Temperature dependent XAFS studies of local atomic structure of the perovskitetype zirconates
ABSTRACT Temperature dependent preedge and extended xray absorption fine structure measurements at the Zr K edge for the perovskitetype zirconates PbZr0.515Ti0.485O3 (PZT), PbZrO3 (PZ), and BaZrO3 are performed. To carry out a more accurate study of the weak reconstruction of the local atomic structure we employed a combination of two techniques: (i) analysis of the preedge fine structure, and (ii) analysis of the Fourier transform of the difference between χ(k) functions obtained at different temperatures. A detailed investigation of local atomic structure in the cubic phase for all the crystals is also performed. It is shown that neither the displacive nor the orderdisorder model can describe correctly the changes of local atomic structure during phase transitions in PZ and PZT. A spherical model describing the local atomic structure of perovskitetype crystals suffering structural phase transitions is proposed.

Article: Effect of the ferroelastic order parameter on the formation of lead titanatezirconate phases
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ABSTRACT: A phase diagram identical to the xT diagram for lead zirconatetitanate (PZT) solid solutions (PbZr1 − x Tix O3) was obtained on the basis of a statistical 12minima model in the vicinity of the cubic phase boundary. The applicability of this model to the phase transitions in PZT is discussed.Bulletin of the Russian Academy of Sciences Physics 01/2010; 74(9).  [Show abstract] [Hide abstract]
ABSTRACT: The ferroelectricantiferroelectric phase transitions induced by hydrostatic pressure in solid solutions based on lead zirconatetitanate (PZT) with introducing 20 at % tin into B sites and composites based on these ceramics have been studied. In the composites with the same composition of solid solution, the transition pressure can be varied within wide ranges depending on the type of binders. The latter is due to the vitrification of the binder and, consequently, the formation of a rigid framework preventing the transmission of pressure to the ceramic matrix.Physics of the Solid State 54(5). · 0.77 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The ferroelectricantiferroelectric phase transitions in lead zirconatetitanatebased solid solutions have been considered with allowance made for anharmonicity of the crystal potential. In the phase diagram of lead zirconatetitanate, the boundary separating the regions of the ferroelectric and antiferroelectric states are shifted toward higher titanium concentrations. The calculated and experimental phase diagrams are presented for such cases.Physics of the Solid State 54(5). · 0.77 Impact Factor
Page 1
Temperature dependent XAFS studies of local atomic structure of the perovskitetype zirconates
R. V. Vedrinskii,1E. S. Nazarenko,1,2M. P. Lemeshko,1V. Nassif,3,5O. Proux,4,5A. A. Novakovich,1and Y. Joly2
1Institute of Physics, Rostov State University, 194 Stachky Avenue, RostovonDon 344090, Russia
2Laboratoire de Cristallographie, CNRS, l’Université Joseph Fourier, 166 Boîte Postale, F38042 Grenoble Cedex 9, France
3CEA/Grenoble, DRFMC/SP2M/NRS, F38054 Grenoble Cedex 9, France
4Laboratoire de Géophysique Interne et Tectonophysique, UMR CNRS, Université Joseph Fourier,
F38400 SaintMartinD’Hères, France
5BM30b CRGFAME, European Synchrotron Radiation Facility, F38043 Grenoble Cedex 9, France
?Received 31 July 2005; revised manuscript received 8 March 2006; published 17 April 2006?
Temperature dependent preedge and extended xray absorption fine structure measurements at the Zr K edge
for the perovskitetype zirconates PbZr0.515Ti0.485O3?PZT?, PbZrO3?PZ?, and BaZrO3are performed. To carry
out a more accurate study of the weak reconstruction of the local atomic structure we employed a combination
of two techniques: ?i? analysis of the preedge fine structure, and ?ii? analysis of the Fourier transform of the
difference between ??k? functions obtained at different temperatures. A detailed investigation of local atomic
structure in the cubic phase for all the crystals is also performed. It is shown that neither the displacive nor the
orderdisorder model can describe correctly the changes of local atomic structure during phase transitions in PZ
and PZT.Aspherical model describing the local atomic structure of perovskitetype crystals suffering structural
phase transitions is proposed.
DOI: 10.1103/PhysRevB.73.134109PACS number?s?: 61.10.Ht, 63.90.?t, 77.90.?k
I. INTRODUCTION
Perovskitetype materials are fundamentally and techno
logically important for their ferroelectric and piezoelectric
properties. Most of the perovskite oxides are cubic at high
temperatures and often have a variety of lowersymmetry
phases at lower temperatures. To realize the microscopic na
ture of the phase transitions in perovskites, it is important to
ascertain how their local atomic structure changes as a func
tion of temperature especially near the phase transition
points. Nowadays the most widespread methods of local
structure studies employ xray absorption fine structure
?XAFS?. In this contribution we investigate the temperature
dependence of the local atomic structure for perovskitetype
zirconates using XAFS of Zr K spectra in both the extended
?EXAFS? and preedge regions.
Among the materials under consideration the ferroelectric
PbZr1−xTixO3solid solutions have attracted special attention
owing to their unusually large piezoelectric coefficients near
the morphotropic phase boundary which divides regions with
tetragonal and rhombohedral structures.1This fact allows us
ing the PbZr1−xTixO3ceramics in various piezoelectric and
ferroelectric devices. The results obtained in this paper for
PbZr0.515Ti0.485O3?PZT? are compared with those obtained
for lead zirconate PbZrO3?PZ?, which is an end member of
the PZT solid solutions, and crysalline paraelectic BaZrO3
?BZ?, which is cubic at all temperatures.
The local structure rearrangement during phase transitions
in perovskitetype crystals is under discussion for several
decades. Nowadays two alternative structural models are of
ten used for perovskitetype materials. The first, “displacive”
model2assumes that in the lowtemperature phases cation
sites are displaced along the polar axes relative to the oxygen
framework and in the cubic phase they are located in the
ideal perovskite positions. According to another, the so
called “eightsite” model,3the cations are displaced from the
centers of oxygen octahedrons to offcenter positions located
along eight ?111? directions in all the phases. The number of
such offcenter positions occupied by the cations changes as
a result of phase transitions, which are considered to be of
the orderdisorder type. The eightsite model is not a unique
nsite model to describe the phase transitions in perovskites.
In particular, six and 12site models can also be used.4Ac
cording to them the cations are displaced from the centers of
oxygen octahedrons along the axes of fourfold and twofold
symmetry, respectively.
The results of EXAFS studies of perovskitetype oxides
are contradictory. Some authors did not find significant
change of the firstshell contribution to EXAFS at the phase
transition points for the powder samples and hence consid
ered the eightsite model to be valid5,6and the transitions to
be of the orderdisorder type. However, analysis of the po
larized XAFS performed for single crystals showed that in
the lowtemperature phases the displacive model is in good
agreement with the experimental data, whereas the eightsite
model provides better agreement with the local atomic struc
ture in the cubic phase.7,8The idea that different models of
local atomic structure are appropriate in different phases was
recently supported by firstprinciples calculations9and NMR
studies10of the atomic structure of the BaTiO3crystal.
In the present paper the XAFS of Zr K spectra obtained
for powder samples is employed. To carry out a more accu
rate study of local atomic structure reconstruction, a combi
nation of two methods is used: ?i? differential analysis of the
preedge fine structure ?PEFS?, and ?ii? the “differential
EXAFS” method, i.e., the analysis of the Fourier transform
of the difference between ??k? functions obtained for differ
ent temperatures.
II. EXPERIMENT
Powder samples of BaZrO3and PbZr0.515Ti0.485O3were
prepared at the Institute of Physics at Rostov State Univer
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Page 2
sity by standard solidstate reactions of BaCO3, ZrO2and
PbO, ZrO2, TiO2, respectively. Several grindings and firings
in air at temperatures up to 1300 °C for BZ and 1240 °C for
PZT were performed. To prepare the PZ sample a single
crystal was milled. Xray powder diffraction measurements
confirmed that the samples were singlephase ones.
Preedge and EXAFS Zr Kedge spectra were collected at
the European Synchrotron
Grenoble, France? at the beamline BM30b ?FAME?.11The
storage ring was run at energy 6.0 GeV with the electron
current about 30 mA. Spectra were recorded in the transmis
sion mode using a doublecrystal Si?220? monochromator.
The full fan delivered by the bending magnet source was
focused in the horizontal plane by the second crystal of the
monochromator and by the second Rhcoated mirror in the
vertical plane. Harmonic rejection is achieved with two Rh
coated mirrors, before and after the monochromator. Finally,
a feedback system was used to maximize the output of the
twocrystal xray monochromator. The spectra were scanned
in the range of 17.8–19.22 keV, with a 0.5 eV energy step.
The samples were prepared from ground ceramic diluted
with BN and pressed into tablets.
Kedge xray absorption spectra for PZT ceramics were
measured at room temperature, which is the lowest tempera
ture of the tetragonal phase,1at the temperature 100 °C,
which is far from any phase transition, at 300 °C, which is
close to the Curie point ?360 °C?, and at 500 °C in the
paraelectric cubic phase. For comparison purposes the spec
tra for PZ and BZ were collected for the same set of tem
peratures. At 20 and 100 °C the PZ crystal is monoclinic
with antiferroelectric displacements of Zr atoms. The Curie
temperature for PZ is about 230°C.12,13Thus for the spectra
measurements at 300 and 500 °C PZ was in the cubic phase
far from the phase transition point. BZ is cubic for all the
temperatures.14
RadiationFacility
?ESRF,
III. RESULTS AND DISCUSSION
A. Preedge fine structure analysis
The preedge fine structure of the B atom K absorption
spectrum provides valuable information on the local atomic
structure of BO6octahedrons in ABO3perovskite crystals.
PEFS appears before the main rise of the B K spectrum and
it is caused by transitions of the B atom 1s electrons to the
lower conduction bands originating from atomic d states of
the transition metal atoms B. As was shown earlier,15if the B
atoms are displaced from their centrosymmetrical positions,
in the B atom PEFS there appears an additional peak, which
is absent otherwise. This peak is caused by mixing of unoc
cupied p and d states of the B atom and it is called
“the pd peak” hereafter.As was shown by calculations,15the
pd peak is significantly more sensitive to local distortions of
the BO6octahedrons than other features of the PEFS. For a
polycrystalline sample the total area I under this peak is pro
portional to the meansquare displacement ?MSD? ???x ??2? of
the B atom from the center of the BO6octahedron:15
I ??
i
???xi?2? = ???x ??2?,
?1?
where ?xiis the displacement of the B atom from the center
of the ith OBO atomic chain ?i=1,2,3? along this chain
and ???xi?2? is the corresponding MSD. If the xray electric
field vector e ? is directed along the ith OBO chain of a
singlecrystal sample, the pd peak area is proportional to
???xi?2?.
Experimental studies of the Ti K xray absorption near
edge structure ?XANES? for a PbTiO3?PT? single crystal16
have shown strong angular and temperature dependence of
the pd peak. It was found that if e ? is parallel to the axis of
fourfold symmetry of the tetragonal PT crystal this peak is
very intense at room temperature and decreases when the
temperature increases. On the contrary, if e ? is perpendicular
to this axis the pd peak is weak at room temperature and it
increases at higher temperatures. In agreement with the cal
culations, other features of the PEFS are nearly independent
of temperature and polarization. At the same time, the aver
aged pd peak area determined from the Ti K spectrum of a
powder PT sample17slightly decreases when the temperature
increases. This result seems to be quite strange since, accord
ing to ?1?, the averaged pd peak area is proportional to the
MSD of the Ti atom from the center of the TiO6octahedron
and one can expect that this value should increase at higher
temperatures. Such an expected dependence of the pd peak
area on temperature really takes place for the EuTiO3crystal,
which is paraelectric at all temperatures and does not suffer
structural phase transitions18unlike the ferroelectric PT crys
tal.
The results obtained for the niobates KNbO3?KN? and
NaNbO3?NN?, which undergo structural phase transitions,
are similar to those for PT. The Nb K XAFS studies per
formed for KN ?Refs. 7 and 8? and NN ?Ref. 19? single
crystals showed strong dependence of the preedge area on
temperature and polarization. On the other hand the averaged
preedge area determined from the Nb K spectra measured for
the powder samples is almost temperature independent in a
wide temperature interval.
These results can be reasonably explained within the fol
lowing assumption. The potential surface for the atom B can
be approximated by one of the three curves shown in Fig. 1,
where r is the distance from the atom B to the immediate
center of the BO6octahedron. In the case of paraelectric
ABO3 crystals with harmonic crystal lattice dynamics
?EuTiO3? the potential surface is a parabolic function shown
by curve Fig. 1?a? ?onesite model? ?singlewell potential sur
face?. In such a case the MSD and the averaged preedge area
increase, when the temperature increases, in agreement with
the experiment. In the case of anharmonic ABO3crystals
suffering structural phase transitions ?PT, KN, and NN? the
most probable potential surfaces take on the deepdouble
well ?Fig. 1?b?? and shallowdouble well ?Fig. 1?c?? forms.
The maximum value of the deepdoublewell potential curve
in Fig. 1?b? ?r=0? very much exceeds the minimum one ?r
=r0?. This means that the difference between these two val
ues is much greater than the temperature measured in the
energy scale. In such a case the MSD and the averaged
preedge area are almost temperature independent as they re
ally are in the case of KN and NN. On the contrary, the
maximum value of the shallowdoublewell potential curve
?Fig. 1?c?? slightly exceeds the minimum one. Then the MSD
and the averaged preedge area decrease when the tempera
VEDRINSKII et al.
PHYSICAL REVIEW B 73, 134109 ?2006?
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Page 3
ture increases as is the case of PT. Certainly, the potential
surfaces under consideration are angularly dependent, but the
preedge structure measurements performed for powder
samples do not provide information on this dependence.
The preedge regions of the experimental Zr K XANES
spectra for BZ, PZ, and PZT powder samples obtained in the
present investigation are shown in Figs. 2–4. The differences
between the spectra measured at higher temperatures and at
the room temperature are presented in the insets. Unfortu
nately, it is impossible to analyze the PEFS of the Zr K
spectra in more detail, as is possible in the case of PT, due to
the large Zr K hole width ??K?3.84 eV? but taking into
account the results for PT mentioned above,16one can rea
sonably assume that the dependence of the total preedge area
on temperature is mainly caused by the pd peak. In order to
study the sensitivity of the total preedge area to the MSD
???x ??2?, the Zr K XANES spectra for the cubic BZ crystal
were calculated for different displacements of the Zr atom
from its centrosymmetrical position in the cubic lattice. The
simulations were performed by the full multiple scattering
FIG. 1. The potential surfaces for the atom B in different ABO3
perovskites: ?a? EuTiO3 and BaZrO3, ?b? KNbO3, PbZrO3,
PbZr0.515Ti0.485O3, and ?c? PbTiO3, r is the distance from the atom
B to the center of the BO6octahedron.
FIG. 2. Preedge region of the Zr K spectrum at different tem
peratures for BaZrO3. Inset: difference between the spectra for 100,
300, and 500 °C and that for 20 °C.
FIG. 3. Preedge region of the Zr K spectrum at different tem
peratures for PbZrO3. Inset: difference between the spectra for 100,
300, and 500 °C and that for 20 °C.
FIG. 4. Preedge region of the Zr K spectrum at different tem
peratures for PbZr0.515Ti0.485O3. Inset: difference between the spec
tra for 100, 300, and 500 °C and that for 20 °C.
TEMPERATURE DEPENDENT XAFS STUDIES OF LOCAL¼
PHYSICAL REVIEW B 73, 134109 ?2006?
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Page 4
method using the XKDQ code.15,20The calculated spectra
were broadened taking into account the Zr K hole width and
experimental resolution. The results obtained are presented
in Fig. 5. One can see in the inset that the differences be
tween the spectra calculated for different Zr atom displace
ments and those experimentally obtained for BZ ?Fig. 2? are
of the same order. On the contrary, the analogous variations
of the PEFS experimentally obtained for PZ and PZT crys
tals are significantly less. These results reveal that the poten
tial surface for the Zr atom in the BZ crystal is similar to a
single well, whereas PZ and PZT can be described within the
deepdoublewell model.
Using PEFS data we estimated also the average displace
ments r0=????x ??2? of the B atoms from the centers of the
BO6octahedrons. Comparing Figs. 3–5 one can conclude
that the r0value for PZ is essentially less than that for PZT
and does not exceed 0.1 Å. This estimation is in agreement
with the diffraction data for PZ at room temperature, which
gives r0?0.075 Å within the assumption that local and glo
bal structures are close to each other at room temperature as
they are for the KN crystal.7,8
Taking into account the results presented above, one can
conclude that the PEFS data for the perovskitetype oxides
suffering structural phase transitions, such as KN, NN, PZ,
and PZT, make plausible a spherical model of their local
atomic structure. According to this model, an atom B ?Nb,
Zr, Ti? is situated near the surface of a sphere of small radius
r0?“central” sphere? at all temperatures. The center of this
sphere coincides with the immediate center of the BO6octa
hedron at each moment. The distribution of the B atom on
the surface of the central sphere can be complicated and can
change significantly with temperature. The last statement is
supported by the results of the PEFS studies performed for
KN and NN single crystals.7,8,19The spherical model is a
generalizationof the
nsite
considered.3,4It is supposed in the nsite models that on the
surface of the central sphere there are several sites, whose
positions, contrary to the spherical model, do not vary de
pending on temperature and only their occupancies are tem
perature dependent. The spherical model, like the nsite
models, is obviously inconsistent with the displacive model
of phase transitions in the perovskites. The spherical model
also does not presume the orderdisorder model of the phase
transitions, since these transitions, according to the spherical
model, can result in complicated redistribution of the B at
oms on the surface of the central sphere.
modelsthat areoften
B. EXAFS Analysis
The local atomic structure of the ZrO6octahedrons for
BZ, PZ, and PZT was also studied by a Zr Kedge EXAFS
TABLE I. Parameters of the first coordination shell for the
BaZrO3crystal at different temperatures. N, coordination number,
R, Zr–O distance, and ?2, DebyeWaller factor.
T ?°C?
NR ?Å?
?2?Å2?
R factor ?%?
20
100
300
500
6
6
6
6
2.11
2.11
2.12
2.12
0.0020
0.0022
0.0039
0.0047
0.7
1.5
1.2
1.6
FIG. 5. The results of PEFS calculations for BaZrO3performed
for different displacements r0of the Zr atom from its centrosym
metrical position in the cubic lattice. Inset: difference between the
spectra calculated for different Zr atom displacements and that for
ideal perovskite lattice.
FIG. 6. ?Color online? Absolute values ?dashed ?blue? lines? and
real parts ?solid ?black? lines? of the k3weighted FT of the Zr
EXAFS signal measured at 500 °C ?on the top? and the differential
FT for BaZrO3. The temperatures are indicated in the figure.
VEDRINSKII et al.
PHYSICAL REVIEW B 73, 134109 ?2006?
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Page 5
analysis. The EXAFS processing was performed by the
IFEFFIT package.21The selection of the best set of variables
for each model follows from the minimum value of the
figureofmerit criterion in this program, denoted the R
factor.22Scattering paths were determined by the FEFF7
code.23
We performed a complete analysis for the first coordina
tion shell of the Zr atom for the cubic BZ crystal at all
temperatures and for PZ and PZT in the cubic phase at
500 °C. Owing to the low symmetry of PZ and PZT at lower
temperatures, the EXAFS fitting is unreliable in this case due
to the great number of structural parameters to be deter
mined. To investigate the reconstruction of the pair radial
distribution function ?PRDF? for PZ and PZT at lower tem
peratures we employed the Fourier transforms ?FTs? of the
difference normalized EXAFS functions ?T?k?−?500?k?,
TABLE II. Parameters of the first coordination shell for PbZrO3and PbZr0.515Ti0.485O3in the cubic phase
?500 °C?. N, coordination number, R, ZrO distance, r0, radius of the central sphere, ?2, DebyeWaller factor,
R0, average ZrO distance determined from the full first shell PRDF, and ?2, variance of the PRDF.
Model
NR ?Å?
r0?Å?
?2?Å2?
R0?Å?
?2?Å2?
R factor ?%?
R? factor ?%?
PbZrO3
One site
Eight site
6
3
3
2
2
2
2.11
2.07
2.15
2.06
2.11
2.16
0
0.075
0.075
0.075
0.075
0.075
0.0070
0.0050
0.0050
0.0035
0.0076
0.0035
PbZr0.515Ti0.485O3
0.0070
0.0024
0.0063
0.0019
0.0040
0.0077
2.11
2.11
0.0070
0.0069
1.9
1.7
0.3
0.27
Twelve site
2.11 0.00671.70.32
One site
Eight site
6
3
3
2
2
2
2.09
2.05
2.17
2.04
2.11
2.18
0
0.1
0.1
0.1
0.1
0.1
2.09
2.11
0.0067
0.0077
3.5
0.8
0.44
0.1
Twelve site2.11 0.00790.90.13
FIG. 7. ?Color online? The results of fitting
performed for different structural models for
PbZrO3: ?a? one, ?b? eight, and ?c? 12site
model. Left panels: absolute values of the Fourier
transform of the k3weighted ??k? ?solid ?black?
lines, experiment; dashed ?blue? lines, fitting re
sults?. Right panels: pair radial distribution
functions.
TEMPERATURE DEPENDENT XAFS STUDIES OF LOCAL¼
PHYSICAL REVIEW B 73, 134109 ?2006?
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Page 6
where ?500?k? is the signal obtained at 500 °C and ?T?k? is
that measured at the temperature T.
The Fourier transforms of the differencenormalized
EXAFS functions for BZ are shown in Fig. 6. One can see
that the variations of the first coordination shell signal are
relatively small and the main feature of the difference FT for
BZ is a modification of the third coordination shell signal ?in
the R range 3.8–4.2 Å which corresponds to the third ?Zr?
shell?. Most probably this is caused by an increase of the
magnitude of the “tilting” mode vibrations on temperature.
Such an effect destroys the linear Zr–O–Zr atomic chains
and, as a result, demolishes the focusing processes in these
chains and causes a decrease of the third coordination shell
signal.
The BZ spectrum was analyzed within the onesite model
for all temperatures. The k range for the Fourier transforma
tion was 2.8–11.2 Å−1. Fitting was performed in the R range
0.9–1.9 Å. The results are presented in Table I. One can see
that the PRDF is a Gaussian with high accuracy at all the
temperatures. Hence, both EXAFS and PEFS data prove the
lattice dynamics of the BaZrO3crystal to be harmonic in the
temperature range considered. This conclusion is in agree
ment with the absence of phase transitions for BZ.
The EXAFS data processing for PZ and PZT at 500 °C
was performed for different models of their local atomic
structure: one, eight, 12, and sixsite models and the uni
form model. According to the last one, the Zr atom is uni
formly distributed on the surface of the central sphere. In that
case it was possible to synthesize the analytical PRDF and
then to calculate the XAFS function with the radius of the
central sphere and the DebyeWaller factor as parameters. At
the same time for the nsite models the standard fitting with
the IFEFFIT code was performed. The k range for the Fourier
transformation was reduced to the interval 1.9–11.8 Å−1for
the PZ due to a low signaltonoise ratio at k?12 Å−1,
whereas this parameter for PZT allowed using a wider k
range for the Fourier transformation: 1.9–14.4 Å−1. The
spectra were fitted in the R range 0.9–1.9 Å in both cases.
The best results were obtained for the eight and 12site
models. They are presented in Table II in comparison with
the values obtained for the onesite model.
It is necessary to note that within both the eight and
12site models we considered that all the Zr atom sites are
situated on the surface of the central sphere of small radius r0
according to the PEFS data. We calculated also the firstshell
PRDF in each case and determined from these functions the
average Zr–O distance R0and its variance ?2, which are also
presented in Table II. All PRDFs were considered to be a
simple superposition of Gaussian functions with the param
eters summarized in the same table. The absolute values of
the Fourier transform and the full PRDF calculated for PZ
and PZT for different models are shown in Figs. 7 and 8.
As one can see, the PRDF obtained for PZ within the
onesite model is close to those obtained within the eight
and 12site models, and the R factors for all the models are
almost the same. Thus, the anharmonicity in the cubic phase
of the PZ crystal is relatively small. At the same time the R?
factor, which takes into account the different number of vary
ing parameters, is slightly better for the eightsite model. R?
is related to the R factor, i.e., the latter is divided by the
number of degrees of freedom ?
FIG. 8. ?Color online? The results of fitting
performed for different structural models for
PbZr0.515Ti0.485O3: ?a? one, ?b? eight, and ?c?
12positional model. Left panels: absolute values
of the Fourier transform of the k3weighted ??k?
?solid ?black? lines, experiment; dashed ?blue?
lines, fitting results?. Right panels: pair radial dis
tribution functions.
VEDRINSKII et al.
PHYSICAL REVIEW B 73, 134109 ?2006?
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Page 7
? =?2?k?R
?
+ 2?− Nvar,
?2?
where ?k and ?R are the fitting ranges in the k and R spaces,
and Nvaris the number of variables in the fit. In the consid
ered case the R? factor is useful for clear comparison of the
results of fitting because we employ different numbers of
varying parameters for the 12site and the one and eightsite
models.
In the case of PZT the onesite model provides essentially
worse R and R? factors than the eight and 12site models. In
addition, the PRDFs, obtained for the last two models are
close to each other and are dramatically asymmetric. Hence,
theanharmonicity inthe
PbZr0.515Ti0.485O3solid solution is essentially greater than in
the cubic phase of PZ and one can resume that the Ti atoms
essentially influence the local atomic structure of the ZrO6
octahedrons in PZT, although the Zr–O average distances are
the same for PZ and PZT.
It is worth noting that the calculations for the uniform
models provide worse fitting results ?the calculated R factor
is greater 3% for PZ and PZT crystals? and for the sixsite
cubicphase ofthe
model nonphysical values of the DebyeWaller factor were
obtained. Hence, the distribution of the Zr atom on the sur
face of the central sphere is not uniform even in the cubic
phase. The Zr atom occupies several positions on this surface
and the number of such positions is not equal to 6.
Taking into account literature data9,10and more reliable
?2values obtained in the case of the eightsite model, we
guess that such local atomic structure is preferable for both
PZ and PZT in the cubic phase. If this model ?as well as the
12site model? was appropriate at lower temperatures then
the EXAFS signal for the first coordination shell would not
change strongly when the temperature decreases as it does in
the case of BZ. The Fourier transforms of the difference
EXAFS functions for PZ and PZT are shown in Figs. 9 and
10, respectively. As it follows from Fig. 9, the firstshell
signal really changes weakly for PZ in the cubic phase ?T
=300 °C?. On the contrary there is strong temperature de
pendence below the phase transition points ?230 °C for PZ
and 360 °C for PZT?. This means that either the eight or
12site model is not valid for the lowertemperature phases
of PZ and PZT and the phase transitions in these crystals
cannot be described within the simple orderdisorder model.
FIG. 9. ?Color online? Absolute values ?dashed ?blue? lines? and
real parts ?solid ?black? lines? of the k3weighted FT of the Zr
EXAFS signal measured at 500 °C ?on the top? and the differential
FT for PbZrO3. The temperatures are indicated in the figure.
FIG. 10. ?Color online? Absolute values ?dashed ?blue? lines?
and real parts ?solid ?black? lines? of the k3weighted FT of the Zr
EXAFS signal measured at 500 °C ?on the top? and the differential
FT for PbZr0.515Ti0.485O3. The temperatures are indicated in the
figure.
TEMPERATURE DEPENDENT XAFS STUDIES OF LOCAL¼
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Page 8
IV. CONCLUSIONS
The local atomic structure of the perovskitetype zircon
ates BaZrO3, PbZrO3, and PbZr0.515Ti0.485O3is studied by Zr
K spectrum EXAFS and preedge structure analysis in a wide
temperature interval. The results obtained in the present pa
per and previous results for the titanates and niobates reveal
that the PEFS intensity is almost temperature independent in
the case of powder samples for perovskites suffering struc
tural phase transitions whereas this intensity increases at
higher temperatures for perovskites that do not suffer phase
transitions. Since the PEFS intensity is determined by the
mean square displacement of the B atom ?B=Zr,Ti,Nb?
from the center of the BO6octahedron, the temperature in
dependence of PEFS for the perovskites suffering structural
phase transitions is assumed to be evidence for the spherical
model of the local atomic structure of these crystals. Accord
ing to this model the B atoms at all temperatures are situated
on the surface of a sphere of small radius ?central sphere?
whose center coincides with the immediate center of the BO6
octahedron at each moment. The spherical model does not
presume existence of particular sites for the B atoms on this
surface, which are the same at all the temperatures, and ac
cording to this model the distribution of the B atoms on the
central sphere surface can depend on the temperature. The
results of EXAFS analysis performed for PZ and PZT are in
agreement with results of the spherical model. The best re
sults in the cubic phase at 500 °C are obtained for the eight
site model. On the contrary, the differential EXAFS analysis
demonstrates that the eightsite model is not appropriate in
the case of the lowersymmetry phases of PZ and PZT.
Hence, neither displacive nor orderdisorder models are suf
ficient for the description of the phase transitions in the zir
conates studied.
The EXAFS and PEFS results reveal strong anharmonic
ity of the crystal lattice dynamics for PZT whereas it is rela
tively small for PZ in the cubic phase. The dramatic differ
ence between the local atomic structures of the ZrO6
octahedrons for PZT and PZ demonstrates a strong influence
of the Ti atoms on this structure. On the contrary the crystal
lattice dynamics is harmonic for BZ crystals in a wide tem
perature range.
ACKNOWLEDGMENTS
We are grateful to V. P. Sakhnenko for helpful discus
sions, L. A. Resnichenko for the sample preparation, J.L.
Hazemann for the help in organization of the experiment,
and V. Dmitriev for providing the heater. The studies were
supported by the Russian Ministry of Science and Education
Grant No. R662. E.N. acknowledges partial support from the
French Government ?CNOUS?.
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