Zuo-Guang. Ye Advanced Dielectric Piezoelectric and Ferroelectric Materials: Synthesis, Characterisation and Applications
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Handbook of dielectric, piezoelectric and ferroelectric materials830
This anisotropy in resistivity of the HF sample can be explained as
follows.
In our previous report,
6
we have shown SEM photographs of the
perpendicular plane and the parallel plane in the HF Bi
4
Ti
3
O
12
ceramics, and
concluded that thin plates of the crystallite are piled up along the forging
axis and that the grains have a high degree of orientation in the ceramics.
Therefore, if the influence of grain boundaries and porosity can be ignored,
the resistivity ρ [//] or ρ [⊥] in the parallel [//] or perpendicular [⊥] direction
to the forging axis corresponds, respectively, to ρ
c
(= ρ
33
) or ρ
a
(or ρ
b
) (= ρ
11
)
in c axis or a (or b) axis of the single crystal with bismuth oxide layer
structure. In earlier treatments
30
of conduction in Bi
4
Ti
3
O
12
single crystal, an
anisotropy in electrical conductivity σ
a
(or σ
b
) and σ
c
in a (or b) axis and c
axis was observed, whose σ
c
(= σ
33
) is significantly smaller than σ
a
(or σ
b
)
(= σ
11
) in the single crystal due to the layered structure. The observed value
30
of σ
a
(or σ
b
) at room temperature to about 250°C was four to five times as
PBT
PBT + CeO
2
(0.11 wt%)
PNC–2
PNC–5
PNC–10
PNC–20
Temp. (°C)
190 150 100 50 20
Resistivity ρ (Ωcm)
10
16
10
15
10
14
10
13
10
12
10
11
10
10
2.15 2.5 3.0 3.4
1000/
T
(1/K)
27.7
Temperature dependence of resistivity ρ in the OF PNC system.
WPNL2204
Grain orientation and electrical properties of bismuth 831
large as that of σ
c
, namely, σ
a
/σ
c
= σ
11
/σ
33
= ρ
33
/ρ
11
= 4 ~ 5. Thus the
anisotropy in conductivity of the HF ceramics as well as the dielectric properties
can be estimated from those of the single crystals.
The anisotropy in the conductivity between the OF ceramics and the HF
ones is less than that of single crystals, but the anisotropy in resistivity found
in our present measurement is 2 to 3 for both ρ [//]/ρ [OF] and ρ [OF]/ρ [⊥].
To account for this anisotropy, it is assumed
31
that the //⊥ aggregate is
statistically homogeneous and isotropic and that there neither exists an
additional phase at crystal boundaries nor that surface effects occur at these
boundaries. Then the two most commonly used estimates for macroscopic
conductivity σ* in ceramic specimens are given
31
by Eqs (27.3) and (27.4).
σσσσ* =
1
3
( + + )
11 22 33
27.3
1
*
=
1
3
1
+
1
+
1
11 22 33
σ
σσσ
27.4
PNC–10 HF (//)
PNC–10 OF
PNC–10 HF (⊥)
2.0 2.5 3.0 3.5
1000/
T
(1/K)
Temp. (°C)
200 150 100 50 20
Resistivity ρ (Ωcm)
10
14
10
13
10
12
10
11
10
10
27.8
Temperature dependence of resistivity ρ in the HF PNC-10 (HF
[⊥], [//]), with that of the OF ones.
WPNL2204
Handbook of dielectric, piezoelectric and ferroelectric materials832
where σ
11
= σ
a
, σ
22
= σ
b
, and σ
33
= σ
c
are conductivity in the single crystal.
It can be shown that Eqs. (27.3) and (27.4) are actually upper and lower
bounds, respectively, on effective macroscopic conductivity. If σ
11
≅ σ
22
and
σ
11
/σ
33
= σ
a
/σ
c
≅ 4.5, then Eq. (27.3) easily leads to the following equation:
σ
σ
σ
σ
*
2 + 1
3
3.3
33
11
33
≅
≅
27.5
Also, Eq. (27.4) can be rewritten as follows:
σ
σ
σ
σ
*
3
2 + 1
2.1
33
33
11
≅
≅
27.6
Hence, the effective conductivity σ*/σ
33
in OF (non-oriented) ceramics can
be estimated from Eqs. (27.5) and (27.6) to have some value between 2.1
and 3.3. The observed value of σ*/σ
33
= ρ [//]/ρ [OF] over the temperature
range of 50 to 150°C is approximately 2.5, showing close agreement between
the measured and calculated results.
Figure 27.9 shows the temperature dependence of the resistivity of SBTT2
(x) and SBTT3 (x). The resistivity, ρ, of the BIT (m = 3, x = 0) ceramic was
Resistivity ρ (Ω cm)
10
16
10
14
10
12
10
10
10
8
2.2 2.4 2.6 2.8 3.0 3.2 3.4
1000/
T
(K
–1
)
BIT
SBTa
SBTT3(1.0)
SBTT3(0.3)
SBTT2(1.25)
SBTT3(0.5)
27.9
Temperature dependence of the resistivity of SBTT2 (
x
) and
SBTT3 (
x
).
Temperature (°C)
150 100 50
WPNL2204
Grain orientation and electrical properties of bismuth 833
about 10
11
Ωcm. SBTT ceramics have the high value of about 10
14
–10
15
Ω
cm except for the SBTT3 (0) (BIT) ceramic. It is thought that a reason of this
improvement is due to substitution of unstable Ti
4+
ions by stable Ta
5+
ions.
From the result of ρ, SBTT ceramics except BIT seem to be suitable for
heavy poling conditions with high applied fields at high temperatures.
27.4.4
D
–
E
hysteresis loops and remanent polarization
D–E hysteresis loops for HF and OF ceramics were observed by a standard
Sawyer–Tower circuit at 50 Hz. Samples for hysteresis loop measurements
have a thickness of 0.3–0.5mm and an area of 10–50mm
2
with fired-on
silver paste or vacuum-evaporated silver electrodes.
As shown in Fig. 27.10, hysteresis loops of both HF and OF BIT ceramics
HF [⊥]
E
c
= 50 kV/cm
P
r
= 37 µC/cm
2
(a)
HF [//]
E
c
= 17 kV/cm
P
r
= 3.3 µC/cm
2
(b)
OF
E
c
= 33 kV/cm
P
r
= 9.3 µC/cm
2
(c)
27.10
Typical hysteresis loops of HF and OF ceramics at room
temperature (at 50Hz), (a) the perpendicular [⊥], (b) the parallel [//]
and (c) OF.
WPNL2204
Handbook of dielectric, piezoelectric and ferroelectric materials834
were observed at room temperature. The shapes of the hysteresis loops in
Fig. 27.10 resemble those of BIT thin films which were prepared by an RF
sputtering method.
32
The spontaneous polarization P
s
,
12
lying in the monoclinic
a
m
–c
m
plane with an angle of about 5° to the a
m
-axis, exhibits two components,
P
sa
= 50 ± 10 µC/cm
2
along the a
m
-axis and Psc = 4 ± 0.1 µC/cm
2
along the
c
m
-axis, approximately. When a strong electric field is applied, the spontaneous
polarization direction in each crystal tends to switch to the equivalent direction
nearest to that of the applied field. In the case of the perovskite-type structure,
a simplified assumption has usually been adopted that under a strong poling
field each randomly oriented crystallite becomes a single domain polarized
in the closest direction of the 6, 12 or 8 directions possible in the tetragonal,
orthorhombic or rhombohedral state, respectively. The reduced saturated
remanent polarization P
r
/P
s
is calculated as:
(3 2 /8) tan (1/ 2 )
–1
= 0.831,
(3/π) tan
–1
2
= 0.912 or (
3
/2) = 0.866, respectively.
33
On another assumption – that only 180° switching, which is accompanied
by no mechanical strain, takes place – the remanent polarization is 1/2 of P
s
,
since every axis is randomly distributed over every direction.
34
Thus, a
considerably high percentage of domains are oriented along the polarizing
field, in fully polarized ferroelectric ceramics with perovskite type structure.
For the case of bismuth layer structure ferroelectric ceramics, completely
saturated remanent polarization is calculated in a similar way. Though a 90°
switching is accompanied by mechanical strains (elongation, contraction,
and heat), their effects are neglected in the calculations. The results are as
follows:
• Perfect orientation (F = 1). Here, every c
m
-axis is oriented along the
forging axis and every a
m
-axis lies randomly in the plane perpendicular
to the forging axis.
– Poling along the forging axis. Every c
m
-axis switched (180°-reversal),
and remanent polarization P
r
[//] is calculated as
P
r
[//] = P
sc
– Poling perpendicular to the forging axis in the case of only 180
°
switching: Every a
m
-axis is switched (180°-reversal), and remanent
polarization P
r
[⊥] is calculated as
P
r
[⊥] = (2/π) P
sa
= 0.637 P
sa
– Poling perpendicular to the forging axis in the case of both 180
°
and 90
°
switchings: Every a
m
-axis is switched to one of four directions,
namely along one of the ±a
m
and ±b
m
-axes, which is located closest
to the poling field. Hence,
PPP
rsasa
[] =
22
= 0.900 ⊥
π
WPNL2204
Grain orientation and electrical properties of bismuth 835
• Random orientation (F = 0).
– Case of only 180
°
switching:
P
PP
PP
r
sa sc
sa sc
=
( + )
2
= 0.500 ( + )
– Case of both 180° and 90° switchings:
PPPPP
rsascsasc
=
1
2
+
1
2
= 0.707 + 0.500
Figure 27.11 shows the dependence of P
r
/P
s
on the degree of orientation
F. Observed values are obtained from 50Hz hysteresis loops. Samples of
intermediate value of F (0.2–0.7) are particularly fabricated by controlling
the soaking time t
p
in the HF process. Calculated values are given only for
F = 0 and F = l. They are connected tentatively by straight dotted lines,
though the relation between P
r
and F is unknown. The value of 50
( (50 + 4 ))
22
≅
µC/cm
2
is used as P
s
(= ( + ))
s
2
s
2
PP
ac
. Namely, the
observed value of the remanent polarization P
r
[⊥] for F = 0.95 is estimated
to be about 82% of the calculated one in F = 1 for both 180° and 90°
switchings, which is supposed to be the case in the observation of the hysteresis
loop. This seems to be due mainly to the lack of saturation in the loops (Fig.
27.10), since a sufficiently strong voltage cannot be applied. At all events, it
is apparent that the HF process is more effective in producing a high remanent
polarization than the OF process, the ratio P
r
[⊥]/P
r
[//] and P
r
[⊥]/P
r
[OF]
being about 11 and 4, respectively, for F = 0.95 at room temperature. Thus
Calculated [⊥] (180° and 90° switchings)
Calculated [⊥] (180° switching)
P
r
/
P
s
1.0
0.8
0.6
0.4
0.2
F
0 0.2 0.4 0.6 0.8 1.0
27.11
The dependence of
P
r
/
P
s
, on the degree of orientation
F
(䊊 calculated, | observed).
WPNL2204
Handbook of dielectric, piezoelectric and ferroelectric materials836
HF is expected to be more useful for piezoelectric and pyroelectric applications.
In these applications, however, the ceramics are poled and kept without
electric fields, and P
r
will be less than the value measured from the hysteresis
loop, and may correspond to the case for only 180° switching since 90°
switchings tend to be depoled by mechanical strains induced in their switchings.
Figure 27.12 shows the remanent polarization, P
r
of SBTT2(x) and SBTT3(x)
at RT as a function of Ta concentration (x). The values of P
r
and E
c
in SBTT2
decrease sharply with increasing of Sr or Ta concentration (x). This tendency
almost corresponds to the compositional dependence of T
c
. The P
r
of SBTT3
(0.3) was the largest (P
r
= 12.3µC/cm
2
) in the SBTT system. The D–E
hysteresis loop of the BIT ceramic was not saturated sufficiently because of
the electrical breakdown at about 70kV/cm. On the other hand, the electrical
breakdown of the SBTT3 (0.3) ceramic did not occur up to about 140kV/cm
because the resistivity was very high. Therefore, large piezoelectricity is
expected for this composition. On SBTT2 ceramics, the E
c
becomes higher
with the decreasing concentration of Ta. Therefore, the D–E hysteresis loop
of the SBTT2 ceramics was not saturated sufficiently.
27.4.5 Piezoelectric properties
The electromechanical properties of poled ferroelectric ceramics depend
strongly on the poling conditions, namely, poling temperature, poling field,
and poling time. The high-temperature poling process seems to be very
effective for activating piezo- and pyroceramics with a high Curie temperature
or large coercive field such as BLSF or PbTiO
3
-based materials. To pole at
a high temperature, the BLSF ceramics must have high resistivity at that
Remanent porarization,
P
r
(µC/cm
2
)
15
10
5
0
SBTT (OF)
P
r
E
c
at RT
P
r
E
c
SBTT3
SBTT2
0 0.5 1.0 1.5 2.0
Ta concentration (
x
)
120
100
80
60
40
20
0
Coercive field,
E
c
(kV/cm)
27.12
Remanent polarization,
P
r
,
and coercive field,
E
c
, of the
SBTT2(
x
) and SBTT3(
x
) as a function of Ta concentration (
x
) at room
temperature and 50Hz.
WPNL2204
Grain orientation and electrical properties of bismuth 837
temperature to avoid thermal breakdown or damage during the poling process.
The empirical data show that the Mn-dopant is very effective in reducing
conductivity at high temperatures.
Specimens for piezoelectric and pyroelectric measurements were poled in
a stirred silicone oil. Poling conditions of applied field, E
p
, temperature, T
p
,
and time, t
p
, are about 5–30kV/mm, 150–200°C and 1–15min, respectively.
Piezoelectric properties were measured by means of a resonance–antiresonance
method on the basis of IEEE standards using an impedance analyzer (YHP
4192A and 4194A). The electromechanical coupling factor, k
33
, was calculated
from the resonance and antiresonance frequencies. The free permittivity,
ε
33
T
, and the loss tangent, tan δ
33
, were determined from the capacitance
measurement at 1 or 10kHz of the poled specimen. The piezoelectric strain
constants, d
ij
, the piezoelectric voltage constants, g
ij
, and the elastic constants,
s
jj
E
, were calculated from the coupling factor, k
ij
, the free permittivity,
ε
ii
T
,
the frequency constant, N
ij
, and the measured density, ρ
o
.
Figure 27.13 shows electromechanical coupling factors, k
33
and k
31
, of the
longitudinal and the transverse modes, along with the anisotropy, k
33
/k
31
, in
the coupling factor k of the NCBT (OF) system as a function of Ca concentration
(x) in mol. The k
33
shows a peak at x = 0.05, corresponding to the maximum
of ε
s
(at T
c
), while the k
31
has a minimum value at this composition, resulting
in a high value for the anisotropy, k
33
/k
31
. This composition (x = 0.05) seems
Coupling factors
k
33
,
k
31
(%)
18
16
14
12
10
8
6
4
2
0
Anisotropy in
k
,
k
33
/
k
31
8
7
6
5
4
3
2
1
0 0.1 0.2 0.3
Ca (mol) (
x
)
NCBT system
(OF)
k
33
k
31
k
33
/
k
31
27.13
Electromechanical coupling factors,
k
33
and
k
31
, for each
vibration mode and the anisotropy,
k
33
/
k
31
, in the
k
of the NCBT
system (OF) as a function of Ca mol (
x
).
WPNL2204
Handbook of dielectric, piezoelectric and ferroelectric materials838
to be the most suitable for piezoelectric properties.
Since the grain orientation effects on the piezo- and pyroelectric properties
by the HF technique give almost proportional enhancements to those of non-
oriented (OF) samples, the preparation of grain-oriented (HF) samples was
made only for the composition with 5 mol% Ca concentration (x = 0.05),
which seems to be the most favourable for piezoelectric and pyroelectric
activities (Fig. 27.13). The HF samples were almost smoothly deformed at
temperatures of 1100–1200 °C. The grain orientation factor, F, of the HF
ceramics is more than 90% and the values of the respective samples are
given in Table 27.1.
Figure 27.14 shows the coupling factors, k
33
and k
31
, of the Mn-doped
NCBT-5 (+Mn(wt%)) (HF and OF) as a function of Mn doping concentration
in wt%. The k
33
of the HF sample has a maximum value of about 0.4 at 0.2
wt% of Mn. On the other hand, the k
31
of the HF or the OF sample shows low
values of about 0.03 or less. As a result, the anisotropy, k
33
/k
31
, in the coupling
factor k of the HF NCBT-5 + Mn(0.2) reaches about 17, which is three or
more times larger than that of the non-oriented (OF) samples or the usual
PZT piezoelectric ceramics.
Table 27.1 gives typical values of the elastic, piezoelectric, and dielectric
(EPD) constants of the NCBT+Mn ceramics, comparing grain-oriented (HF)
samples with non-oriented (OF) ones. The T
c
is higher than 660°C. The
ε
33
T
is one-third of that of the conventional PZT ceramics. The values of k
33
, d
33
,
or g
33
of the grain-oriented (HF) ceramics are more than two times as large
as that of non-oriented (OF) ceramics, while their values of the (31) mode
show few changes. The large anisotropy, k
33
/k
31
or d
33
/d
31
, was enhanced by
the grain orientation. This means that the HF NCBT ceramics have a larger
d
h
g
h
(= (d
33
– 2d
31
)(g
33
– 2g
31
)) constant than that of the OF ones or the
Coupling factor
k
(%)
50
40
30
20
10
0
0.0 0.1 0.2 0.3 0.4 0.5
+ Mn (wt%)
k
33
(HF)
k
33
(OF)
k
31
(HF)
k
31
(OF)
NCBT–5
27.14
Coupling factors,
k
33
and
k
31
, of the NCBT-5 (HF and OF) as a
function of Mn doping concentration (wt%).
WPNL2204
Grain orientation and electrical properties of bismuth 839
conventional PZT ceramics. Therefore, these piezoceramic materials are
preferable for the hydrophone application at high temperatures, or for high-
frequency resonators.
The high mechanical quality factor, Q
m
, was obtained for BLSF ceramics
in some previous reports. For example, Nanao et al. [35] and Shibata et al.
[36] reported that the Q
m
shows 9000 in thickness (t)-mode for Bi
3
TiNbO
9
–
BaBi
2
Nb
2
O
9
solid solution and 11000 in planar (p)-mode for SrBi
2
Ta
2
O
9
–
CaBi
2
Ta
2
O
9
solid solution, respectively. The common features of these reports
are that the end members of these systems, Bi
3
TiNbO
9
and CaBi
2
Ta
2
O
9
,
have a very high T
c
above 800°C. These data suggest the possibility of high
Q
m
can be obtained by BLSF materials with high T
c
. By this concept, the
piezoelectric properties of Bi
3
TiTaO
9
(BTT) (m = 2) (SBTT2(1)) based solid
solution systems such as SBTT2 and SBTT3 with high Curie temperatures
seem to have high Q
m
values.
About the SBTT2 system, the T
c
of the SBT (SBTT2(2)) ceramic is
280°C and becomes higher with the increasing amount of modified BTT so
that the T
c
is higher than 900°C. The Q
m
and k
p
were enhanced with the
maximum value of 9000 and 0.12, respectively, on the SBTT2 (1.375) with
poling conditions of E
p
= 7–10kV/mm, T
p
= 250°C, and t
p
= 7min. On the
other hand, SBTT2 (1.25) with the poling condition of T
p
= 300°C shows the
maximum Q
m
of 13500 in the (p)-mode. This value is extremely high in
usual piezoelectric ceramics. Figure 27.15 shows the frequency dependence
of impedance, Z (magnitude |Z|, and phase θ), of (p)-, (33)- and (15)-vibration
modes for the SBTT2 (1.25) ceramic. Using the same poling conditions, Q
m
values of (33) and (15) modes for SBTT2 (1.25) were about 8800 and 6000,
respectively. The Q
m
of SBTT2 ceramic is higher than 6000. It is thought
that high Q
m
of SBTT2 causes the high T
c
and large E
c
shown in Figs. 27.6
and 27.12, respectively. Temperature coefficients of the resonance frequency,
TC-f
r
, of SBTT2 (1.25) were –82 ppm/°C for (33) mode and –97 ppm/°C for
(15) mode, respectively.
Table 27.2 summarizes the piezoelectric properties of OF and HF SBTT
ceramics. The orientation factor, F
i
of the SBTT3 (0.3) ceramic is 70% which
is relatively low. The k
33
value of the HF SBTT3 (0.3) ceramic is 0.37. This
value is about three times larger than that of the non-oriented sample. Comparing
with k
33
value between the HF BIT and SBTT3 (0.3) ceramic, the k
33
of SBTT3
(0.3) shows larger than that of BIT. It is thought that
these results are caused by the change of the resistivity. In other words, through
the poling treatment, the saturated k
33
value is not observed on
the BIT ceramic because of electrical breakdown in this study. The
piezoelectric constant, d
33
, of the HF SBTT3 (0.3) ceramic shows
45.3pC/N. This d
33
is relatively large in the BLSF and is larger than that of the
HF BIT ceramic. If the saturated k
33
can be obtained on the BIT ceramic, the
k
33
must be larger than that of SBTT3 (0.3) ceramic. Poling treatments of
WPNL2204