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Silver addition in La2CuO4 ceramics
Materials Letters 58 (2004) 1237 – 1240 www.elsevier.com/locate/matlet
Silver addition in La2CuO4 ceramics C.C. Wang, X. Zheng, J. Zhu * Electron Microscopy Laboratory, School of Materials Science and Engineering, Tsinghua University, Beijing 100084, PR China Received 9 May 2003; received in revised form 8 September 2003; accepted 17 September 2003
Abstract The effects of Ag addition on the microstructural and electrical properties of sintered La2CuO4 have been studied. Unexpectedly, Agdoped sample shows strong limitation of grain growth. The resistivity behavior of the variable range hopping was observed in the low temperature range (13 – 41 K) and the ordinary thermal activation process was observed in the high temperature range (41 – 90 K). A model was proposed to deduce the accurate transition temperature and transition range. The experimental results indicate that the addition of Ag not only increases the hole density but also creates sufficient disorder in the sample. D 2003 Elsevier B.V. All rights reserved. Keywords: Silver addition; La2CuO4 ceramics; Electrical properties
1. Introduction It is well documented that silver is the most suitable dopant for improvement in the superconducting properties of oxide ceramics such as Y –Ba – Cu – O [1 –9] and Bi– Sr –Ca – Cu – O [10] systems. The effects of Ag (or Ag2O) doping are proved to be the grain enlargement and alignment [11], which are responsible for the observed phenomena such as a hightemperature shift of the point at zero resistivity in resistivity measurements as well as an increase in critical current density. From the viewpoint of application of superconducting materials, extensive investigations have been performed on those systems with Tc higher than liquid nitrogen temperature (77 K). However, the role of silver in La2CuO4 system is not well established. In the present work, we have investigated the effects of Ag addition on the microstructural and electronic properties of sintered La2CuO4 ceramics, and show contrary to that of Y – Ba – Cu – O system, the function of silver addition in sintering of La2CuO4 is to limit the grain growth.
2. Experimental La2O3 and CuO were used as the starting materials. The mixture was heated at 1100 jC for 2 days with * Corresponding author. Tel.: +86-10-62794026; fax: +86-1062772507. E-mail address: [email protected] (J. Zhu). 0167-577X/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.matlet.2003.09.014
intermediate grinding. The prepared powder identified as single phase of La2CuO4 by powder X-ray diffraction (XRD) performed on Rigaku D/Max-RB diffractometer. This powder was thoroughly mixed with 5 wt.% Ag2O powder, and then pressed into pellet and calcined at 930 jC for 20 h. The ultimate pellet has the same XRD pattern as the pure La2CuO4 pellet as shown in Fig. 1, and a room temperature resistance of about a few ohm, which is much smaller than that of pure La2CuO4 (about kV). The resistivity measurement was done by standard four-point ac method. Particle-size and morphology characteristics of the samples were examined by scanning electron microcopy (SEM) (JSM 6301).
3. Results and discussion Fig. 2 shows the SEM photographs of Ag-doped and undoped La2CuO4 ceramics. We see the grains of the Agdoped sample are much smaller than those of undoped sample. This feature is contrary to that of Ag-doped Y – Ba – C –O system, which shows marked grain growth in Agdoped sample. It should be noted that the grains of Agdoped La2CuO4 sample have smooth and indistinct outlines, which is strong indicative of a molten state and glassy phase in the grain surfaces and grain boundaries. This could be due to partial melting of the mixture in the presence of Ag2O. It can also be seen from Fig. 1 that the intensity of the main peaks of the Ag-containing sample becomes
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C.C. Wang et al. / Materials Letters 58 (2004) 1237–1240
where q01 and T0 are constants. At high temperatures, T > Ttr, the resistivity is expressed by: q2 ¼ q02 expðE=k B T Þ
ð2Þ
where E is activation energy, q02 is constant, and kB is the Boltzmann constant. The least squares fittings of the two mechanisms are shown as a solid line in Fig. 4 and the main parameters resulting from the fits are given in Table 1. Except for q01, these parameters are in approximate agreement with literature data also given in Table 1. For such a low value of q01, we have no explanation. So one gets the total resistivity: qðT Þ ¼ q1 ðT Þf ðT Þ þ q2 ðT Þ½1 f ðT Þ
Fig. 1. XRD patterns of (a) pure LCO and (b) Ag-containing LCO ceramics.
ð3Þ
where f(T) is the weighting function. It is important to deduce the accurate transition temperature since this temperature can give detail information about the role of silver addition in La2CuO4 ceramics. To this end, a model similar to superconducting islands emerging from the antiferromagnetic background with decreasing temperature can be used.
smaller. A reasonable reason for this feature is that the glassy phase around the grains absorbs extra X-ray energy. Furthermore, a possible explanation to the absence of improvement in grain size may be due to the liquid phase along the grain boundaries that hinder the grain growth for the decreased driving force [12]. Fig. 3 shows a typical EDS mapping image of silver. It reveals a relatively uniform distribution of Ag atoms. In other words, Ag atoms exist continuously along the grains and hence increase the quality of the grain boundaries glassy phase, which is responsible for the improved resistivity behavior of the doped material. On the other hand, small silver-rich regions are also visible, which is a common feature in Ag-doped cuprate materials [5]. However, no silver signal appears in the XRD pattern, which implies that the fraction of agglomerated silver is smaller below the resolution of XRD equipment. The temperature dependence of the resistivity of Agdoped La2CuO4 sample is presented in Fig. 4, in which log q is plotted against T 1/4. We see the temperature dependence of resistivity can be divided into two regions with an intermediate transition range and a transition temperature between them. The transition temperature Ttr is estimated to be 46 K. For sake of clarity, the data of high temperature region (46 – 90 K) are replotted against T 1, shown in the inset. From these representations, the curves approach straight lines indicating variable range hopping (VRH) and ordinary thermally activated (OTA) behavior, respectively. That is, at low temperatures, T < Ttr, the data are well described by the known Mott’s variable range hopping law: q1 ¼ q01 exp½ðT0 =T Þ1=4
ð1Þ
Fig. 2. SEM photographs of Ag-doped (a) and undoped (b) La2CuO4 ceramics.
C.C. Wang et al. / Materials Letters 58 (2004) 1237–1240
1239
Fig. 3. EDS mapping image of Ag. The bar is 8 Am.
We can suppose that as temperature decreases, the islands exhibiting VRH mechanism appear from the background showing OTA mechanism. It is naturally expected that the transition temperatures obey certain distribution law due to fluctuation. A normal distribution has been assumed: 2 1 2 f ðT t Þ ¼ pffiffiffiffiffiffiffiffi eðT t T tr Þ =2r 2pr
ð4Þ
where f(Tt) is probability density function, Ttr is the most probable transition temperature, and r2 is the squared
deviation. For a certain temperature, T, the weight function can be easily derived from the following integration f ðT Þ ¼
Z
l
f ðT t Þ dT t
ð5Þ
T
This integration has the similar form to Fermi distribution function and can be written as f ðT Þ ¼
1 eðT T tr Þ=D
ð6Þ
þ1
where D is the parameter describing the width of distribution of the transition temperatures. Taking Eqs. (3) and (6), the experimental data can be perfectly fitted. The result from the fit is given as a solid line in Fig. 5. The fit yields Ttr = 41.383 K, D = 2.485 K. The transition temperature is larger than that of undoped sample which is found to be 30 K according to Ref. [15]. Similar feature has been found in Zn-doped La2CuO4 by Yang et al [16], that is, with increasing doping level the transition temperature becomes larger. This proves, according to Eqs. (1) and (2) and the values of q01 and q02 given in Table 1, that the value of T0 in Mott’s VRH law also becomes larger with the increasing doping level. Since the quantity kBT0 represents the mean
Table 1 Parameters obtained from the least squares fittings, characterizing the electrical properties of La2CuO4 ceramics Fig. 4. Temperature dependence of the resistivity for the Ag-doped La2CuO4 ceramic. The data are plotted vs. T 1/4; the same data of high temperature region (46 – 90 K) are replotted vs. T 1 in the inset. In certain temperature regions, the curves approach straight lines which indicate VRH and thermally activated behavior, respectively. The straight lines are the results from the least squares fittings using Eqs. (1) and (2).
q01 (V cm) 8
4.56 10 1.8 10 2 13.3 10 2
T0 (K) 4,200,802 2,600,000 26,700
q02 (V cm) 2
2.93 10
These parameters are defined in Eqs. (1) and (2).
E (meV)
Reference
16.14 16 24
This work [13] [14]
1240
C.C. Wang et al. / Materials Letters 58 (2004) 1237–1240
3. A model proposed to elicit the accurate transition temperature and transition range, and found to be 41.383 and 2.485 K, respectively. 4. The efficacy of Ag doping is believed to be the increment of hole density and disorder in the sample.
Acknowledgements
Fig. 5. A perfect agreement between experimental data and fit can be obtained based on Eqs. (3) and (6).
energy difference between localized states separated by less than one localization length, namely k B T0 ¼ 4v c ½gðE F Þn3 1
ð7Þ
where g(EF) is the density of states at the Fermi energy, n is the localization length, and vc is constant, in three-dimensional case it is expected to be about 4. The enlargement of T0 reflects a smaller localization length or a lower density of states. According to Ref. [17], g(EF) is insensitive to composition, suggesting that the addition of a few percent of Ag is inadequate to change the density of states near Fermi energy. Kastner et al [13] reported that the addition of Li in both ceramic and crystal La2CuO4 samples has low resistivity but high value of T0. They discussed that the role of Li doping is to raise the hole density and create disorder. The same features of Ag-doped La2CuO4 were found in the present work. So we believe that the efficacy of Ag doping not only increases the hole density resulting in lower resistivities, but also creates sufficient disorder causing the reduction of localization length. Therefore a higher T0 value can be observed.
4. Conclusion In summary, we have: 1. The addition of Ag places restriction on the grain growth. This could be due to the presence of a molten state on the grain surfaces and grain boundaries. 2. The result of resistivity measurement indicates that a transition occurs from VRH mechanism to the ordinary thermal activation process with increasing temperature.
We wish to thank Z.X. Liu, Y.J. Yan and W. Miao for their help during the experiments. We acknowledge financial support from the Chinese National Natures Science Foundation and National 973 Project. This work was supported in part by the State Key Lab of New Ceramics and Fine Processes.
References [1] P.N. Peters, R.C. Sisk, E.W. Urban, C.Y. Huang, M.K. Wu, Appl. Phys. Lett. 52 (1988) 2066. [2] D. Pavuna, H. Berger, M. Affronte, J. Van der Mass, J.J. Capponi, M. Guillot, P. Lejay, J.L. Tholence, Solid State Commun. 68 (1988) 535. [3] D. Kumar, M. Sharon, R. Pinto, P.R. Apte, S.P. Pai, S.C. Purandare, L.C. Gupta, R. Vijayaraghavan, Appl. Phys. Lett. 62 (1993) 3522. [4] R.K. Singh, D. Bhattacharga, P. Tiwari, J. Narayan, C.B. Lee, Appl. Phys. Lett. 60 (1992) 255. [5] T.H. Tiefel, S. Jin, R.C. Sherwood, M.E. Davis, G.W. Kammlott, P.K. Gallagher, D.W. Johnson Jr., R.A. Fastnacht, W.W. Rhodes, Mater. Lett. 7 (1989) 363. [6] L. Ganapathi, A. Kumar, J. Narayan, J. Appl. Phys. 66 (1989) 5935. [7] Y. Matsumoto, J. Hombo, Y. Yamaguchi, M. Nishida, A. Chiba, Appl. Phys. Lett. 56 (1990) 1585. [8] O. Ishii, T. Konaka, M. Sato, Y. Koshimoto, Jpn. J. Appl. Phys. 29 (1990) L1075. [9] P.R. Apte, R. Pinto, A.G. Chourey, S.P. Pai, J. Appl. Phys. 75 (1994) 4258. [10] Y. Matsumoto, J. Hombo, T. Mitsunaga, Mater. Res. Bull. 24 (1989) 1469. [11] R. Pinto, P.R. Apte, S.P. Pai, D. Kumar, Physica, C 207 (1993) 13. [12] W.D. Kingery, H.K. Bowen, D.R. Uhlmann, Introduction to Ceramics, 2nd ed., Wiley, New York, 1976, p. 459. [13] M.A. Kaster, R.J. Birgeneau, C.Y. Chen, Y.M. Chiang, D.R. Gabbe, H.P. Jenssen, T. Junk, C.J. Peters, P.J. Picone, T. Thio, T.R. Thurston, H.L. Tuller, Phys. Rev. B 37 (1988) 111. [14] J. Tateno, N. Masaki, A. Iwase, Phys. Lett. A 138 (1989) 313. [15] P. Lunkenheimer, G. Knebel, A. Pimenov, G.A. Emel’chenko, A. Loidl, Z. Phys. B 99 (1996) 507. [16] H.S. Yang, P.C. Li, Y.S. Chai, M. Yu, Z.Q. Li, D.S. Yang, L. Zhang, Y.H. Wang, M.D. Li, L.Z. Cao, Y.Z. Long, Z.J. Chen, Acta Phys. Sin. 51 (2002) 679. [17] M. Hucker, V. Kataev, J. Pommer, J. Harrass, A. Hosni, C. Pflisch, R. Gross, B. Buchner, Phys. Rev. B 59 (1999) R725.
Silver addition in La2CuO4 ceramics C.C. Wang, X. Zheng, J. Zhu * Electron Microscopy Laboratory, School of Materials Science and Engineering, Tsinghua University, Beijing 100084, PR China Received 9 May 2003; received in revised form 8 September 2003; accepted 17 September 2003
Abstract The effects of Ag addition on the microstructural and electrical properties of sintered La2CuO4 have been studied. Unexpectedly, Agdoped sample shows strong limitation of grain growth. The resistivity behavior of the variable range hopping was observed in the low temperature range (13 – 41 K) and the ordinary thermal activation process was observed in the high temperature range (41 – 90 K). A model was proposed to deduce the accurate transition temperature and transition range. The experimental results indicate that the addition of Ag not only increases the hole density but also creates sufficient disorder in the sample. D 2003 Elsevier B.V. All rights reserved. Keywords: Silver addition; La2CuO4 ceramics; Electrical properties
1. Introduction It is well documented that silver is the most suitable dopant for improvement in the superconducting properties of oxide ceramics such as Y –Ba – Cu – O [1 –9] and Bi– Sr –Ca – Cu – O [10] systems. The effects of Ag (or Ag2O) doping are proved to be the grain enlargement and alignment [11], which are responsible for the observed phenomena such as a hightemperature shift of the point at zero resistivity in resistivity measurements as well as an increase in critical current density. From the viewpoint of application of superconducting materials, extensive investigations have been performed on those systems with Tc higher than liquid nitrogen temperature (77 K). However, the role of silver in La2CuO4 system is not well established. In the present work, we have investigated the effects of Ag addition on the microstructural and electronic properties of sintered La2CuO4 ceramics, and show contrary to that of Y – Ba – Cu – O system, the function of silver addition in sintering of La2CuO4 is to limit the grain growth.
2. Experimental La2O3 and CuO were used as the starting materials. The mixture was heated at 1100 jC for 2 days with * Corresponding author. Tel.: +86-10-62794026; fax: +86-1062772507. E-mail address: [email protected] (J. Zhu). 0167-577X/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.matlet.2003.09.014
intermediate grinding. The prepared powder identified as single phase of La2CuO4 by powder X-ray diffraction (XRD) performed on Rigaku D/Max-RB diffractometer. This powder was thoroughly mixed with 5 wt.% Ag2O powder, and then pressed into pellet and calcined at 930 jC for 20 h. The ultimate pellet has the same XRD pattern as the pure La2CuO4 pellet as shown in Fig. 1, and a room temperature resistance of about a few ohm, which is much smaller than that of pure La2CuO4 (about kV). The resistivity measurement was done by standard four-point ac method. Particle-size and morphology characteristics of the samples were examined by scanning electron microcopy (SEM) (JSM 6301).
3. Results and discussion Fig. 2 shows the SEM photographs of Ag-doped and undoped La2CuO4 ceramics. We see the grains of the Agdoped sample are much smaller than those of undoped sample. This feature is contrary to that of Ag-doped Y – Ba – C –O system, which shows marked grain growth in Agdoped sample. It should be noted that the grains of Agdoped La2CuO4 sample have smooth and indistinct outlines, which is strong indicative of a molten state and glassy phase in the grain surfaces and grain boundaries. This could be due to partial melting of the mixture in the presence of Ag2O. It can also be seen from Fig. 1 that the intensity of the main peaks of the Ag-containing sample becomes
1238
C.C. Wang et al. / Materials Letters 58 (2004) 1237–1240
where q01 and T0 are constants. At high temperatures, T > Ttr, the resistivity is expressed by: q2 ¼ q02 expðE=k B T Þ
ð2Þ
where E is activation energy, q02 is constant, and kB is the Boltzmann constant. The least squares fittings of the two mechanisms are shown as a solid line in Fig. 4 and the main parameters resulting from the fits are given in Table 1. Except for q01, these parameters are in approximate agreement with literature data also given in Table 1. For such a low value of q01, we have no explanation. So one gets the total resistivity: qðT Þ ¼ q1 ðT Þf ðT Þ þ q2 ðT Þ½1 f ðT Þ
Fig. 1. XRD patterns of (a) pure LCO and (b) Ag-containing LCO ceramics.
ð3Þ
where f(T) is the weighting function. It is important to deduce the accurate transition temperature since this temperature can give detail information about the role of silver addition in La2CuO4 ceramics. To this end, a model similar to superconducting islands emerging from the antiferromagnetic background with decreasing temperature can be used.
smaller. A reasonable reason for this feature is that the glassy phase around the grains absorbs extra X-ray energy. Furthermore, a possible explanation to the absence of improvement in grain size may be due to the liquid phase along the grain boundaries that hinder the grain growth for the decreased driving force [12]. Fig. 3 shows a typical EDS mapping image of silver. It reveals a relatively uniform distribution of Ag atoms. In other words, Ag atoms exist continuously along the grains and hence increase the quality of the grain boundaries glassy phase, which is responsible for the improved resistivity behavior of the doped material. On the other hand, small silver-rich regions are also visible, which is a common feature in Ag-doped cuprate materials [5]. However, no silver signal appears in the XRD pattern, which implies that the fraction of agglomerated silver is smaller below the resolution of XRD equipment. The temperature dependence of the resistivity of Agdoped La2CuO4 sample is presented in Fig. 4, in which log q is plotted against T 1/4. We see the temperature dependence of resistivity can be divided into two regions with an intermediate transition range and a transition temperature between them. The transition temperature Ttr is estimated to be 46 K. For sake of clarity, the data of high temperature region (46 – 90 K) are replotted against T 1, shown in the inset. From these representations, the curves approach straight lines indicating variable range hopping (VRH) and ordinary thermally activated (OTA) behavior, respectively. That is, at low temperatures, T < Ttr, the data are well described by the known Mott’s variable range hopping law: q1 ¼ q01 exp½ðT0 =T Þ1=4
ð1Þ
Fig. 2. SEM photographs of Ag-doped (a) and undoped (b) La2CuO4 ceramics.
C.C. Wang et al. / Materials Letters 58 (2004) 1237–1240
1239
Fig. 3. EDS mapping image of Ag. The bar is 8 Am.
We can suppose that as temperature decreases, the islands exhibiting VRH mechanism appear from the background showing OTA mechanism. It is naturally expected that the transition temperatures obey certain distribution law due to fluctuation. A normal distribution has been assumed: 2 1 2 f ðT t Þ ¼ pffiffiffiffiffiffiffiffi eðT t T tr Þ =2r 2pr
ð4Þ
where f(Tt) is probability density function, Ttr is the most probable transition temperature, and r2 is the squared
deviation. For a certain temperature, T, the weight function can be easily derived from the following integration f ðT Þ ¼
Z
l
f ðT t Þ dT t
ð5Þ
T
This integration has the similar form to Fermi distribution function and can be written as f ðT Þ ¼
1 eðT T tr Þ=D
ð6Þ
þ1
where D is the parameter describing the width of distribution of the transition temperatures. Taking Eqs. (3) and (6), the experimental data can be perfectly fitted. The result from the fit is given as a solid line in Fig. 5. The fit yields Ttr = 41.383 K, D = 2.485 K. The transition temperature is larger than that of undoped sample which is found to be 30 K according to Ref. [15]. Similar feature has been found in Zn-doped La2CuO4 by Yang et al [16], that is, with increasing doping level the transition temperature becomes larger. This proves, according to Eqs. (1) and (2) and the values of q01 and q02 given in Table 1, that the value of T0 in Mott’s VRH law also becomes larger with the increasing doping level. Since the quantity kBT0 represents the mean
Table 1 Parameters obtained from the least squares fittings, characterizing the electrical properties of La2CuO4 ceramics Fig. 4. Temperature dependence of the resistivity for the Ag-doped La2CuO4 ceramic. The data are plotted vs. T 1/4; the same data of high temperature region (46 – 90 K) are replotted vs. T 1 in the inset. In certain temperature regions, the curves approach straight lines which indicate VRH and thermally activated behavior, respectively. The straight lines are the results from the least squares fittings using Eqs. (1) and (2).
q01 (V cm) 8
4.56 10 1.8 10 2 13.3 10 2
T0 (K) 4,200,802 2,600,000 26,700
q02 (V cm) 2
2.93 10
These parameters are defined in Eqs. (1) and (2).
E (meV)
Reference
16.14 16 24
This work [13] [14]
1240
C.C. Wang et al. / Materials Letters 58 (2004) 1237–1240
3. A model proposed to elicit the accurate transition temperature and transition range, and found to be 41.383 and 2.485 K, respectively. 4. The efficacy of Ag doping is believed to be the increment of hole density and disorder in the sample.
Acknowledgements
Fig. 5. A perfect agreement between experimental data and fit can be obtained based on Eqs. (3) and (6).
energy difference between localized states separated by less than one localization length, namely k B T0 ¼ 4v c ½gðE F Þn3 1
ð7Þ
where g(EF) is the density of states at the Fermi energy, n is the localization length, and vc is constant, in three-dimensional case it is expected to be about 4. The enlargement of T0 reflects a smaller localization length or a lower density of states. According to Ref. [17], g(EF) is insensitive to composition, suggesting that the addition of a few percent of Ag is inadequate to change the density of states near Fermi energy. Kastner et al [13] reported that the addition of Li in both ceramic and crystal La2CuO4 samples has low resistivity but high value of T0. They discussed that the role of Li doping is to raise the hole density and create disorder. The same features of Ag-doped La2CuO4 were found in the present work. So we believe that the efficacy of Ag doping not only increases the hole density resulting in lower resistivities, but also creates sufficient disorder causing the reduction of localization length. Therefore a higher T0 value can be observed.
4. Conclusion In summary, we have: 1. The addition of Ag places restriction on the grain growth. This could be due to the presence of a molten state on the grain surfaces and grain boundaries. 2. The result of resistivity measurement indicates that a transition occurs from VRH mechanism to the ordinary thermal activation process with increasing temperature.
We wish to thank Z.X. Liu, Y.J. Yan and W. Miao for their help during the experiments. We acknowledge financial support from the Chinese National Natures Science Foundation and National 973 Project. This work was supported in part by the State Key Lab of New Ceramics and Fine Processes.
References [1] P.N. Peters, R.C. Sisk, E.W. Urban, C.Y. Huang, M.K. Wu, Appl. Phys. Lett. 52 (1988) 2066. [2] D. Pavuna, H. Berger, M. Affronte, J. Van der Mass, J.J. Capponi, M. Guillot, P. Lejay, J.L. Tholence, Solid State Commun. 68 (1988) 535. [3] D. Kumar, M. Sharon, R. Pinto, P.R. Apte, S.P. Pai, S.C. Purandare, L.C. Gupta, R. Vijayaraghavan, Appl. Phys. Lett. 62 (1993) 3522. [4] R.K. Singh, D. Bhattacharga, P. Tiwari, J. Narayan, C.B. Lee, Appl. Phys. Lett. 60 (1992) 255. [5] T.H. Tiefel, S. Jin, R.C. Sherwood, M.E. Davis, G.W. Kammlott, P.K. Gallagher, D.W. Johnson Jr., R.A. Fastnacht, W.W. Rhodes, Mater. Lett. 7 (1989) 363. [6] L. Ganapathi, A. Kumar, J. Narayan, J. Appl. Phys. 66 (1989) 5935. [7] Y. Matsumoto, J. Hombo, Y. Yamaguchi, M. Nishida, A. Chiba, Appl. Phys. Lett. 56 (1990) 1585. [8] O. Ishii, T. Konaka, M. Sato, Y. Koshimoto, Jpn. J. Appl. Phys. 29 (1990) L1075. [9] P.R. Apte, R. Pinto, A.G. Chourey, S.P. Pai, J. Appl. Phys. 75 (1994) 4258. [10] Y. Matsumoto, J. Hombo, T. Mitsunaga, Mater. Res. Bull. 24 (1989) 1469. [11] R. Pinto, P.R. Apte, S.P. Pai, D. Kumar, Physica, C 207 (1993) 13. [12] W.D. Kingery, H.K. Bowen, D.R. Uhlmann, Introduction to Ceramics, 2nd ed., Wiley, New York, 1976, p. 459. [13] M.A. Kaster, R.J. Birgeneau, C.Y. Chen, Y.M. Chiang, D.R. Gabbe, H.P. Jenssen, T. Junk, C.J. Peters, P.J. Picone, T. Thio, T.R. Thurston, H.L. Tuller, Phys. Rev. B 37 (1988) 111. [14] J. Tateno, N. Masaki, A. Iwase, Phys. Lett. A 138 (1989) 313. [15] P. Lunkenheimer, G. Knebel, A. Pimenov, G.A. Emel’chenko, A. Loidl, Z. Phys. B 99 (1996) 507. [16] H.S. Yang, P.C. Li, Y.S. Chai, M. Yu, Z.Q. Li, D.S. Yang, L. Zhang, Y.H. Wang, M.D. Li, L.Z. Cao, Y.Z. Long, Z.J. Chen, Acta Phys. Sin. 51 (2002) 679. [17] M. Hucker, V. Kataev, J. Pommer, J. Harrass, A. Hosni, C. Pflisch, R. Gross, B. Buchner, Phys. Rev. B 59 (1999) R725.