Partial Electronic and Ionic Conductivities ofNanocrystalline Ceria Ceramics

Sangtae Kim, Jürgen Fleig, Joachim Maier

Max Planck Institute for Solid State ResearchStuttgart, Germany

IMSPEMASWarsaw, Poland

September 26, 2003

Contents

Introduction -Different conduction pathways in polycrystalline ceramics and their superposition

-Bricklayer model-Core-space charge model for grain boundary

Detectability in impedance spectroscopy

-Highly conductive grain boundary-AgBr bicrystal-AgCl polycrystalline ceramics-AgCl polycrystalline ceramics with microelectrodes

-Highly blocking grain boundary-SrTiO3 polycrystalline ceramics with microelectrodes-SrTiO3 bicrystal

-Highly selective grain boundary for partial electronic and ionic conduction-nanocrystalline CeO2 ceramics-Quantitative analysis based on space charge models

x

yz

Conduction in polycrystalline electroceramics

Electroceramics for practical applicationsare polycrystalline forms.

Importance of understanding grain boundaryeffects relative to the bulk effect on total conduction

Impedance analysis

x

yz

Bricklayer model

For quantitative analysis

Assumption:• cubic-shaped grains of identical size and property• identical, homogeneous grain boundaries

Bulk

Grainboundary (gb)

dgc= 2b

dg

2

Space chargezones (sc)

Grain boundarycore (gc)

Core-space charge model

J. Jamnik, et al.,Solid State ionics, 75, 51 (1995)

Equivalent circuit

gggcscgb d

bd26

jˆ

ˆ)3/1(ˆ

ˆˆ)3/2(ˆˆˆ

||

gbgb

gbgbgbgbm

Effective complex conductivity

J. Maier, Ber. Bunsenges. Phys. Chem., 90, 26 (1986)

||ˆ)3/2(ˆˆ gbgbm )( 1 gb

1||1 )3/2(ˆ

gbgbm

1)3/1( gbgb )0(

annealing

Highly conductive space charge zones with blocking grain boundary core:AgBr bicrystal

0 1 2 3 4 5 60

1

2 Z

10-5 real part / x

w-1

0-5

imag

inar

y pa

rt/

x96oC

190oC1h

300oC1h

w/oannealing

J. Maier,Ber. Bunsenges. Phys. Chem., 90, 26 (1986)

real part / 10-5 , 1010 F-1

wZ (fresh)

0

-2

-4

0 2 4 6 8

wZ (annealed)

0

-1

-2

-3

0 2 4 6

imag

inar

y pa

rt / 1

0-5 W

annealing

Highly conductive space charge zones with blocking grain boundary core:AgCl polycrystalline ceramic

J. Maier, Ber. Bunsenges. Phys. Chem., 90, 26 (1986)

Microelectrodeon grain

Microelectrodeon grain boundary

Measurement principle25 m

Highly conductive space charge zones:AgCl polycrystalline ceramic - Microelectrodes

inverse resistancein 10-9S/cm

1 Hz

Zre/ G0 25 50 75 100 125 150 175 200

- Zim

/ G

0

25

50

75

100

on grainon grain boundary

1 Hz

23.9 34.6 8.4 7.87.2

7.5

5.45.1

11.8

7.9

8.9

9.09.5

31.7 66.1 31.740.5

64.1

J. Fleig, J. Maier, Solid State Ionics, 86-88, 1351 (1996)

Charge carrier accumulation in space charge zones

Ag+

Ag+

Ag+

Ag+

Ag+

Ag+

Ag+

gb corespace charge zone

Ag-vacancyconcentration

space charge potential = 300 mV

VAg

VAg

VAg

VAg

VAg

VAg

VAgVAgVAgVAg

VAgVAgVAgVAg

space charge zone

Ag-vacancyconcentration

VAg

VAg

VAg

VAg

VAg

VAg

VAg VAg VAgVAg

VAg VAg VAg VAg

2 2 xx

2

)/exp(1)/exp(1)(

x

xc

xc

v

v

v

v

1/)(

1/)(2/1

2/1

vv

vvv

cxccxc

Gouy-Chapman Profile

2/1

22

ceTkB

Measurement principle

Blocking space charge zones: Fe-doped SrTiO3 polycrystalline ceramic:Microelectrodes

a

b

0 1e+9 2e+9 3e+9 4e+90

1e+9

2e+9- Z

im/

a

Zre/ 0 1e+9 2e+9 3e+9 4e+9

- Zim

/

0

1e+9

2e+9

b

Z real / 0 2e+9 4e+9 6e+9 8e+9 1e+10

0

2e+9

4e+9

0 V 0,2 V 0,6 V 1,0 V

-Z im

/

bS. Rodewald, et al.,J. Am. Ceram. Soc., 84, 521 (2001)

2nm

5 tilt grain boundary: [Fe] = 21018cm-1

Blocking space charge zones: Fe-doped SrTiO3 bicrystal

x

5 103x

4 103x

3 103x

2 103x

1 103x

1 103x00 3 103x 5 103x 7 103x

T = 598KP = 105 PaO2

xxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxxxx

xxxxxxx

zero bias200 mV400 mV600 mV

x

1 MHz 20 Hz

-Im Z

/ W

Re Z / W

2*

2exp)(

xc

xc

h

h

2/1)0(4*

Tke

B

Mott-Schottky Profile

Charge carrier depletion in space charge zones

space chargezone'FeTi

Defect concentration

h•

space chargezone

Vo••

x* *

2nm

mean space charge potential 650 mV

Space charge effects on the partial electronic and ionic conductivity ofnanocrystalline CeO2 ceramic

Defect equilibrium in CeO2

22/12 OeVO OxO

Mixed conductor

Vo••

Def

ect

con c

e ntr

atio

n

x

gcbulk bulk

e´

][][2 eVO For intrinsic

S. Kim, J. Maier, J. Electrochem. Soc, 149, J73 (2002)

e´

Nanocrystalline CeO2

Vo••

Nanocrystalline CeO2

Ionic conductivity behavior of nanocrystalline CeO2 ceramic:0.15 mol% Gd-doped CeO2

S. Kim, J. Maier, J. Electrochem. Soc, 149, J73 (2002)

Vo••

e´

x

Gd´

0 1x104 2x104 3x104 4x1040

1x104

2x104

3x104

4x104

-Z''/

ohm

Z'/ohm

0 1x106 2x1060

1x106

2x106

a403.9oC, in air

Pt/n-CGO/YSZ/Pt

-Z´´/

ohm

Z´/ohm

10-5 10-4 10-3 10-2 10-1

105

491 oCPt/n-CGO/Pt/YSZ/Pt Rb+Rgb

DC

R/oh

m

pO2/p0

R1 + R2 ~ Rdc

t ~ ion

Pt/n-CGO/YSZ/Pt

Vo••

e´

x

Gd´

1.36 1.38 1.40 1.42 1.44 1.46 1.48103

104

105

106

107

0.73 eV

1.5 eV

bulk

grain boundaryin air

/ohm

-cm

1000T-1/K-1

10-5 10-4 10-3 10-2 10-1103

104

105

106

107

108

109

grain boundary

bulk

404 oC

/ohm

-cm

pO2/P0

Electronic conductivity behavior of nanocrystalline CeO2 ceramic:Nominally pure CeO2

Pt|nano-CeO2|YSZ|Pt

1.32 1.36 1.40 1.44 1.48

10-5

10-4

10-3

1.1 eV

1.35 eV

Air t

ion

t - ion = e

1.8 eV

T/K

Scm

-1

1000T-1/K-1

1.9 eV

0.0 5.0x105 1.0x1060.0

5.0x105

1.0x106

Air412.1 oC

-Z´´/

ohm

Z´/ohm

= 33

10-5 10-4 10-3 10-2 10-110-7

10-6

491 oC t

ion

t-ion=e

- 0.26

/Sc

m-1

pO2/p0

Pt|nano-CeO2|Pt

S. Kim, J. Maier, J. Electrochem. Soc, 149, J73 (2002)

Vo••

e´

x

A´

S. Kim et al., Phys. Chem. Chem. Phys., 5, 2268 (2003)

Effective defect concentration in the space charge zone

1: accumulated defect 2: depleted defect 3: dopant

1

2

1

2

1

2

1

2

3

jcln jclnjclnFor z1 = -z2

2

1

3

2

2/120

21)(ccm

2/1101

|| )( cm

2/11102/1

21

|| )(1)(

cccm

2/12201

2 )(1)(

cccm

4/3220

2 )(1)(

ccm

4/3220

2 )(1)(

ccm

1

2

3

20

22/3

22 ln1)(

cc

cm

1

2

3

)(1)( 4/1

24/3

202/1

12

cccm

2/1110

102/1

21

||

)]/[ln(1)(

ccc

cm

2/120220

2/12

2 )]/[ln(11)(ccccm

12

3

2

13

a b c

d e f

g h i

j k l

m2

1

32

1

3

2

1

3

2

13

po

Gouy-Chapman

Mott-Schottky

Combined

Model For 2z1 = -z2 For z1 = -2z2

2

1

3

2

1

3

2

13n

0 00

2

2/120

21)(ccm

2/1101

|| )( cm

20

22/3

22 ln1)(

cc

cm

2/12201

2 )(1~)(

cccm

)(1~)( 4/1

24/3

202/1

12

cccm

20

2

22/1

12 ln1~)(

cc

ccm

20

2

22/1

12 ln1)(

cc

ccm

2/1101

|| )( cm

2/1101

|| )( cm 2/1101

|| )( cm 2/1101

|| )( cm

2/1101

|| ~)( cm 2/1101

|| ~)( cm 2/1101

|| ~)( cm

2/11102/1

21

|| )(1)(

cccm 2/1

1102/12

1|| )(1)(

cccm

Quantitative analyses of pO2 and T dependence for based on Mott-Schottky model: Gd-doped nano-CeO2

022

ln)0(2

lnln

OBO

v

PTke

Pc

22

lnln

lnln 0,

O

v

O

vm

Pc

P

Quantitative analyses Experimental results

10-5 10-4 10-3 10-2 10-1103

104

105

106

107

108

109

grain boundary

bulk

404 oC

/ohm

-cm

pO2/P0

VTT

1.0/1

)0(1

OV Space charge potential for

V3.0)0(

Tke

TkeB

B

b

gb

/)0(4/)0(2exp

J.Fleig et al., J. Appl. Phys., 87(5), 2372 (2000)

TT

e/1

)0(1)0(2

Tk

Tk v

Bvm

B /1ln

/1ln ,,

,, vvm EE

1.36 1.38 1.40 1.42 1.44 1.46 1.48103

104

105

106

107

0.73 eV

1.5 eV

bulk

grain boundaryin air

/ohm

-cm

1000T-1/K-1

eV8.0

0 1x104 2x104 3x104 4x1040

1x104

2x104

3x104

4x104

-Z''/

ohm

Z'/ohm

Vo••

e´

x

Gd´

Concentration profilein n-CGO

)/ln(100

*

,

vvvv

vm cccu

Mott-Schottky situation

Quantitative analyses of pO2 and T dependence for || based on Mott-Schottky model: Nominally pure nano-CeO2

1.32 1.36 1.40 1.44 1.48

10-5

10-4

10-3Air t

ion

t - ion = e

1.8 eV

T/K

Scm

-1

1000T-1/K-1

-- 1.9 eV

10-5 10-4 10-3 10-2 10-110-7

10-6

491 oC t

ion

t-ion=e

- 0.26

/Sc

m-1

pO2/p0

Experimental results

-1/4

Quantitative analyses

22ln

)0(lnln

OBO

n

PTke

Pc

22

lnln

lnln 0

||,

O

n

O

nm

Pc

P

TTeEn /1

)0(1)0(

- 2.37§ eV + 0.4 eV

§ Tuller and Nowick, J. Electrochem. Soc.,122, 255 (1975)

Tc

Tue

Tk nnnm

B /1ln

/1ln

/1ln 0

||,

- 1.97 eV

0.0 5.0x105 1.0x1060.0

5.0x105

1.0x106

Air412.1 oC

-Z´´/

ohm

Z´/ohm

= 33

Mott-Schottky situation

)/ln(10

0*||

,

nn

nnnm cccu

Lower impurity concentrationn-CeO2-x

Vo••

e´

x

A´

Summary

Not only highly resistive but also highly conductive grain boundary effects are demonstrated with respect to detectability of impedance spectroscopy

In ceria, grain boundary becomes highly selective for electronic and ionic conduction. This can be quantitatively explained based on the space charge models.

microelectrode on grain potential distribution

method to obtain bulk conductivity

bulk 8·10 -9 1/ cm

Quantitative analysis numerical finite element calculations

Most potential drops close to microelectrode R as for microelectrode on single crystal

more complicated numerical analysis grain boundary conductance

(w · ) 4·10-11 1/

potential distributionmicroelectrode on grain boundary