Electric-field induced phase transitions in rhombohedral PZN-xPT

8 Pages·0.26 MB·

by  B. Noheda

Electric-field induced phase transitions in rhombohedral Pb(Zn1/3Nb2/3)1−xTixO3
∗
B. Noheda and Z. Zhong, D.E. Cox, and G. Shirane
Brookhaven National Laboratory, Upton, New York 11973
2 S-E. Park
0 Fraunhofer-IBMT Technology Center Hialeah,
0 Hialeah, Florida 33010
2

n
a P. Rehring
J Materials Research Laboratory,
1 The Pennsylvania State University,
1 University Park, Pennslyvania 16802

] (Dated: February 6, 2008)
i
c
s High-energy x-ray diffraction experiments peformed on rhombohedral Pb(Zn1/3Nb2/3)1−xTixO3
- (PZN-x%PT)crystalswithx=4.5and8%showthatanelectricfieldappliedalongthe[001]direction
l induces the tetragonal phase, as proposed by Park and Shrout. Our experiments reveal that in
r
mt PZN-4.5%PT such phase change occurs via a third phase with monoclinic symmetry, MA, which
is observed at intermediate field values. This is in agreement with first-principles calculations by
. FuandCohenpredictingtherotationofthepolarization betweentherhombohedralandtetragonal
t
a phases in this material. A different polarization path between the rhombohedral and tetragonal
m phases, through a second monoclinic phase, M , has been previously reported in PZN-8%PT. The
C
microscopiccharacterization ofthesecrystalsallows ustoexplaintheultra-highmacroscopic strain
-
d observedinPZN-x%PTunderanelectricfield. Moreover,someunusualscatteringprofilesdisplayed
n by exceptionally good crystals, are experimental evidence of the high anharmonicities and near-
o degeneracy of thedifferent phases in these extremely deformable materials.
c
[ PACSnumbers: 77.65.-j,61.10.Nz,77.84.Dy

1
v
I. INTRODUCTION crucial in explaining the outstanding properties of these
2
materials.
8
1 Piezoelectric single crystals of the relaxor- ferro- Monoclinic phases have been observed in the
01 oelreicetnrtiecdmaaltoenrigalaPnb([Z0n011/]3Ndibr2e/c3t)io1−n,xTsihxoOw3(ePxZceNp-txio%nPaTlly) tmeomspteirmatpuorret-acnotmppioesziotieolenctprhicasseydstieamgrsa,mPsbo(fZtrh1−rexeToixf)tOh3e
2
large piezoelectric deformations, more than 1% [1, 2]. (PZT) [5], PZN-x%PT [6, 7, 8], and very recently also
0
/ In their pioneering work, Park and Shrout[2] proposed in Pb(Mg1/3Nb2/3)1−xTixO3 (PMN-PT) [9, 10, 11, 12],
at thattheoriginoftheultra-highstrainvaluesobservedin for compositions aroundthe morphotropic phase bound-
m [001]-orientedPZN-8%PT(8PT)wasarhombohedral-to- ary(MPB),whichrepresentsthenearlyverticallimitbe-
tetragonal phase transition induced by the electric field. tweenthe rhombohedralandthe tetragonalphases. Fur-
-
d Later, Liu et al.[3] reported similar behavior in PZN- thermore,ithasbeenobservedthattheregionofstability
n 4.5%PT(4.5PT)(seeFig. 1a). Arevolutionintheworld of those new phases is enlargedfollowing the application
o ofpiezoelectricdevicesseemscertaintooccurifthephys- of an electric field [4, 13, 14]. Optical [15] and x-ray
c
icalpropertiesofsuchhighlydeformablematerialscanbe diffraction [16, 17] measurements have also indicated a
:
v understood and controlled. symmetry lowering in poled 8PT.
i
X Diffractionexperimentson8PTunderanapplied[001] In contrast to the rhombohedral or tetragonal phases,
field have revealed the true long-range symmetry evolu- the polarization vectors in the monoclinic phases are no
r
a tion to be from a rhombohedral to a monoclinic phase longer constrained to be directed along a symmetry axis
[4]. These measurements were performed on relatively and can rotate within the monoclinic plane. However,
thick samples, and a single tetragonal phase could not different polarization rotation paths have been observed
be reached before a sample breakdown (see Fig. 1b). in these materials, resulting in two types of monoclinic
However it was shown that it is the existence of such a distortion, MA (as found in PZT) and MC (as found in
monoclinic phase, rather than a tetragonalone, which is 8PT) with space groups Cm and Pm, respectively. As
illustrated in Fig. 1c, in the M type, the monoclinic
A
plane is the pseudo-cubic (1-10) plane and the unit cell
is doubled in volume with respect to the 4 ˚A pseudo-
∗Correspondingauthor,e-mail: [email protected] cubic unit cell. In the MC type, the unit cellis primitive
a) 2
PZN-4.5%PT
andthemonoclinicplaneisthepseudo-cubic(010)plane.
Veryrecently,VanderbiltandCohen[18]reporteda nat-
ural derivation of these monoclinic phases by extending
theDevonshireexpansionofthefreeenergyuptoeighth-
order, which is indicative of the large anharmonicity in-
trinsic to these highly-piezoelectric materials. We are
using their notationfor the variousphases. A strongan-
harmonicity of the potential surfaces in lead oxides has
also been proposed by Kiat et al.[19] based on experi-
mental observations.
First-principles calculations by Bellaiche et al. have
succeeded in reproducing the monoclinic phase in PZT,
both at zero electric field [20] and also under an applied
field[21]. Mostimportantly,thecalculationshaveshown
that the huge increase in the piezoelectric coefficients
close to the MPB of these materials is directly related
to polarization rotation between the rhombohedral [111]
andtetragonal[001]polaraxes[22]and,ultimately,tothe
existence of a monoclinic phase [20]. This has very im-
portant consequences for a fundamental understanding
b)
of the piezoelectric properties in these compounds.
4.10
In this new and revealing context, a detailed interpre-
tation of the various observations is rcequired, with the c
goal of making the novel high-strain pmiezoelectric sys- t
tems as control)lable and convenient as the PZT-based
Å
materialsincurrentus4e..0W8ehaveaccordinglyperformed
(
high-energy x-ray diffraction experiments on rhombohe-
s
dral 4.5PT andr8PT crystals with an electric field ap-
e
plied in-situ along the [001] direction, and studied how
t
e
thesymmetryemvolves. Afield-inducedlong-rangetetrag- PZN-8%PT
onal phase has in fact4b.e0en6observed in both 4.5PT and FIG. 1: a) Macroscopic strain vs. electric field for 4.5PT
a
8PT compositiorns, thus confirming Paark and Shrout’s after ref. 3. b) Lattice parameters vs. electric field for 8PT,
a adapted from ref.4. c) Polarization vectors in the perovskite
thesis[2]. Thespe experiments, togethemr with those re-
unit cell, shown by thick arrows. The thick lines represent
cently reported for 8PT [4, 14, 17], 9PT [6, 7] and
e thepathsfollowedbytheendofthepolarizationvectorinthe
xPT (x 10%)c[8], provide a much clearer picture of
the field≥-inducettid beha4vi.o0r4in rhombohebdralPZN-x%PT. monoanlo(cTli)niacnpdhaosretsh,oirnhobmetbwicee(nOt)hephrhasoems.boThhederMalA(R, )M,Bte,trMagC-
This work alsoLaprovides the link betweenmthe anomalous notationais adopted following Vanderbilt and Cohen[18]
macroscopicstrainvaluesinthesematerialsandthe evo- t
lutionofthestructuralparameterunderanappliedfield.
4.02 pliedalongthe [111]direction,no changeof symmetryis
0 10 20 obse3rv0edandthe4c0rystalint5h0eorderedstateisstillrhom-
II. EXPERIMENTAL bohedral. As described above, in this work the crystals
E (kVa/rcepmole)d along the [001]direction. Very narrowmosaics
4.5PT and 8PT samples were grown by the high- were observed in the diffraction patterns demonstrating
temperature flux technique described in Ref. [2]. The the excellent quality of the crystals.
samples were then oriented and cut in the form of rect- Single-crystaldiffraction experiments were carriedout
R
angular parallelepipeds, with sides ranging from 0.5 to at the National Synchrotron Light Source, on beamlines
3mm, and at least two of the faces perpendicular to an X17B1 and X22A, with high-energy x-rays of 67 keV
[001] direction. Gold was sputtered on two of the 00M1 A ( 0.18 ˚A) and 32 keV ( 0.38 ˚A), respectively. High-
faces of acll )the samples, and thin wires were att{ached} e∼nergy x-rays are needed∼to observe the crystal struc-
to enable an electric field to be applied along the [M001] ture undMerneath the skin of the sample, which extends
direction. It should be noted that rhoTmbohedral PZNC- a few micronBs below the surfaces[4, 23]and behaves dif-
O
x%PT crystals as-grownhave relaxor character and are, ferently from the bulk, as shown by Ohwada et al. [14].
therefore,crystallographicallydisordered. Inordertoin- At X17B1, the high-flux monochromatic beam was ob-
duce the ferroelectric long-range ordered state it is nec- tained from a superconducting wiggler device by use of
essary to pole them under an electric field. This poling a Si(220)crystal in Laue-Bragggeometry. At X22A, the
is typically accomplished by applying a field of about 10 third-order reflection of a Si(111) monochromator crys-
kV/cm at room temperature. If the electric field is ap- tal was used to provide the 32 keV beam. Both beam-
PZN-4.5%PT 3
a /(cid:214) 2
4.08
m
R M
b /(cid:214) 2 PZN-4.5%PT
A
) m
Å 4.09
c
( m
M T
s b = 9A0.08o
r
e
t
e c
m 4.08 t
)4.06
aÅ
c
r(
a m
s D l/l
p
r
e
et
e 4.07
c
m
i
t
ta
a
r
La
p4.04

e 4.06 a /(cid:214) 2
c
m
i
t
t
a
0 10 20 30 40
L
E(kV/cm)
FIG. 2: Evolution of lattice parameters with an electric field FIG. 3: Evolution of lattice parameters with an electric field
applied along the [001] direction in a 4.5PT crystal (dimen- applied along the [001] direction in the second 4.5PT crys-
sions34x3.0x15mm3)intherhombohedralandmonoclinicphases, tal in the monoclinic and tetagonal phases, as observed by
a
asobservedbyhigh-energyx-raydiffraction(top). Meshscans high-energy x-ray diffraction. The thick lines represents the
intheHHLzoneofrecipbroca/l(cid:214)sp2acearoundthepseudo-cubic macroscopictunipolarstrainalongthe[00I1n]tdeinrescittiyo n(Kocbptasi)n e d
(220) reflection are shownmin th e bottom plots for E= 20 bydilatometricmeasurementso nthesamesample. Thethin-
kV/cm (bottom-left) and E= 30kV/cm (bottom-right). In- nerlines are a guide tothe eye.
437- 500
tensities are on a linear scale
E= 20 kV/cm 62- 125
0.005 0.005 E= 30 kV/cm
4.04 III. RESULTS
Three 4.5PT crystals (A, B and C) were studied. In
crystals A and B the monoclinic phase was unambigu-
lionesareequippedwithfour-circleHuberdiffractometers,
wi0th Si0(2.210) and Si(111) analyzer-crystals mounted in ously observed for E ¡ 30 kV/cm, consistent with the
9 macroscopic strain measurements shown in Fig. 1a [2].
the diffraction path at X17B1 and X22A, respectively.
-
0.000 0.0T0h0e results obtained for crystal A are summarized in
L b Fig. 2. The initial state at E = 0, for which a /√2
m
Forth0e.0diffractionexperimentswithanin-situ electric > cm > bm/√2, corresponds to a rhombohedral phase
field applied, a special sample holder was constructed in with ar =4.055˚A and αr =89.9o [24]. Under the appli-
whichthesam0plewiresweresolde1re0dtothe high-volta2ge0 cationofanele3c0tricfieldalongthe[40001]direction,amon-
leads, and the samples were unclamped and free to de- oclinic phase of MA-type is induced for E < 30 kV/cm,
form. The samples were coated with a silicone dieleEctr(ickVa/scshmown)byasteadydecreaseinam/√2andbm/√2,and
-0c.o0m05pound (GC Electronics-type Z5) to prevent arcing, a corresponding increase in cm (Fig. 2, top), and by a
-0.005
andkeptinplace withatiny dabofvacuumgrease. The mesh scan in the reciprocal HHL plane (the monoclinic
maximum value of the applied field was limited by the plane) around the pseudocubic (220) reflection at E =
dielectric breakdown of the samples; in the case of the 20 kV/cm (Fig. 2, bottom-left). This monoclinic phase
thin1n.9e9st5samples(d=2.000.50mm),fields2a.s00h5ighas45kV/2c.0m10 is1s.i9m95ilar to the o2n.0e0o0bserved in 2P.0Z0T5[5], in whic2h.0a1m0
were achieved. and b are rotated 45o about the pseudocubic [001] di-
H =K m H = K
m m m m
PZN-8%PT HOL zone around (200)
4
c
0.02 0.02
a) d)
PZN-4.5%PT HHL zone around (330)
c
0.02 0.02
a) d)
0.01 0.01
0.01 0.01
0.00 0.00
L L
-0.01 -0.01
0.00 E= 0 kV/cm E= 12 kV/cm 0.00
L -0.02 -0.02 L
3.000 3.005 3.010 3.000 3.005 3.010
0.02 0.02
b) c)
0.01 0.01
-0.01 -0.01
0.00 0.00
L L
-0.01 -0.01
0 KV/cm
35 KV/cm
E= 7 kV/cm E= 10kV/cm
-0.02 -0.02 -0.02 -0.02
3.000 3.005 3.010 3.000 3.005 3.010
1.99 H=K2.00 2.01 H=K 2.02 1.99 2.00 2.01 2.02
I (kcps)
7.3-15, 0.9-1.8, 0.1-0.2
0.02 0.02
c)
b)
FIG. 4: Mesh scans around thepseudo-cubic(330) reflection
intheHHLzoneofthereciprocalspaceforthesecondcrystal FIG. 5: Mesh scans around the pseudo-cubic(200) reflection
of 4.5PT at E= 0 (a), 7 (b), 10 (c) and 12 (d) kV/cm. The in the H0L (or 0KL) zone of reciprocal space for 8PT at E=
intensities are plotted on a logarithmic scale 0 (a), 9 (b), 15 (c) and 35 (d) kV/cm. The intensities are
plotted on a logarithmic scale
0.01 0.01
rection and are approximately equal to a √2, and c
o m
∼
a , where a is the pseudocubic lattice parameter. The
o o ent;theyshowedunambiguouslyacrossoverbetweenthe
intensity distribution observed at 20 kV/cm in Fig. 2
monoclinicandtetragonalphases,butatananomalously
(bottom-left) arises from the presence of four different
lowvalue of˜11kV/cmforthis composition. The evolu-
0.0M0A domains formed when the field is applied along the tion of the lattice parameters under a [001] electric fi0e.l0d0
L [001] direction, as previously explained in ref. 10. Peak s forthiscrystalisshowninFig. 3. Inthiscase,thetetrag- L
are observed at two different positions along the longi-
onal phase, characterized by two lattice parameters a
t
tudinal scans around H = K = 2, corresponding to a
m and c , is indeed observed at high fields, as proposed by
t
and b respectively. The splitting between the pair of
m Park and Shrout on the basis of macroscopic measure-
peaks at the smaller value of H = K (i.e. the larger lat-
ments [2]. When the field is decreased, the tetragonal
tice parameter a ) along the transverse (field) direction
-0.0is1related to themmonoclinic angle, β = 90.08o. For E distortion ct/at also decreases; however, the tetrago-0na.0l1
phase does not transform directly into a rhombohedral
= 30 kV/cm, the mesh scans have a more complicated
phase at low fields. Instead, a monoclinic phase is ob-
appearance in that most of the intensity has coalesced
served as a splits into a and b , and the angle β be-
t m m
within a single broad region, but with a distribution of tweena andc becomesslightlygreaterthan90o. This
m m
lattice parameters (Fig. 2, bottom-right), which we in-
9 KV/cm monoclinic phase is also of MA-t1yp5e, KanVd a/cs cman be seen
terpret as an incomplete transformation to a tetragonal
in Fig. 3, the crystal remains monoclinic even at E =
-0.0p2hase. However, even at E = 35 kV/cm, we did not ob- 0. It is noteworthy that at this point, c a /-√02.0,2
serve a s1i.n9g9le tetrago2n.0al0phase, p2ro.0b1ably beca2u.s0e2of the 1.99 2.00 2.01 2m.0∼2 m
corresponding to the singular case of a monoclinic cell
existence ofseveralregionswith differenttransformation
H, K with the polarization v eHct,o rKlying along the rhombohe-
fields.
dral polar axis [111], probably as a result of the under-
The results obtained for crystal C were rather differ- lying monoclinic distortion of the oxygen octahedra. In
Intensity (Kcps)
21-50 0.7-1.6 0.1-0.3
5
ordertorecoverthe initialrhombohedralphase,itwould PZN-8%PT
be necessary to apply a field in the reverse direction.
Fig. 4 shows the region of theMreciprocal HHL plane
around the pseudocubic (330) reflectcion for several dif- T
ferent values of E. The intensity distributions observed
4.10
inFigs. 4a-c(E=0,7and10kV/cm,respectively)arise
from the four different M monoclinic domains formed
A c
when the field is applied along the [001] direction, as
t
noted previously. Once again, peaks are observedat two
)differentpositionsalongthe longitudinalscansaroundH
Å
=K=3,correspondingtoa andb respectively. Note
m m
(
that H = K = L = 3 is defined in order to reflect the

svalueofc atE=0,sothatthe valueH= K=3inthe
m
r
escans4m.e0an8s that am = cm. The splitting between the
tpair of peaks at the smaller value of H = K corresponds
eto a monoclinic anglecof β = 90.13o . As the field is in-
m
creased,botha andb decrease,asshownbytheshifts
m mm
ato largerH = K values. At E = 12 kV/cm, the intensity
rhas coalesced into a single peak (Fig. 4d) and the crys-
a
tal is in the tetragonal phase (i.e. a = b , β = 90o).
p m m
From Fig. 3, it is seen that the transformation occurs

eat about 11 kV/cm. The composition of the crystal C
4.06
cwas confirmed using dielectric measurement, with T
max
tibeing 170oC. In addition to the exceptionally low phase
attransition field, the strain behavior asasociated with the
Lphase transition in Fig. 3 does not showmthe typicalhys-
teretic jump at the transition field. We suspect that the
defectstructureandsubsequentabnormaldomainconfig-

urationmayaffectits phasetransitionbehavior. Further
investigation is on going.
FIG. 6: Evolution of lattice parameters with an electric field
4.5P4T.0th4erefore behaves differently than 8PT, as can
applied along the [001] direction for a 8PT crystal. Solid
be readily inferred from Fig.1b. As reported in ref. 4,
symbols represent the monoclinic lattice parameters. Open
application of a [001] electric field to the latter yields a
symbolsrepresentthetetragonallaatticeparameters. Inverted
monocliniccellofM -type,withaprimitivecellofabout
C trianglesshowtheresultsofmeasuremtentsofthecparameter
4˚Aalongtheedge. Inthe8PTcasethecharacteristicin-
with a 100 µm beam at two different depths in the crystal ,
tensitydistributionresultingfromthefourpossiblemon- as illustrated schematically in the inset.
oclinic domains is observed in the 0KL (or H0L) zone of
b
reciprocal space, since the monoclinic angle is now con-
m
)
tained within the (010) plane. Figs. 5a-d show such
.
gintens4ity.0d2istributions aroundthe pseudo-cubic (200)re-
eflection,forseveraldifferentvaluesoftheappliedelectric
dfield, E= 0, 9, 15 and 35 kV/cm, respectively. Unlike
oclinic and tetragonal phases depends on the sample
(
4.5PT, bm remains approximately constant at K= 2.015 composition, as well as on the experimental conditions,
o
asthefieldisincreased,whilea decreases,approaching
0 m such as mechanical clamping. High energy x-ray diffrac-
0.1
b (see also Fig.1b). At sufficiently high fields, a be-
9m m tion has revealed that the critical fields at which the
-comes equal to bm and the crystal becomes tetragonal, monoclinic-to-tetragonal phase change takes place are
showing a single reflection around the (200) point in re-
different acrossthe sample thickness[14], most likely due
b
ciprocal space (Fig.5d), as also illustrated by the dotted
to a distribution of strain. Fig. 6 shows the lattice pa-
lines in0Fi.g0. 1b.
rametersofoneofthe8PTcrystalsunderan[001]electric
Whenthefie0ldisremoved,thec1ry0staldoesnotbecom2e0 field. The res3ult0s are very similar4to0those in Fig. 1b[4]
rhombohedral,but resembles 4.5PTinthis respect, with but in this case the tetragonal phase could be reached.
am =cm = bm, β = 90o. However, unlike MA, in this We observedanintermediateregion(7<E<20kV/cm)
6 6
case the equality am =cm corresponds to a higher sEym-(kVin w/hcichmthe t)wo phases,monoclinic MC and tetragonal,
metry than MC, namely orthorhombic, O (see also Fig. coexist. Measurements of the c lattice parameter made
1c)[5]. This ”pseudo-monoclinic” O phase (O*) has re- withanarrowbeamabout100µminwidth(invertedtri-
centlybeenobservedinthephasediagramofPZN-x%PT angles in Fig. 6) showed that the tetragonal phase was
for 9PT and 10PT[6, 7, 8]. indeed reachedatdifferent fieldvalues acrossthe sample
Aswehavementioned,thecrossoverbetweenthemon- thickness, between 7-20 kV/cm.
6
IV. DISCUSSION

The most outstanding feature of the [001]-oriented
rhombohedralPZN-x%PTcrystalsis the extremely high
deformation that can be obtained under the application
ofanelectricfield. Ofparamountinterestfromtheappli-
PZN-xPT
cationspoint-of-viewisthatlargeelongationscanbe ob-
tained with very little hysteresis, which means virtually
4.5%
no domain-wall motion. As observed in the ∆l/l mea-
surements plotted in Fig.3, the macroscopicdeformation
of about 0.6% in 4.5PT for E 40kV/cm, corresponds
≤
very closely to the elongation of the unit cell along the
field direction. The observed total strain is due partly
to polarization rotation and elongation in the M phase
A
between4[1011]and[001]andpartlyduetothec-axiselon-
8%
gation of the unit cell in the tetragonal phase. However,
achangeofslopeisclearlyobservedinboth∆l/landthe
c parameter with applied field at the M -T phase tran-
A
sit ion, from which it can be inferred directly that the
)
pimezoelectric modulus (elongation per volt) in the mon-
oclinic phase is about five times larger than that in the
c
te/tragonal phase.
V T
The observed macroscopic strain depends on the ini-
k
tia(l domain configuration,and thus, onthe previous his-

to ry of the crystal. The coincidence of the microscopic
an d macroscopic measurements in Fig. 2 indicates that
]
th1e crystal consisted only of domains with polarizations
350o away from the field dirMection [001] (see refs. 2, 25).
0
When the field is applied, the polarization of the do-
m| [ains r2ota0tes until the crystalAbecomes tetragonal and
| FIG. 7: Sketch of the [001]-electric field vs. composition
m onodomain with the polarization parallel to the field.
E phase diagram for PZN-x%PT
However, a negative electric field or mechanical pres-
sure alongthe field directioncanfavordomains with po-
larizations closer to the plane perpendicular to the field,
asrecently describedforthe PZTcase[26]. This factcan which can also produce some exotic and unusual diffrac-
explain the dramatic differences observed between the tion intensity distributions, especially for compositions
stress-free-bipolar and slightly-clamped-unipolar strain veryclosetotheMPB.Fig. 8ashowsthethree-peakpat-
curves reported by Viehland [17] on 8PT crystals. The tern usually observed in 8PT crystals in the HOL zone
deep strain level of -0.6% and the aggregate strain level aroundthe pseudo-cubic (200)reflection at E=0, arising
of 1.2% observed in the bipolar strain curve of ¡001¿- from theMfour different monoclinic domains[4]. However,
oriented8PTcrystalscorrespondto the maximumspon- on one occasion a very interesting rod-like intensity dis-
C
taneous strain observed for MC, i.e., the strain between tribution was observed in the same crystal upon the re-
the monoclinic a and b, and b and c axes, respectively movaloftheelectricfield(Fig. 8b),thed-spacingsofthe
(see Fig. 10b). rods being identical to those of the Bragg peaks. Un-
The extreme sensitivity of these materials to the ex- fortunately, we were never able to reproduce such a rod
0 5 10 15
perimental conditions, in particular to stress, is an in- pattern, but we speculate that this interesting behavior
dication of the near-degeneracy of the different phases maybeduetoacomplicateddomainformation. Another
around their MPB’s. Although the exact field v axlue s(%at PebxaTmipOleof)unusualdiffusescatteringisshowninFig. 8c.,
which the phase transitions happen would need to be correspon3ding to the same region of the reciprocalspace
determined for very specific experimental conditions, we of a 8PT crsytal under a 25 kV/cm [001]-electric field.
still can sketch an electric field vs. composition phase Most of the crystal has transformed into the tetragonal
diagram for rhombohedral PZN-x%PT as shown in Fig. phase characterized by a single lattice parameter in this
7. ClosetotheMPBat8PT,theMA phaseisonlystable zone(asinFig.5d). Thesharpnessofthisreflectionshows
atverylow fields[14], while no MC phase has beenso far the excellent quality of the crystal and the accuracy of
observed for 4.5PT. the electric field orientation. However, when plotted on
An intricate and history-dependent domain configura- a logarithmic scale (as in Fig. 8c), a fascinating fish-like
tion is another consequence of the high degeneracy of shape is revealed, indicating that a small fraction of the
the various phases displayed by the PZN-xPT system, sample retains a distribution of both, lattice parameters
7
To conclude, the polarization rotation path has been
PZN-8%PT
investigated for rhombohedral 4.5PT and 8PT single

crystals under a [001] electric field. In 4.5PT the po-
a)
larizationvectorrotatesdirectlyfrom[111]towards[001]
via a monoEcli=ni c0M kVph/acsem. In 8PT, which lies closer to
A
0.01 the MPB, the polarization vector jumps at a relatively
low field to the (010)plane androtates in this plane, via
a monoclinic M phase, towards [001] when the field is
C
increased[4]. For both compositions a single tetragonal
phase has been observed at high fields. The behavior of
0.00 the lattice parameters as a function of electric field can
L
account for the ultra-high macroscopic piezoelectric de-
formationsintermsofthemicroscopicdeformationofthe
unit cell (rotation plus elongation).
Onoccasions,uniquecontourplotshavebeenrecorded,
-0.01
especiallyforthe8PTcrystals,whichshowverypeculiar
intensitydistributionsandarebelievedtoreflecttheexis-
tence ofheavilytwinnedmaterialsandcomplicatedlocal
1.99 2.00 2.01 effects. Fur2t.h0e2r work is neede2d.0t3o fully understand some
of these features; in particular, a detailed study of the
complicated diffuse scattering would provide very use-
b)
ful information about the local order in these materials.
E= 0 kV/cm
However, we may safely conclude that all the reported
0.01
observations are consequences of the high anharmonic-
ity andthe delicate energybalance betweenthe different
phases in these highly deformable materials.
L
0.00

Acknowledgments
FIG.8: a)Typicalprofilesobservedfor8PTintheHOLzone
ofreciprocalspacearoundthepseudo-cubic(200)reflectionat
Stimulating discussions with G. Baldinozzi, L. Bel-
E=0. b)Exampleofanunusualprofileobservedinthesame
regio-0n..0c1) An unusual intensity distribution observed for the laiche, L.E. Cross, B. Dkhil, M. Durbin, K. Hirota, K.
samecompositioninthetetragonalphase. Theintensitiesare Ohwada, J-M. Kiat, D. Vanderbilt, D. Viehland, and T.
on a logarithmic scale Vogt, as well as the technical support of A. Langhorn
are gratefully acknowledged. Financial support by DOE
1.99 2.00 2.01 2.02 2.03
under contractNo. DE-AC02-98CH10886andthe Office

and monoclinic angle. of Naval Research is also acknowledged.
c)
0.02 E= 25 kV/cm
[1] J. Kuwata, K. Uchino, and S. Nomura, Jpn.J. Appl. Cox, B.Nohedaand G.Shirane,J. Phys.Soc. Japan (in
P0h.0y1s., Part1 21, 1298 (1982). press). E-print: cond-mat/00106552.
[2] S-E. Park and T.R. Shrout, J. Appl. Phys. 82, 1804 [8] D. La-Orauttapong, B. Noheda, Z-G. Ye,P.M. Gehring,
(1997). J.Toulouse, D.E.Cox,andG.Shirane,Phys.Rev.B(in
[3] S-F. Liu, S-E. Park, T. Shrout and L.E. Cross, J. Appl. press). E-print: cond-mat/0108264
L 0.00
Phys.85, 2810 (1999) [9] G. Xu, H. Luo, H. Xu and Z. Yin, Phys. Rev. B 64,
[4] B.Noheda,D.E.Cox,G.Shirane,S-E.Park,L.E.Cross, 020102(2001)
and Z. Zhong, Phys.Rev. Lett.86, 3891 (2001). [10] Z-G.Ye,B.Noheda,M.Dong,D.E.Cox,andG.Shirane,
[5]-B0..0N1oheda, D. E. Cox, G. Shirane, J.A. Gonzalo, L.E. Phys. Rev.B 64, 184114 (2001).
Cross, and S-E.Park, Appl.Phys. Lett 74, 2059 (1999); [11] J.-M.Kiat,Y.Uesu,B.Dkhil,M.Matsuda,C.Malibert,
B.Noheda,J.A.Gonzalo,L.E.Cross,R.Guo,S-E.Park, and G. Calvarin, Phys.Rev.B. (in press).
D.E.Cox,andG.Shirane,Phys.Rev.B61,8687(2000); [12] A.K.SinghandD.Pandey,J.Phys.:Condens.Matt.13,
-0.02
B. Noheda,D.E. Cox, G.ShiraneR,Guo, B. Jones, and L931 (2001)
L.E. Cross , P1hy.9s.9Rev.B. 63, 14210.030(2001). 2.01 [13] R. Guo2,.L0.2E. Cross, S-E. 2P.a0rk3, B. Noheda, D.E. Cox ,
[6] D.E.Cox,B.Noheda,G.Shirane,Y.Uesu,K.Fujishiro, and G. Shirane, Phys.Rev.Lett. 84, 5423 (2000).
H,K
and Y. Yamada,Appl. Phys.Lett 79, 400 (2001). [14] K. Ohwada, K. Hirota, P.W. Rehrig, P.M. Gehring, B.
[7] Y. Uesu, M. Matsuda, Y. Yamada, K. Fujishiro, D.E. Noheda, Y. Fujii, S-E. Park, and G. Shirane, J. Phys.
Intensity (Kcps)
41 - 80; 0.2- 0.4
8
Soc. Japan 70, 2778 (2001) 64, 060103(R) (2001)
[15] D-S. Paik, S-E. Park, S. Wada, S-F. Liu and T. Shrout, [22] H. Fu and R.E. Cohen, Nature 403, 281 (2000).
J. Appl.Phys. 85, 1080 (1999) [23] B. Noheda, D.E. Cox, and G. Shirane, Ferroelectrics (in
[16] M.K. Durbin, J.C. Hicks, S.-E. park, and T.R. Shrout, press). E-print: cond-mat/0109545.
J. Appl.Phys. 87, 8159 (2000). [24] It can be easily shown that in the rhombohedral phase
[17] D. Viehland, J. Appl. Phys. 88, 4794 (2000); D. a , b and c are not longer independent, and are re-
m m m
Viehland, J. Powers and L. Ewart, J. Appl. Phys. 88, latedtotherhombohedrallatticeparameters,a andα ,
r r
4907 (2000). as follows: a = 2a cos(α /2), b = 2a sin(α /2) and
m r r m r r
[18] D.VanderbiltandM.H.Cohen,Phys.Rev.B.63,94108 c =a .Themonoclinicangle,β,isthendefinedas180o-
m r
(2001). φ, where cos(φ)=[1−2sin2(α /2)]/cos(α /2).
r r
[19] J-M. Kiat, G. Baldinozzi, M. Dunlop, C. Malibert, B. [25] L.E.Cross, AIPConferenceProceedings,vol.535,pp.1-
Dkhil, C. Menoret, O. Masson, and M.T. Fernandez- 15 (2000)
Diaz, J. Phys.: Condens. Matter 12, 8411 (2000) [26] P. Chaplya and G. P. Carman, J. Appl. Phys. 90, 2578
[20] L. Bellaiche, A. Garcia, and D. Vanderbilt, Phys. Rev. (2001)
Lett.84, 5427 (2000)
[21] L.Bellaiche,A.Garcia, andD.Vanderbilt,Phys.Rev.B