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Solid Oxide Fuel Cells
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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 highgrade 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 cogeneration.
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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.
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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.
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History of Solid Oxide Fuel Cells
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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 monazite
sand 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.
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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 its
technological applications in devices.
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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 CermatecAdvanced Ionic Technologies, which is working on units
upto 10kW in capacity, running on diesel fuel, which would
be used for mobile power generation.
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The US Department of Energy (DoE) announced that an SOFC-microturbine cogeneration 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 for
SOFC 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. The
first 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.
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SOFC Benefits and Limitations
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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.
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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.
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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 the
active 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.
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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.
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Cell Reactions
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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.
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Anode reaction : H2(g) + O2- → H2O(g) + 2eAnode reaction : CO(g) + O2- → CO2 (g) + 2e –
Combined anode : aH2(g) + bCO(g) + (a + b)O2- → aH2O(g) + bCO2 (g)
reaction
+ 2(a + b)eOverall cathode : 1/2(a + b)O2 (g) + 2(a + b)e − → (a + b)O 2reaction
Overall reaction : 2(a + b)O 2(g) + aH2 (g) + bCO(g) → aH2O(g) + bCO2 (g)
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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 )
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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 anode
and 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.
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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%.
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Cell Components
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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.
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Electrolytes
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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
5.3
These 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 oxideconducting solid electrolytes that are of potential use in SOFCs belong
to 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).
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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
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Oxygen vacancies—created by doping—make the migration ofO 2ion 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 the
zirconia during manufacture. This choice is mainly due to availability
and cost
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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
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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
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Figure .2 shows, as an example, variation of ionic conductivity
with operating temperature for various electrolyte materials.
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Zirconia systems
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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
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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.
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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 for
ZrO2–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, ntype 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.
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Limitations and approaches
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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 of
Zr 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)
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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.
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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
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Perovskite-based systems
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Mixed metal oxides offer unique advantages for wide applications due to their tailormade 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 elements
of 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
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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
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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 high
temperature 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 freezedrying and plasma spray-drying. The advantage of the latter method is that the
conversion of residue into the desired product is a simultaneous process.
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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 multiphase 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 material
itself 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.
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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 showing
high 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.
52
Ishihara et al have shown that LaGaO3-based oxides with the perovskite structure have
higher 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 their
calculation 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
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cation.
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.
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Tolerance factor (t)
The tolerance factor is defined in terms
of ionic radii as
t = (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.
55
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)/V
where V is the volume of the unit cell and was calculated using the
empirical equation derived by
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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,
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and increase in lattice distortion decreases the ionic conductivity