Transcript Characterisation of electroceramics using Impedance

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.
Background to combined Z’’, M’’ spectroscopy.

Example
La-doped BaTiO3 ceramics


Conclusions
Typical Electrical Microstructures
C = (eoe’A)/d
I
II
III
Clear indicates insulating regions
Shading indicates semiconducting regions
Semiconductivity either by chemical doping or
oxygen loss.
Each region can be represented
(to a simple approximation) as a
single parallel RC element
For many electroceramics Rgb >> Rb and the
parallel RC elements are connected in series.
Brickwork layer model shows Cgb >> Cb
Rb
Rgb
t = RC
Cb
Cgb
Data analysis using (Z*, M*) works well for seriestype equivalent circuits
For a single parallel RC element
Z* = Z’ - jZ’’
Z’ =
R
1 + [wRC]2
Z’’ = R.
wRC
1 + [wRC]2
Recall : M* = jwCoZ*
M’ =
w2CoR2C
1 + [wRC]2
M’’ = Co
wRC
C 1 + [wRC]2
Each RC element produces an arc in Z* and M* (or a
Debye peak in Z’’ and M’’ spectroscopic plots),
however:-
Z* (and Z’’ spectra) are dominated by large R (gb’s)
M* (and M’’ spectra) are dominated by small C (bulk)
Such an approach is useful for studying ceramics with
insulating grain boundaries/surface layers and
semiconducting grains.
Rb = 20 kW
Rgb = 1MW
Cb = 60 pF
Cgb = 1.25 nF
1.0
wRbCb = 1
1.0
0.02
Rb
M'' /10-3
w
Z'' /MW
0
0.5
wRgbCgb = 1
w
0
Rb + Rgb
Rgb
0
0.5
Z' /MW
e0/Cb
0.02
1.0
1.0
e0/Cgb
M' /10-3
2.0
e0/(Cb + Cgb)
Combined Z’’ , M’’ spectroscopic plot
Notes:
wRbCb = 1
0.6
M''max = eo/ 2Cb
wRgbCgb = 1
Z''max = Rgb/2
0.4
0.50
Z'' /MW
0.2
grain
boundary
•Appearance of Debye peaks in
the frequency window depend
on t for the various RC
elements.
M'' /10-3
•Limits
0.25
R > 108 W => t is high
bulk
=> wmax < 1 Hz
0
0
0
1
2
3
4
5
log (Frequency /Hz)
6
7
R < 102 W => t is low
=> wmax > 10 MHz
The doping mechanism in La-BaTiO3
1010 1
 /Wcm
3
106
102
2
1
2
>>
4
Rmin - 0.3 -0.5 atom%
doping (ptcr devices)
heated in air > 1350 oC
followed by rapid
cooling.
3
La-content (atom %)
Is there a change in doping mechanism with La-content ?
Low x : donor (electronic) doping, La3+ + e- => Ba2+
High x : Ionic compensation, La3+ => Ba2+ + 1/4Ti4+
Phase diagram studies showed that for samples prepared
in air ionic compensation was favoured
Ba1-xLaxTi1-x/4O3 where 0 ≤ x ≤ 0.25
IS showed all ceramics with x > 0 to be electrically
heterogeneous when processed in air and all showed
the presence of semiconducting regions.
Electrical measurements are inconsistent with the phase
diagram results!!
2 (0.3at%)
300
3 (3 at%)
1.5
4 (20 at%)
15
0.2
Composition 3 (3 at%)
1350 C, Air
Composition 2 (0.3 at%)
1400 C air,
quenched to 25 C
1.0
200
M'' /10-4
Z'' /Wcm
1.5
M'' /10-3
10
0.10
Composition 4 (20at%)
1350 C, Air
Unpolished
M'' /10-3
Z'' /MW
1.0
Z'' /MWcm
0.1
0.05
100
0.5
0
0
10
0
10
1
10
2
10
3
10
4
10
5
6
10
10
7
8
10
Frequency /Hz
5
0.5
0
0
0
10
0
10
1
10
2
10
3
10
4
10
5
10
6
10
7
10
0
10
1
10
2
10
3
750
-20
Composition 3
x = 0.03,
1350 C
quenched in air
50
Z'' (MW)
500
Z'' /Wcm
0
250
50
-10
5
10
106
102
104
0
(b)
250
500
750
Z' /Wcm
0
10
20
Z' (MW)
RT = 675 W at 25 oC
10
5
Frequency /Hz
(a)
Frequency /Hz
106
4
10
RT > 1 MW at 25 oC.
10
6
10
7
0
8
10
All samples processed at 1350 oC in flowing O2 as
opposed to air were insulating at room temperature.
Composition 3 ( 3at%)
Air (25 C)
O2 (25 C)
15
O2 ( 479 C)
0.2
Composition 3 (3 at%)
1350 C, Air
100
0.2
x = 0.03, 25 C
1350 C, O2
M'' /10-3
10
1.0
M'' /10-3
Z'' /MW
Z'' /MWcm
1.0
x = 0.03, 479 C
1350 C, O2
M'' /10-3
Z'' /MW
0.1
50
0.1
0.5
0.5
5
0
0
10
0
10
1
10
2
10
3
10
4
10
Frequency /Hz
5
10
6
7
10
0
10
0
10
1
10
2
10
3
10
4
10
5
Frequency /Hz
10
6
10
7
0
10
8
0
0
0
10
1
10
10
2
10
3
4
10
10
5
10
6
7
10
10
8
Frequency /Hz
Cgb ~ 0.12 nF Cb ~ 46 pF
Arrhenius behaviour of Rb and Rgb for
Ba1-xLaxTi1-x/4O3 processed in O2
-3
-4
log (s/W -1)
3
x = 0.03 (O2)
0.69eV
-5
-6
x = 0.03 (O2)
1.41 eV
grain boundary
bulk
-7
1.2
1.4
1.6
1.8
1000K/T
2
2.2
Is oxygen loss the source of the
semiconductivity in samples processed in air?
Ba1-xLaxTi1-x/4O3-d
Oox => 1/2O2 + 2Vo.. + 2e’
Samples were processed in Argon at 1350 oC and
all were semiconducting at room temperature.
Processing in Ar at 1350 oC
Composition 3 (3at%)
200
750
0.75
x = 0.03, 25 C
1350 C, Ar
x = 0.03, 25 C
1350 C, Ar
25
Z'' /W
0.5
M'' /10-4
100
500
Z'' /W
0.25
0
250
25
105
106
104
0
10
(b)
0
10
1
10
2
10
3
10
4
10
5
Frequency /Hz
10
6
10
7
0
10
0
8
(a)
250
500
Z' /W
RT ~ 522 W; Rgb ~ 510 W Rb ~ 12 W, Cgb ~ 2.4 nF
750
Arrhenius behaviour of Rb and Rgb for
Ba1-xLaxTi1-x/4O3-d processed in Ar at 1350 oC.
-2
Ar
0.06 eV
log (s/W-1)
-3
bulk
-4
4
Ar
0.12 eV
-5
grain boundary
-6
3
5
7
9
1000K/T
11
13
Return to processing in air at 1350 oC.
Composition 3 (3 at%): dc insulator at 25 oC
Composition 4 (20 at%): dc insulator at 25 oC
Composition 3
15
0.2
Composition 3 (3 at%)
1350 C, Air
M'' /10-3
10
Z'' /MWcm
At least three RC
elements present.
0.1
No change in response
on polishing the pellets.
5
0
0
10
0
10
1
10
2
10
3
10
4
10
5
10
6
7
10
-3
Frequency /Hz
W at 25
oC
Rb ~ Rinner + Router < 1 kW
Cgb ~ 5-6 nF
Couter ~ 0.2 nF, Cinner < 0.2 nF
log (s/W -1)
RT ~ Rgb >
107
x = 0.03 (O2)
0.69eV
-4
3
-5
x = 0.03 (air)
1.12 eV
-6
Air
x = 0.03 (O2)
1.41 eV
grain boundary
bulk
-7
1.2
1.4
1.6
1.8
1000K/T
2
2.2
Composition 3 processed in air at 1350 oC
Oxidised,
insulating grain
boundary region
Oxygen deficient,
semiconducting,
outer grain region
Oxygen deficient,
semiconducting
interior
R1
R2
R3
C1
C2
C3
Composition 4
1.5
0.10
Composition 4 (20at%)
1350 C, Air
Unpolished
M'' /10-3
Z'' /MW
1.0
0.05
Four elements present ?
Z’’ :
fmax < 10 Hz, R > 2 MW
0.5
M’’ :
0
10
(a)
0
10
1
10
2
10
3
4
10
10
5
Frequency /Hz
10
6
10
7
0
8
10
fmax ~ 102 Hz, 0.1 MW, C ~ 7 nF
fmax ~ 104 Hz, ~ 1 kW, C ~ 7 nF
fmax > 107 Hz, < 1kW, C < 1 nF
Dramatic change on polishing the pellet.
Unpolished
1.5
0.10
x = 0.20, 25 C
1350 C, Air
Unpolished
Polished
1.25
M'' /10-3
Z'' /MW
0.10
x = 0.20, 25 C
1350 C, Air
Polished
M'' /10-3
Z'' /kW
1.0
0.75
0.05
0.05
0.5
0.25
0
10
0
10
1
10
2
10
3
4
10
10
5
10
6
10
7
0
8
10
10
0
10
1
10
2
10
3
4
10
10
5
10
6
10
7
0
8
10
Frequency /Hz
Frequency /Hz
3.5
RT ~ Rgb = 2.04 kW
log (f max /Hz)
3
Cgb = 7.5 nF
2.5
2
1.5
1
0
0.05
0.1
0.15
t /mm
0.2
0.25
Both Rb and Rgb obey the
Arrhenius law.
Composition 4 (20% La)
-2
Ar
-3
log (s/W-1)
Ar
0.06 eV
bulk
Ar
-4
Oxidised, insulating
surface layer
air
0.09 eV
Ar
0.12 eV
-5
Air
air
0.20 eV
grain boundary
Oxygen deficient,
semiconducting interior
Rsl
Rb
Rgb
Csl
Cb
Cgb
-6
3
5
7
9
11
13
1000K/T
Conclusions
Oxygen loss is responsible for semiconductivity in
‘Ba1-xLaxTi1-x/4O3’ ceramics
O2
Ar
Air
x = 0.03
x = 0.20
Conclusions

IS is an invaluable tool for probing electrical
heterogeneities in electroceramics. This is especially
true when oxygen concentration gradients are
responsible for inducing semiconductivity.

Combined Z’’, M’’ spectroscopic plots are a convenient
and efficient method of visually inspecting the data to
allow rapid assessment of the electrical microstructure
in many electroceramics.
Acknowledgements
Finlay Morrison
Tony West
EPSRC for funding.
Extras
1.
2.
3.
e’ vs T for a range of x.
Arrhenius plot of Rb and Rgb for air (1200 C)
and O2 (1350 C) processed ceramics.
Analysis of composition 2.
Excellent dielectrics when processed in O2
Ba1-x Lax Ti1-x/4O3
30000
100 kHz
0.06
Permittivity, e'
25000
0.05
20000
0.04
0.08
15000
0.025
0.10
x=0
10000
5000
0
-200
-150
-100
-50
0
50
o
Temperature / C
100
150
200

Arrhenius plot
Composition 2
300
1.5
Composition 2 (0.3 at%)
1400 C air,
quenched to 25 C
ptcr effect
5.5
1.0
200
5
-4
M'' /10
Z'' /Wcm
100
0.5
log (/ohm.cm)
4.5
RT ~ Rgb
4
3.5
0
10
0
10
1
10
2
10
3
10
4
10
5
6
10
10
7
8
10
0
Rb ~ 15 W
3
Frequency /Hz
2.5
0
100
200
300
o
Temperature / C
750
106
50
500
Z'' /Wcm
0
250
50
105
106
104
0
(b)
250
500
Z' /Wcm
750
400