1. 2 Solid Oxide Fuel Cells 3 Solid oxide fuel cells (SOFCs) offer substantial potential for heat and power generation. They promise to be useful in.

1

2

Solid Oxide Fuel Cells

3

Solid oxide fuel cells (SOFCs) offer substantial potential for heat and power generation. They promise to be useful in large, high-power applications such as full-scale industrial and large scale electricity generating stations. Some fuel cell developers see SOFCs being used in motor vehicles. A SOFC system usually utilizes a solid ceramic as the electrolyte and operates at high temperatures (973–1,273 K) and this high temperature is beneficial for co-generation of both electricity and high-grade heat at user sites, thus, increasing total system efficiency to about 85%.Further, this high operating temperature allows internal reforming, promotes rapid electrocatalysis with non-precious metals, and produces high quality byproduct heat for co-generation.

4

SOFCs are best suited for provision of power in utility applications due to the significant time required to reach operating temperatures. However, high operating temperatures impose restrictions on materials which can otherwise be effectively used for designing a complete device. Lowering of fuel cell performance occurs over a period of time and is related to the deterioration of material properties and interfacial reactions between various fuel cell components.

5

The objective of this presentation is to provide emphasis on materials (electrolytes, electrodes, interconnects), interfacial reactions and cell configurations for SOFC. Interested persons can refer various reviews.

6

History of Solid Oxide Fuel Cells

7

SOFC originated from Nernst glower, initially intended as a light source to replace carbon filament lamps at the end of the 19th century. The device employed, namely, Nernst mass, composed of yttria-stabilized zirconia (YSZ), a predominantly ionic conductor in air. Emil Baur, a Swiss scientist and his colleague H Preis experimented with solid oxide electrolytes in the late 1930s using such materials as zirconium, yttrium, cerium, lanthanum and tungsten oxide. The operation of the first ceramic fuel cell at 1,273 K, by Baur and Preis, was achieved in 1937 using coke and magnetite as fuel and oxidant, respectively. In the 1940s, Davtyan of Russia added monazitesand to a mixture of sodium carbonate, tungsten trioxide and soda glass, in order to increase the conductivity and mechanical strength. Davtyan’s design, however, also experienced undesirable chemical reactions and short-life ratings. By the late 1950s, research into solid oxide technology began to accelerate at the Central Technical Institute in the Hague, Netherlands, at the Consolidation Coal Company, Pennsylvania, USA, and by General Electric, Schenectady, New York, USA. A discussion of fuel cells in 1959 noted the problems associated with solid electrolytes, such as relatively high internal electrical resistance, melting, and short-circuiting due to semiconductivity.The promise of a high-temperature cell that would be tolerant to carbon monoxide and use a stable solid electrolyte continued to draw attention. Intense activity in SOFC research commenced in the 1960s with programmes driven by space, submarine and military applications and basic research mainly increasing conductivity.

8

Researchers at Westinghouse, for example, experimented with a cell using zirconium oxide and calcium oxide in 1962. However, from the mid 1980s, research on SOFC focused on the development of new materials and itstechnological applications in devices.

9

More recently, increasing energy prices and advances in materials technology have induced work on SOFCs, and a recent report noted that about 40 companies were working on these fuel cells. These include Global Thermoelectric’s Fuel Cell Division, which is developing cells designed at the Julich Research Institute in Germany, and Cermatec-Advanced Ionic Technologies, which is working on units upto 10kW in capacity, running on diesel fuel, which would be used for mobile power generation.

10

The US Department of Energy (DoE) announced that an SOFC-microturbine co-generation unit has been evaluated, since April 2000, by the National Fuel Cell Research Center in Edison, Southern California, USA. The fuel cell was built by Siemens Westinghouse and the microturbine by Northern Research & Engineering Corporation. In a year of actual operating conditions, the 220 kW SOFC, running on natural gas, is achieving an efficiency of 60%. Also, a world record forSOFC operation, roughly eight years, still stands, and the prototype cells have demonstrated two critical successes: the ability to withstand more than 100 thermal cycles, and voltage degradation of less than 0.1% per thousand hours. Moreover, a 140kW peak power SOFC co-generation system, supplied by Siemens Westinghouse, is presently operating in The Netherlands. This system has operated for over 16,600 h, becoming the longest running fuel cell in the world. Thefirst demonstration of the commercial prototype cells in a full-scale SOFC module is equally significant. Partners in a technology development program, DoE and Siemens Westinghouse hope to place a 1MW fuel cell co-generation plant in operation within this year.

11

12

SOFC Benefits and Limitations

13

In general, SOFC may be defined as a ceramic multilayer system working at high temperatures and employing gaseous fuel and oxidant. Such characteristics offer a number of advantages over other types of fuel cells and generators. SOFCs also impose a number of various limitations that are responsible for their slow development. The merits and demerits of SOFCs are given in Table 5.2. SOFCs advantages are: they can be modular, they can be distributed to eliminate the need for transmission lines, they operate quietly and they are vibration free. SOFCs could provide higher system efficiency, higher power density and simpler designs than fuel cells based on liquid electrolytes. At low costs, they could compete with combined cycle gas turbines for distributed applications. The high cell operating temperature enables high reactant activity and therefore, facilitates fast electrode kinetics (large exchange currents) and reduced activation polarization. This is especially advantageous as precious platinum electrocatalysts are not required and the electrodes cannot be poisoned by carbon monoxide. As a result, carbon monoxide is a potential fuel in SOFCs. Moreover, the operating temperatures are sufficiently elevated, so performance issues are not related to kinetics (activation over-potentials) but to ohmic losses due to charge transport across components and component interfaces.

14

The benefits of SOFCs also include:

Energy security: reduce oil consumption, cut oil imports, and increase the amount of the country’s available electricity supply.

Reliability: achieve operating times in excess of 90% and power available 99.99% of the time.

Low operating and maintenance cost: the efficiency of the SOFC system will drastically reduce the energy bill (mass production) and have lower maintenance costs than their alternatives.

Constant power production: generate power continuously unlike backup generators, diesel engines or Uninterrupted Power Supply (UPS).

Choice of fuel: allow fuel selection: hydrogen may be extracted from natural gas, propane, butane, methanol or diesel fuel.

15

Until now, SOFCs have been most fuel-efficient, operating at 1,273 K. Unfortunately, this high temperature decreases the cell lifetime and increases the cost of materials substantially, since expensive high temperature alloys are used to house the cell, and expensive ceramics are used for the interconnections. Lowering of operating temperature has been recognized worldwide as the key point for low-cost SOFCs. The reduction in the temperature will therefore allow the use of cheaper interconnecting and structural components such as stainless steel. A lower temperature will also ensure a greater overall system efficiency and a reduction in the thermal stresses in theactive ceramic structures, leading to a longer expected lifetime of the system. It will also make it possible to use cheaper interconnect materials such as ferritic steels, without protective coatings of lanthanum chromate (LaCrO3).The operating temperature 873–1,273 K of the SOFC requires a significant start-up time.

16

17

18

The operating temperature 873–1,273 K of the SOFC requires a significant start-up time. The cell performance is sensitive to operating temperature. A 10% drop in temperature results in ~ 12% drop in cell performance, due to the increase in internal resistance to the flow of oxygen ions. The high temperature also demands that the system include significant thermal shielding to protect personnel and to retain heat.

19

Cell Reactions

20

A single SOFC unit consists of two electrodes (an anode and a cathode) separated by the electrolyte (Fig. 5.1). Fuel (usually hydrogen, H2, or methane, CH4) arrives at the anode, where it reacts with oxide ions from the electrolyte, thereby releasing electrons (e− ) to the external circuit. On the other side of the fuel cell, oxidant (O2 or air) is fed to the cathode, where it supplies the oxide ions (O 2-) for the electrolyte by accepting electrons from the external circuit. The electrolyte conducts these ions between the electrodes, maintaining overall electrical charge balance. The flow of electrons in the external circuit provides useful power. Its typical operating temperature is 1,273 K; the electrolyte is an oxygen-ion conductor, and the free energies (as a consequence, the associated Nernst potential) of the overall reactions are substantially lower than at lower temperatures (43.3 kcal/mol at 1,200K vs 54.6 kcal/mol at 300K for H2). The heat of reaction is almost independent of temperature, therefore the potential (ideal efficiency) is reduced by the high temperature operation.

21

Anode reaction : H2(g) + O2- → H2O(g) + 2e-

Anode reaction : CO(g) + O2- → CO2 (g) + 2e –

Combined anode : aH2(g) + bCO(g) + (a + b)O2- → aH2O(g) + bCO2 (g)reaction + 2(a + b)e-

Overall cathode : 1/2(a + b)O2 (g) + 2(a + b)e − → (a + b)O 2- reaction

Overall reaction : 2(a + b)O 2(g) + aH2 (g) + bCO(g) → aH2O(g) + bCO2 (g)

22

The reversible voltage E ◦ is the maximum that can be achieved by an SOFC under specified conditions of temperature and gas composition. E ◦ can be calculated from the Nernst equation. The voltage of an operating cell E is always lower than E. ◦. As the current is drawn from the fuel cell, the cell voltage falls due to internal resistance and polarization losses. Thus, the voltage of an operating cell is given as

E = E0 − IRi − (ηa + ηc )

23

24

25

where, IRi is the internal resistance or ohmic loss, (I is cell current, Ri is internal resistance of the cell), and ηa and ηc, over-potentials of the anode and cathode, respectively. Ohmic losses result from the resistance of the electrolyte and other cell components. Over-potential losses are associated with the electrochemical reactions taking place at the interface between the electrodes and the electrolyte. The kinetics of these reactions (oxidation of hydrogen and CO at the anodeand reduction of oxygen at the cathode) play a critical role in

determining polarization losses in SOFCs. Other reactions in SOFCs are of fuel contaminants such as sulphides and the reforming of hydrocarbon gases at the anode.

26

The actual efficiency and electrical energy will be lower if there is voltage loss due to iR drop or polarization effects. Maintenance of temperature level requires cooling of the cell to remove a quantity of heat equal to the difference between the heat of reaction and electricity produced The heat removed is the difference in enthalpy between the products and reactants leaving the generator at a high temperature (1,273 K); it can be used either to produce more electricity or in applications requiring high-grade heat. Thermodynamic analysis shows that the electric efficiency is over 80%.

27

Cell Components

28

The desirable characteristics of each of the components of the SOFC are listed below.• Good stability (chemical, phase, morphological and dimensional),• Appropriate conductivity,• Chemical compatibility with other components of the cell,• Similar thermal expansion coefficient to avoid cracking during the cell operation,• Dense electrolyte to prevent gas mixing,• Porous anode and cathode to allow gas transport to the reaction sites,• High strength and toughness properties,• Fabricability,• Amenable to particular fabrication conditions,• Compatibility at higher temperatures at which the ceramic structures are fabricated,• Low cost.

29

Electrolytes

30

31

The required properties of electrolytes used in SOFCs are mainly fixed by the high operating temperatures which dictate constraints of different types as given in Table 5.3These constraints have restricted the choice to oxide-based ceramics when the charge carrier is an ion associated with the oxidant (O2) or the fuel (H2, hydrocarbon).Typical electrolyte materials available for use in SOFC are zirconia, ceria and a new family of perovskites based on oxide of lanthanum and gallium, LaGaO3 (ABO3), doped at both A- and B- sites. In the latter type of materials, LaGaO3 doped at the A-site with strontium, Sr, and at theB-site with magnesium, Mg (LSGM), have exhibited highest conductivity. The oxygen-ion conductivity, in general, increases in the order: zirconia systems < doped ceria < LSGM. The most investigated oxide-conducting solid electrolytes that are of potential use in SOFCs belongto the fluorite-type solid solutions with the general formula MO2–M’ O or M’O2–M’ 2O3, where M’O2 is the basic oxide and M’ O or M’’ 2O3 are the dopant with M = Zr, Hf, Ce;M = Ca and M = Sc, Y, Ln (rare earth).

32

Cerium oxide doped with samarium (SDC), (Ce0.85Sm0.15)O1.925

• Cerium oxide doped with gadolinium (GDC), (Ce0.90Gd0.10)O1.95

• Cerium oxide doped with yttrium (YDC), (Ce0.85Y0.15)O1.925

• Cerium doped with calcium (CDC), (Ce0.88Ca0.12)O1.88

• Lanthanum gallate ceramic that include lanthanum strontium gallium magnesium (LSGM),(La0.80 Sr0.20)(Ga0.90 Mg0.10) O2.85 or (La0.80 Sr0.20)(Ga0.80 Mg0.20) O2.80

• Bismuth yttrium oxide (BYO), (Bi0.75Y0.25)2O3

• Barium Cerate (BCN), Ba(Ce0.90Nd0.10)O3

• Strontium Cerate (SYC), Sr(Ce0.95Yb0.05)O3

33

Oxygen vacancies—created by doping—make the migration ofO 2- ion species possible in these materials. Current technology employs several ceramic materials for the active SOFC components.Although a variety of oxide combinations has been used for solid non-porous electrolytes, the most common to date has been the stabilized zirconia with conductivity based on oxygen ions (O2- ), especially yttria-stabilized zirconia (Y2O3 stabilised ZrO2 or YSZ, (ZrO2)0.92(Y2O3)0.08 for example) in which a tiny amount of the element yttrium, a silvery-grey metal, is added to thezirconia during manufacture. This choice is mainly due to availability and cost

34

YSZ exhibits purely oxygen ionic conduction (with no electronic conduction). The crystalline array of ZrO2 has two oxide ions to every zirconium ion. But in Y2O3 there are only 1.5 oxide ions to every yttrium ion and therefore results in vacancies in the crystal structure where oxide ions are missing. The oxide ion hops from anode to cathode through the electrolyte. The most commonly used stabilizing dopants are CaO, MgO, Y2O3, Sc2O3 and certain rare earth oxides such as Nd2O3, Sm2O3 and Yb2O3. Other oxide based ceramic electrolytes that can be used in SOFCs include

35

Cerium oxide doped with samarium (SDC), (Ce0.85Sm0.15)O1.925

• Cerium oxide doped with gadolinium (GDC), (Ce0.90Gd0.10)O1.95

• Cerium oxide doped with yttrium (YDC), (Ce0.85Y0.15)O1.925

• Cerium doped with calcium (CDC), (Ce0.88Ca0.12)O1.88

• Lanthanum gallate ceramic that include lanthanum strontium gallium magnesium (LSGM),(La0.80 Sr0.20)(Ga0.90 Mg0.10) O2.85 or (La0.80 Sr0.20)(Ga0.80 Mg0.20) O2.80

• Bismuth yttrium oxide (BYO), (Bi0.75Y0.25)2O3

• Barium Cerate (BCN), Ba(Ce0.90Nd0.10)O3

• Strontium Cerate (SYC), Sr(Ce0.95Yb0.05)O3

36

Figure .2 shows, as an example, variation of ionic conductivity with operating temperature for various electrolyte materials.

37

38

Zirconia systems

39

Yttria doped zirconia is the commonly used electrolyte material in SOFCs. Yttria stabilized zirconia(YSZ) having high strength and toughness as the electrolyte in SOFC is desirable. A strong and tough electrolyte is less sensitive to the presence of flaws and imparts better fracture resistance to the fuel cell during fabrication and operation. Several approaches have been taken to improve the mechanical properties of YSZ. The mechanical properties of a YSZ electrolyte obviously vary depending on the characteristics of starting powders used in the fabrication (such as particle size, particle size distribution, and agglomerate strength), the fabrication route and fabrication conditions. At room temperature, YSZ (8 mol% Y2O3) typically has a bending strength of about 300–400 Mpa and fracture toughness of about 3MN m3/2. The tetragonal phase with 2.5–3 mol% Y2O3 content has high strength (~ 1, 000MPa at RT) but the conductivity is lower by a factor of about 3 compared with 8–8.5 mol% Y2O3–ZrO2 compositions for which the maximum value for ionic conductivity has been reported (0.18S cm−1 at 1,273K and 0.052S cm−1 at 1,073 K).16,18 However, all compositions between 3 and 5.5 mol% Y2O3 are in the two phase field at the fuel cell operating temperatures and undergo phase separation as required by the equilibrium phase diagram

40

The 9.0–10 mol% Y2O3–ZrO2 compositions are in a single (cubic) phase region and therefore show relatively small decrease in ionic conductivity as a function of time at the operating temperatures of the fuel cell. Other causes of conductivity degradation affecting the long term performance of the electrolyte include coherent growth of precipitates, formation of inhomogeneous composition, phase boundaries, local ordering or microdomain formation and changes to the composition of the grain boundary phase(s). Some compositions in the Sc2O3–ZrO2 system have ionic conductivity, about twice that of the best reported in the Y2O3–ZrO2 system. At 1,073K for 8–10 mol% Sc2O3–ZrO2 compositions, the ionic conductivity (0.11–0.12S cm−2) is comparable with that of doped ceria and LSM. However, for most compositions in the Sc2O3–ZrO2 system, the conductivity is known to degrade rapidly with time at the fuel cell operating temperatures due to the metastable nature of phases formed at sintering temperatures.

41

In spite of sustaining search towards the suitable choice of electrolytes for SOFCs, doped zirconia has been selected. The salient features of its electrical conductivity are the following:

• Isothermal variation of conductivity shows a maximum at 9 mol% of dopant forZrO2–M2O3 systems.• The activation energy is close to 0.8 eV for the composition of maximum conductivity• For a particular composition, the conductivity increases as the radius of the dopant cation approaches that of Zr4+. Thus, the best conductivity in Zr-based system is obtained with ZrO2–Sc2O3 system (R4+

Zr = 0.80Å and R3+Sc = 0.81Å).

• In the working temperature range of SOFCs, a decrease in ionic conductivity with time is observed.• Electrolytic domain extends over several orders of magnitude of oxygen partial pressures with a significant influence of temperature. In highly reducing media, n-type electronic conductivity predominates.In spite of these limitations, yettria stabilized zirconia (YSZ) with the composition(ZrO2)0.92 (Y2O3)0.08 is employed still as a solid electrolyte.

42

Limitations and approaches

43

Apart from lowering the operating temperatures of SOFCs with the aim of minimizing component degradation with time and reduction of cost of auxillary parts such as heat exchangers and piping, few other features also assume importance. For instance, (1) reduction of the Ohmic losses due to electrolyte resistance. Attempts have been made to produce gas-tight layers of YSZ, with appropriate thickness and microstructure with minimum resistance, (2) to develop more conductive electrolytes with lower activation energy. In zirconia category, pyrochlore solid solutions of the general formula M2Zr2O7 (M = rare earth ions) were investigated for possible substitution ofZr by transition metals.22–26 Recently25 it was found that both, magnitude and ratio of ionic and electronic conductivities in Gd2(ZrxTi1−x)2O7 and Y2(ZrxTi1−x)2O7 can be varied by a systematic change in x. Ionic conductivity predominates at high X values, but is lower than that of YSZ (1/5th at 1273 K)

44

Ceria-based electrolytes Ceria-systems have conductivities higher than most zirconia-based electrolytes

(with the exception of scandia doped zirconia). However, they develop electronic conductivity in reducing environments and cannot be employed without the protective coating of a stable electrolyte such as doped zirconia on the fuel side. However, ceria and zirconia, in contact with each other, form solid solutions at temperatures as low as 1,473 K, exhibiting much lower ionic conductivity than either zirconia or ceria doped electrolytes. The plot of conductivity in the CexZr0.82−xGd0.18O1.91 system as a function of x, exhibited a minimum in conductivity at Ce/Zr ratio of 1.0 or x = 0.41. The behaviour was explained in terms of the decrease in the free volume in the lattice through which oxygen ions can migrate freely.31 The use of thin layers of doped ceria as an intermediate

phase between La(Co, Fe)O3 electrodes and zirconia based electrolytes has also been proposed to increase interface stability and eliminate the formation of undesirable phases such as La2Zr2O7 and SrZrO3. However, for any application when zirconia and ceria-based electrolyte materials are in contact with each other either during preparation or subsequent use, it is imperative that temperatures above 1,473K are avoided, otherwise serious degradation in performance will occur.

45

Although CeO2− and Bi2O3− based solid solutions show higher ionic conductivities than YSZ,their tendency to be reduced in the presence of fuel gas excludes them for use in SOFCs

46

Perovskite-based systems

47

Mixed metal oxides offer unique advantages for wide applications due to their tailor-made solid state, surface and morphological characteristics. Among the mixed metal oxides, perovskite-type oxides are the prominent ones. Typical perovskite oxide has the general formula ABO3. Although most numerous and interesting compounds with the perovskite structure are oxides, some carbides, nitrides, halides and hydrides also crystallize in this structure. The broad diversities of properties that these compounds exhibit is derived from the fact that around 90% of the metallic elementsof the Periodic table are known to be stable in a perovskite-type oxide structure. They also form the possibility of synthesizing multicomponent perovskites by partial substitution of cations in positions A and B, giving rise to substituted compounds with formula of A1-x A’x B 1-xB’x O3.In perovskite related materials, A ions can be rare earth, alkaline earth, alkali and other large ions such as Pb2+ and Bi3+ that fit into the dodecahedral site of the framework. The B ions can be 3d, 4d and 5d transition metal ions which occupy the octahedral sites. A list of A and B ions that can be accommodated on perovskite lattice is given in Table. 4

48

49

Optimum preparation of these materials has proved to be challenging, requiring diverse synthetic approaches dictated by the ultimate end use. For instance, materials-oriented applications require densification by high temperature sintering to minimize both surface area as well as surface free energy, thereby to maximize the mechanical strength. In contrast, catalytic materials have to maintain sufficiently high surface area to maximize their participation and activity in chemical reactions. These materials are prepared by a variety of methods

50

Solution preparation: Traditional ways of making perovskites generally adopt mixing the consitutent oxides, and hydroxides and carbonates or one of them. However, these materials possess large particle size and therefore, this approach frequently requires repeated mixing and extended heating at high temperatures to generate a homogeneous and single phase material. To surmount the disadvantages of low surface area and limited control of the microstructure inherent in the hightemperature process, precursors generated by sol–gel preparations or co-precipitation of metal ions by precipitating agents such as hydroxide, cyanide, oxalate, carbonate and citrate ions have been employed. The gel or co-precipitation precursors can offer molecular or near molecular level mixing and provide a reactive environment during the course of subsequent heating and decomposition. The improved solid state diffusion resulting from improved mixing requires lower temperature conditions compared to traditional approaches. Advantages of later methods include better control of stoichiometry and purity, greater flexibility in formation of thin films as well as new compositions and an enhanced ability to control particle size. This method can be classified based on the means adopted for solvent removal: (1) Precipitation with subsequent processes such as filtration and centrifugation. (2) Thermal processes such as evaporation, sublimation, combustion as well as freeze-drying and plasma spray-drying. The advantage of the latter method is that the conversion of residue into the desired product is a simultaneous process.

51

Solid state reactions: Traditional processing of perovskite materials employs solid state reactions between metal carbonates, hydroxides and oxides. Impurities may originate from raw materials, milling vessels and calcination containers. Further, high temperature required for reaction completion and coarse particles, may result in multi-phase formation. These problems should be minimized or eliminated to generate high performance homogeneous materials.

Gas phase preparations: This approach finds its application when the deposition of perovskite films with specific thickness and composition are desired. Physical techniques such as laser ablation, molecular beam epitaxy desputtering, magnetron sputtering, electron beam evaporation and thermal evaporation are employed. These methods are classified into two categories based on the target they use. The first case uses separate targets where different speed of deposition for each element has to be determined, while the second case uses the preformed perovskite materialitself as target and the stoichiometric phase is transported to the substrate by sputtering or ablation techniques. Gas phase deposition can be further divided into three categories: (1) deposition at a low substrate temperature followed by a post-annealing at elevated temperatures; (2) deposition at an intermediate temperature (873–1,073 K) followed by a post annealing treatment; (3) deposition at the appropriate crystallization temperature.

52

These characteristics account for the large variety of applications in which these perovskites are used. Other important aspects of perovskites are related to the stability of mixed oxidation states in the crystal structure. This is illustrated by the discovery of a metallic behaviour in Cu2+–Cu3+ mixed valence in La–Ba–Cu oxide, which greatly favoured the development of perovskites showinghigh temperature superconductivity. Because of their controllable physical and chemical properties, these compounds offer excellent opportunity to correlate with reactivity and both surface and bulk properties or one of them.

53

Ishihara et al have shown that LaGaO3-based oxides with the perovskite structure havehigher electrical conductivity than YSZ and have high ionic transference number close to one at wide oxygen pressures. Perovskite-type oxides have been considered to be potential material for solid electrolytes of SOFCs. The search for an ionic conductor has been based on empirical or valid reasoning. Kilner and Brook examined the series of rare earth aluminates (LnAlO3; Ln:La– Dy) using theoretical calculation of migration enthalpy for oxygen ions and association enthalpy between an oxygen vacancy and a dopant cation. Their calculations show that the migration enthalpy increases when ionic radius of rare earth element becomes larger from Dy to La. They explained this phenomenon using the concept of critical radius, but the agreement between theircalculation and their experiment for (La or Dy) AlO3 was poor. After that, Sammells and coworkers investigated the correlation between activation energy (Ea) for ionic conduction and the lattice free volume for a wider range of perovskite-type compounds. They reported that the activation energy for anion migration became smaller as the free volume was increased. This means that a large open space in the lattice is desirable in order to obtain high oxygen ion mobility. However, there is an optimum size and an optimum quantity of alio-valent dopant to obtain maximum conductivity in the fluorite-type oxides, where the dopants cause very little expansion or contraction of the fluorite lattice. It remains a question why a large free volume is necessary for high ionic conductivity only in the perovskites. Ranløv et al examined the electrical conductivity of rare earth aluminates as a function of A site ion radius, and found that the electrical conductivity increased and the activation energy for oxygen ion migration decreased when radius of A site ion is increased. Recently, Nomura and Tanase reported that the maximum electrical conductivity and the minimum apparent activation energy were both achieved when the free volumes were around 0.013 nm3 per unit cell in the perovskite series having La for A site cation.

54

Although these studies have contributed to the understanding of ionic conduction of perovskite type oxides, factors contributing to the ionic conductivity have not been clearly established yet. In 1999, Hayashi et al, made an attempt to establish a guiding principle for high ionic conductors and to investigate the mechanism of ionic conduction from a viewpoint of basic solid state chemistry. In this study, data on electrical conductivity of perovskites and brown-millerites reported as oxygen ion conductors were collected from the literature and the correlations between the electrical conductivity of these compounds and the structurally related parameters, such as tolerance factor,specific free volume and oxygen deficiency, were examined. The optimum conditions to obtain high ionic conductivity of perovskite-type oxides were proposed based on the analysis.

55

Tolerance factor (t)The tolerance factor is defined in terms of ionic radii ast = (rA + ro)/ √2(rA + rO) where rA and rB are the mean ionic radii for A and B site cations taking into account the coordination numbers respectively, and ro is the radius of oxygen ion, 0.140 nm.

56

Specific free volume

Sammells and co-workers used the term lattice free volume defined as the unit cell volume minus the total volume of the constituent ions. Normally, the specific free volume is used rather than the free volume, because it is convenient in order to compare various kinds of perovskite-type oxides. The specific free volume is defined as follows;Specific free volume = free volume / unit cell volume = (V − total volume of the constituent ions)/Vwhere V is the volume of the unit cell and was calculated using the empirical equation derived by

57

Oxygen deficiency (δ)

The oxygen deficiency δ of the doped perovskites is expressed by ABO3−δ and is calculated using the electrical neutrality condition.Perovskite-type oxides reported as oxygen ion conductors have been surveyed and collected from the literature. Their electrical conductivities at 1,000K are listed in Table 5. An average value was used for electrical conductivity when there were more than two reports on the same compound. The change in electrical conductivities as a function of the tolerance factor t for various groups of perovskite-type compounds exhibited a maximum value of electrical conductivity at the tolerance factor around 0.96. The ideal perovskite is the cubic structure with the tolerance factor of 1.0. The perovskite structure is stable in the range 0.75 < t < 1.0, and is cubic in the range t > 0.95. Yokokawa et al reported that the compounds became more stable as t approached 1.0, indicating a relationship between the enthalpy of formation of perovskites and the tolerance factor. Lattice distortion from the cubic geometry is associated with a high degree of anisotropy in oxygen sites, and increase in lattice distortion decreases the ionic conductivity