X-ray and neutron diffraction investigations of the structural phase transformation
sequence under electric field in 0.7 Pb ( Mg 1 ∕ 3 Nb 2 ∕ 3 ) - 0.3 PbTiO 3 crystal
Feiming Bai, Naigang Wang, Jiefang Li, D. Viehland, P. M. Gehring, Guangyong Xu, and G. Shirane
Citation: Journal of Applied Physics 96, 1620 (2004); doi: 10.1063/1.1766087
View online: http://dx.doi.org/10.1063/1.1766087
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X-ray and neutron diffraction investigations of the structural
phase transformation sequence under electric field
in 0.7Pb„Mg
1/3
Nb
2/3
…-0.3PbTiO
3
crystal
Feiming Bai,
a)
Naigang Wang, Jiefang Li, and D. Viehland
Department of Materials Science and Engineering, Virginia Tech, Blacksburg, Virgina 24061
P. M. Gehring
NIST Center for Neutron Research, NIST, Gaithersburg, Maryland 20899
Guangyong Xu and G. Shirane
Department of Physics, Brookhaven National Laboratory, Upton, New York 11973
(Received 16 December 2003; accepted 2 May 2004)
The structural phase transformations of 0.7Pb共Mg
1/3
Nb
2/3
兲O
3
-0.3PbTiO
3
共PMN-30%PT兲 have been
studied using x-ray diffraction (XRD) and neutron scattering as a function of temperature
and electric field. We observe the phase transformational sequence (i) cubic 共C兲→ tetragonal
共T兲→ rhombohedral (R) in the zero-field-cooled (ZFC) condition; (ii) C→ T→ monoclinic
共M
C
兲→ monoclinic 共M
A
兲 in the field-cooled (FC) condition; and (iii) R→ M
A
→ M
C
→ T with
increasing field at fixed temperature beginning from the ZFC condition. Upon removal of the field,
the M
A
phase is stable at room temperature in the FC condition, and also in the ZFC condition with
increasing field. Several subtleties of our findings are discussed based on results from thermal
expansion and dielectric measurements, including (i) the stability of the M
A
phase, (ii) a difference
in lattice parameters between inside bulk and outside layer regions, and (iii) a difference in the phase
transition temperature between XRD and dielectric data. © 2004 American Institute of Physics.
[DOI: 10.1063/1.1766087]
I. INTRODUCTION
Single crystals of Pb共Mg
1/3
Nb
2/3
兲O
3
-PbTiO
3
(PMN-PT)
and Pb共Zn
1/3
Nb
2/3
兲O
3
-PbTiO
3
(PZN-PT) have attracted
much attention as high performance piezoelectric actuator
and transducer materials.
1
An electric field induced
rhombohedral-to-tetragonal phase transition was proposed by
Park and Shrout to explain the origin of the ultrahigh elec-
tromechanical properties. Structural studies of
Pb共Zr
1−x
Ti
x
兲O
3
(PZT) were the first that revealed the exis-
tence of a ferroelectric monoclinic phase, which was sand-
wiched between the rhombohedral (R) and tetragonal (T)
phases near a morphotropic phase boundary (MPB).
2,3
Two monoclinic phases M
A
and M
C
have since been
reported in PZN-x% PT.
4–6
The M
A
and M
C
notations are
adopted following Vanderbilt and Cohen.
7
A phase diagram
has been reported for PZN-x% PT crystals in the zero-field-
cooled (ZFC) condition.
8,9
Recent neutron diffraction studies
of the effect of an electric field E on PZN-8% PT by Ohwada
et al. have shown that a cubic 共C兲→ T→ M
C
transforma-
tional sequence occurs when field-cooled (FC), and that an
R→ M
A
→ M
C
→ T sequence takes place with increasing E at
350 K beginning from the ZFC condition. An electric field
versus temperature 共E-T兲 diagram was constructed based on
these experiments.
The same M
A
and M
C
phases have also been reported in
PMN-x% PT.
10–12
Figure 1(a) shows the phase diagram of
PMN-x% PT in the ZFC condition, replotted according to
recent data published by Noheda et al.
12
The M
C
phase ex-
tends from x=31% to x=37%. For x⬍ 31%, the phase dia-
gram shows a rhombohedral phase as well as a new phase,
designated as X, with an average cubic structure
共a=b=c兲.
12–14
Investigations of poled PMN-35% PT crystals
have revealed an M
A
phase at room temperature.
10
Diffraction experiments under an in situ applied electric
field together with basic principles calculations on PZT have
provided a direct link between the M
A
phase and high elec-
tromechanical deformations.
3,15
According to the polariza-
tion rotation theory,
16
while the direction of the polarization
vector in a conventional ferroelectric tetragonal (or rhombo-
hedral) phase is fixed to the [001](or [1111]) direction, the
monoclinic symmetry allows the polarization vector to con-
tinuously rotate in a plane. The polarization rotational path-
ways in the M
A
and M
C
phases are illustrated in Fig. 1(b),
where the polarization of the M
A
phase is confined to the
共11
¯
0兲
c
plane and the polarization of M
C
is confined to the
共010兲
c
plane. Diffraction experiments of PZN-8% PT with an
applied in situ electric field have given direct evidence of
these polarization rotational pathways and monoclinic
phases.
4,9
However, the transformational sequence has not
yet been experimentally established for PMN-x% PT under
electric field.
In this investigation, our focus is on establishing the
structural transformation sequence of PMN-30% PT as a
function of temperature and electric field. PMN-30% PT,
similar to PZN-8% PT, has a composition just outside of the
monoclinic phase [see arrow in Figure 1(a)]. Careful experi-
ments have been performed using both x-rays and neutrons,
a)
Author to whom correspondence should be addressed; electronic mail:
fbai@vt.edu
JOURNAL OF APPLIED PHYSICS VOLUME 96, NUMBER 3 1 AUGUST 2004
0021-8979/2004/96(3)/1620/8/$20.00 © 2004 American Institute of Physics1620
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starting from an annealed condition and by (i) cooling the
sample from 550 to 300 K under constant electric field and
(ii) gradually increasing E at constant temperature. The re-
sults unambiguously identify a transformational sequence of
C→ T→ M
C
→ M
A
in the FC condition and of R→ M
A
→ M
C
→ T with increasing E at constant temperature in the
ZFC condition.
II. EXPERIMENTAL DETAILS
Neutron and x-ray diffraction measurements were per-
formed on a PMN-30% PT crystal of dimensions 4⫻4
⫻3mm
3
. Crystals were grown by a top-seeded modified
Bridgman method, and were obtained from HC Materials
(Urbana, IL). All faces of the crystal were polished to a
0.1
m finish. A gold electrode was then deposited on two
4⫻ 4mm
2
faces by sputtering. The normal to the face on
which the electrode was deposited (used to apply an electric
field) is designated as (001) or the c axis. Before measure-
ments were begun, the crystal was annealed at 550 K. Care-
ful investigations were performed using both x-rays and neu-
trons, by starting from this annealed condition in both cases
and by gradually increasing E during sequential FC measure-
ments. The lattice constant of PMN-30% PT in the cubic
phase at T=500 K and E=0 kV/cm is a=4.024 Å, and thus
one reciprocal lattice unit (or 1 r.l.u. ) corresponds to
a
*
共=b
*
兲=2
/a=1.561 Å
−1
. All mesh scans presented in this
paper are plotted in this reciprocal unit.
The x-ray diffraction (XRD) studies were performed us-
ing a Philips MPD high resolution x-ray diffractometer
equipped with a two-bounce hybrid monochromator, an open
three-circle Eulerian cradle, and a domed hot stage. A
Ge共220兲 cut crystal was used as an analyzer, which had a
resolution of ⬃0.0068° (or 0.43 arc sec). The x-ray wave-
length was that of Cu 共 =1.5406 Å兲 and the x-ray generator
was operated at 45 kV and 40 mA. The penetration depth in
PMN-30% PT at this x-ray wavelength is on the order of
10
m. Careful polishing and subsequent annealing were re-
quired in order to achieve sharp diffraction peaks—it is im-
portant to point this out because prior studies have revealed
extremely broad peaks using Cu radiation. The neutron scat-
tering experiments were performed on the BT9 triple-axis
spectrometer located at the NIST Center for Neutron Re-
search. Measurements were made using a fixed incident neu-
tron energy E
i
of 14.7 meV, obtained from the (002) reflec-
tion of a pyrolytic graphite monochromator, and horizontal
beam collimations of 10
⬘
-46
⬘
-20
⬘
-40
⬘
. We exploited the
(004) reflection of a perfect Ge crystal as analyzer to achieve
unusually fine q resolution near the relaxor (220) Bragg
peak, thanks to a nearly perfect matching of the sample and
analyzer d spacings. Close to the (220) Bragg peak, the q
resolution along the wave vector direction is about
0.0012 Å
−1
共⌬q/q⬇2⫻10
−4
兲.
14
Both x-ray and neutron mea-
surements were performed as a function of temperature and
dc electrical bias. Extremely sharp q resolution is needed to
detect the subtle broadening and splitting of the Bragg peaks
using either x-ray or neutron probes.
III. IDENTIFICATION OF PHASE TRANSFORMATIONAL
SEQUENCE
Our electric field–temperature measurements are sum-
marized in Fig. 2. This is done for convenience of the readers
— raw data will be presented in the following sections. The
top panel of this figure gives the field-cooled diagram, where
measurements were made under a constant field on cooling
from 500 K, whereas the bottom panel was obtained by in-
creasing E beginning from the ZFC condition at each fixed
temperature. Circles represent the transition temperatures
and fields determined from each increasing field sequence.
Arrows are used to indicate the scanning direction and range
of the corresponding measurement sequence.
A. XRD Investigations
1. Phase stability in zero-field -cooled condition
The temperature dependence of the lattice parameter was
investigated under zero electric field 共E=0 kV/cm兲. The
specimen was first heated up to 700 K, and it was confirmed
that the structure was cubic. Measurements were then made
on cooling. A cubic to tetragonal phase transition was ob-
served near 405 K associated with 90° domain formation,
which was confirmed by observing a peak splitting of the
(200) reflection. By fitting the (200) reflection with a double
Gaussian function, we obtained the temperature dependence
FIG. 1. (a) Phase diagram of the PMN-PT solid solution system. The data
points come from published results by Noheda et al. (Ref. 12). The open
arrow indicates the concentration studied. (b) Polarization rotation path in
the perovskite M
A
and M
C
unit cells. C,R,T,O, and M refer to cubic,
rhombohedral, tetragonal, orthorhombic, and monoclinic regions,
respectively.
J. Appl. Phys., Vol. 96, No. 3, 1 August 2004 Bai
et al.
1621
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of the lattice constants c
T
and a
T
, as shown in the top panel
of Fig. 3. On further cooling, a subsequent tetragonal to
rhombohedral transformation was found near 385 K. This
was manifested by the development of a splitting of the
(220) reflection and a simultaneous disappearance of the
(200) peak splitting. The rhombohedral lattice parameters
and tilt angle 共
␣
兲 were calculated by fitting the (220) reflec-
tion to (220) and 共22
¯
0兲 peaks. The temperature dependence
of
␣
is shown in the bottom panel of Fig. 3. Our x-ray results
under zero field are in close agreement with the x-ray powder
diffraction results on PMN-30% PT of Noheda et al.
12
2. Phase stability in field-cooled condition
The temperature dependence of the lattice parameter was
investigated under electric fields of 1 and 2 kV/cm. The
specimen was first heated up to 550 K, where it was con-
firmed that the structure was cubic. An electric field was then
applied and measurements were made on cooling. For E
=1 kV/cm, a cubic to tetragonal phase transition was ob-
served on cooling near 430 K, as determined by the starting
temperature at which 2
began decreasing (i.e., the c param-
eter increasing) in the (002) profile on cooling. A tetragonal
to monoclinic M
C
transformation was found near 365 K, and
on further cooling a subsequent monoclinic M
C
to mono-
clinic M
A
transition occurred. After increasing E to 2kV/cm,
the T→ M
C
and M
C
→ M
A
transition temperatures decreased,
and the phase stability ranges of both T and M
C
phases in-
creased.
A sketch of the unit cells and domain configurations in
the reciprocal 共h01兲 plane for the M
A
and M
C
phases is
shown in Figs. 4(a) and 4(b), respectively. For the M
A
phase,
a
m
and b
m
lie along the pseudocubic 关1
¯
1
¯
0兴 and 关11
¯
0兴 direc-
tions, and the unit cell is doubled in volume with respect to
the pseudocubic unit cell. For the M
C
phase, a
m
and b
m
lie
along the [100] and [010] directions, and the unit cell is
FIG. 2. E-T diagram. Top panel is obtained from FC structural measure-
ments. Bottom panel shows data from the increasing electric-field process
after ZFC. Arrows indicate the scanning directions and ranges of the corre-
sponding measurement sequences. Circles represent the transition tempera-
tures and fields determined from each sequence.
FIG. 3. The dependence of the lattice parameters (top panel) and
␣
(bottom
panel) on temperature under zero electric field.
FIG. 4. Sketch of the unit cell and domain configuration in the reciprocal
(h01) plane for monoclinic phases. (a) Top, unit cell of M
A
phase; bottom,
domain configuration in reciprocal space, illustrating the two a domains of
M
A
. (b) Top, unit cell of M
C
phase; bottom, domain configuration in recip-
rocal space, illustrating the two a domains (unshaded) and one b domain
(shaded) of M
C
phase.
1622 J. Appl. Phys., Vol. 96, No. 3, 1 August 2004 Bai
et al.
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primitive. In both cases, the angle between a
m
and c
m
is
defined as

. Usually, monoclinic symmetry leads to a very
complicated domain configuration. However, once the field
is applied, the c axis is fixed along the field direction. The
monoclinic domain configuration then consists of two b do-
mains related by a 90° rotation around the c axis, and each of
the b domains contains two a domains in which a
m
forms
angles of either

or 180°−

.Inthe共H0L兲
cubic
zone, only
two a domains can be observed for the M
A
phase, as shown
in Fig. 4(a); whereas one b domain and two a domains can
be observed for the M
C
phase, as shown in Figure 4(b).
To best illustrate the observed transformational se-
quence, XRD mesh scans around (200) and (220) reflections
are shown in Fig. 5 taken at temperatures of 375, 350, and
300 K. These scans were all obtained under an applied dc
electrical bias of E=1 kV/cm. For T=375 K, the lattice con-
stant c
T
is elongated, whereas a
T
is contracted. This indicates
a phase with tetragonal symmetry. For T=350 K, the (200)
reflection was found to split into three peaks, consisting of
two (200) peaks and a single (020) peak; whereas the (220)
reflection was found to be splitted into two peaks. These
results indicate a phase with monoclinic M
C
symmetry. On
further cooling, significant changes in the mesh scans were
found. For T=300 K, the (200) reflection was found to split
only into two peaks, which can be attributed to the presence
of two domains, whereas the (220) reflection was found to
split into three peaks. This indicates a phase with monoclinic
M
A
symmetry. The room temperature mesh scans are consis-
tent with those previously reported by Ye et al. for PMN-
35% PT crystals,
10
demonstrating that the M
A
phase is stable
in the FC condition. Moreover, our results also give conclu-
sive and direct evidence of an M
C
→ M
A
transition on cool-
ing in the FC condition for PMN-30% PT. This is different
from the results for PZN-8% PT single crystals, where an
M
C
→ M
A
transition was not observed in the FC condition.
9
Figure 6 shows the temperature dependence of the struc-
tural data in the FC condition for E=1 kV/cm. The top panel
of this figure shows the lattice parameters, and the mono-
clinic tilt angle 共

−90°兲 is shown in the bottom panel. The
lattice constant c
T
共a
T
兲 gradually increases (decreases) with
decreasing temperature. Near T=365 K, where the T→ M
C
transition occurs, the value of the lattice constants abruptly
changes and a monoclinic tilt angle of

Mc
−90°⬇0.08°
forms between the (001) and (100). In the M
C
phase region,
the lattice parameters a
Mc
, b
Mc
, c
Mc
and

Mc
are relatively
temperature independent over the range of temperatures in-
vestigated. The value of b
Mc
can be viewed as a natural ex-
tension of the a
T
lattice parameter; the value of a
Mc
is close
to the value of the cubic lattice parameter, whereas the value
of c
Mc
is notably different than from either c
T
, a
T
,ora
c
. Near
T=330 K, the lattice constants and the tilt angle abruptly
change, where the M
C
→ M
A
transition occurs. Again, in the
M
A
phase region, it was found that lattice parameters are
only weakly temperature dependent over the range of tem-
peratures investigated.
3. Phase stability at fixed temperatures with
increasing E
The field dependence of the lattice structure was inves-
tigated at various temperatures. The specimen was first
heated up to 550 K and then cooled under zero field. This
was done at the beginning of measurements at each tempera-
FIG. 5. Mesh scans around the (200) and (220) reciprocal lattice positions at
different temperatures in field-cooled process.
FIG. 6. Temperature dependence of the lattice parameters (top panel) and
90°−

(bottom panel) observed in field-cooled process. For the M
A
phase,
the lattice parameters a
Ma
/ 冑2, b
Ma
/ 冑2, and c
Ma
are plotted; whereas, for the
M
C
phase the lattice parameters a
Mc
, b
Mc
, and c
Mc
are plotted. Solid lines
drawn through the data points are guides to the eyes.
J. Appl. Phys., Vol. 96, No. 3, 1 August 2004 Bai
et al.
1623
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