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

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where A and B are larger and smaller cations. The crystal structure of A

based oxides consists of one perovskite-type block and one rock salt-type AO

block. Thus, it is interesting to study the structural disorders and diffusion path

of oxide ions in the A

-based oxides and compare the results with those

of perovskite-type materials. Here we also review the structural disorder

and diffusion paths of oxide ions in the K

NiF

-type (Pr

0.9

0.1

)

(Ni

0.74

0.21

0.05

4+d

[15].

6.2 High-Temperature Neutron Powder Diffractometry

Some ABO

3–d

perovskite-structured materials, where A and B represent larger

and smaller cations, are ionic conductors, while some other ABO

3–d

perovskite-

type compounds are mixed conductors. Heavy elements such as La and Ba

occupy the A site, but because the mobile O anion is a light element, conventional

X-ray powder diffractometry is not sensitive to positional and occupational

disordering of oxide ions. To investigate the diffusion path of mobile oxide

ions, and structural disorder and crystal structure in perovskite-structured ionic

and mixed conductors [5, 6, 8, 10–14], we applied a high-temperature neutron

powder diffraction method. Our reasons for choosing this method were as

follows [24]:

1. The coherent scattering length of the O atom is relatively large compared

with its X-ray scattering factor. Figure 6.1 illustrates the relative scattering

abilities of the oxygen atom in both methods.

2. At high temperatures, the sample surface is often altered by processes such as

sintering, grain growth, cracking, evaporation, and thermal expansion; this

can lead to shifts in diffraction peak intensity and position. Thus, it is often

difficult to perform structural refinement and electron density analysis using

conventional high-temperature X-ray diffraction data measured with

Fig. 6.1 Circles representing the relevant sizes of the square of the X-ray scattering factor (left)

and the neutron scattering length (right) of oxygen atoms in (La

0.8

0.2

)(Ga

0.8

0.15

0.05

2.8

where the size of the square of the X-ray scattering factor of the cation is assumed to be the same

as that of the neutron scattering length of the cation

118 M. Yashima

Bragg–Brentano geometry. In contrast, structural analysis based on high-

temperature neutron powder diffraction data is less subject to the influence

of sintering, grain growth, cracking, evaporation, and thermal expansion.

3. The lack of electronic interference allows for a simple density map. An

electron-density map from X-ray diffraction data includes not only the struc-

tural disorders but also the electron clouds. In contrast, the nuclear density

map from neutron diffraction data does not include the electron clouds.

4. The neutron form factor is independent of the scattering angle, which allows

for high precision in the elucidation of atomic displacement parameters and

structural disorder.

5. The low absorption of neutron by the furnace itself is less damaging to the

data quality.

We devised and fabricated a new furnace for high-temperature neutron

diffraction measurements (Fig. 6.2) [24], using molybdenum silicide heaters to

heat the sample. The merits of the molybdenum silicide heater are as follows:

1. It can be used in air for long periods at temperatures of up to 1900 K without

degradation.

2. A furnace based on this heater is superior to a mirror furnace in terms of

temperature homogeneity.

3. Low-temperature degradation, which is often seen in LaCrO

heaters, does

not occur.

Using the furnace, neutron powder diffraction measurements were con-

ducted in air from room temperature to 1850 K using a 150-detector system,

HERMES [25], i nstalled at the JRR-3 M reactor at the Japan Atomic Energy

Agency, Tokai, Japan (Fig. 6.2) [24, 26]. The furnace was placed on a sample

table, and neutrons with wavelength 1.82 A

were obtained using the (331)

reflection of a Ge monochromator. Although diffraction data where d

spacingislessthan0.93A

cannot be measured using HERMES, the

Fig. 6.2 Photograph of the

furnace [24] placed on the

sample table of the neutron

diffractometer HERMES [25]

6 Perovskite-Type Oxides and Related Materials 119

diffractometer has sufficient intensity and power to collect data with good

counting statistics for nuclear density analysis. Diff raction data were col-

lected in the range 2y ¼38–1578 at step interval s of 0.18. The sample tempera-

ture was kept constant during data collection, and was monitored using a Pt/

Pt-13 wt% Rh thermocouple in contact with the sample.

6.3 Data Processing for Elucidation of the Diffusion Paths of

Mobile Oxide Ions in Ionic Conductors: Rietveld Analysis,

Maximum Entropy Method (MEM), and MEM-Based Pattern

Fitting (MPF)

The experimental diffraction data were analyzed by a combined technique

involving Rietveld analysis, the maximum entropy method (MEM), and

MEM-based pattern fitting (MPF) [10–15]. Rietveld analysis, which is used to

refine the crystal structure from the powder diffraction data by a least squares

method, was carried out using the RIETAN-2000 program [27], which yields

structure factors and their errors after structural refinement. It is known that

MEM can be used to obtain a nuclear density distribution map based on

neutron structure factors and their errors [5, 6, 8, 10–15, 26–29]; any type of

complicated nuclear density distribution is allowed so long as it satisfies the

symmetry requirements. MEM calculati ons were carried out using the PRIMA

program [29]. To reduce the bias impos ed by the simple structural model in the

Rietveld refinement, an iterative procedure known as the REMEDY cycle [29]

was applied after MEM analys is (Fig. 6.3). In this procedure, structure factors

Fig. 6.3 Flow chart of the combined technique involving Rietveld analysis, MEM and MPF.

The REMEDY cycle, in which MEM and MPF are performed alternately and repeatedly,

improves the reliability of the nuclear density. F

(Rietveld) is the observed structure factor

obtained from the Rietveld analysis. F

(MEM) is the structure factor calculated from the

MEM nuclear density. F

(MPF) is the observed structure factor, which is obtained from the

MPF analysis

120 M. Yashima

(MEM) were calculated by Fourier transform of the nuclear densities

obtained by MEM analysis. In the subsequent MEM-based pattern fitting

(MPF), the structure factors F

(MEM) obtained in the previous MEM analysis

were fixed, and parameters irrelevant to the structure—e.g., scale factor, pro-

file, unit cell, and background parameters—were refined using RIETAN-2000

[27]. The obs erved structure factors evaluated after the MPF, F

(MPF), were

then analyzed again by MEM. MPF and MEM analyses were alternated until

the reliability indices no longer decreased (REMEDY cycle). The REMEDY

cycle allowed us to obtain a reliable nuclear density distribution (Fig. 6.3).

When the MEM is successful in obtaining a nuclear density, the reliability factors

based on the structure factors (R

) and on the Bragg intensities (R

or R

)in

the MPF analysis are lower than those in the Rietveld analysis.

6.4 Diffusion Path of Oxide Ions in the Fast Oxide Ion Conductor

(La

0.8

0.2

)(Ga

0.8

0.15

0.05

2.8

[10]

6.4.1 Introduction

Lanthanum gallate-based materials with an ABO

3–d

perovskite-type structure

have higher oxide ion conductivity than conventional yttria-stabilized zirconias

[9, 30]. The crystal structure of these materials ha s been the subject of a number

of investigations [31–39], and the diffusion path of oxide ions in lanthanum

gallates has been studied by computational methods [40, 41] and by diffracto-

metry [36]. Here, we describe the temperature dependence of the diffusion paths

and structural disorder of oxide ions in (La

0.8

0.2

)(Ga

0.8

0.15

0.05

2.8

1665, 1471, and 1069 K [10]. For comparison, we also describe the nuclear

density distribution of LaGaO

at 1663 K [42]. Comparison of structural

disorder in (La

0.8

0.2

)(Ga

0.8

0.15

0.05

2.8

and LaGaO

is interesting

because the oxide ion conductivity of (La

0.8

0.2

)(Ga

0.8

0.15

0.05

2.8

about 10

times higher than that of LaGaO

(Fig. 6.4 [42]).

6.4.2 Experiments and Data Processing

In this work, we used a material with the chemical composition (La

0.8

0.2

)

(Ga

0.8

0.15

0.05

2.8

because doping of Co, Sr, and Mg into lanthanum

gallate effectively enhances oxide ion conductivity (Fig. 6.4 [42]) [43]. A high-

purity sample was synthesized via solid-state reactions [10]. Chemical analysis of

the final product showed a composition of (La

0.80(3)

0.20(3)

)(Ga

0.80(6)

0.15(6)

0.050(7)

2.8(3)

, where the number in parentheses is the error in the last

digit. Neutron powder diffraction experiments were carried out at 1069.2 

1.6, 1470.7  1.3, and 1664.6  1.4 K in air using a furnace with MoSi

heaters

[24], as described above, and the HERMES diffractometer [25]. Neutron

6 Perovskite-Type Oxides and Related Materials 121

diffraction data for LaGaO

were obtained in air at 1663 K. The wavelength of

the incident neutrons was 1.8207 A

. Powder patterns were obtained in the range

2y ¼58–1558. The experimental diffraction data were analyzed using a combina-

tion of the Rietveld method and MPF, with the RIETAN-2000 program [27], and

MEM, using the PRIMA program [29].

6.4.3 Results and Discussion

The crystal structure of (La

0.8

0.2

)(Ga

0.8

0.15

0.05

2.8

was successfully

refined, assuming an ideal perovskite-type structure with the space group



3m at 1665 K (Fig. 6.5) and at 1471 K. At 1069 K, the material was analyzed

assuming R



3c symmetry, because the R



3c reflections forbidden for the Pm



phase exist at this temperature [10]. The refined crystallographic parameters are

shown in Table 6.1. The unit-cell volume of the pseudo-fluorite lattice increases

with temperature due to thermal expansion. The atomic displacement para-

meters of the oxygen atom are large and anisotropic (Fig. 6.5(a) and Table 6.1).

The isotropic atomic displacement parameters of all cations, and the equivalent

isotropic atomic displacement parameters of the oxide ions, increase with

increasing temperature (Table 6.1), corresponding to higher oxide ion conduc-

tivity at higher temperatures (Fig. 6.4 [42]) [43]. The equivalent isotropic atomic

displacement parameters of the oxide ions are higher than those of the cations,

suggesting higher diffusivity for the oxide ions.

Fig. 6.4 Arrhenius plot of

oxide ion conductivity

of LaGaO

(closed circles)

and (La

0.8

0.2

)

(Ga

0.8

0.15

0.05

2.8

(LSGMC, open circles) [42].

The structural origin of the

difference in ionic

conductivity between the

two materials can be seen in

Fig. 6.6(a,d)

122 M. Yashima

MEM analysis was carried out using the structure factors obtained by

Rietveld analysis; 17, 16, and 56 structure factors were obtained for data

measured at 1665, 1471, and 1069 K, respectively. We measur ed the peak

intensity of cubic 100 reflection at the lowest 2y position, because the intensity

of the 100 reflection contributes the most information to MEM analysis. MEM

calculations were performed using 64 64 64 and 96 96 235 pixels for the

cubic and trigonal structures, respectively. The R factor based on the Bragg

intensities, R

, was considerably improved by the REMEDY cycle (Table 6.1),

indicating the validity of these nuclear density distributions for (La

0.8

0.2

(Ga

0.8

0.15

0.05

2.8

. The isosurface of nuclear density obtained from the

REMEDY cycle provided much information on the complexity of structural

disorder and diffusion paths of oxide ion in the crystal (Figs. 6.5(b) and 6.6).

Simple models consisting of atom sph eres were no longer appropriate to

describe the positional distribution of the oxide ions.

To visualize the structural disorder and diffusion paths, the MEM nuclear

density distribution map in the (100) plane is shown in Fig. 6.6. The ox ide ions

in the cubic Pm



3m phase exhibit a large anisotropic distribution, corresponding

to large anisotropy in the atomic displacement parameters (Table 6.1). The

most striking feature is the diffusion path of the oxide ions. Roughly speaking,

the diffusion paths are along the [110], [011], and [101] directions, forming a

three-dimensional network of pathways. The diffusion path does not follow the

edge of the BO

[= (Ga

0.8

0.15

0.05

5.6

] octahedron along the <110>

direction (shown as straight dotted line between the ideal O1 and O2 positions

in Fig. 6.5(b)), but displays an arc shape (curved solid line with arrows),

maintaining a constant distance from the B-site cation (G in Fig. 6.5(b)). This

curved feature is consistent with the results obtained by computational methods

Fig. 6.5 (a) Refined crystal structure and (b) isosurface of nuclear density at 0.05 fm A

3

cubic Pm



3m (La

0.8

0.2

)(Ga

0.8

0.15

0.05

2.8

at 1665 K [10]. LS, (La

0.8

0.2

) cation; G,

(Ga

0.8

0.15

0.05

) cation

6 Perovskite-Type Oxides and Related Materials 123

Table 6.1 Crystallographic parameters and reliability factors for (La

0.8

0.2

)(Ga

0.8

0.15

0.05

2.8

[10]

Temperature, space group

Unit-cell parameters

Unit-cell volume

1069.2  1.6 K, R



a=b=5.5587(9) A

; c=13.629(3) A

V=364.7(1) A

=60.78(2) A

)***

1470.7  1.3 K, Pm



a=3.9618(2) A

V=62.184(4) A

1664.6  1.4 K, Pm



a=3.9744(2) A

V=62.779(4) A

0.8

0.2

Wyckoff

Position / g

6a / 1.0 1b / 1.0 1b / 1.0

x, y, z 0, 0, 1/4 1/2, 1/2, 1/2 1/2, 1/2, 1/2

Atomic displacement parameters U

=2U

=0.025(4) A

;

=0.033(9) A

;

=0 A

; U

0.028 A

U=0.0391(9) A

U=0.0454(9) A

0.8

0.15

0.05

Wyckoff

Position / g

6b / 1.0 1a / 1.0 1a / 1.0

x, y, z 0, 0, 0 0, 0, 0 0, 0, 0

Atomic displacement parameters U

=2U

=0.016(4) A

;

=0.018(7) A

;

=0 A

=0.017 A

U=0.0274(9) A

U=0.0343(9) A

O Wyckoff

Position / g

18e / 0.9333 3d / 0.9333 3d / 0.9333

x, y, z 0.529(4), 0, 1/4 1/2, 0, 0 1/2, 0, 0

Atomic displacement parameters U

=0.028 A

; U

=0.039(10) A

;

=2U

=0.018(8) A

;

=0.087(11) A

;

=0.5U

=0.012(3) A

=0.0712 A

;

=0.0268(12) A

;

=0.0935(13) A

;

=0 A

=0.0817 A

;

=0.0292(13) A

;

=0.0935(13) A

;

¼U

¼0A

Reliability factors in the Rietveld

refinement*

=6.53%, R

=4.97%,

Goodness of fit ¼1.492,

=3.16%, R

=1.90%

=6.90%, R

=5.20%,

Goodness of fit ¼1.610,

=3.63%, R

=2.23%

=6.35%, R

=4.94%,

Goodness of fit ¼1.485,

=2.68%, R

=2.39%

Reliability factors in the final

MEM-based whole-pattern fitting*

=1.92%, R

=1.52% R

=2.03%, R

=1.24% R

=1.91%, R

=1.34%

Reliability factors in the final MEM

analysis**

(MEM) ¼1.74%

(MEM) ¼2.04%

(MEM) ¼1.18%

(MEM) ¼1.35%

(MEM) ¼1.48%

(MEM) ¼1.46%

Note: g, occupancy; x, y, z, fractional coordinate.

*Standard Rietveld indices; **reliability factors: MEM analysis; ***V

, unit-cell volume of the pseudo-perovskite cell.

124 M. Yashima

[40, 41] and with the potential map obtained using a probability density func-

tion technique [36]. Here, for the first time, we have obtained a diffusion path

from the nuclear density distribution and demonstrated its temperature depen-

dence [10]. The nuclear density in the area of the diffusion path is greater at

1665 K (Fig. 6.6(a)) than at 1471 K (Fig. 6.6(b)), which is consistent with

an increase in oxide ion conductivity with increasing temperatur e (Fig. 6.4

[42]) [43]. Notably, the oxide ions in the low-temperature tri gonal phase are

localized near the equilibrium positions (Fig. 6.6(c)), although they are spread

over a wide area between the ideal positions in the high-temperature cubic phase

(Fig. 6.6(a, b)). This interesting distribution indicates that the more symmetrical

Fig. 6.6 Nuclear density distributions on the (100) plane of cubicPm



3m (La

0.8

0.2

(Ga

0.8

0.15

0.05

2.8

at (a) 1665 K and (b) 1471 K, and (c) on the (012) plane of trigonal



3c (La

0.8

0.2

)(Ga

0.8

0.15

0.05

2.8

at 1069 K, with contours in the range from 0.3 to

4.0 fm A

3

(0.3 fm A

3

step) [10]. (d) Nuclear density distribution on the (012) plane of

trigonal R



3c LaGaO

at 1663 K [42]. G and O denote the B-site cation (Ga

0.8

0.15

0.05

)

and the oxide ion, respectively. The diffusion path of the oxide ion is not along the straight line

between the ideal positions, but along the curved solid line avoiding the G ion [white arrows in

(a)]. The thin black straight line and thick black dashed line in Fig. 6(c, d) show the Pm



3m and



3c unit cells, respectively. In the low-temperature trigonal structure, the oxide ions are

localized near the equilibrium position, while in the high-temperature cubic phase the oxide

ions are spread over a wide area between the ideal sites

6 Perovskite-Type Oxides and Related Materials 125



3m phase has a lower activation energy for the migration of oxide ions. As

shown in Fig. 6.6(a,d), the oxide ions in cubic (La

0.8

0.2

)(Ga

0.8

0.15

0.05

2.8

have a greater distribution than in trigonal LaGaO

. This finding

is consistent with the difference in oxide ion conductivity between the two

compounds (Fig. 6.4 [42]).

6.5 Diffusion Path of Oxide Ions in an Oxide Ion Conductor,

0.64

(Ti

0.92

0.08

2.99

, with a Double Perovskite-Type

Structure [11]

6.5.1 Introduction

As mentioned earlier, some perovskite-related ABO

3–d

phases possess high

oxide ion conductivity. In Section 6.4, we described the diffusion path of mobile

oxide ions in a solid solution of cubic perovskite-type doped lanthanum gallate

(La

0.8

0.2

)(Ga

0.8

0.15

0.05

2.8

[10]. However, although there is a wide

variety of perovskite-related structures (e.g., A-site-deficient doubl e perovs-

kite-type structure), there were no reports concerning diffusion paths in such

materials. The lanthanum titanate solid solution La

(2x)/3

(Ti

1–x

3–d

(M ¼Al

or Nb, 0.05 x 0.20), where d denotes the concentration of oxygen defects,

has an A-site-deficient layered perovskite-type structure [19–21, 44–53], and

exhibits high oxide ion conductivity at high temperatures [21, 44]. Yoshioka [21]

studied the electrical properties of La

(2–x)/3

(Ti

1–x

3–d

(x = 0.05–0.15) and

reported that a sample with x = 0.10 displayed the highest ionic conductivity

(10

–2

Scm

1

at 973 K). In this section, we describe the crystal structure and

pathway of oxide ion diffusion in La

0.64

(Ti

0.92

0.08

3–d

(x = 0.08) [11].

6.5.2 Experiments and Data Processing

The La

0.64

(Ti

0.92

0.08

2.99

specimen was prepared via solid-state reactions

[11, 20]. ICP-OES chemical analysis indicated that the chemical formula of the

final product was La

0.636(1)

(Ti

0.921

0.079(1)

2.993(1)

. The value for oxygen

(2.993) was calculated based on electrical neutrality and suggests that the

amount of oxygen defects is small. Neutron powder diffraction data for

0.64

(Ti

0.92

0.08

2.99

were collected at 769 K, 1281 K, and 1631 K using

the furnace [24] and HERMES diffractometer [25] as described above. Incident

neutrons with a fixed wavelength of 1.8143 A

were used. Powder diffraction

data were measured over the range 2y =38–152.628. The sample temperature

was maintained to within 1.5 K during each measurement. The diffraction

data were analyzed by the Rietveld method, followed by application of MEM

and M PF, using the RIETAN-2000 [27] and PRIMA [29] programs.

126 M. Yashima

6.5.3 Results and Discussion

Rietveld analysis of the neutron powder diffraction patterns of

0.64

(Ti

0.92

0.08

2.99

at 769 K, 1281 K, and 1631 K was performed assuming

a tetragonal P4/mmm structure (a ¼b  a

, c  2a

subscript p denotes

pseudo-cubic perovskite-type structure) . The refined unit-cell and structural

parameters and R factors are summ arized in Table 6.2 [11]. The unit-cell

parameters increase with temperature, as does the unit-cell volume due to

thermal expansion. Figure 6.7(a) shows the crystal structure of the material

Table 6.2 Refined crystallographic parameters and reliability factors in Rietveld and MPF

analyses for La

0.64

(Ti

0.92

0.08

2.99

[11]

Temperature 769 K  1.5 K 1281 K  1.5 K 1631 K  1.5 K

Atom/Site Parameter

a (A

) 3.8827(2) 3.9019(2) 3.9172(2)

c (A

) 7.8684(4) 7.9118(4) 7.9249(5)

La1 U ( 10

2

) 1.33(7) 2.83(9) 3.99(12)

La2 U ( 10

2

) 0.8(2) 1.9(3) 1.3(3)

Ti,Nb z

U ( 10

2

)

0.2625(6)

0.54(10)

0.2640(7)

1.95(12)

0.2621(9)

2.51(14)

O1 U

( 10

2

)

( 10

2

)

( 10

2

)

2.5(2)

1.3(3)

2.12

4.5(2)

2.3(3)

3.76

5.1(3)

2.8(4)

4.32

O2 U

( 10

2

)

( 10

2

)

( 10

2

)

3.7(2)

0.2(2)

2.58

5.5(2)

1.1(3)

4.05

6.4(3)

1.9(4)

4.91

O3 z

( 10

2

)

( 10

2

)

( 10

2

)

( 10

2

)

0.2340(3)

2.6(2)

0.11(10)

3.16(12)

1.97

0.2344(4)

4.4(2)

1.04(11)

4.81(14)

3.41

0.2373(5)

5.6(3)

1.53(14)

5.9(2)

4.36

Reliability factors* R

=5.76%,

=4.28%

Goodness of fit:

3.16

=5.38%,

=3.59%

=5.21%,

=3.83%

Goodness of fit:

2.87

=4.19%,

=4.36%

=5.00%,

=3.73%

Goodness of fit:

2.82

=4.33%,

=5.06%

Reliability factors** R

=6.03%,

=3.27%

=4.17%,

=3.13%

= 4.05%,

=3.33%

Note: * Reliability factors in Rietveld analysis. ** Reliability factors in MEM-based

pattern fitting. Tetragonal space group P4/mmm (No. 123) Z =2. U, Atomic displacement

parameter; z, fractional coordinate. Occupancies for La1, La2, O1, O2, and O3 sites are

assumed to be 1.0, 0.271, 1.0, 0.9972, and 0.9972, respectively. Occupancies of Ti and Nb

atoms at the Ti,Nb site are assumed to be 0.9209 and 0.0791, respectively. In analyses, atom

positions were: La1 1a (0, 0, 0); La2 1b (0, 0, 1/2); Ti,Nb 2h (1/2, 1/2, z); O1 1c (1/2, 1/2, 0); O2

1d (1/2, 1/2, 1/2); O3 4 i (1/2, 0, z). Site symmetries give constraints: U

= U

=0 at

O1, O2, and O3 sites; U

= U

at O1 and O2 sites. Only independent atomic displacement

parameters are given.

6 Perovskite-Type Oxides and Related Materials 127