Ishihara T. (Ed.) Perovskite Oxide for Solid Oxide Fuel Cells (Fuel Cells and Hydrogen Energy)

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occur. Sunde et al. [7] have recently pointed out some of these effects when

using the potential step method. By far the most direct method of measure-

ment is the use of isotope exchange followed by secondary ion mass specto-

metry (SIMS) depth profiling, as descri bed in our earlier publications [8,9],

often known as the isotope exchange depth pro filing tech nique (IE DP).

This technique yields the tracer diffusion coefficient, D,andthemajority

of the data included in this review were obtained using the IEDP/SIMS

method.

5.1.3 The Surface Exchange Coefficient

The oxygen surface exchange coefficient, k, is another important kinetic

parameter associated with the measurement of oxygen transport rates in

these oxide materials. It is a measure of the neutral oxygen exchange flux

crossing the surface of the oxide, at equilibrium, as described by the following

reaction [10]:

þ V



þ e

$ O

(5:9)

This flux will be dependent upon the surface vacancy concentration, the

surface electron concentration, and the dissociation rate of the dioxygen mole-

cule; however, at present, the rate-limiting step has yet to be identified. Kilner

et al. [11] have derived a simple relationship for the surface exchange coefficient

in terms of the bulk and surface vacancy concentrations, in an attempt to

explain the apparent correlation found between the activation enthalpy for

the surface exchange coefficient and the diffusion coefficient, in a number of

La-based perovskites. Adler et al. [12] have also arrived at a similar relationship

for k, by consideration of the AC electrode behavior of symmetrical cells with a

‘‘double’’ cathode structure. As already mentioned, the exact mechanisms of

oxygen surface exchange remain elusive; however, the vacancy concentration is

clearly a very important parameter.

On a more practical level, the influence of the surface exchange on

cathode performance has been recently emphasized by both Adler et al.

[12] and St eele [13 ]. They have both stressed the importance of a character-

istic length L

defined as the ratio of the two parameters D/k. This length is

the c hangeover point at which the permeation flux of oxygen through a

thin mixed conducting membrane (such as a cathode) changes fr om being

limited by diffu sion in the membrane to being limited by the surface

exchange process. For a more detailed discussio n of the interpretation of

the surface exchange c oefficient, the reader is referred to the work of Maier

[14] and De Souza [15].

98 J.A. Kilner et al.

5.1.4 Defect Chemistry and Oxygen Transport

A large number of different materials adopt the perovskite structure, however

in terms of the oxygen transport the most studied are materials for applications

in solid oxide fuel cells (SOFCs) and oxygen separation membranes. The

materials are usually 3,3-perovskites (with the general formu la A

3þ

)

with lanthanum on the A site, a transition metal on the B site, and acceptor

doped on the A site, usually with strontium. One of the main feat ures of these

mixed conducting perovskites is that they show a large range of stoichiometry,

which can vary from hypostoichiometric to hyperstoichiometric; this will alter

both the electrical conductivity and the oxygen exchange and transport proper-

ties. To understand the oxygen transport properties, we first look at the theo-

retical defect structure of these mixed con ducting perovskites and then compare

the predicted behavior with experimental results.

5.1.5 Defect Equilibria

The defect structure of these materials is far from simple, with a number of

coincident defect equilibria contributing to the observed behavior. First, we

must consider the intrinsic defect processes for a hypothetical mixed conductor

1–x

3d

, which undergoes Schottky disorder together with intrinsic

electronic disorder. Following an analysis given in [16]:

‘‘0’’ ! V

000

þ V

000

þ 3V



(5:10)

‘‘0’’ ! e

þ h



(5:11)

Equation (5.11) can also be viewed as the dissociation of the effectively

neutral B cation (+3) into two charge states (+2 and +4):

! B

þ B



(5:12)

For perovskites with variable valent B cations, the redox processes that occur

in the lattice must also be taken into account. Oxidation of the lattice can lead to

oxygen excess material in which cation vacancies form [17].

þ 6B

! 3O

þ V

000

þ V

000

þ 6 B



(5:13)

In this oxygen excess region, the formation of cation vacancies will have the

effect of strongly decreasing the oxygen vacancy concentration through the

Schottky equilibrium.

5 Diffusivity of the Oxide Ion in Perovskite Oxides 99

Compensation of the acceptor can occur either by elect ronic or by a vacancy

mechanism, or perhaps more importantly for these materials, by a combination

of the two.

2SrO þ

þ 2B

! 2Sr

þ 3O

þ 2B



(5:14)

2SrO ! 2 Sr

þ 2O

þ V



(5:15)

The resulting neutrality condition then contains all the possible defect species

3 V

000



þ 3 V

000



þ Sr



þ B



¼ 2 V





þ B





(5:16)

To construct a Brouwer diagram to depict the relative concentration of these

defects with P

, it is necessary to define a series of approximations to the full

neutrality condition. The first of these corresponds to a region (R I) where d > 0

and where the material is hyperstoichiometric.

3 V

000



þ 3 V

000



¼ B





(5:17)

This region is followed by a stoichiometric region (R II) where the material

acts a s a controlled valence semiconductor and d ¼0.



¼ B





(5:18)

One of the most important features of these materials is that the compensa-

tion of the acceptor does not change abruptly from electronic to vacancy

compensation, but there is an extensive region in which the compensation is

mixed. Here the material is hypostoichiometric; d now becomes negative and

lies between 0 and –x/2, where x is the concentration of the acceptor (R III).



¼ 2 V





þ B





(5:19)

Next there is a region (R IV) where the material is vacancy compensated and

the value of d is fixed at d ¼x/2.



¼ 2 V





(5:20)

And finally, the material becomes reduced (R V), and we get the production

of oxygen vacancies and electrons:



¼ 2 V





(5:21)

100 J.A. Kilner et al.

The five regions are shown in Fig. 5.1 for a general 3,3 acceptor (A

2þ

)-doped

perovskite with the rare earth ion (RE) on the A site, RE

1x

To compare with experimental data, we now need to e xamine a number of

materials. Nonstoichiometry data for three 3,3 acceptor-doped perovskites

with the B cations Mn, Fe, and Co are shown in Fig. 5 .2 as a function of P

at 10008C [18,19]. It is clear that the manganite is hyperstoichiometric (R I, d > 0)

at high P

s(P

 1), even though it is acceptor doped. As the P

is lowered,

the manganite shows a plateau corresponding to R II behavior, i.e., d ¼ 0. This

behavior implies that the oxygen vacancy concentration will be very low indeed,

and this remains true even for quite heavily acceptor doped material. The

manganite material shown in Fig. 5.2 does not become hypostoichiometric

(R III, d < 0) until oxygen partial pressures approaching 10

10

atm. are reached.

Thus, under normal SOFC cathode operating conditions, the manganite

materials are expected to have low vacancy concentrations and consequently

IIIIIIIVV

][2

••

][

][2

V =

••

][2

][

••

−

][

Ap =

][6

///

Vp =

+δ

–δ

]Log[V

••

Log

n-type p-type

p-type

][

−

••

∝

][][

REO

AV =

••

][

−

••

∝

][

−

••

∝

][

−

••

∝

Neutrality

condition

LogP

Fig. 5.1 Brouwer diagram for an acceptor-doped RE

1x

oxide showing the oxygen

content, d, oxygen vacancy concentration, V





, and electrical conductivity, s, as a function

of oxygen partial pressure [59]

5 Diffusivity of the Oxide Ion in Perovskite Oxides 101

low oxygen self-diffusivities. A more extensive set of nonstoichiometery

isotherms for the manganite compositions has been published by Tagawa

et al. [20].

Incomparisontothemanganite,thecobaltiteandferriteareseentobein

the mixed compensation region (R III) at high P

s,wherethevalueofd lies

between 0 and x/2. Thus, fairly high oxygen vacancy concentrations, and

consequently oxygen diffusivities, are to be expected under normal cathodic

conditions. For the ferrite, a plateau is seen at the lower P

that corresponds

to R IV behavior, indicating that the acceptor is vacancy compensated and the

material would become a predominantly ionic conductor. From these data,

and the preceding analysis, it is obvious that there are significant changes in

the defect populations in these acceptor-doped materials that depend on the

temperature, oxygen partial pressure, and perhaps most importantly, the

identity of the transition m etal in the B-cation site. We now look at the way

in which composition changes affect the oxygen transport properties of t hese

oxides.

5.2 Diffusion in Mixed Electronic-Ionic Conducting

Oxides (MEICs)

MEICs display some very interesting electrochemical properties and because

of this are used as cathodes for the SOFC, both at high and intermedi ate

temperatures, and in permeation membranes for the separation of oxygen.

log

[

/(atm)

]

–20 –15 –10 –5 0

3 - δ

2.75

2.80

2.85

2.90

2.95

3.00

3.05

MnO

3–δ

0.6

0.4

FeO

3–δ

0.7

0.3

0.8

0.2

CoO

3–δ

Fig. 5.2 Nonstoichiometry

data for the acceptor-doped

perovskites La

1x

3d

(B ¼ Mn, Fe, and Co) as a

function of P

at 10008C

[18, 19]

102 J.A. Kilner et al.

The materials chosen for the development of commer cial application are based

on perovskite MEICs; however, most of them have very complex compositions

involving both A- and B-site substitution. This situation can lead to problems in

any discussion of the literature on these materials because families of materials

are often referred to by the use of acronyms. For example, LSM and LSCF are

often used to denote cathode materials, but these acronyms cover a range of

materials of various levels of Sr substitution, B-site substitution, and often A-

site deficiency, leading to sets of materials with very different properties. The

exact composition must thus be used to compare the oxygen transport proper-

ties within and between each group of materials. As a further note of caution, it

is also rare to see detailed analysis of the purity of the materials, which might

affect the transport of oxygen, particularly in ceramic samples where the grain

boundaries can affect the overall transport rates.

5.2.1 Effect of A-Site Cation on Oxygen Diffusivity

Two types of substitution into the A site in the perovskite structure are possible.

Aliovalent doping occurs when the oxidation stat e of the substituting ion is

different from the host ions, thus introducing effective charges for the substitute

ion. To mainta in electrical neutralit y, these charges have to be compensated by

the formation of oppositely charged defects. This state can be achieved either

by changing the oxidation state of the B cations (electronic compensation) or by

the formation of oppositely charged vacancies (ionic compensation), as was

discussed earlier for acceptor-doped materials. Isovalent doping occurs when

the oxidation state of the substituting and host ions is identical. As a result, no

charges are introduced into the A-site sub-lattice and no charge compensation

is required; however, there will be elastic strain effects because of the size

mismatch of the host and the substituting cation.

Several combinations of elements have been used as A-site host and substitu-

tional ions. Historically, lanthanum has been a host ion of a choice for the past

several decades due to its large ionic radius and relative availability. Alkaline

earth elements have been used as substitutional ions due to their close size match

to the lanthanides and thermodynamic stability at the operational conditions of

the SOFC. The effect of alkaline earth doping on the oxygen tracer diffusion

coefficient in several families of perovskite compounds is shown in Fig. 5.3a

(for Sm

1x

CoO

at 7938C[21]andLa

1x

CoO

at 8008C[22–24])and

Fig. 5.3b (for La

1x

CrO

at 9008C [25], La

1x

MnO

at 9008C [23, 26],

and La

1x

FeO

at 10008C [27]). All these data were obtained from experi-

ments carried out at high oxygen partial pressures ( 1 bar), to simulate opera-

tion in an SOFC cathode environment. Note from observation of Fig. 5.3a that

although all the isothermal diffusivities increase with an increase in the acceptor

doping, the changes seen for the cobalt-based materials (by six orders of

5 Diffusivity of the Oxide Ion in Perovskite Oxides 103

magnitude) are much larger that the relatively modest increases seen for the Cr

and Mn analogues.

It is generally accepted that oxygen diffusion in these perovskite compounds

occurs via oxygen vacancy mechanism. Consequently, the increase in the diffu-

sion coefficient with doping is most likely caused by the increased concentration

of oxygen vacancies. However, as we have seen, the identity of the B cation will

determine which of the neutrality approximations is valid for each group of

materials (i.e., RI, II, III, etc.). Thus, the spectacular increase of the oxygen

tracer diffusion coefficient in cobaltites with doping is related to the large values

of oxygen hypostoichiometry observed in those compounds (R III) [28]. How-

ever, some care is needed in this interpretation at this stage as it must be

remembered that the diffusivity arises as a result of the product of the vacancy

concentration and the vacancy diffusion coefficient (Eq. 5.8), which we examine

in more detail below.

5.2.2 The Effect of B-Site Cation on Oxygen Diffusivity

Only one systematic study has been carried out to investigate the effect of B-site

cation on oxygen diffusivity [23]. The effect of doping La

0.8

0.2

MnO

3d

with

cobalt is shown in Fig. 5.4. The substitution enhances the diffusivity by five

orders of magnitude and the surface exchange coefficient by two orders of

magnitude at 10008C. This is quite an interesting finding, because the level of

strontium substitution on the A site remains constant. Clearly, the nature of the

B cation is again determining the nature of the neutrality approximation, and it

would be apparent from the earlier data given in Fig. 5.2 that we are moving

from La

0.8

0.2

MnO

3+d

(R I) to La

0.8

0.2

CoO

3d

(R III).

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

–5

–6

–7

–8

–9

–10

–11

–12

–13

–4

1-x

CoO

1-x

CoO

(cm

–1

)

Site fraction Sr (x)

–10

–11

–12

–13

–14

0.0 0.2 0.4 0.6 0.8 1.0

1-x

CrO

1-x

MnO

1-x

FeO

(cm

–1

)

Site fraction Sr and Ca (x)

Fig. 5.3 Effect of aliovalent doping on the tracer diffusion coefficient in (a)RE

1x

CoO

(RE ¼ La, Sm at 8008C [21–24]) and (b)La

1x

TmO

(A ¼ Sr, Ca; Tm ¼ Cr, Mn at 9008C

[22, 25, 26], and Tm ¼ Fe at 10008C [ 27]). Nominal pressure during the experiments was 1 atm

except for [22, 27] where a pressure of 34 and 40 torr was used, respectively

104 J.A. Kilner et al.

5.2.3 The Effect of A-Site Cation Vacancies

on Oxygen Diffusivity

The effect of A-site vacancies on oxygen diffusion in perovskite materials has

been studied in lanthanum-deficient La

1y

MnO

(y ¼ 0, 0.1) [26]. It was found

that introduction of 10% La vacancies has no effect on the values of oxygen

tracer diffusion coefficient. The activation energy for oxygen diffusion

increased from the value of 2.49 eV in a stoichiometric sample to 3.05 eV in

0.9

MnO

. It was assumed that oxygen vacancies formed by the introduction

of La deficiency, are bound in to the defect complexes (e.g., V

000

 V





Similarly, no effect of A-site deficiency was observed on the parameters of

chemical diffusion of oxygen in (La

0.85

0.15

)

CoO

3d

(s ¼ 0.98, 1 [29]).

5.2.4 Temperature Dependence of the Oxygen

Diffusion Coefficient

In addition to following the isothermal effects, it is also quite important to

understand the changes that take place in the observed activation energy for

diffusion as a function of the composition. The ease of oxygen ion diffusion in

perovskite structure is usually attributed to the value of the apparent activation

energy estimated from the Arrhenius plots of diffusion coefficient. This appar-

ent activation energy, E

, however, consists of several terms, as indicated in the

following equation:

¼ H

þ H

(5:22)

Here H

is the enthalpy of vacancy migration, H

is the enthalpy of vacancy

formation, and  H

is the enthalpy of vacancy–dopant association, e.g.:

þ V



, Sr







(5:23)

0.0 0.2 0.4 0.6 0.8 1.0

–4

–5

–6

–7

–8

–9

–10

–11

–12

–13

(cm

–1

) and k(cm s

–1

)

Site fraction Co (x)

Fig. 5.4 The oxygen self-

diffusion coefficient, D, and

surface exchange coefficient,

k, for La

0.8

0.2

1x

3d

at 10008C as a function

of Co site y [23]

5 Diffusivity of the Oxide Ion in Perovskite Oxides 105

H

affects the stoichiometric vacancy concentration wher eas H

affects

the mobile vacancy concentration and H

only enters into the vacancy diffu-

sion coefficient. Thus, if we can determine the stoichiometric vacancy concen-

tration (or, more accurately, the mobile vacancy concentration), then we can

extract the value of D

, leading to a value for  H

First, let us look at the overall effect of alkaline earth doping on the apparent

activation energy of tracer diffusion in La

1x

TmO

(A ¼ Sr, Ca Tm ¼ Mn,

Fe, Cr), and RE

1x

CoO

(RE ¼ La, Sm), shown in Fig. 5.5(a) and 5.5(b),

respectively. Although a large scatter of data is present, presumably due to

differences in oxygen partial pressure during diff usional anneals, it is evident

that the activation energy increases with doping for Mn- and Cr-b ased perovs-

kites and decreases with doping for Fe- and Co-based perovskites.

To clarify some of this differing behavior, the vacancy diffusion coefficients

have been estimated from oxygen tracer diffusion experiments and using ther-

mogravimetric studies to provide the stoichiometric vacancy concentration. A

correlation factor, f, of 0.69 was used in the calculation. The calculated values of

the vacancy diffusion coefficient in several families of perovskite materials are

shown in Fig. 5.6. Remarkably, and as mentioned earlier, the values calculated

for perovskite oxides, with significantly different oxygen diffusion coefficients

and temperature dependencies, appear to have very similar values of vacancy

diffusion coefficient. The activation energy of vacancy diffusion in the perovs-

kite structure is 0.94  0.07 eV irrespective of the nature of the constituent

ions. This value is close to the migration enthalpy for oxygen vacancies calcu-

lated by atomistic simulation techniques for 0.67 eV (LaMnO

3d

) [30] and in the

range 0.6–0.8 eV reported for several perovskites by Islam [31].

0.0 0.2 0.4 0.6 0.8 1.0

1.0

1.5

2.0

2.5

3.0

3.5

4.0

act.

(eV)

Site fraction Sr and Ca (x)

1-x

CrO

1-x

MnO

1-x

FeO

act.

(eV)

0.0 0.1 0.2 0.3 0.4 0.5 0.6

1.0

1.5

2.0

2.5

3.0

3.5

Site fraction Sr (x)

1-x

CoO

1-x

CoO

Fig. 5.5 The effect of aliovalent doping on the apparent activation energy of tracer diffusion

in La

1x

MnO

(a) at 1 atm [23,26] and 0.13 atm [60], La

1x

CrO

(a) at 0.13 atm [25],

1x

FeO

(a) at 0.06 atm [27, 36], La

1x

CoO

(b) at 1 atm [23,61], and 34 tor [22],

1x

CoO

(b) at 1 atm [21]

106 J.A. Kilner et al.

There are several very interesting implications from this finding. It would

suggest that the differences seen between the activation energies measured for

the different pe rovskite materials are the result of changes in the values of either

the association or vacancy formation energies. It is difficult to discriminate

between the two components; however, some observations are helpful.

1. The majority of the materials under discussion here are composed of perovskites

made nonstoichiometric by the substitutionofLabySr.Theextentofvacancy

trapping, of the form shown in Eq. (5.23), can be estimated from atomistic

calculations of the association enthalpy, H

. This value has been calculated by

Islam [32] for the related Sr-doped lanthanum gallate material to be essentially

zero, implying that trapping would not occur and that the vacancies are essen-

tially free to participate in the migration process. The major part of this trapping

energy has been shown to be the elastic contribution due to the size mismatch

between the host and the substitutional cation [2], and hence the close size match

of the La

3þ

(1.36 A

) and Sr

2þ

(1.44 A

) ions leads to a minimization of this term.

2. The close match of D

from very different materials was obtained using the

stoichiometric vacancy concentrations determined by Thermogravimetric

Analysis (TGA); this implies that all these vacancies are mobile and hence

that trapping is negligible.

If we can discount the effects of vacancy trapping, then the major differ-

ences seen in the activation enthalpy are ascribable to differences in the

vacancy formation energy. Tagawa et al. [33] have noted that the partial

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2

1E-7

1E-6

1E-5

1E-4

1500 1200 900 600

1-x

CoO

x = 0.1 [34],

x=0.2 [23],

x = 0.5 [23]

1-x

FeO

x = 0 [36],

x = 0.1 [34],

x = 0.25 [34]

0.9

0.1

CrO

[62]

0.6

0.4

0.2

0.8

3−δ

[37]

(cm

–1

)

–1

x 10

–1

)

0.85

0.15

1.85

1.99

0.88

0.12

1.88

CeO

1.92

Temperature (°C)

Fig. 5.6 Temperature dependence of the oxygen vacancy diffusion coefficient in perovskites:

1x

CoO

3d

(x ¼ 0.1 [34], x ¼ 0.2 [23], x ¼ 0.5 [23]), La

1x

FeO

3d

(x ¼ 0 [36], x ¼ 0.1

[34], x ¼ 0.25 [34]), La

0.9

0.1

CrO

3d

[62], La

0.6

0.4

0.2

0.8

3d

[37]. Data for fluorite-

based oxides (Zr

0.85

0.15

1.85

,Zr

0.88

0.12

1.88

,UO

1.99

, and CeO

1.92

) have been taken from

reference [34]

5 Diffusivity of the Oxide Ion in Perovskite Oxides 107