Enhanced conductivity in ionic conductor-insulator composites: numerical models in two and three dimensions

We describe a two-dimensional (2D) and a three-dimensional (3D) percolation model for ionic conductor-insulator composites such as copper(I) bromide-titanium dioxide (CuBr-TiO₂) or lithium iodide-alumina (LiI-Al₂O₃). These composites present an enhanced conductivity closely related to the insulator concentration. This effect is explained by the formation of highly conducting space charge regions near the phase boundaries which are represented by good conductor bonds. Our numerical model takes into account grain size and correlation effects. The dimension has a leading role for the conduction properties. In the 2D case, the good conductor bonds do not percolate, whatever the insulator concentration, and the maximum conductivity of the composite samples is of the same order as that of the ionic conductor grains. The behavior of the system is very different in the 3D case where, for a large domain of composition, the good conductors percolate through the regions between the conductor grains. For the CuBr-TiO₂ composites the conductivity versus composition curve is bell-shaped. Conversely, in the LiI-Al₂O₃ system, a linear relation between the conductivity and the insulator volume fraction is obtained in the experiments. Our model gives a plausible interpretation of the conductivity in both systems. Received 10 April 2001     

A Mixed-Transfer-Matrix Method for Simulating Normal Conductor/Perfect Insulator/Perfect Conductor Random Networks

We develop a mixed-transfer-matrix approach for computing the macroscopic conductivity of a three-constituent normal conductor/perfect insulator/perfect conductor random network. This is applied to two-dimensional and three-dimensional samples at a percolation threshold. Such networks are simulated in order to test whether a diluted percolating network of normal conducting bonds remains in the same universality class of critical behavior when a finite fraction of those bonds have been replaced by perfectly conducting bonds. Also tested by such simulations is whether a percolating mixture of normal and perfectly conducting bonds remains in the same universality class of critical behavior when a finite fraction of the normal bonds are replaced by perfectly insulating bonds. These questions are crucial for some recently published exact results which connect the macroscopic electrical and elastic responses of percolating networks.     

Alkali metal ion-poly (ethylene oxide) complexes. II. Effect of cation on conductivity

Complexes of alkali metal salts with various polymers have for some time been recognized as fast ionic conductors. Polymer electrolyte fast ion conductors are currently under consideration for use in high energy density electrochemical cells. In order to aid in our understanding of the mechanism of ionic conductivity we have examined systematically complexes of poly(ethylene oxide) (PEO) with the alkali metal salt series of Li⁺, Na⁺, K⁺, Rb⁺ and Cs⁺ with both tetraflouroborate (BF₄^-) and trifluoromethanesulfonate (CF₃SO₄^-) anions. The ratio of monomer to salt was 10:1 in all cases. Complex impedance measurements were made on all samples in the temperature range 40°–125°C. With CF₃SO₄^- as the anion a definite trend was apparent with the smallest cation Li⁺ being the worst conductor and Cs⁺, the largest cation, being the best. When BF₄^- salts are used, the Na⁺ complex is found to be the best conductor and Rb⁺ the worst. This study, in connection with our earlier studies, has shown that synergy between cation and anion in the polymer matrix is an important consideration in determining the ionic conductivity.     

Universal microstructure and conductivity relaxation of polymer-conductor composites across the percolation threshold

Micro-structural and impedance analysis of series of insulating polymer/conductor composites (PCC) as a function of frequency and volume fractions of the conductor (f_con) have been studied. Evidences of conductivity relaxation have been noticed with a correlation with the sample micro-structure. This has been understood and explained in terms of equivalent electrical circuit model of the material established through complex impedance spectroscopy (CIS) across the percolation threshold (f_c) for all the PCC. CIS analysis confirmed that PCC with f_con ≥ f_c, exhibit conductivity/interfacial relaxation due to polarization of Maxwell–Wagner–Sillars (MWS) type at f_c and the relaxation frequency increases with increase of f_con. The modulus spectroscopy analysis suggests the presence of two types of relaxations in different frequency ranges; (i) dipolar relaxation associated with the flipping of dipoles present in the pure polymer for f_con < f_c and (ii) the conductivity/interfacial relaxation due to the formation of artificial MWS dipoles at the interface of the two components. A long range dc conductivity appears at f_con ≥ f_c and Jonschers universal fractional power law is satisfied for both the regions of f_con < f_c and f_con ≥ f_c in all PCC.     

Anomalous phenomenon of conductivity of the amorphous fast ionic conductor B2O3−0.7Li2O−0.7LiCl during the crystallization process

This paper presents a new experimental method for studying the effect of crystallization of amorphous fast ionic conductors on conductivity, which includes heating the specimen to the selected temperature and annealing the specimen within a fixed time, quenching the specimen in order to freeze its high temperature structure, then returning to a fixed temperature and measuring the conductivity. This method gets rid completely of the effect of temperature on conductivity and thus the effect of structure on conductivity can be studied. It has been found with this method for the first time that during the crystallization process the conductivity of amorphous fast ionic conductor B₂O₃-0.7Li₂O-0.7LiCl increases at the beginning with temperature, and then after passing a maximum, the conductivity decreases. This result coincides with that of the relative rate of crystallization obtained by the author with X-ray diffraction technique at the same temperature range. The interface at the crystalline and amorphous two-phase boundary is thought to be responsible for the anomalous phenomenon.     

Broadband dielectric spectroscopy of inhomogeneous and composite weak conductors

ABSTRACT

In this paper, we discuss broadband dielectric spectroscopy from mHz up to the infrared range mainly for materials with inhomogeneous weak conductivity, including conductor-dielectric nanocomposites. Our discussion is based on the effective medium approximation (EMA) and experiments modeled by this approach are reviewed. We discuss core–shell composites modeled by coated-spheres (Hashin–Shtrikman model) and normal composites with a possible percolation of the conductor component resulting in sharp or smeared percolation threshold of the DC conductivity and diverging static permittivity in the former case. The sharp percolation threshold is modeled by the Bruggeman EMA or by general EMA with arbitrary percolation threshold and arbitrary critical exponents of the DC conductivity and static permittivity. For the case of smeared percolation threshold in the case of complex topologies, we use the Lichtenecker model allowing for partial percolation of both the components. Finally, numerous papers reporting negative permittivity in weakly conducting materials are criticized and concluded to be due to spurious effects.     

Electrochemical promotion of a metal catalyst supported on a mixed-ionic conductor

It has been found that the catalytic activity and selectivity of a metal film deposited on a solid electrolyte could be enhanced dramatically and in a reversible way by applying an electrical current or potential between the metal catalyst and the counter electrode (also deposited on the electrolyte). This phenomenon is know as NEMCA [S. Bebelis, C.G. Vayenas, Journal of Catalysis, 118 (1989) 125–146.] or electrochemical promotion (EP) [J. Prichard, Nature, 343 (1990) 592.] of catalysis.Yttria-doped barium zirconate, BaZr_0.9Y_0.1O_3 − α (BZY), a known proton conductor, has been used in this study. It has been reported that proton conducting perovskites can, under the appropriate conditions, act also as oxide ion conductors. In mixed conducting systems the mechanism of conduction depends upon the gas atmosphere that to which the material is exposed. Therefore, the use of a mixed ionic (oxide ion and proton) conducting membrane as a support for a platinum catalyst may facilitate the tuning of the promotional behaviour of the catalyst by allowing the control of the conduction mechanism of the electrolyte. The conductivity of BZY under different atmospheres was measured and the presence of oxide ion conduction under the appropriate conditions was confirmed. Moreover, kinetic experiments on ethylene oxidation corroborated the findings from the conductivity measurements showing that the use of a mixed ionic conductor allows for the tuning of the reaction rate.     

Directed spiral site percolation on the square lattice

A new site percolation model, directed spiral percolation (DSP), under both directional and rotational (spiral) constraints is studied numerically on the square lattice. The critical percolation threshold p _c ≈ 0.655 is found between the directed and spiral percolation thresholds. Infinite percolation clusters are fractals of dimension d _f ≈ 1.733. The clusters generated are anisotropic. Due to the rotational constraint, the cluster growth is deviated from that expected due to the directional constraint. Connectivity lengths, one along the elongation of the cluster and the other perpendicular to it, diverge as p → p _c with different critical exponents. The clusters are less anisotropic than the directed percolation clusters. Different moments of the cluster size distribution P _s(p) show power law behaviour with | p - p _c| in the critical regime with appropriate critical exponents. The values of the critical exponents are estimated and found to be very different from those obtained in other percolation models. The proposed DSP model thus belongs to a new universality class. A scaling theory has been developed for the cluster related quantities. The critical exponents satisfy the scaling relations including the hyperscaling which is violated in directed percolation. A reasonable data collapse is observed in favour of the assumed scaling function form of P _s(p). The results obtained are in good agreement with other model calculations. Received 10 November 2002 / Received in final form 20 February 2003 Published online 23 May 2003 RID="a" ID="a"e-mail: santra@iitg.ernet.in     

Percolation with excluded small clusters and Coulomb blockade in a granular system

We consider dc-conductivity σ of a mixture of small conducting and insulating grains slightly below the percolation threshold, where finite clusters of conducting grains are characterized by a wide spectrum of sizes. The charge transport is controlled by tunneling of carriers between neighboring conducting clusters via short “links“ consisting of one insulating grain. Upon lowering temperature small clusters (up to some T-dependent size) become Coulomb blockaded, and are avoided, if possible, by relevant hopping paths. We introduce a relevant percolational problem of next-nearest-neighbors (NNN) conductivity with excluded small clusters and demonstrate (both numerically and analytically) that σ decreases as power law of the size of excluded clusters. As a physical consequence, the conductivity is a power-law function of temperature in a wide intermediate temperature range. We express the corresponding index through known critical indices of the perco lation theory and confirm this relation numerically.     

The optimisation of mixed conduction in potential S.O.F.C. anode materials

The success of the SOFC rests heavily on materials selection. In this work we address the optimisation of mixed conductivity in fluorite compounds in the search for new improved SOFC anodes based upon oxides. The mobility of electronic carriers is considered to be much higher than that of ionic defects, therefore, doping a good ionic conductor with a small concentration of reducible transition metal ions can form promising mixed conductors. Zirconia based mixed conductors were studied for two reasons. Firstly, zirconia, stabilised in the defect fluorite structure, exhibits a high level of ionic conductivity. Secondly it is the most common electrolyte material for a S.O.F.C. An anode based on zirconia would therefore be expected to offer a good physical compatibility with the electrolyte material and to exhibit a high ionic contribution to total conductivity. Work on the system ZrO₂-Nb₂O₅-Y₂O₃ showed that the influence of composition on conduction could be determined. This enabled the optimisation of both the electronic and ionic contributions to conduction by compositional selection. These factors were extended to explain conductivity behaviour observed in the comparable system ZrO₂-TiO₂-Y₂O₃. Paper presented at the 5th Euroconference on Solid State Ionics, Benalmádena, Spain, Sept. 13–20, 1998.     

非晶态Cu+导体分相和晶化行为的XRD和SEM研究

对非晶态Cu⁺快离子导体0.4CuI-0.3Cu₂O-0.3P₂O₅在等温热处理条件下测量离子电导率的同时,进行了X射线衍射(XRD)与扫描电子显微术(SEM)研究。结果表明:初始的非晶态材料是分相的;随着等温热处理,分离的非晶第二相逐渐消失,并发生非晶态晶化;晶态的γ-CuI与Cu₂P₂O₇先后析出,逐渐长大。此材料的分相和晶化行为同电导率反常性的对应,再一次证实了非晶态快离子导体中的相界效应及其普遍意义。 关键词：     

非晶态离子导体Li2B2O4晶化前期的离子导电性

本文研究了非晶态离子导体Li₂B₂O₄的离子电导率与温度的关系,特别着重于晶化前期的离子迁移特性。当温度低于T_K(≈310℃)时,离子电导率遵从Arrhenius关系。当高于晶化温度(≈411℃)时,以晶态中的离子迁移为主。在T_kc时,电导率偏离热激活机制呈反常增高。我们把这一过程称为晶化前期过程。可以用自由体积模型进行描述。晶化前期又可分为两部分:当温度低于、T_p(≈380℃)时,由于自由体积的重新分布,导致了电导率的增高;当T>T_p时,出现了少量微晶,但晶化量小于5%,由于非晶母体与微晶之间的界面效应使得离子导电性显著增强。可以通过室温淬火,把晶化前期非晶态的状态保持到室温,从而有可能制备出离子电导率高于纯非晶态的材料。 关键词：     

Bond percolation with parallelism restriction on square lattices

As a simple approximation for the ±J spin glass we studied bond percolation on square lattices. However, two neighboring chains of ferromagnetic bonds are required for spins to be regarded as connected. We determine the percolation thresholdp _c =0.8282±0.0002 and the critical exponent =0.75 _–0.05 ^+0.02 for this specific percolation by means of Monte-Carlo simulation on square lattices (up to 150×150).     

Superior properties of SmBCO coated conductors at high magnetic fields and elevated temperatures

In addition to the well investigated YBa₂Cu₃O_7?δ (Y-123, YBCO) compound, many other rare earth-123 compounds are candidate materials for the production of coated conductors. Sm-123 seems to be an excellent alternative because of its higher transition temperature (T_c) and higher critical current densities (J_c) in external magnetic fields. Because of the fast decrease of J_c in YBCO at elevated temperatures, especially around the boiling point of liquid nitrogen, the slightly higher T_c can be an important advantage. Recently, significant progress has been made in the production of long length Sm-123 based coated conductors. We report here on transport measurements on these conductors in the liquid nitrogen temperature range. The critical current densities were determined as a function of the applied field and the crystallographic orientation under maximum Lorentz force configuration. A shift of the c-axis (～7°) from the tape normal was found. The conductor properties were compared to those of commercially available YBCO coated conductors. The critical current densities as well as the irreversibility fields are higher in the SmBCO tapes, thus demonstrating the superior properties of the Sm-123 compound.     

Monte Carlo study of phase diagram for correlated site-bond percolation in two dimensions

At the critical point of the square Ising model, the percolation threshold for randomly active bonds between up spins is close top _Bc =0.60 and seems compatible with the predictionp _Bc =1-exp(–2J/k _B T _c )=0.586 of Coniglio and Klein. Longer simulations on larger lattices are necessary for a more precise clarification.     

Physical studies on composites Ag7I4VO4-Al2O3

The electrical properties of the solid electrolytes Ag₇I₄VO₄-Al₂O₃ (0-40 mol% Al₂O₃) are investigated. The electrical conductivity, dielectric constant and dielectric loss are increased by increasing the concentration of Al₂O₃; showing a maximum at 30 mol% Al₂O₃. The conductivity is found to be increased by decreasing the particle size of Al₂O₃. The results are explained using the random resistor network model (RRN). This is due to the formation of a highly conducting interface layer along the matrix-particle interface. This layer is destroyed at concentrations higher than 30 mol% Al₂O₃.     

Nanotechnology studies of layered fluoride superionic conductors

A computer simulation by a molecular dynamics method at constant volume has been performed on a model material that is composed of accumulating two different fluoride conductors: ⋯BaF₂–CaF₂–BaF₂–CaF₂⋯. The average value of CaF₂ and BaF₂ for the lattice constant of the new layered material is prepared to hold its mechanical strength. The CaF₂ region is compressed and the BaF₂ region is stretched along the c axis (z axis) in the thermal equilibrium state. It is obtained that the diffusion coefficient and ionic conductivity of F− ions in the layered fluoride conductors increases with decreasing periods, more specifically with the number of interfaces. The layer depth dependence on transport coefficients approximately coincides with the experiment.     

Alternating current electrical conductivity of high-density polyethylene-carbon nanofiber composites

High-density polyethylene (HDPE)-carbon nanofiber (CNF) composites with good dispersion of fillers in the polymer matrix were melt-compounded in a Haake mixer. The dependences of the alternating current conductivity of such nanocomposites on the filler content, temperature, and DC bias were investigated. The results showed that the electrical conducting behavior of HDPE-CNF nanocomposites can be well characterized by the direct current conductivity ( s_DC \sigma_{{{\rm DC}}}^{} , characteristic frequency (f_c) and critical exponent (s . It was found that s_DC \sigma_{{{\rm DC}}}^{} of percolating HDPE-CNF nanocomposites increases with increasing filler concentration and follows the scaling law of percolation theory. Increasing temperature caused a reduction of s_DC \sigma_{{{\rm DC}}}^{} , leading to the occurrence of positive-temperature-coefficient effect near the melting temperature of HDPE matrix. Application of DC bias led to an increase of s_DC \sigma_{{{\rm DC}}}^{} due to the creation of additional conducting paths within the polymer composites. The characteristic frequency generally followed the same tendency as s_DC \sigma_{{{\rm DC}}}^{} . The s values of percolating composites were slightly higher than those predicted by the percolation theory, indicating the presence of tunneling or hopping conduction in these composites.     

Enhancement of ionic conductivity by dispersed oxide inclusions: Influence of oxide isoelectric point and cation size

Doping of a halide salt by dispersion of oxide particles rather than subtitutional impurities is a proven method of enhancing the extrinsic ionic conductivity of the host. The conductivity mechanism in any space-charge layer at the oxide/host interface is determined by the chemical reactions at the interface. These interactions are discussed by analogy with the particle hydrates. The enhancement of the F⁻-ion conductivity in PbF₂ is predicted to be via F⁻-ion vacancies in the space-charge region and to increase with decreasing oxide isoelectric point and increasing normal anion coordination of the oxide cation. This prediction accounts satisfactorily for the relative enhancement factors measured for PbF₂ containing dispersed CeO₂, SiO₂, ZrO₂ and Al₂O₃.