Electric-field-induced and 
temperature­induced phase transitions in 
high-strain ferroelectric 
Pb(Mg1/3Nb2/3)0.67Ti0.33O3 single crystal
Authors: R. R. Chien, C.-S. Tu, V. Hugo Schmidt, and 
F.-T. Wang
This is an author-created, un-copyedited version of an article published in Journal of Physics: 
Condensed Matter. IOP Publishing Ltd is not responsible for any errors or omissions in this 
version of the manuscript or any version derived from it. The Version of Record is available online 
at https://dx.doi.org/10.1088/0953-8984/18/35/018.
R.R. Chien, C.-S. Tu, V.H. Schmidt, and F.-T. Wang, “Electric-field-induced and 
temperature­induced phase transitions in high-strain ferroelectric Pb(Mg1/3Nb2/3)0.67Ti0.33O3 
single crystal,” Journal of Physics: Condensed Matter 18, 8337-8344 (2006). doi: 
10.1088/0953-8984/18/35/018.
Made available through Montana State University’s ScholarWorks 
scholarworks.montana.edu 
Electric-field-induced and temperature-induced phase
transitions in high-strain ferroelectric
Pb(Mg1/3Nb2/3)0.67Ti0.33O3 single crystal
R R Chien1, Chi-Shun Tu2, V Hugo  Schmidt1 and F-T Wang2
1 Department of Physics, Montana State University, Bozeman, MT 59717, USA
2 Graduate Institute of Applied Science and Engineering, Fu Jen University, Taipei 242, Taiwan
Abstract
This work is to study electric (E)-field-induced and temperature-induced phase 
transitions in (001)-cut Pb(Mg1/3Nb2/3)0.67Ti0.33O3 (PMNT33%) single crystal, 
which are critical concerns for piezoelectric applications. Dielectric properties 
and domain structures (by polarizing microscope) are measured as functions of 
temperature and E field. The hysteresis loop of the polarization versus E field 
at room temperature is also measured. Without any E-field application, upon 
heating a first-order-type phase transition sequence rhombohedral
(R) → rhombohedral/monoclinic/[001]tetragonal (R/M/T001) → cubic (C) 
takes place near 350 and 430 K, respectively. Under a dc E-field application 
along [001] at room temperature, [001] tetragonal (T001) phase domains are 
induced by various phase transition sequences, i.e. R → T001, R  → M → 
T001, R → T → T001, and R → M → T → T001, as the  E-field strength 
increases. In addition, E-field-induced microcracking is observed in this work.
(Some figures in this article are in colour only in the electronic version)
1. Introduction
Relaxor-based ferroelectric single crystals of Pb(Mg1/3Nb2/3)1−x TixO3 (PMNTx) and
Pb(Zn1/3Nb2/3)1−xTix O3 (PZNTx), which have a morphotropic phase boundary (MPB)
between the R and T phases, have attracted much attention due to their high performance
in piezoelectric-related applications [1–6]. These crystals exhibit piezoelectric properties
about ten times better than the ceramics that are generally used, such as an extremely
large electromechanical coupling factor k33 (>94%), ultrahigh piezoelectric coefficients
(>2500 pC N−1), a large strain level (up to ∼1.7%), and low hysteresis [7–9]. An E-
field poling is usually performed on these materials to enhance the piezoelectric performance
before application. The ultrahigh piezoelectric response is attributed to polarization rotation
12
3
Temperature (K)
ε '
 
(x
10
4 )
150 200 250 300 350 400 450
0.2
0.4
0.6
ε '
'  
(x
10
3 )
200 300 400
1
2
3
1/
ε '
 
(x
10
-
4 )
T  (K )
Figure 1. Temperature-dependent dielectric permittivity measured at 10 kHz upon heating and
cooling in the unpoled (001)-cut PMNT33% crystal. The inset is the reciprocal of ε′.
induced by an external dc E field between the T and R phases through intermediate (M)
or orthorhombic (O) symmetries [10]. It has generated great interest in investigating phase
(structural) transitions near the MPB under the application of thermal, E-field, and stress to
understand the underlying mechanism of the piezoelectric properties [11].
In this report, we study E-field-induced and temperature-induced phase transitions in
a (001)-cut PMNT33% single crystal by dielectric permittivity and domain observations
with polarizing microscopy. The hysteresis loop of polarization versus E field was also
measured at room temperature (RT). By using relations of crystallographic symmetry and
optical extinction, polarizing light microscopy provides a real-time direct observation of the
polarization orientations in ferroelectric domains and their corresponding crystal phases.
Physical properties of PMNTx under E-field application, such as the phase (structural
symmetry) nature, depends strongly on titanium content, crystallographic orientation, strength
of the external poling E field, and temperature [11–14]. In order to understand the physical
origin of the E-field-induced phase transitions, in section 3 we shall compare this result
with our previous results from PMNTx crystals with various crystallographic orientation and
titanium content, i.e. (001)-cut PMNT24%, (111)-cut PMNT33%, and (001)-cut PMNT40%
crystals [15–17].
2. Experimental procedure
The lead magnesium niobate–lead titanate crystal PMNT33% was grown using a modified
Bridgman method and was cut perpendicular to a 〈001〉 direction after aligning it by x-ray
diffraction. The Ti concentration (x%) was determined from x = [Tm (◦C) + 10]/5, where
Tm is the dielectric maximum temperature obtained upon heating without E-field poling, as
shown in figure 1 [13]. Before any measurement described below, the sample was annealed
above 200 ◦C. For dielectric measurements, a Wayne–Kerr Precision Analyzer PMA3260A
with four-lead connections was used to obtain the real (ε′) and imaginary (ε′′) parts of dielectric
permittivity. A Janis CCS-450 cold-head was used with a Lakeshore 340 temperature controller.
The sample dimensions are 7.8×3.1×0.6 mm3, and gold electrodes were deposited on sample
(001) surfaces by dc sputtering. Two processes were used in the dielectric measurements,
called ‘zero-field-heated’ (ZFH) and ‘zero-field-cooled’ (ZFC), in which the data were taken
upon heating and cooling, respectively, without any E-field poling. The hysteresis loop of the
polarization versus E field was taken at RT by using a Sawyer–Tower circuit at f = 46 Hz.
The domain observations as functions of temperature and E field were made by using a
Linkam THMS600 heating/cooling stage mounted on a Nikon E600POL polarizing microscope
with a 0◦/90◦ crossed polarizer/analyser (P/A) pair. The detailed experimental configuration
can be found in [18]. The sample thickness is about 65 µm. Transparent conductive films of
indium tin oxide (ITO) were deposited on sample (001) surfaces by dc sputtering. The 〈110〉
orientation of the sample edge was determined by x-ray diffraction and aligned with one of the
crossed P/A:0◦ axes so that the extinction angles shown in all domain micrographs are measured
from 〈110〉. In E-field-dependent domain observation, a dc E field was applied along [001]
at RT.
3. Results and discussion
3.1. Temperature-dependent dielectric permittivity
Figure 1 shows the temperature-dependent real part ε′ and imaginary part ε′′ of the dielectric
permittivity at measuring frequency f = 10 kHz from ZFH and ZFC, respectively. The
maximum temperatures (Tm) of ε′ (ZFH) and ε′ (ZFC) occur at 425 and 420 K, respectively.
Obvious thermal hystereses are observed in the temperature regions ∼250–400 K and
∼415–430 K, respectively. As shown in the inset of figure 1, two steep dips in the reciprocal
of ε′ are seen at 340 (320 K) and 425 (420 K) for ZFH (ZFC). Both steep phenomena and
thermal hystereses imply two first-order-type transitions near 340 K (320 K) and 425 K (420 K),
respectively, upon heating (cooling).
3.2. Principle of polarizing microscopy
Through measuring optical extinction angles from polarizing microscopy, various
crystallographic symmetries (or phases) can be determined for most cases. For interpreting
domain structures obtained from polarizing microscopy, a review of principles of optical
extinction for the (001)-cut crystal can be found in [19]. Figure 2 shows the (001)-cut projection
with all four sides folded out. The inner square outlines the front face of the cube.
In this study, the extinction angles are measured with regard to 〈110〉, as shown in figure 2,
in which the solid crosses within the symbols represent the orientation of the extinction. Thus,
R phase domains represented by triangles with solid crosses in figure 2 have extinction at 0◦
(or 90◦). T phase domains represented by squares with solid crosses have extinction at 45◦. T
phase domains with polarization P along the [001] axis represented by the solid black square
in the centre have extinction at every orientation of the crossed P/A pair and will be written
as ‘T001’ in the following discussion. The O phase domains represented by circles with solid
crosses have extinctions at 0◦ (or 90◦) or 45◦, whereas R domains only give extinctions at 0◦.
Thus, the (001)-cut shown in figure 2 clearly distinguishes R phases from T phases by the 45◦
difference in extinction angle. Any extinctions at angles other than 0◦ (or 90◦) and 45◦ must be
from the M or triclinic (Tri) phase domains. Note that all the phases except the Tri phase have
Figure 2. Relation between the optical extinction orientations corresponding to the ferroelectric
polarization directions for various phases and domains projected on the (001) plane. Dashed, dash–
dotted, and dotted lines represent MA -, MB -, and MC-type monoclinic phase domains, respectively.
The definition of MA , MB , and MC phases can be found in [11] and [21].
Figure 3. Temperature-dependent domain structures without any E-field poling. Domain
micrographs taken at various temperatures with P/A: 0◦ for the top row, and P/A: 45◦ for the bottom
row.
been reported in various PMNT crystals. Our large observed variation in extinction angle with
E field or temperature indicates M domains whose polarization P can vary with E field through
a large angle, whereas the polarization directions are nearly fixed for R, T, or O domains as the
E field or temperature varies.
3.3. Thermal-induced phase transition
What is the temperature-dependent phase transition in the unpoled PMNT33% crystal? In
figure 3, domain micrographs taken at various temperatures with P/A angle = 0◦ are shown
in the top row and P/A angle = 45◦ are shown in the bottom row. As shown in figure 3(a),
the domain matrix at RT (298 K) mostly exhibits extinction at 0◦ with respect to the 〈110〉
direction, indicating an R phase. If O or T phase domains exist, there will also be extinction
Figure 4. Domain micrographs taken with a P/A of 45◦ (except the insets) at RT for a value of
E of (a) 0 kV cm−1, (b) 4.8 kV cm−1, (c) 11 kV cm−1, (d) 17 kV cm−1, (e) 28 kV cm−1, (f)
34 kV cm−1, (g) 34 kV cm−1, and (h) 0 kV cm−1 (right after the E field is removed). The area
in black indicated by ‘S’ is the silver paste and the wire. The dashed lines show the ITO thin-film
boundaries. ‘T001’ indicates the [001] tetragonal phase domain.
at P/A: 45◦. However, no extinction was observed at P/A: 45◦, as shown in figure 3(b). As
temperature increases to 343 K, some of the domain matrix exhibits a continuous change in
birefringence, shown as the brighter area in figure 3(c), which corresponds to an M phase.
It indicates that the crystal has the coexistence of a dominant R phase and some minor M
phase domains, i.e. R(M). Near 350 K, the domain matrix shows an apparent change, which
is consistent with the dielectric anomalies in figure 1. Some stripe-like domains display total
extinction at all P/A angles, which indicates a T001 phase, as shown in figure 3(d). The M phase
domain of the crystal at the corners exhibits extinctions in the ranges 10◦–15◦ and 75◦–80◦. As
the temperature increases further, the domain area and the range of extinction angle for the M
phase expand, and the T001 phase domains also expand, as seen in figures 3(e) and (f). Near
430 K, the C phase begins to appear as stripes with a total extinction at every P/A angle besides
the T001 phase domains. In addition, a small portion of the domain matrix exhibits extinction
angles of 55◦–75◦ and 30◦–50◦, as circled in figure 3(g), indicating the M phase. Near 433 K,
the whole crystal becomes cubic phase. In brief, an R → R(M) → R/M/T001 → C phase
transition sequence takes place near 343, 350 and 430 K upon heating, respectively. R(M)
indicates the coexistence of a dominant R phase and some minor M phase domains. R/M/T001
indicates the coexistence of R, M, and T001 phase domains.
3.4. E-field-induced phase transition and microcracking
The E-field-dependent domain structures at RT, as shown in figure 4, are taken at a P/A of
45◦ while a dc E field is applied along [001]. At E = 0 kV cm−1 (figure 4(a)), the domain
matrix exhibits an R phase with extinction at a P/A of 0◦, as shown in the inset. As the E field
increases, the domain matrix does not change apparently until 4.1–4.8 kV cm−1, as illustrated
in figure 4(b). The domain matrix mostly still retains the R phase (inset of figure 4(b)), but
T001 and M/T phases were induced near the cracking area and exhibit extinctions at every
P/A angle and in the range 15◦–65◦, respectively. M/T represents the coexistence of M and
T phases with more M phase than T phase domains. Note that the coercive field EC for this
(001)-cut crystal is about 3 kV cm−1, as given in figure 5. As the field increases to 11 kV cm−1
(figure 4(c)), the T001 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
-12 -8 -4 0 4 8 12
-40
-30
-20
-10
0
10
20
30
40(001)33%
(111)33%
(001)24%
P (µC/cm2)
E (kV/cm)
Figure 5. Hysteresis loops of polarization versus E field obtained at RT from (001)-cut PMNT33%,
(111)-cut PMNT33%, and (001)-cut PMNT24% crystals. The results of (001)-cut PMNT24% and
(111)-cut PMNT33% are inserted from [15] and [16], respectively, for comparison.
T phases with various nonzero-degree extinction angles, such as 5◦–15◦, 20◦–50◦, and 50◦–
75◦. But a small portion of the domain matrix still remains in the R phase, as indicated in
figure 4(c). With increasing E field, this E-field-induced transition is continuously evidenced
by the expansion of the T001 phase domain, shown as a black area of the domain matrix in
figures 4(d)–(f). At E = 34 kV cm−1, most of the domain matrix becomes a macroscopic T001
phase domain, except for some small R, T, and M phase domains with extinction angles of 0◦,
45◦, and ∼15◦–45◦, as illustrated in figure 4(f). It is interesting that T phase domains usually
appear near the cracks. In addition, a few domains exhibiting no extinction at any P/A angle
are embedded in the T001 domain matrix, perhaps due to crystal defects and local strain caused
by underlying M phase distortions with several different orientations.
As indicated by ‘CE ’ in figure 4(b), the microcracking caused by the dc E-field poling
process starts to develop at E ∼ 4.8 kV cm−1 along [100] (or [010]) from the pre-existing
crack ‘C’ due to the polishing process. In a (001)-cut PMNT40% crystal with an E field
applied along [001], we also found that microcracks are inclined to develop along [100] (or
[010]) [17]. However, no microcracking was found in a (001)-cut PMNT24% single crystal
with E = 44 kV cm−1 applied along [001] at RT [15]. As shown in figures 4(c)–(f), the crack
is enlarged by the increasing field strength. At E = 34 kV cm−1 (figure 4(g)), the crack reaches
the sample edge and the crystal breaks into two pieces. The crystal still maintains the same R,
T, T001, and M phase domains as before it breaks (figure 4(f)). After the field is removed
(figure 4(h)), the polarizing microscope picture becomes brighter than for E = 34 kV cm−1
(figure 4(g)). The crystal does not return to an R phase, as seen originally at zero field
(figure 4(a)). Instead, the speckled appearance of the picture implies that R, T001, T, and M
phase microdomains coexist with numerous microdomains that have no extinction at any P/A
angle, which perhaps is caused by the stress exerted by local polar microdomains of M phases
with various orientations.
Figure 5 shows the polarization hysteresis behaviours versus E field at RT for (001)-cut
PMNT33% (this work), (111)-cut PMNT33%, and (001)-cut PMNT24% crystals [15, 16].
In (001)-cut PMNT33% crystal, the coercive field EC ∼= 3 kV cm−1, remanent polarization
Pr ∼= 12 µC cm−2, and spontaneous polarization PS ∼= 15 µC cm−2. The polarization
hysteresis behaviour of the (001)-cut rhombohedral PMNT24% crystal is similar to the (001)-
cut PMNT33%. The (111)-cut PMNT33% has a higher coercive field, EC ∼= 6.5 kV cm−1,
and a much larger remanent polarization Pr ∼= 30 µC cm−2, and spontaneous polarization
PS ∼= 33 µC cm−2. The ratio between PS ∼= 15 µC cm−2 measured along [001] and PS ∼=
33 µC cm−2 measured along [111] at RT is fairly close to 1/
√
3. The deviation from 1/
√
3
may come from the different electrodes of silver paste and gold thin films for the (111)-cut
and (001)-cut samples, respectively. 1/√3 is the projection fraction of the [111] rhombohedral
polarization on the [001] axis. Note that the applied E field in the hysteresis measurement of
the (001)-cut PMNT33% crystal is along [001]. This confirms that the PMNT33% crystal
is rhombohedral phase at RT. A (001)-cut tetragonal PMNTx% crystal has a much higher
coercive field, EC = 8.25 kV cm−1, and a remanent polarization Pr = 34.2 µC cm−2, where
x% = 39.4% is calculated with the formula we used for determining the Ti concentration stated
in section 2 [20]. Therefore, the polarization hysteresis behaviour of PMNT crystals depends
on the crystallographic orientation and symmetry (phase).
This (001)-cut PMNT33% crystal cannot completely reach a T001 monodomain at
E = 34 kV cm−1 applied along [001] at RT. In recent studies, a (111)-cut PMNT33%
crystal gradually reaches an R111 monodomain at E = 12 kV cm−1 applied along [111] at
RT [16]. A (001)-cut PMNT40% single crystal becomes entirely T001 monodomain under
E = 33 kV cm−1 applied along [001] [17]. However, a (001)-cut PMNT24% single crystal
cannot reach a T001 monodomain under E = 44 kV cm−1 applied along [001] at RT [15].
Therefore, a monodomain with orientation along the poling field was not always obtained
under the maximum E-field strength in every crystal at RT as expected, such as the (001)-
cut PMNT24% with E field applied along [001] [15]. 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 favoured by the temperature, such as the (111)-cut PMNT33% and (001)-cut PMNT40%
crystals [16, 17]. A similar result was reported by Zhang et al that the E-field strength for
the induced M → T phase transformation decays exponentially with increasing temperature
in PMNT33% crystals [13]. T polar directions are favoured at the higher temperature in
PMNT33% crystals, so that less E-field poling strength is needed to induce the T phase with
the field applied along [001].
What is the physical origin of the T001 phase domains induced at RT by a dc E field
applied along [001] in PMNT crystals? In the (001)-cut PMNT24% crystal, an R → T001
phase transition was induced near E = 4 kV cm−1 through MA phase domains as the E
field increases along [001] at RT, i.e. R → MA → T001 [15]. In the (001)-cut PMNT40%
crystal, the T001 phase domains were induced near E = 11 kV cm−1 at RT by the process
of polarization rotation of T → M → T001, and this T001 phase expands through the whole
crystal as the E field increases further [17]. Similarly, in this (001)-cut PMNT33% crystal
the T001 phase domains were induced near E = 4.1 kV cm−1 at RT and expand significantly
at E = 11 kV cm−1 by various phase transition sequences R → T001, R → M → T001,
R → T → T001, and R → M → T → T001.
4. Conclusions
In this unpoled (001)-cut PMNT33% sample, a first-order-type R → R/M/T001 → C phase
transition sequence takes place near 350 and 430, respectively, upon heating. Under the
E-field application along [001], the [001] tetragonal (T001) phase domains were induced by
various phase transition sequences, i.e. R → T001, R → M → T001, R → T → T001, and
R → M → T → T001. The T001 phase domains expand through the whole crystal via the M
phase with increasing E field. The intermediate M phases play an essential role in bridging
higher symmetries while the E-field-induced transitions are taking place. This confirms our
previous findings in (001)-cut PMNT24%, (111)-cut PMNT33%, and (001)-cut PMNT40%
crystals [15–17]. By comparison with our previous results in PMNTx% (x = 24%, 33%,
and 40%) [15–17], we found that whether or not a single domain can be induced by a dc E
field strongly depends on the crystal temperature, i.e. it depends on whether the polar axis of
the induced single domain is favoured by the temperature. In addition, we also found that E-
field-induced microcracks are inclined to develop along [100] (or [010]), which is the growth
direction of the T001 phase domain that is being induced by a dc E field applied along [001].
Acknowledgments
The authors would like to express their sincere thanks to Dr H Luo for the crystal. This
work was supported by US Department of Defense (DoD) Experimental Program to Stimulate
Competitive Research (EPSCoR) Grant No. N00014-02-1-0657 and National Science Council
(NSC) Grant No. 94-2112-M-030-004.
References
[1] Kuwata J, Uchino K and Nomura S 1981 Ferroelectrics 37 579
[2] Choi S W, Shrout T R, Jang S J and Bhalla A S 1989 Ferroelectrics 100 29
[3] Shrout T R, Chang Z P, Kim N and Markgraf S 1990 Ferroelectr. Lett. 12 63
[4] Noheda B 2002 Curr. Opin. Solid State Mater. Sci. 6 27–34
[5] Singh A K and Pandey D 2003 Phys. Rev. B 67 064102
[6] Shuvaeva V A, Glazer A M and Zekria D 2005 J. Phys.: Condens. Matter 17 5709
[7] Park S-E and Shrout T R 1997 J. Appl. Phys. 82 1804
[8] Park S-E and Hackenberger 2002 Curr. Opin. Solid State Mater. Sci. 6 11
[9] Han P, Yan W, Tian J, Huang H and Pan H 2005 Appl. Phys. Lett. 86 052902
[10] Fu H and Cohen R E 2000 Nature 403 281
[11] Davis M, Damjanovic D and Setter N 2006 Phys. Rev. B 73 014115
[12] Tu C-S, Chien R R, Wang F-T, Schmidt V H and Han P 2004 Phys. Rev. B 70 220103
[13] Feng Z, Luo H, Guo Y, He T and Xu H 2003 Solid State Commun. 126 347
[14] Zhang S, Luo J, Xia R, Rehrig P W, Randall C A and Shrout T R 2006 Solid State Commun. 137 16
[15] Chien R R, Schmidt V H, Tu C-S, Hung L-W and Luo H 2004 Phys. Rev. B 69 172101
[16] Tu C-S, Schmidt V H, Chien R and Shih I-C 2003 Appl. Phys. Lett. 83 1833
[17] Chien R R, Schmidt V H, Hung L-W and Tu C-S 2005 J. Appl. Phys. 97 114112
[18] Tu C-S, Schmidt V H, Shih I-C and Chien R 2003 Phys. Rev. B 67 020102
[19] Schmidt V H, Chien R, Shih I-C and Tu C-S 2003 AIP Conf. Proc. 677 160
[20] Hu C, Fang B, Luo H, Sun Y and Guo J 2003 Ceram. Int. 29 145
[21] Vanderbilt D and Cohen M H 2001 Phys. Rev. B 63 094108