Sodium (Na) Super (S) Ionic (I) Conductors (CON) (or NASICONs, for example Nai+xZr2 Pj-xSixOi?) are crystalline solids А1В2(Р04)з, where A is a monovalent cation and В is either a single or combination of tri, tetra, and penta valent ions. These compounds are a class of structurally isomorphous 3D framework compounds possessing high conductivity, often comparable to that of liquid electrolytes at higher temperatures. The high ionic conductivity of these materials is used in making devices such as membranes, fuel cells, and gas sensors. Advantages of IS method for such materials’ investigation consist in the fact that it comes down to measuring the response of the system to very weak external influences (polarization by AC), deviating the system from equilibrium; therefore, in the process of measurements there is a noticeable change in solid electrolyte. Ionic conductivity of NASICONs even at room temperature is quite high (-KT4 -1(T3 S/cm), which allows to uniquely interpret hodo- graphs of impedance.

In Ahmadu, Tomas, Jonah, Musa, and Rabiu (2013), impedance spectra of mixed alkali Na0 2sLi0 75Zr2(P04)3 were modeled based on an equivalent electric circuit consisting of resistor (R) and capacitance (Q elements. Polycrystalline materials are known to exhibit intragrain and grain boundary impedances and thus they can be represented by the equivalent circuit shown in Figure 3.15. The circuit has two RC elements joined together in series representing the grain (Rg, Cg) and grain boundary (Rgb, Cgb) (Figure 3.16).

Figure 3.17 shows the frequency dependence of the imaginary part of impedance (Z'j at different temperatures. Only one prominent peak is observable at each temperature and it systematically shifts toward higher frequencies with increase in temperature after an initial decrease. This implies a thermal activation of the conductivity relaxations that are within a decade of frequency (1.55 x 107—2.32 x Ю6 Hz) in the temperature range (470- 600K). The electrical conductivity and dielectric behavior of Na0 25Li0 ^sZ^PO^j was investigated in the GHz range of frequency using a model RC circuit (Figure 3.15). The values that authors received for activation energy for the grain boundary and bulk were ~0.40 and 0.36 eV, respectively. Similarly, the maximum conductivity obtained for the bulk was 0.3 S/m, which compares favorably with typical NASICON materials. The dielectric permittivity e' showed

Model RC circuit for polycrystalline materials

FIGURE 3.15 Model RC circuit for polycrystalline materials.

Reproduced from Ahmadu ct al., 2013, Diamond Open Access Publishing Policy

Presenting the grain (R, C) and grain boundary (J?, C)

FIGURE 3.16 Presenting the grain (Rg, Cg) and grain boundary (J?gb, Cgb).

Complex plane plots (Z" vs. Z') at different temperatures. Reproduced from Ahmadu et al., 2013, Diamond Open Access Publishing Policy

FIGURE 3.17 Complex plane plots (Z" vs. Z') at different temperatures. Reproduced from Ahmadu et al., 2013, Diamond Open Access Publishing Policy.

a non-Debye behavior and has maximum value of 136, which is high in comparison with the most reported values for this family of compounds. Complex nonlinear least squares fitting results indicate a good fit to composite equivalent circuit parameters. Moreover, further fitting using the generic battery model suggests the material could be potential solid electrolyte material for lithium ion rechargeable battery applications due to the quality of the fitting parameters obtained. Thus, in electrochemical studies of solid electrolytes, IS plays a huge role, and its capabilities with the advent of modern devices significantly increase. But a variety of responses should be taken into account depending on the nature of the sample being studied and set of experimental conditions. Information on the microstructure and composition of the solid electrolyte gives the opportunity to make a choice in favor of one or another equivalent circuit for the interpretation of the impedance spectrum.


Electroceramics are high technology materials whose properties and, hence, applications depend on a complex interplay of structural, processing, and compositional variables. The particular property of interest may be a bulk property of the crystals, in which case, fully dense ceramics free from grain boundary phases are desired. Good examples of this are ceramic electrolytes such as Na 8-alumina, Na20- 8A1203, used as an Na+ ion conducting membrane in Na/S batteries and YSZ, 0.9(Zr02)0.1(Y203), used as an oxide ion conducting membrane in SOFCs and oxygen sensors.

Surface layers on electroceramics are often found on electroceramics. A good example of objects where we can study surface layers, are glasses. Glass is a solid solution obtained by cooling a molten mixture of silicates and metal oxides and having the mechanical properties of solids. The composition of the glass includes various oxides: SiO2iNa20, CaO, MgO, B203. A1203, and others. Among the types of inorganic glasses (borosilicate, borate, etc.), a particularly large role in practice belongs to silica-fused glasses - silicate glasses. The simplest composition is glass obtained by melting pure silica to form a vitreous mass.

A good example is provided by lithium silicate (Irvine, Sinclair, & West, 1990). Although this transparent glass is apparently atmosphere-stable and water-insoluble, it does in fact form a hydrated/carbonated surface layer very quickly during cooling of the melt. This shows up in the impedance spectrum (see Figure 3a in Irvine et al., 1990) as an additional poorly resolved semicircle. A glass without this layer (see Figure 3b in Irvine et ah, 1990) shows only one semicircle, corresponding to lithium ion conduction through the bulk of the glass and a nearly vertical, low frequency “spike” representing charge build-up at the blocking metal electrodes.

Using IS, it is possible to study the conditions for formation/removal of the surface layer and the associated kinetics. For example, by analyzing the impedance spectra of electrically conductive ceramics based on two-component oxide ionic conductors of the СаО-АЬОз system by the quantities related to intragranular, it is possible to distinguish conductivity and electrical conductivity through grain boundaries. As an example, in Irvine, Sinclair, and West (1990), Figure la presents impedance diagrams for oxygen-ion conductor Са12А114Оз3. Each semicircle in the diagram corresponds to a parallel combination capacitance and resistance. The numerical values of the resistances can be obtained from the points of intersection of the circle with the Z axis, and the capacitance values can be obtained from the equation for the maximum frequency value /max = RCco. For correlation between experimental values of capacity and theoretically expected for certain processes, we can use Table 3.3. Thus, in the given example, the left semicircle, for which the experimental value of C is 1 x 10-12 F corresponds to the volumetric resistance of individual grains of the sample. Right semicircle with value C = 4 x 10-9 F characterizes the resistance of grain boundaries. Using these quantities, it is possible to construct the temperature dependences of the volumetric and grain-boundary conductivity of the sample. Thus, using IS, conditions and kinetic patterns of formation or removal of the surface layer can be studied.

Perovskite family lead-free ceramics such as for example Ba(Fe0.5Nbo.5)03 ВаТЮ3 (Meera et al., 2012) has been widely studied for their high dielectric and ferroelectric properties in different temperature and frequency ranges, up to about 10 MHz and ~700 K. Similar studies have been carried out on other compositions from this family by some researchers (l-.-)Ba(Feo.5Nbo.5)C>3-.YBaTi03 (Singh, Kumar, & Rai, 2011), Bi(Mgo.5Tio.5)03-PbTi03 (Sharma, Rai, Hall, & Shackleton, 2012), and (Ko.sBio.sXFeo.sNbo^Ch (Sahoo, Pradhan, Choudhary, & Mathur, 2012). Both modulus spectroscopy and dielectric conductivity formalism were employed to study dielectric relaxation phenomena. The temperature dependence of dielectric and loss spectra was investigated. These compounds show a typical negative temperature coefficient behavior like that of semiconductors. The frequency dependence of AC conductivity is well fitted to Jonscher’s single power law.


Mixed conductivity oxides find important applications in SOFCs, both as cathodes and anodes, and in semi-permeable membranes for (partial) oxidation reactions. A very important aspect of these applications is the transfer and reduction of the amount of oxygen in the environment at the gas/solid interface or vice versa. The general transfer reaction can be represented as 02g + 4c' + 2F(f ♦--* 2Ox0. The article (Boukamp, Hildenbrand, Nammensma, &

Blank, 2011) evaluates the effects of layer thickness, oxygen diffusion, and surface exchange rate on the general finite length diffusion. A simple model was obtained for the impedance of a dense La0 6Sr0 4Co0 2Fe0 803^ (LSCF) cathode with different thickness deposited by pulsed laser deposition (PLD) on 2.5 mm thick Ce0.9Gdo.iOi 95 pellets in a three-electrode arrangement. The PLD was performed with a KrF excimer laser, using a fluency of 2.6 J/cnr and a frequency of 20 Hz. The LSCF target was an isostatically pressed pellet on a rotating holder.

The laser ablation occurred in a vacuum chamber in 0.02 mbar oxygen ambient. The CGO substrates were heated to 750°C during deposition. The reference electrode was provided by a Pt- wire bonded with a little Pt-ink into a groove at half height at the cylindrical side of the pellet. For the counter electrode, a similar PLD layer with ditferent thickness was applied. The proper derivation of the impedance of such an arrangement of electrodes is not yet available in the literature. The impedance is obtained for an electrode with a dense layer of mixed conductive oxide, provided that the electronic resistance can be ignored. The effect of layer thickness on electrode properties and some preliminary results on the addition of chromium are also presented. Analysis of the surface shows that the PLD process easily leads to significant contamination of the Cr surface of the LSCF. An analysis of EIS shows that the effect on the exchange rate of this Cr contamination is still negligible. The use of a porous Pt-counter electrode is not advisable, as the electrode properties are inferior to the LSCF electrodes and will result in a strong pseudo-inductive artifact in the impedance (see Figure 3.18).

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