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Crossover from ferroelectric to relaxor behavior in BaTi1-

_xSn_xO3 solid solutionsV. V. Shvartsmana; J. Decab; Z. K. Xuc; J. Banysd; P. Keburisd; W. Kleemanna

a Angewandte Physik, Universität Duisburg-Essen, D-47048 Duisburg, Germany b Institute of Physics,University of Silesia, Pl-40-007 Katowice, Poland c Department of Physics and Materials Science, CityUniversity of Hong Kong, Kowloon, Hong Kong, China d Faculty of Physics, Vilnius University, LT-10222 Vilnius, Lithuania

Online publication date: 04 December 2010

To cite this Article Shvartsman, V. V. , Dec, J. , Xu, Z. K. , Banys, J. , Keburis, P. and Kleemann, W.(2008) 'Crossover fromferroelectric to relaxor behavior in BaTi1-_xSn_xO3 solid solutions', Phase Transitions, 81: 11, 1013— 1021To link to this Article: DOI: 10.1080/01411590802457888URL: http://dx.doi.org/10.1080/01411590802457888

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Phase Transitions

Vol. 81, Nos. 11–12, November–December 2008, 1013–1021

Crossover from ferroelectric to relaxor behavior in

BaTi1ZxSn

xO3 solid solutions

V.V. Shvartsmana, J. Decab, Z.K. Xuc, J. Banysd,

P. Keburisd and W. Kleemanna*

aAngewandte Physik, Universitat Duisburg-Essen, D-47048 Duisburg, Germany; bInstitute ofPhysics, University of Silesia, Pl-40-007 Katowice, Poland; cDepartment of Physics and

Materials Science, City University of Hong Kong, 83 Tat Chee, Kowloon, Hong Kong, China;dFaculty of Physics, Vilnius University, LT-10222 Vilnius, Lithuania

(Received 18 May 2008; final version received 6 June 2008)

Dielectric relaxation of BaTi1�xSnxO3 ceramics is investigated by means ofdielectric spectroscopy. The gradual crossover from ferroelectric to relaxorbehavior is characterized by vanishing of the contribution due to domain wallsand appearance of relaxation related to reorientation of polar nanosized regions.Typical behavior of relaxors is observed only in ceramics with x¼ 0.30, while thecompositions with 0.175� x� 0.25 show coexistence of both ferroelectric andrelaxor features. The relaxor properties are supposed to be due to both weakrandom fields and disorder inherent in pure BaTiO3.

Keywords: barium titanate; relaxor ferroelectrics; dielectric spectroscopy; polarnanoregions; random fields; domain walls

1. Introduction

Relaxor ferroelectrics (‘‘relaxors’’ for short) have attracted significant interest due to their

superior dielectric and electromechanical properties [1]. The most typical feature of

relaxors is a strongly broadened frequency-dependent peak of the dielectric permittivity

versus temperature, whose position shifts to lower temperatures when the frequency

decreases [2]. It is widely accepted that the specific properties of the relaxors are closely

related to their peculiar polar structure. Namely, short-range ordered polar nanometric

regions (PNRs) appear in these materials already far above the temperature of the

maximum of the dielectric permittivity, Tm [4]. PNRs manifest themselves in deviations of

various material characteristics from the behavior predicted for the paraelectric state, in

particular those depending on hP2i [4,5]. Typically, the relaxor behavior is observed in

compositions with charge disorder, where cations with different valences randomly occupy

equivalent crystallographic positions. Such charge disorder is a source of quenched electric

random fields (RFs), which prevent the formation of a long-range ordered ground state in

ferroics with continuous symmetry of the order parameter [6], e.g. in relaxors with the

perovskite structure [7]. On the other hand, statistical fluctuations of RFs promote

nucleation of PNRs at high temperatures in the paraelectric state [8]. At high

*Corresponding author. Email: wolfgang.kleemann@uni-due.de

ISSN 0141–1594 print/ISSN 1029–0338 online

� 2008 Taylor & Francis

DOI: 10.1080/01411590802457888

http://www.informaworld.com

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temperatures, PNRs have the size of several nanometers and are highly dynamic. This state

is called the ergodic relaxor state, since interactions between PNRs are supposed to be

weak and the system quickly goes back to the initial state after some excitation [5]. On

cooling, both growth of individual PNRs and an increase of their number take place. As a

result interactions between PNRs become stronger and finally at a certain temperature a

transition into a short-range ordered glass-like (non-ergodic relaxor) or into a long-range

ordered ferroelectric state occurs [5].

Recently, considerable interest has been focused onto the investigation of environment-

friendly lead-free relaxors, in particular those based on the ferroelectric BaTiO3. In such

materials the relaxor behavior is observed not only in compositions with a heterovalent

cation substitution [9,10], but also in solid solutions with isovalently substituted Ti4þ, as

for example in BaTi1�xSnxO3 (BTSn) [11–14]. However, in the latter case the relaxor-like

behavior is observed only at fairly large substitution rates. More than 20% of the original

cations have to be exchanged in comparison with 5–8% for the heterosubstituted

compositions. Of particular interest are compositions from an intermediate concentration

range (8–20%), where the dielectric permittivity exhibits a maximum much broader than

that in BaTiO3, however, without the frequency shift typical of relaxors. Such behavior is

occasionally denoted as diffused phase transition (DPT) in order to distinguish it from the

relaxor one. The ferroelectric nature of compositions with DPT behavior was proven by

piezoresponse force microscopy and by analysis of frequency spectra of the complex

dielectric permittivity, "( f ) [13]. It is believed that compositions with x40.20 exhibit

relaxor behavior [11,14]. This conclusion is mainly based on the observation that in these

compositions the frequency dispersion of Tm follows the empirical Vogel–Fulcher law,

fðTmÞ ¼ f0 exp �Ea

kðTm � TVFÞ

� �

, ð1Þ

which is esteemed to be typical of relaxors. Here f is the measuring frequency, f0 is a

characteristic frequency, Ea is the activation energy, and TVF is the Vogel–Fulcher

temperature, which corresponds to freezing of the PNR dynamics in relaxors. However, it

was shown that the Vogel–Fulcher type relationship does not necessary imply ‘‘freezing’’

in the system and may also be observed in the case when the static permittivity has a

temperature maximum and the relaxation spectra nondivergently broadens on cooling

[15]. In order to confirm that freezing really occurs, the temperature evolution of the

frequency spectra of the dielectric permittivity has to be analyzed [16].

In the present article we report on dielectric spectroscopy studies of BaTi1�xSnxO3

ceramics (x¼ 0.10–0.30) in a broad temperature and frequency range. At difference with

previous reports [11,14] we found that among our samples only the composition with

x¼ 0.30 behaves similarly to canonical relaxors, whereas in compositions with x¼ 0.15–

0.25 a gradual crossover from ferroelectric to relaxor behavior takes place.

2. Experiment

Ceramic samples of BaTi1�xSnxO3 with x¼ 0.10–0.30 were prepared by a conventional

ceramic technology. Details of the sintering procedure can be found elsewhere [12]. The

complex dielectric permittivity, "¼ "0 � i"00, was measured using a Solartron 1260

impedance analyzer equipped with a Solartron 1296 dielectric interface. The samples

were electroded by vacuum deposition of copper and subsequent deposition of gold films.

The measurements were performed in the frequency range of 10�3�105Hz, at

1014 V.V. Shvartsman et al.

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temperatures 1005T5500K stabilized in a self-built measuring cell by a Lake Shore 340

temperature controller. The dependences of the complex dielectric permittivity both at

a fixed frequency, "( f ), and at a fixed temperature, "(T ), were measured. Dielectric

measurements in the high frequency range of 10MHz–1.25GHz were performed using

a computer-controlled high frequency dielectric spectrometer.

3. Experimental results

Figure 1 shows the temperature dependences of the real part, "0(T), of the dielectric

permittivity, measured at different frequencies, 10�1� f� 105Hz, on BaTi1�xSnxO3

ceramics with x¼ 0.10–0.30. All samples exhibit a broad maximum on "0(T), whose

position, Tm, is shifted to lower temperatures upon increasing the tin concentration. At the

same time the width of this peak increases. Typical of relaxors, the dependence of Tm on

the probing frequency is extremely weak in composition with x50.20; the total shift of Tm

over six frequency decades is only about 1–2K. It becomes more pronounced in samples

with larger tin content. Nevertheless, in compositions with x¼ 0.20 and 0.25 this

dispersion is limited to the high frequency range and becomes negligible below a certain

frequency (Figure 2). Only in the sample with x¼ 0.3 we observed a continuous downward

shift of Tm typical of relaxors in the whole experimental frequency range. The Tm( f )

dependences observed in the composition with x� 0.2 is well described by a power law of

the respective frequency,

fðTmÞ / ðTm=Tg � 1Þz�: ð2Þ

Here, Tg corresponds to the transition temperature, and z� is the dynamical critical

exponent. Such a power law is derived within the framework of the theory of dynamical

critical scaling in the vicinity of a continuous phase transition at Tg. For a conventional

phase transition, the value of z� usually equals approximately 2, while for different glass

100 150 200 250 300 3500

5

10

15

20

25

f

4

3

6e′ (1

03)

T (K)

1

25

f

Figure 1. Temperature dependences of the real part of the dielectric permittivity of theBaTi1�xSnxO3 ceramics with x¼ 0.10 (a), 0.15 (b), 0.175 (c), 0.20 (d), 0.25 (e), and 0.30(f) measured at frequencies f¼ 0.1Hz�100 kHz on a logarithmic scale (arrows indicate the increaseof the frequency).

Phase Transitions 1015

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transitions it varies between about 4 and 12 [17]. The best fit parameters for our samples

with x¼ 0.20–0.30 are listed in the Table 1. One can see that the value of the dynamical

exponent increases from z�� 2.5� 0.2 for BTSn20 to z�� 9.9� 0.3 for BTSn30. Obviously

this result hints at a transformation from a conventional to a glass-like transition. It

should be mentioned that the Tm( f ) dependences can also be approximated by the

standard Vogel–Fulcher law (Equation (1)), however, the fit is less satisfactory.

The parameters of the best Vogel–Fulcher fits are also listed in Table 1. One can see

227 228 229 230

−5

0

5

10

15

(c)

(b)

(a)

172 176 180 184

−5

0

5

10

15

ln (

f/H

z)

Tm (K)

120 130 140 150 160

−5

0

5

10

15

Figure 2. Frequency dependence of the peak temperature Tm( f ) of "0 (T) of BaTi1-xSnxO3 ceramics

with x¼ 0.20 (a), 0.25 (b), and 0.30 (c), plotted as ln(f/Hz) vs. Tm, and fitted by the critical power law(Equation (2)) (dashed lines).

Table 1. Best-fit parameters of the Tm vs. f dependences for BaTi1�xSnxO3 compositions withx¼ 0.20–0.30.

Power law Vogel–Fulcher law

x Tg (K) z� f0 (Hz) Ea (eV) TVF (K)

0.20 227.1� 0.1 2.5� 0.2 4� 106 (5.8� 0.5)� 10�4 226.5� 0.10.25 171.0� 0.3 3.9� 0.4 5� 105 (1.7� 0.4)� 10�3 170.1� 0.10.30 115.1� 0.4 9.9� 0.3 1� 1011 (6.0� 0.4)� 10�2 98� 1

1016 V.V. Shvartsman et al.

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that for the samples with x¼ 0.20 and 0.25 the values of TVF are very close to the Tg values

estimated from a fit to the power law (Equation (2)). On the other hand, the values of the

activation energy Ea for these compositions are much smaller than 0.01 eV usually found

for relaxors. Only for BTSn30 the Vogel–Fulcher fit yields values of Ea and f0 typical of

relaxors.

For a more detailed insight into the dielectric relaxation of the studied compositions

the frequency spectra of dielectric permittivity were measured at fixed temperatures

around Tm. Figure 3 shows the frequency dependences of the imaginary part of the

dielectric permittivity, "00 ( f ). In the compositions with x¼ 0.10–0.175 (Figure 3(a)–(c)),

apart from an increase of "00 at low frequencies which may be related both to a charge

transport (conductivity, Maxwell-Wagner relaxation at grain boundaries and internal

imperfections) [18] and to irreversible motion (‘‘creep’’) of domain walls [19], a broad

maximum (or several maxima superimposed) is observed in the frequency range of

10�1–105Hz. This contribution was analyzed in detail in our previous work [13]. It was

shown that it corresponds to a superposition of Debye-type relaxation processes of

individual domain walls segments. Usually the distribution of activation energies results in

a non-Debye-type total response, which may be approximated by a polydispersive model,

for example by the Cole-Cole one [18]. While in BTSn10 such domain wall dynamics can

be described by only one polydispersive relaxation process, two separate contributions

are revealed for the BTSn15 and BTSn17.5 ceramics. These relaxation processes were

attributed to the breathing modes of polar nanoregions and of pinned segments of

ferroelectric domain walls, respectively [13].

Along with the aforementioned mid frequency relaxation, a strong increase of "00 at

f41 kHz is observed in BTSn17.5. In the compositions with higher tin content, this high-

frequency relaxation becomes dominant, while the mid-frequency relaxation disappears.

On further cooling, this ‘‘critical’’ frequency decreases, simultaneously the rise of "00

becomes more gradual, starting already at f� 10�1Hz. We propose this dispersion of "00

( f ) to refer to the low-f wing of a Debye-like relaxation process, whose inverse relaxation

time is situated at higher frequencies, f� 106–109Hz. Such relaxation being typical of

relaxors is supposed to be related to the reorientation of PNRs [20]. On cooling the PNRs

grow and the interaction between them becomes stronger. As a result, their dynamics is

slowing down. This manifests itself both in a broadening of the relaxation time

distribution and in its shift towards longer relaxation times. Since "00 is a measure of the

distribution function of relaxation times such evolution should be reflected by the shape of

the "0 ( f ) dependences. Indeed, in the samples with x40.2 the high-frequency relaxation is

shifted down to smaller frequencies upon decreasing the temperature, at the same time the

rise of "00 becomes more gradual. Finally, at temperatures below 110–130K the spectra

broaden strongly and become almost flat. This probably indicates a transition into a glassy

state, which is accompanied by a freezing of the relaxation dynamics. It has to be

mentioned that this critical temperature is approximately the same for all samples with

x� 0.20.

4. Discussion

Comparison between the relaxation spectra of different BTSn ceramics reveals

qualitatively different behavior for compositions with x� 0.175 and x� 0.20, respectively.

In the latter ones, the contribution related to ferroelectric domain walls disappears, instead

a relaxor-typical relaxation is observed. Does a crossover from ferroelectric to relaxor

Phase Transitions 1017

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behavior takes place at x¼ 0.2? Our experimental data point out that this boundary is

smooth rather than sharp. Indeed, already in BTSn17.5 we observe a high-frequency

relaxation similar to that found in compositions with larger tin content. On the other

hand, the freezing of the relaxation in the BTSn20 and BTSn25 ceramics occurs essentially

0

3

6

10−1 101 103 1050

3

6

0

3

6

0

4

8

12

16

0

1

2

3

10−1 101 103 1050

4

8

300 K 290 K 285 K

280 K 275 K 270 K

265 K

240 K

(b) x =0.15

280 K 240 K

270 K 230 K

260 K 220 K

250 K 210 K

e″ (

10

2)

f (Hz)

(c) x =0.175

340 K

330 K

320 K

310 K

300 K

290 K

280 K

260 K

(a) x =0.10

200 K 110 K

190 K 100 K

175 K

165 K

155 K

130 K

(e) x =0.25

240 K

230 K

220 K

190 K

170 K

130 K

110 K

(d) x =0.20

200 K 130 K

180 K 120 K

160 K 110 K

150 K 85 K

140 K

f (Hz)

(f) x =0.30

Figure 3. Frequency dependences of the imaginary part of the dielectric permittivity ofBaTi1�xSnxO3 ceramics with x¼ 0.10 (a), 0.15 (b), 0.175 (c), 0.20 (d), 0.25 (e), and 0.30 (f),all measured in the frequency range 10�2–105Hz. In all graphs the solid and open symbolscorrespond to temperatures above and below Tm ( f¼ 100 kHz), respectively.

1018 V.V. Shvartsman et al.

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below the transition temperatures estimated from the Tm( f ) dependences. In other words,

the relaxing elements (reorientable PNRs) exist in these compositions even after the

transition takes place. Only for the BTSn30 sample Tg corresponds approximately to the

freezing of the PNRs dynamics observed by the spectra of the dielectric permittivity.

Hence, we propose the following sequence of low temperature states for the BTSn system:

the samples with x� 0.15 are in a ferroelectric state below Tm, in compositions with

0.175� x� 0.25 a ferroelectric transition occurs, but also regions with dynamic PNRs exist

below the transition temperature, and only BTSn30 shows a behavior close to the

canonical relaxor one.

The transformation to relaxor behavior in BTSn is related to the disorder within the

B-sites of the perovskite-type ABO3 unit cell. Indeed, the ferroelectricity in barium titanate

resides on a cooperative shift of Ti4þ cation into a certain direction from the center of the

oxygen octahedron. The larger tin cation cannot go off-center, giving rise to random

breaking of the correlated displacement along Ti–O–Ti–O chains [9,13]. Spatial

fluctuations of the defected (‘‘broken’’) bonds result in fluctuations of the polar

correlations, which in turn are responsible for the formation of precursor polar clusters

already above Tm [13]. As the tin content increases, the regions with an accumulated

concentration of broken bonds will occupy a larger part of the sample. As a consequence,

the polar correlations are strongly diminished and ferroelectric domains are less likely to

nucleate. However, due to the distortions arising around the tin ions [21] a redistribution

of the charges and a local formation of charged centers results. These are sources of local

random fields, whose quenched spatial fluctuations act as pinning centers of the thermally

fluctuating polarization [8]. Clearly, this kind of random fields is much weaker than that

stemming from heterovalent cation substitution as in conventional relaxors. Hence, the

relaxor properties of BTSn require relatively high doping levels.

In our previous work [13] we supposed that PNRs in BTSn ceramic appear only above

a certain doping level, when the effects of random fields become substantial. Recently,

however, we found that even in BTSn10 a high-frequency relaxation is already observed

above Tm at frequencies 108–109Hz (Figure 4). A similar relaxation starting above Tm was

observed also in pure BaTiO3 [22]. It was related to a hopping of the off-center Ti4þ

10−2 100 102 104 106 108

10

20

30

40

50

e″ (

10

2)

f (Hz)

220 K

240 K

260 K

280 K

300 K

320 K

340 K

360 K

Figure 4. Frequency dependences of the imaginary part of the dielectric permittivity ofBaTi1�xSnxO3 ceramics with x¼ 0.10 measured in the frequency range 10�3–2� 109Hz.

Phase Transitions 1019

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cations between symmetry-related potential wells, pointing out that the phase transition in

BaTiO3 rather follows an order–disorder scenario [23] than a purely displacive one [24].

Moreover, it was shown that this relaxation corresponds to a correlated Ti4þ hopping

motion within a volume of approximately 3 nm3. One can assume that such dynamic

‘‘superparaelectric’’ moments exist already in pure barium titanate and form precursors of

the PNRs in BaTiO3-related solid solutions like BTSn. Detailed investigations of the

dielectric relaxation of BTSn compositions in the frequency range 107–1010Hz are now in

progress.

5. Conclusions

The gradual crossover from ferroelectric to relaxor behavior has been studied in solid

solutions of BaTi1�xSnxO3. Dielectric spectroscopical data evidence a ferroelectric state in

compositions with x50.175. Relaxor-typical relaxations related to the reorientation of

PNRs appear in compositions with higher tin content. However, the phase transitions in

ceramics with x¼ 0.20 and 0.25 occur at higher temperatures than the freezing of PNRs

dynamics. Only in BTSn30 the relaxor-typical transition into a glass-like state takes place.

The relaxor properties in BTSn are supposed to be induced by weak random fields. On the

other hand, dynamic superparaelectric moments that exist also in pure barium titanate are

proposed to be precursors of PNRs in related solid solutions.

Acknowledgement

This research was supported by the European Community within STREP NMP3-CT-2006-032616(MULTICERAL).

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Phase Transitions 1021

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