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Materials Transactions, Vol. 44, No. 5 (2003) pp. 935 to 939
#2003 The Japan Institute of Metals
Small Dopant Effect on Static Grain Growth and Flow Stress in Superplastic TZP
Hidehiro Yoshida* , Hitoshi Nagayama and Taketo Sakuma
Department of Advanced Materials Science, Graduate School of Frontier Science, The University of Tokyo, Tokyo 113-8656, Japan
Static grain growth behavior in 1 mol% of GeO2 , TiO2 , MgO or BaO-doped ZrO2 –3 mol%Y2 O3 (3Y-TZP) was examined at 1400 C with a
special interest in dopant effect on superplastic flow stress in fine-grained 3Y-TZP. The static grain growth can be described as normal grain
growth in single-phase ceramics, and growth constant K for each material is in the order of 10% flow stress of the superplastic flow. The value of
K in cation-doped TZP is correlated well with dopant cation’s ionic radius. Assuming activation energy for diffusivity of constituent ion can be
given as a linear function of strain caused by difference in the ionic size of dopant cation, the dependence of the growth constant and the flow
stress on the ionic radius can be described as a function of the ionic radius of the dopant cation. The activation energy for the diffusivity in cationdoped TZP estimated from the calculation is in good agreement with the experimental data. The small dopant effect on the superplastic flow
stress is well described by the activation energy as the function of the dopant cation’s ionic size.
(Received January 14, 2003; Accepted March 24, 2003)
Keywords: grain growth, superplasticity, tetragonal zirconia polycrystal, dopant effect
1.
Introduction
Since high temperature superplastic deformation in ceramic materials was experimentally observed,1) the superplastic behavior has been investigated in various kinds of
ceramics. Tetragonal ZrO2 polycrystal (TZP) with an average
grain size of less than 1 mm is one of the most representative
ceramic materials, which exhibit large tensile elongation at
high temperature.2–7) For instance, the elongation of 800%
was obtained in TZP at 1550 C under the strain rate of
8:3 105 s1 ,2) and 1038% in SiO2 -doped TZP at 1400 C
under the strain rate of 1:3 104 s1 .7) More recently, it has
been pointed out that the superplastic stress-strain behavior in
TZP is sensitively affected by residual impurities.8,9) The
impurity effect was carefully investigated so far, but there are
no descriptions of the dependency on type or amount of
impurities. In our previous study, the superplastic behavior in
1 mol% of cation-doped TZP was systematically investigated, and a good correlation between the flow stress and
dopant cation’s ionic radius was found: a smaller cation
contributes to a larger stress reduction in TZP, and larger
cations raise the flow stress.10) Origin of the dopant effect has
not been clarified yet, but because the high temperature
plastic deformation in fine-grained TZP is rate-controlled by
diffusion matter transport,6,11) the reduction of the flow stress
may be interpreted as a result of enhancement in the
diffusivity of constitutive ions in TZP due to the cation
doping.10) However, it is difficult to measure or predict the
apparent diffusivity in cation-doped TZP so far.
Grain growth is a common phenomenon in fine-grained
TZP, which has been numerously investigated from the
viewpoint of powder processing and microstructure development in particular.12–15) The static grain growth is
phenomenologically analyzed by kinetics of grain size as a
function of time. In the classical theory for grain growth, the
grain size can be given as16)
dm d0m ¼ Kt
where d0 is the initial grain size, d is the grain size at time t, m
*Corresponding
author: E-mail: [email protected]
is the grain growth exponent, and K is the growth constant.
The reported data of the parameters are scattered, but in the
case of normal grain growth in single-phase TZP, m ¼ 2 is
often used for the phenomenological analysis.13,15,17) The
detailed mechanism of the grain growth in TZP has not been
classified yet, but it is supposed that matter transport by
diffusion in the vicinity of the grain boundaries is the ratecontrolling mechanism for the normal grain growth. The
growth constant K thus must be related to the diffusivity in
TZP, and estimation of K value is expected to produce an
important information about the dopant effect on the superplastic flow stress in TZP. In the present study, the static grain
growth behavior was investigated in ZrO2 –3 mol%Y2 O3
(3Y-TZP) and 1 mol% of cation-doped 3Y-TZP. The dopant
effect on the grain growth behavior and the superplastic flow
stress will be discussed from the viewpoint of ionic radius
dependence of activation energy for the diffusivity.
2.
Experimental Procedure
The materials used in this study were tetragonal ZrO2 –
3 mol%Y2 O3 polycrystal (3Y-TZP) and 1 mol% of BaO,
MgO, TiO2 , or GeO2 -doped 3Y-TZP. 3Y-TZPpowder
(TZ3Y; Tosoh Co., Ltd.), barium oxide (BaO, Soekawa
chemical Co., Ltd.), magnesium oxide (MgO, Ubekosan,
Japan), titanium oxide (TiO2 , Sumitomo Cement Co., Ltd.)
and germanium oxide (GeO2 , Rare Metallic Co., Ltd.) were
used as starting materials. 3Y-TZP powders and the oxide
powders were mixed, ball-milled in ethanol together with
5 mm diameter high-purity (>99:9%) zirconia balls for 24 h,
dried and shifted through a 60 mesh sieve for granulation.
The green compacts were prepared by pressing the mixed
powders into bars with a cemented carbide die under a
pressure of 33 MPa, and then isostatically-pressed under a
pressure of 100 MPa. The green compacts were sintered at a
temperature in the range 1400 or 1450 C for 2 h in air to
obtain an average grain size of about 0.4 mm and relative
density of about or more than 99% for theoretical value in all
samples. The sintering temperature is listed in Table 1. Heat
treatment for investigation of grain growth behavior was
conducted at 1400 C for the annealing time in the range of 5–
936
H. Yoshida, H. Nagayama and T. Sakuma
Table 1
Sintering temperature, relative density and an average grain size in cation doped and undoped TZP.
Chemical composition
Sintering temperature
Relative
Average grain
( C)
density (%)
size (mm)
1450
1400
99.8
99.9
0.45
0.37
ZrO2 –3 mol%Y2 O3 (TZP)
1 mol%GeO2 -doped TZP
1 mol%TiO2 -doped TZP
1400
99.6
0.31
1 mol%MgO-doped TZP
1400
99.9
0.39
1 mol%BaO-doped TZP
1450
98.5
0.48
20 hours. Microstructures were examined with a scanning
electron microscope (SEM; JSM-5200, JEOL). The grain
size was measured by a linear intercept method using SEM
photographs.
High-temperature mechanical experiments were carried
out under uniaxial tension in air at a constant cross-head
speed using an Instron-type testing machine equipped with a
resistance-heated furnace (AG-5000C; Shimazu Co., Ltd.).
The initial strain rate and temperature were 1:2 104 s1
and 1400 C, respectively. The test temperature was measured by a Pt-PtRh thermocouple attached to each specimen
and kept to within 1 C. The size of the specimens was
2 2 mm2 in cross-section and 13.5 mm in gauge length for
tensile tests.
3.
Results and Discussion
The average grain size of the present materials is in a range
of 0.3–0.5 mm as summarized in Table 1. Fairly uniform and
equiaxed grain structure was obtained for the present
materials. As shown in our previous reports, it has been
revealed with high-resolution transmission electron microscopy technique that there is no second phase such as second
phase particles and cubic zirconia phase in small amount of
cation doped, fine-grained 3Y-TZP with the dopant level of
1–2 mol% contains.10) It is thus considered that 1 mol% of
cation-doped TZP is essentially a single-phase material.
Figure 1 is an example of the stress-strain curves in the
present materials at 1400 C and an initial strain rate of
1:3 104 s1 . The dopant content is 1 mol% in each
material, but the stress-strain curves change with the cation
doping. The flow stress in 3Y-TZP is reduced by TiO2 or
MgO doping, and the flow stress in GeO2 -dope 3Y-TZP is
about one-half of that in 3Y-TZP. On the other hand, the flow
stress is slightly increased by BaO-doping. The superplastic
flow is usually discussed from the following constitutive
equation,
"_ ¼ A n dp expðQsup =RTÞ
where A is the material constant, n and p are the stress and
grain size exponents, Qsup is the activation energy for
superplastic deformation, respectively. The experimental
values of these parameters are fairly scattered,6) but the
most probable values are n ¼ 2, p ¼ 2 and Qsup may
correspond to the activation energy for grain boundary
diffusion.18) Figure 2 shows a logarithmic plot of the flow
stress at the nominal strain of 10% against initial grain size in
the cation doped and undoped TZP, which is annealed at
temperature in a range of 1450–1500 C for 2–4 h in order to
obtain the materials with different grain size.10) The straight
line for each sample is drawn by assuming p/n of 1. The flow
stress in the present materials is in the following order, TZP
+ Ba > undoped TZP > TZP + Mg > TZP + Ti > TZP +
100
1400°C
.
εinitial=1.3 × 10-4s-1
3Y-TZP
+1mol%BaO
+MgO
+TiO2
+GeO2
True Stress, σ / MPa
30
25
10% Flow Stress, σ / MPa
50
35
.
εinitial=1.3 × 10-4s-1, 1400°C
TZP+1mol%BaO
undoped
3Y-TZP
20
+MgO
15
+TiO1.5
ð1Þ
10
10
+GeO2
5
5
0.3
0
0
100
200
300
0.5
0.7
0.9
2.0
Initial Grain Size, d0 / µm
Nominal Strain, ε (%)
Fig. 1 An example of the stress-strain curves in 3Y-TZP and 1 mol% of
BaO, MgO, TiO2 or GeO2 -doped 3Y-TZP at 1400 C and an initial strain
rate of 1:3 104 s1 .
Fig. 2 A logarithmic plot of flow stress at nominal strain of 10% against
initial grain size in 1 mol% cation-doped and undoped 3Y-TZP, which is
annealed at temperature in a range of 1450–1500 C for 2–4 h in order to
obtain the materials with coarse grains.10)
Small Dopant Effect on Static Grain Growth and Flow Stress in Superplastic TZP
2
d d02
¼ Kt
ð2Þ
where d0 is the initial grain size, d is the grain size at time t
and K is the growth constant. The value of K must contain
various kinds of parameters such as the grain boundary
mobility, molar volume and the surface energy. As shown in
our previous report, the static grain growth in TZP and TZP5 wt% TiO2 can be actually given by a parabolic form as eq.
(2).17) Figure 3 shows the plot of d2 d02 against the
annealing time in the present materials at 1400 C. The
square of the grain size against the annealing time exhibits a
single straight line for each material, and the value of the
proportionality constant K can be estimated from the slope of
the lines. Figure 4 shows a plot of K value in cation-doped
3Y-TZP against ionic radius of dopant cation, which is
defined for eight-fold coordination except germanium ion for
six-fold coordination.21) For comparison, data in undoped
3Y-TZP is also plotted with the ionic radius of yttrium cation.
The value of K is decreased with increasing the ionic radius.
The order of K value in cation-doped 3Y-TZP is correlated
with that of the flow stress as seen in Fig. 2. This fact
indicates that both the flow stress and the growth constant
involve the same factor which is affected by ionic radius of
the dopant cation.
The temperature dependence of K is usually expressed as
K ¼ K0 expðQg =RTÞ
ð3Þ
where K0 is a pre-exponential term, Qg is the activation
energy for grain growth, R is the gas constant and T is the
1.0
1400°C
3Y-TZP
+0.1mol%GeO2
+0.1mol%TiO2
+0.1mol%MgO
+0.1mol%BaO
0.6
2
2
d - d0 / µm
2
0.8
0.4
1400°C
0.04
TZP+1mol%Ge
K=K0 × ( r / r 0 )
K0=9.8 × 10-3
a1=3
0.03
0.02
0
5
10
15
20
Annealing Time, t / h
Fig. 3 A plot of d 2 d02 against the annealing time in undoped and 1 mol%
of cation-doped 3Y-TZP at 1400 C.
-a1
+Ti
+Mg
0.01
+Ba
3Y-TZP
0.00
0.04
0.06
0.08
0.10
0.12
Ionic Radius, r / nm
0.14
0.16
Fig. 4 A plot of K value in 1 mol% cation-doped 3Y-TZP against ionic
radius of dopant cation, which is defined for eight-fold coordination except
germanium ion for six-fold coordination.21)
absolute temperature.22) The value of Qg cannot be understood definitely because an early stage of static grain growth
in TZP has not been completely analyzed yet, but Qg is
supposed to be associated with the activation energy for
diffusion.17) There are no basis for believing that Qsup and Qg
are essentially the same, but both of them are probably
associated with the activation energy of the grain boundary
diffusivity in zirconia, which must be affected by cation
doping. Moreover, because the order of K value in cationdoped 3Y-TZP is correlated with that of the flow stress, both
Qsup and Qg consist of the activation energy of grain
boundary diffusivity, which is affected to the dopant cation’s
ionic size. In this study, Qsup and Qg are assumed to be the
same, and relationship between and ionic size of dopant
cation will be derived from the result in Fig. 2.
As shown in Fig. 2, the flow stress in 3Y-TZP is decreased
by the doping of smaller cation than yttrium, but is increased
by large cation doping. The fact suggests that the doping of
smaller cation may enhance the diffusion as an accommodation process of superplastic deformation, nevertheless the
diffusion is suppressed by large size dopant cation. It can be
thus assumed that the activation energy Q is a monotonic
increasing function of the ionic radius r in the first
approximation. The activation energy can be given as
follows,
Q ¼ Q0 þ a1 RT lnðr=r0 Þ
0.2
0
0.05
Growth Constant, K / µm2h-1
Ge. Since the high temperature plastic flow in fine-grained
TZP is rate-controlled by diffusion, the difference in the flow
stress is supposed to result from change in the diffusivity in
3Y-TZP due to the cation doping.
The grain growth in single-phase ceramics with a fairly
uniform grain size is usually treated by the rate equation of
normal grain growth,19,20)
937
ð4Þ
where a1 is the material constant, r0 is the ionic radius for
yttrium cation reported to be 0.1019 nm. It is assumed by eq.
(4) that the activation energy in TZP is a linear function of
strain due to the difference among the ionic size of the dopant
and matrix cation. By substituting eq. (4) for eq. (3), K can be
written as
K ¼ K0 expðQ0 =RTÞ ðr=r0 Þa1
ð5Þ
In Fig. 4, the value of K is plotted by solid line calculated
from eq. (5) using K0 ¼ 9:8 103 mm2 h1 and a1 ¼ 3. The
calculated value is in good agreement with the experimental
data. On the other hand, the constitutive equation for
superplastic deformation of eq. (1) can be rewritten as
follows,
"_ ¼ a2 n expðQ=RTÞ
ð6Þ
where a2 is the material constant including grain size term. It
should be noted that the grain size and the strain rate are
assumed to be constant under the tensile testing conditions.
The flow stress in 3Y-TZP 0 can be given by
0 ¼ a2 ="_ expðQ0 =RTÞ. By substituting eq. (4) for eq. (6),
the flow stress can be given as follows,
a2
n ¼ expðQ0 =RTÞ ðr=r0 Þa1
"_
¼ 0n ðr=r0 Þa1
ð7Þ
and hence flow stress increment due to the cation doping can be given by the following equation,
-1
H. Yoshida, H. Nagayama and T. Sakuma
Activation Energy, E / kJ . mol
938
560
1400°C
.
εinitial=1.3 × 10-4s-1
+Ba
540
+Sc
520
+Ce
+Nd
+Ti
+Mg
500
+Gd
3Y-TZP
+Nb
Q=Q0+a1RT ln(r/r0)
Q0=520kJ/mol
a1=3
480
+Ge
460
0.06
0.09
0.12
0.15
Ionic Radius of Dopant Cation, r / nm
Fig. 6 A comparison of the activation energy for superplastic flow
experimentally obtained in various kind of cation-doped 3Y-TZP23) with
theoretical curve calculated from eq. (4) using Q0 ¼ 520 kJ/mol and
a1 ¼ 3.
¼ 0
¼ 0 ðr=r0 Þa1 =n 1 :
ð8Þ
Figure 5 shows a plot of the flow stress increment against
ionic radius of the dopant cation under the initial strain rate of
1:3 104 s1 at 1400 C. In Fig. 5, the calculated curve of
eq. (8) is also plotted using 0 ¼ 30 MPa, a1 ¼ 3 and n ¼ 2.
The calculated curve is in good agreement with the experimental data. In addition, the value of 0 is not so different
from the flow stress experimentally obtained in 3Y-TZP of
26 MPa. From eq. (4), the activation energy for the superplastic deformation in 1 mol% cation-doped 3Y-TZP can be
estimated using the fitting parameter of a1 obtained in Fig. 4.
Figure 6 shows a comparison of the activation energy for
superplastic flow experimentally obtained in various kind of
1 mol% cation-doped 3Y-TZP23) with the theoretical curve
calculated from eq. (4) using Q0 ¼ 520 kJ/mol and a1 ¼ 3.
The calculated curve corresponds fairly well with the
30
.
1400°C, εinitial=1.3 × 10-4s-1
d=0.5µm
TZP
+1mol%BaO
Stress Increment, ∆σ / MPa
20
10
undoped 3Y-TZP
0
+MgO
-10
-20
-30
0.050
+TiO2
σ =σ0 ((r/r0)a1/n-1)
σ0=30MPa
a1/n=1.5
+GeO2
0.075
0.100
0.125
Ionic Radius, r / nm
0.150
Fig. 5 A plot of flow stress increment against ionic radius of the dopant
cation under initial strain rate of 1:3 104 s1 at 1400 C.
experimental data. This result indicates that the description
of the activation energy as shown in eq. (4) is a reasonable
assumption as a first-approximation for that of the diffusivity
as the rate-controlling mechanism of both superplastic flow
and the static grain growth in cation-doped 3Y-TZP. The
diffusivity in cation-doped TZP, which is related to the
accommodation process for the flow stress and the grain
growth behavior, can be evaluated from the activation energy
as a function of dopant cation’s ionic size.
In our previous report, it has been revealed that small
amount of dopant cation tends to segregate in the vicinity of
the grain boundaries in fine-grained TZP. For instance, it was
found that small amount of Si4þ , Mg2þ and Al3þ cations
segregated at the grain boundary over a width of 5 nm in
5 mass% (SiO2 +2 mass%Al2 O3 ) or (SiO2 +2 mass%MgO)doped TZP.24) The previous result suggests that the doped
cations in the present materials also segregate at the grain
boundary. It is thus supposed that the segregation of the
dopant cation is the origin of the dopant effect on the
superplastic and grain growth behavior. The change in the
grain boundary diffusivity must be related to atomic interaction between the grain boundary and the segregated dopant
cations. Estimation of excess energy caused by the segregation has been reported by many authors, but focusing on
atomic size effect, elastic interaction between dopant cation
and low angle tilt boundary has been theoretically calculated
so far. For example, White and Coghlan reported that the
elastic energy Es at the low angle tilt boundary with dopant
cations’ segregation can be given by Es ¼
ð1 =1 þ Þ, where is the atomic volume of dopant,
is Poisson’s ratio, is the sum of the normal stress
components of the dislocation array and is the equilibrium
dilatation of the atom.25) In other words, the elastic energy
stored by the grain boundary segregation is proportional to
the dopant atom’s volume. The fact must be related to the
present result of a1 3. Further experimental and theoretical
analysis on the grain boundary chemistry should be made in
order to reveal the origin of the dopant effect on the
superplastic and grain growth behavior in cation-doped TZP.
Small Dopant Effect on Static Grain Growth and Flow Stress in Superplastic TZP
4.
Conclusion
Superplastic flow stress and static grain growth in 3Y-TZP
are very sensitive to small amount of dopant of cation even in
the dopant level of 1 mol%. The flow stress change due to the
cation doping is supposed to be caused mainly by the change
in diffusivity of constituent ions; the diffusion as an
accommodation process for superplastic deformation must
be enhanced by doping of smaller cation, but retarded by
larger cation’s doping. The static grain growth constant in
cation-doped TZP is also correlated well with the flow stress.
On the assumption that activation energy for diffusion can be
described as a linear function of strain due to difference in the
ionic size of dopant cation, the growth constant and the flow
stress can be described as a function of dopant cation’s ionic
size. Calculated values of the growth constant and the flow
stress are in good agreement with the experimental data. In
addition, the calculated activation energy is in good agreement with the experimental data estimated from the superplastic flow. The diffusivity in cation-doped TZP, which is
related to the accommodation process for the flow stress and
the grain growth behavior, can be evaluated from the
activation energy as a function of dopant cation’s ionic size.
Acknowledgements
The authors wish to express their gratitude to the Ministry
of Education, Culture, Sports, Science and Technology and
Japan Society for the Promotion of Science for the financial
support by a Grant-in-Aid for Scientific Research (A)(2)13305052 and Grant-in-Aid for Encouragement of Young
Scientists (2)-13750647. The authors would like to thank
Professor A. H. Chokshi for his suggestion on grain growth
mechanism.
939
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