Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 1/36 UNIVERSITY OF OSLO Grain boundary resistance in ionic conductors

Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 1/36

UNIVERSITY OF OSLO

Grain boundary resistance in ionic conductors

Christian Kjølseth

Department of Chemistry, University of OsloCentre for Materials Science and Nanotechnology (SMN)Forskningsparken, Gaustadalléen 21, 0349 Oslo, Norway


UNIVERSITY OF OSLOIntroduction

Grain boundary core – space charge model

Brick layer model

Grain boundary resistance

Grain boundaries in ionic conductors

Experimental investigation

Background ApplicationsFuel cell

Membrane

Challenge: Decrease the grain boundary resistance to get a high total proton conductivity

+ --

H+

conductor

e

O2+N2

H2O+N2

H2

H2+N2

H2 N2

H+and electronicconductor

R. Haugsrud

R. Haugsrud

Outline

Experiments - bias

Experiments – electron accumulation

Quantification

Experiments – uniaxial pressure

Some examples

Short summary


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Introduction

What is a grain boundary?

• Structural definition:A narrow zone corresponding to one crystallographic

orientation to another, thus separating one grain from another. The atom in each grain are arranged in an orderly pattern, the irregular junction of the two adjacent grains is known as the grain boundary.

• Electrical definitionThe zone between two grains which have electrical

properties differing that of grain interior. The grain boundary properties is dependent on external conditions such as temperature and atmosphere.


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Grain boundaries in ionic conductors

Grain boundaries usually conduct better than grain interior

→ The grain boundaries acts as conducting channels e.g. protons in LaPO4

• High temperature firing of LaPO4 leavs amorphous LaP3O9 in the grain boundaries

• Increases conductivity over grain interior material

• Conductivity increases with decreasing grain size

σgrain interior < σgrain boundary

Harley, Yu, de Jonghe, Solid State Ionics 178 (2007) 769


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0 1x108 2x108 3x108 4x108 5x108

0

1x108

2x108

3x108

4x108

5x108

BaZr0.9

Y0.1

O3- in wet O

2 at 225 °C

X /

Oh

m c

m

R / Ohm cm

In various functionally designed ionic conductors the grain boundary conductivity is lower than grain interior.

→ This may lead to significant contributions to the total resistance

E.g. Oxygen ion conductors :Y-doped ZrO2 (YSZ) [1]Gd-doped CeO2 (CGO) [2]

Mixed conductors: Fe-doped SrTiO3 [3]

Proton conductors:Ba3Ca1+xNb2-xO9-3x/2[4] Gd-doped BaCeO3 [5]Y-doped BaZrO3 [6]Ca-doped LaNbO4 [7]

[1] X. Guo, W. Sigle, J. Fleig, J. Maier, Solid State Ionics 154-155 (2002) 555[2] A. Tschope, E. Sommer, R. Birringer, Solid State Ionics 139 (2001) 255 [3] X. Guo, J. Fleig, J. Maier, Journal of the Electrochemical Society 148 (2001) J50 [4] H.G. Bohn, T. Schober, T. Mono, W. Schilling, Solid State Ionics 117 (1999) 219 [5] S.M. Haile, D.L. West, J. Campbell, Journal of Materials Research 13 (1998) 1576[6] H.G. Bohn, T. Schober, Journal of the American Ceramic Society 83 (2000) 768 [7] R. Haugsrud, T. Norby, Nature Materials 5 (2006) 193

Grain boundaries in ionic conductors σgrain interior > σgrain boundary


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Grain boundary resistance

Possible contributions to grain boundary resistance

• Grain boundary core• Space Charge Layer (SCL)

• Nonstoichiometry

• Secondary phases• Impurity phases (often

siliceous)• Secondary phases also have

boundary cores and SCLs

• Electrochemical reaction impedances


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- complex impedance as a function of frequency

- σgrain interior from knowledge of sample geometry

- σgrain boundary challenging because of no grain boundary geometry knowledge

- ”Brick layer model”

- semicircles can be fit to (RQ) subcircuit elements

-

Brick layer model

1nQ jYZ

Impedance spectroscopy


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Brick layer model

G = edge length

g = grain boundary thickness

Grain interiors

Electrode

Series grain boundaries

Parallel grain boundraies

L = length

AA

LGg

L

Total length and area of all perpendicular grain boundaries (g<<G)

AGg2

A

LL

||

||Total length and area of all parallel grain boundaries


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Rgb┴

Qgb┴

Qbulk

Rbulk

Rgb||

Qgb||

Parallel grain boundaries

Series grain boundaries

Rgb┴

Qgb┴Qbulk+gb||

||gbbulk R

1R

1

Dedicated Rebecca Svensøy

||gbbulk

||

gbbulk

n~nn

YYY

Assumtion: Transport in parallel and series grain boundraies occures by the same mechanism.

Brick layer model


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gigb

gigb1 G

g2

L

A

R

1

R

1

R

1 ||

gb

gb2 g

G

L

A

R

1

R

1

gigb1 G

g2

gb2 g

G

ii R

1

A

L

gb

gi2

1

2

2

1

G

g

G

g2

R

R

gb

gi

1

2

2

1

G

g

R

R

gi1

gbgi

Brick layer model

Gg


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Assume

and because the dielectric properties of grain interior and grain boundary are often similar

we combine to

finally

Brick layer model

0gigb20gigi1 g

G

L

ACC

L

ACC

G

g

C

C

2

1

gigb

gbgb

gigb

1

RC

C

A

L

σgrain interior > σgrain boundary

Constant phase element

1n1n1

0

1 // RYR

C

[5] S.M. Haile, D.L. West, J. Campbell, Journal of Materials Research 13 (1998) 1576


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Grain boundary core

x = 0

λ*

x δgb

log [Concentration] /Potential

++++++++++

φ

Δφ(0)

Grain interior Grain interior

Space charge layer

Space charge layer

Δφ(0) schottky barrier height δgb grain boundary width λ* space charge layer width

[H+]

[Acceptor]


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log

Co

nce

ntr

atio

n

++++++++++

Grain interior Space-charge layer

OOH

Grain boundary core

/ZrY

log

Co

nce

ntr

atio

n

++++++++++


OOH

Grain boundary core

/ZrY

Gouy-Chapman• Both charge carriers follows the electrical field • Applicable at high temperature, where cations are sufficiently mobile

Mott-Schottky • One charge carrier is immobile (the dopant) while the counter majority charge carrier is depleted

Consider two major charge carriers


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• Two defects; Protons and acceptors

• Acceptor-concentration profile frozen

• Electrochemical potential of protons

• Equilibrium:

• Electrical potential difference:

• Normalised concentration:

)()()(HB

0HH

xexcTkµxη ln

)()(c)(HB

0HH

eTkµη ln

)()(HH

ηxη

)(

)()(

H

HB

xc

cln

e

Tk)()x(x

Tk

xe

c

xc

BH

H )()(

)(exp


log

Co

nce

ntr

atio

n

++++++++++


OOH

Grain boundary core

/ZrY

→ Δφ(x) is the electrostatic potential in relation to

the grain interior

x = 0x = ∞


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• Δφ(x) can be solved from the Poisson’s equation:

Q(x): charge density at position xε: dielectric constant

• Assume Mott-Schottky approximation

• Define the Debye length (LD) and the space charge layer width (λ*)

• Normalized concentration

)()(

x1

dx

xd2

2

Q

→ Normalized concentration gives

the concentration profile in the space

charge layer

log

Co

nce

ntr

atio

n

++++++++++


OOH

Grain boundary core

/ZrY

x = 0x = ∞

)()()( YY ecxecxQ

21

Y2B

D2

)(ce

TkL

21

Y

21

BD

0202

)(

)()(*

ecTk

eL

2

DH

H

41

L

x

c

xc *

exp)(

)(


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Derivation of the Schottky barrier height

• Partial conductivity:

• Concentration and conductivity ratios, assuming equal mobilities:

• Apparent effective specific grain boundary resistivity and conductivity:

• Further substitution:

HHH

uec

Tk

xex

xxc

c

Bgi

gi

H

H )(exp)(

)()(

)(

xTk

xed

1

B0gbgi

gb

gi

)(exp

*

*

0

0 Y

B

gb

gi d1

)(* )(

)()(

)(exp

x

xec

Tk

xe

)(

)(

)(exp)(

)(exp

)(

0

0

B

B

B02

10

d0

1

Tke

Tke

xTk

xe

Tke

Tke

B

B

02

0

)(

)(exp

log

Co

nce

ntr

atio

n

+++++++++Grain

interior Space-charge layer

OOH

Grain boundary core

/ZrY

x = 0x = ∞


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• Ratio of conductivities:

• Activation energies:

• Difference between activation energies:

• If Schottky barrier height is temperature independent:

Tke

Tke

B

B

gb

gi

020/

/exp

Tk

TE

B

A1d

d ln

T

TTkeEE

1d

0d0

110 B

giA

gbA

)(

)())((

TkeEE BgiA

gbA 0 )(

e

TkEE BgiA

gbA0

)(

log

Co

nce

ntr

atio

n

++++++++++


OOH

Grain boundary core

/ZrY

)()()( 00

→ Δφ(0) is a measure of the magnitude

of the depletion


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Summary of mathemathics

• Two dominating defects• Mott-Schottky: one defect is immobile with constant conc. profile up to the interface

21

BD

0e2

TkL

*Space charge layer length

Tk

zeTk

σ

σ

B

B

gb

gi

02

0ze

)(

)(exp

Schottky barrier height (Δφ(0))

21

ZrY2

BD

2

)(/ce

TkL

Debye length

2

DOH

OH

4

1

O

O

L

x

c

xc *

exp)(

)( Normalized concentration

0 1 2 3 4 5 610-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

BaZr0.9

Y0.1

O3- in wet O

2

No

rma

lize

d c

on

ce

ntr

ati

on

Distance from grain boundary core / nm

300 °C 250 °C 200 °C

++++++++++++++++++


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Example: Oxygen ion conductor

Grain interior Grain interiorGrain boundary core

++++++++++++

OV

OV

OV

OV

OV

OV

OV

OV

OV

)(

)(0

)(

Po

ten

tial

,

log

Co

nce

ntr

atio

n

/ZrY /

ZrY

OV

OV

Space charge layer


p pnn


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Example: Proton conductor

Grain interior Grain interiorGrain boundary core

++++++++++++

OOH

OOHOOH

OOH

OOH

OOH

OOH

OOH

OOH

)(

)(0

)(

Po

ten

tial

,

log

Co

nce

ntr

atio

n

/ZrY /

ZrY

OOH

OOH

Space charge layer


p pnn


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Experimental investigation

Experiments - bias



Quantification


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+ Bias -

log

Co

nce

ntr

atio

n

• At equilibrium and zero bias state the two space charge layers are symmetrical

• After applying a dc bias voltage, one space charge layer is shortened, while the other is extended

++++++

Grain interior

Space-charge layer

OOH

OOH

Space-charge layer

Grain interior

OOH

++++++

Grain interior

Space-charge layer

OOH

OOH

Space-charge layer

Grain interior

OOH

++++++

Grain interior

Space-charge layer

OOH

OOH

Space-charge layer

Grain interior

OOH

++++++

Grain interior

Space-charge layer

OOH

OOH

Space-charge layer

Grain interior

OOH

++++++

Grain interior

OOH

OOH

Space-charge layer

OOH

++++++

Grain interior

OOH

OOH

Space-charge layer

OOH

→ Such a situation should cause nonlinear grain boundary electrical properties under dc bias voltage

Grain boundary voltage drop needs to be large to derive information about a single grain boundary

gbelegbgi

gbbiasgbOneOver NRRR

RUU

)(

Experiments - bias


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0.0 2.0x107 4.0x107 6.0x107-4.0x107

-2.0x107

0.0

2.0x107

4.0x107

R / Ohm cm

-X /

Oh

m c

m

BaZr0.9

Y0.1

O3- in wet O

2 @ 225oC

0 V 3 V 9 V 15 V

0 1 2 3 4 5

0.0

1.0x10-4

2.0x10-4

3.0x10-4

4.0x10-4

5.0x10-4

6.0x10-4

7.0x10-4

Cur

rent

/ m

A

Voltage over an average grain boundary, Uaverage gb

/ mV

OV

OOH

Acceptor doped ceria

The current voltage relation for individual grain boundary was nonlinear

→ supports the space charge concept

Guo, S. Mi, R. Waser, Electrochemical and Solid-State Letters 8 (2005) J1

BaZr0.9Y0.1O3-δ

•Varistor behavior

• Protons diffuse into the space charge layer and decreases the potential

→ supports the space charge concept

C. Kjølseth, Ø. Prytz, P.I. Dahl, R. Haugsrud, T. Norby, submitted to SSI – SSPC-14 Kyoto 2008

Experiments - bias


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log

Co

nce

ntr

atio

n +++++++++


OOH

Grain boundary core

/ZrY

n

10-48 10-38 10-28 10-18 10-810-9

10-8

10-7

10-6

10-5

10-4

/

S c

m-1

pO2 / atm

Grain interior Grain boundary

BaZr0.9

Y0.1

O3- at 250C

• pO2 dependency for specific grain interior and grain boundary conductivity

• Micro and nano-crystalline ceria shows n-type contribution to the total conductivity

• Acceptor doped BaZrO3 shows n-type grain boundary conduction while ionic grain interior conduction under reducing conditions

X. Guo, W. Sigle, J. Maier, Journal of the American Ceramic Society 86 (2003) 77

C. Kjølseth, H. Fjeld, P.I. Dahl, C. Estournès, R. Haugsrud, T. Norby, Submitted (2008)



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Space-charge layer

Grain interior

TiO2

TiO2

TiO2

TiO2

Grain interiorSpace-charge layer

–

–

–

Ti2O3

Ti2O3

Ti2O3

+

+

+

+++++

Addition of secondary phase• Under reducing conditions electrons from the reduction of Ti4+ to Ti3+ accumulates in the space charge layer making the proton depletion less severe• Problem: the sample becomes mixed conducting if the electrons are mobile

TiO2 in YSZ• 8 mol% TiO2 in two samples with different grain size• Solute conc. at grain boundaries decreases with decreasing grain size• upon reduction fewer electrons at the grain boundaries of the sample with smallest grain size

Oxidizing

Reducing

X. Guo, R. Waser, Progress in Materials Science 51 (2006) 151



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• Pure samples exhibit equal mechanical

electrical properties

• Both microregions, grain interior and grain

boundary are mechanically equal or similar in

nature

0

0

P

PP

• In situ impedance spectroscopy on samples

subjected to uniaxial mechanical stresses

• Grain interior and grain boundary resistance

increases upon application of stress

→ when Δb = Δgb no secondary phases exists in

the grain boundaries, the grain interior and grain

boundary form a unique mechanical entity

→ supports space charge theory J.-C. M'Peko, M. Ferreira de Souza, Applied Physics Letters 83 (2003) 737.


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Quantitative analysis of pO2 and T dependence of partial conductivities based on the space charge model• Mott-Schottky model• case: oxygen ion conductor with hole conduction in grain boundaries

pO2 dependency of oxygen vacancies• Assume that λ* and Δφ(0) is independent of pO2

• pO2 dependence of can be simplified

Quantification

0p

2O

ln

* 0

p

0

2O

ln

gb

VO

2

O

22

O

2

O

2

O

O

V

OBO

V

O

0V

O

gb

V

p

c

p

02

p

c

p

c

p ln

ln

lnln

ln

ln

ln

ln

ln

Tk

e

log

Co

nce

ntr

atio

n ++++++++++Grain

interior Space-charge layer

OV

Grain boundary core

/ZrY

x = 0x = ∞

p

2O

OhVtotal p

OVtotal In N2

0OV 2O

p

H.J. Park, S. Kim, Journal of Physical Chemistry C 111 (2007) 14903


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Quantification

pO2 dependency of holes

• Simplify the pO2 dependence of :

• Agrees with obtained results

Temperature dependence of oxygen vacancies• The temperature dependence of is given by

• we have

gb

VO

T1

BT1

V

T1

gb

V 0

T

10

2OO

k

elnln

x2

xB

VV OO

Tk

eexp

• The electron neutrality gives

• This is in agreement with measured data

OM V2Acc /

0p

2

O

O

gb

V

ln

ln

4

1

p

c

p

0

p

c

p

c

p22222 O

h

OBO

h

O

0h

O

gbh

ln

ln

ln

ln

ln

ln

ln

ln

ln

ln Tk

e

gbh



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Quantification

Temperature dependency of holes

• its relation to oxygen vacancy dependence when

• values are consistent with experimental data

T1h

gb

h

010EE

T

e

2

EEEE OO

Vgb

V

hgbh

OVh 00

• which in terms of activation energy can be expressed (using )

• Calculated values for Δφ(0) using conductivities fits with values obtained by activation energies

T1B

lnkE

T1V

gb

V

0102EE

OO

T

e

Tke

Tke

B

B

gb

gi

020/

/exp



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Quantification

Confirm the separate analysis of holes and oxygen vacancies using the defect equation

• using the relation

• we get

• confirmed by and

• values are quantified

21

2OOV

2h

OxOO22

1

pc

cKh2OVgO

,)(

OO V

2

h0V

20h

c

c

c

c

2

1

pp2

2

O

2 O

gb

V

O

gbh

ln

ln

ln

ln

0p

2

O

O

gb

V

ln

ln

4

1

p2O

gbh

ln

ln



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• Non-linearity observed [x]

• Electronic contribution in samples

with micro/nano grains [x]

• gb increases with increasing

doping level

• (0) increases with decreasing

doping level

Schottky barrier heights at 400 °C: 1.0 mol% Y2O3-doped CeO2: 0.47 V

10 mol% Y2O3-doped CeO2: 0.34 V

Oxygen ion conductor; Yttria-doped ceria

Some examples



UNIVERSITY OF OSLOOxygen ion conductor; Yttria-doped zirconia

Some examples

• Schottky barrier height temperature dependent

• Schottky barrier height at 400 °C: 0.25 V



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• mixed conductor of oxygen vacancies

and holes

• gi: electronic and ionic partial

conductivities comparable

• gb conductivity mainly electronic

• Larger depletion of oxygen vacancies

than holes in space-charge layer

→ Difference in charge numbers makes

oxygen vacancy concentration decay

more steeply than hole concentration

Mixed conductor; Fe-doped SrTiO3

Some examples

X. Guo, J. Fleig, J. Maier, Journal of the Electrochemical Society 148 (2001) J50


UNIVERSITY OF OSLOProton conductors: Y-doped BaZrO3

Some examples

0 1000000 2000000 3000000 4000000 5000000

0

1000000

2000000

3000000

4000000

5000000

BaZr0.9

Y0.1

O2.95

- SPS sample

(Spark Plasma Sinterd)

at 275oC in wet O2

-X

/

R /

-7000 0 7000

-7000

0

7000

BaZr0.9

Y0.1

O2.95

- SPS sample

(Spark Plasma Sinterd)

at 275oC in wet O2

-X

/

R /

10-48 10-38 10-28 10-18 10-810-9

10-8

10-7

10-6

10-5

10-4

/

S c

m-1

pO2 / atm

Grain interior Grain boundary

BaZr0.9

Y0.1

O3- at 250C

1 2 3 4 5

4x10-9

6x10-9

8x10-9

10-8

1.2x10-8

1.4x10-8

1.6x10-8

1.8x10-8

spc

gb /

S c

m-1

Voltage over an average grain boundary, Uaverage gb

/ mV

Schottky barrier height at 250 °C in wet O2

Δφ(0) = 0.5 V

pO2 dependency additional n-type conduction in the grain boundaries under reducing conditions

grain boundary conductivity increases with increasing bias

Increased concentration of Y in the grain boudnaries compared to grain interior

C. Kjølseth, H. Fjeld, P.I. Dahl, C. Estournès, R. Haugsrud, T. Norby, Submitted (2008)


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Some examples

Proton conductors: Sr-doped LaNbO4

• High grain boundary resistance

• Schottky barrier height 0.7 V at 400 °C

0 2 4 6 8 100

2

4

6

8

-X /

M

cm

R / Mcm

1

10100

1M

Rbulk Rgb Relectrode

Qbulk Qgb Qelectrode

H. Fjeld, unpublished data

1.5 1.6 1.7 1.8 1.9 2.010-13

10-12

10-11

10-10

10-9

10-8

10-7

10-6

10-5

400 350 300 250

bulk,

gb /

S c

m-1

1000T-1 / K-1

Grain boundary

°C

Bulk

1200 °C


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Short summary

• Blocking impurities in the grain boundary increases the resistance

• Grain boundary resistance exits in pure materials

• Depletion of charge carriers in space charge layers adjacent to a charged core can account for this intrinsic grain boundary resistance

• A grain boundary core – space charge model has been developed

• Experiments investigating the grain boundary response to dc bias, increased concentration of electrons and electrical properties under uniaxial load can give indications on the existence of space charge layers

• Quantitative analysis have proven the existence in several materials

Thank you for listening


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Decreasing the resistance

Immobile negative effective defects → localized electrons

Space-charge layer

Grain interior

TiO2

TiO2

TiO2

TiO2


–

–

Ti2O3

Ti2O3

Ti2O3

+

+

+

+++++

–

Documents

Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 1/36 UNIVERSITY OF OSLO Grain boundary resistance in ionic conductors