI, and several glassy electrolytes. In spite of their overall similarity, however, the spectra also display characteristic differences in their shapes and in their scaling behaviour, the latter feature causing, e.g., Arrhenius or non-Arrhenius temperature dependences of the dc conductivity. The observed characteristics of the spectra, both the common and the more specific ones, are well reproduced with the help of two coupled rate equations describing the evolution of the ion dynamics with time. This treatment is based on the jump relaxation model, and is called the concept of mismatch and relaxation (CMR).

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

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).

Concept of Mismatch and Relaxation Explains DC and AC Conductivities of Fragile Glass-Forming Ionic Melts

In fragile glass-forming ionic melts, spectra of the ionic conductivity have been taken in wide ranges of frequency and temperature. In our experiments, we have studied and over more than ten decades on the frequency scale, including the far infrared. The results exhibit characteristic traits, and a clear-cut picture is found to emerge from them. We present a phenomenological description of our data as well as a set of equations which fit them surprisingly well. Those equations are then traced back to their dynamic origins on atomic scales of length and time. The underlying dynamic principle which is thus revealed is called the concept of mismatch and relaxation (CMR). © 2001 The Electrochemical Society. All rights reserved.

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

Below the microwave regime, conductivity spectra of crystalline ionic conductors like RbAg 4I 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).

Dynamics of mobile ions in crystals, glasses and melts

In crystalline, glassy and molten electrolytes, the dynamics of the mobile ions is best studied by taking conductivity spectra, i.e., by measuring ionic conductivities in the entire range from dc to far-infrared frequencies. Experimental conductivity spectra are reviewed and discussed, with particular emphasis on their high-frequency plateaux and their low-frequency scaling properties. The concept of mismatch and relaxation (CMR) is shown to provide a general basis for understanding the spectra in terms of the ion dynamics. The conductivity spectra of crystalline fast ion conductors are, e.g., explained by the jump relaxation model, which builds on the CMR. In glassy electrolytes, the mobile ions encounter different kinds of site, and the jump relaxation model has to be modified accordingly. Formulating the CMR without reference to the existence of fixed sites yields a description of the ion dynamics in simple molten salts. The model is thus able to reproduce both the conductivity spectra of fragile molten salts and the characteristic temperature dependence of their dc values. The remarkable low-frequency scaling behaviour of glassy electrolytes is considered a manifestation of the particular long-time properties of the CMR.

Concept of Mismatch and Relaxation Derived from Conductivity Spectra of Solid Electrolytes

ABSTRACTCrystalline ion conductors like RbAg4I5 and others display a characteristic shape of their dispersive conductivities at frequencies below the microwave regime. As the temperature is decreased, the onset of the dispersion is shifted to lower frequencies and thus the characteristic shape of the dispersion becomes visible in an increasingly broad frequency range. In a log-log plot of the frequency-dependent conductivity, the slope is found to increase continuously, but not to surpass unity. For the first time, this behavior is now consistently explained. The particular shape of the dispersion is shown to be equivalent to a proportionality of the rates of relaxation via the singleand many-particle routes. This is the essence of the concept of mismatch and relaxation (CMR). Model conductivity spectra based on the CMR include the UDR (universal dynamic response) as well as the NCL (nearly constant loss) behavior. Both universalities are thus traced back to a common dynamic origin.