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Solid solution Ba1−xPbxTiO3 and its thermal expansion
Journal of Alloys and Compounds 353 (2003) 1–4
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Solid solution Ba 12x Pb x TiO 3 and its thermal expansion Xianran Xing*, Jinxia Deng, Zhenqi Zhu, Guirong Liu Department of Physical Chemistry, University of Science and Technology Beijing, Beijing 100083, PR China Received 10 September 2002; received in revised form 15 October 2002; accepted 15 October 2002
Abstract The solid solution limit of Ba 12x Pb x TiO 3 was determined in the composition range of 0#x#1.0. All solid solution compounds were indexed in tetragonal symmetry with lead titanate structure type at room temperature. The cell parameters of Ba 12x Pbx TiO 3 continuously, but nonlinearly, change with x. The structure of Ba 0.5 Pb 0.5 TiO 3 is tetragonal in the temperature range RT–330 8C and in cubic system beyond 330 8C with HTXRPD. The intrinsic thermal expansion coefficients of Ba 12x Pbx TiO 3 (x50, 0.5, 1.0) were obtained. The correlation between thermal expansion and ferroelectric properties is briefly discussed. 2002 Elsevier Science B.V. All rights reserved. Keywords: Solid solution Ba 12x Pb x TiO 3 ; Thermal expansion; Phase transition; High temperature X-ray powder diffractometry (HTXRPD)
1. Introduction It is well known that ferroelectric properties have been observed in lead, barium and barium lead titanate ceramics [1,2]. For more than half a century the structures of these compounds were well investigated by many groups [3– 10]. Especially the anomalous positive temperature coefficient of resistivity (PTCR) of barium titanate (over 120 8C) attracts much attention. The Curie point of barium titanate can be shifted to lower temperatures by substituting strontium for barium, or zirconium for titanium, and to higher temperatures by substituting lead for barium. The effort was successfully made to obtain PTCR effects with Curie points of 360 8C for Ba 0.35 Pb 0.65 TiO 3 and 420 8C for Ba 0.2 Pb 0.8 [11–13]. Analogously some studies were also made on other mixed titanate or zirconate ceramics, for example on strontium barium, or, strontium lead [7,14– 16]. Such solutions in ferroelectric ceramics are technologically important because it allows the electric properties to be tailored to practical applications. Another considerable advantage of solid solutions of ceramics is to adjust the thermal expansion in order to reach compatibility with other ceramic devices [17–19]. The ceramics of perovskites are usually prepared at high temperatures and involve one or two phase transitions. To *Corresponding author. Tel.: 186-10-6233-4200; fax: 186-10-62333477. E-mail address: [email protected] (X. Xing).
overcome the thermal shock damage of these materials becomes a substantial problem. It depends on the thermal expansion coefficients (TECs). Fortunately, previous work and our recent research reveal that lead titanate exhibit very special TECs [3,20]. Below the Curie point of lead titanate (490 8C), the c axis decreases, the a axis increases, and the cell volume shrinks with increasing temperature. Such a negative thermal expansion (NTE) in lead titanate permits us to make some promising strategies for materials designs. One of the important policies is to prepare zero and specific TEC titanate ceramics by doping lead into the solid solutions. The purposes of the present study were to determine the solid solution limit of barium lead titanate by the X-ray powder diffraction (XRPD) method, to measure the intrinsic thermal expansions of the solid solution compounds, and to examine the TEC behavior upon changing solubility.
2. Experimental
2.1. Sample preparation Samples were prepared by a solid-state reaction at high temperatures. The starting materials were Pb(NO 3 ) 2 and BaCO 3 (both analytical-reagent grade) and TiO 2 (99.9% purity). The starting reagents were weighed in the proper molar ratios, mixed, fully ground together using an agate
0925-8388 / 02 / $ – see front matter 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0925-8388(02)01178-7
2
X. Xing et al. / Journal of Alloys and Compounds 353 (2003) 1–4
mortar and pestle and pressed into small pellets, measuring 13 mm in diameter and 2–3 mm in thickness. The pellets were calcined in a platinum crucible at 500 8C for 24 h and at 950 8C for another 24 h, then quenched in air. After this procedure had been repeated twice, the samples were sintered at specific temperatures (from 950 to 1250 8C) for 24 h and slowly cooled to room temperature in the furnace. The final sintering temperature depends on the lead content in a given sample. The samples with high lead contents were sintered at a lower temperature.
2.2. X-ray powder diffractometry Phase identification and structural characterization were conducted using 21 kW extra-power powder XRD (Model M21XVHF22, Mac Science, Yokohama, Japan), with CuKa radiation, curved crystal graphite monochromators, and scintillation counter (SC) detectors. Two fully automatic vertical goniometers were allocated at both sides of the self-rotating anode (SRA) target. An attachment for high-temperature measurements was assembled at the left goniometer. Because the sample holder remained in an almost horizontal position, the sample could not fall from the sample holder at high temperatures. The scanning speed of the 2u angle was 48 / min, the heating speed was 10 8C / min, and the sample was maintained at the specified temperature for 15 min, to reach thermal balance. Air was incorporated into the sample chamber. For measuring the lattice parameters of the compound, pure silicon powder was added to the sample, as an internal standard.
Fig. 1. XRPD patterns of Ba 12x Pb x TiO 3 .
decreased with x in the solid solution. The cell parameter variations are continuous, but nonlinear with x in the range of 0#x#1.0. Such tendencies are of great importance to
2.3. Thermal analysis The DSC measurements were performed using a thermal analysis system (Model STA 409, Netzsch Geraetebau, Germany), in air, at a heating rate of 10 8C / min, in an alumina crucible, with a-Al 2 O 3 powder as a reference. Because the samples might slowly react with alumina crucibles, the cooling curves were not measured. Data were collected from RT to 1000 8C.
3. Results and discussion Light yellow ceramic pellets, nominally the compound Ba 12x Pb x TiO 3 , were synthesized, as described, and were isolated as a pure phase. The XRPD patterns of the solid solution compounds at RT were indexed in tetragonal system with space group P4mm, as shown in Fig. 1. It is evident that the reflections, such as (001) and (100), (110) and (101), (002) and (200), are clearly split and the distances between the two theta positions of these peaks became larger with increasing solubility x. Fig. 2(a) and (b) show the dependence of the cell parameters on x in the solid solution Ba 12x Pb x TiO 3 . It was found that the c axis increased, the a axis decreased and the cell volume also
Fig. 2. (a) Cell parameters of Ba 12x Pb x TiO 3 with solubility. (b) Cell volumes of Ba 12x Pb x TiO 3 with solubility.
X. Xing et al. / Journal of Alloys and Compounds 353 (2003) 1–4
predict the Curie points and ferroelectric properties of the barium lead titanates. Using high temperature XRPD (HTXRPD), the structural changes of Ba 0.5 Pb 0.5 TiO 3 with temperature were determined. It was found that the axis a( 5 b) expanded, the c axis contracted with temperature. A phase transition occurred at 330 8C. Above 330 8C, the lattice constants (a 5 b 5 c) linearly increase with temperature (shown in Fig. 3(a) and (b)). In the temperature range 25–320 8C, the Ba 0.5 Pb 0.5 TiO 3 reflections were indexed in the tetragonal system, and beyond the critical point at 330 8C the structure became cubic. However, a thermal contraction hysteresis was observed across the phase transition. Although the structure changes of Ba 0.5 Pb 0.5 TiO 3 are very similar to those of PbTiO 3 (see Fig. 4), the c /a ratios are much larger than the latter at specific temperatures and result in cell volume expansion. For a comparison of data obtained with the same accuracy [10,17], the structure of BaTiO 3 was measured using HTXRPD and the lattice parameters are plotted in Fig. 5. In general, the bulk TEC can be expressed by the following equations
Fig. 3. (a) Cell parameters of Ba 0.5 Pb 0.5 TiO 3 with temperature. (b) Cell volume with temperature of Pb 0.5 Ba 0.5 TiO 3 .
3
Fig. 4. Cell parameters of PbTiO 3 with temperature.
1 ≠V b 5 ] ? ] or Vo ≠T
1 DV b¯ 5 ] ? ] Vo DT
where b and b¯ are TEC and average TEC, and V, T are cell volume and temperature, respectively. The average bulk TECs of the solid solution compounds Ba 12x Pb x TiO 3 were calculated and listed in Table 1. Table 1 clearly demonstrates that neither the bulk thermal expansion coefficient nor the Curie point of Ba 0.5 Pb 0.5 TiO 3 are mean values of the two end compounds in the solid solution Ba 12x Pb x TiO 3 . However, Nomura and Sawada simply described the permittivity and the Curie point as being linearly correlated with the solubility in the solid solution Ba 12x Pb x TiO 3 [11]. This result seems unrealistic and might give rise to substantial errors for predicting the ferroelectric properties. For example, the Curie point of Ba 0.8 Pb 0.2 TiO 3 was determined at 170 8C (on set) or at 175 8C (peak) from their measurement of the specific heat, but the value predicted by them was beyond 200 8C. The Roberts equation is expressed as
Fig. 5. Cell parameters of BaTiO 3 with temperature.
X. Xing et al. / Journal of Alloys and Compounds 353 (2003) 1–4
4 Table 1 Average TEC of Ba 12x Pb x TiO 3 Compound
BaTiO 3 Ba 0.5 Pb 0.5 TiO 3 PbTiO 3
TEC (310 25 (8C)) T phase
Temp. (8C)
C phase
Temp. (8C)
1.56 1.15 21.62
RT–120 RT–330 RT–490
4.08 4.05 3.55
120–950 330–950 490–950
Curie point (8C) 120 330 490
Acknowledgements 1 1 da ]5b 2]?] C 3a dT where C is the Curie–Weiss constant, and a is the atomic polarizability. Usually the second term of the above equation is small. Therefore we can conclude that the ferroelectric properties are highly correlated with the thermal expansion of ceramics. With the DSC technique, we tried to determine the relation between the Curie points and the solubilities by measurements of the phase transitions in the solid solution Ba 12x Pb x TiO 3 . Excepting the two end compounds PbTiO 3 (490 8C) and BaTiO 3 (120 8C), the heat effects of Ba 12x Pb x TiO 3 (x50.4, 0.5, 0.6) are too weak to be detected, so we abandoned such efforts.
4. Conclusions 1. The solid solution limit of Ba 12x Pb x TiO 3 was determined and lead atoms can completely substitute for barium atoms in the composition range 0#x#1.0. The lattice parameters of Ba 12x Pb x TiO 3 continuously change with solubility, but the changes are nonlinear. 2. The structural changes of Ba 0.5 Pb 0.5 TiO 3 with temperature were determined. These structural changes of Ba 0.5 Pb 0.5 TiO 3 are very similar to those of PbTiO 3 and BaTiO 3 . The phase transition occurs at 330 8C. The bulk thermal expansion coefficients of BaTiO 3 , Ba 0.5 Pb 0.5 TiO 3 and PbTiO 3 were determined by HTXRPD. 3. The ferroelectric properties are highly correlated with the thermal expansion in titanate ceramics. Both ferroelectric properties and thermal expansion are proposed to be nonlinearly correlated with the solubility in the solid solution Ba 12x Pb x TiO 3 (0#x#1.0).
This work were financially supported by National Natural Science Foundation of China (No. 29971004, 20171006), and Funds of Ministry of Education of China for Training Ph.D. Candidates (No. 2001008005).
References [1] A. von Hippel (Ed.), Dielectric Materials and Applications, Technology Press; Wiley, Cambridge, MA; New York, 1954. [2] L.L. Hench, D.B. Dove, Physics of Electric Ceramics, Marcel Dekker, New York, 1971. [3] G. Shirane, S. Hoshino, J. Phys. Soc. Jpn. 6 (1951) 265–270. [4] A.M. Glazer, S.A. Mabud, Acta Cryst. B34 (1979) 1065–1070. [5] S.A. Mabud, A.M. Glazer, J. Appl. Cryst. 12 (1979) 49–53. [6] R.J. Nelmes, W.F. Kuhs, Solid State Commun. 54 (1985) 721–723. [7] G. Shirane, K. Suzuki, A. Takeda, J. Phys. Soc. Jpn. 7 (1952) 12–18. [8] J. Kobayashi, R. Ueda, Phys. Rev. 99 (1955) 1900–1901. [9] O. Yamaguchi, A. Rarai, T. Komatsu, J. Am. Ceram. Soc. 69 (1986) C256–C257. [10] R.H. Buttner, E.N. Maslen, Acta Cryst. B48 (1992) 764–769. [11] S. Nomura, S. Sawada, J. Phys. Soc. Jpn. 6 (1951) 36–39. [12] Y.N. Venevtsov, V.S. Bondarenko, G.S. Zhdanov, V.V. Chkalova, N.G. Stember, Kristallografiya 6 (1961) 375–380. [13] M. Kuwabara, S. Suemura, M. Kawahara, Ceram. Soc. Bull. 64 (1985) 1394–1398. [14] H. Cheng, T. Lin, C. Hu, I. Lin, J. Am. Ceram. Soc. 76 (1993) 827–832. [15] D. Wang, L. Li, Z. Gui, J. Chin. Ceram. Soc. 24 (1996) 585–589, (in Chinese). [16] C.K. Lee, I.N. Lin, C.T. Hu, J. Am. Ceram. Soc. 77 (1994) 1340–1344. [17] D. Taylor, J. Ther. Exp. Data 84 (1985) 181–188. [18] T.A. Mary, J.S.O. Evans, T. Vogt, A.W. Sleight, Science 272 (1996) 90–92. [19] X. Xing, Z. Zhu, X. Qiu, G. Liu, Rare Metals 20 (2001) 1–4. [20] X. Xing, J. Deng, Z. Zhu, J. Cheng, G. Liu, Refinements and novel thermal expansion on lead titanate, (2002) in preparation.
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www.elsevier.com / locate / jallcom
Solid solution Ba 12x Pb x TiO 3 and its thermal expansion Xianran Xing*, Jinxia Deng, Zhenqi Zhu, Guirong Liu Department of Physical Chemistry, University of Science and Technology Beijing, Beijing 100083, PR China Received 10 September 2002; received in revised form 15 October 2002; accepted 15 October 2002
Abstract The solid solution limit of Ba 12x Pb x TiO 3 was determined in the composition range of 0#x#1.0. All solid solution compounds were indexed in tetragonal symmetry with lead titanate structure type at room temperature. The cell parameters of Ba 12x Pbx TiO 3 continuously, but nonlinearly, change with x. The structure of Ba 0.5 Pb 0.5 TiO 3 is tetragonal in the temperature range RT–330 8C and in cubic system beyond 330 8C with HTXRPD. The intrinsic thermal expansion coefficients of Ba 12x Pbx TiO 3 (x50, 0.5, 1.0) were obtained. The correlation between thermal expansion and ferroelectric properties is briefly discussed. 2002 Elsevier Science B.V. All rights reserved. Keywords: Solid solution Ba 12x Pb x TiO 3 ; Thermal expansion; Phase transition; High temperature X-ray powder diffractometry (HTXRPD)
1. Introduction It is well known that ferroelectric properties have been observed in lead, barium and barium lead titanate ceramics [1,2]. For more than half a century the structures of these compounds were well investigated by many groups [3– 10]. Especially the anomalous positive temperature coefficient of resistivity (PTCR) of barium titanate (over 120 8C) attracts much attention. The Curie point of barium titanate can be shifted to lower temperatures by substituting strontium for barium, or zirconium for titanium, and to higher temperatures by substituting lead for barium. The effort was successfully made to obtain PTCR effects with Curie points of 360 8C for Ba 0.35 Pb 0.65 TiO 3 and 420 8C for Ba 0.2 Pb 0.8 [11–13]. Analogously some studies were also made on other mixed titanate or zirconate ceramics, for example on strontium barium, or, strontium lead [7,14– 16]. Such solutions in ferroelectric ceramics are technologically important because it allows the electric properties to be tailored to practical applications. Another considerable advantage of solid solutions of ceramics is to adjust the thermal expansion in order to reach compatibility with other ceramic devices [17–19]. The ceramics of perovskites are usually prepared at high temperatures and involve one or two phase transitions. To *Corresponding author. Tel.: 186-10-6233-4200; fax: 186-10-62333477. E-mail address: [email protected] (X. Xing).
overcome the thermal shock damage of these materials becomes a substantial problem. It depends on the thermal expansion coefficients (TECs). Fortunately, previous work and our recent research reveal that lead titanate exhibit very special TECs [3,20]. Below the Curie point of lead titanate (490 8C), the c axis decreases, the a axis increases, and the cell volume shrinks with increasing temperature. Such a negative thermal expansion (NTE) in lead titanate permits us to make some promising strategies for materials designs. One of the important policies is to prepare zero and specific TEC titanate ceramics by doping lead into the solid solutions. The purposes of the present study were to determine the solid solution limit of barium lead titanate by the X-ray powder diffraction (XRPD) method, to measure the intrinsic thermal expansions of the solid solution compounds, and to examine the TEC behavior upon changing solubility.
2. Experimental
2.1. Sample preparation Samples were prepared by a solid-state reaction at high temperatures. The starting materials were Pb(NO 3 ) 2 and BaCO 3 (both analytical-reagent grade) and TiO 2 (99.9% purity). The starting reagents were weighed in the proper molar ratios, mixed, fully ground together using an agate
0925-8388 / 02 / $ – see front matter 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0925-8388(02)01178-7
2
X. Xing et al. / Journal of Alloys and Compounds 353 (2003) 1–4
mortar and pestle and pressed into small pellets, measuring 13 mm in diameter and 2–3 mm in thickness. The pellets were calcined in a platinum crucible at 500 8C for 24 h and at 950 8C for another 24 h, then quenched in air. After this procedure had been repeated twice, the samples were sintered at specific temperatures (from 950 to 1250 8C) for 24 h and slowly cooled to room temperature in the furnace. The final sintering temperature depends on the lead content in a given sample. The samples with high lead contents were sintered at a lower temperature.
2.2. X-ray powder diffractometry Phase identification and structural characterization were conducted using 21 kW extra-power powder XRD (Model M21XVHF22, Mac Science, Yokohama, Japan), with CuKa radiation, curved crystal graphite monochromators, and scintillation counter (SC) detectors. Two fully automatic vertical goniometers were allocated at both sides of the self-rotating anode (SRA) target. An attachment for high-temperature measurements was assembled at the left goniometer. Because the sample holder remained in an almost horizontal position, the sample could not fall from the sample holder at high temperatures. The scanning speed of the 2u angle was 48 / min, the heating speed was 10 8C / min, and the sample was maintained at the specified temperature for 15 min, to reach thermal balance. Air was incorporated into the sample chamber. For measuring the lattice parameters of the compound, pure silicon powder was added to the sample, as an internal standard.
Fig. 1. XRPD patterns of Ba 12x Pb x TiO 3 .
decreased with x in the solid solution. The cell parameter variations are continuous, but nonlinear with x in the range of 0#x#1.0. Such tendencies are of great importance to
2.3. Thermal analysis The DSC measurements were performed using a thermal analysis system (Model STA 409, Netzsch Geraetebau, Germany), in air, at a heating rate of 10 8C / min, in an alumina crucible, with a-Al 2 O 3 powder as a reference. Because the samples might slowly react with alumina crucibles, the cooling curves were not measured. Data were collected from RT to 1000 8C.
3. Results and discussion Light yellow ceramic pellets, nominally the compound Ba 12x Pb x TiO 3 , were synthesized, as described, and were isolated as a pure phase. The XRPD patterns of the solid solution compounds at RT were indexed in tetragonal system with space group P4mm, as shown in Fig. 1. It is evident that the reflections, such as (001) and (100), (110) and (101), (002) and (200), are clearly split and the distances between the two theta positions of these peaks became larger with increasing solubility x. Fig. 2(a) and (b) show the dependence of the cell parameters on x in the solid solution Ba 12x Pb x TiO 3 . It was found that the c axis increased, the a axis decreased and the cell volume also
Fig. 2. (a) Cell parameters of Ba 12x Pb x TiO 3 with solubility. (b) Cell volumes of Ba 12x Pb x TiO 3 with solubility.
X. Xing et al. / Journal of Alloys and Compounds 353 (2003) 1–4
predict the Curie points and ferroelectric properties of the barium lead titanates. Using high temperature XRPD (HTXRPD), the structural changes of Ba 0.5 Pb 0.5 TiO 3 with temperature were determined. It was found that the axis a( 5 b) expanded, the c axis contracted with temperature. A phase transition occurred at 330 8C. Above 330 8C, the lattice constants (a 5 b 5 c) linearly increase with temperature (shown in Fig. 3(a) and (b)). In the temperature range 25–320 8C, the Ba 0.5 Pb 0.5 TiO 3 reflections were indexed in the tetragonal system, and beyond the critical point at 330 8C the structure became cubic. However, a thermal contraction hysteresis was observed across the phase transition. Although the structure changes of Ba 0.5 Pb 0.5 TiO 3 are very similar to those of PbTiO 3 (see Fig. 4), the c /a ratios are much larger than the latter at specific temperatures and result in cell volume expansion. For a comparison of data obtained with the same accuracy [10,17], the structure of BaTiO 3 was measured using HTXRPD and the lattice parameters are plotted in Fig. 5. In general, the bulk TEC can be expressed by the following equations
Fig. 3. (a) Cell parameters of Ba 0.5 Pb 0.5 TiO 3 with temperature. (b) Cell volume with temperature of Pb 0.5 Ba 0.5 TiO 3 .
3
Fig. 4. Cell parameters of PbTiO 3 with temperature.
1 ≠V b 5 ] ? ] or Vo ≠T
1 DV b¯ 5 ] ? ] Vo DT
where b and b¯ are TEC and average TEC, and V, T are cell volume and temperature, respectively. The average bulk TECs of the solid solution compounds Ba 12x Pb x TiO 3 were calculated and listed in Table 1. Table 1 clearly demonstrates that neither the bulk thermal expansion coefficient nor the Curie point of Ba 0.5 Pb 0.5 TiO 3 are mean values of the two end compounds in the solid solution Ba 12x Pb x TiO 3 . However, Nomura and Sawada simply described the permittivity and the Curie point as being linearly correlated with the solubility in the solid solution Ba 12x Pb x TiO 3 [11]. This result seems unrealistic and might give rise to substantial errors for predicting the ferroelectric properties. For example, the Curie point of Ba 0.8 Pb 0.2 TiO 3 was determined at 170 8C (on set) or at 175 8C (peak) from their measurement of the specific heat, but the value predicted by them was beyond 200 8C. The Roberts equation is expressed as
Fig. 5. Cell parameters of BaTiO 3 with temperature.
X. Xing et al. / Journal of Alloys and Compounds 353 (2003) 1–4
4 Table 1 Average TEC of Ba 12x Pb x TiO 3 Compound
BaTiO 3 Ba 0.5 Pb 0.5 TiO 3 PbTiO 3
TEC (310 25 (8C)) T phase
Temp. (8C)
C phase
Temp. (8C)
1.56 1.15 21.62
RT–120 RT–330 RT–490
4.08 4.05 3.55
120–950 330–950 490–950
Curie point (8C) 120 330 490
Acknowledgements 1 1 da ]5b 2]?] C 3a dT where C is the Curie–Weiss constant, and a is the atomic polarizability. Usually the second term of the above equation is small. Therefore we can conclude that the ferroelectric properties are highly correlated with the thermal expansion of ceramics. With the DSC technique, we tried to determine the relation between the Curie points and the solubilities by measurements of the phase transitions in the solid solution Ba 12x Pb x TiO 3 . Excepting the two end compounds PbTiO 3 (490 8C) and BaTiO 3 (120 8C), the heat effects of Ba 12x Pb x TiO 3 (x50.4, 0.5, 0.6) are too weak to be detected, so we abandoned such efforts.
4. Conclusions 1. The solid solution limit of Ba 12x Pb x TiO 3 was determined and lead atoms can completely substitute for barium atoms in the composition range 0#x#1.0. The lattice parameters of Ba 12x Pb x TiO 3 continuously change with solubility, but the changes are nonlinear. 2. The structural changes of Ba 0.5 Pb 0.5 TiO 3 with temperature were determined. These structural changes of Ba 0.5 Pb 0.5 TiO 3 are very similar to those of PbTiO 3 and BaTiO 3 . The phase transition occurs at 330 8C. The bulk thermal expansion coefficients of BaTiO 3 , Ba 0.5 Pb 0.5 TiO 3 and PbTiO 3 were determined by HTXRPD. 3. The ferroelectric properties are highly correlated with the thermal expansion in titanate ceramics. Both ferroelectric properties and thermal expansion are proposed to be nonlinearly correlated with the solubility in the solid solution Ba 12x Pb x TiO 3 (0#x#1.0).
This work were financially supported by National Natural Science Foundation of China (No. 29971004, 20171006), and Funds of Ministry of Education of China for Training Ph.D. Candidates (No. 2001008005).
References [1] A. von Hippel (Ed.), Dielectric Materials and Applications, Technology Press; Wiley, Cambridge, MA; New York, 1954. [2] L.L. Hench, D.B. Dove, Physics of Electric Ceramics, Marcel Dekker, New York, 1971. [3] G. Shirane, S. Hoshino, J. Phys. Soc. Jpn. 6 (1951) 265–270. [4] A.M. Glazer, S.A. Mabud, Acta Cryst. B34 (1979) 1065–1070. [5] S.A. Mabud, A.M. Glazer, J. Appl. Cryst. 12 (1979) 49–53. [6] R.J. Nelmes, W.F. Kuhs, Solid State Commun. 54 (1985) 721–723. [7] G. Shirane, K. Suzuki, A. Takeda, J. Phys. Soc. Jpn. 7 (1952) 12–18. [8] J. Kobayashi, R. Ueda, Phys. Rev. 99 (1955) 1900–1901. [9] O. Yamaguchi, A. Rarai, T. Komatsu, J. Am. Ceram. Soc. 69 (1986) C256–C257. [10] R.H. Buttner, E.N. Maslen, Acta Cryst. B48 (1992) 764–769. [11] S. Nomura, S. Sawada, J. Phys. Soc. Jpn. 6 (1951) 36–39. [12] Y.N. Venevtsov, V.S. Bondarenko, G.S. Zhdanov, V.V. Chkalova, N.G. Stember, Kristallografiya 6 (1961) 375–380. [13] M. Kuwabara, S. Suemura, M. Kawahara, Ceram. Soc. Bull. 64 (1985) 1394–1398. [14] H. Cheng, T. Lin, C. Hu, I. Lin, J. Am. Ceram. Soc. 76 (1993) 827–832. [15] D. Wang, L. Li, Z. Gui, J. Chin. Ceram. Soc. 24 (1996) 585–589, (in Chinese). [16] C.K. Lee, I.N. Lin, C.T. Hu, J. Am. Ceram. Soc. 77 (1994) 1340–1344. [17] D. Taylor, J. Ther. Exp. Data 84 (1985) 181–188. [18] T.A. Mary, J.S.O. Evans, T. Vogt, A.W. Sleight, Science 272 (1996) 90–92. [19] X. Xing, Z. Zhu, X. Qiu, G. Liu, Rare Metals 20 (2001) 1–4. [20] X. Xing, J. Deng, Z. Zhu, J. Cheng, G. Liu, Refinements and novel thermal expansion on lead titanate, (2002) in preparation.