of NA
http://journals.cambridge.org Downloaded: 11 Mar 2015 IP address: 157.182.150.22
Effect of intergranular glass films on the electrical conductivity
of 3Y-TZP
M. Godickemeier, B. Michel, A. Orliukas, P. Bohac, K. Sasaki, and L. Gauckler
Nichtmetallische
Werkstoffe,
ETH Zurich, CH-8092 Zurich, Switzerland
H. Heinrich, P. Schwander, and G. Kostorz
Institut of Applied Physics, ETH-Zurich, CH-8093 Zurich, Switzerland
H. Hofmann and O. Frei
Alusuisse Lonza Services AG, CH-8212 Neuhausen, Switzerland
(Received 3 June 1993; accepted 11 January 1994)
The electrical conductivity of 3Y-TZP ceramics containing SiO
2
and AI2O3 has
been investigated by complex impedance spectroscopy between 500 and 1270 K. At
low temperatures, the total electrical conductivity is suppressed by the grain boundary
glass films. The equilibrium thickness of intergranular films is 1-2 nm, as derived
using the "brick-layer" model and measured by HRTEM. A change in the slope of the
conductivity Arrhenius plots occurs at the characteristic temperature Tb at which
the macroscopic grain boundary resistivity has the same value as the resistivity of the
grains. The temperature dependence of the conductivity is discussed in terms of a series
combination of RC elements.
I. INTRODUCTION
Thin intergranular glass films which are composed
of SiO
2
, A1
2
O
3
, and Y
2
O
3
are formed in Y-TZP ceramics
at high sintering temperatures.
1
"
7
They promote sintering
of the starting powders as well as grain growth during
the post-annealing process and affect the electrical and
mechanical properties of Y-TZP ceramics.
8
"
11
It has been
shown that the equilibrium film thickness is limited
to about 1-2 nm,
4
'
12
'
14
and excess amounts of glass
segregate in grain triple junctions, in pores, and on the
surface of the specimens.
4
'
5
'
11
The equilibrium width of
intergranular films depends on the corresponding inter-
facial energies and on the viscosity of the glass phase
at the temperature of sintering or post-annealing.
15
'
16
A
surplus of A1
2
O
3
is proposed to act as a scavenger for
SiO
2
,
removing it from grain boundaries.
17
-
18
The glass
phase can also be partially squeezed out from the grain
boundaries to three grain pockets by applying a com-
pressive stress.
19
Accordingly, in hot-pressed specimens
of Y-TZP at 1823 K some "clean" grain boundaries
were observed, which did not contain any detectable
intergranular phase.
16
The Arrhenius plots [Iog(cr7) vs l/T] of the total
(dc) conductivity of zirconia-based solid electrolytes
often exhibit a change of slope at 800-1200 K, owing to
a decrease in activation energy at high temperatures.
20
"
22
Rather controversial explanations for the origin of this
curvature of the Arrhenius plots have been given in the
literature.
23
"
30
The majority of studies suggests that in the
low-temperature region immobile associated complexes,
such as [Y
Zr
Vo]', are formed between extrinsic oxygen
vacancies and oppositely charged dopant ions. The ther-
mal dissociation of these complexes would require a
supplementary energy in addition to the activation energy
for the simple migration of "free" charge carriers.
23
"
26
According to this concept, three general stages of
the ionic conductivity are proposed to exist in solid
electrolytes as a function of temperature.
27
'
31
The first
bend in the Arrhenius curve occurs on cooling from
the high temperature "intrinsic stage I" to the "extrinsic-
dissociated stage II" at which all extrinsic charge carriers
are claimed to be mobile. The intrinsic stage exhibits
a higher activation energy that is necessary not only
for the migration but also for the formation of intrinsic
charge carriers. At the transition temperature I
—>
II, the
concentration of thermally activated intrinsic charge car-
riers becomes equal to the total concentration of extrinsic
charge carriers generated by doping. Another bend in the
Arrhenius plot at lower temperatures is assumed to occur
from the extrinsic-dissociated stage II to the "extrinsic-
associated stage III". Since the activation energy of the
low-temperature stage III includes an additional energy
for the dissociation of defect complexes, it is again
higher than the activation energy of the middle stage II,
which corresponds to the energy for the migration of
free extrinsic charge carriers only. At the temperature
of the second transition (II
—»
III), the concentration of
thermally dissociated, "mobile" extrinsic charge carriers
is supposed to be equal to the concentration of extrin-
sic charge carriers which are still associated and "im-
mobile". Supposing association energies of 0.2-0.5 eV,
Nowick and Park
27
have calculated the temperature at
1228
J.
Mater. Res., Vol. 9, No. 5, May 1994 © 1994 Materials Research Society
http://journals.cambridge.org Downloaded: 11 Mar 2015 IP address: 157.182.150.22
M. Godickemeier et at.: Effect of intergranular glass films on the electrical conductivity of 3Y-TZP
which a half of the total amount of extrinsic oxygen
vacancies would be free. They suggested this tempera-
ture to be the lower "break point temperature" of the
Arrhenius plots.
Other authors have interpreted the slope change of
Arrhenius plots (stages II to III) to be due to changing
from the volume-controlled conductivity of the grains,
prevailing at high temperatures, to the grain-boundary-
controlled conductivity at low temperatures,
28
"
30
due to
microcracking,
21
phase transformation,
28
'
32
or even as a
mere artifact of the experimental technique.
33
A formation of dopant-vacancy associates in the
proposed "extrinsic-associated range (III)" was claimed
to reduce the concentration of "free" charge carriers in
stabilized zirconias with increasing dopant con-
tent.
2334
"
36
Assuming associated defect complexes,
Weller and Schubert
26
have questioned the current ac-
cepted values of intragrain bulk conductivities and their
activation energies obtained by impedance spectroscopy
measurements and proposed a revision of the classical
interpretation of this widely used experimental meth-
od.
28
-
37
"
39
On the other hand, no difference between "mo-
bile"
and "immobile" lattice defects was found in the
studies of Orliukas et
a/.,
40
Casselton,
41
and Anantha-
padmanabhan et
al.
42
To explain the blocking effect of the grain bound-
aries,
two models, in terms of an electrical connec-
tion of the bulk and the segregated grain boundary
material either in series or parallel, are given in the
literature.
8
'
9
'
14
-
37
-
43
'
44
According to the first, "brick layer"
or series model,
8
'
9
'
20
conducting grains are separated by
a continuous film of a less conducting grain-boundary
phase. The second, "easy path" or parallel model,
45
-
46
assumes only a partial blocking of the current path due
to a discontinuous distribution of an insulating phase
between conducting grains.
In the present work the intergrain relaxation of
the ionic conductivity has been studied by complex
impedance spectroscopy on 3Y-TZP specimens contain-
ing different amounts of the grain boundary glass phase.
The purpose of this study was to clarify the relation-
ship between the chemical composition of the starting
material which determines the amount of the inter-
granular phase and the electrical properties of 3Y-TZP
ceramics and to provide a better understanding of the
bend in Arrhenius plots of total conductivity observed
in zirconia-based solid electrolytes at 800-1200 K.
II.
EXPERIMENTAL
The compositions of the investigated 3Y-TZP sam-
ples are shown, with respect to their SiO
2
-Al
2
O
3
con-
tent, in Fig. 1. The samples lie along the lines A, B,
C, D, and E, which correspond to the SiO
2
/Al
2
O
3
ratios of 1/0, 4/1, 1/1, 1/4, and 0/1, respectively. The
B
B1°
C10
'' ,'' •' *
D5
A---"'",''
'
D3
'
*
E10
/
/
E
0.00 0.25 0.50 0.75 1.00
AI
2
0
3
[
wt %]
FIG. 1. The compositions of 3Y-TZP samples with respect to SiO
2
AI2O3 impurities.
total amount of both oxides is given approximately in
tenths of a weight % by the sample number and varies
from about 0.1 wt. % for the C-l sample to 1 wt. % in
samples B-10, C-10, D-10, and E-10. The coprecipitated
3Y-TZP powder without impurity additions has been
considered as the reference (sample R-0). For com-
parison, a sample from the pure commercial powder
TZ-3Y (Toshoh Corporation, <0.005 wt. % SiO
2
and
<0.002 wt. % A1
2
O
3
), which is designated as TZ-3Y,
as well as a very contaminated sample F-46 containing
4.6 wt. % of both impurities in total have also been
investigated.
All 3Y-TZP sintered specimens were prepared using
coprecipitated ultrafine powders. The SiO
2
and A1
2
O
3
impurities were introduced as SiCl
4
and A1C1
3
into the
solution of ZrOCl
2
and YC1
3
before the wet-chemical
precipitation. The only exception is the sample F-46,
which was prepared by mixing of the reference powder
R-0,
calcined at 1023 K, with a fine SiO
2
powder
(Aerosil OX50, Degussa) in an attritor mill. All other
coprecipitated powders were calcined at 1223 K for
8 h. The calcined powders have specific surface areas
between 11 and 36 m
2
/g. Their chemical analysis is
shown in Table I.
The starting powders were uniaxially cold pressed
at 100 MPa and sintered for 1 h in air at 1773 K.
The density of all sintered samples was >96% of the
theoretical value. The ceramic microstructures were re-
vealed by thermal etching of polished specimens at
1720 K for 30 min. Only the tetragonal crystalline phase
was detected by x-ray diffraction after sintering. The
average linear grain size parameter, / (see Table II), was
determined as the mean intercept length on SEM photo-
micrographs (JEOL, JEM-6400) by the linear-intercept
method.
47
'
48
It varies in the range of 300 nm to 430 nm.
J.
Mater. Res., Vol. 9, No. 5, May 1994 1229
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M. Godickemeier et al.: Effect of intergranular glass films on the electrical conductivity of 3Y-TZP
TABLE I. Chemical composition of Y-TZP powders.
Sample
TZ-3Y
R-0
A-3
A-5
A-7
B-3
B-5
B-10
C-l
C-5
C-10
D-3
D-5
D-10
E-3
E-5
E-10
F-46
SiO
2
:
A12O3
ratio
2.50
> 1
>33
>51
>72
2.56
4.88
4.00
2.00
1.09
1.04
0.39
0.38
0.25
<0.11
<0.06
<0.03
2.23
SiO
2
<0.005
0.03
0.33
0.51
0.72
0.23
0.39
0.76
0.06
0.25
0.47
0.09
0.15
0.19
<0.03
<0.03
<0.03
3.15
A1
2
O
3
<0.002
<0.03
<0.01
<0.01
<0.01
0.09
0.08
0.19
0.03
0.23
0.45
0.23
0.40
0.77
0.28
0.47
0.89
1.41
Y
2
O
3
(wt. %)
5.140
5.33
5.41
5.38
5.40
5.23
5.32
5.21
5.38
5.25
5.33
5.35
5.52
5.41
5.31
5.27
5.21
6.62
Na
2
O
0.023
0.08
0.04
0.05
0.05
0.01
0.01
<0.01
0.02
0.04
0.03
0.03
0.04
0.02
0.01
0.03
0.03
0.07
cr
<0.01
0.01
0.01
0.07
0.02
0.01
0.01
<0.01
0.13
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
2 imp.
0.10
0.15
0.39
0.64
0.80
0.34
0.49
0.97
0.24
0.53
0.96
0.36
0.60
0.99
0.33
0.54
0.96
4.64
BET (m
2
/g)
15.2
11
18
21
24
17
19
21
17
20
18
21
19
19
16
15
17
36
Complex impedance spectroscopy at alternating
fields of variable frequency
37
"
39
-
45
has been used to
distinguish between the intragrain and the grain
boundary contribution to the charge transport. The total
impedance of the ceramic specimens originates from the
impedance contribution of the grains and from interfacial
effects on grain boundaries and electrodes. A simplified
equivalent circuit consists of three resistors in series,
each shunted by a capacitor in parallel.
The complex impedance measurements using a PC-
controlled HP Precision LCR meter 4284A were carried
TABLE II. Linear average grain sizes of annealed 3Y-TZP samples.
Grain size / (nm)
Sample
TZ-3Y
R-0
A-3
A-5
A-7
B-3
B-5
B-10
C-l
C-5
C-10
D-3
D-5
D-10
E-3
E-5
E-10
F-46
Time: 1 h
300
320
320
360
350
430
380
390
340
380
380
380
430
380
390
410
410
300
5h
510
440
810
510
580
1010
620
470
10 h
580
560
960
660
810
1280
1060
720
out between 500 and 1200 K in air, on sintered cylindri-
cal samples 10 mm in diameter and 1-2 mm thick, using
the two-point probe technique. The frequency range
was 40 Hz to 1 MHz. Platinum electrodes were painted
on the specimens by applying a conductive platinum
paste (Demetron 308A) and sintered onto the surface
at 1073 K. The temperature was controlled to ±2 °C.
III.
RESULTS AND DISCUSSION
A. Impedance spectroscopy
An example of the frequency dependence of the
real part of the specific electrical impedance, p' ~ Z' •
L/A,
where Z' =
U
R
/I
R
is the real part of the complex
impedance Z = Z' + iZ", L is the sample length, and
A the electrode area, is shown in Fig. 2 (sample E-10).
10000
10 100 1000 10000 100000 1000000
f[Hz]
FIG. 2. Grain, grain boundary, and electrode dispersions of the real
part of complex specific impedance (sample E-10).
1230
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Mater. Res., Vol. 9, No. 5, May 1994
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M. Godickemeier ef a/.: Effect of intergranular glass films on the electrical conductivity of 3Y-TZP
The relaxation dispersions of individual impedance con-
tributions (grains, grain boundaries, and electrodes) shift
toward higher frequencies with increasing temperature.
This indicates that these dispersions are thermally ac-
tivated. Usually it is not possible to observe all three
dispersions simultaneously, due to a limited frequency
range used in this study (40 Hz-1 MHz). At temper-
atures below 500 K only the grain dispersion can be
seen at high frequencies.
40
The grain boundary and
the electrode dispersion are too slow to be detected
at this temperature. In the medium temperature range
(500 K-800 K), we can observe two dispersions, that
of the grains and that of the grain boundaries. Finally,
above 800 K the intragrain dispersion shifts out of the
frequency window and the sluggish dispersion due to the
slower electrode processes becomes visible.
In Fig. 3 the frequency dependence of the specific
imaginary impedance contribution, p" = Z"
•
L/A, is
shown. From this figure the individual dispersion regions
of grains, grain boundaries, and electrodes can be seen
more distinctly.
The complex impedance data can be displayed in the
complex impedance plane with real part p' as the ab-
scissa and the imaginary part p" as the ordinate (Cole-
Cole diagram). A typical complex impedance spectrum
of 3Y-TZP (sample E-10) at a medium temperature of
596 K is shown in Fig. 4. Since the time constants (r =
RC) of individual RC-elements differ by orders of mag-
nitude, individual semicircles of the grains and that of
the grain boundaries can clearly be distinguished in this
temperature range. The real specific impedance sections
between the distinct minima in the imaginary part p"
reveal the macroscopic specific resistivities of the grains
(p'
G
) and the grain boundaries (P'GB), respectively. The
macroscopic specific resistivity of the grain boundaries
is equal to the difference between the total (dc) spe-
cific resistivity of the sample (p r) and the macroscopic
1200
0 500 1000 1500 2000 2500
P' [Ohm m]
FIG. 4. Complex impedance diagram at 596 K (sample E-10).
specific resistivity of the grains:
PGB
= PT ~ Pa- More-
over, from the maximum of imaginary impedance p" at
the top of each semicircle, the relaxation frequency w
of the corresponding process can be determined from
the relation
COT
= 1, where co =
2irf
R
,
is the angular
frequency [rad- s"
1
], /R the corresponding frequency of
the applied electrical ac-field [Hz], and T = RC the time
constant of the relaxation circuit.
B. Microstructure
The microstructures of the sintered 3Y-TZP speci-
mens reveal for samples TZ-3Y, R-0, C-l, D-3, and the
whole E series only very small amounts of the glass
phase in triple points. On the other hand, all samples
of both the B and C series as well as samples D-5 and
D-10 contain large glass pockets surrounded by cubic
grains (Fig. 5). Segregations of the glass phase at triple
points can also be observed in samples of the A series
containing silica additions without alumina.
1000
100 i
E
I
O
0.1
Grain boundaries
Grain
Electrodes
•k
10 100 1000 10000 100000 1000000
f[Hz]
FIG. 3. Frequency dependence of imaginary part of complex specific
impedance (sample A-l). FIG. 5. Glass segregations after sintering (sample B-10).
J. Mater. Res., Vol. 9, No. 5, May 1994 1231
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M. Gddickemeier et al.: Effect of intergranular glass films on the electrical conductivity of 3Y-TZP
The annealing of selected samples at 1773 K for 5
and 10 h at 1773 K caused the separation of the tetrago-
nal and cubic phase and a gradual grain coarsening. The
linear average grain sizes, /, are given as a function of
annealing time in Table II. When the tetragonal grains
reach a critical size, the tetragonal zirconia transforms on
cooling to the monoclinic phase. This phase transition,
which occurs in specimens annealed longer than 20 h, is
accompanied by the formation of numerous microcracks
and causes an abrupt increase of the grain boundary
resistivity due to the partial blocking of the conduction
path by microcracks. From Fig. 6 the development of the
microstructure around a glass pocket during annealing
of the B-3 sample is visible.
High resolution electron micrographs (Philips CM 30
at 300 kV, super twin lens, C
s
= 1.1 mm, LaB
6
cath-
ode) of grain boundary regions revealed in all samples
homogeneous amorphous films about 0.5-2 nm thick.
No "clean" grain boundaries without intergranular phase
have been observed, even in the E series. In 3Y-TZP
samples containing a large amount of the glass phase
lOum
(a)
I.' . i. .
—
7
*..*•* ,---''
1 >
(b)
(C-5,
B-10), the excess of the glass phase accumulates
at three-grain pockets and at the surface. Figure 7 shows
a three-grain junction area of the sample C-10 and an
intergranular glass layer about 1-2 nm thick. The EDX
and PEELS (parallel electron energy loss spectroscopy)
analysis of the glass in triple grain junctions and in large
multi-grain pockets showed that the segregated amor-
phous phase contains oxides of all four elements, Si,
Al,
Y, and Zr, except that in samples with both low
SiO
2
/Al
2
O3 ratio and low total impurity content no Y
and Zr, and in the A series also no Al, could be detected.
The glass phase in pockets of the C-10 sample consists
of 42 wt. % SiO
2
, 22 wt. % A1
2
O
3
, 21 wt. % Y
2
O
3
, and
15 wt. % ZrO
2
(Fig. 8). This composition of the grain
boundary phase is in a good agreement with the results
of other authors,
1
'
3
'
5
'
14
'
16
which also showed the presence
of Si, Al, Zr, and a high concentration of Y.
C. The "brick layer" model
To analyze the electrical conductivity of a ceramic
material in which the intergranular phase is present as
a three-dimensional connected network of continuous
films,
the brick layer model can be used.
8
'
9
'
14
'
49
'
50
Ac-
cording to the brick-layer model, it is assumed that
the bulk material consists of conducting grains, cubes
with an edge length a, separated by a thin homogeneous
grain boundary layer of low conductivity of the thick-
ness <5
g
b. Since
<5
gb
< a and a
GB
^ &G, the parallel
conduction along the grain boundaries can be neglected.
The equivalent electrical circuit consists then of a simple
series combination of two RC-elements (grain and grain
boundary). The total (dc) resistance of the sample, R
T
=
R
G
+ R
GB
, is the sum of the resistance of grains R
G
and
grain boundaries R
GB
. Usually the macroscopic specific
conductivities a'
T
, <r'
G
, and a
GB
are calculated from
resistivity values, using the relation:
a[ = l/p[= l/(R
r
L
T
/A
T
),
where L
T
= L
G
+ L
GB
= n{a + 8
GB
) is the total
length of the sample between the electrodes, n = L
T
/a
is the number of grain boundaries perpendicular to the
current direction, and A
T
= A
G
+ A
GB
is the total cross-
section area of the sample. Since
L
GB
/L
T
= S
gb
/(a +
<5g
b
),
it can easily be shown that the length fraction of
grain boundaries L
GB
amounts to L
T
•
8
gb
/(a
+ <5
gb
) =
LT
' Sgb/a and that of grains L
G
to L
T
•
a/{a + S
gb
) =
LT.
For the cross section of the current path through the
area fractions of grains A
G
, we obtain:
A
G
= A
T
• a
2
/(a +
§
gb
/2)
2
= A
T
•
a/(a + <5
gb
) = A
T
.
FIG. 6. Microstructure development during annealing at 1773 K
(sample A-5): (a) 10 h and (b) 30 h.
Omitting the parallel grain boundary conduction path
along the length of the sample, the microscopic specific
1232
J.
Mater. Res., Vol. 9, No. 5, May 1994
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M. Godickemeier et at.: Effect of intergranular glass films on the electrical conductivity of 3Y-TZP
FIG. 7. HREM of a triple-point junction and an intergranular glass film (sample C-10).
300
g 200
100
+
0 2
100 SEC
10
12
14
FIG. 8. EDX analysis of the glass phase segregated in a large pocket (sample C-10).
J.
Mater. Res., Vol. 9, No. 5, May 1994
Zr
16
18 20
ENERGY (KEV)
1233
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M. Godickemeier ef at.: Effect of intergranular glass films on the electrical conductivity of 3Y-TZP
conductivity of the grain and grain boundary material at
low contents of glass phase (a > <5
gb
) is then given by,
a
G
=
and a
GB
= a'
GB
• S
gb
/a
(1)
In order to eliminate the size effect of ceramic grains, the
macroscopic specific grain boundary resistivities, p'
gb
=
^GB
"
A
T
/L
T
,
have been converted to the normalized
macroscopic resistivities per unit area of the grain bound-
ary surface,
51
r
GB
, according to the relation,
= P
r
GB =
where a = 1.5/ is the corresponding cube edge length
derived from the linear average grain size of the ceramic
sample, /.47>48 The microscopic specific resistivity of the
grain boundary glass material, pGB = RGB
•
A
T
/L
G
B,
is
then the ratio of the macroscopic resistivity per unit
area r
GB
to the grain boundary thickness <5
G
B(/°GB
=
''GB/SGB)- In case the thickness of the intergranular
glass films is known, the microscopic permittivity of the
grain boundary material, e
GB
, can also be derived from
the macroscopic grain boundary capacitance, C
G
B (see
Table III), according to the relationship:
Using the "brick layer" model,
8
-
14
we obtain:
e
G
B =
CT-GB
•
8
GB
/(a2irf
R
€
0
) =
CGB/e0
•
(8GB/a),
(2)
where e
0 =
8-85 pF/m is the permittivity of free space.
Table III summarizes our experimental results on the
electrical properties of grain boundaries at 673 K.
Figure 9 shows the relationship between the normal-
ized grain boundary resistivity r
GB
at 673 K and the
content of total impurities. Neither the total impurity
concentration nor the increasing SiO
2
content alone
are responsible for the increase of the grain boundary
resistance. Much more important is the combination of
the appropriate impurities which determines the amount
of the glass phase, especially the SiO
2
/Al
2
O3 ratio (see
Table I). The normalized grain boundary resistivity of
both series A and E, to which only one of the glass
components, SiO
2
or A1
2
O
3
, has been added, remains
almost as low as the pure standard material (R-0) even
at high total additive levels. On the other hand, the B,
C, and D series containing both SiO
2
and Al
2
O
3
exhibit
relatively high normalized intergrain resistivities as soon
as the total additive content exceeds a threshold value of
about 0.3-0.5 wt. %. Already 0.2 wt. % of silica leads
to a dramatic increase of the normalized grain boundary
resistivity if enough alumina is present in the sample.
The resistivities remain then constant at higher im-
purity levels.
Figure 10 shows the dependence of normalized re-
sistivity of intergrain films on the SiO
2
/Al
2
O
3
ratio.
The highest resistivities are found in samples containing
both impurities in the SiO
2
/Al
2
O
3
ratio of 1/1 to 3/1.
Pure silica does not melt at the sintering tempera-
ture.
Additional oxides, especially alumina and yttria,
are necessary for the formation of the liquid phase
at this temperature. We can assume that the appropri-
ate amounts of Y
2
O
3
and ZrO
2
are supplied by the
matrix to form the glass melt. The glass-forming re-
gion of the ternary SiO
2
-Al
2
O
3
-Y
2
O system,
52
'
53
which
TABLE III. Relevant parameters of the grain boundaries in 3Y-TZP samples at 673 K.
Macroscopic specific resistivities
Sample
PGB
(ohm
•
m) ohm
•
m
2
)
Time constant, r
(10-
6
s)
3.98
7.96
17.67
15.92
15.92
53.00
63.66
69.23
18.78
127.32
106.16
10.66
63.66
31.83
19.89
13.21
13.21
79.58
Capacity, C
GB
(nF/m)
50
80
88
64
80
62
71
66
59
71
61
66
77
48
62
78
74
32
TZ-3Y
R-0
A-3
A-5
A-7
B-3
B-5
B-10
C-l
C-5
C-10
D-3
D-5
D-10
E-3
E-5
E-10
F-46
100
200
250
200
850
900
1050
320
1800
1750
160
830
670
320
170
180
2480
36
48
96
135
105
548
513
614
163
1026
998
91
535
382
187
105
111
1116
1234
J. Mater.
Res.,
Vol.
9, No. 5, May 1994
http://journals.cambridge.org Downloaded: 11 Mar 2015 IP address: 157.182.150.22
M.
Godickemeier
et al.:
Effect
of
intergranular glass films
on the
electrical conductivity
of
3Y-TZP
E
.c
O
10
O
m
a
1200 -
1000 -
800 -
600 -
400 -
200 -
0 -
B3/
/
D3
**~
R0
• A
C5
•t—
/
/
D5
—-• ^=d
B5 /
' A5
9 E5
•
~*-
A7
•
C10
B10
-•
D10
E10
0.0 0.2 0.4 0.6 0.8 1.0
Total Impurities [wt%]
FIG. 9. Normalized grain boundary resistivity at 673 K as a function
of impurity content.
AI.O,
sio,
L
0
0 10 20 30 40 50 60 70 80
90100
wt%
SiO
2
—
FIG. 11. Region of glass-forming melts in the SiC>2-
system
52
at 1773 K.
- 100
-90
-80
-70
-60
-50
-40
-30
6*
CM
-20
is liquid at the sintering temperature of 1773 K, is
shown in Fig. 11. The arrows outgoing from the binary
SiO
2
-Al
2
O
3
subsystem mark the compositional lines on
which our sample series are located.
Assuming total yttria saturation from the Y-TZP
matrix, only the appropriate SiO
2
/Al
2
O3 impurity ratio
determines the final composition of the intergranular
glass phase. The melt composition lowest in A1
2
O
3
lies
in this ternary system in the sketched part of the phase
diagram at about 10 wt. % A1
2
O
3
and 50 wt. % SiO
2
(a
in Fig. 11). This glass composition is in equilibrium with
solid SiO
2
. For the A series containing SiO
2
additive
only, the amount of the ternary glass phase of composi-
tion a lies at ten times their A1
2
O
3
impurity-content in
wt. % (10 wt. % A1
2
O
3
). For the B series, the content of
glass of composition designated with a corresponds to
twice the SiO
2
concentration in wt. % (50 wt. % SiO
2
).
0.1 1 10
SiO
2
/AI
2
O
3
-Ratio
FIG. 10. Normalized grain boundary resistivity at 673 K as a function
of the SiO
2
/Al
2
O
3
ratio.
On the other side of the diagram, the Al
2
O
3
-rich melt
composition which is in equilibria with solid A1
2
O
3
is
at 35 wt.% A1
2
O
3
and 35 wt. % SiO
2
(b in Fig. 11).
The alumina rich series C, D, and E will form glass of
composition b in amounts corresponding to about three
times their SiO
2
concentration in wt. % (35 wt. % SiO
2
).
The calculated glass contents of all specimens in wt. %
are given in Table IV. \
Although the liquidus of the quaternary SiO
2
-
Al
2
O
3
-Y
2
O
3
-ZrO
2
system has not yet been elucidated,
we can expect an analogous region of glass melts at
1773 K, lying between 10 wt. % A1
2
O
3
and 50 wt. %
SiO
2
on the SiO
2
-rich side and 35 wt. % A1
2
O
3
and
35 wt. % SiO
2
on the Al
2
O
3
-rich side of the quasi-binary
edge.
This assumption is supported by EDX analysis
of glass areas in the triple grain junctions showing
systematic variations of the glass phase composition in
function of the SiO
2
/Al
2
O
3
ratio.
From the densities of the bulk 3Y-TZP material
and of the SiO
2
-Al
2
O
3
-Y
2
O
3
glass compositions, we
can determine the volume content of the glass phase
using the following simplified equation, valid for small
concentration of the glass:
Vol. % glass = wt. % glass
•
D
TZ
p/D
giass
,
where
D
TZ?
= 6.08 g/cm
3
is the theoretical density of
3Y-TZP and £>
g
i
ass
the density of the glass phase.
The density of the glass phase depends on its compo-
sition, and varies especially with the yttria content. For
the ternary SiO
2
-Al
2
O
3
-Y
2
O
3
glass of composition a
(see Fig. 11) with a content of 10 wt.% alumina, the
density is known
54
to be 3.2 g/cm
3
; for the alumina
rich glass b the density
54
is 3.5 g/cm
3
. The appropriate
volume content of glass can now be calculated for
J.
Mater.
Res., Vol. 9, No. 5, May 1994
1235
http://journals.cambridge.org Downloaded: 11 Mar 2015 IP address: 157.182.150.22
M. Godickemeier
ef
a/.: Effect
of
intergranular glass films
on the
electrical conductivity
of
3Y-TZP
TABLE IV. Derived specific properties of intergranular glass films at 673 K.
Glass content
Sample
TZ-3Y
R-0
A-3
A-5
A-7
B-3
B-5
B-10
C-l
C-5
C-10
D-3
D-5
D-10
E-3
E-5
E-10
F-46
Wt.%
0.015
0.09
0.10
0.10
0.10
0.46
0.78
1.52
0.18
0.75
1.41
0.27
0.45
0.57
0.09
0.09
0.09
6.30
Vol. %
0.026
0.15
0.19
0.19
0.19
0.86
1.46
2.61
0.31
1.29
2.42
0.46
0.77
0.98
0.15
0.15
0.15
10.8
"LID
V
1
-"
(nm)
0.04
0.24
0.30
0.34
0.33
1.87
2.82
5.23
0.53
2.48
4.71
0.88
1.67
1.88
0.29
0.31
0.31
18.16
0GB
(eq)
(10^
S/m)
(eq)
1.11
5.00
3.13
2.52
3.14
3.41
5.50
8.52
3.25
2.41
4.72
9.67
3.29
4.93
1.55
2.95
2.79
16.27
0.50
4.52
6.21
4.55
5.68
20.31
15.51
44.56
6.93
34.92
57.00
11.51
22.51
17.39
3.47
4.44
4.21
130.81
each composition from
the
amount
of
SiO
2
and
A1
2
O
3
impurities
and is
given
in
Table
IV.
Figure
12
shows
the
normalized grain boundary
resistivity
at 673 K as a
function
of the
calculated
glass content
in
vol. %.
At
glass contents
of
more than
1 vol.
%, the
intergranular resistivity remains approx-
imately constant (sample series
B, C, and D).
This
indicates that
an
equilibrium thickness
of the
intergranu-
lar film
has
already been achieved
and the
further excess
of the glass phase segregated
at
triple grain junctions
and
on
the
surface
of the
specimens.
From
the
volume fraction
of the
glass phase
and
the average linear grain size
/
(Table
II), the
equiva-
1200
-
1000
-
800
-
600
-
400
-
200
-
0
-
/f\
/I
E*A *D3
•-•RO
C5
/
/
/
^——~-_BL_——
• D10
C10
•
B10
_--
T
E
_c
O
O
(9
1.0 1.5 2.0 2.5 3.0
Glass Phase Content [Vol%]
FIG. 12. Normalized grain boundary resistivity at 673 K as a function
of the glass content.
lent thickness
of the
grain boundary layer «5
G
B
(eq) can
be calculated. Assuming
the
total amount
of the
glass
phase
is
homogeneously distributed between neighbor-
ing grains
and no
segregation
in
triple points occurs,
according
to the
"brick-layer" model,
we
obtain that
the
equivalent thickness
of the
grain boundary layer,
5GB
(eq),
is
proportional
to the
ratio
of the
volume
of the
glass phase
to the
volume
of the
bulk grain material:
<5GB
(eq) = (a/3)
•
[vol.
%
glass/(100
-
vol.
%
glass)]
(3)
where
a = 1.5/ is the
average cube length
and a/3 =
1/2 is the
ratio
of the
cube volume
to the
half
of the
cube surface.
47
The calculated equivalent thickness
of
intergranular
glass films
is
given
in
Table
IV.
Figure
13
shows
the
dependence
of the
normalized resistivity
at 673 K ver-
sus
the
equivalent film thickness.
The
threshold
for the
constant resistivity
is
found
at 1-2 nm.
This equilibrium
film thickness value corresponds
to two to
four mono-
layers
of
SiO
4
-tetrahedra
of the
dimension
of 0.48 nm.
The macroscopic grain boundary resistivities
at
673
K as a
function
of the
annealing time
at 1773 K
are shown
in Fig. 14.
During
the
annealing process
the macroscopic specific grain boundary resistivities
decrease
in
samples
B-10 and C-10, in
which
the
equilibrium thickness
of
intergranular glass films
has
already been achieved.
On the
other hand,
in
samples
having
low
glass contents
(R-0, A-7, C-l, and
E-10),
the value
of the
macroscopic grain boundary resistivity
remains constant. This behavior
can be
assigned
to the
grain coarsening which reduces
the
number
of the
grain
1236
J.
Mater.
Res., Vol. 9, No. 5, May 1994
http://journals.cambridge.org Downloaded: 11 Mar 2015 IP address: 157.182.150.22
M. Godickemeier
ef al.:
Effect
of
intergranular glass films
on the
electrical conductivity
of
3Y-TZP
E
o
9
o
m
(9
1200
-
1000
-
800
-
600
-
400-
200
-
12
3 4 5 6
Equivalent Glass Film Thickness
[nm]
FIG. 13. Normalized grain boundary resistivity at 673 K as a function
of the equivalent thickness of the intergranular film.
boundaries perpendicular
to the
current direction. Only
in "saturated" samples
the
glass phase
is
squeezed
out
from
the
grain boundaries during
the
grain growth.
D. Specific properties
and the
equilibrium
film thickness
The microscopic specific electrical properties
of the
intergranular phase, cr
GB
(eq) and eGB (eq),
shown
in
Table
IV,
were derived according
to Eqs. (1) and (2)
from
the
calculated values
of
equivalent thickness
<5
GB
(eq)
and the
experimentally found macroscopic values
of
PGB
and
CQB
(Table
III). The
resulting microscopic
spe-
cific conductivity
of the
intergranular phase
at 673 K
varies between
1.1 X KT6 S/m and 1.6 X 10"5 S/m
and
the
dielectric constant from
0.5 to 130.8 at 693 K.
However,
at low
glass phase contents
the
estimated
equivalent mean thickness
is
smaller than
the
expected
2000
E
O
m
(3
1500 -
1000 -
500
-
Time
[h]
FIG. 14. Macroscopic specific grain boundary resistivity at 673 K as
a function of annealing time.
equilibrium value
of 1—2 nm, and a
continuous inter-
granular glass layer cannot
be
formed.
As a
result,
the
current path partially avoids crossing
the
disjointed glass
films
and
shunt over
the
"clean" grain boundaries. This
parallel current path results
in
lower values
of
PGB
(Table
III) and
cr
GB
(eq), as
well
as in too low
values
of
eGB (eq) for the
samples TZ-3Y,
R-0, C-l, and the
whole
A and E
series.
On the
other hand,
for
equiva-
lent thicknesses much exceeding
the
equilibrium width
of intergranular films (samples
B-10, C-10, and
F-46),
too high values
for
cr
GB
(eq) and eGB (eq) are
obtained.
In order
to
verify these results,
we
want
to
compare
the specific properties
of the
glass phase which
we
found
by
analyzing
the
experimental results using
the
brick layer model with
the
properties
of
bulk glass
material.
Two
glasses have been prepared
by
melting
the
appropriate amounts
of
oxides
at 1973 K. The
first glass
with
the
eutectic composition
of the
SiO
2
-Al
2
O
3
-Y2O3
system
(46 wt. %
SiO
2
,
22 wt. %
A1
2
O
3
,
and 32 wt. %
Y
2
O
3
) melts
at 1617 K.44"46 The
second glass that
was
prepared
as a
bulk sample corresponds
to the
quater-
nary composition found
in the
three grain junctions
by
EDX analysis
(42 wt.
% SiO
2
,
22 wt. %
A1
2
O
3
,
21 wt. %
Y
2
O
3
,
and 15 wt. %
ZrO
2
).
Figure
15
shows
the
temperature dependences
of
the permittivity,
e', and Fig. 16 the
Arrhenius plots
of
the
conductivities
of
both glasses.
At 693 K the
permittivity
of the
ternary eutectic glass
is 7.5 and
that
of the
quaternary glass containing ZrO
2
is 15.7.
The corresponding specific conductivities
at 693 K are
5.18
•
10"
7
S/m for the
ternary glass
and 6.34
•
10"7 for
the quaternary
one. The
activation energies
of the
elec-
trical conductivities
of
these glasses
are 1.11 ± 0.02 eV
and
1.21 ± 0.02 eV,
respectively.
All
these properties
are
in
good agreement with
the
values
of the
specific
properties
of the
intergranular glass phase, calculated
500
600 700 600 900 1000 1100 1200
Temperature
[K]
FIG. 15. The temperature dependence of the real part of the complex
dielectric permittivity of SiO2-Al2O3-Y2O3-(ZrO2) glasses (for
compositions, see text).
J.
Mater.
Res., Vol. 9, No. 5, May 1994
1237