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Application of Impedance Spectroscopy to characterise grain boundary and surface layer effects in electroceramics. Derek C Sinclair Department of Engineering Materials University of Sheffield, UK. Outline. Introduction Typical electrical microstructures for electroceramics. - PowerPoint PPT Presentation
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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
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