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

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molar enthalpy for oxidation/reducti on in the LSM materials is substantial

and thus account for the large values of activation energy seen in these

materials.

The decrease in activation energy seen for the cobalt- and iron-based

perovskites with increasing the substitution of La with Sr is also caused by

changes in the vacancy formation component. In early work the energy of

vacancy formation was calculated to decrease with alkaline earth doping in

1x

FeO

3d

and La

1x

CoO

3d

[34]. Later, Lankhorst and Bouwmeester

[35] provided a model for this effect for La

1x

CoO

3d

by considering terms

due to the gradual filling of a broad conduction band by the electrons produced

by vacancy formation.

Interestingly, the vacancy diffusion coefficients in several oxides with the

fluorite structure have also been included in Fig. 5.6 and display values

close to the ones found in the perovskites but with a slightly lower activation

energy of 0.47–0.62 eV [36]. This result implies that the vacancy diffusion

coefficient (mobility) of the oxygen vacancies in these different oxide struc-

tures is very close, and that the major discriminator for oxygen diffusion is

the free vacancy concentrations and the degree of vacancy trapping. The lack

of trapping in the Sr-substituted La perovskites is certainly an important

factor in achieving the very high oxygen diffusion coefficients measured for

these materials.

5.2.5 The Effect of Oxygen Pressure

Rather surprisingly little work has been done on the effect of oxygen partial

pressure on the diffusivity of oxyge n, probably because of the experimental

difficulties in obtaining reliable pressure dependence data. One interesting

study that adds weight to the previous argu ment about the vacancy diffusion

coefficient is shown in Fig. 5.7 [37]. This work on the mixed conducting, mixed

B-site perovskite La

0.6

0.4

0.2

0.8

3d

shows the oxygen diffusivity decreas-

ing with increasing oxygen pressure at 8008C. If the stoichiometric vacancy

concentration determined from TGA measurements taken at the same tem-

perature is used to derive the vacancy diffusion coefficient, we see again that the

isothermal vacancy diffusion coefficient is constant and corresponds well to the

values obtained in Fig. 5.6.

5.3 Oxygen Diffusion in Ionic Conducting Perovskites

There are several La-based perovskites that display predominantly ionic con-

ductivity: these are the materials based on LaYO

[38], LaAlO

[39], and LaGaO

[40]. In the gallate, the oxygen ion conductivity is enhanced by doping both the

108 J.A. Kilner et al.

A- and B sites with Sr and Mg, respectively. The oxygen ion diffusivity is easily

obtained in these materials from the ionic conductivity, and only a few measure-

ments have been made of the tracer diffusivity. For the main material of the series

1x

1y

3(x+y)/2

(LSGM 8282) [40], the measured oxygen diffusi-

vity is higher than that in 9.5 mol% yttria-stabilized zirconia (YSZ), as shown in

Fig. 5.8. This finding again is most probably due to the finding in the section on

MEICs that there is very little trapping of the vacancies in these La-based

perovskites, yielding very high mobile vacancy concentrations.

log

[PO

/(bar)]

–2.5 –2.0 –1.5 –1.0 –0.5 0.0

log

[D*/(cm

/s) or D

/(cm

/s)]

–8

–7

–6

–5

–4

Fig. 5.7 Dependence of the

tracer diffusion coefficient

and the vacancy diffusion

coefficient D

on the partial

pressure in La

0.6

0.4

0.2

0.8

3d

at 8008C [37]

0.70.80.91.01.11.21.3

–16

–14

–12

–10

–8

–6

–4

Log

/(cm

–1

)]

–1

)

9.5 mol% YSZ

0.9

0.1

LSGM 9182

LSGM 8282

Fig. 5.8 Arrhenius plot of

the oxygen ion diffusivity in

ionic conductors with

fluorite (9.5 mol% YSZ [63])

and perovskite (La

0.9

0.1

[38], LSGM 9182 [40],

and LSGM 8282 [40])

structures

5 Diffusivity of the Oxide Ion in Perovskite Oxides 109

5.4 Oxygen Diffusion in Perovskite-Related Materials

There is a large number of materials with structures related to the parent perovskite

structure; these include the Ruddleston-Popper series (A

n+2

n+1

3n+4

), of

which the first member has the K

NiF

structure (n ¼1). Materials of this type

have been inv estigated recently for their oxygen diffusion properties, most

notablytherareearth-basedRE

NiO

4d

. These materials have an oxygen

excess at high oxygen partial pressures and display diffusion by oxygen inter-

stitials. These materials, although interesting, are not reviewed further in this

chapter.

Some interesting findings have very recently been published on materials with the

double perovskite structure. Doubling the perovskite formula gives the composition

. By having 50% substitution on the A site by a substitutional (A*) ion gives

the formula AA*B

. If the substitutional ion has a lower valence, then a material

such as AA*B

5+d

can be obtained. It has been recently recognized that ordering

of A and A* ions can play an important role in the oxygen diffusion in these

perovskite-related materials. High-resolution electron microscopy study of the

double perovskites GdBaCo

5+d

(0  d  1) revealed that Gd and Ba ions were

ordered in the alternative (0 0 1) layers with oxygen vacancies located predominantly

in the GdO planes [41]. This particular arrangement of oxygen vacancies appeared

to facilitate oxygen transport. The high values of oxygen tracer diffusion (around

9

1

at 5758C) and low values of the activation energy for oxygen tracer

diffusion of 0.60 eV were observed in GdBaCo

5+d

[42] and PrBaCo

5+d

[43].

5.5 Correlations Between Oxygen Diffusion Parameters

Many attempts have been made to rationali ze the differences seen in the diffu-

sion of oxygen in the perovskites in terms of a simplified parameter such as the

tolerance factor, t 

ðr

þr

ﬃﬃ

ðr

þr

. Hayashi et al. [44] evaluated a large amount of

available data on the ionic conductivity in perovskite materials. They came to

the conclusion that the highest ionic conductivity occurred when the perovskite

has a tolerance factor around 0.96, large specific free volume (unit cell volume

minus volume of constituent ions), and a ratio of dopant to host ion ionic radii

of around 1.05. As a result, perovskites with Sr substitution for La exhibit the

highest values of ionic conductivity. In addition, computer simulations showed that

Sr ion substituted on La site has the lowest solution energy in several series of

perovskite compounds [45,46]. Several attempts have been made to correlate

parameters of diffusion or ionic conductivity (mostly the activation energy) with

the structure and chemical composition of the perovskite material [11, 44, 47–49].

For example, a decrease in the activation energy of oxygen diffusion in perovskites

was observed with the decrease of the average metal–oxygen bond [47], increase

inthefreevolume[47],andincreaseinthecritical radius of saddle point, which

is traversed by the diffusing oxygen ions and defined by the triangle formed by two

110 J.A. Kilner et al.

A cations and one B cation [48]. Furthermore, it has been observed that correla-

tions exist between measured transport parameters, e.g., the relationship between

the self-diffusion coefficient and the surface exchange coefficient [11].

Recently, the analysis of a large set of available tracer diffusion data in

perovskite materials revealed a correlation between the measured values of pre-

exponential coefficient and activation energy during oxygen diffusion [49]. In

acceptor-doped LaMnO

LaCoO

, LaFeO

,LaCrO

, and donor-doped ATiO

(A ¼Ba, Sr, Ca), a linear correlation was observed between the activation energy

of the process and the logarithm of the pre-exponential coefficient (Fig. 5.9). This

correlation, called the Meyer–Neldel rule (MNR), or compensation law, is

observed in a wide range of thermally activated processes in physics, chemistry,

and biology [50]. For example, the parameters of silicon diffusion in silicate

materials [51], proton diffusion in perovskite-type oxides [52], and Pd self-diffu-

sion [53] were all shown to obey the Meyer–Neldel rule.

The expression for the tracer diffusion coefficient (Eq. (5.4)) can be rewritten

as follows:



fð1  c

Þa

 exp

S

þ S





exp 

H

þ H



(5:24)

where all symbols have the meanings defined previously. As discussed earlier,

several processes could take place during oxygen diffusion, namely, oxygen ion

migration, vacancy formation, and dissociation of the oxygen vacancies from

trap sites (e.g., dopant cations). Consequently, the entropies of migration, S

;

vacancy formation, S

; defect association, S

; and the enthalpies of migra-

tion, H

; vacancy formation, H

and defect association, H

; are included

in Eq. (5.24). Although the nonexponential parameters in Eq. (5.24) depend on

012345

–8

–10

–6

–4

–2

Manganites

Titanites

012345

–8

–6

–4

–2

Log

/(cm

–1

)]

Log

/(cm

–1

)]

act

(eV) E

act

(eV)

Ferrites

Cobaltites

Chromates

Fig. 5.9 Relationships between the activation energy of oxygen tracer diffusion and the

logarithm of pre-exponential coefficient in ferrites (a), chromates (a), cobaltites (a),

manganites (b), titanates (b). The lines are a guide to the eye

5 Diffusivity of the Oxide Ion in Perovskite Oxides 111

the chemical composition of perovskite material and the environmental para-

meters (predominantly temperature and oxygen partial pressure), it is doubtful

that their variation can result in the observed values of the pre-exponential

coefficient, which differ by several orders of magnitude. Indeed, the correlation

factor, f, is estimated to be around 0.67 in perovskite structure [34]; the lattice

parameter of a pseudo-cubic perovskite cell, a

, is around 4  1A

for a large

number of perovskite materials [54]; the characteristic lattice frequency, n

,is

around 10

–10

Hz [55]; and the number of equivalent near-neighbor sites, z,

is 6 in the ideal cubic perovskite. The major variation among the nonexponen-

tial terms is expected for the fraction of unoccupied equivalent sites (1 – c).

For example, oxygen stoichiometry, d, varies by three orders of magnitude in

Sr-doped cobaltite, La

1x

CoO

3d

[18, 56]. At the same time, the variation of

of more than nine orders of magnitude is observed (Fig. 5.9a). Conse-

quently, the MNR is naturally observed only when a linear relationship

between any of the entropy and enthalpy terms is present .

There are several models that attempt to relate the entropy and the enthalpy of

thermally activated processes in general and diffusion in particular. Zener [57]

proposed that the major part of the free energy of the activated state is associated

with elastic distortion of the lattice caused by the diffusing ion. An alternative

relationship between the entropy, S

, and the enthalpy of diffusion, E

, was used

by Almond and West [58] to explain the MNR in AgI–Ag

MoO

glasses:

¼ E

(5:25)

where temperature, T

, was related either to the melting temperature or tem-

perature of an order–disorder transition in the material. Recently, a model

treating multiple excitations, proposed by Yelon et al. [55], showed that the

MNR should be naturally expected in some activated processes. They stated that

in a system where the activation barrier of a process, dH, is significantly higher than

the energy of a single excitation, E

, the assemblage of several excitations is

required to surmount the activation barrier. Consequently, an increase of the

activation barrier will result in the increase of the number of excitations required.

This, in turn, will increase the configurational entropy of the system.

5.6 Conclusions

This chapter describes the diffusion of oxygen ions in perovskite oxides with

particular emphasis on the materials used in design of solid oxide fuel cells. A

generic defect model for perovskites with aliovalent substitution on the A site is

presented. A limited review of available oxygen tracer diffusion data in several

families of perovskite materials (manganite, cobaltites, ferrites, etc.) is given.

The oxygen tracer diffusion coefficient is shown to vary by about 10 orders of

magnitude and is dependent upon many factors, including temperature, oxygen

partial pressur e, and the nature of the A- and B-site ions. Oxygen diffusion

112 J.A. Kilner et al.

occurs via a vacancy diffusion mechanism in these materials. It is shown that the

concentration of mobile oxygen vacancies has a dominant effect on the oxygen

diffusivity in perovskite materials. At the same time, the vacancy diffusion does

not appear to be dependent on the nature of the A- and/or B-site ions in the

perovskite structure and has an activation energy of 0.94 0.07 eV. The effect

of aliovalent doping on the apparent activation energy of oxygen tracer diffu-

sion is rather complex and depends on the transition metal on the B site. Several

experimentally observed correlations between parameters of oxygen diffusion

(e.g., Meyer–Neldel rule) are discussed.

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116 J.A. Kilner et al.

Chapter 6

Structural Disorder, Diffusion Pathway of Mobile

Oxide Ions, and Crystal Structure in Perovskite-

Type Oxides and Related Materials

Masatomo Yashima

6.1 Introduction

Solid oxides with high ionic conductivity have attracted considerable attention

for reasons of their many possible applications, including solid oxide fuel cells

(SOFCs), sensors, catalysts, and batteries. Oxide ion (O

2

) conductors such as

zirconia (ZrO

) solid solutions [1, 2], bismuth oxide (Bi

)-based materials

[3–6], ceria (CeO

)-based solid solutions [7, 8], and lanthanum gallate-based

compounds [9, 10] have be en widely investigated. The development of improved

electrolyte and electrode materials requires a better understanding of the

mechanism of ionic conduction, and crucial to this is comprehension of the

crystal structure at high temperatures at which these mate rials work most

efficiently [5, 6, 8, 10–15]. The detailed structural analysis enables the observa-

tion of the structural disorders and diffusion paths of mobile ions in ionic and

mixed conductors [5, 6, 8, 10–15].

Doped lanthanum gallate materials (La

1–x

)(Ga

1–y–z

3–d

areusedaselectrolytesforSOFCs[9, 16]. Doped lanthanum cobaltites

(La

1–x

)(Co

1–y

3–d

, mixed ionic-electronic conductors, are widely

used as electrode materials for SOFCs [17, 18]. Doped lanthanum titanate

0.64

(Ti

0.92

0.08

2.99

has an A-site deficient ABO

3–d

double perovskite-

type structure at high temperatures [11, 19, 20]. This material is an ionic

conductor [21], and it should be interesting to investigate structural

disorder and diffusion paths in a double perovskite-type structure and

to compare the results with those of cubic perovskite-type oxides. In this

chapter, we review the structural disorder and diffusion paths of oxide

ions in the perovskite-structured materials (La

0.8

0.2

)(Ga

0.8

0.15

0.05

3–d

[10], La

0.64

(Ti

0.92

0.08

2.99

[11], (La

0.6

0.4

)CoO

3–d

[12], and (La

0.6

0.4

)

(Co

0.8

0.2

3–d

[13]. A

-based oxides with K

NiF

-type structure have

extensively been studied as new mixed ionic-electronic conductors [22, 23],

M. Yashima (*)

Tokyo Institute of Technology, Yokohama 226–8502, Japan

e-mail: yashima@materia.titech.ac.jp

T. Ishihara (ed.), Perovskite Oxide for Solid Oxide Fuel Cells,

Fuel Cells and Hydrogen Energy, DOI 10.1007/978-0-387-77708-5_6,

Ó Springer ScienceþBusiness Media, LLC 2009

117