Application of Impedance Application of Impedance Spectroscopy to characterise Spectroscopy to characterise grain boundary and surface grain boundary and surface

layer effects in layer effects in electroceramics.electroceramics.

Derek C SinclairDerek C Sinclair

Department of Engineering Department of Engineering MaterialsMaterials

University of Sheffield, UKUniversity of Sheffield, UK

OutlineOutline IntroductionIntroduction

Typical electrical microstructures for Typical electrical microstructures for electroceramics.electroceramics.

Background to combined Z’’, M’’ Background to combined Z’’, M’’ spectroscopy.spectroscopy.

ExampleExample

La-doped BaTiOLa-doped BaTiO33 ceramics ceramics

ConclusionsConclusions

Typical Electrical Typical Electrical MicrostructuresMicrostructures

I II III

Clear indicates insulating regionsClear indicates insulating regions

Shading indicates semiconducting Shading indicates semiconducting regionsregions

Semiconductivity either by chemical Semiconductivity either by chemical doping or oxygen loss. doping or oxygen loss.

C = (C = (oo’A)/d’A)/d

For many electroceramics RFor many electroceramics Rgbgb >> R >> Rbb and the parallel RC elements are and the parallel RC elements are connected in series. Brickwork layer connected in series. Brickwork layer model shows Cmodel shows Cgbgb >> C >> Cbb

Each region can be Each region can be represented (to a simple represented (to a simple approximation) as a approximation) as a single parallel RC single parallel RC elementelement

RRbb RRgbgb

CCbb CCgbgb

= RC= RC

Data analysis using (Z*, M*) works Data analysis using (Z*, M*) works well for series-type equivalent well for series-type equivalent

circuitscircuits

For a single parallel RC element For a single parallel RC element

Z* = Z’ - jZ’’Z* = Z’ - jZ’’

Z’ = RZ’ = R Z’’ = R. Z’’ = R. RCRC

1 + [1 + [RC]RC]22 1 + [ 1 + [RC]RC]22Recall : M* = Recall : M* = jjCCooZ*Z*

M’ = M’ = CCooRR22CC M’’ = C M’’ = Coo RCRC 1 + [1 + [RC]RC]22 C 1 C 1 + [ + [RC]RC]22

Each RC element produces an arc in Z* and M* (or Each RC element produces an arc in Z* and M* (or a Debye peak in Z’’ and M’’ spectroscopic plots), a Debye peak in Z’’ and M’’ spectroscopic plots),

however:-however:-

Z* (and Z’’ spectra) are dominated by large R Z* (and Z’’ spectra) are dominated by large R (gb’s)(gb’s)

M* (and M’’ spectra) are dominated by small C M* (and M’’ spectra) are dominated by small C (bulk)(bulk)

Such an approach is useful for studying ceramics Such an approach is useful for studying ceramics with insulating grain boundaries/surface layers with insulating grain boundaries/surface layers

and semiconducting grains. and semiconducting grains.

RRbb = 20 k = 20 k R Rgbgb = 1M = 1M

CCbb = 60 pF C = 60 pF Cgbgb = 1.25 = 1.25 nFnF

0 0.5 1.0

1.0

0.5

Z' /M

Z'' /M

0 0.02

0.02

RgbCgb = 1

Rb

Rb + Rgb

Rgb

1.0 2.0

1.0

M' /10-3

M'' /10-3

0

RbCb = 1

0/Cb

0/(Cb + Cgb)

0/Cgb

Combined Z’’ , M’’ spectroscopic plot Combined Z’’ , M’’ spectroscopic plot

0 1 2 3 4 5 6 7

0.6

0.4

0.2

0

log (Frequency /Hz)

Z'' /M

0

0.25

0.50

M''max = o/ 2Cb

M'' /10-3

bulk grain boundary

Z''max = Rgb/2

RgbCgb = 1

RbCb = 1

Notes:Notes:

•Appearance of Debye Appearance of Debye peaks in the frequency peaks in the frequency window depend on window depend on for for the various RC the various RC elements. elements.

•LimitsLimits

R > 10R > 1088 is high is high

=> => max max < 1 Hz< 1 Hz

R < 10R < 1022 => => is low is low

=> => maxmax > 10 MHz > 10 MHz

The doping mechanism in La-The doping mechanism in La-BaTiOBaTiO33

>> 4

/

cm

102

106

1010

1 2 3

La-content (atom %)

1

2

3 RRminmin - 0.3 -0.5 - 0.3 -0.5 atom% doping atom% doping (ptcr devices) (ptcr devices) heated in air > heated in air > 1350 1350 ooC followed C followed by rapid cooling.by rapid cooling.

Is there a change in doping mechanism with Is there a change in doping mechanism with La-content ? La-content ?

Low x : donor (electronic) doping, LaLow x : donor (electronic) doping, La3+3+ + + ee-- => Ba => Ba2+2+

High x : Ionic compensation, LaHigh x : Ionic compensation, La3+3+ => => BaBa2+2+ + 1/4Ti + 1/4Ti4+4+

Phase diagram studies showed that for Phase diagram studies showed that for samples prepared in samples prepared in airair ionic compensation ionic compensation was favouredwas favoured

BaBa1-x1-xLaLaxxTiTi1-x/41-x/4OO33 where 0 ≤ x ≤ 0.25 where 0 ≤ x ≤ 0.25

IS showed all ceramics with x > 0 to be IS showed all ceramics with x > 0 to be electrically heterogeneous when processed electrically heterogeneous when processed

in air and in air and allall showed the presence of showed the presence of semiconducting regions.semiconducting regions.

Electrical measurements are inconsistent with Electrical measurements are inconsistent with the phase diagram results!!the phase diagram results!!

2 (0.3at%) 2 (0.3at%) 3 (3 at%) 3 (3 at%) 4 (20 at%) 4 (20 at%)

250 500 750

750

500

250

0

Z' /cm

Z'' /cm

106105

104

50

50

0

(b)

106

10 0

10 1

10 2

10 3

10 4

10 5

10 6

10 7

10 8

300

200

100

0

Frequency /Hz

Z'' /cm

0

0.5

1.0

1.5

M'' /10-4

Composition 2 (0.3 at%) 1400 C air,

quenched to 25 C

10

010

110

210

310

410

510

610

7

15

10

5

0

Frequency /Hz

Z'' /Mcm

0

0.1

0.2

M'' /10-3

Composition 3 (3 at%)1350 C, Air

10 0

10 1

10 2

10 3

10 4

10 5

10 6

10 7

10 8

1.5

1.0

0.5

0

Frequency /Hz

Z'' /M

0

0.05

0.10

M'' /10-3

Composition 4 (20at%) 1350 C, Air Unpolished

(a)

RRTT > 1 M > 1 Mat 25 at 25 ooC.C.

RRTT = 675 = 675 at at 25 25 ooCC

10 20

-20

-10

0

Z' (M)

Z'' (M)

102

Composition 3 x = 0.03, 1350 C

quenched in air

All samples processed at 1350 All samples processed at 1350 ooC in C in flowing Oflowing O22 as opposed to air were as opposed to air were insulating at room temperature.insulating at room temperature.

100

101

102

103

104

105

106

107

15

10

5

0

Frequency /Hz

Z'' /Mcm

0

0.1

0.2

M'' /10-3

Composition 3 (3 at%)1350 C, Air

10 0

10 1

10 2

10 3

10 4

10 5

10 6

10 7

10 8

100

50

0

Frequency /Hz

Z'' /M

0

0.1

0.2

M'' /10-3

x = 0.03, 25 C 1350 C, O2

10 0

10 1

10 2

10 3

10 4

10 5

10 6

10 7

10 8

1.0

0.5

0

Frequency /Hz

Z'' /M

0

0.5

1.0

M'' /10-3

x = 0.03, 479 C 1350 C, O2

Composition 3 ( 3at%)Composition 3 ( 3at%)

Air (25 C) OAir (25 C) O22 (25 C) (25 C)OO22 ( 479 C) ( 479 C)

CCgbgb ~ 0.12 nF C ~ 0.12 nF Cbb ~ ~ 46 pF46 pF

-7

-6

-5

-4

-3

1.2 1.4 1.6 1.8 2 2.2

1000K/T

log

(s/

-1)

grain boundary bulk

x = 0.03 (O2) 0.69eV

x = 0.03 (O2) 1.41 eV

33

Arrhenius behaviour of RArrhenius behaviour of Rbb and R and Rgbgb for for

BaBa1-x1-xLaLaxxTiTi1-x/41-x/4OO33 processed in O processed in O22

Is oxygen loss the source of the Is oxygen loss the source of the semiconductivity in samples semiconductivity in samples

processed in air?processed in air?BaBa1-x1-xLaLaxxTiTi1-x/41-x/4OO3-3-

OOooxx => 1/2O => 1/2O22 + 2V + 2Voo

.... + 2e + 2e’’

Samples were processed in Argon at Samples were processed in Argon at 1350 1350 ooC and all were semiconducting C and all were semiconducting

at room temperature.at room temperature.

Processing in Ar at 1350 Processing in Ar at 1350 ooCC

Composition 3 (3at%)Composition 3 (3at%)

250 500 750

750

500

250

0

Z' /

Z'' /25

0

25

105

104

106

x = 0.03, 25 C1350 C, Ar

(a)

100

101

102

103

104

105

106

107

108

200

100

0

Frequency /Hz

Z'' /

0

0.25

0.5

0.75

M'' /10-4

x = 0.03, 25 C1350 C, Ar

(b)

RRTT ~ 522 ~ 522 ; R; Rgbgb ~ 510 ~ 510 R Rbb ~ 12 ~ 12 CCgbgb ~ 2.4 nF~ 2.4 nF

Arrhenius behaviour of RArrhenius behaviour of Rbb and R and Rgbgb for for

BaBa1-x1-xLaLaxxTiTi1-x/41-x/4OO3-3- processed in Ar at processed in Ar at 1350 1350 ooC.C.

-6

-5

-4

-3

-2

3 5 7 9 11 13

1000K/T

log

(s/

-1) bulk

Ar0.06 eV

Ar0.12 eV

grain boundary

44

Return to processing in air at 1350 Return to processing in air at 1350 ooC.C.

Composition 3 (3 at%): dc insulator Composition 3 (3 at%): dc insulator at 25 at 25 ooCC

Composition 4 (20 at%): dc insulator Composition 4 (20 at%): dc insulator at 25 at 25 ooC C

Composition 3Composition 3

100

101

102

103

104

105

106

107

15

10

5

0

Frequency /Hz

Z'' /Mcm

0

0.1

0.2

M'' /10-3

Composition 3 (3 at%)1350 C, Air

RRTT ~ R ~ Rgbgb > 10 > 1077 at 25 at 25 ooCC

RRbb ~ R ~ Rinnerinner + R + Routerouter < 1 < 1 kk

CCgbgb ~ 5-6 nF ~ 5-6 nF

CCouter outer ~ 0.2 nF, C~ 0.2 nF, Cinnerinner < < 0.2 nF0.2 nF

At least three RC At least three RC elements present.elements present. No change in No change in response on response on polishing the polishing the pellets.pellets.

-7

-6

-5

-4

-3

1.2 1.4 1.6 1.8 2 2.2

1000K/T

log

(s/

-1)

grain boundary bulk

x = 0.03 (O2) 0.69eV

x = 0.03 (O2) 1.41 eV

x = 0.03 (air) 1.12 eV

33

AirAir

Oxygen deficient, semiconducting

interior

Oxygen deficient, semiconducting, outer grain region

Oxidised, insulating grain boundary region

R3 R2 R1

C3 C2 C1

Composition 3 processed in air Composition 3 processed in air at 1350 at 1350 ooCC

Composition 4Composition 4

10 0

10 1

10 2

10 3

10 4

10 5

10 6

10 7

10 8

1.5

1.0

0.5

0

Frequency /Hz

Z'' /M

0

0.05

0.10

M'' /10-3

Composition 4 (20at%) 1350 C, Air Unpolished

(a)

Four elements present ? Four elements present ?

Z’’ : Z’’ :

ffmaxmax < 10 Hz, R > 2 M < 10 Hz, R > 2 M

M’’ : M’’ :

ffmaxmax ~ 10 ~ 1022 Hz, 0.1 M Hz, 0.1 MC C ~ 7 nF~ 7 nF

ffmaxmax ~ 10 ~ 1044 Hz, ~ 1 k Hz, ~ 1 k C C ~ 7 nF~ 7 nF

ffmaxmax > 10 > 1077 Hz, < 1k Hz, < 1k, C , C < 1 nF< 1 nF

Dramatic change on polishing the pellet.Dramatic change on polishing the pellet.

1

1.5

2

2.5

3

3.5

0 0.05 0.1 0.15 0.2 0.25

t /mm

log

(f m

ax /

Hz)

10 0

10 1

10 2

10 3

10 4

10 5

10 6

10 7

10 8

1.25

0.75

0.25

Frequency /Hz

Z'' /k

0

0.05

0.10

M'' /10-3

x = 0.20, 25 C 1350 C, Air

Polished

10 0

10 1

10 2

10 3

10 4

10 5

10 6

10 7

10 8

1.5

1.0

0.5

0

Frequency /Hz

Z'' /M

0

0.05

0.10

M'' /10-3

x = 0.20, 25 C 1350 C, Air Unpolished

UnpolishedUnpolished PolishedPolished

RRTT ~ R ~ Rgbgb = 2.04 k = 2.04 k

CCgbgb = 7.5 nF = 7.5 nF

Both RBoth Rbb and R and Rgbgb obey the Arrhenius obey the Arrhenius law.law.

-6

-5

-4

-3

-2

3 5 7 9 11 13

1000K/T

log

(s/

-1)

bulk

Ar0.06 eV

Ar0.12 eV

air0.20 eV

grain boundary

air0.09 eV

Oxidised, insulating surface layer

Oxygen deficient, semiconducting interior

Rsl Rb Rgb

Csl Cb Cgb

Composition 4 (20% La)Composition 4 (20% La)

AirAir

AArr

ArAr

ConclusionsConclusions

Oxygen loss is responsible for Oxygen loss is responsible for semiconductivity in ‘Basemiconductivity in ‘Ba1-x1-xLaLaxxTiTi1-x/41-x/4OO33

’’ ceramicsceramics

OO22 ArAr

AirAir

x = x = 0.030.03

x = x = 0.200.20

Conclusions Conclusions

IS is an invaluable tool for probing electrical IS is an invaluable tool for probing electrical heterogeneities in electroceramics. This is heterogeneities in electroceramics. This is especially true when oxygen concentration especially true when oxygen concentration gradients are responsible for inducing gradients are responsible for inducing semiconductivity. semiconductivity.

Combined Z’’, M’’ spectroscopic plots are a Combined Z’’, M’’ spectroscopic plots are a convenient and efficient method of visually convenient and efficient method of visually inspecting the data to allow rapid assessment inspecting the data to allow rapid assessment of the electrical microstructure in many of the electrical microstructure in many electroceramics. electroceramics.

AcknowledgementsAcknowledgements

Finlay MorrisonFinlay Morrison

Tony WestTony West

EPSRC for funding.EPSRC for funding.

Extras Extras

1.1. ’ ’ vs T for a range of x.vs T for a range of x.

2.2. Arrhenius plot of RArrhenius plot of Rbb and R and Rgbgb for air for air (1200 C) and O(1200 C) and O22 (1350 C) (1350 C) processed ceramics.processed ceramics.

3.3. Analysis of composition 2.Analysis of composition 2.

Excellent dielectrics when Excellent dielectrics when processed in Oprocessed in O22

Ba1-xLaxTi1-x/4O3

0

5000

10000

15000

20000

25000

30000

-200 -150 -100 -50 0 50 100 150 200Temperature /oC

Per

mit

tivi

ty,

'

x = 0

0.04

0.06

0.08

0.10

0.05

100 kHz

0.025

Arrhenius plot Arrhenius plot

-7

-6

-5

-4

-3

1 1.5 2 2.5

1000K/T

log

(b

-1)

x = 0.20

1350 oC O2

x = 0.20

1200 oC air

x = 0.20post anneal

1350 oC O2

x = 0.03

1350 oC O2

Composition 2Composition 2

10 0

10 1

10 2

10 3

10 4

10 5

10 6

10 7

10 8

300

200

100

0

Frequency /Hz

Z'' /cm

0

0.5

1.0

1.5

M'' /10-4

Composition 2 (0.3 at%) 1400 C air,

quenched to 25 C

250 500 750

750

500

250

0

Z' /cm

Z'' /cm

106105

104

50

50

0

(b)

106

2.5

3

3.5

4

4.5

5

5.5

0 100 200 300 400

Temperature /oC

log

( /

oh

m.c

m)

RRTT ~ ~ RRgbgb RRbb ~ 15 ~ 15

ptcr ptcr effecteffect