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

Подождите немного. Документ загружается.

The expression requires that the concentrations are all given in the same

units, so that the standard concentrations cancel, and that the partial pressure

of water is given in bars. The electroneutrality condition in our case reads:

2½v



þ½OH



¼½Acc

¼constant (11:4)

where Acc

hereafter denotes acceptors in general. Note that an electroneutral-

ity such as this comprises volume or molar concentrations, not site fractions.

The foregoing electroneutrality has two limiting cases: if protons dominate (at

low temperatures), ½OH



½Acc

¼constant. The constancy arises from the

acceptors being frozen in or being all dissolved so that varying solubility is not

effective.

On the other hand, if protons are in the minority so that

2½v



½Acc

¼constant, the proton concentration becomes:

½OH



¼ð½O

½v



p

1=2

¼½O



1=2

½Acc



1=2

exp

DH

2RT

(11:5)

If one operates with small defect concentrations, we may assume that ½O



equals the concentration of oxide ion sites, and for molar concentrations this

equals 3 in perovskites.

We can also obtain an analytical solution to the full electroneutrality. If we

combine the equilibrium expression with the electroneutralit y condition and

assume ½O

¼½O¼constant

½v



þ½OH



, we obtain, for the concentra-

tion of protons:

½OH



¼

½OK

1 þ

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1 þ

8½Acc



½O



(11:6a)

If we instead assume the more general ½O

þ½v



þ½OH



¼½O¼constant,

we obtain:

½OH



¼

½OK

1 þ

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1 

2½Acc



½O

½Acc



½O

8½Acc



½O



4½Acc



½O



4  K

(11:6b)

which is a reorganized version of the same equation given by Kreuer et al. [12]

At moderate dopant and defect concentrations, the two solutions provide the

same concentration for practical purposes. Note that the proton concentration

comes out in molar fraction or volume concentration corresponding to the unit

that is used for ½O and ½Acc

. In molar concentration, [O] = 3 for perovskites.

The concentration of oxygen vacancies is now obtained simply from the

concentration of protons and the electroneutrality (Eq. (11.4)). The

220 T. Norby

concentration of other (minority) defects can be found by linking to the vacancy

concentration by appropriate defect-chemical reactions.

and its thermodynamic parame ters are important in that they determine

whether the material is primarily dominated by oxygen vacancies or by protons.

This point can be investigated by studying the proton concentration versus

temperature using, for example, IR spectroscopy, thermogravimetry, or con-

ductivity, and this has been done for many perovskites. It turns out that the

entropy change DS

ends up around 120 J/mol K, as expected empirically for

the loss of 1 mole of gas, while the enthalpy change DH

varies widely. Some

perovskites, such as BaCeO

, have large negative values (exothermic) of more

than 150 kJ/mol, and they are thus dominated by protons in wet atmospheres,

and it takes a high temperature to shift the equilibrium to the left. Others, such

as SrTiO

, have moderate negative enthalpies and are dominated by protons

only at relatively low temperatur es. Finally, there are perovskites such as

LaGaO

in which protons are never observed under any conditions and

where modeling verifies that the enthalpy of hydration is actually positive [13].

In an attempt to find correlations between hydration thermodynamics and

other materials properties, Norby et al. [14] noted that the best so far encompasses

the difference in electronegativity between the B-site and A-site constituents of the

perovskite. Figure 11.1 shows an update of this correlation plot. Although other

correlations to electronegativity differences are in use [15], ours is yet not rationa-

lized to any extent, and probably represents only a first or rough approximation,

judged from the scatter. A linear regression of the data yields the following:

ðkJ=molÞ¼173ð9Þþ370ð42ÞDX

BA

(11:7)

We have recently tried to chall enge the correlation and reduce the scatter that

arises from the uncertain extraction of enthalpies from ‘‘equilibrium’’ measure-

ments by measuring the enthalpy directly in calorimeters, notably combined

DSC/TG instruments where the wat er exchange and associated enthalpy can be

recorded simultaneo usly. It has so far turned out that combination instruments

lack the isothermal stability to obtain significant results.

We are also examining hydration of some Pb-based perovskites such as PbZrO

where the electronegativity difference, the entry on the x-axis in Fig. 11.1, is negative.

The correlation then predicts these perovskites to have very large negative hydration

enthalpies and to be very strongly hydrated. The results so far, both by experiments

and by density functional theory (DFT) simulations [16], suggest that the hydration

is significant but moderate and that the correlation must be modified. It may be, for

instance, that it is the absolute value of the electronegativity difference which must be

applied.

Some perovskites with smaller band gaps have acceptor dopants compen-

sated by electron holes rather than oxygen vacancies, especially at lower tem-

peratures and, of course, high oxygen activities. In principle, this will depress

the tendency of proton dominance; BaPrO

is predicted to have a large negative

enthalpy of hydration of oxygen vacancies (Eq. 11.3), but the dominance of

11 Proton Conductivity in Perovskite Oxides 221

holes suppresses the protons [17]. Put differently, the hydration of the electron

holes, which can be written:

OðgÞþ2O

þ 2h



¼ 2OH



ðgÞ (11:8)

is less favorable than the hydration of oxygen vacancies.

11.2.3 Proton Diffusion

The protons, always residing on oxide host ions, exhibit thermal rotational and

stretching vibrations. They may be located in a variety of local energy minima,

depending on which neighboring oxide ion(s ) they are directed toward.

Depending on the O–O distance, the protons may set up hydrogen bonds,

OH–O, between the two oxide ions, decrease their distance somewhat, and

affect the structure slightly.

Fig. 11.1 Hydration

enthalpy vs. difference in

Rochow–Allred

electronegativities between

B- and A-site constituents in

perovskites. The linear

regression gives D H

(kJ/

mol) =

173(9) + 370(42) DX

B–A

222 T. Norby

The protons rotate around their oxide ion hosts. The activation barrier for

rotational diffusion is generally low so that these rotations are easy [18], but

they lead to no long-range proton migration. The stretching vibrations, on the

other hand, may lead to a jump to the next oxide ion. The diffusivity of protons

may be expressed:

¼ð1  x

ÞaZs

OHO

exp

m;H

exp

DH

m;H

¼ð1  x

ÞD

0;H

exp

DH

m;H

(11:9)

where x

is the fraction of protons over oxide ion sites so that 1  x

is the

probability that the target of the jump is free to accept a proton (assuming that

all sites are occupied by an oxide ion with or without one proton), a is a factor

arising from geometry, Z is the number of neighbors, s

OHO

is the jump distance

(effectively the O–O distance as long as the rotation is tacitly assumed part of

the jump), n

is the effective attempt vibrational frequency, and DS

m;H

and

m;H

are the entropy and enthalpy of activation of migration, respectively.

We may normal ly take x

to be small and thus ð1  x

Þ1.

In normal three-dimensional lattice diffusion (for non-protonic specie s), a =

1/6, and the vibrational frequency is defined such that aZn

is the effective

frequency of attempts in any direction. For protons in oxides, it is more reason-

able to let a =1,Z =1,andn

=10

1

.Ifs

OHO

= 2.81 A

, and we

additionally let DS

m;H

= 0, then we get, for the pre-exponential of proton

diffusivity, D

0;H

¼ s

OHO

= 7.8  10

6

/s = 7.8  10

2

/s, but, as

we sh all see below, this is not obt ained in practice.

Proton transport exhibits a large isotope effect between protons and deu-

terons. This is often of the order of

2  1.4 and is thus attributed to the

classical ratio of atte mpt vibrat ional frequencies based on the reduced mass of

OH versus OD. However, it is now fairly well accepted that it is more

reasonable to attribut e it to the semiclassical difference in zero-point energy

of the proton versus the deuteron, that gives the proton an activation energy

of the final jump (when the oxide ions are close during their vibrations) which

is 0.04–0.06 eV lower than for deuterons. Thus, while most of the activation

energy is assigned to the O–O vibrations, a small part is still attributed to the

proton jump, and this latter part has a 0.04–0.06 eV lower energy for protons

than for deuterons. This difference happens to give a ratio of 1.4 or slightly

higher at temperatures where proton conduction is typically investigated (a

few hundred degrees centigrade). The pre-exponential of proton migration

may still hold the classical isotope effect, but probably has also other isotope

effects (such as the so-called sticking probability) that may actually cancel the

classical one or even reverse it [19]. The pre-exponential of proton migration

should, in addition to the effect of the low sticking probability, be lowered by

the frequency of oxide ion vibrations. For simplicity, one might think of the

oxide ion vibration frequency of around 10

Hz as the first estimate entering

11 Proton Conductivity in Perovskite Oxides 223

in the mobility of protons rather than the proton’ s own 10

Hz. When

mobility is extracted from proton conductivities, it usually comes out a factor

10–100 lower than estimated from classical proton jumps, in accordance with

the above. Thus, it is realistic to expect D

0;H

to be in the range 10

7

–10

6

sor10

3

–10

2

/s.

The activation energy for a proton to jump to the next oxide ion is

dependent on the O–O distance, because the electron density decreases and

potential increases in between. The activation energy is thus high in unpolar-

izable, stiff lattices, whereas it decreases considerably and temporarily during

O–O vibrations in softer lattices. These vibrations comprise the diminishment

of the O–O distance but also the linearization of the bent OH–O hydrogen

bond required to facilitate the proton transfer [18]. For this reason, the

activation energy of proton migrati on is well above 1 eV in close-packed

lattices such as Al

, is intermediate at 0.7–1 eV in lattices with larger

cations, such as rare earth sesquioxides, and usually as low as 0.5  0.1 eV

in perovskites.

It is interesting to note that the proton activation energy, seemingly regard-

less of class of oxide, is usually around two-thirds of the activation energy for

oxygen vacancy migration. This point may be understood by the fact that the

proton is totally reliant on the oxide lattice vibrations. The same activation

barrier has to be overcome, but while the oxide ion mu st make its way all the

way through the barrier saddle point to arri ve in the vacancy, the proton can

jump or tunnel when the oxide ion on which it sits has made it most of the way

(two-thirds of the barrier height).

The low activation enthalpy of proton mobility in perovskites may be

attributed to the large A-site cations, which allow considerable dynamics in

and between the BO

octahedra, and to the fact that the octahedra are corner

sharing so that jumps can take place within the octahedra as soon as the proton

has rotated into the appropriate direction from the previous jump. The low

activation energy of migration, combined with the low defect energies (accep-

tance of large concentrations of dopants and charge-compensating defects), is

what makes the perovskites such good proton conductors.

It appears that cubic perovskites exhibit higher diffusivities of protons than

less symmetrical lattices. This difference is most easily rationalized by the oxide

ion sites being equivalent, so that there are no sites that act as traps by requiring

a higher activation energy for the liberating jump.

11.2.4 Charge Mobility and Conductivity of Protons

The charge mobility of protons is given via the Nernst–Einstein equation, as

follows:

0;H

exp

DH

m;H

¼ u

0;H

exp

DH

m;H

(11:10)

224 T. Norby

where we have again assumed ð1  x

Þ1. Ideally, the pre-exponential

0:H

0;H

is approximately 0.1 m

K/Vs = 1000 cm

K/Vs for proton

migration, but the real attempt frequency and sticking probability lower this to

0.001–0.01 m

K/Vs = 10–100 cm

K/Vs.

The conductivity s

of any species i is given by its charge z

e, volume

concentration of charge carrier particles c

, and mobility u

¼ z

(11:11a)

If the concentration is, instead, expressed as volume concentration of moles

of charge carriers c

m,i

, the conductiv ity becomes:

¼ z

m;i

(11:11b)

For protons, z = 1, and it is convenient to obtain the conductivity in terms of

the fraction of protons over oxide ion sites x

and the molar concentration of

oxide ion sites c

m;O

2:

¼ Fx

m;O

2u

(11:12a)

or, in terms of the molar fraction of protons x

m;H

and the molar concentration

of the oxide c

¼ Fx

m;H

(11:12b)

In regions where the proton concentration is given by the acceptor dopants,

m;H

¼ x

m;Acc

¼ constant and the activation energy of proton conduction is

given by that of the proton mobil ity. In regions where the protons are minor

defects, and oxygen vacancies instead compensate the accep tors, the concentra-

tion term has a temperature dependency given by DH

=2 so that the ov erall

activation enthalpy of proton conduction is DH

¼ DH

m;H

þ DH

=2. As

is negative for proton-conducting oxides, and most often DH

=2 is larger

in magnitude than DH

m;H

, the conductivity decreases with increasing tempera-

ture at high temperatures where the protons have become a minority. All in all,

the proton conductivity typically goes through a maximum as a function of

temperature.

11.2.5 Proton Conductivity in Acceptor-Doped Simple Perovskites,

ABO

Proton conductivity is found in a range of perovskites, ABO

, covering all

combinations of valence of the A and B cations. The protonic defects have to

be compensated by some effectively negative defect, most often acceptor

11 Proton Conductivity in Perovskite Oxides 225

substituents. The next prerequisite seems to be, as discussed earlier, that the

electronegativity difference between B and A is not too large to favor hydration

of the oxygen vacancies.

Figure 11.2 shows the partial proton conductivity for a number of acceptor-

doped perovskites, calculated from data for proton mobility and

thermodynamics of hydration.

Among III–III perovskites, La

is the only common A-site cation. LaScO

hydrates well but exhibits medium proton mobility and a proton conductivity

peaking just above 10

3

S/cm. LaYO

and LaErO

are also perovskite related,

but with lower tolerance factors and lower conductivity.

LaCrO

, LaMn O

, LaFeO

, and LaCoO

have increa singly acidic B-site

cations and decreasing band gaps, and reliable findings of protons or proton

conductivity are not report ed for these oxides. For LaMnO

and LaFeO

[30],

we have ourselves actively looked for evidence of effects of protons but found

none.

Fig. 11.2 Partial proton

conductivity vs. 1/T for bulk

(grain interior) of selected

perovskites at pH

0.03 atm, calculated on basis

of proton mobility and

hydration thermodynamics

parameters. Acceptor level is

chosen as 10 mol% (3.33%

of oxide ions are protonated

at full hydration) for

BaZrO

[20], BaCeO

[12],

BaTbO

[21], BaThO

[21],

SrCeO

[22], SrTiO

[20, 23],

SrZrO

[20], CaZrO

[24,

25], LaScO

[26], and

LaErO

[27]. Data for

BCN17

(Ba

1.17

1.83

8.745

) [28]

and Ba

YSnO

5.5

[29] are

calculated with acceptor

levels as in formula. Curves

should represent reasonable

estimates of partial proton

conductivity in temperature

range of measurement, but

may otherwise contain large

errors caused by

correlations between the

parameters used

226 T. Norby

Sr- and Mg-substituted LaGaO

(LSGM) is another member where no

protons are found [31]. Lattice modeling of this material has indeed predicted

the hydration enthalpy to be positive (endothermic) [32].

Among II–IV perovskites we find the best proton conductors . BaZrO

BaCeO

, BaTbO

, and BaThO

all exhibit large negative hydration enthalpies

and small activation energies for proton migration. The proton conductivity

peaks above 10

2

S/cm. They have large grain boundary resistances, especially

for BaZrO

, which has the largest band gap. It seems that the grain boundary

resistance decreases with decreasing band gaps and increasing partial electronic

conduction, but it is unclear whether this reflects the proton transport itself or

variations in electronic transport properties across the grain boundary.

BaTiO

does not hydrate much and exhibits only a small proton conductiv-

ity. Combining Ba with more acidic tetravalent cations is not known to lead to

proton uptake or proton conductivity.

Moving to stront ium-based perovskites, we find the same trend as for the

barium members. However, the conductivity is smaller, peaking between 10

3

and 10

2

S/cm for the best ones (SrZrO

and SrCeO

). SrCeO

is one of the best

studied proton conductors, but the tolerance factor is low and the material is on

the verge of decomposition into the binary oxides. It is therefore very vulnerable

to reaction wi th CO

, for example.

Also, a few calci um-based perovskites are proton conducting, notably

CaZrO

, which is used in hydrogen sensors for molten aluminium . It may be

noted that CaCeO

does not exist . Both CaTiO

and SrTiO

hydrate, but only

significantly at relatively low temperatures, and thus exhibit modest proton

conductivities.

Along the same scheme as for Ba perovskites, combinations with acidic and/

or ambivalent B-site cations, e.g., in SrMnO

or SrFeO

, do not lead to

hydration.

I–V perovskites such as KTaO

were early on found to exhibit proton

conduction [4], but the conductivity was low, and fundamental properties

such as hydration therm odynamics have not been investigated in detail.

One may consider that WO

and ReO

represent 0–VI perovskites. Hydra-

tion as such is not well described for WO

, but it dissolves hydrogen that ionizes

to protons and electrons and forms a bronze. It is interesting to note that the

mineral bernalite, Fe(OH)



O, possesses a ReO

-like perovskite structure

in which Fe occupies the B sites, OH the ‘‘oxygen’’ sites, and water molecules a

fraction (typically 25%) of the A sites.

Complex perovskites employ usually two B-site cations of different valence,

typically in simple ratios to form certain valence sums. Many of these are used

as electroceramics in which the B-sit e cation ordering is essential, but the

valence sum is made up such that the oxygen sublattice is kept full. An example

of this is BaCa

1/3

2/3

(BCN), often written as Ba

CaNb

. By increasing

the Ca content at the cost of Nb, charge-compensating oxygen vacancies are

introduced, for instance, in the classical ‘‘BCN18’’ or Ba

1.18

1.82

8.73

(Fig. 11.2 includes data for BCN17.) An example of another class is

11 Proton Conductivity in Perovskite Oxides 227

1+x

1–x

6–x

[33] and analogues [34]. Bot h the hydration thermody-

namics and proton mobility and conductivity of such complex perovskites

can be said to follow the systematics of the simple perovskites. It has been

argued that the complex perovskites have the advantage that the doping can be

done simply by shifting the ratio of the two B-site cations and not introducing

another dopant ion. However, it is the present author’s view that the extra

cation is already there by having two B-site cations, and that little or nothing is

gained.

The most interesting aspect of complex perovskites probably lies in the

possibility to order the B-site cations that are present in a simple ratio, e.g.,

1:2 or 1:1, so as to avoid carrier traps, and at the same time have a moderate

oxygen deficiency (lower than the 1/6 of the Brownmillerite-type stoichiome-

tries). One of these classes is repres ented by Ba

YSnO

5.5

(or Ba

Here, 1 in 12 of the oxygen positions is vacant. The material hydrates, probably

helped by the basicity of the Y

ion, and is a good proton conductor (see

Fig. 11.2). Another class is exemplified by Ba

(Ca

, the ‘‘BCN50’’ end

member of Ca-enriched BCN. At sufficiently low temperature and high pH

they may go through a phase transformation into an ordered or disordered

oxyhydroxide, as we shall come back to later.

Ruddlesden–Popper-phas es, with general composition A

n+1

3n+1

, are

more basic than the normal perovskite end members ABO

and in principle

more attractive to protons, but only modest proton conductivities have been

found, notably in Sr

TiO

[35].

11.2.6 Effects of Defect–Acceptor Interactions

Oxygen vacancies are often found to be effectively associated to acceptor

dopants according to the following equilibrium:



þ Acc

¼ðv

AccÞ



(11:13)

The hy dration of this associate, according to the following:

OðgÞþðv

AccÞ



þ O

¼ 2OH



þ Acc

(11:14)

can perhaps be expected to be less favorable (less exothermic) than that of the

free vacancies, provided that the protons dissolved are less associated to the

acceptor. Although this is probably an important factor in many systems, it is

mainly neglected in interpretation of data for hydration. The defect chemistry

and ‘‘master curves’’ of proton concentration (similar to the foregoing Eqs.

(11.6a) and (11.6b)) can be derived for hydration of associated vacancies, but

this is not further covered here.

228 T. Norby

Eventually, at sufficiently low temperatures, protons will themselves tend to

be trapped by acceptors according to this equation:



þ Acc

¼ðOH

AccÞ

(11:15)

This reaction is not studied as well as the corresponding reaction for oxygen

vacancies. However, Kreuer et al. [20] found that BaZrO

doped with Y had a

somewhat lower activation energy and higher conductivity than with the same

amount of Sc, and they attributed this to oxide ions coordinated to Sc becoming

more electron rich (basic), thus bonding protons more strongly. The stronger

trapping by Sc comes despite Sc

having a better size fit to the Zr

sites,

emphasizing, according to Kreuer et al., that the acid–base character of the

cations (including electronegativity) plays a large role for mobility as well as for

hydration. The effe ct on the activation energy is nevertheless modest (0.43 eV

for Y vs. 0.50 for Sc). Although it gives two orders of magnitude higher proton

conductivity at 1008 C in the work by Kreuer et al., the effect will be much

reduced at operating temperatures.

All in all, it seems that there are effects of dopants, but trapping in associates

such as those described by Eq. (11.11) are hardly evidenced experimentally in

conductivity measurements so far.

11.2.7 Grain Boundaries

State-of-the-art proton-conducting perovskite oxides are troubled by remark-

ably high grain boundary impedances. This problem is most prominent for

BaZrO

, wher e for a long time the true bulk impedance was too small to be

detected in impedance spectroscopy [36]. It is likely that the grain boundary

impedance for protons has the same origin as that for oxygen vacancies in

many oxygen ion-conducting oxides, such as Y-stabilized ZrO

(YSZ) and

acceptor-doped CeO

. The grain boundary core attracts an excess of oxygen

vacancies because this minimizes the energy of the misfits between the two

lattices. Possibly, protons act as terminators of ‘‘dangling bonds’’ in the grain

boundary core and are also enriched there. The core thus attains a net

positive charge, which is balanced by a net negative charge of the space

charge layer (SCL) around the core [37]. This negative charge comes about

by a deficiency in positive species (such as oxygen vacancies, protons, and

holes) and a surplus of negative species (such as electrons and acceptor

dopants).

Much work has been invested in understanding and reducing the grain

boundary proton resistance, esp ecially with regard to the effects of A-s ite

nonstoichiometry and impurities. We shall not treat this here but just men-

tion that, somewhat surprisingl y, the grain boundary resistance disappeared

11 Proton Conductivity in Perovskite Oxides 229