Mixed Ionic Conductors Research Articles

A Machine Learning‐Enhanced Framework for the Accelerated Development of Spinel Oxide Electrocatalysts

AbstractThe surging demand for sustainable energy has spurred intensive research into electrochemical conversion devices such as fuel cells, water splitting, and metal‐air batteries. The performance of oxygen electrocatalysts significantly impacts overall electrochemical efficiency. Recently, spinel oxides (AB2O4) have emerged as promising candidates; however, the scarcity of prior studies underscores the need for a thorough and comprehensive exploration. This study presents a computational framework that integrates machine learning and density functional theory (DFT) calculations for the systematic screening of 1240 spinel oxides. The data scarcity is addressed while enhancing prediction accuracy. Selected candidates are identified to outperform the benchmarking perovskite oxide. Additionally, their potential as mixed ionic and electronic conductors with a 3D network of ion diffusion pathways is highlighted. To further enhance the understanding and prediction of stability, catalytic activity, and reaction mechanisms, a new undemanding descriptor is introduced: the covalency indicator. This study offers a design principle for the development of high‐performance spinel oxide oxygen electrocatalysts.

Transformer enables ion transport behavior evolution and conductivity regulation for solid electrolyte

Ab initio molecular dynamics (AIMD) is an important technique for studying ion transport within solid electrolyte and interface effects between electrode and electrolyte, which is particularly critical for the rational design of new energy materials. However, AIMD is limited by the high-cost density functional theory (DFT) solution process and is unable to reach the time scale of the entire dynamic simulation, resulting in time-consuming AIMD calculations and a considerable scarcity of AIMD-based conductor data. Here, we propose a sequence relational large model based on transformer (T-AIMD) to infer ion diffusion from mean square displacement sequence data and hybrid multi-source material descriptor. T-AIMD successfully learns the whole long-range atomic diffusion to predict the ionic conductivity (σ) of any ion in any crystal structure to find fast-ion conductors, thus reducing the cost of AIMD simulation by a factor of 100. Using T-AIMD, we built the largest database of mixed ion conductors, and the σ of representative solid electrolytes has been successfully validated in previous battery experiments. Further, the manufactured solid-state battery with the predicted promising electrolyte exhibits almost no obvious capacity decay after 50 cycles with a high initial specific capacity of 1270 mAh g−1, which is promising to help devices work in extreme environments while guaranteeing battery life. By speeding up the prediction time of AIMD, the proposed T-AIMD opens the door for scientists to explore the atomic and molecular behaviors of other molecules/materials on long time scales, and will ultimately benefit the exploration of other key scientific questions in the energy field.

General synthesis of ionic-electronic coupled two-dimensional materials.

Two-dimensional (2D) AMX2 compounds are a family of mixed ionic and electronic conductors (where A is a monovalent metal ion, M is a trivalent metal, and X is a chalcogen) that offer a fascinating platform to explore intrinsic coupled ionic-electronic properties. However, the synthesis of 2D AMX2 compounds remains challenging due to their multielement characteristics and various by-products. Here, we report a separated-precursor-supply chemical vapor deposition strategy to manipulate the chemical reactions and evaporation of precursors, facilitating the successful fabrication of 20 types of 2D AMX2 flakes. Notably, a 10.4 nm-thick AgCrS2 flake shows superionic behavior at room temperature, with an ionic conductivity of 192.8 mS/cm. Room temperature ferroelectricity and reconfigurable positive/negative photovoltaic currents have been observed in CuScS2 flakes. This study not only provides an effective approach for the synthesis of multielement 2D materials with unique properties, but also lays the foundation for the exploration of 2D AMX2 compounds in electronic, optoelectronic, and neuromorphic devices.

Unravelling the La dopant induced physicochemical changes and the electrical behaviour on BaFeO3 under oxidising and reducing atmospheres

Electroceramic oxides like La-doped BaFeO3 garner greater interest owing to their tunability of mixed ionic conduction. However, reports on the effect of La on the microstructural changes, the type of conduction mechanism under different atmospheres and the negative charge transfer influenced by the Fe-O hybridization in Ba1−xLaxFeO3−δ are hardly available. Doping La induces cation vacancies and Fe reduction, creating nanorod decorated surface after the high-temperature treatment. Conductivity studies expose the rate-limiting steps for hydrogen oxidation reaction (HOR) and oxygen reduction reaction (ORR) as the ohmic resistances and Ba segregation effects. Among the samples studied, Ba0.9La0.1FeO3−δ performs better at 800 °C with an activation energy of ∼0.35 eV under both oxidizing and reducing atmospheres. Surface analysis after EIS reveals Fe and O with different oxidation states that enhance the total conductivity. The amount of hydroxyl species retained (23.66% for Ba0.9La0.1FeO3−δ ) and the ratio of the adsorbed to the lattice oxygen (15.33% for Ba0.9La0.1FeO3−δ ) gives insight on HOR and ORR activities. Also, computational studies validated the negative charge transfer mechanism of the samples under thermally assisted oxidation. The results indicate Ba0.9La0.1FeO3−δ as a tuneable electrode for solid oxide cells.

Time-resolved Spectroelectrochemical Investigation of Organic Mixed Conductors.

Organic mixed ionic and electronic conductors (OMIECs) are an emerging class of materials that have been applied for a wide range of electrochemical applications. Due to the complexity inherent to the ionic-electroniccoupling, understanding the underlying mechanisms involved in the OMIEC operation is an exciting and very lively research field. In this work, we highlight the use of time-resolved Vis-NIR spectroelectrochemistry tocharacterize these materials. We discuss an example, where we show that by combining this tool with spectraldecomposition, we are able to understand fundamental aspects of the doping in an OMIEC film. The methodswe present here can be generalized and used to characterize any electrochromic material.

Interplay between cation composition and charge transport characteristics in GAxFAyMA1-x-yPbI3 halide perovskites

Halide perovskites (HPs) are a well-known class of mixed electronic and ionic conductors with diverse applications in optoelectronic devices. The simultaneous transport of ionic and electronic carriers has beneficial and detrimental effects depending on the intended applications. There is an extensive understanding of the charge transport characteristics in HPs since the phenomenon is of applied relevance. However, considering that several applications use compositions containing mixed cations, a deeper understanding of how the degree of substitution and the characteristics of the substituent cations affect the charge transport characteristics is needed. To this end, we experimentally studied the ionic conductivity (σion), current–voltage hysteresis (J–E hysteresis), mobility (μe) and density (ne) of electronic carriers, and bandgap energies (Eg) of up to 24 compositions of methylammonium lead iodide partially substituted with guanidinium and formamidinium. The results indicate that σion, J–E hysteresis, and μe decrease with the degree of substitution, with the J–E hysteresis being smaller the larger size of the substituent cation. At the same time, σion appears to be lower in compositions with equimolar substituents, in which the entropy of mixing is maximum. On the other hand, a slight increase in ne was observed with the substitution degree, showing highest values for FA+-rich compositions, where Eg is the lowest. The results advance the understanding of how it is possible to customize charge transport properties through the rational design of compositions in HPs.

Review on Fe-based double perovskite cathode materials for solid oxide fuel cells

As a clean and efficient energy conversion device, solid oxide fuel cells have been garnering attention due to their environmentally friendly and fuel adaptability. Consequently, they have become one of the current research directions of new energy. The cathode, as the electrochemical reaction site of an oxidation atmosphere in solid oxide fuel cells, plays a key role in determining the output performance. In recent years, the development of double perovskite cathode materials with mixed ionic and electronic conductors has made significant progress in intermediate-temperature (600-800 °C) fuel cells. These materials have the potential to deliver higher power densities and improved stability, making them promising candidates for future fuel cell applications. The Fe-based double perovskite structure cathode material has gained extensive attention due to its adjustable crystal structure and performance, as it has A(A’) or B(B’) positions in its AA’BB’O6 structure. This material has several advantages, such as high oxygen catalytic activity, low thermal expansion coefficient, and compatibility with the thermal expansion of the electrolyte. An increasing number of researchers have been exploring the performance reaction mechanism of double perovskite by modifying and adjusting its material microstructure, crystal structure, and electronic structure. In this paper, the research progress of LnBaFe2O5 and Sr2Fe2-xMoxO6 double perovskite cathode materials is reviewed to highlight the effects of various modification methods developed on electrochemical performance of these materials. Furthermore, the potential future research directions of double perovskite cathode materials are prospected.

Transmission line revisited - the impedance of mixed ionic and electronic conductors.

This contribution provides a comprehensive guide for evaluating the one-dimensional impedance response of dense mixed ionic and electronic conductors based on a physically derived transmission line model. While mass and charge transport through the bulk of a mixed conductor is always described by three fundamental parameters (chemical capacitance, ionic conductivity and electronic conductivity), it is the nature of the contact interfaces that largely determines the observed impedance response. Thus, to allow an intuitive adaptation of the transmission line model for any specific measurement situation, the physical meanings of terminal impedance elements at the ionic and electronic rail ends are explicitly discussed. By distinguishing between charge transfer terminals and electrochemical reaction terminals, the range of possible measurement configurations is categorized into symmetrical, SOFC-type and battery-type setups, all of which are explored on the basis of practical examples from the literature. Also, the transformation of an SOFC electrode into a battery electrode and the relevance of side reactions for the impedance of battery electrodes is discussed.

The dynamic nature of electrostatic disorder in organic mixed ionic and electronic conductors.

Charge dynamics in disordered media is described invariably assuming that the energy landscape for hopping site energy is stationary. Within the same framework, the correlation between low electronic disorder and high charge mobility is considered extremely robust, despite the emergence of materials with mixed ionic and electronic conductivity (OMIECs) that display high mobility coexisting with large disorder. We show in this work that the disorder of OMIEC polymers is highly dynamical, i.e. the on-site energy for charge transport fluctuates with a characteristic time comparable with that of electron transport. Under these conditions, the disorder of the "frozen" system is not relevant for the charge carrier, whose dynamics are instead controlled by the underlying dynamics of the material. Deep traps exist but have a finite lifetime. The combination of classical simulations and quantum chemical calculations on the nanosecond timescale seems ideal to disclose and characterise the phenomenon.

Solar-Powered Water Electrolysis Using Hybrid Solid Oxide Electrolyzer Cell (SOEC) for Green Hydrogen—A Review

The depletion of fossil fuels in the current world has been a major concern due to their role as a primary source of energy for many countries. As non-renewable sources continue to deplete, there is a need for more research and initiatives to reduce reliance on these sources and explore better alternatives, such as renewable energy. Hydrogen is one of the most intriguing energy sources for producing power from fuel cells and heat engines without releasing carbon dioxide or other pollutants. The production of hydrogen via the electrolysis of water using renewable energy sources, such as solar energy, is one of the possible uses for solid oxide electrolysis cells (SOECs). SOECs can be classified as either oxygen-ion conducting or proton-conducting, depending on the electrolyte materials used. This article aims to highlight broad and important aspects of the hybrid SOEC-based solar hydrogen-generating technology, which utilizes a mixed-ion conductor capable of transporting both oxygen ions and protons simultaneously. In addition to providing useful information on the technological efficiency of hydrogen production in SOEC, this review aims to make hydrogen production more efficient than any other water electrolysis system.

Developing ABO3 perovskites synthesized by the Pechini method for their potential application as cathode material in solid oxide fuel cells: Structural and electrical properties

In this research, the effect of La substitution by Pr cation in the A-site of ABO3 perovskites was carried out using the Pechini method for use in solid state fuel cells (SOFCs). The atomic compositions of Pr varied from x=0.35, 0.49, 0.53, 0.56, 0.63 and 0.7 in the La0.7−xPrxCa0.3MnO3 (LPCM) perovskites. The XRD patterns indicated that all the perovskites crystallized in the orthorhombic system with Pnma space group, but only in atomic compositions of 0.53 and 0.70 is possible to obtain pure phases; whereas the other compositions present narrow peaks of La and Pr oxides that are reduced with the amount of the cationic substitution. The Rietveld methodology and its analysis by the Goldsmith tolerance factor indicated that the stability of the samples was achieved through Jahn-Teller distortion in the b-axis. The Mn3+/Mn4+ atomic ratios determined by XPS measurements suggested that the substitution of La ions by Pr promotes the hole doped system instead of electron system. The electrical conductivity showed that the synthesized perovskites are mixed ionic and electronic conductors which positively influence their application in SOFCs. In particular, the La0.17Pr0.53Ca0.3MnO3 may be a good cathode candidate for these devices.

Predicting Fast Oxygen Ion Conductors Via Descriptors for Migration Barrier Based on Electronic Structure and Lattice Dynamics

Solid-state oxygen ion conductors are of paramount importance to solid oxide fuel cells and electrolytic cells. However, with the oxygen ion conductors proposed to date, these technologies require too high (close to 800 oC) temperatures to operate, leading to technological challenges and high costs. Therefore, it is of primary importance to design faster oxygen ion conductors at intermediate and low temperatures (below 400 oC) that can enable sustainable energy technologies to mitigate climate change. Descriptors for oxygen ion conduction are highly desirable to identify promising materials, which can be done by leveraging fast-growing statistical and machine learning approaches for screening of material databases [1]. Recently, computational tools combined with experiments have allowed researchers to gain atomistic insights and relate ion transport to features of the lattice dynamics [2] and electronic structure [3] of a given material. In this work, building upon the previous literature, we leverage both the lattice dynamics and electronic structure to predict the migration barrier for oxygen migration in pure and mixed electronic ionic conductors and search for promising oxygen ion conductors.Using density functional theory simulations, we model oxygen migration in perovskite, rutile, fluorite, and Ruddlesden-Popperoxides. We analyze oxygen ion transport in pure and mixed electronic ionic conductors and oxygen vacancies with and without charge. We study changes in the electronic structure during oxygen migration within the solid host lattice in different oxides. By analyzing trends of migration barrier and electronic density of states, we relate the migration barrier to the electronic structure of the transition state. Our results show that the migration barrier depends on the capability that the host lattice has of screening charge associated with the mobile ion in the transition state, which if increased would lower the localization of charge around the mobile ion and in turn the oxygen migration barrier. In pure ionic conductors – where no charge is associated with the mobile ion - the migration barrier is largely dependent on the M-O strength. Based on the mechanistic understanding derived by these initial analyses, we further relate oxygen ion conductivity to the lattice dynamics. We show that in pure ionic conductors, increasing migration barrier follows trends of increasing oxygen vibrational frequency based on phonon-electron coupling, which also relates the prefactor of Arrhenius law with the migration barrier. However, when trying to predict trends of the migration barrier across different crystal structures or mixed ionic conductors, no single descriptor can capture the complex physiochemistry behind oxygen migration. Thus, we leverage statistical learning tools to identify multivariate descriptors and analyze specific features of lattice moieties that improve oxygen ion conduction. The results of this work provide mechanistic understanding of oxygen ion migration and strategies to accelerate the designs of fast oxygen ion conductors.

(Invited) Redox Chemistry Driven by Atmospheric Pressure Plasma Jet

Plasmas may be considered as mixed ionic and electronic conductors. From an electrochemical point of view, a conducting gas presents a wonderful opportunity to explore redox reactions without all the restrictions a solvent medium provides. Identifying a plasma medium suitable to allow electrochemical measurements can be technically challenging, often due to the electrical energy used to create the plasma. However, atmospheric pressure plasma jets (APPJ)1&2 have been shown to be accessible and convenient as laboratory plasma sources. They present a medium that may be considered as an electrode, due to the presence of electrons or as electrolytes, due to their electrical conduction.3 Although its definition is not too important, the presence of free electrons gives an opportunity to drive reduction processes.The interesting aspect of non-thermal plasmas, and the root of their interesting chemistry, is partly due to the imbalance of thermal kinetic energy distribution between the electron and all the other species, neutral or ionized. As a consequence plasma jets are found in routine industrial applications such as etching or cleaning of surfaces for adhesion promotion. Furthermore, there is a growing body of evidence to suggest that APPJ may be used for the treatment of solid tumors. These highly energized electrons can drive redox reactions, as well as other chemical reactions, at solid or liquid can be unexpected. In this presentation I will explore the use of APPJ for reduction of metal oxides under potentiostatic control and material synthesis.4-6 References Ratcliffe, L.V., et al., Surface analysis under ambient conditions using plasma-assisted desorption/ionization mass spectrometry. Analytical Chemistry, 2007. 79(16): p. 6094-6101.Golda, J., et al., Concepts and characteristics of the 'COST Reference Microplasma Jet'. Journal of Physics D-Applied Physics, 2016. 49(8).Rumbach, P.; Bartels, D. M.; Sankaran, R. M.; Go, D. B., The solvation of electrons by an atmospheric-pressure plasma. Nature Communications 2016, 6, 7248.Sener, M. E., Quesada Cabrera, R., Parkin, I.P., Caruana, D. J., Facile formation of black titania films using an atmospheric-pressure plasma jet, Green Chemistry 2022 , 24, 2499-2505.Sener, M. E., Palgrave, R., Quesada Cabrera, R., Caruana, D. J., Patterning of Metal Oxide thin Films using H2/He Atmospheric Pressure Plasma Jet. Green Chemistry 2020, 22, 1406-1413.Sener, M. E.; Caruana, D. J., Modulation of copper(I) oxide reduction/oxidation in atmospheric pressure plasma jet. Electrochemistry Communications 2018, 95, 38-42.

Correlation between conductivity and structural parameters in Sr-doped LaMO3 (M = Al, Ga, In, Er, and Y) for solid oxide membranes

To understand the effect of the B site species in La-based perovskites, the electrical conductivity of La0.9Sr0.1MO3-δ (M = Al, Ga, In, Er, and Y) was studied under varying oxygen partial pressures ranging from 600 and 800 °C under humidified and dry conditions. The oxygen-ion conductors La0.9Sr0.1AlO3-δ and La0.9Sr0.1GaO3-δ exhibited no significant change in conductivity under humidified and dry conditions. In contrast, the mixed-ion conductor La0.9Sr0.1InO3-δ (LSI) and proton conductors La0.9Sr0.1ErO3-δ (LSEr) and La0.9Sr0.1YO3-δ (LSY) exhibit relatively significant changes under humidified and dry conditions. In addition, the conductivities of LSEr and LSY could be affected by the concentration of CO used to reduce the conductivity. Finally, this study demonstrated that as the unit cell volume divided by Z increased, the ionic conductivity changed from an oxygen ion conductor to a mixed conductor, and finally to a proton conductor.

The Influence of Regiochemistry on the Performance of Organic Mixed Ionic and Electronic Conductors.

Thiophenes functionalised in the 3-position are ubiquitous building blocks for the design and synthesis of organic semiconductors. Their non-centrosymmetric nature has long been used as a powerful synthetic design tool exemplified by the vastly different properties of regiorandom and regioregular poly(3-hexylthiophene) owing to the repulsive head-to-head interactions between neighbouring side chains in the regiorandom polymer. The renewed interest in highly electron-rich 3-alkoxythiophene based polymers for bioelectronic applications opens up new considerations around the regiochemistry of these systems as both the head-to-tail and head-to-head couplings adopt near-planar conformations due to attractive intramolecular S-O interactions. To understand how this increased flexibility in the molecular design can be used advantageously, we explore in detail the geometrical and electronic effects that influence the optical, electrochemical, structural, and electrical properties of a series of six polythiophene derivatives with varying regiochemistry and comonomer composition. We show how the interplay between conformational disorder, backbone coplanarity and polaron distribution affects the mixed ionic-electronic conduction. Ultimately, we use these findings to identify a new conformationally restricted polythiophene derivative for p-type accumulation-mode organic electrochemical transistor applications with performance on par with state-of-the-art mixed conductors evidenced by a μC* product of 267 F V-1 cm-1 s-1 .

The Influence of Regiochemistry on the Performance of Organic Mixed Ionic and Electronic Conductors.

Thiophenes functionalised in the 3-position are ubiquitous building blocks for the design and synthesis of organic semiconductors. Their non-centrosymmetric nature has long been used as a powerful synthetic design tool exemplified by the vastly different properties of regiorandom and regioregular poly(3-hexylthiophene) owing to the repulsive head-to-head interactions between neighbouring side chains in the regiorandom polymer. The renewed interest in highly electron-rich 3-alkoxythiophene based polymers for bioelectronic applications opens up new considerations around the regiochemistry of these systems as both the head-to-tail and head-to-head couplings adopt near-planar conformations due to attractive intramolecular S-O interactions. To understand how this increased flexibility in the molecular design can be used advantageously, we explore in detail the geometrical and electronic effects that influence the optical, electrochemical, structural, and electrical properties of a series of six polythiophene derivatives with varying regiochemistry and comonomer composition. We show how the interplay between conformational disorder, backbone coplanarity and polaron distribution affects the mixed ionic-electronic conduction. Ultimately, we use these findings to identify a new conformationally restricted polythiophene derivative for p-type accumulation-mode organic electrochemical transistor applications with performance on par with state-of-the-art mixed conductors evidenced by a μC* product of 267 F V-1 cm-1 s-1.

Measurement of electronic conductivity in mixed ionic and electronic conductor (MIEC) via a novel embedded microcontact method

Electronic conductivity plays an important role on the performance and durability of energy devices containing mixed ionic and electronic conductors (MIEC). Over the past decades, it has been realized that the classical Hebb-Wagner(H-W) method has some critical limitations or issues that may limit its accuracy or testing feasibility, such as relatively long relaxation time towards steady state and challenges on sealing. In this study, we reported an embedded microcontact ionic blocking electrode to minimize these issues. Using this method, the activation energy in Ce0.9Gd0.1O1.95 (GDC10) are measured, respectively as, 2.51 and 1.44 eV, for n type electronic and p type hole conductivity. The values are similar to those reported in literature as 2.51 and 1.45 eV, respectively, for n and p type conduction also in GDC10 via non-embedded ionic-blocking electrode. At a refence oxygen partial pressure of 0.21 atm, the n type conductivity, σe(0), is obtained as 1.05×10−7, 2.81×10−6, 4.28×10−5 S cm−1 at 600, 700, and 800 °C, respectively, and the p type conductivity, σh(0), is obtained as 1.18×10−4, 5.86×10−4, 3.51×10−3 S cm−1 at 600, 700, and 800 °C, respectively. The new method could be an effective technique to determine electronic conduction in other MIECs.

Resonant X-ray Diffraction Reveals the Location of Counterions in Doped Organic Mixed Ionic Conductors

Resonant X-ray Diffraction Reveals the Location of Counterions in Doped Organic Mixed Ionic Conductors

Garnet-type solid-state mixed ionic and electronic conductor

Low ion and electron conductivities of the cathode and poor cathode interface performance severely limit the application of garnet solid-state batteries. While various approaches have been developed to improve the cathode interface contact or enhance ion and electron transport, none of these methods can simultaneously achieve high interfacial electrochemical activity and chemical stability. In this work, we propose to develop a single-phase garnet-type mixed ionic and electronic conductor (MIEC) as the cathode framework, which is expected to achieve the unification of high activity and high stability at the cathode interface. Combining first-principles calculations and ultrafast sintering techniques, we have synthesized and screened a series of garnet-type MIECs by introducing transition metals into garnet SSEs. Among the garnet-type MIECs, Li43Fe3La24Zr12Ta4O96 (3Fe) not only exhibits an excellent electronic conductivity of up to 2.87 × 10−4 S cm−1 but also maintains an ionic conductivity of 4.57 × 10−5 S cm−1. The high electronic conductivity is believed to originate from the high-temperature reduction phase formed during the rapid sintering process under inert conditions. A small polaron hopping mechanism is proposed to explain the electronic conductivity based on electronic structure calculations and activation energy analysis. Since garnet-type MIECs have the same crystal structure as garnet solid-state electrolytes (SSEs) and transition metal elements similar to those of oxide cathode materials, they potentially have good cosintering stability with both electrolytes and cathodes. This work provides a new strategy to solve the cathode interface problem in garnet solid-state batteries.

Scaling studies of temperature dependence of electric conductivity and electric modulus spectra of solid solution Sr2-xLaxSnO4 (x ≤ 0.10) Ruddlesden Popper Oxide

The mixed ionic and electronic conductor oxide with formula Sr2-xLaxSnO4 (S2LS) within x ≤ 0.10 were synthesized via the conventional ceramic route and investigated. The structural analysis revealed the formation of single-phase materials with a tetragonal crystal structure. The presence of Sn in the form of Sn4+/Sn2+ ions and oxygen vacancies in the synthesized samples were investigated by X-ray photoelectron spectroscopy. The alternating current (AC) conductivity and modulus spectra of S2LS systems were obtained as functions of frequency and temperature and further scaled. The AC conductivity data were analyzed using Jonscher's power law (JPL) fitting to determine the hopping frequencies, DC conductivities, and power exponents. The obtained activation energy value suggests the dependence of conductivity primarily on the mobility of charge carriers. The conductivity spectra were analyzed using various formalisms, viz., Ghosh scaling and Rolling scaling, to understand the conduction mechanism. The scaling behaviors of AC conductivity and modulus spectra reflect the temperature-independent conduction mechanism of the system.