CHAPTER- ONE

GENERAL INTRODUCTION

1.1. What is a fuel cell?

A fuel cell is an electrochemical energy conversion device. The

electricity is generated at the electrode/electrolyte interface through

chemical reactions. For example, when the oxidant (O2) and the fuel

(usually H2 or CO) are mixed together , they combine to produce water

(H2O) and energy in any form (i.e. heat or electricity), because the Gibbs

free energy of H2O is smaller than that for H2 or CO and ½ O2 [1,2]. Thus,

the fuel cell is a device that generate electrical energy by making two half

reactions occur separately at two different electrodes. These two half

reactions can be acquired by separating the fuel from the oxidant. The

electrolyte serves as a barrier to gas diffusion, but permits ion transport.

Accordingly, the half cell reactions can occur at the anode and cathode,

producing ions that can traverse the electrolyte. If the electrolyte conducts

O2–, oxide ion, H2 will be oxidized at the anode and O2 will be reduced

simultaneously at the cathode to form the oxide ions, after migrating a

cross the electrolyte will react with H+ and electrons at the anode. The

flow of ionic charge through outside circuit and it is this balance that

produces does not need recharging. As long as the fuel and air are

supplied, it can continue to supply the heat and electrical power

indefinitely.

2

Table 1.1: Types of fuel cells with their important features [3,4]

Type Electrolyte Mobile ion Fuel Operation

temperature oC

Polymer

Exchange

Membrane

(PEMFC)

Sulfonated

Polymers

(Nafion®)

(H2O)nH+

H2

CH3OH

70–110

Alkali fuel

cell (AFC)

Aqueous

KOH

OH– H2 100–250

Phosphoric

acid fuel cell

(PAFC)

H3PO4

H+

H2

150–250

Molten

carbonate

fuel cell

(MCFC)

(Na,K)2 CO3

32−CO

Hydrocarbons

CO

500–700

Solid Oxide

fuel cell

(SOFC)

(Zr, Y)O2–δ

O2–

hydrocarbons

CO

700–1000

3

1.2. Various types of fuel cells

The electrolyte may be conducting oxide ion, hydroxide ion, proton

and carbonate ion, based on which many categories of fuel cell under

development are all known today. Since the ionic conduction is a

thermally activated process, the type of electrolyte determines the fuel

cell’s temperature of operation. Table 1.1 [3,4] lists the various categories

of fuel cells along with their mobile ionic species and temperatures of

operation and the fuels that are typically used. Briefly, these types can be

summarized along with their general chemistry [5–9] as follows:

1.2.1. Proton exchange membrane fuel cells (PEMFC)

It is also known as the solid polymer electrolyte fuel cell (SPEFC).

The overall cell reaction and half reactions at the anode and cathode are

as follows:

Anode: H2 2H+ +2e– Eo=0.0 V (1.1)

Cathode: 2H++ ½ O2 + 2e– H2O Eo=1.23 V (1.2)

Overall: H2 + ½ O2 H2O Ecell= 1.23 V (1.3)

The maximum theoretical voltage is 1.23 V. Fig. 1.1 shows a schematic

sketch for PEMFC. Perfluorosulfonic is fabricated as an ion exchange

membrane electrolyte. The electrodes are made with Pt, impregnated

porous material with hydrophobic coating. The main advantages of this

type of fuel cell are no liquid electrolytes, no concentration gradient or

gas crossover due to solid electrolytes. The disadvantages are that the

4

ElectrolyteCathodeAnode

e- e-

Perfluorosulfonic

(H2O)nH+

O2

H2O

H2

Fig.1.1: Schematic sketch for PEMFC.

ElectrolyteCathodeAnode

e- e-

KOH (5-12 N)

OH-

O2

H2O

H2

Fig.1.2: Schematic sketch for AFC.

5

membrane undergoes freeze drying below 0oC and the anode reaction

inhibited in the presence of CO. Moreover, it is necessary to keep the

membrane continuously water saturated and the operation temperature is

limited to 60oC to avoid water evaporation.

1.2.2. Alkaline Fuel cells (AFC)

Usually a concentrated KOH solution is used for the electrolyte

(5N to 12N). It is schematically presented in Fig. 1.2. Noble metal loaded

porous carbon is practically used as electrodes. The overall cell reactions

of AFC are the same as the PEMFC in the production of water. The half

reactions are:

Anode: H2+2OH– 2H2O+2e– Eo=–0.829 V (1.4)

Cathode: H2O+ ½ O2+2e– 2OH Eo=+0.401 V (1.5)

The main disadvantages of these cells are, electrolyte creep, which

cause sealing problems, formation of carbonate in the presence of CO2

and the uses of expensive gas diffusion electrodes.

1.2.3. Phosphoric acid fuel cells (PAFC)

PAFC uses either air or oxygen as the oxidant gas and hydrogen as

the fuel gas (Fig. 1.3). The electrolyte consists of 100% H3PO4. The

electrodes are made from Teflon (PTFE) bonded Pt supported on carbon

black. The maximum theoretical voltage is the same as that of the

PEMFC. The anode and cathode reactions are as follows:

6

ElectrolyteCathodeAnode

e- e-

H3PO4 100%

H+

O2

H2O

H2

Fig1.3: Schematic sketch for PAFC.

ElectrolyteCathodeAnode

e- e-

K2CO3 : Li2CO3 , 38 : 62

CO32-

O2

H2O

H2

CO2

or CH4

Fig.1.4: Schematic sketch for MCFC.

7

Anode: H2 2H+ + 2e– Eo =0.00 V (1.6)

Cathode: 2H++ ½ O2 +2e– H2O Eo=1.23 (1.7)

The main advantage of the PAFC over other fuel cells is that it can

tolerate CO2 from the air. However, the disadvantages are that the

corrosion of the cell components, ohmic polarization and slower oxygen

kinetics.

1.2.4. Molten Carbonate fuel cells (MCFC)

The anode and cathode of the MCFC (Fig. 1.4) are made a porous

Ni doped with 10% Cr and Li–doped NiO cermets, respectively. A

mixture consisting of Li2CO2 and K2CO3 in the molar ratios 62:38.

Stream methane is used as the anode gas feed. Air or oxygen with

recycled CO2 from the anode stream is used as the cathodes feed. The

overall cell reaction can be written as production of water and CO2. The

half reactions are as follows:

Anode: 232 HCO +− CO2 + H2O+2e (1.8) –

Or OCCO32 +− 2CO2 + 2e (1.9) –

Cathode: ½ O2 +CO2+e– (1.10) 32CO −

The advantages of MCFC is the high efficiency and smaller

activation polarization at high temperatures of operation, but the

corrosion of construction and electrode materials due to the elevated

temperature is still the only disadvantage.

8

1.2.5. Solid Oxide fuel cells (SOFC)

The SOFC as shown in Fig. 1.5 represents a third generation of

fuel cells in terms of commercialization. Electrode materials for the

SOFC are usually Ni–zirconia cermets for the anode and Sr–doped

lanthanum manganate for the cathode. Yttria stabilized zirconia is used as

the electrolyte. The overall cell reaction is the same as the MCFC, but the

half cell reaction are quite different:

Anode: 2H2+2O2– 2H2O +4e– (1.11)

Or 2CO + 2O2– 2CO2 +4e– (1.12)

Cathode: O2 +4e– 2O2– (1.13)

The main advantage of SOFC over other fuel cells is that it has the

highest efficiency (60%) at highest operation temperatures (>700oC). The

high temperature allows internal reforming fuels and promotes rapid

reaction kinetic and mass transfer. The materials compability at around

1000oC is one of the major disadvantages. However, a severe ohmic

polarization is produced below this temperature.

1.3. Operating concept and configuration of SOFCs

Today’s SOFCs [10–14] utilize yttria stabilized zirconia (YSZ),

containing typically 8–10 mol% Y2O3 as the electrolyte. A cermets

composed of Ni+YSZ with the mole ratio of 1:1 as anode and La1–x

SrxMnO3–δ with 0.15≤ x ≤0.25 as cathode. The interconnect material is

9

ElectrolyteCathodeAnode

e- e-

10 mol % YSZ

O2-

O2

H2O

H2

or CO

Fig.1.5: Schematic sketch for SOFC.

Fig.1.6: Schematic operating concept of SOFCs [17].

10

alkali doped LaCrO3 (lanthanum chromite) with specific dopant such as

Sr, Ca, Mg, etc. SOFC usually operates at a high temperature range (700–

1000oC) [15,16]. A simplified operating concept is illustrated in Fig. 1.6

[17]. There are two types of SOFC electrolytes: oxide–ion and proton

conductors. Although, the conduction mechanisms of these conductors

are quite different, the operating principles are the same for both types of

cells. During operation, oxygen from air transports through the porous

cathode to gas–cathode–electrolyte three phase boundaries, where it

catalytically combines with incoming electrons from the external circuit

to from oxide ion. The electrolyte conducts oxide ion to the anode–

electrolyte interface, where it is electrochemically oxidized to liberate

electrons and produce water vapour. The electrons, which can not pass

through the external circuit containing a motor or other electric load that

consumes the power generated by the cell. To achieve the desired power

input, individual cells must be bundled into an array of series–parallel

electrically connected cells. Generally, the SOFCs are configurated in

two suitable designs: a planar (Fig. 1.7a) [18] and tubular SOFC (1.7b)

[19] designs. In the tubular SOFC, components are arranged in the form

of a hollow tube with the cell constructed in layers around a tubular

cathode; air flows through the inside of the tube and fuel flows around

the exteriors, while in planar design, the components are arranged in flat

11

(a)

(b)

Fig.1.7: Configuration for SOFCs.(a) a planar [18] and (b) tubular

designs [19].

12

stacks with air and fuel flowing through channels built into the cathode

and anode.

SOFCs produce a power output of 2–100 kW and can attain 220 –

300 kW when used in SOFC/gas turbine hybrid system. The electrical

efficiencies are 45–55% with the total efficiencies of 80–85% with

cogeneration of waste heat [20]. These do not use platinum as catalysts,

but instead use cheaper materials such as Ni and NiO and they can use

natural gas directly without reforming it externally to H2 and CO [21].

These features make SOFCs increasingly important as candidates for

medium–to–large powered applications like industrial power supplies in

hospital, hotels and universities and long distance vehicle power supplies

as well as for stationary power.

1.4. Oxide–ion conductors for SOFC applications

The operating concept of SOFCs is based on an oxide–ion

conductor (electrolyte), sandwiched between the electrodes, which allows

the migration of oxide ions, O2– from the cathode to the anode and

therefore they react with the fuel to generate electrical power. Oxide–ion

conductors are solid oxides in which oxide ions migrate through the

crystal framework formed by the cation sublattice. This usually occurs

via a series of “hops” between adjacent and equivalent sites in the oxide

sublattice due to the presence of vacancies. For introducing oxide–ion

vacancies two strategies have been investigated [22–24]:

13

One is to select an oxide with an intrinsic vacancy concentration; the

other is to substitute cations that have an aliovalency to the host ion in

cation array, thereby creating an extrinsic vacancy concentration.

In oxides with high intrinsic vacancy concentration, the

electrostatic interactions between the mobile ions result in the ordering of

oxide ion vacancies below a transition temperature and thereby producing

a sudden increase in conductivity. For oxides with extrinsic vacancy

concentration, an alivoalent cation vacancies are trapped due to which the

activation energy significantly increases.

In general, yttria stabilized zirconia with 8–10% Y2O3 is the most

commonly used oxide–ion conductor in practical SOFCs. This electrolyte

material is based on the stabilized fluorite structure [25–29], which

possesses the highest ionic conductivity at about 8% Y2O3. The fluorite–

type zirconia can also be stabilized by doping with the rare earth elements

such as Sc [30], Sm [31] and Gd [32]. However, the high operating

temperature, required for good ionic conductivities of YSZ leads to

several materials problems, such as the formations of poor conductivity

products a as result of the interfacial diffusion of Sr and La between LSM

electrode and electrolyte, distortion of electrical electrolyte and electrode

contacts due to different thermal expansion coefficients [33]. Recently,

many researches have been devoted to find new oxide–ion conductors for

14

Fig1.8: Temperature dependence of ionic conductivity for some oxide–

ion conductors [34].

15

intermediate temperature–SOFC applications (∼ 500–800oC). Such

candidate materials must possess the following features:

(i) Good oxide ion conductivity at moderate temperature (500–

800oC) without structural phase transition and decomposition.

(ii) The electrochemical stability against O2 at operating

temperature must be at least 1.2 V.

(iii) The electronic conductivity must be negligible over the entire

or most of the employed range of oxygen partial pressures and

temperatures.

(iv) Dense, gas–tight, pore–free preparation of the material with

good adhesion to both anode and cathode materials.

(v) Stability against chemical reactions with anode, cathode and

sealing materials.

(vi) Charge–transfer and electrolyte–electrode interface resistances

must be negligible.

There are various types of oxide–ion conductors both in terms of

chemical and crystal structures. Fig. 1.8 shows the temperature

dependence of ionic conductivity for selected oxide–ion conductors [34].

The potential oxide–ion conductors along with their technological

problems encountered when used in IT–SOFCs are illustrated in Table

1.2 [35].

16

Table 1.2: Potential oxide–ion conductors and their technological

problems when employed in IT–SOFC application [35].

Oxide ion electrolyte Structure

type

Critical materials issues when used in IT–

SOFCs

Y2O3–doped ZrO2 Fluorite

Poor ionic conductor, incompatible with perovskite–type cathode materials (e.g., Sr–doped LaMO3 (M = Mn, Co) at elevated temperatures and long period of operation time.

Sc2O3–doped ZrO2 Fluorite Expensive, long–term performance is not known.

Rare–earth–doped CeO2

Fluorite Not stable in the low–oxygen partial pressure, poor mechanical stability, large grain boundary resistance at lower temperature.

Sr + Mg–doped LaGaO3

Perovskite Not stable at low oxygen partial pressures, forms carbonates in CO and CO2 atmospheres, Ga–evaporates in H2 atmosphere, incompatible with Ni anode at elevated temperatures.

Ba2In2O5 Brownmillerite Not stable at low oxygen partial pressures,

poor ionic conductor at low temperature, shows first–order phase transition accompanied by structural change, degradation in CO2 atmosphere with the formation of BaCO3.

Doped Bi4V2O11 Aurivillius Stable over a limited range of oxygen partial pressures.

BaBi4Ti3InO14.5 Aurivillius Moderate ionic conductor, electrochemical stability at low and high oxygen partial pressures is not known, may form carbonates in CO2 atmosphere.

Gd2Ti2O7 Pyrochlore Poor ionic conductor and not stable at low oxygen partial pressures at elevated temperatures.

Doped BaCeO3 Perovskite Chemically not stable in CO2–containing atmospheres, exhibits hole (p–type) and electronic (n–type) conduction at high and low oxygen partial pressures, respectively, at elevated temperatures.

Sr3Ti1.9Al0.1O7−x Ruddlesden– Popper

Poor ionic conductor, p–type electronic conduction at high oxygen partial pressures.

17

1.4.1. Doped cerias

Doped cerias are based on stabilized fluorite structure, which can

be achieved by doping the parent CeO2 with di–and/or trivalent cations.

Rare earth doped cerias, such as Ce0.8Sm0.2O1.9 and Ce0.8Gd0.2O1.9 are

found to be potential oxide–ion conductors [36,37] for SOFC applications,

because of their high oxide–ion performance compared to YSZ. For

example, the Ce0.9Gd0.1O1.925 , abbreviated as CGO 10 has an ionic

conductivity of 0.01 S.cm–1 at 500oC. However, the main disadvantage in

using doped cerias as SOFC electrolyte is that they show n–type

electronic conduction at temperatures above 700oC at lower oxygen

partial pressures due to the partial reduction of Ce4+ to Ce3+ at the anode

[38–40].

1.4.2. LSGM family

LSGM oxide–ion conductors are perovskite–type ABO3 phases

derived from lanthanum gallate, LaGaO3. The ionic conductivity of

LSGM with composition, La1–xSrxGa1–yMgyO3–δ for x=0.2 and y=0.17 is

four orders of magnitude higher than that of stabilized zirconia [41,42]. It

has been found that the oxide–ion performance of LSGM is much more

enhanced when doped with Sr compared to Ca and Ba [43,44]. Further

more, introduction of small amounts of Co onto Ga site of LSGM leads to

enhanced ionic conductivity and results only in a small increase in the

electronic conduction [45]. The major disadvantage in using LSGM–

18

based materials as electrolyte for SOFCs are that the formation of

secondary phases, reduction and volatilization of gallium oxide [46].

1.4.3. LAMOX family

LAMOX–based oxide–ion conductors are derived from the parent

lanthanum molybdate with a general formula, La2Mo2O9 [47–49]. The

oxide–ion conductivity of La2Mo2O9 is slightly higher than that of the

best stabilized zirconia (e.g. 6 × 10–2 S.cm–1 at 800oC). It exhibits an

abrupt order–disorder, α→β transition. The good ionic conductivity is

associated with the high temperature β–phase, which is isostructural to β–

SnWO4 (Fig. 1.9) [50]. The substitutions on the cationic and anionic sites

of La2Mo2O9 can suppress the phase transition and thereby stabilize the

highly conducting β–phase at room temperature [51,52]. Fig. 1.10

compares the temperature dependence of ionic conductivity for selected

LAMOX oxide–ion conductors with that of 8% YSZ [53]. The only

disadvantage of these materials is the mixed ionic and n–type electronic

conductivity at elevated temperatures and lower oxygen partial pressures

[54].

1.4.4. δ–Bi2O3–based ceramics

Bi2O3 exhibits α → δ transition at around 705oC [55], which leads

to an increase in the oxide–ionic conductivity by almost three order of

magnitude. The high temperatures δ–phase has a cubic fluorite structure

19

Sn

W

ca

b

La

Mo

ca

b

O2

O1

O3 Lone pair

Fig.1.9: The crystal structure of β–La2MoO9 compared to that of β–

SnWO4, with one extra oxygen site in place of the tin lone pair

[50].

Fig.1.10: Compression of ionic conductivity of LAMOX based oxide–ion

conductors with that of YSZ [53].

20

with extremely high oxide ionic vacancies (25%). This phase is

predominantly ionic conductor [56]. The highly conducting δ–phase can

be stabilized down to temperatures significantly lower than the α→δ

transition temperature by addition of rare earth elements, such as Y, Dy

and Er [57–60]. These substitutions show much less pronounced

transition behaviour but retain the overall high conductivity. The

conductivity of a binary system, (Bi2O3)0.75 (Ln2O3)0.25 is slightly higher

for Ln=Er compared to that for Ln=Y [58,61]. However, oxide–ion

conductors based on Bi2O3 have limited use for SOFC applications [60]

due to a number of specific disadvantages, like the high reactivity,

volatilization of Bi2O3 , easy reducibility at low oxygen pressures, low

mechanical strength and high thermal expansion. In addition, the

stabilized δ–Bi2O3 fluorite–type phase undergoes a decomposition at

temperatures below 600oC.

1.4.5. Aurivillius family

The bismuth Aurivillius phases are mixed oxide with a general

formula, (Bi2O2) (An–1BBnO3n+1), where Bi atoms are located at the vertices

of square–pyramidal BiO6 units linked by shared edges. These infinite

bismuthate layers alternate with (An–1BnB O3n+1) perovskite–like sheets built

from edge–sharing octahedra, where n denotes the octahedral thickness,

which usually ranges from 1 to 5. A is a mono–, di–or trivalent cation and

21

B is a cation with average size [62–64]. Bi4V2O11 is Aurivillius related

oxygen–deficient compound [65], which is the parent compound of many

oxide–ion conductors generally called BIMEVOX (Bi2V1–xMxO5.5–y

M=Cu2+, Ni2+, Cr3+, Co2+….) [66–69]. For example, Bi2Cu0.1V0.9O5.35

(BICUVOX.10) exhibits a conductivity of 10–3 S.cm–1 at 250oC, which is

about two orders of magnitude higher than that of the parent compound.

However, a detailed explanation on this class will be discussed in the next

section.

Other Aurivillius–type oxide–ion conductors could also be

prepared with higher octahedral thicknesses (i.e n ≥ 3), such as

BaBi2Sr2M'2 M"O11.5 (M'=Nb, Ta; M"=Ga, Al) and BaBi4Ti3MO14.5

(M=Sc, In, Ga). The highest ionic conductivity was reported for the

BaBi4Ti3InO14.5 (10–2 S.cm–1 at 900oC) [70].

1.4.6. Brownmillerite–like phases

Brownmillerite–type Ba2In2O5 shows a fast oxide–ion conduction

just above an order–disorder transition at 930oC [23]. The structure of

Ba2In2O5 resembles that of brownmillerite A2BB2O5 , which consists of

alternating perovskite layers of corner sharing BO6 octahedra and layers

of BO4 tetrahedra. The oxide–ion vacancies in the perovskite layers are

responsible for the high ionic conductivity. It can be noted that the

chemical substitution of indium with higher valent cations, such as Zr ,

Ce and Sn stabilizes the disordered cubic perovskite structure and thus

4+

4+ 4+

22

enhances the ionic conductivity [71,72]. Generally, the electrical

conductivity of Ba2In2O5 is fully oxide–ion in dry atmospheres, mixed

ionic and p–type electronic under oxidizing conditions and protonic in

water containing gas mixtures. Fig. 1.11 shows that temperatures

dependence of selected Ba2In2O5–based materials in comparison with 8%

YSZ [53]. Compared to stabilized zirconia, the use of doped Ba2In2O5

might be advantageous at moderate temperatures.

1.4.7. Apatite–type phases

Apatite–type phases have a general formula, A10–x (MO4)6O2,

where M=Si or Ge and A is rare earth or alkaline earth cations [73–76].

The A site cations are located in cavities created by MO4 tetrahedra. An

additional oxygen sites (O5) form channels through the structure, Among

few exceptions, the oxide–ion conductivity in hexagonal apatites,

La10Si6O27 and Nd10Si6O27 , reported by Nakayama et al. [73, 74] is much

interesting. Fig. 1.12 compares the ionic conductivity of these apatites

with that of doped bismuth oxide and YSZ [77]. However, the ionic

conductivity can be enhanced by substitution of Si with small amounts of

Al without creating further vacancies, as found in the system

La9.33+x3Si6–xAlxO26 [78].

1.4.8. Pyrochlore–type phases

Pyrochlore–type materials are structurally related to (A,B)O2 perovskite.

Their structure consists of an ordered eight fluorite units, each of

which has a natural oxide–ion vacancy. The general formula can be

23

Fig.1.11: Comparison of ionic conductivity of Ba2In2O5–based oxide–ion

conductors with that of YSZ [53].

Fig.1.12: Comparison of ionic conductivity of apatite type oxide–ion

conductors with that of conventional ones [77].

24

written as A2BB2O7 . This unoccupied site provides pathways for fast

oxygen transport [79–81]. Typical examples for this type of oxide–ion

conductors are Gd2Ti2O7 and Gd2Zr2O7. However, the introduction of

disordered extra vacancies can lead to more interesting oxide–ion

conductors. The highest ionic performance has been reported for

Cd1.9Ca0.1Ti2O6.95 (e.g. 5 × 10–2 S.cm ) at 800 C [82]. –1 o

1.5. BIMEVOX family of oxide–ion conductors (Structural aspects

and conductivity behaviour)

BIMEVOXes (BI=bismuth, ME=metal, V=vanadium, OX=oxide)

are solid solutions based on V and /or Bi substitution in Bi4V2O11 [66].

The parent compound crystallizes as α–phase at room temperature

[83,84]. It exhibits two phase transitions on heating:

α-(monoclinic) β-(orthorhmbic)447 oC

(1.14)

γ-(tetragonal)β-(orthorhmbic)567 oC

(1.15)

The existence of two other phase, one γ' just before melting and a second

α' during cooling, has also been reported. However, these phases have

never been fully characterized. Recently, a metastable intermediate ε–

phase, in the temperature range ∼ 650–690oC has been characterized as an

orthorhombic distortion of the tetragonal γ–phase [85]. The tetragonal γ–

phase represents the fully disordered state, whereas the α–and β–phase

25

are based on ordering of oxide ion vacancies located in the vanadium

coordination polyhedra [86]. The crystal structure of Bi4V2O11 belongs to

the well–known Aurivillius–type family. It consists of alternating layers

of and , where represents oxide ion vacancies. Fig.

1.13 presents the idealized Aurivillius–type crystal structure of γ–

Bi

n

nOBi +222 ][

n

nVO −25.3 ][

4V2O11 [87]. The (Bi2O2)2+ layers exhibit Bi atom in a square pyramidal

coordination with four Bi–O bonds of approximate length 2.3Å. The Bi

6s2 lone pairs are stereochemically active and point to vacant sites

between four corner sharing vanadium polyhedra in the vanadate layers.

The bismuthate layers sandwich the vanadate sheets with lone pair

orbitals pointing directly towards each other through the vacant site in the

vanadate layers [88].

It is important to point that the high temperature γ–Bi4V2O11

exhibits fast ionic conductivity of about 0.1S.cm–1 at 600oC. However,

the conductivity is only 0.01 S.cm–1 at 500oC in β–phase with high

activation energy of 1 eV, whereas the conductivity of α–phase at 300oC

is 10–5 S. cm–1 with activation energy of 0.6 eV [83]. These different

conductivities and activation energies, corresponding to α–, β– and γ–

polymorphs of Bi4V2O11 have been obviously correlated with the degree

of disorder of their specific crystal structures [89,90]. It is clear that the

disordering of oxide ion vacancies above 567oC is responsible for the

remarkably high ionic conductivity in the tetragonal γ–phase. Because of

26

Fig.1.13: Idealized Aurivillius–type crystal structure of γ–Bi4V2O11 [87].

Table 1.3: Stability range of the γ–phase for various BIMEVOXes [103].

BIMEVOX ME stability of range (x)

BICUVOX Co2+ 0.07–0.17

BICUVOX Cu2+ 0.07–0.12

BIMNVOX Mn3+ 0.10–0.25

BITIVOX Ti4+ 0.12–0.25

BIZRVOX Zr4+ 0.10–0.15

BISBVOX Sb5+ 0.15–0.50

BITAVOX Ta5+ 0.15–0.45

27

the attractive conduction properties of the γ–phase, many attempts to

stabilize this phase at room temperature have been devoted using a

doping strategy [66–69, 91–102]. The γ–type of structure can be

stabilized at room temperature by the appropriate doping on the vanadium

site with other aliovalent or isovalent cations, which prevent the ordering

of the vacancies and formation of the β– and/or α–phases. The simple

substitution reaction can be written as:

Bi2O3+(1–x)/2 V2O5+xMeOy→Bi2MexV1–xO5.5–[(5–n)x/2] (1.16)

where n is depending on the valence state of Me cation. The product

formulation can be abbreviated as BIMEVOX.x, where x value represents

the amount of dopant with respect to one vanadium atom. Depending

upon the nature and the concentration of the Me dopant, the γ–or β–

BIMEVOX is stabilized. Table 1.3 [103] lists the stability range of the γ–

phase for various BIMEVOXes. In addition a theoretical solid solution

limit (xmax) can be predicated for all types of substitution for vanadium,

according to the proposed equatorial (EV) model [104], which yields this

relation.

l−+

−=

3CNδ23x max (1.17)

where CN is the coordination number of dopant cation in a BIMEVOX

environment, l is the charge of dopant cation and δ represents the loss in

stoichiometric oxygen due to a partial reduction of V5+ to V4+ during the

28

preparation procedures [105,106]. However, the value of δ is very

negligible, whenever the compound was prepared in a strong oxidizing

atmosphere. It has been found that the values of calculated xmax for most

studied BIMEVOXes are in perfect agreement with the experimental

results.

Importantly, the AC impedance spectroscopic studies on most γ–

BIMEVOXes exhibit two line domains in their Arrhenius plots of

conductivities [67,98].The lower temperature domain has conductivity in

the order of 10–3 S.cm–1, which is usually associated with partially

ordered γ'–phase. Another one is noticed at higher temperatures above

500oC, which is associated with fully disordered γ–phase, having high

conductivities in the order 10–1S. cm–1 at ∼600oC. Fig. 1.14 [87] shows

the Arrhenius plots of conductivity for some γ–BIMEVOXes along with

the parent compound and other conventional oxide–ion conductors as

reference materials. Excellent ionic conductivities have been reported for

Cu–, Ni–and Co–substituted systems [66,107,108], which show oxide ion

transference numbers close to unity at moderate temperatures [109]. It

can be noted that the composition dependence of ionic conductivity for

most studied BIMEVOXes can be distinguished into two temperature

regions: high temperature (≥600oC) and low temperature (≤ 300oC)

conductivities [69,98–102,110–112].The low temperature conductivities

29

-1

-2

-3

-4

-5

1.1 1.3 1.5 1.7 1.8 2.0lo

g σ

(S.c

m-1

)1000/T(K-1)

γ

γ'BICUVOX.10

BICOVOX.10CGO

YSZ

Bi4V2O11

α

β

γ

Fig.1.14: Comparison of temperature dependence of conductivity for

some γ–BIMEVOXes with that for conventional oxide–ion

conductors [87].

30

generally exhibit a maximum in the composition ranges of γ'–

stabilization, while the high temperature conductivities show an

exponential decay with increasing the value of x. It has been found that

the substituent cations is the BIMEVOX environment do not have the

same flexibility of coordination exhibited by V5+. This generally results in

increased defect trapping effects, which negatively contribute to the total

electrical conductivity. Moreover, V4+, resulting from some extent of V

reduction, has the same effect. Thus, an increase in V reduction results in

an increase in the defect trapping, leading to lowering in the overall

conductivities and higher activation energies [88].

Many studies have been undertaken to rationalize the defect

structure in γ–BIMEVOXes [66,113]. However, the best studies are those

based on a high resolution powder neutron diffraction recorded on some

quenched γ– BIMEVOXes [88, 114, 115], which evidenced that there is a

remarkable disordering in the oxide ion vacancies in the perorskite– like

sheets (vanadate layers) and that the vacancies are mainly located in the

equatorial planes of these layers. Fig. 1.15 presents the possible vanadium

coordination environments in γ– BIMEVOXes, involving equatorial

(bridging) or/and apical (non– bridging) vacancies [116]. These studies

confirm the existence of two principal types of M/V polyhedra; distorted

octahedral (Fig.16 b) and distorted tetrahedra (Fig. 16 c). These have

31

Fig.1.15: Possible vanadium coordination environments in BIMEVOXes.

The oxide–ion vacancy is denoted by blank cube [116].

Fig.1.16: Refined oxygen positions in γ–BIMEVOXes (a) Average

crystallographic vanadium coordination, (b) derived distorted

octahedron, (c) derived distorted tetrahedrone [104].

32

been also evidence by 51V solid state NMR [117]. As a consequence, two

limiting models [104, 166] have been proposed. The equatorial vacancy

(EV) model, which assumes that all vacancies are located in the

equatorial oxygen sites, while the apical vacancy (AV) model suggests

that all vacancies are located in the apical oxygen sites. The AV model

predicts a 3:1 ratio of octahedra to tetrahedra, while in the EV model, this

ratio is 1:1. In addition, the EV model predicts that the average vanadium

polyhedron is five– coordinate, whereas in the AV model the average

vanadium polyhedron has 75% octahedral and 25% tetrahedral character.

Importantly, these model were used to present a reasonable mechanism of

ionic conduction in the BIMEVOXes. Generally, this mechanism

involves movement of equatorial oxide ions/ vacancies between

vanadium octahedra and tetrahedra with formation of a five– coordinate

intermediate, which results in the effective two– dimensional movement

of the vanadium polyhedra through the structure, which is influenced by

many structural factors, such as the polarization and arrangement of 6s2

Bi lone pairs with respect to the vacancies.

33

1.6. Synthesis routes

The standard approach to the synthesis of oxide–ion conductors in

polycrystalline form is the direct solid state reaction (ceramic route) of a

mixture of metal oxide starting materials at high temperature [118–123].

The ratios of the starting materials will control the stoichiometry of the

product, provided the volatilities of the starting materials are relatively

low. Despite, the solid state reaction is widespread used for preparation of

many oxide–ion conductors, this method has several disadvantages,

which can be summarized as follows [124]:

(i) High temperatures are generally needed in solid state synthesis

to improve reaction rates and to facilitate solid state diffusion

e.g. synthesis of CGO oxide–ion conductor requires above

about 1200 oC. In addition, the phase or compound may be

unstable or decomposes at such high temperatures.

(ii) A slow kinetics of solid state reaction. Generally, the solid state

reaction takes place at the interface of the two solids, through

which the reactants diffuse from the bulk. The diffusion process

is thermally activated, which can be further enhanced by

continuous regrinding and reheating the reaction mixture, which

result in bringing fresh surfaces in contact. However, portions

of the desired product might be lost during such treatments.

34

(iii) The product obtained by this method is often not homogeneous

in composition.

There are many alternative synthesis methods, which have been

developed to overcome some or all these disadvantages. Two of these

techniques have been employed in this study: sol–gel synthesis, which is

performed at relatively lower temperatures and results in more

homogeneous product with particles smaller than those obtained from the

intermediate grindings of the conventional solid synthesis routes. The

second technique is the microwave– assisted solid synthesis, which

employs the microwave ovens rather than the conventional (resistance)

heating, leading to a speeding up of the reaction.

1.6.1. Sol– gel synthesis

The sol–gel (solution– gelation) process is a versatile–based

process for making ceramic and glassy materials. In general, the sol– gel

process involves the formation of a sol (colloidal suspension of ca. ≥ 200

nm solid particles) and subsequent crosslinking to form a viscous gel

[125]. To prepare solids using the sol–get synthetic route, a sol of

reactants is first prepared in a suitable liquid. Sol preparation can be

either simply the dispersal of an insoluble solid or addition of a precursor,

which reacts with the polar solvent to form a colloidal product. A typical

example of the first is the dispersal of oxides or hydroxides in water with

pH adjusted so that the solid particles remain in suspension rather than

35

precipitate out [126,127]. A typical of the second method is the addition

of the metal alkoxide to water [128,130]; the alkoxides are hydrolyzed

giving the hydroxide or oxide as the colloidal product:

M−OR + H2O → M – OH + ROH (1.18)

M−OR + M−OH → M−O −M + ROH (1.19)

The sol is either then treated by dehydrating and /or polymerizing or

simply left over time to form a gel. This process is called gelation, which

prevents the development of inhomogeneities within the material. It

should be noted that the sol→gel transformation occurs when the system

passes through what is called a gel point [131] at which the sol suddenly

changes from a viscous liquid state to a solid phase gel. Dry gel can be in

two forms depending on the drying method employed: a xerogel is

formed under slow evaporation, while an aerogel is formed by

supercritical solvent extraction using CO2 [132]. Aerogels are highly

foam– like and porous materials that consist of ∼ 99% air, while xerogels

exhibit significant shrinking with higher densities. To obtain dense

ceramics, the dry gel is heated. The heat serves several purposes

[133 – 134]– it decomposes anions and organic residues in the precursors

metal complex to give free oxides, it allows rearrangement of the

structure of oxides, it allows crystallization to occur. Alternatively, the

sol can be used directly, based on post– treatments applied, to synthesize

36

a wide variety of materials, such as ultra–fine powders, thin film coatings

and ceramic fibers (Fig.1.17).

Because of a high cost of the precursors, especially that of

alkoxides, the growing interest during the past years in the area of sol–gel

processes has focused on searching for relatively effective precursors

with lower cost. Among these, is a citrate precursor. Citric acid diluted in

water can be used as a chelating agent for the cations. The pH of the

solution is then neutralized by addition of a base, such as ammonia to

obtain complete precipitation. The gel can be achieved by worming the

sol at ∼ 90 oC with continuous stirring. This method, so called sol–gel

citrate route has been quite interesting features for SOFC applications

[135–139]. Importantly, sol–gel citrate route exhibits numerous

advantages over the conventional ceramic reaction, such as low cost, soft,

safety, lower temperatures of preparation and high interdispersion of

cations that leads eventually to increase the homogeneity of the final

oxide with significantly enhanced yield.

1.6. 2. Microwave synthesis

We are all familiar with use of microwave radiation is cooking

food, where it increases the speed of reaction. Recently, this method has

been utilized to synthesize solid state materials, such as mixed oxides.

The first solid state reaction experiments were performed in modified

domestic microwave ovens, and these are still used, but more specialized

37

Metal alkoxide solution

Hydrolysis polymerization

Sol

Coating

Wet gel

Xerogel film

Dense film

Heat

Precipitating

Uniform particles

Spinning

Furnace

Ceramic fibers

Xerogel

Solve

nt

evap

orat

ion

Solvent

extraction

AerogelHeat

Dense ceramics

Gelating

Fig.1.17: Various products obtained from sol–gel synthesis.

38

microwave ovens have also been developed to give more control over the

conditions [140]. It is noteworthy that microwaves are generally

electromagnetic radiation, whose wavelength lie in the range 10–3−1m

(frequency range 0.3 − 300 GHz). A large part of the microwave

spectrum is used for communication purposes and only narrow frequency

windows centered at 900 MHz and 2.45 GHz are utilized for microwave

heating purposes.

For understanding the interaction of materials with microwaves,

these materials can be recognized into three categories [141,142]:

(i) Microwave reflectors like bulk metals and alloys (e. g. brass).

These materials are used for making microwave guides.

(ii) Microwave transmitters like fused quartz, zircon, several

glasses and ceramics and Teflon. These are used for

manufacturing cookware and container for performing

microwave– assisted reactions.

(iii) Microwave absorbers, which absorb energy from the

microwave and get heated up very rapidly. These constitute

the most important class of materials for microwave

synthesis.

The interaction of dielectric materials with microwaves leads to what

is generally known as dielectric heating [143]. Electric dipoles present in

such materials respond to the applied electric field of microwaves. The

39

reorientation dynamic of the dipoles in the applied alternating field is

significant for microwave heating. Generally, in a liquid or solid, the

molecules or ions are not free to rotate and so the heating is not the result

of the absorption of microwave by molecules undergoing rotational

transitions as they would in the gas phase. In solid or liquid, the

alternating electric field of the microwave radiation can act in two ways.

If charged particles are present that can move freely through the solid or

liquid, then these will more under the influence of the field, producing an

oscillating electric current. Resistance to their movement causes energy to

be transferred to the surroundings as heat. This is resistive heating. If no

particles are present that can move freely, but molecules or units with

dipole moments are present, then the electric field acts to align the dipole

moment. This effect produces dielectric heating. It can be noted that the

dipolar species in any medium possesses a characteristic relaxation time

(τ) and the dielectric constant (ε), which are frequency−dependent. These

quantities govern the dielectric heating process; the dielectric constant

determines the extent of dipole orientation and the relaxation time and

dielectric loss govern how efficiently the absorbed radiation is converted

to heat.

A necessary condition for the use of microwave heating in solid

state synthesis is that one component of the reaction mixture must absorb

microwaves. Table 1.4 presents most important microwave–absorbing

40

Table 1.4: Most important microware–absorbing materials.

Materials Exposure time (min) Attained temperature

(oC)

C (amorphous, <1μm) 1 1283

C (graphite, <1μm) 1.75 1073

V 1 357

W 6.25 690

MnO2 6 1287

NiO 6.25 1305

V2O5 11 714

WO3 6 1270

MoS2 7 1106

ZnBr2 7 574

1200

1100

1000

600

800

700

6000 5 10 15 20

Time (min)

Tem

pera

ture

(K)

Fig.1.18: Time–temperature profile for the microwave heating of V2O5

[147].

41

materials with their temperatures attained and corresponding exposure

times when irradiated in a domestic microwave oven(2.45 GHz) operated

at maximum power level of 1kW [144, 145]. It is clear that amorphous

carbon powder is the highest microwave absorber. The simplest

microwave– assisted solid state reaction is that occurs between C

(charcoal) and Si to obtain β– SiC [146]. SiC has been successfully

prepared by the microwave irradiation (2.45 GHz) in a domestic

microwave oven at a maximum power level of 1 kW. The entire reaction

was completed in less than 10 minutes. The temperature attained under

such conditions was very much lower than in conventional heating. It can

be pointed that Si is not a susceptor to microwaves at ordinary

temperatures, whereas charcoal is. Therefore, the reaction is initiated by

microwave heating of carbon, as a result of the excitation of weak

graphite bonds by the microwave irradiation. Importantly, V2O5 is also

microwave susceptor (Table 1.4). Fig.1.18 exhibits the time– temperature

profile for the microwave heating of V2O5 at a power of 980 W [147].

The temperature at definite time can be measured by interrupting

microwave irradiation and inserting a thermocouple into the cavity of

oven [146]. When V2O5 is one constituent of reaction mixture, the

reaction is initiated by the microwave heating of V2O5 and does not

require the presence of graphite as secondary microwave susceptor [148].

There are many studies, employing V2O5 reactant as the main microwave

42

susceptor, which revealed satisfactory results [147,149,150]. However,

this offered a motivation to use of the microwave–assisted route for the

synthesis of new substituted BIMEVOXes in which V2O5 is one of their

essential constitutions.

1.7. Characterization methods

The early attempts to discover new synthetic routes, particularly for

synthesis of fast ion conductors, introduce challenge of selecting the

appropriate physical method required for the careful investigation of

compounds in a given chemical system. The results obtained from the

characterization steps serve as a guide towards the synthesis of the

desired phase. Generally, there are several special characterization

methods, which are used to investigate the structures of oxide–ion

conductors, each technique with its own strengths and weaknesses.

However, this section describes just some of the more commonly

available techniques, which have been utilized in this study, and

information can be gleaned from each one.

1.7.1. Powder X–ray diffraction (PXRD)

Power XRD is perhaps the most widely used X–ray diffraction

technique for characterizing solid materials. As the name suggests, the

sample is usually in a powered from, consisting of fine grains of single

crystalline material to be used [151–155]. Crystalline solids consist of

regular array of atoms, ions or molecules with interatomic spacing of the

43

order of 100 pm. For diffraction to take place, the wavelength of the

incident radiation has to be of the same order of magnitude as the spacing

of the grating (dhkl), Where h, k and l are Miller indices. Fig. 1.19a

illustrates the Bragg condition for the reflection of X–rays by a crystal. A

parallel beam of monochromatic X–ray (usually Ni– filtered CuKα) is

incident to the planes at an angle θhkl. For the reflected beams to emerge

as a single beam of reasonable intensity, they must arrive in phase with

one another. This is known as constructive interference. The difference in

path length between the two parallel beams gives Bragg equation as:

λ = 2 dhkl sin θhkl (1.20)

The diffracted beams make an angle of 2θ with the incident beam.

The sample is rotated to bring as many planes as possible into the

diffraction collected. Powder diffraction data are always collected on an

automatic diffractometer (Fig. 1.19b), equipped with a computer to record

the angle and the intensity of the diffracted beams, which can instantly be

plotted as intensity against 2θ. The peak positions, intensities, widths and

shapes all provide important information, which can be summarized as

follows:

(i) Powder X–ray diffraction is usually used as a fingerprint method

for detecting the presence of a compound or phase in a product.

44

AD

IB

E GF

CH

X-ray detectorX-ray source

2θ

θ

θθdhkl

(a)

Fig.1.19: Bragg reflection from a set of crystal planes with spacing dhkl.

(b) Diagram of powder X–ray diffractometer.

(b) 0 20 40 60 80 100 120

-2000

0

2000

4000

6000

8000

10000

12000

14000

16000

Inte

nsity

2θ( degrees)

sample

Detector

X-ray source

2θθ

Measuring circle

45

This is only possible by the existence of a huge library of powder

diffraction patterns that is regularly updated, known as Joint

Committee for Powder Diffraction Standards (JCPDS) files, which

are available on CD–ROM and now on software programs.

(ii) It is useful for following the phase transitions by determining the

variation in the shape of diffraction patterns and/or in refined unit

cell parameters (a,b,c) as a function of composition and/or

temperature, which is thereby used to construct the phase diagram

of a given system.

(iii) It is a useful technique for following the progress of a solid state

reaction and determining mechanisms. It is a common feature of

solid state reaction that reaction mixtures become more crystalline

on heating , which is evidenced by PXRD pattern becoming

sharper.

(iv) It is possible to evaluate the crystallite size using Debye–Scherrer

formula, which is based on the fact that as the crystallite size

decreases, the width of the diffraction peak increases.

1.7.2 Fourier transform–Infrared (FT–IR)

The infrared spectrum of a sample is collected by passing a beam

of infrared light (usually mid–IR; 4000–400 cm–1) through the sample. If

IR beam is Fourier transformed (processed by an interferometer) prior to

be absorbed by the sample, the recorded spectrum in this case is called

46

FT–IR [156,157]. This technique is also useful in characterizing fast ionic

conductors. Most oxide–ion conductors exhibit structural phase

transitions and FT–IR spectra can provide valuable insights. For example,

it has been found that the disappearance of a particular vibrational mode

is associated with structural phase transitions in the system [158].

Moreover, the variation in the fine structure in FT–IR spectra can be

considered as an evidence for the existence of crystallographic

ordering/disordering phenomena in the oxide environment [159].

1.7.3. Thermal analysis techniques

Thermal analysis comprises a group of techniques in which a

physical property of a substance is measured as a function of temperature,

when the substance is subjected to a controlled temperature program.

These techniques are useful for investigating phase transitions,

decompositions, loss of water or oxygen and for constructing phase

diagrams [140,160,161]. In thermogravimetric analysis (TGA)

experiments, changes in the mass of a sample are monitored as a function

of time as the temperature is increased at a controlled uniform rate. The

experiments are usually performed in air or in an inert atmosphere, such

as He, Ar or N2. Some instruments like Perkin Elmer, Schimatzu, TA, etc.

are equipped with two pans (holders); one is for the test sample and

another for inert reference material, such as α–Al2O3 (Fig. 1.20a). Each

pan is connected to a voltmeter through a sensor (thermocouple).

47

(a)

Exothermic

EndothermicDiff

eren

tial t

empe

ratu

re

T ( oC)

T ( oC)

Wei

ght

Mres

Tonset

(b)

(c)

Fig.1.20: (a) Schematic illustration of DTA/DSC cell, (b) DTA and (c)

TGA curves.

48

Such instruments are used for recording the difference in temperature

between the sample and reference materials against either time or

temperature as the two pans are subjected to identical temperature

regimes in an environment heated or cooled at a controlled rate. Such

experiment is referred to as differential thermal analysis (DTA). If the

difference in the heat flow into the sample pan to that of the reference pan

is monitored, the technique is so called Differential scanning calorimetry

(DSC).

However, both DTA and DSC are basically similar in providing the

same characterization information. Any reaction in the sample will be

translated as a peak in the DTA plot (differential temperature vs.

temperature) as shown in Fig. 1.20b. Endothermic reactions give a

decrease in temperature and exothermic ones an increase. Therefore, the

peaks appear in opposite directions. DTA can be used to study thermal

properties and phase changes. Many pieces of information [162,163] can

be obtained from DTA curves, such as the transition temperatures (onset

temperatures of the peak) , the microstructural constitution at phase

changes, which is related to the slope of the curve and the enthalpy

change of transition, which is deduced from the area under the DTA peak.

However, TGA experiments are very useful for following the loss

of water of crystallization or volatiles, such as oxygen and for

investigating thermal decompositions of precursor metal complexes

49

prepared by sol–gel route. In TGA curves, where a weight is plotted

against temperature (Fig. 1.20c), two interesting pieces of information are

obtained; the weight loss onset temperature (Tonset) and the residual or ash

mass (Mres).

1.8. Electrical properties of oxide–ion conductors

DC conductivity measurements are useful in accurately

determining the long–range ion migration in fast ion conductors.

However, the difficulty in performing DC measurements is in finding an

electrode material that is compatible with the solid electrolyte and that

does not give polarization effects at the electrode–oxide–ion conductor

interface, which thereby the cell behaves as a capacitor. The alternative to

DC conductivity measurement is the use of AC impedance spectroscopy,

which has become a powerful tool for investigation of the ionic

conductivity in oxide–ion conductors [164,165]. Impedance is a totally

complex resistance encountered when a current flows through a circuit

made of resistors, capacitors or inductors or any combination of these. In

impedance spectroscopy, the voltage (current) response to an alternating

current (voltage) is measured as a function of frequency. AC impedance

measurements are often made with a Wheatstone bridge type of apparatus

(Fig. 1.21a) in which the resistance (R) and capacitance (C) of the sample

are balanced against variable resistors and capacitors. During balancing

of the impedance bridge at a certain frequency, the bridge readings give

50

the value of complex impedance (Z*(ω)), corresponding to composite R

and C values of the cell, which change with frequency. In practice, the

impedance data are represented by a complex plane plot (Cole–Cole plot)

[166], which involve plotting the imaginary part of impedance (Z")

against the real part (Z'):

Z* (ω)=Z'(ω)+jZ"(ω); j= 1− (1.21)

Therefore, the analysis of AC impedance data of oxide–ion conductors

may require complex equivalent circuits [167–169] as shown in the insets

of Fig. 21b–e.

For the simplest equivalent circuit (Fig. 21b) that contains a

resistance and capacitance in series, the values of Z' and Z" are given by:

222

2

222 1"

1'

CRCRZand

CRRZ

ωω

ω +=

+= (1.22)

where, ω is the angular frequency (ω=2πf). It can be noted that the

equations become more complicated as the number of circuit elements

increases.

Most oxide–ion conductors, particularly BIMEVOXes [99,170–

174] in their polycrystalline forms, exhibit two semicircular arcs with an

inclined spur at the lowest frequencies as shown in Fig. 21e. The overall

resistance of the sample (Rt) is a combination of grain and grain boundary

resistances, Rg and Rgb. Both resistances are in parallel with their

associated capacitances, Cg and Cgb, respectively. The interface between

51

sample

(a)

(b) (c)

(d) (e)

R1

C1

Fig.1.21:(a)Wheatstone bridge of AC impedance measurements,

(b–e) Various complex impedance plots with their equivalent

circuits.

Z''(

Z''(o

hm)

'(o

Z''(o

hm)

Z'(ohm) Z'(ohm)

Z'(ohm) Z'(ohm)

ohm

)Z'

hm)

R

C

R

C1

C2

Rg Rgb

Cg Cgb

Rg Rgb

Cg Cgb

Cdl

Re

52

the electrodes and oxide–ion conducting material is characterized by its

double layer capacitance (Cdl), which is effectively in series with the

sample resistance. It is noticed that the grain boundary resistance may not

necessarily be larger than Rg. This is due to the fact that the grain

boundary layer may be several orders of magnitude thinner than the

grains. Importantly, the total AC conductivity is given by:

⎟⎠⎞

⎜⎝⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛=

AL

R1σ

tAC (1.23)

where A is the flat surface area of electrodes and L is their separation.

The activation energy of conduction is easily calculated from the slope of

logσT vs. 1000/T plots using a linear square fitting according to

Arrhenius dependence:

⎟⎠⎞

⎜⎝⎛ −

=kTEAT aexpσ (1.24)

It is also possible to measure the magnitude of sample polarization, which

is typically associated with the dielectric permittivity (ε):

⎟⎠⎞

⎜⎝⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛=

AL

εCε

o

(1.25)

where εo is the permittivity of free space, 8.85 x 10–14 Fcm–1 AC

impedance spectroscopy is also useful technique for investigating phase

transitions and for studying microstructural properties of oxide–ion

conductors, such as the inter–particle effects between the grain interiors

and grain boundaries, the charge carrier accumulation and the kinetics of

relaxation processes.

53

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