Zuo-Guang. Ye Advanced Dielectric Piezoelectric and Ferroelectric Materials: Synthesis, Characterisation and Applications
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Handbook of dielectric, piezoelectric and ferroelectric materials350
domains. However, for E ≥ 30kV/cm spot-like domains that do not exhibit
extinction at 0° appear in the domain matrix as shown in the inset of Fig.
12.12(e). These spot-like domains exhibit extinction at angles within a few
degrees of 20°, indicating M phase. After the E field was removed (Fig.
12.12f), domains exhibit very different structures compared with the domains
in the beginning at E = 0 kV/cm, showing a hysteretic poling process, in
agreement with the hysteresis loop shown in Fig. 12.13. Note that the polarizing
microscope results also aid in interpreting the hysteresis loop in Fig. 12.13.
The loop appears saturated, so one might think that as the field along [001]
is reversed, a single [001] domain is switched into a single [00
1
] domain.
Alternatively, one might think that the crystal converts from the four R
100 µm
<110>
(a) 0kV/cm
(d) 28kV/cm
(b) 4kV/cm
(e) 44kV/cm
(c) 17kV/cm
(f) 0kV/cm
12.12
E-field-dependent domain micrographs taken with P/A: 45°
(except for insets) at room temperature for dc
E
field applied
perpendicular to the (001)-cut plane of the PMN–24%PT crystal. P/A:
0° was aligned with the <110> sample edge. ‘N’ indicates the area
without ITO films (adapted from Chien
et al
., 2004). A color version
of the figure can be found in Chien
et al
. (2004).
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Electric field-induced domain structures and phase transitions 351
domains with a positive polarization component along [001] to the four
domains with a negative component along [001]. From the domain pictures
in Fig. 12.12 it is apparent that the hysteresis loop represents only incomplete
switching.
12.5.2 (001)-cut PMN–33%PT crystal
Figure 12.14 shows the domain micrographs taken with various P/A angles
at room temperature for various E-field strengths while a dc E field was
applied along [001] in a (001)-cut PMN–33%PT single crystal. The domain
micrograph taken at P/A: 0° appears the same as that taken at P/A:90°. At E
= 0 kV/cm (Fig. 12.14a), the domain matrix mostly exhibits extinction at
P/A = 0° with respect to the <110> direction, indicating an R phase according
to the optical extinction pattern discussed in Section 12.3. If O or T phase
domains exist, there will also be extinction at P/A: 45°. However, no extinction
was observed at P/A: 45°. The domain matrix has no obvious changes until
4.1–4.8kV/cm as shown in Fig. 12.14(b). The domain matrix mostly still
retains R phase, but T
001
and M/T phases are induced near the cracking area,
as indicated by the arrow in Fig. 12.14(b). The T
001
phase domain exhibits
extinction at every P/A angle (i.e. total optical extinction), whereas the M/T
phase domain exhibits extinction angles at ~15–65°. M/T represents the
coexistence of M and T phases with more M phase than T phase domains.
295K
360K
380K
415K
–20
–10
0
20
10
–8 –6
–4 –2 02468
E
(kV/cm)
P
(µC/cm
2
)
12.13
The hysteresis loops of polarization vs. E field for various
temperatures in the (001)-cut PMN–24%PT crystal.
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Handbook of dielectric, piezoelectric and ferroelectric materials352
Note that the coercive field E
C
for the PMN–33%PT crystal is about 3kV/cm
as given in Fig. 12.15. As the field increases to 11kV/cm (Fig. 12.14c), the
T
001
phase domain significantly expands as crossed stripes along [100] and
[010] from the cracking area. Some of the R phase domains have also
transformed to M and T phase with various non-zero-degree extinction angles,
such as 5–15°, 20–50°, and 50–75°. However, a small portion of the domain
E
<110>
<110>
A
P
P/A: θ°
(d)
E
= 34kV/cm
(c)
E
= 11kV/cm
(b)
E
= 4.8kV/cm
(a)
E
= 0kV/cm
12.14
Domain micrographs taken with P/A angle from 0° to 90° in
(001)-cut PMN–33%PT crystal at room temperature (a) under no field,
and under the E-field strengths of (b) 4.8 kV/cm, (c) 11kV/cm, and (d)
34 kV/cm applied perpendicular to the paper. The boundaries of ITO
electrodes are indicated by the dashed lines. ‘S’ indicates silver
paste.
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Electric field-induced domain structures and phase transitions 353
matrix circled in Fig. 12.14(c) still remains in the R phase. With increasing
E field, this E-field-induced transition is continuously evidenced by the
expansion of the T
001
phase domain shown as a black area of the domain
matrix. At E = 34kV/cm, most of the domain matrix becomes macroscopic
T
001
phase domain except for some small R, T, and M phase domains with
extinction angles of 0°, 45°, and ~15–45° as shown in Fig. 12.14(d). In
addition, a few domains exhibiting no extinction at any P/A angle are embedded
in the T
001
domain matrix, perhaps due to crystal defects and local strain
caused by underlying M phase distortions with various different orientations.
In brief, the E-field-dependent phase transition sequences at room temperature
in the (001)-cut PMN–33%PT include R→T
001
, R→M→T
001
, R→T→T
001
,
and R→M→T→T
001
. With a fixed P/A angle (Fig. 12.16), the E-field-induced
transition is continuously evidenced by the expansion of the T
001
phase
domain as the E field increases. The (001)-cut PMN–33%PT and PMN–
24%PT crystals show similar behavior in the hysteresis loop of polarization
vs. E field (Fig. 12.15). However, the polarizing light micrographs in Fig.
12.12 and 12.16 exhibit some visual difference between the two crystals in
the formation of the E-field-induced T
100
phase domains.
12.5.3 (001)-cut PMN–40%PT crystal
Figure 12.17 shows the E-field-dependent domain structures taken with P/A:
45° for the PMN–40%PT crystal while a dc E field was applied along [001]
at room temperature. As the P/A reading 0° was aligned with the [010]
sample edge, every optical extinction angle expressed in the picture is the
(001) 33%
(001) 24%
–20
–15
–20–10
–20–5
0
5
10
15
20
–8 –6 –4 –2 0 2 4 6 8
E
(kV/cm)
P
(µC/cm
2
)
12.15
Hysteresis loops of polarization vs.
E
field for (001)-cut PMN–
24%PT and PMN–33%PT crystals.
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Handbook of dielectric, piezoelectric and ferroelectric materials354
12.16
E
-field-dependent domain micrographs taken with P/A: 45° at
room temperature for dc
E
field applied perpendicular to the (001)-
cut plane of the PMN–33%PT crystal. ‘S’ indicates silver paste. ‘C’
and ‘C
E
’ indicate cracks caused by polishing and E field poling,
respectively (adapted from Chien
et al
., 2006). A color version of the
figure can be found in Chien
et al
. (2006).
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Electric field-induced domain structures and phase transitions 355
angle between one of the P/A pair axes and [010]. ‘C’ indicates a crack
caused by the polishing and E-field poling process. At E = 0 kV/cm (Figure
12.17a), the domain matrix mostly exhibits an extinction at 0° and some at
non-zero degrees such as 18° and 82° with respect to the [010] direction,
indicating the coexistence of a dominant T phase with polarizations P along
the [100] and [010] axes and some minor M phase. As the E field increases,
the domain matrix does not evidently change until 11kV/cm as seen in Fig.
100µm
[010]
12.17
E-field-dependent domain micrographs taken with P/A: 45° at
room temperature for dc
E
field applied perpendicular to the (001)-
cut plane of the PMN–40%PT crystal. P/A: 0° was aligned with [010]
sample edge. ‘C’ indicates microcracking (adapted from Chien
et al
.,
2005a). A color version of the figure can be found in Chien
et al
.
(2005a).
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Handbook of dielectric, piezoelectric and ferroelectric materials356
12.17(b). At E = 11kV/cm, the domain structure displays the T
001
domain
with polarization P along the [001] axis, which is associated with optical
extinction at every orientation of the crossed P/A pair (i.e. total optical
extinction), and some M domains with various non-zero-degree extinction
angles, such as 12°, 68°, 80°, and 82° at the expense of the T phase domains.
This indicates that some domains have transformed to T
001
and M phase.
With increasing E field, more of the M phase domains have been poled to the
T
001
domain as shown in the dark area in Fig. 12.17(c), and the other M
domains have changed their polarization orientations with various non-zero-
degree extinction angles, such as 12° and 16°. Most of the domain matrix
exhibits total optical extinction (i.e. the T
001
phase domains) except a stripe
oriented along [010] as the E field reaches 25kV/cm (Fig. 12.17d). The
entire crystal becomes T
001
monodomain near E = 33 kV/cm as seen in Fig.
12.17(e). After the E field was removed (Fig. 12.17f), the domain structure
did not return to the broad T
100
and T
010
domains separated by the 90°
domain walls as shown in Fig. 12.17(a). However, the extinction pattern is
in agreement with T microdomains with polarizations P along the [100] or
[010] axes.
12.5.4 Summary for various crystal cuts and
compositions
In the (001)-cut PMN–24%PT crystal, an R→T
001
phase transition is induced
near E = 4kV/cm through M
A
phase domains as E field increases along [001]
at room temperature, i.e. R→M
A
→T
001
. In the (001) PMN–40%PT crystal,
the T
001
phase domains are induced near E = 11kV/cm at room temperature
by the process of polarization rotation of T→M→T
001
, and this T
001
phase
expands through the whole crystal as the E field increases further. Similarly,
in the (001)-cut PMN–33%PT crystal the T
001
phase domains are induced
near E = 4.1kV/cm at room temperature and expand significantly at E =
11 kV/cm by various phase transition sequences R→T
001
, R→M→T
001
,
R→T→T
001
, and R→M→T→T
001
. Therefore, the intermediate M phases
play an essential role in bridging higher symmetries while the E-field induced
transitions are taking place in the PMN–PT crystals.
The E-field-induced phase results at room temperature differ for the three
crystals with various Ti content, while a high dc E field is applied across the
crystal cut plane (001). The (001)-cut PMN–40%PT crystal becomes T
001
monodomain near E = 33kV/cm. On the other hand, the (001)-cut PMN–
24%PT and (001)-cut PMN–33%PT crystals cannot reach a T
001
monodomain
under the maximum E field of 44 and 34kV/cm, respectively. However, the
(111)-cut PMN–33%PT crystal gradually reaches an R
111
monodomain at E
= 12kV/cm applied along [111] at room temperature (Tu et al., 2003b).
Therefore, a monodomain with the orientation along the poling field was not
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Electric field-induced domain structures and phase transitions 357
always obtained under the maximum E-field strength in every crystal at room
temperature as expected. The E-field-induced monodomain can be achieved
in the PMNT crystals if the dc poling field is along the polar axes of the phase
favored by the temperature, such as the (111)-cut PMN–33%PT and (001)-
cut PMN–40%PT crystals. For instance, T polar directions are favored at
room temperature in the (001)-cut PMN–40%PT so that less E-field poling
strength is needed to induce the T phase domains with the field applied along
[001]. On the other hand, the T phase is not favored at room temperature in
the (001)-cut PMN–24%PT so that it takes higher E-field poling strength to
induce the T phase domains. By comparison with the results for (001)-cut
PMN–x%PT (x = 24, 33, and 40) and (111)-cut PMN–33%PT crystals, it was
found that whether or not a monodomain can be induced by a dc electric field
strongly depends on crystallographic orientation, PT content, and temperature.
More details of the results and discussion were reported for a (001)-cut
PMN–24%PT crystal (Chien et al., 2004), (111)-cut PMN-33%PT crystals
(Tu et al., 2003a,b), a (001)-cut PMN–33%PT crystal (Chien et al., 2006),
and a (001)-cut PMN–40%PT crystal (Chien et al., 2005a).
12.5.5 Microcracking in PMN–PT single crystals
Microcracking caused by a dc E-field poling process was observed in the
PMN–33%PT and PMN–40%PT crystals with a dc E field applied along
[001] at room temperature. However, no microcracking was found in the
PMN–24%PT crystal (Fig. 12.12) under E = 44kV/cm applied along [001]
and the PMN–33%PT with E field applied along [111] (Tu et al., 2003b). In
the PMN–33%PT crystal with a dc E field applied along [001] as shown in
Fig. 12.16, the microcracking indicated by ‘C
E
’ starts to develop at E ~
4.8kV/cm along [100] (or [010]) from the pre-existing crack ‘C’. The crack
is enlarged by increasing field strength. At E = 34kV/cm, the crack reaches
the sample edge and the crystal breaks into two pieces. The crystal still
maintains the same R, T, T
001
, and M phase domains as before it breaks (Fig.
12.16f). In the PMN–40%PT crystal (Fig. 12.17) with a dc E field applied
along [001], the microcracking starts to develop at ~12.5kV/cm along [010]
and the cracks tend to develop along [100] (or [010]), which is the growth
direction of the T
001
phase domain that is being induced by a dc E field
applied along [001]. The crack is also enlarged by increasing field strength.
12.6 Field-poling effect on optical properties
Wavelength-dependent optical transmission from 0.3 to 2.1
µ
m given in Fig.
12.18 for a (001)-cut PMN–35%PT single crystal exhibits little absorption
before reaching the cut-off wavelength λ ≅ 0.4
µ
m, which is the same with
and without a prior E-field poling. The same cut-off wavelength λ ≅ 0.4
µ
m
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Handbook of dielectric, piezoelectric and ferroelectric materials358
was also observed in different PMN–PT crystals with different orientations
and Ti contents. Figure 12.18 is shows that a prior poling process can enhance
the optical transmission by about 20%, probably because of reduction of
internal reflection by domain walls and strains. The cut-off at λ ≅ 0.4
µ
m
implies an average electronic energy gap of about 3.0eV.
Figure 12.19 shows ordinary n
o
and extraordinary n
e
refractive indices
measured at room temperature without poling and with a prior poling (E =
5.4kV/cm). In the prior poling process, the crystal was poled at room
temperature along a <010> direction which is the optical axis of the uniaxial
T symmetry. After a prior poling at E = 5.4kV/cm, the crystal shows a
noticeable ‘negative’ uniaxial birefringence and n
e
– n
o
is about –0.0129 at
λ = 0.790
µ
m. The birefringence does not increase noticeably even with a
higher poling field (E > 5.4 kV/cm). For instance, after poling at E = 12kV/
cm, the refractive indices are n
o
= 2.5025 and n
e
= 2.4908 at λ = 1.323
µ
m,
and n
o
= 2.5583 and n
e
= 2.5466 at λ = 0.790
µ
m. The Cauchy equations
obtained from fitting data for the sample poled at 5.4kV/cm are n
0
(λ) =
2.4716 + 0.0483/λ
2
+ 0.0029/λ
4
and n
e
(λ) = 2.4606 + 0.0467/λ
2
+ 0.0032/λ
4
,
where
λ
is in
µ
m.
Without poling, the crystal shows very small birefringence |n
o
– n
e
| which
is less than 0.004 at λ = 0.790
µ
m. The birefringence is non-zero because the
light goes through a few domains of different size, so the various domains do
not completely cancel the birefringence. Different unpoled crystals of the
same composition can be expected to show different residual birefringence
values. The Cauchy equations obtained from fitting measured data for this
particular unpoled sample are n
o
(λ) = 2.4649 + 0.0512/λ
2
+ 0.0023/λ
4
and
n
e
(λ) = 2.4720 + 0.0488/λ
2
+ 0.0022/λ
4
.
PZN–10%PT
without poling
With prior poling at
E
= 5.4kV/cm
Without poling
PMN–35%PT
Wavelength (µm)
2.01.81.61.41.21.00.80.60.4
100
80
60
40
20
0
Optical transmission (%)
12.18
Optical transmission without poling and with prior poling at
E
= 5.4°kV/cm for a (001)-cut PMN–35%PT crystal, and without poling
for a (001)-cut PZN–10%PT crystal.
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Electric field-induced domain structures and phase transitions 359
The calculation of phase-matching angle for second harmonic generation
shows that the phase-matching condition does not exist for poling E field
<12kV/cm. More optical properties of transmission and refractive indices
were studied in PMN–PT (Tu et al., 2005), PZN–PT (Tu et al., 2006c) and
PIN–PT (Tu et al., 2006b,d) crystals.
12.7 Relation of results to Landau free energy
From the foregoing results, it is evident that PMN–PT crystals near the
morphotropic phase boundary composition are delicately balanced among
several possible phases. In fact, small distortions from the cubic parent
phase can result in the crystal structure being in six of the seven crystal
systems. Of these seven, only the hexagonal system is ruled out, and the
triclinic system is yet to be seen.
As seen from Figs 12.2–12.4, the spontaneous polarization vector P can
point in a variety of directions for these phases. There are six directions for
the T domains, eight for the R domains, and 12 for the O domains, totaling
12.19
Refractive indices measured at room temperature for a (001)-
cut PMN–35%PT crystal (adapted from Tu
et al
., 2005).
n
e
n
o
n
e
n
o
Error: ± 0.002
(001) PMN–35%PT
(a) Without poling
(b) With prior
E
-field poling
(
E
= 5.4kV/cm)
Wavelength (µm)
0.4 0.6 0.8 1.0 1.2 1.4
Refractive indices
2.7
2.6
2.5
2.7
2.6
2.5
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