Dielectric, hypersonic, and domain anomalies of ( PbMg 1/3 Nb 2/3 O 3 ) 1−x ( PbTiO 3 )
x single crystals
Chi-Shun Tu, C.-L. Tsai, V. Hugo Schmidt, Haosu Luo, and Zhiwen Yin 
 
Citation: Journal of Applied Physics 89, 7908 (2001); doi: 10.1063/1.1370998 
View online: http://dx.doi.org/10.1063/1.1370998 
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/89/12?ver=pdfcov 
Published by the AIP Publishing 
 
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Dielectric, hypersonic, and domain anomalies
of „PbMg1Õ3Nb2Õ3O3…1Àx„PbTiO3…x single crystals
Chi-Shun Tua) and C.-L. Tsai
Department of Physics, Fu Jen University, Taipei, Taiwan 242, Republic of China
V. Hugo Schmidt
Department of Physics, Montana State University, Bozeman, Montana 59717
Haosu Luo and Zhiwen Yin
Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 201800,
People’s Republic of China
~Received 2 January 2001; accepted for publication 16 March 2001!
Dielectric permittivities, Brillouin backscattering spectra, polarization-electric field hysteresis loops,
and domain structures have been measured as a function of temperature in relaxor-based
ferroelectric single crystals (PbMg1/3Nb2/3O3)12x~PbTiO3!x(PMN-xPT) for x50.24 and 0.34. For
PMN-24%PT, a diffuse phase transition which is associated with a broad frequency-dependent
dielectric maximum was observed near 380 K. As the temperature increases, the PMN-24%PT
crystal gradually develops cubic regions and is fully converted into the cubic state near 375 K. An
extra dielectric anomaly appears at 370 K, possibly due to the percolating polar cluster induced by
an external electric field. PMN-34%PT exhibits a nearly normal ferroelectric phase transition near
445 K from the tetragonal to the cubic phase. In addition, a weak diffuse phase transition observed
near 280 K may result from partial conversion of rhombohedral phase to tetragonal phase. The
dielectric thermal hysteresis confirms that the transitions near 280 and 445 K are diffuse first order
and first order, respectively. The dielectric permittivities of PMN-24%PT and PMN-34%PT obey
the relation, «m8 /«8( f ,T)511@T2Tm( f )#g/2dg2 , above the temperature of permittivity maximum
Tm . © 2001 American Institute of Physics. @DOI: 10.1063/1.1370998#
I. INTRODUCTION
Relaxor ferroelectrics generally mean complex perovs-
kites with and ABO3-type unit cell and are crystals in which
unlike-valence cations belonging to a given site ~A or B! are
presented in the correct ratio for charge balance, but are situ-
ated randomly on these cation sites.1–4 These randomly dif-
ferent cation charges give rise to random fields, which tend
to make the phase transitions ‘‘diffuse’’ instead of sharp as
in normal ferroelectrics.3,4 Lead–magnesium niobate,
Pb~Mg1/3Nb2/3!O3 ~PMN!, is one of the most interesting re-
laxor ferroelectric ~FE! materials. PMN has a disordered
complex structure in which the Mg21 and Nb51 cations ex-
hibit only short range order on the B site. Near 280 K the
PMN crystal undergoes a diffuse phase transition character-
ized by a broad frequency-dependent dielectric maximum.
PMN has cubic symmetry at room temperature with space
group Pm3m , whereas below 200 K a small rhombohedral
distortion ~pseudocubic! was observed.1,5 The normal FE
crystal PbTiO3 has tetragonal symmetry with space group
P4mm at room temperature and has a normal FE phase tran-
sition taking place at Tc5760 K with long-range FE order
occurring below Tc .6
The relaxor-based FE crystals
(PbMg1/3Nb2/3O3)12x~PbTiO3!x(PMN-xPT) are expected to
show properties of both relaxor ferroelectric PMN and nor-
mal ferroelectric PT. PMN-xPT naturally has a morphotropic
phase boundary ~MPB! in the range of ;28–;36 mol % of
PT.7 In other words, as the temperature decreases, the mixed
crystals of PMN-xPT(0.28<x<0.36) have successive phase
transitions: cubic paraelectric ~PE! phase→tetragonal FE
phase→rhombohedral FE phase. The spontaneous deforma-
tions of the tetragonal state appear along the equivalent ^001&
directions, giving six fully FE domain states with the spon-
taneous polarization Ps and the optical axes ~OA! oriented
parallel to ^001&. In the low temperature region, the crystals
exhibit a polar rhombohedral phase with the Ps and the OA
oriented along the ^111& direction.
Paik et al. showed that a field of 20 kV/cm in PZN-
8%PT destroys the rhombohedral state and induces a single
tetragonal domain.8 By in situ x-ray diffraction, Durbin et al.
confirmed that the field-induced crystallographic change
occurs.9 By optical microscopy, with field applied along
^001&, Belegundu et al. confirmed that tetragonal and rhom-
bohedral domains coexist at room temperature and even
down to 2100 °C.10 Perhaps the strain caused by the pres-
ence of the eight ^111&-type domains is partly relieved by the
presence of tetragonal ^001& domains induced by the external
dc field.
Single crystals of PMN-PT have been reported to exhibit
much larger piezoelectric constants and electromechanical
coupling factors compared with those in the
PbZrO3 – PbTiO3 ~PZT! family of ceramics.11–13 Such high
piezoelectric performance, which converts mechanical and
a!Author to whom correspondence should be addressed; electronic mail:
phys1008@mails.fju.edu.tw
JOURNAL OF APPLIED PHYSICS VOLUME 89, NUMBER 12 15 JUNE 2001
79080021-8979/2001/89(12)/7908/9/$18.00 © 2001 American Institute of Physics
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electric energies, is crucial in medical imaging, telecommu-
nication, and ultrasonic devices and may revolutionize these
applications.14 Much work has been undertaken on the
growth and characterization of relaxor-based ferro-
electrics.15–21 However, limited attention has been paid to
phase transitions and domain structures in these crystals, es-
pecially phase coexistence near the MBP.17,21 It is believed
that the phase coexistence near the MPB plays an important
role in the high electromechanical coupling effect. Therefore,
we carried out temperature-dependent measurements of di-
electric permittivity, Brillouin light scattering, P – E hyster-
esis loops, and polarized light microscopy on PMN-24%PT
and PMN-34%PT single crystals.
II. EXPERIMENTAL PROCEDURE
The lead magnesium niobate–lead titanate single crys-
tals, PMN-24%PT and PMN-34%PT, were grown using a
modified Bridgman method with bottom seed.15 The samples
were cut perpendicular to the $001% direction and were not
electrically poled. Here, direction ‘‘$%’’ refers to the
pseudocubic axes. For dielectric permittivities and P – E hys-
teresis loops, the sample surfaces were coated with silver
paste electrodes. The applied electric field was along the
pseudocubic $001% direction. A variable-frequency Wayne–
Kerr precision analyzer ~PMA3260A! with four-lead connec-
tions was used to obtain capacitance and resistance. The
heating/cooling rate for dielectric measurement was 1.5
K/min. For the field-cooled-zero-field-heated ~FC-ZFH! di-
electric measurement, the PMN-24%PT sample was first
cooled from 470 K ~cubic phase! to room temperature with a
dc bias field of E56 kV/cm along the $001% direction. Then
the dielectric permittivity was measured upon heating with-
out a bias field. The P – E hysteresis loops were measured by
using a Sawyer–Tower circuit in which the P – E loop was
obtained within two to four cycles of electric field at fre-
quency of 47 Hz. A Janis CCS-450 closed cycle refrigerator
was used with a LakeShore 340 temperature controller.
Longitudinal acoustic ~LA! phonon spectra were ob-
tained from the Brillouin backscattering. The samples were
illuminated along the $001% direction with an Innova 90
plus-A3 argon laser with wavelength l5514.5 nm. The
transverse acoustic ~TA! mode was not observed in this
work. Scattered light was analyzed by a Burleigh five-pass
Fabry–Pe´rot interferometer. The free spectral range of the
Fabry–Pe´rot interferometer was determined by measuring
the LA phonon shift of fused quartz. Due to the weak inten-
sity factor and low optical transmission, the signal/noise
~S/N! ratio of the LA phonon spectra is about 2–3 for both
the PMN-24%PT and PMN-34%PT crystals, even though
the S/N ratio from the fused quartz is greater than 60. The
Brillouin scattering data were taken during a heating se-
quence.
The domain structures were studied by a Nikon
E600POL polarized light microscope ~PLM!. The samples
were cut perpendicular to the $001% direction and were finely
polished. In order to minimize superposition of domains, the
thickness of the samples is less than 65 mm. A Linkam
THMS600 heating/cooling stage mounted on the microscope
was used for studying domain structures as a function of
temperature. Domain structures were observed between par-
alleled polarizer-analyzer along the $001% direction using a
quarter-wave plate. In the tetragonal phase, adjacent domains
are usually polarized 90° to each other and form strip-like
domain walls.22 Due to strain birefringence and total reflec-
tion at the boundary, the 90° domain wall is usually visible
in the polarized light. In the rhombohedral phase, when ob-
serving the ^001& cut of a platelet between crossed polarizers
along the ^001& direction, the cross section of the optical
indicatrix will exhibit extinction directions parallel to the
^110& equivalent directions.
FIG. 1. Temperature dependences of ~i! «8 and ~ii! «9 for ~a! PMN-24%PT
and ~b! PMN-34%PT, obtained during a heating process. The insets are
enlargements of «8 and e9.
7909J. Appl. Phys., Vol. 89, No. 12, 15 June 2001 Tu et al.
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III. EXPERIMENTAL RESULTS
Figures 1~a! and 1~b! show the temperature dependences
of the real «8 and imaginary «9 parts of the dielectric permit-
tivity. The insets of Fig. 1~b! are enlargements of «8 and «9
to clarify the dispersion behaviors which appear below 410
K. Compared with the prototypical relaxor PMN, the «8 of
PMN-24%PT shows similar frequency-dependent behavior,
with much higher values of «m8 ;1.53104 and Tm;380 K.
Tm corresponds to the temperature giving maximum value
em8 of the dielectric permittivity. However, near 445 K the
dielectric permittivity e8 of PMN-34%PT exhibits a nearly
normal FE transition with very slight frequency dispersion.
Both the values of «m8 ;2.33104 and Tm;445 K of PMN-
34%PT are greater than those in PMN and PMN-24%PT due
to more PT content. In PMN-34%PT, «8 shows a broad weak
plunge accompanied by a dispersion near room temperature,
which may be connected to a diffuse phase transition of part
of the crystal from the rhombohedral to the tetragonal phase.
A sharper but weak frequency-dependent anomaly in the «9
FIG. 2. ~i! Brillouin frequency shift, ~ii! half width, and ~iii! «8 vs tempera-
ture for ~a! PMN-24%PT and ~b! PMN-34%PT. The dielectric data are
taken at f 550 kHz upon heating. The dashed lines are guides for the eye.
FIG. 3. Thermal hysteresis behavior of «8 for ~a! PMN-24%PT and ~b!
PMN-34%PT, taken at f 550 kHz. The insets are the reciprocal of «8.
7910 J. Appl. Phys., Vol. 89, No. 12, 15 June 2001 Tu et al.
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data @Fig. 1~b!# was observed near 390 K and may result
from partial conversion of rhombohedral phase to cubic
phase.
Figures 2~a! and 2~b! show, respectively, the tempera-
ture dependences of the phonon frequency, half width, and
dielectric permittivity e8. As shown in Fig. 2~a!, the acoustic
phonon frequency of PMN-24%PT exhibits a broad mini-
mum near 380 K, which corresponds to the broad dielectric
maximum. The acoustic phonon frequency of PMN-34%PT
@Fig. 2~b!# shows two successive minima near 280 and 445
K, respectively. Figures 3~a! and 3~b! show the temperature-
dependent data of «8 from cooling and heating processes at
measuring frequency f 550 kHz. The insets of Figs. 3~a! and
3~b! show the reciprocal behaviors of e8. Below ;380 K
PMN-24%PT exhibits a thermal hysteresis in a wide tem-
perature range. For PMN-34%PT, two clear thermal hyster-
eses were observed in the regions of ;150–300 and ;380–
460 K. In particular, typical dielectric behavior of a first-
order FE phase transition appears near 445 K.23
P – E hysteresis loops are shown in Figs. 4~a! and 4~b!.
At room temperature, the remanent polarization Pr of PMN-
24%PT is 15 mC/cm2, and is about the same as the sponta-
neous polarizations Ps defined as the intercept at zero field of
the straight-line portion of the hysteresis loop. By compari-
son, PMN-34%PT has Pr of 28 and Ps near 32.5, and PT
has24,25 Ps of 52 in these units. The coercive field Ec , how-
ever, is not monotonic with the PT content. It goes from 3.4
kV/cm for PMN-24%PT to 8.0 for PMN-34%PT, and is back
down to 6.75 for PT.24 We cannot explain this Ec depen-
dence, but will discuss the Ps dependence on the PT content.
If one would assume a linear dependence of Ps on the PT
content, then Ps for PMN-24%PT would be about 30
mC/cm2. This estimate assumes that the FE phase remains
tetragonal. In reality, it consists of rhombohedral clusters
near room temperature.7 Accordingly, we assume that Ps has
magnitude of 30 mC/cm2 for each cluster, and that for large
field along the ^001& the cluster polarizations lie in the four
^111& directions with a 11 component along c. Then the net
Ps is along c and is reduced by the factor 1/) to 17 mC/cm2,
which is close to the measured value of 15 mC/cm2. The
temperature-dependent behaviors of Pr are plotted in
Figs. 5~a! and 5~b!. Instead of a gradual temperature-
dependent behavior of polarization as seen in PMN,26 a sharp
FIG. 4. P – E hysteresis loops of ~a! PMN-24%PT and ~b! PMN-34%PT
upon heating.
FIG. 5. Temperature dependence of Pr for ~a! PMN-24%PT and ~b! PMN-
34%PT. The solid and dashed lines are guides for the eye.
7911J. Appl. Phys., Vol. 89, No. 12, 15 June 2001 Tu et al.
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change was observed near 370 and 440 K for PMN-24%PT
and PMN-34%PT, respectively. The thermal hysteresis be-
havior implies a metastable state near the phase transition
temperature.23
Temperature-dependent domain structures are shown in
Figs. 6~a! and 6~b!. At lower temperature phase, the domain
structures of PMN-24%PT exhibit complicated interference
patterns probably caused mostly by clusters or microdomains
FIG. 6. ~a! ~Color! Successive domain structures of PMN-24%PT.
7912 J. Appl. Phys., Vol. 89, No. 12, 15 June 2001 Tu et al.
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but partly by domains. As shown in Fig. 6~a!, those regions
~indicated by arrows! which exhibit optically isotropic back-
ground color possibly correspond to rhombohedral
~pseudocubic! clusters with the extinction directions along
^110&.21 We expect a rhombohedral phase in these domain
regions for two reasons. First, according to the MPB,7 PMN-
24%PT has only rhombohedral distortion near room tem-
perature. Second, pure PMN crystal remains optically isotro-
pic without formation of macrodomains and shows a
pseudocubic symmetry down to very low temperature.27 As
FIG. 6. ~b! ~Color! Successive domain structures PMN-34% PT..
7913J. Appl. Phys., Vol. 89, No. 12, 15 June 2001 Tu et al.
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the temperature increases, the domain structures gradually
change and go completely into the optically isotropic cubic
phase near 375 K. On the other hand, the rhombohedral state
with interference color domains suggests that macrorange FE
clusters have been triggered by the substitution of 24% Ti41
for the B site complex ions (Mg1/3Nb2/3!41. It is believed that
the introduction of Ti41 increases the size of local polar do-
mains by strengthening the off-center displacement and en-
hances the interactions between micropolar domains, leading
to macroscopic symmetry breaking of the pseudocubic state
in small portions of the crystal.
The PMN-34%PT crystal corresponds to the MPB com-
position in the PMN-PT system, and is expected to have
complex domain structures. As shown in the ‘‘~a!’’ pattern of
Fig. 6~b!, domain structures of PMN-34%PT can be distin-
guished as three different regions. Region A ~that has the
major area!, characterized by strip-like 90° domain walls,
corresponds to the tetragonal phase.22 Those regions which
exhibit optically isotropic background color, as indicated by
arrows in Fig. 6~b!, possibly correspond to rhombohedral
clusters with the extinction directions along ^110&.21 Thus,
regions B and C, which exhibit complex interference patterns
with unsharp domain walls, possibly correspond to rhombo-
hedral clusters. PMN-34%PT shows similar domain struc-
tures with a mixture of two different states down to very low
temperature ~below 200 K!. Upon heating, domain structures
of the A region exhibit a sharp change near 445 K and this
major volume of the PMN-34%PT crystal goes into the op-
tically isotropic cubic state. However, residue of the 90° do-
main walls still can be seen in the region of 445–460 K. It
may indicate that the internal stress requires higher tempera-
ture to release.
Different individual domain regions exhibit a large dis-
parity not only in interference patterns, but also in transition
temperatures. For instance, upon heating, the B and C re-
gions of PMN-34%PT @Fig. 6~b!# exhibit a continuous
change and go into the optically isotropic cubic phase near
438 K. But, strip-like 90° domain walls of A region show no
apparent change up to ;445 K. Since the MPB depends
sensitively on the relative Ti41 occupancy on the B site,
these phenomena suggest an inhomogeneous distribution of
the Ti41 concentration in the crystal. Physical analysis by the
JEOL 6100 electron microscope has revealed inhomogeneity
of the local composition for the B site ions Mg21, Nb51, and
Ti41. In the PMN-34%PT platelet that we measured, the
Ti41 concentration varies about 63% from its nominal or
average composition. Such a fluctuation is believed to result
from a quenched unequal occupation of the B site by the
competitive ions Mg21, Nb51, and Ti41. By micro-Brillouin
scattering, the spatial microheterogeneity was also detected
in the PMN-35%PT crystal.28
IV. DISCUSSION
A. PMN-24%PT
What are the physical origins of the temperature-
dependent anomalies shown in Figs. 1~a!–6~a! for PMN-
24%PT? The dielectric permittivity «8 @Fig. 1~a!# exhibits
broad frequency-dependent behavior with maxima located
near 380 K. The value of Tm is quite consistent with the
temperature ;38565 K ~cubic PE↔rhombohedral FE!
predicated in Ref. 7. As the temperature increases, the acous-
tic phonon frequency @Fig. 2~a!# shows a gradual softening
and reaches a weak minimum near 380 K, indicating a so-
called diffuse phase transition. Similar acoustic and dielec-
tric anomalies were seen in pure PMN.29 In addition, the
phonon damping of PMN-24%PT exhibits gradual growth
FIG. 7. Temperature dependence of «8 obtained from the FC-ZFH of PMN-
24%PT.
FIG. 8. «m8 /«8 vs (T2Tm)g for ~a! PMN-24%PT and ~b! PMN-34%PT at
measuring frequencies of 50 kHz and 1 MHz.
7914 J. Appl. Phys., Vol. 89, No. 12, 15 June 2001 Tu et al.
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with a broad maximum located near 380 K. Such a damping
anomaly reveals that order parameter fluctuations are the
dominant dynamic mechanism in the vicinity of a diffuse
phase transition.
Ye and Dong recently examined domain morphology in
flux-grown PMN-PT single crystals with 20%, 35%, and
50% Ti by polarized light microscopy.21 At room tempera-
ture, the 20% Ti crystal had only a rhombohedral cluster.21
According to the MPB of PMN-PT system,7 both 20%PT
and 24%PT compounds have only rhombohedral phase near
room temperature. As revealed in Fig. 6~a!, the PMN-24%PT
crystal gradually transforms into the macroscopically cubic
phase and is fully converted to the cubic phase near 375 K,
indicating coexistence of rhombohedral and cubic phases in
a wide temperature range. It is believed that the diffuse phase
transition near 380 K, seen in Figs. 1~a! and 2~a!, reflects the
strongly local structural fluctuations between cubic PE and
rhombohedral FE clusters.
Probably the most convincing evidence for the FE nature
of PMN-24%PT is the extra peak in the zero-field-heated
dielectric permittivity seen after field cooling in a dc bias
field (E56 kV/cm) to the domain state, shown in Fig. 7. The
coercive field Ec is less than 4 kV/cm in the temperature
range measured. An extra peak superimposed on the broad
background of the dielectric permittivity is clearly evident at
370 K. The temperature for this anomaly ~but not its ampli-
tude! is independent of frequency. A similar field-induced
dielectric anomaly was observed in the PMN system.3,30 By
heating the PMN crystal in a dc electric field, a long-range
FE phase transition associated with an extra dielectric peak
at Tc;212 K was found.3 It was concluded that the peak at
Tc;212 K in PMN is connected to the percolating polar
cluster due to the suppression of the random fields originat-
ing from charged compositional fluctuations at the B site.3 It
is well known that in relaxor ferroelectrics the highly sensi-
tive local polar clusters are easily affected by external per-
turbations, contrary to normal ferroelectrics; an external elec-
tric field may enhance the interactions between local polar
microclusters and induces marked changes.4,31 Thus, it is
reasonable to expect that the extra peak at 370 K in the
FC-ZFH dielectric permittivity ~Fig. 7! is attributed to the
establishment of the long-range percolating FE cluster during
the FC process. In addition, the broad dispersive permittivity
peak following FC has magnitude of 14 000 ~Fig. 7!, about
10% lower than the 15 500 value shown in Fig. 1~a! for ZFC.
Perhaps the FC process induces domain reorientations, hence
reduces the domain wall contributions to the dielectric per-
mittivity. Another possibility is that this reduction could be a
consequence of partial poling of the network of nonpercolat-
ing FE clusters by the external electric field. Additional in-
formation concerning the FE nature of PMN-24%PT is ob-
tained from P – E hysteresis loops. As shown in Fig. 5~a!, a
step-like discontinuity in Pr was observed near 370 K.
B. PMN-34%PT
For a normal FE phase transition, the transition tempera-
ture occurs near where the acoustic phonon frequency has a
discontinuous change.23 In PMN-34%PT, the acoustic pho-
non frequency has an irregular minimum near 445 K. Corre-
spondingly, a sharp damping maximum @Fig. 2~b!# which
could possibly be associated with the Landau–Khalatnikov-
like maximum was also detected near 445 K. Such a damp-
ing anomaly is usually related to rapid growth of a long-
range FE cluster.29 The real part «8 of the dielectric
permittivity exhibits a sharp change near 445 K. This value
is quite consistent with the transition temperature 43565 K
~cubic PE↔tetragonal FE! predicated in Ref. 7. In addition,
a clear thermal hysteresis exists in the temperature region of
;380 K,T,;460 K, indicating a metastable state near the
phase transition temperature. Domain structures @Fig. 6~b!#
also reveal that the PMN-34%PT crystal turns into the cubic
region above 445 K. Thus, PMN-34%PT possesses a nearly
normal first-order phase transition at Tc;445 K from the te-
tragonal FE to the cubic PE phase.
Near room temperature, as shown in Fig. 1~b!, the di-
electric permittivity «8 of PMN-34%PT exhibits a gradual
step down with a weak frequency dispersion. The imaginary
part «9 also shows complicated frequency dispersions in a
wide temperature range. Correspondingly, the acoustic pho-
non frequency reaches a weak minimum near 280 K. A wide
thermal hysteresis was observed below 360 K down to very
low temperature. Domain structures @Fig. 6~b!# verify that
both tetragonal and rhombohedral domains coexist from very
low temperature ~below 200 K! up to possibly ;435 K. Re-
cent domain morphology obtained by Ye and Dong con-
firmed that a flux-grown PMN-35%PT single crystal at room
temperature had a mixture phase of tetragonal and rhombo-
hedral domains.21 Based on the above results, one can con-
clude that gradual-evolution anomalies of phonon frequency
and dielectric permittivity near 280 K in PMN-34%PT are
due to local structural fluctuations between rhombohedral
and tetragonal clusters. We call this a first-order transition
for two reasons. First, the thermal hysteresis in the dielectric
permittivity shows that the system is metastable in this tem-
perature region. Metastability can occur for first-but not
second-order transitions.23 Second, the point groups of the
tetragonal and rhombohedral symmetries do not have a
group–subgroup relation, so a transition between these
phases must be of first order. The usual distinctions between
first-and second-order transitions, such as discontinuity in
dP/dT , do not apply for diffuse phase transitions.
To characterize the temperature dependence of the di-
electric permittivity «8 above Tm , we fitted the experimental
data to the empirical formula,32–34
«m8
«8~ f ,T ! 511
@T2Tm~ f !#g
2dg
2 , ~1!
TABLE I. Parameters from the fits of Eq. ~1! to the dielectric permittivity «8
~above Tm!.
g
dg
~50 kHz!
dg
~1 MHz!
PMN-24%PT 1.83 21.7 22.8
PMN-34%PT 1.33 6.34 6.49
7915J. Appl. Phys., Vol. 89, No. 12, 15 June 2001 Tu et al.
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where «m8 corresponds to the maximum value of the dielec-
tric permittivity at Tm . The value of g(1<g<2) is the ex-
pression of the degree of dielectric relaxation in a relaxor-
based FE material. When g51, Eq. ~1! expresses Curie–
Weiss behavior, while for g52, Eq. ~1! is identical to
Smolensky’s formula that can be used to fit well the dielec-
tric permitivity of PMN above Tm .35,36 The parameter dg has
been used as a measure of degree of diffuseness for the dif-
fuse phase transition in relaxor-based ferroelectrics.33 Based
on Eq. ~1!, dg can be determined from the slope of «m8 /«8 vs
(T2Tm)g, which is linear. Figures 8~a! and 8~b! show the
plots of «m8 /«8 vs (T2Tm)g. The solid and dashed lines are
the best fits of Eq. ~1! to the dielectric data obtained at 50
kHz and 1 MHz, respectively. The fitting values of param-
eters are given in Table I. It was found that the experimental
data in the temperature regions ~Tm<T<Tm170 K for
PMN-24%PT and Tm<T<Tm125 K for PMN-34%PT!
obey empirical Eq. ~1!. The parameter dg shows a weak
tendency to change with frequency. Also, no correlation be-
tween the parameter g and measuring frequency was found.
Compared with PMN-34%PT, PMN-24%PT possesses big-
ger values of dg and g. In other words, PMN-24%PT has
stronger degrees of diffuseness and relaxation behavior in the
region of diffuse phase transition. However, at higher tem-
perature regions ~T.Tm170 for PMN-24%PT and T.Tm
125 for PMN-34%PT!, slight deviations from Eq. ~1! were
found in both crystals that could be attributed to the contri-
bution of ionic conductivity activated by thermal energy.
Bokov and Ye recently demonstrated that, in PMN and
PMN-25%PT ~ceramic sample!, the dielectric permittivity g8
obeys the relation «A8 /«8511(T2TA)2/2dA2 in a wide tem-
perature range above Tm .36 However, such an empirical qua-
dratic law could not fit better than Eq. ~1! in the dielectric
data of PMN-24%PT and PMN-34%PT systems. We cannot
explain this contradiction. The search to find a universal for-
mula describing the temperature dependence of «8 in the vi-
cinity of diffuse phase transition continues.
V. CONCLUSIONS
In PMN-24%PT, a coexistence of rhombohedral and cu-
bic phases, which is characterized by the broad dielectric
maximum and gradual evolution of the acoustic phonon, was
observed in a wide temperature range. In other words, the
PMN-24%PT crystal gradually transforms into the cubic
phase and is fully converted to the cubic state above 375 K.
In addition, the dielectric thermal hysteresis implies that the
diffuse phase transition near 380 K is first-order type. The
FC-ZFH dielectric result shows that an extra FE anomaly
appears at 370 K, possibly due to the percolating polar clus-
ter induced by an external electric field.
A nearly normal FE phase transition is seen near 445 K
in PMN-34%PT. Near 280 K a weak diffused phase transi-
tion was observed and is attributed to local structural fluc-
tuations between rhombohedral and tetragonal phases. The
thermal hysteresis of the dielectric permittivity verifies that
phase transitions near 280 and 445 K are, respectively, dif-
fuse first order and first order. Besides, the dielectric permit-
tivities of PMN-24%PT and PMN-34%PT obey the relation,
«m8 /«8( f ,T)511@T2Tm( f )#g/2dg2 , in a wide temperature
range above Tm .
ACKNOWLEDGMENTS
This work was supported by Grant No. NSC89-2112-M-
030-006 ~Republic of China! and DOD EPSCoR Grant No.
N00014-99-1-0523.
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