Page 1

Temperature dependent XAFS studies of local atomic structure of the perovskite-type 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, Rostov-on-Don 344090, Russia

2Laboratoire de Cristallographie, CNRS, l’Université Joseph Fourier, 166 Boîte Postale, F-38042 Grenoble Cedex 9, France

3CEA/Grenoble, DRFMC/SP2M/NRS, F-38054 Grenoble Cedex 9, France

4Laboratoire de Géophysique Interne et Tectonophysique, UMR CNRS, Université Joseph Fourier,

F-38400 Saint-Martin-D’Hères, France

5BM30b CRG-FAME, European Synchrotron Radiation Facility, F-38043 Grenoble Cedex 9, France

?Received 31 July 2005; revised manuscript received 8 March 2006; published 17 April 2006?

Temperature dependent preedge and extended x-ray absorption fine structure measurements at the Zr K edge

for the perovskite-type 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

order-disorder 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 perovskite-type 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

Perovskite-type 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 lower-symmetry

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 x-ray absorption fine structure

?XAFS?. In this contribution we investigate the temperature

dependence of the local atomic structure for perovskite-type

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 perovskite-type crystals is under discussion for several

decades. Nowadays two alternative structural models are of-

ten used for perovskite-type materials. The first, “displacive”

model2assumes that in the low-temperature 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 “eight-site” model,3the cations are displaced from the

centers of oxygen octahedrons to off-center positions located

along eight ?111? directions in all the phases. The number of

such off-center positions occupied by the cations changes as

a result of phase transitions, which are considered to be of

the order-disorder type. The eight-site model is not a unique

n-site model to describe the phase transitions in perovskites.

In particular, six- and 12-site 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 perovskite-type oxides

are contradictory. Some authors did not find significant

change of the first-shell contribution to EXAFS at the phase

transition points for the powder samples and hence consid-

ered the eight-site model to be valid5,6and the transitions to

be of the order-disorder type. However, analysis of the po-

larized XAFS performed for single crystals showed that in

the low-temperature phases the displacive model is in good

agreement with the experimental data, whereas the eight-site

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 first-principles 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-

PHYSICAL REVIEW B 73, 134109 ?2006?

1098-0121/2006/73?13?/134109?8?/$23.00©2006 The American Physical Society134109-1

Page 2

sity by standard solid-state 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. X-ray powder diffraction measurements

confirmed that the samples were single-phase ones.

Preedge and EXAFS Zr K-edge 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 double-crystal 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 Rh-coated 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

two-crystal x-ray 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.

K-edge x-ray 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 p-d peak” hereafter.As was shown by calculations,15the

p-d 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 mean-square 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 O-B-O atomic chain ?i=1,2,3? along this chain

and ???xi?2? is the corresponding MSD. If the x-ray electric

field vector e ? is directed along the ith O-B-O chain of a

single-crystal sample, the p-d peak area is proportional to

???xi?2?.

Experimental studies of the Ti K x-ray absorption near-

edge structure ?XANES? for a PbTiO3?PT? single crystal16

have shown strong angular and temperature dependence of

the p-d 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 p-d 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 p-d 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 p-d 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 p-d 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? ?one-site model? ?single-well 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 deep-double-

well ?Fig. 1?b?? and shallow-double well ?Fig. 1?c?? forms.

The maximum value of the deep-double-well 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 shallow-double-well 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?

134109-2

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 p-d 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?

134109-3

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

deep-double-well 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 perovskite-type 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

n-site

considered.3,4It is supposed in the n-site 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 n-site

models, is obviously inconsistent with the displacive model

of phase transitions in the perovskites. The spherical model

also does not presume the order-disorder 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 K-edge EXAFS

TABLE I. Parameters of the first coordination shell for the

BaZrO3crystal at different temperatures. N, coordination number,

R, Zr–O distance, and ?2, Debye-Waller 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?

134109-4

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

figure-of-merit 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, Zr-O distance, r0, radius of the central sphere, ?2, Debye-Waller factor,

R0, average Zr-O 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? 12-site

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?

134109-5

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 difference-normalized

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 one-site 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 six-site 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 Debye-Waller factor as parameters. At

the same time for the n-site 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 signal-to-noise 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 12-site

models. They are presented in Table II in comparison with

the values obtained for the one-site model.

It is necessary to note that within both the eight- and

12-site 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 first-shell

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

one-site model is close to those obtained within the eight-

and 12-site 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 eight-site 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?

12-positional 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?

134109-6

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 12-site and the one- and eight-site

models.

In the case of PZT the one-site model provides essentially

worse R and R? factors than the eight- and 12-site 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 six-site

cubicphase ofthe

model nonphysical values of the Debye-Waller 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 eight-site 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

12-site 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 first-shell

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

12-site model is not valid for the lower-temperature phases

of PZ and PZT and the phase transitions in these crystals

cannot be described within the simple order-disorder 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

PHYSICAL REVIEW B 73, 134109 ?2006?

134109-7

Page 8

IV. CONCLUSIONS

The local atomic structure of the perovskite-type 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 eight-site model is not appropriate in

the case of the lower-symmetry phases of PZ and PZT.

Hence, neither displacive nor order-disorder 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?.

1D. E. Cox, B. Noheda, G. Shirane, Y. Uesu, K. Fujishiro, and Y.

Yamada, Appl. Phys. Lett. 79, 400 ?2001?.

2J. Harada, J. D. Axe, and G. Shirane, Phys. Rev. B 4, 155 ?1971?.

3R. Comes, M. Lambert, and A. Guinier, Solid State Commun. 6,

715–719 ?1968?.

4L. Godefroy, A. Derouiche, and A. Benzagouta, Ferroelectrics

54, 13 ?1984?.

5N. Sicron, Y. Yacoby, E. A. Stern, and F. Dogan, J. Phys. IV 7,

C2-1047 ?1997?.

6N. de Mathan, E. Prouzet, E. Husson, and H. Dexpert, J. Phys.:

Condens. Matter 5, 1261 ?1993?.

7V. A. Shuvaeva, K. Yanagi, K. Yagi, K. Sakaue, and H. Terauchi,

Solid State Commun. 106, 335 ?1998?.

8V. A. Shuvaeva, K. Yanagi, K. Yagi, K. Sakaue, and H. Terauchi,

J. Synchrotron Radiat. 6, 367 ?1999?.

9M. I. Marques, Phys. Rev. B 71, 174116 ?2005?.

10B. Zalar, V. V. Laguta, and R. Blinc, Phys. Rev. Lett. 90, 037601

?2003?.

11O. Proux, X. Biquard, E. Lahera, J.-J. Menthonnex, A. Prat, O.

Ulrich, Y. Soldo, P. Trévisson, G. Kapoujvan, G. Perroux, P.

Taunier, D. Grand, P. Jeantet, M. Deleglise, J.-P. Roux, and J.-L.

Hazemann, Phys. Scr. 115, 970 ?2005?.

12E. Sawaguchi, G. Shirane, and Y. Takagi, J. Phys. Soc. Jpn. 6,

333 ?1951?.

13G. Shirane, E. Sawaguchi, and Y. Takagi, Phys. Rev. 84, 476

?1951?.

14P. E. Petit, F. Guyot, and F. Farges, J. Phys. IV 7, C2-1065

?1997?.

15R. V. Vedrinskii, V. L. Kraizman, A. A. Novakovich, Ph. V. De-

mekhin, and S. V. Urazhdin, J. Phys.: Condens. Matter 10, 9561

?1998?.

16B. Ravel and E. A. Stern, J. Phys. IV 7, C2-1223 ?1997?.

17B. Ravel, E. A. Stern, and Y. Yacoby, Jpn. J. Appl. Phys., Part 1

32, 782 ?1993?.

18B. Ravel and E. A. Stern, Physica B 208/209, 316 ?1995?.

19V. A. Shuvaeva, Y. Azuma, K. Yagi, K. Sakaue, and H. Terauchi,

J. Synchrotron Radiat. 8, 833 ?2001?.

20J. Kokubun, K. Ishida, D. Cabaret, F. Mauri, R. V. Vedrinskii, V.

L. Kraizman, A. A. Novakovich, E. V. Krivitskii, and V. E.

Dmitrienko, Phys. Rev. B 69, 245103 ?2004?.

21M. Newville, J. Synchrotron Radiat. 8, 322 ?1999?; http://cars9.

uchicago. edu/ifeffit/

22Computer code IFEFFIT, Chap. 5, formula ?5.7?, http:/cars9.

uchicago.edu/~newville/feffit/feffit. ps

23A. L. Ankudinov and J. J. Rehr, Phys. Rev. B 56, R1712 ?1997?.

VEDRINSKII et al.

PHYSICAL REVIEW B 73, 134109 ?2006?

134109-8