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Thermal expansion in the Burns-phase of barium titanate stannate
Solid State Communications 129 (2004) 757–760 www.elsevier.com/locate/ssc
Thermal expansion in the Burns-phase of barium titanate stannate Volkmar Muellera,*, Lothar Ja¨gerb, Horst Beigea, Hans-Peter Abichtb, Thomas Mu¨llerb b
a Fachbereich Physik, Martin-Luther-Universita¨t Halle, F.-Bach-Platz 6, D-06108 Halle, Germany Fachbereich Chemie, Martin-Luther-Universita¨t Halle, Kurt-Mothes-Str.2, D-06120 Halle, Germany
Received 8 December 2003; accepted 29 December 2003 by P. Wachter
Abstract The thermal expansion ST has been measured in the system BaTi12xSnxO3, both for the pure compositions x ¼ 0 (BT) and x ¼ 1 (BS), and for solid solutions 0:025 # x # 0:2 (BTS). For all ceramics examined, a non-linear temperature dependence ST ðTÞ has been observed at elevated temperatures T . 400 K: This is related to thermally generated impurities and, below the Burns-temperature Td of BT and BTS, to the non-linear strain contribution of polar nanoregions. With increasing Sn-content x; a steep increase of the Burns-temperature is found in BTS for compositions x $ 0:025: q 2004 Elsevier Ltd. All rights reserved. PACS: 77.80.Bh; 77.84.Dy; 65.70. þ y Keywords: A. Barium titanate stannate; D. Diffuse phase transition; D. Thermal expansion
1. Introduction The Burns-temperature Td is the temperature where randomly oriented polar nanoregions become detectable within the otherwise non-polar paraelectric phase of several ferroelectrics. Originally observed in BaTiO3 due to the characteristic anomaly of the refractive index [1], polar precursor clusters were later on detected in PbTiO3 [2], KNbO3 [3] and in the relaxor ferroelectrics PLZT [4], PMN, PZN [5], K2Sr4(NbO3)10 [6], and SBN [7]. The behavior in the Burns-phase was shown to be closely related to the shape of the permittivity peak centered at the temperature Tm p Td ; as well as to the low-temperature behavior of specific heat and thermal conducticity [8]. As shown by neutron scattering, polar nanoregions have a decisive influence on the lattice dynamics of relaxor ferroelectrics, and are at the origin of the anomalous q-dependent damping of the polar TO-modes observed in PMN [9]. A variety of experimental techniques, including refractive index measurements [1], Raman scattering [10], SHG [11], neutron powder diffraction [12] and neutron elastic scattering [13], dynamic light scattering [14] and dielectric * Corresponding author. Tel.: þ49345-5525544; fax: þ 493455527158. E-mail address: [email protected] (V. Mueller). 0038-1098/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2003.12.035
measurements [15– 17] has been employed to confirm the existence and value of Td : It was pointed out by Bhalla et al. [7] that, due to electrostrictive coupling between the lattice strain and the polar nanoregions, Td should also be detectable from thermal expansion measurements. Indeed, deviations from the linear temperature dependence of the thermal strain had been observed at temperatures T q Tm in PLZT [18], SBN [7] and Ba(Ti,Sn)O3 [19], and had been attributed to the condensation of randomly oriented local polarization at Td : Solid solutions BaTi12xSnx03 (BTS-x) may be considered as a prototype system for ferroelectrics showing the diffuse phase transition [21 – 24]. With increasing Sn-content, the dielectric anomaly accompanying the paraelectric – ferroelectric phase transition broadens [20] and Tm decreases [21]. Above Tm ; the permittivity significantly deviates from the Curie – Weiss law for x $ 0:1 [25], whereas compositions x $ 0:2 belong to the relaxor state of BTS, as confirmed by the frequency dependence Tm ð f Þ [25,26]. In this paper, we studied thermal expansion in the Burnsphase of BTS-ceramics. Our investigations cover the pure components BaTiO3 (BT) and BaSnO3 (BS), the relaxor ferroelectric BTS-20 and BTS in the range 0:025 # x # 0:1 corresponding to compositions with diffuse ferroelectric phase transition. The results show that thermal expansion
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V. Mueller et al. / Solid State Communications 129 (2004) 757–760
data, although basically suitable to elucidate Td ; should be analyzed with care, as they comprise an additional contribution due to thermally generated impurities. From the isolated strain contribution of the polar nanoregions, it will be shown that Td strongly increases with the degree of disorder in BTS. 2. Experimental The BTS-ceramics examined ð0 # x # 0:2Þ were obtained from conventional mixed-oxide powder. Additionally we provide data for BT- and BS-ceramics sintered from non-conventional powder, which was obtained by thermolysis of Ba-Ti- and Ba-Sn-glycolates, respectively [27]. The ceramics were sintered for ts ¼ 1 h at Ts ¼ 1670 K: Samples were cut as parallel-epipeds (20 £ 6.5 £ 2 mm3) and placed in a NETZSCH model 402 pushrod dilatometer with fused silica sample holder. The temperature was measured with a Platinum-10% Rhodium/Platinum thermocouple type S attached to the sample. The samples were heated up to T0 ¼ 680 K and cooled to room temperature afterwards. We restrict our analysis to data obtained upon cooling within the temperature range 370 K # T # 660 K; where the constant cooling rate T_ ¼ 2 ^ 0:1 K=min was established. 3. Results The thermal expansion data ST ðTÞ shown in Fig. 1 were measured for the pure compounds BT and BS. Similar to previous approaches [7,18], we approximate data ST ðTÞ at high temperatures by a straight line, and obtain for BTceramic significant deviations from the linear temperature dependence at temperatures T , TdðSÞ < 560 K: The temperature TdðSÞ roughly corresponds to the result Td < 575 K previously obtained from a similar analysis of the
Fig. 1. Thermal expansion of BT- and BS-ceramic. The lines represent linear fits of the data taken at T . 600 K:
temperature dependent optic index of diffraction in BTsingle crystals [1]. However, TdðSÞ in BT is poorly defined, as we also detect at T . TdðSÞ slight deviations from the linear temperature dependence ST ðTÞ: Therefore, TdðSÞ depends on the range in which the high-temperature data are fitted. Moreover, we observe a clearly non-linear temperature dependence ST ðTÞ also in BS-ceramic (see Fig. 1). Since polar clusters in the Burns-phase of ferroelectrics represent precursors of the polar low-temperature phase, the nonlinear thermal strain in the non-ferroelectric BS-ceramic should be ascribed to a non-ferroelectric strain contribution SðnfÞ T : According to the Gru¨neisen theory of thermal expansion, the expansion coefficient above the Debye-temperature may be a slowly varying function of temperature, which would lead to intrinsic non-linearity ST ðTÞ: In addition, extrinsic contributions to STðnfÞ due to thermally generated defects may arise at high temperatures [28]. Clearly, both intrinsic and extrinsic contributions to the non-linearity of ST ðTÞ should not be restricted to BS, but can be expected in a similar way in BT. Indeed, the imaginary part of the low-frequency permittivity increases at elevated temperatures T . 380 K; which is presumably related to increasing conductivity due to defect generation. The assumption of a non-ferrolectric strain contribution in BT is further corroborated by the high-temperature behavior of the thermal expansion coefficients aðTÞ ¼ dST = dT shown in Fig. 2, which was determined from experimental data ST ðTÞ taken for BS and BT, respectively. To reduce scattering, data points plotted equidistantly on the T-axis represent average values for the particular temperature interval. At high temperatures, aðTÞ shows a nearly linear temperature dependence, both in BT and in BS. Upon further cooling, the temperature dependence changes in BT
Fig. 2. Thermal expansion coefficient a for BT and BS ceramic obtained from conventional mixed-oxyde powder (open symbols) and glycolate powder (full symbols), respectively. Dashed lines represent fits of data taken at T . 500 K; the full line is a guide for the eyes.
V. Mueller et al. / Solid State Communications 129 (2004) 757–760
and aðTÞ starts to decrease more steeply. This decrease becomes obvious below the temperature Tdp < 480 K: As aðTÞ shows in BS a linear temperature dependence within the whole temperature range examined, the anomaly in BT should be ascribed to the polar nanoregions being the precursor of the ferroelectric phase transition at Tc ¼ 403 K: Within the temperature range Tc , T , Tdp ; the strain accompanying the polar nanoregions dominates the temperature dependence aðTÞ in BT. For Tdp , T , Td ; however, the random polarization is small and its nonlinear strain contribution hidden by the non-ferroelectric strain STðnfÞ : This hampers the accurate estimate of Td from thermal expansion data. In particular we cannot decide from our data whether a sharp transition temperature Td exists in BT or the assumption of a smeared transition range is more appropriate. Clearly Tdp derived from the data shown in Fig. 2 should be considered as lower temperature limit for the existence of polar nanoregions in BT. In addition, the comparison of BT-ceramics derived from conventional and non-conventional powder, respectively, clearly shows that both STðnfÞ ðTÞ and SðfÞ T ðTÞ are basically insensitive to the ceramic precursors and, therefore, to the microstructure of the ceramic. The strain contribution SðfÞ T due to precursor polarization in the Burns-phase of BTS can be expressed as 2 SðfÞ T ¼ ðQ11 þ 2Q12 ÞkP l; 2
ð1Þ
where kP l is the autocorrelation function of the polarization, and Q11 and Q12 electrostriction coefficients of the ceramic. To study the compositional influence on the thermal expansion in the paraelectric phase of BTS, we analyze the difference DST ¼ ST ðT; xÞ 2 ST ðT; x ¼ 0Þ between data ST ðT; xÞ measured for the particular BTScomposition, and the thermal expansion ST ðT; 0Þ obtained for the pure BT-ceramic. Results DST ðTÞ are shown for several BTS-ceramics in Fig. 3. For temperatures T . Tc ðx ¼ 0Þ; the thermal expansion of BT and BTS-2.5 is almost the same, as DST ðx ¼ 0:025Þ basically vanishes in this temperature range (see Fig. 3). Consequently the temperature dependence of both the nonferroelectric and the ferroelectric strain contribution does not change in BTS for small Sn-content x # 0:025: For x ¼ 0:05; a high temperature range with DST < 0 should be distinguished from the range T , Td ðx ¼ 0:05Þ < 575 K; where the temperature dependence ST ðTÞ significantly differs from those observed for x # 0:025: This behavior can be understood in terms of an increased Burnstemperature in BTS-5. Apparently Td further increases with x; and reaches values outside our temperature-window for x $ 0:1; as we do not observe for these compositions the high temperature range with DST ¼ 0: Therefore, no information about the absolute value DST was obtained for BTS with x $ 0:1: The data plotted in Fig. 3 were set to DST ð640 KÞ ¼ 0: For x $ 0:05; the increase of DST ðTÞ upon cooling saturates at the temperature Td ð0Þ < 500 K; which may be
759
Fig. 3. Difference DST ðxÞ ¼ ST ðxÞ 2 ST ð0Þ between the thermal expansion of BTS-x and BT for several compositions.
regarded as estimate of the Burns-temperature for compositions with x # 0:025: Thus we observe that Td in BTS increases rather steeply with x; starting from Td # 500 K for x ¼ 0:025 to Td $ 680 K for x ¼ 0:1: This demonstrates the crucial influence of the Sn-content on the thermal strain contribution due to precursor polarization in BTS. In particular, chemical heterogeneity apparently facilitates the condensation of polar nanoregions. A similar behavior was recently observed from neutron elastic scattering experiments in PZN-xPT, where the increase of Td due to addition of the ferroelectric PT was attributed to stronger correlations between the polar nanoregions [13]. Note that this effect becomes considerably less obvious from the thermal expansion of BTS if simply ST ðTÞ-curves (as plotted in Fig. 1) are analyzed, as the total thermal strain is significantly influenced by the non-linear contribution STðnfÞ due to thermally generated impurities, which appears to be much less sensitive to the chemical composition. To summarize, we have shown that the non-linear temperature dependence of thermal expansion in BTS results from the superposition of the strain component SðfÞ due to precursor polarization, arising at the Burnstemperature Td ; and a non-ferroelectric strain contribution SðnfÞ related to thermally generated defects. Comparing data obtained at different Sn-level, the unknown non-ferroelectric strain was eliminated, and a steep increase of Td ðxÞ was detected for compositions x . 0:025 corresponding to the diffuse phase transition state of BTS.
Acknowledgements The authors acknowledge support from DFG (Schwerpunktprogramm 1136 ‘Substitutionseffekte in ionischen Festko¨rpern’).
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V. Mueller et al. / Solid State Communications 129 (2004) 757–760
References [1] G. Burns, F.H. Dacol, Solid State Commun. 42 (1982) 9. [2] W. Kleemann, F.J. Scha¨fer, D. Rytz, Phys. Rev. B 34 (1986) 7873. [3] W. Kleemann, F.J. Scha¨fer, M.D. Fontana, Phys. Rev. B 30 (1984) 1148. [4] G. Burns, F.H. Dacol, Phys. Rev. B 28 (1983) 2527. [5] G. Burns, F.H. Dacol, Solid State Commun. 48 (1983) 853. [6] G. Burns, F.H. Dacol, Phys. Rev. B 30 (1984) 4012. [7] A.S. Bhalla, R. Guo, L.E. Cross, G. Burns, F.H. Dacol, R.R. Neurgaonkar, Phys. Rev. B 36 (1987) 2030. [8] J.J. De Yoreo, R.O. Pohl, Phys. Rev. B 32 (1985) 5780. [9] P.M. Gehring, S. Wakimoto, Z.-G. Ye, G. Shirane, Phys. Rev. Lett. (2001) 277601. [10] G. Burns, F.H. Dacol, Solid State Commun. 58 (1986) 567. [11] T. Heinz, G. Burns, N. Halas, Bull. Am. Phys. Soc. 31 (1986) 603. [12] J. Zhao, A.E. Glazounov, Q.M. Zhang, B. Toby, Appl. Phys. Lett. 72 (1998) 1048. [13] D. La-Orauttapong, J. Toulouse, Z.-G. Ye, W. Chen, R. Erwin, J.L. Robertson, Phys. Rev. B 67 (2003) 134110. [14] W. Kleemann, P. Licinio, T. Woike, R. Pankrath, Phys. Rev. Lett. 86 (2001) 6014.
[15] D. Viehland, S.J. Jang, L.E. Cross, M. Wuttig, Phys. Rev. B 46 (1992) 8003. [16] V. Bovtun, J. Petzelt, V. Porokhonskyy, S. Kamba, Y. Yakimenko, J. Eur. Ceram. Soc. 21 (2001) 1307. [17] J. Dec, W. Kleemann, V. Bobnar, Z. Kutnjak, A. Levstik, R. Pirc, R. Pankrath, Europhys. Lett. 55 (2001) 781. [18] H. Arndt, G. Schmidt, Ferroelectrics 79 (1988) 443. [19] C. Kajtoch, Doctor’s thesis Martin-Luther-University HalleWittenberg, 1990. [20] N.S. Novosil’tsev, A.L. Khodakov, Sov. Phys. Tech. Phys. 1 (1956) 306. [21] G.A. Smolensky, V.A. Isupov, Zh. Tekh. Fiz. 24 (1954) 1375. [22] G.A. Smolensky, J. Phys. Soc. Jpn. 28 (1970) 26. [23] G. Schmidt, Phase Trans. 20 (1990) 127. [24] L.E. Cross, Ferroelectrics 151 (1994) 305. [25] N. Yasuda, H. Ohwa, S. Asano, Jpn. J. Appl. Phys. 35 (1996) 5099. [26] V. Mueller, H. Beige, H.-P. Abicht, Appl. Phys. Lett. (2004) in press. [27] L. Ja¨ger, V. Lorenz, T. Mu¨ller, H.-P. Abicht, M. Ro¨ssel, H. Go¨rls, Z. Anorg. Allg. Chem. (2004) 629 in press. [28] M.F. Merriam, R. Smoluchowski, D.A. Wiegand, Phys. Rev. 125 (1962) 65.
Thermal expansion in the Burns-phase of barium titanate stannate Volkmar Muellera,*, Lothar Ja¨gerb, Horst Beigea, Hans-Peter Abichtb, Thomas Mu¨llerb b
a Fachbereich Physik, Martin-Luther-Universita¨t Halle, F.-Bach-Platz 6, D-06108 Halle, Germany Fachbereich Chemie, Martin-Luther-Universita¨t Halle, Kurt-Mothes-Str.2, D-06120 Halle, Germany
Received 8 December 2003; accepted 29 December 2003 by P. Wachter
Abstract The thermal expansion ST has been measured in the system BaTi12xSnxO3, both for the pure compositions x ¼ 0 (BT) and x ¼ 1 (BS), and for solid solutions 0:025 # x # 0:2 (BTS). For all ceramics examined, a non-linear temperature dependence ST ðTÞ has been observed at elevated temperatures T . 400 K: This is related to thermally generated impurities and, below the Burns-temperature Td of BT and BTS, to the non-linear strain contribution of polar nanoregions. With increasing Sn-content x; a steep increase of the Burns-temperature is found in BTS for compositions x $ 0:025: q 2004 Elsevier Ltd. All rights reserved. PACS: 77.80.Bh; 77.84.Dy; 65.70. þ y Keywords: A. Barium titanate stannate; D. Diffuse phase transition; D. Thermal expansion
1. Introduction The Burns-temperature Td is the temperature where randomly oriented polar nanoregions become detectable within the otherwise non-polar paraelectric phase of several ferroelectrics. Originally observed in BaTiO3 due to the characteristic anomaly of the refractive index [1], polar precursor clusters were later on detected in PbTiO3 [2], KNbO3 [3] and in the relaxor ferroelectrics PLZT [4], PMN, PZN [5], K2Sr4(NbO3)10 [6], and SBN [7]. The behavior in the Burns-phase was shown to be closely related to the shape of the permittivity peak centered at the temperature Tm p Td ; as well as to the low-temperature behavior of specific heat and thermal conducticity [8]. As shown by neutron scattering, polar nanoregions have a decisive influence on the lattice dynamics of relaxor ferroelectrics, and are at the origin of the anomalous q-dependent damping of the polar TO-modes observed in PMN [9]. A variety of experimental techniques, including refractive index measurements [1], Raman scattering [10], SHG [11], neutron powder diffraction [12] and neutron elastic scattering [13], dynamic light scattering [14] and dielectric * Corresponding author. Tel.: þ49345-5525544; fax: þ 493455527158. E-mail address: [email protected] (V. Mueller). 0038-1098/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2003.12.035
measurements [15– 17] has been employed to confirm the existence and value of Td : It was pointed out by Bhalla et al. [7] that, due to electrostrictive coupling between the lattice strain and the polar nanoregions, Td should also be detectable from thermal expansion measurements. Indeed, deviations from the linear temperature dependence of the thermal strain had been observed at temperatures T q Tm in PLZT [18], SBN [7] and Ba(Ti,Sn)O3 [19], and had been attributed to the condensation of randomly oriented local polarization at Td : Solid solutions BaTi12xSnx03 (BTS-x) may be considered as a prototype system for ferroelectrics showing the diffuse phase transition [21 – 24]. With increasing Sn-content, the dielectric anomaly accompanying the paraelectric – ferroelectric phase transition broadens [20] and Tm decreases [21]. Above Tm ; the permittivity significantly deviates from the Curie – Weiss law for x $ 0:1 [25], whereas compositions x $ 0:2 belong to the relaxor state of BTS, as confirmed by the frequency dependence Tm ð f Þ [25,26]. In this paper, we studied thermal expansion in the Burnsphase of BTS-ceramics. Our investigations cover the pure components BaTiO3 (BT) and BaSnO3 (BS), the relaxor ferroelectric BTS-20 and BTS in the range 0:025 # x # 0:1 corresponding to compositions with diffuse ferroelectric phase transition. The results show that thermal expansion
758
V. Mueller et al. / Solid State Communications 129 (2004) 757–760
data, although basically suitable to elucidate Td ; should be analyzed with care, as they comprise an additional contribution due to thermally generated impurities. From the isolated strain contribution of the polar nanoregions, it will be shown that Td strongly increases with the degree of disorder in BTS. 2. Experimental The BTS-ceramics examined ð0 # x # 0:2Þ were obtained from conventional mixed-oxide powder. Additionally we provide data for BT- and BS-ceramics sintered from non-conventional powder, which was obtained by thermolysis of Ba-Ti- and Ba-Sn-glycolates, respectively [27]. The ceramics were sintered for ts ¼ 1 h at Ts ¼ 1670 K: Samples were cut as parallel-epipeds (20 £ 6.5 £ 2 mm3) and placed in a NETZSCH model 402 pushrod dilatometer with fused silica sample holder. The temperature was measured with a Platinum-10% Rhodium/Platinum thermocouple type S attached to the sample. The samples were heated up to T0 ¼ 680 K and cooled to room temperature afterwards. We restrict our analysis to data obtained upon cooling within the temperature range 370 K # T # 660 K; where the constant cooling rate T_ ¼ 2 ^ 0:1 K=min was established. 3. Results The thermal expansion data ST ðTÞ shown in Fig. 1 were measured for the pure compounds BT and BS. Similar to previous approaches [7,18], we approximate data ST ðTÞ at high temperatures by a straight line, and obtain for BTceramic significant deviations from the linear temperature dependence at temperatures T , TdðSÞ < 560 K: The temperature TdðSÞ roughly corresponds to the result Td < 575 K previously obtained from a similar analysis of the
Fig. 1. Thermal expansion of BT- and BS-ceramic. The lines represent linear fits of the data taken at T . 600 K:
temperature dependent optic index of diffraction in BTsingle crystals [1]. However, TdðSÞ in BT is poorly defined, as we also detect at T . TdðSÞ slight deviations from the linear temperature dependence ST ðTÞ: Therefore, TdðSÞ depends on the range in which the high-temperature data are fitted. Moreover, we observe a clearly non-linear temperature dependence ST ðTÞ also in BS-ceramic (see Fig. 1). Since polar clusters in the Burns-phase of ferroelectrics represent precursors of the polar low-temperature phase, the nonlinear thermal strain in the non-ferroelectric BS-ceramic should be ascribed to a non-ferroelectric strain contribution SðnfÞ T : According to the Gru¨neisen theory of thermal expansion, the expansion coefficient above the Debye-temperature may be a slowly varying function of temperature, which would lead to intrinsic non-linearity ST ðTÞ: In addition, extrinsic contributions to STðnfÞ due to thermally generated defects may arise at high temperatures [28]. Clearly, both intrinsic and extrinsic contributions to the non-linearity of ST ðTÞ should not be restricted to BS, but can be expected in a similar way in BT. Indeed, the imaginary part of the low-frequency permittivity increases at elevated temperatures T . 380 K; which is presumably related to increasing conductivity due to defect generation. The assumption of a non-ferrolectric strain contribution in BT is further corroborated by the high-temperature behavior of the thermal expansion coefficients aðTÞ ¼ dST = dT shown in Fig. 2, which was determined from experimental data ST ðTÞ taken for BS and BT, respectively. To reduce scattering, data points plotted equidistantly on the T-axis represent average values for the particular temperature interval. At high temperatures, aðTÞ shows a nearly linear temperature dependence, both in BT and in BS. Upon further cooling, the temperature dependence changes in BT
Fig. 2. Thermal expansion coefficient a for BT and BS ceramic obtained from conventional mixed-oxyde powder (open symbols) and glycolate powder (full symbols), respectively. Dashed lines represent fits of data taken at T . 500 K; the full line is a guide for the eyes.
V. Mueller et al. / Solid State Communications 129 (2004) 757–760
and aðTÞ starts to decrease more steeply. This decrease becomes obvious below the temperature Tdp < 480 K: As aðTÞ shows in BS a linear temperature dependence within the whole temperature range examined, the anomaly in BT should be ascribed to the polar nanoregions being the precursor of the ferroelectric phase transition at Tc ¼ 403 K: Within the temperature range Tc , T , Tdp ; the strain accompanying the polar nanoregions dominates the temperature dependence aðTÞ in BT. For Tdp , T , Td ; however, the random polarization is small and its nonlinear strain contribution hidden by the non-ferroelectric strain STðnfÞ : This hampers the accurate estimate of Td from thermal expansion data. In particular we cannot decide from our data whether a sharp transition temperature Td exists in BT or the assumption of a smeared transition range is more appropriate. Clearly Tdp derived from the data shown in Fig. 2 should be considered as lower temperature limit for the existence of polar nanoregions in BT. In addition, the comparison of BT-ceramics derived from conventional and non-conventional powder, respectively, clearly shows that both STðnfÞ ðTÞ and SðfÞ T ðTÞ are basically insensitive to the ceramic precursors and, therefore, to the microstructure of the ceramic. The strain contribution SðfÞ T due to precursor polarization in the Burns-phase of BTS can be expressed as 2 SðfÞ T ¼ ðQ11 þ 2Q12 ÞkP l; 2
ð1Þ
where kP l is the autocorrelation function of the polarization, and Q11 and Q12 electrostriction coefficients of the ceramic. To study the compositional influence on the thermal expansion in the paraelectric phase of BTS, we analyze the difference DST ¼ ST ðT; xÞ 2 ST ðT; x ¼ 0Þ between data ST ðT; xÞ measured for the particular BTScomposition, and the thermal expansion ST ðT; 0Þ obtained for the pure BT-ceramic. Results DST ðTÞ are shown for several BTS-ceramics in Fig. 3. For temperatures T . Tc ðx ¼ 0Þ; the thermal expansion of BT and BTS-2.5 is almost the same, as DST ðx ¼ 0:025Þ basically vanishes in this temperature range (see Fig. 3). Consequently the temperature dependence of both the nonferroelectric and the ferroelectric strain contribution does not change in BTS for small Sn-content x # 0:025: For x ¼ 0:05; a high temperature range with DST < 0 should be distinguished from the range T , Td ðx ¼ 0:05Þ < 575 K; where the temperature dependence ST ðTÞ significantly differs from those observed for x # 0:025: This behavior can be understood in terms of an increased Burnstemperature in BTS-5. Apparently Td further increases with x; and reaches values outside our temperature-window for x $ 0:1; as we do not observe for these compositions the high temperature range with DST ¼ 0: Therefore, no information about the absolute value DST was obtained for BTS with x $ 0:1: The data plotted in Fig. 3 were set to DST ð640 KÞ ¼ 0: For x $ 0:05; the increase of DST ðTÞ upon cooling saturates at the temperature Td ð0Þ < 500 K; which may be
759
Fig. 3. Difference DST ðxÞ ¼ ST ðxÞ 2 ST ð0Þ between the thermal expansion of BTS-x and BT for several compositions.
regarded as estimate of the Burns-temperature for compositions with x # 0:025: Thus we observe that Td in BTS increases rather steeply with x; starting from Td # 500 K for x ¼ 0:025 to Td $ 680 K for x ¼ 0:1: This demonstrates the crucial influence of the Sn-content on the thermal strain contribution due to precursor polarization in BTS. In particular, chemical heterogeneity apparently facilitates the condensation of polar nanoregions. A similar behavior was recently observed from neutron elastic scattering experiments in PZN-xPT, where the increase of Td due to addition of the ferroelectric PT was attributed to stronger correlations between the polar nanoregions [13]. Note that this effect becomes considerably less obvious from the thermal expansion of BTS if simply ST ðTÞ-curves (as plotted in Fig. 1) are analyzed, as the total thermal strain is significantly influenced by the non-linear contribution STðnfÞ due to thermally generated impurities, which appears to be much less sensitive to the chemical composition. To summarize, we have shown that the non-linear temperature dependence of thermal expansion in BTS results from the superposition of the strain component SðfÞ due to precursor polarization, arising at the Burnstemperature Td ; and a non-ferroelectric strain contribution SðnfÞ related to thermally generated defects. Comparing data obtained at different Sn-level, the unknown non-ferroelectric strain was eliminated, and a steep increase of Td ðxÞ was detected for compositions x . 0:025 corresponding to the diffuse phase transition state of BTS.
Acknowledgements The authors acknowledge support from DFG (Schwerpunktprogramm 1136 ‘Substitutionseffekte in ionischen Festko¨rpern’).
760
V. Mueller et al. / Solid State Communications 129 (2004) 757–760
References [1] G. Burns, F.H. Dacol, Solid State Commun. 42 (1982) 9. [2] W. Kleemann, F.J. Scha¨fer, D. Rytz, Phys. Rev. B 34 (1986) 7873. [3] W. Kleemann, F.J. Scha¨fer, M.D. Fontana, Phys. Rev. B 30 (1984) 1148. [4] G. Burns, F.H. Dacol, Phys. Rev. B 28 (1983) 2527. [5] G. Burns, F.H. Dacol, Solid State Commun. 48 (1983) 853. [6] G. Burns, F.H. Dacol, Phys. Rev. B 30 (1984) 4012. [7] A.S. Bhalla, R. Guo, L.E. Cross, G. Burns, F.H. Dacol, R.R. Neurgaonkar, Phys. Rev. B 36 (1987) 2030. [8] J.J. De Yoreo, R.O. Pohl, Phys. Rev. B 32 (1985) 5780. [9] P.M. Gehring, S. Wakimoto, Z.-G. Ye, G. Shirane, Phys. Rev. Lett. (2001) 277601. [10] G. Burns, F.H. Dacol, Solid State Commun. 58 (1986) 567. [11] T. Heinz, G. Burns, N. Halas, Bull. Am. Phys. Soc. 31 (1986) 603. [12] J. Zhao, A.E. Glazounov, Q.M. Zhang, B. Toby, Appl. Phys. Lett. 72 (1998) 1048. [13] D. La-Orauttapong, J. Toulouse, Z.-G. Ye, W. Chen, R. Erwin, J.L. Robertson, Phys. Rev. B 67 (2003) 134110. [14] W. Kleemann, P. Licinio, T. Woike, R. Pankrath, Phys. Rev. Lett. 86 (2001) 6014.
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