Oxygen ion conduction and structural disorder in conductive oxides

0022-3697(94)00272-X

J. Phys. Chem. Solids Vol. 55, No. 12, pp. 1393-1404, 1994 Copyright 0 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0022-3697/94 S7.M) + 0.00

OXYGEN ION CONDUCTION AND STRUCTURAL DISORDER IN CONDUCTIVE OXIDES HARRY

L. TULLER

Crystal Physics and Electra-Ceramics Laboratory, Department of Materials Science & Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A. Abstract-Defect-free crystals do not conduct ions. Increasing disorder initially translates into enhanced atomic transport. Heavily defective crystals, however, often exhibit successively lower levels of atomic diffusivity as the defect level is increased. This dilemma may be addressed by considering that highly disordered solids tend towards order. Interesting insights may be obtained by considering compounds with related structures which can be induced to go through order-disorder transitions either by change in temperature or composition. A number of such systems will be considered including materials with structures related to the fluorite and perovskite structures. The significance of these considerations on the application of such materials in solid state electrochemical devices will also be addressed as are the key contributions made by Arthur S. Nowick and co-workers towards our understanding of defect-dopant interactions in such systems. A. oxides, C. thermogravimetric chemical properties, D. defects.

Keywords:

analysis, D. diffusion, D. electrical conductivity, D. electro-

INTRODUCTION

A number of historic events have occurred over the last several decades which have markedly influenced our views concerning the need for enhanced energy conservation and lowered emissions of hydrocarbons, nitrous oxides, and other troublesome gases. First, came the oil embargo of the 1970s which led to widespread fuel shortages and rapid run-ups in petroleum costs. At the same time, the recognition that hydrocarbon fuels represented a finite, irreplaceable resource sensitized the world to the need for conservation. This opinion has only been further strengthened in the past 1O-l 5 years by the rapid loss in confidence in the long term viability of nuclear energy in replacing conventionally fueled power plants. Second, scientists became aware of depletions in the protective ozone layer, the greenhouse effect due to excess CO2 emissions, health threatening smog aided by NO, emissions and forest ravaging acid rain. A major consequence of these events has been new government regulations inducing, for example, auto manufacturers to design and build more fuel efficient and less polluting vehicles. Even more drastic measures have recently been introduced by the State of California which will shortly require that a percentage of vehicles in the state be emission free. These regulations are already being adopted by other states. These events have triggered renewed interest in alternative means for energy conversion, conservation, and storage including solar, wind, and the subject of

this paper, electrochemical. Indeed, whether the source of electricity is photovoltaic, nuclear, wind, or fuel powered generators, the most attractive means for storing off-peak power is by electrochemical means, i.e. batteries. Furthermore, when hydrocarbon or hydrogen fuels are used, fuel cells promise roughly double the fuel conversion efficiency and considerably reduced emissions compared to internal combustion systems. As attractive as electrochemical means appear conceptually, they must satisfy many criteria including high efficiency under practical operating conditions, long life, ease of fabrication, and ultimately, low cost before they can displace conventional systems. Many electrochemical systems remain at the conceptual or developmental stage largely because of material limitations. Nowhere is this more true than in the developing field of solid state ionics which concerns itself primarily with solids which support anamalously high ionic conductivities. Professor Arthur S. Nowick, in the mid-1960s, was one of the first to recognize the opportunities in this area. His contributions to the understanding of ‘fast ion conduction’ and interfacial phenomena in oxygen ion solid electrolytes based on CeO, and, more recently, in a number of protonic conductors including KTa03 and BaCeO,, have had and are continuing to have a major impact on efforts to develop solid oxide fuel cells (SOFC) and sensors. It is Professor Nowick’s ability to relate fundamental science to the ultimate solution of technological problems to which I would like to dedicate this article.

1393

H. L. TULLER

1394 OPTIMIZED IONIC AND MIXED CONDUCTORS

We are all familiar with the role that solid state electronics has played in recent decades in reshaping the way we live through, for example, advances in communications and computation. The materials which make up these devices cover a wide range of electrical conductivities ranging from highly insulating dielectrics, for substrates and capacitors, through semiconductors for diodes and transistors, to metals for interconnects. Even superconductors are now being considered for device applications (see Fig. 1). Similarly, ionic solids exhibit a wide range of ionic conductivities ranging from highly insulating such as a-A&O, to materials which exhibit ionic conductivities comparable to that of liquids. As suggested above, such solids show promise as solid electrolytes in a number of electrochemical devices ranging from sensors to smart electrochromic windows and a variety of batteries and fuel cells as indicated on the ordinate of Fig. 1. Indeed, many solids exist which support substantial levels of both ionic and electronic conductivity simultaneously. Such materials, commonly called mixed ionic-electronic conductors (MIEC) or more simply mixed conductors, obviously fall within the quadrant bounded by the two axes. Since nearly all electrochemical devices interface to the outside world through metal leads, the mixed conductors often play a critical role in enhancing the transfer process between the ionic and electronic conductors. Some of the ways they are used are also illustrated in Fig. 1. Since the key challenge is to achieve adequate levels of ionic conduction in solids. we focus in the

following sections on the role of structural disorder in achieving it. In so doing, we review the use of dopants in generating defects in fluorite-based solid oxide electroytes and cuprate mixed conductors and consider a specific case in which intrinsic structural disorder can be manipulated and controlled by the corresponding control of the lattice constituents of pyrochlore oxides. Last, we conclude with general remarks which apply to both of these cases. Below, we follow, in part, a presentation that we have recently published elsewhere [ 11.

IONIC TRANSPORT IN DEFECTIVE SOLIDS

Dilute solution Defect-free crystals do not conduct ions. Both charged ions, of which ionic solids have of the order of 10zzcn~3, and accessible sites are required to permit transport. This condition may be satisfied either by removing a subset of the ions on the sublattice of interest to form vacancies or by inserting ions into the interstitial sublattice characterized by large numbers of unoccupied sites. This criteria is included explicitly in the expression for ionic conductivity given by oi=y(Nq~/kT)c(l

-c)a’u,exp(-AH,/kT)

in which N is the ion site density, qi, the ionic charge, a, the lattice parameter, uO, the attempt frequency, AH,,,, the migration enthalpy, c, the fractional site occupancy and y, a constant which includes a geometrical factor related to the jump direction and the correlation factor. By focusing on the c(1 - c) factor, it becomes obvious that a, tends towards zero when either c tends to one or zero. The first case corresponds to a fully occupied lattice which includes no vacancies while the latter case reflects the condition in which an interstitial sublattice contains no ions. Classically, ionic conduction depends on the generation of point defects thermally, by impurity compensation and/or by deviation from stoichiometry. The range of defect concentrations typically dealt with under these circumstances is 10’s-10’8cme3 which represents 0.1-100 ppm on the sublattice of interest. Taking Frenkel disorder as an example, one may write: N(l -c)=Nici=(NNi)“*exp(-AH,/2kT)

Fig. 1. A plot illustrating typical applications for ionic and electronic conductors as a function of increasing magnitude of conductivity. Also included are examples of applications which require mixed conduction and therefore fall within the quadrant bound by the two axes.

(1)

(2)

in which Ni and ci are the density and fractional occupancy of the interstitial sublattice and AH, is the Frenkel pair formation energy. Substituting eqn (2) into eqn (1) and noting that c N 1 for dilute solutions

Oxygen ion conduction and structural disorder

1395

gives: ui = ~(N3Ni)“2(q~/kT)a2u, x exp - ([AH,,, + iAH,]/kT).

Generally, satisfy:

the ionic

conductivity

is found

ci = (a,,,/T)exp(-E,,/kT)

(3) to

(4)

for which, in the previous example, the effective activation energy, E,,, is given by E, = AH, + AH,/2

(5)

which includes a migration and a defect formation term. The addition of altervalent dopants can be used to fix the number of defects. For example, assuming vacancy compensation N( 1 - c) = BN,

(6)

where N, is the impurity density and fl is a constant selected to insure charge neutrality. Again, a, will be satisfied by eqn (4) but with the effective activation energy given by E,=AH,.

(8)

in which I is the impurity net charge (_+)x and D is the defect with net charge (T)y. This requires that /3 = x/v. The mass action relation which follows is given by N;N(l

-c)

NDim

= Ki exp( -AH*/kT)

(9)

where N,, is the density of dimers, N; is the density of unassociated impurities, and AH, is the association enthalpy. For conditions of weak dissociation and fl = 1 the concentration of mobile ions is given by: N(1 -c) PCS55/12-c

= (N,Ki)‘/*exp(-AH,/2kT).

I

I

I

I

I

I

I

2

4

6

8

10

12

Mole 46 cao

Fig. 2. Plot of ionic conductivity of CeO,:CaO versus mole % CaO at 280°C illustrating the square root dependence (solid curve) (from Ref. [2]).

Indeed, as illustrated in Fig. 2, Nowick and Park [2] found this prediction to hold to rather high dopant levels in CeO, doped with up to 12 mol% CaO. For B < 1, and weak dissociation N’= I

(

-‘-’ Nhm=(l B >

-/3)N,.

(11)

(7)

Because the defect and dopant are of opposite charge, an attractive coulombic force exists between them, which leads to association at reduced temperatures. Assuming the dopants are dilute and immobile, only dimers will form due to the association of a mobile defect with a fixed dopant. This reaction can be described by: (I-D)“-“oP+I)Y

0

(10)

Substituting eqn (11) into eqn (9) and solving for the defect density, one obtains

N(1 -c)

= B ( 1-B

P*exp(-AH,/kT)

(12)

>

with the surprising result that the unassociated defect density is independent of dopant concentration, as first pointed out by Nowick et al. [2]. Comparing eqns (10) and (12) with eqns (1) and (4), we fhrd for doped crystals with association that E, = AH,,, + AAH,

(13)

in which 1 = i for p=l and 1=1 for 8~1. Note that while it is possible for /I > 1, it is not very common and so will not be treated further here. Nowick and Park [2] calculated the temperature for which calcium-oxygen vacancy dimers in fluorite oxides (p = 1) would dissociate as a function of dopant concentration and association energy. The results, shown in Fig. 3, illustrate that the defects are expected to remain associated to above 1273 K for dopant levels above 2 mol% and AH,, > 0.3 eV.

H. L. TULLER well, in principle, leading to an additional enthalpic term, 1 AH,, in eqn (17). Table 1 summarizes the values that EC can take on for the various cases discussed above. Note ‘r’ depends on the ionization state of the defect and, for example, equals 3 in the reduction reaction described in eqn (16). Note further that the pre-exponential ffiOhas been normalized by dividing through by the constant y(qf/kT)a*u, to give oiO. Doped systems

Fig. 3. The calculated temperature for the break between associated and free vacancy behavior of a fluorite oxide as a function of dopant concentration and association energy

(from Ref. [2]).

Further, the dilute solution model predicts no dependence of AHm and AHA on N,. The defect density may also be modified due to deviations from stoichiometry. For example, reduction may proceed by O,+V;+2e’+

1/202

(14)

for which n = 2[v;] = 2No(l -c) where No is the oxygen ion site density. The corresponding mass action relation is [V;]n*Pg: = Ki exp( - AHRlkT)

(15)

which when solved, gives N,(l -~)=(K~/4)‘/~exp(-AH,/3kT)P~~‘~

(16)

or with eqn (1) aia exp[ -(AH,,, + AH,/3)kT]P&“‘.

(17)

Association between the defects, e.g. [vb;] and reduced host cations, e.g. Ce3+ in CeO, can occur as Table 1. u :,,and E, for a variety of defect models

Defect source Intrinsic disorder Frenkel Schottky Doped crystal Dissociated Associated (B = 1) Associated (# c 1) Nonstoichiometric

Pre-exponential factor, Qicl

Activation energy, ES

(NN,)“’ N

AH,,, + AH,/2

(N$?& -J&* l-8 (Ko,/4)“3P,5;‘6

AH,,, -I-AH,/2

AH,

AH,,, + AH, 12 AH,,, f AHA AH,,, + AHRedor,,

Oxides that crystallize in the fluorite structure (e.g. CeO,, ThO, and stabilized ZQ) accommodate a large fraction of lower valence cations, such as calcium, yttrium and trivalent rare-earths into solid solution, resulting in oxygen deficiencies as high as lo-15%. This is obviously the source of their high oxygen ion conductivities which reach values as high as N 10-l S/cm at 1000°C. Because of stabilized zirconia’s technological importance as the electrolyte in oxygen sensors and solid oxide fuel cells, it has received the lion’s share of attention. In attempts to optimize the ionic conductivity or to clarify the controlling transport mechanisms, literally dozens of investigators have examined the composition and temperature dependence of the electrical conductivity. A key feature observed many times is the maximum ion conductivity which occurs at doping levels corresponding to 5-g% anion vacancies. While the decrease in conductivity and increase in activation energy at higher doping levels are generally attributed to the onset of substantial defect association and ordering, interpretations are complicated by the need to add high dopant levels simply to stabilize the cubic fluorite phase. Many investigators have correlated the conductivity maximum with the minimum dopant level necessary to stabilize the cubic phase. For our purposes, it will be more instructive to examine compounds such as CeO, and ThO, which are stable fluorites even without additives. We will, however, return later to a discussion of zirconia-based solid solutions which exhibit interesting order-disorder phenomena. In an attempt to establish the conditions under which defect interactions become significant in Auorite oxides, Nowick and co-workers [2-61 embarked on a detailed study of dopant-ionic conductivity correlations in CeO,-based solid solutions. First, they concluded [6] that for trivalent doped CeO, (fl = l/2) dopant-vacancy association at reduced temperatures is already significant. For example, they found that CeO, + 0.15 mol% Y,O, possesses an association energy AHA = 0.3 eV and a migration energy AH,,, = 0.67eV. In contrast to expectations, this value of AH, was found to be composition dependent even

Oxygen ion conduction and structural disorder

- -6.5 b 0 3

- -7.0

0.6

’

’

’

’

0.050.1 0.2 0.5 1

’ 2

0

12

3

4

5

6

(I@'&'"

%Y203

Fig. 4. Variation of low temperature activation energy and ionic conductivity at 182°C as a function of mol% Y,O, in CeO,:Y,O, (from Ref. [6]).

Fig. 5. Variation in association enthalpy HA and log ~(182°C) with the l/3 power of yttria concentration in CeO,:Y,O, (from Ref. [6]).

at low values of Y,03 decreasing from 0.30eV to a minimum of - 0.18 eV as the Y, 0, content increased from 0.15 to - 2.0 mol% (see Fig. 4). Above 2 mol% Y203, E, is observed to increase substantially with a corresponding sharp drop in conductivity. Wang et al. [6] attribute the initial decrease in A’HAto an increasingly large overlap between the potential well of the yttrium-oxygen vacancy pair (Yc,V,)’ and the isolated substitutional yttrium ion Yb thereby narrowing the energy difference between the bound and free states of the oxygen vacancy, Vo. More specifically Nowick and co-workers [6] assumed a dopant dependent association enthalpy given by

illustrated

AHA = AHi - AEiDt in which the interaction

energy e2

the

work

of

(18)

co ‘I3

S?+

Ys+ Gd”

I .

(19)

Here, ar, is the effective separation between the centers and c,, = Nt is the dopant concentration. Substituting eqns (18) and (19) into the expression for ui in Table 1 for doped crystals, associated with /3 < 1, it can easily be demonstrated that

c

0.6-

1

0.4-

.j .e m

0.2-

I

Las+

I I 0 EzxpeIimelltal

ocalculated

3

h/

0

'\,

uicl exp

Nowick’s

takes the form

-%ua . 0

AE,, = 4muro

5,

group PI. At levels of Y,O, above -2%, the increase in E, is likely linked to the nucleation of clusters or domains, perhaps resembling those observed in highly reduced CeO,_,, in which the vacancies become ordered and ‘locked’ into the structure [7]. Hammou [8] has also reported similar minima in E, as a function of dopant, in the related Th02-Y203 system. In CeO,-CaO (B = 1) on the other hand, simple (Ca&-Vo) pairing appears to describe observations well, i.e. a square-root dependence of o, on [Ca,,] and a relatively composition-insensitive AHA 5 0.5 eV [2]. Here, in contrast to the /3 = l/2 case above, the vacancy and calcium concentration are equal (/I = 1).

0.8 2e2

Fig.

in

.

(20)

0 0.8

0.9

I.0

1.1

1.2

Ionicladius(A)

Both the linear dependence of AHA and of logo, on the cube root of the dopant density is well

Fig. 6. Variation of association enthalpy with ionic radius in trivalent doped CeO, (from Ref. [9]).

H. L. TULLER

1398

It is interesting to observe the strong dependence of AHA on the relative ionic radius of the dopant to that of the host ion Ce4’. Both the experimental values derived by Nowick’s group [3] and the calculated values obtained by Butler et al. [9] are reported in Fig. 6. The results show a minimum for dopants with radii closely matching those of Ce4+, pointing to the existence of a strong strain component in the defect-impurity binding energy. Kilner [lo] has suggested that a better means for evaluating the relative ion mismatch of dopant and host would be to compare the cubic lattice parameter of the fluorite oxide and that of the pseudo-cubic lattice parameter of the corresponding rare-earth sesquioxide as in Fig. 7. Note the excellent match between CeO, and Gd203. Such comparisons also explain why Sc,O, is an excellent dopant in cubic ZrO, but serves to trap carriers in CeO, [lo]. We have already alluded several times to the possibility that domain-like regimes, characterized by intermediate range order, begin to form in fluorites at dopant levels in the 5% range. Stable and well defined ordered phases are obtained at higher trivalent cation fractions. In particular, in the following discussion, we focus on compounds with the pyrochlore structure with general formula A2B207 in which A is the larger trivalent rare earth or yttrium ion and B is the quadravalent zirconium or titanium

La--

8.6.: no2

Bi O,,

Pr -Nd -Sm -. Ell --

ccoz

Gd .Tb -.

Ho \ Y-

5 x 10-3 -

1 20

I

I

I

30

40

50

-

J 60

od O,,$(mol %) -

Fig. 8. Isothermal conductivity (720°C) for ZrO&d,O, solid solutions (from Ref. Ill]).

ion. Note the equimolar levels of A and B ions and the corresponding loss of one out of eight oxygen ions relative to the ideal fluorite structure. The group of Burggraaf [11,121 made a number of very interesting observations about the properties of this group of materials relative to the defect fluorite phase. Note, for example in Fig. 8, the peak in ionic conductivity in the pyrochlore phase Gd,Zr,O, in comparison to the defect fluorite phases which bound it at either side. This is a surprising result, since pyrochlore is an ordered version of defect fluorite in which A and B ions order on separate sublattices and missing oxygens (vacancies in fluorite) become ordered on the so-called 8b sites (see Fig. 9) rendering them empty interstitial sites. Since the remaining seven oxygens per formula unit now fully occupy the two oxygen sublattices designated as 48f and 8a, ideal pyrochlore is expected to be insulating. As we later demonstrate, some pyrochlores, like Gd,Zr,O,

b 1

Er Tm Yh LU

zro,

-

81

0 SC -.

0

A3+in16c~mMI0

0

0

B&in 16dgrn l/2 IL?112 0

0(1)in48fmmx1/81/8 0(2)in8aZ3mxl/81/81/8

+ VoinEb~3m3/83/83/8

Fig. 7. A schematic of the lattice parameter maps for fluorite and related oxides (from Ref. [IO]).

Fig. 9. Projection of pyrochlore supercell (from Ref. [13]).

Oxygen ion conduction and structural disorder -I -

1399

1.0

Ionic auiv. energy 0.9

g

0.8

L ’

I

.1 ti” 0.7 -

.

‘\/

I

P

.

.

I I

_dP-----

I

b--O'0

0.6

Ca

ON

-5

I 5

0

OCh

looo”c

I 10

15

q AI

20

ionicple-exp. constant

Mole % cation substitution

Fig. 10. Isothermal (IOOOC) dependence of ionic conductivity in the systems (Gd, _.YCa,),Ti,O, and Gd,(Ti, _YA1,,),O, as a function of mol% substitution (from Ref. [16]). 0

exhibit

a degree

nected

with

of intrinsic

the exchange

oxygen of oxygen

disorder between

con-

48f and initially

,

*@

,o--_

-5,

-I

the

8b sites. In GdzTi,O,, this type of intrinsic oxygen disorder is negligible as exemplified by the rather low ionic conductivity of tri < lo-‘S/cm obtained at 600°C [14]. However, like the fluorite oxides, Gd,T&O, can be made conductive by forming solid solutions with lower valent cations. We were particularly attracted to this and related rare earth titanate pyrochlores [15, 161given that dopants with a number of possible valences could be incorporated substitutionally into the AZ+Ti$+ 0, host lattice on either the A or Ti cation sublattice. This provides an excellent opportunity to explore the combined effects of dopant concentration, charge and site location on ion migration and association in an oxygen ion solid electrolyte. Figure 10 shows the dependence of ionic conductivity at 1000°C in the systems (Gd, _.TCa,),Ti,07_X and Gd*(Ti, _l.A1,),07_, on the Ca and Al fraction, respectively. In ea&case, the additive has a single net negative charge relative to the lattice. While the ionic conductivity increases sharply and similarly with increases in acceptor density up to x = y = 0.01, the conductivity of the Ca-substituted system continues to increase for another order of magnitude to x = 0.1. The Al-substituted system shows instead a substantial drop above y = 0.01. The corresponding dependences of the activation energies and conductivity preexponentials on Ca and Al concentrations are shown in Fig. 11. As was the case in Y doped CeO, described above, the initial increases in ionic conductivity are largely due to a composition-dependent activation energy, which in the case of the Ca substituted material, drops sharply from N 0.89 to 0.63 eV for 0.0025
,

/

c?(

empty

0 Ca q AI I

I

I

I

20

15 mole.% cation substitution IO

5

Fig. Il. Dependence of activation energy Ei0nie,and conductivity pre-exponential of the systems of Fig. 10 as a function of mol% substitution (from Ref. [16]).

of Table 1 (j = l/2). While the general trend mirrors that found by Wang et al. [6] in Y doped CeO,, we do not observe the cAj3dependence of Eionic(eqn (19)). We attribute this to the limited data points at x and y values under 0.02. Further studies at low dopant levels are indicated.

;t

@%&a

crz)2~P,

.T=lOOO”C

0 0.8

I 0.9

I 1.0

I

1.1

I 1.2

1 1.3

I 1.4

I

1.5

r&d

Fig. 12. Ionic conductivity of (Gd,,,&,z),Ti,O,, A = Mg, Ca, Sr, K at 1000°Cas a function of normalized ionic radius of A ion (from Ref. [16]).

H. L. TULLER

1400

We have also recently examined the effect of the size of the substituted dopant on the ionic conductivity in the system (Gd,,&,,&Ti20, for A = MgZ+, Ca’+, Sr2+, K’+. Figure 12 shows the ionic conductivity at 1000°C as a function of the ionic radii of these ions normalized relative to that of Gd3+, the host ion. The maximum is obtained with Ca which exhibits the closest match. This is in apparent agreement with the results and predictions shown in Fig. 6 for CeO, in which the dopant which induced the lowest strain in the lattice exhibits the highest conductivity. Further work remains to insure that the three elements Mg, Sr, and K substitute solely on the Gd site. In contrast to the observations in Y doped CeO,, however, the observed maxima in conductivity or minima in activation energy are not due to the onset of extended defect interactions at large dopant levels but rather exceeding the solubility limits of the additives as confirmed by X-ray diffraction and microprobe analysis [ 161. The final example of a doped system that we consider is the mixed conductor La, _ I Sr,CuO, fy, which for certain values of x, exhibits superconductivity at temperatures below approximately 35 K. Since there is a correlation between the onset of superconductivity and the oxygen stoichiometry, it is of interest to characterize oxygen diffusion in this system. This provides improved understanding of the kinetics of oxidation which occur as the cuprate is cooled from processing temperatures towards room temperature. This system is also of interest since the addition of the Sr acceptor on the La site is initially compensated primarily by holes rather than oxygen vacancies as in the examples described above. A trend towards oxygen vacancy compensation at higher Sr contents has, however, been indicated [18]. In our work [19,20], which is summarized here, we indeed confirm this trend but find that it does not translate into a simple dependence of oxygen diffusivity on Sr level. Based on a dilute solution model, one can readily predict the free oxygen vacancy concentration dependence on [SrL] after making some simplifying assumptions regarding the controlling neutrality relation given by [19] P + 2[v;;] = n + 2[01’1+ [S&J.

(21)

The derived defect diagram is shown in Fig. 13. The applicable simplified electroneutrality regimes are as follows: Regime I: zero to very low [Sr] 2[01’] = p.

I

2[OJ(O) I?4 (0) ,,$ 0@ , ’ z[vo-1 (0)

Log KWotd Fig. 13. Defect

diagram for La,_,Sr,CuO,,, Ref. [19]).

(from

Regime II: low [Sr] p = [S&l. Regime III: moderate [Sr] [S&l = 2lVb: I >>[S2V. Regime IV: high [Sr]

MA = A% I& F2Yl in which S2V is short hand for the defect cluster {(Srl,)2Vb:}X. Note here, for purposes of comparing these predictions with proposed models in the literature [21], we have assumed the formation of a trimer rather than a dimer in the association case in which /I = l/2 (see eqn (8)). Focusing on the free vacancy dependence on total Sr level, in Fig. 13 we find that it begins as [Sr] independent in region I, followed by a quadratic, linear, and finally cube root dependence in regions II, III and IV, respectively. Obviously, given the Frenkel relationship (eqn (2)), the oxygen interstitial concentration [Of] shows the opposite dependence on [Sr].

Oxygen ion conduction and structural disorder I

Log ISrl total

Fig.

14. Dependence of oxygen diffusivity La,-, Sr,CuO, + Y on strontium content for three cases

with different -relative oxygen vacancy and interstitial diffusivities (from Ref. [19]).

The measured oxygen diffusivity can be expressed in terms of the concentration of oxygen defects and their diffusivities as follows [19]:

Do, = Do,P(‘l + b$%l.

(22)

Thus, depending on the interstitial-vacancy difIusivity ratio, written in short hand by DilDv,Dox may

-9.50, -10.0 -10.5 -11.0

3

1 _

/ \\\ J

\ \ \

\

-11.5 -

i

\

\

yE -12.0 -

initially increase or decrease as one moves from region I to II’in Fig. 13 as illustrated in Fig. 14. We measured the tracer diffusion of “0 in LaZ_XSrXCuq_Ysingle crystals (X =0 to 0.12) from 400 to 700°C in 1 atm oxygen using a SIMS analysis [19]. Figure 15 summarizes the measured dependence of D on [Sr] at 600°C. As predicted D is initially [Sr] independent but increases between x = 0.02 and 0.03 confirming that D, > Di by a considerable margin. Given that oxygen diffuses by a vacancy method for x > 0.02, the defect model predicts that Do, should continue to increase with [Sr], but with weaker slope at each successive defect regime. Instead, D drops by approximately 3 orders of magnitude between x = 0.03 and 0.07. The proposed explanation by Routbort et al. [21] for the decrease based on the formation of S,V clusters cannot be correct since, as we demonstrated above, this only leads to a weaker increase in [vo] with increasing [Sr] rather than a decrease. Smyth [22] states that the polarizability of perovskite-related oxides reduces the tendency for defect association, but instead stabilizes ordered structures. Superlattice ordering rather than defect association is thus expected leading to the removal of large numbers of mobile defects from circulation. Hong and Smyth [23] have recently proposed that stress and charge imbalances in the layered structure of La, _ ,Sr,CuO, might indeed lead to such long range arrays. By examining the oxygen nonstoichiometry, y, of La, _XSr,CuO,_, (0 < x < 1) as a function of temperature (800-1050°C) and oxygen partial pressure (10e4 to 1 atm) by thermogravimetric analysis [20], we were able to confirm a number of the key observations made above. First, as Fig. 16 demonstrates, compensation for Sr;, changes from predominantly hole to predominantly oxygen vacancy as the Sr content increases from x = 0 towards x = 1.0. Further, as might be expected, hole compensation at a given x value is favored at high PO,while vacancy compensation is favored at low PO,. This transition region may be described by [20]

\

-12.5 -

\ \

-13.0 -

4Cll& + 2v; + or = 4cu,, = 20;

in which Cu& is equivalent to the hole density in the previous model. Considering that

0 ‘\O

-14.0 -

cu];“] + [Cu&] = 1 I -2.0

I -1.8

I -1.6 Log

I -1.4

I -1.2

(23)

\

0 ‘1;

-13.5 -

-14.5 -2.2

1401

I -1.0

-0.8

ISrl

Fig. 15. Dependence of measured oxygen diffusivity on Sr at 600°C. The dashed lines indicontent in La_,Sr,CuO,,, cate that Sr content corresponding to maximum diffusivity is unknown (from Ref. [19]).

W;;l=y

[0;]=4-y [C&“] = x - 2y

I-I. L. TULLER

1402

4.0

T L

3.51

I 0

hole compmsatioa

I 0.2

I 0.4

I 0.6

0.8

strontium ConterlL

1.0

x

Fig. 16. The oxygen nonstoichiometry of L~_,SC,CUO,~~ as determined by TGA analysis. Vertical bars represent range of oxygen content measured between 800 and 1050°C and 10m4and 1 atm P,, for each value of x (from Ref. [20]).

one may recast

eqn (23) into mass action

assuming

unity

activity

coefficients.

measured

oxygen

content

versus

this and

requires

an additional

form as

The

PO, deviates term

actual from

of the form

exp(AH,,/kT) in eqn (24) which multiplies the right hand side in which AH,, represents an excess enthalpy accounting for defect interactions. Fitting our data to the modified form of eqn (24) leads to composition dependent enthalpies for the reaction defined in eqn (23) by AH = -294, -323, - 178, and -151 KJ/mol for x =0.2, 0.4, 0.6, and 1.0, respectively. The enthalpy of defect interaction AH, were derived as follows: AH,, = - 7 12y, - 272~ and -435~ kJ/mol for x = 0.4, 0.6, and 1.0, respectively (20). The negative values indicate that ordering is favored as suspected above in the diffusion study [19]. Intrinsic order Another class of fast ion conductors is represented by solids such as aAg1 or sodium /J alumina which are intrinsically highly disordered. This reflects the fact that only a subset of equivalent ion sites are occupied by ions such that the factor c in eqn (1) is a fraction of unity. This leads to exceptionally high ionic conductivities (a _ 10-l S/cm) for these solids in the temperature range of 150-300°C. Amongst oxygen conductors, B&O, has been known for some time [24] to disorder above -730°C resulting in oxygen ion conductivites well above stabilized zirconia. Its utility in electrochemical devices is limited,

however, due to its propensity to decompose under reducing conditions. In no case, however, has there been an ability to modulate the intrinsic disorder between low and high levels. In the following, we describe our work on the pyrochlore compounds in which such control has been recently demonstrated. Two types of disorder are important in pyrochlores. The first is anti-site disorder on the cation sublattices in which A and B cations switch positions. In the limit of complete randomization of the A and B cations on the 16c and 16d sites, the structure reverts back to the situation in the fluorite case. The second type of disorder, which is relevant to our analysis of ionic transport, concerns a Frenkel-like disorder on the anion sublattice. Here, oxygen ions leave the normally occupied 48f sites and enter the 8b interstitial sites, thereby forming oxygen vacancy-interstitial pairs. Since neither the 8a or 8b sites are interconnected, we expect oxygen transport to occur primarily via vacancy motion within the 48f sublattice. This assumption was confirmed by Moon and Tuller [25] in doping experiments performed on Gdz(Zr,,,Ti0,,)207. A number of earlier studies suggested that there might be a correlation between structural disorder in the pyrochlores and the radius ratio of the A and B cations, r,/r,. Intuitively, one might suspect that as the radius ratio approaches unity, anti-site disorder would increase. Further, as the cation environments of the oxygen ions become more homogeneous, 48f-8b exchange would also become more favorable. Moon and Tuller [26] were able to test this hypothesis by studying compositions in the system Gd2(ZrXTi,_x)207 in which the rA/rBratio was varied

- 0.6

Fig. 17. Ionic conductivity (600°C) and estimated cationic disorder parameter as a function of x in Gd,(Zr,Ti, _-r)207. (after Ref. [25]).

Oxygen ion conduction and structural disorder 2.5

2.0

s

I I I I

qGd nY

I=

74IS

Ld-

I

l-e ’ v

1.0

0.5

(extrinsic control)

1

0

I

1403

-.

-.-

0

4c

‘Q-,__,

I

1

I

I

0.4

0.6

0.8

1.0

I

0.2

J-w-

x (Zr fraction)

xz, Fig. 18. Activation energy for ionic conductivity for Gd,(Zr,Ti,_,),O, and Y,(Zr,Ti,_,)rO, as a function of y. Dashed lines do not indicate parametric fitting (from Refs

Fig. 20. The calculated oxygen vacancy concentration as a function of x in the Gd,(Zr,Ti, _X)2O7system (after Ref. [I]).

~24,251).

oxygen disorder and oxygen vacancy mobility. Consistent with the above observations, it is the increase in oxygen disorder, as reflected in o,,, rather than an increase in oxygen mobility that drives the increase of oi with x. In Fig. 20, we plot &] versus x as derived from the above analysis (Moon and Tuller [26]). Note that intrinsic oxygen disorder ranges from below one part per thousand at x = 0.3 to nearly 1% at x = 1.O. Recent measurements on donor doped Gd,Ti,O, by Kosacki and Tuller [28] have shown that the intrinsic disorder drops further to about one part in 10’ at 1000°C in the titanate end member. The related Y,(Zr,Ti,_,),O, (YZT) system was next studied in order to examine the role of the ratio of the effective ionic radii in the ‘A’ and ‘B’ sites, on structural disorder and transport. As in the above stated hypothesis, the smaller the r,/r, ratio, the larger the A-B anti-site disorder and correspondingly the larger the oxygen Frenkel-like disorder. Comparisons of the magnitudes of q, for YZT and GZT, for the same values of x in Fig. 19, appears to confirm this hypothesis, i.e. rr,(YZT) N 30 a,(GZT). However, because Eionic(YZT) is 0.3-0.5 eV larger than E,,,,(GZT), q,,,,(YZT) remains lower in magnitude below N 1000°C. The higher activation energy is presumably due to YZT’s smaller lattice parameter. Recent neutron diffraction studies on YZT with x = 0.3, 0.45, 0.60, and 0.90 by Heremans and Wuensch [29] confirm the systematic disordering of the oxygen sublattices with the oxygen vacancy fraction on the 48f site increasing from 0.006 (x = 0.3) to 0.0043 (x = 0.45) and finally to 0.078 (x = 0.6). At x = 0.9 all three oxygen sites (48f, 8a, and 8b) are l/S empty, which is consistent with the structure having reverted back to defect fluorite. Surprisingly, the same authors detect significant A-B anti-site disorder only above x = 0.45.

1.74 to 1.47 as x was increased from 0 to 1. Figure 17 illustrates the large increase in the ionic conductivity, 4.5 orders of magnitude at 6OO”C, as Zr is systematically substituted for Ti. Similar results were obtained in the Y,(Zr,Ti, _X)2O7 system (Moon and Tuller [26]). By examining the dependence of the pre-exponential and exponential terms of oi = (cr,/T)exp( - EJkT) as a function of x, as in Figs 18 and 19, it becomes obvious that, outside of the extrinsic-controlled regime at small x, it is largely increases in a,, rather than decreases in Eionicthat contribute to the increases in gions for x values above 0.25. Acceptor doping experiments of Gd, (Zr,Tii _ *)r 0, (GZT) with Ca for values of x = 0.25, 0.3, and 1.0 (Kramer and Tuller [27] and Moon and Tuller [26]) have enabled us to extract values for the intrinsic from approximately

acid

my

gL

,” B

I n I

L-

I n /

J

,’

n

I+’

b (extrinsic - 4 control)

I

I 0.5 0

I

d@-

I

OH0

If

I

I

I

0.2

0.4

0.6

0.8

1.0

%I Fig. 19. Pre-exponential term up for ionic conductivity for the systems described in Fig. 19 as a function of x (from Refs 124,251).

H. L. TULLER

1404

As an interesting aside, significant levels of electronic conductivity can also be obtained in the GZT and YZT systems, particularly for low values of x. This follows

from the ease with which Ti4+ reduces

to T?+ at reduced PO, and elevated temperatures as observed previously, for example, in TiOr [30] and SrTiO, [22]. SUMMARY Few crystalline systems of interest as solid electrolytes or mixed conductors satisfy dilute solution approximations. As Nowick and co-workers showed, defect-impurity association is already dominant at dopant levels of tenths of a percent in fluorite oxides. They further showed that this is often followed by unexpected further increases in ionic conductivity due to potential well overlap between associated and unassociated dopant sites. Similar effects are observed in doped pyrochlore oxides. Further increases in dopants and corresponding defects lead to longer range interactions and ordering with a consequent drop in conductivity. These highly ordered structures, however, e.g. A,B20,, often disorder to a limited degree, leading again to enhanced conductivity. Indeed, as demonstrated above, control of the radius ratio of the A and B ions in the pyrochlore oxides can lead to a nearly continuous variation in the degree of oxygen disorder and correspondingly, the ionic conductivity. Within this periodic variation between highly defective and highly ordered systems, lies the optimum disorder for enhanced ionic conductivity. Arthur S. Nowick has played a key role in directing our thinking about this challenging and intriguing quest. Acknowledgements-The author wishes to thank Professor Arthur S. Nowick, for serving as a model doctoral thesis advisor by always upholding the highest standards of honesty, clarity and dedication to his teaching, research and interaction with students and colleagues. The author also appreciates the support by the Basic Energy Science Division of the U.S. Department of Energy under contract DE-FGO2-86ER45261 for- the work on the pyrochlores and to the Center of Materials Science and Engineering (NSF) 9022933-DMR for the work on the cuprates.

REFERENCES 1. Tuller H. L., in NATO ASI on Defects and Disorder in Crystalline and Amorphous SolirLF(Edited by C. R. A. Catlow), p. 189. Kluwer Academic Publishers, Dordrecht, The Netherlands (1994). 2. Nowick A. S. and Park D. S., in Superionic Conductors (Edited by G. D. Mahan and W. L. Roth), p. 395. Plenum Press, New York (1976).

3. Gerhardt-Anderson R. and Nowick A. S., Solid State Ionics 5, 541 (1981). 4. Gerhardt-Anderson R. and Nowick A. S., in Transport in Nonstoichiometric Compounds (Edited by G. Simkovich and V. S. Stubican), p. 111. Plenum Press,

New York (1985). 5 Gerhardt-Anderson R., Lee W. K. and Nowick A. S.,

4.

J. Phys. Chem. Solids. 48, 563 (1987). 6. Wana D. Y.. Park D. S.. Griffith J. and Nowick A. S., SolidvState Ionics 2, 95 (1981). I. Tuller H. L. and Nowick A. S., J. Phys. Chem. Solids 38, 859 (1977). 8. Hammou A., J. Chim. Phys. 72, 431; 72, 439 (1975). 9. Butler V., Catlow C. R. A., Fender B. E. F. and Harding J. H., Solid State Ionics 8, 109 (1983). 10. Kilner J. A., in Solid State Chemistry, 1982 (Edited by R. Metselaar, H. J. M. Heijligers and J. Schoonman), p. 189. Elsevier Science Ltd. Amsterdam (1983). 11. van Dijk T., de Vries K. J. and Burggraaf A. J., Phys Stat. Sol. 58a, 115 (1980). 12. van Dikjk M. P., de Vries K. J. and Burggraaf A. J., Solid State Ionics g/10. 913 (1983). 13. Haile S. M., Wue&h’B. J. and Prince E., in Neutron Scattering for Materials Science (Edited by S. M. Shaoiro. S. C. Moss. and J. D. Jorgensen). MRS Vol: 166, p. 81. Materials Research Society, Pittsburgh (1990). 14. Moon P. K. and Tuller H. L., in Solid State Ionics (Edited by G. Nazri, R. A. Huggins and D. F. Shriver), MRS Vol. 135, p 149. Materials Research Society, Pittsburgh (1989). 15. Tuller H. L., Kramer S. and Spears M. A., in High Temperature Electrochemical Behaviour of Fast Ion and Mixed Conductors (Edited by F. W. Poulsen, J. J. Bentzen, T. Jacobsen, E. Skou and M. J. L. Ostergard), p. 151. Rise National Laboratory, Roskilde, Denmark (1993). 16. Kramer S. A., PhD Thesis, Massachusetts Institute of Technology, Cambridge, MA, U.S.A. (1994). 17. Kramer S. A. and Tuller H. L.. unnublished results. 18. Michel C. and Raveau B., Rev. Chemie Minerale 21,407 (1984). 19. Opila E. J., Tuller H. L., Wuensch B. J. and Maier J., J. Am. Ceram. Sot. 76, 2363 (1993). 20. Opila E. J. and Tuller H. L., J. Am. Ceram. Sot. 77, 2727 (1994). 21. Routbort J. L., Rothman S. J., Flandenneyer B. K., Nowicki L. J. and Baker J. E., J. Mater. Res. 3, 116 (1988). 22. Smyth D. M., Annu. Rev. Mater. Sci. 15, 329 (1985). 23. Hong D. J. L. and Smyth D. M., J. Solid State Chem. 97, 427 (1992); 102, 250 (1993). 24. Gattow G. and SchrBder, 2. Anorg. Allg. Chem. 318, 176 (1962). 25. Moon P. K. and Tuller H. L., Solid State Ionics 28-30, 470 (1988). 26. Moon P. K. and Tuller H. L., in Solid State Ionics (Edited by G. Nazri, R. A. Huggins and D. F. Shriver), MRS Vol. 135, p. 149. Materials Research Society, Pittsburgh (1989). 27. Kramer S. and Tuller H. L., in Ceramics TodayTomorrow’s Ceramics (Edited by P. Vincenzini), p. 2211. Elsevier Science Publishers, Amsterdam (1991). 28 Kosacki I., Kramer S. and Tuller H. L, Trans. Tech. Publications. To be published. 29. Heremans C., PhD Thesis, Massachusetts Institute of Technology, Cambridge, MA, U.S.A. (1993). 30. Rao C. N. R., Gopalakrishnan J. and Vidyasogor K., Ind. J. Chem. 23A, 265 (1984).