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Excess electrical conductivity in Bi-Sr-Ca-Cu-O compounds
Physica B 165&166 (1990) 1371-1372 North-Holland
EXCESS ELECTRICAL CONDUCTIVITY IN Bi-Sr-Ca-Cu-O COMPOUNDS
J.J. WNUK, L.W.M. SCHREURS, P.J.T. EGGENKAMP, and P.J.E.M. van der LINDEN Research Institute for Materials, University of Nijmegen, Toernooiveld, NL-6525 ED Nijmegen, The Netherlands
We report on measurements of the resistivity of high quality (Bh-xPbxhSr2Ca2Cu301O+y ceramics and single crystals of the (Bil-xPbxhSr2CaCu20S+y phase. The resistivity is perfectly described by the theoretical expression for excess conductivity in the case of a two component order parameter fluctuating in two dimensions. The resistance data can be exactly fitted by one set of parameters starting from the critical temperature up to about 200 K.
1. INTRODUCTION The significant rounding of the resistance vs temperature, R(T), curve above the critical temperature, T c , in hightemperature superconductors, persistent even for the best samples, can be explained assuming thermodynamic fluctuations of the superconducting order parameter (1). As long as good quality samples of high T c materials were not accessible, this rounding could be explained by non-intrinsic effects like sample inhomogeneity or polycrystallinity. Having at our disposal high quality samples belonging to the 2212 and 2223 compounds of the Bi family, we tried to remove these ambiguities by fitting the theoretical formulae to the resistivity data of single crystal and sintered samples.
2. EXPERIMENTAL RESULTS AND ANALYSIS Sintered samples of the 2223 phase were obtained by the solid state reaction resulting in the composition (Bh-xPbxhSr1.92Ca2.Q7Cu2.S01O+y, with x=O.l (2). The lattice dimensions, a=b=0.542 nm, c=3.71 nm, were estimated from the powder X-ray diffraction patterns. The amount of secondary phases was lower than 5% in the best samples. Crystals of the composition (Bh-xPbx )2Srl.S3Cal.OSCu1.8S0s+y, x=0.15, and lattice dimensions a=0.538 nm, b=0.54 nm, c=3.08 nm, were grown by the self-flux method (3).
The temperature dependence of the resistance was measured by a standard dc four point method in an automated system. The temperature was measured with an accuracy better than 0.1 K. The samples were warmed up from liquid nitrogen to room temperature with a rate lower than 1 K/min. An example of the measured R(T) characteristics is shown in figure 1. The effects caused by the thermodynamic fluctuations of the order parameter are strongly enhanced in high-Tc superconductors due to a very small coherence volume (about 3 X 3 X 0.2nm 3 in Bi compounds connected with a hole density ofO.2/Cu per CU02 plane (4) leads to a smearing of the transition t:>.T ~ 30 - 40 K). The conductivity above T c in such case should follow a simple formula aCT) = aN(T)
+ t:>.a(T),
where the excess conductivity, t:>.a(T) = e(t _ 1)-(4-d)/2, t = T /Tc , depends on the dimensionality of the fluctuations, d=I,2,3 (1). aN is the 'normal' conductivity, which can be approximated by aN = (AT + B)-I. Attempts to check the applicability of the above formula to the conductivity of high-Tc superconductors have already been made (see 5,6 and references therein), indicating a difference in dimensionality of the fluctuations observed in BiSrCaCuO compounds compared to those of LaBaCuO, LaSrCuO or RBaCuO (R - Y 0.07 ._..0.06
S
C
0.10
.......0.05 Q)
gO.04
1l 0.03 aj
Q)
()
Q
1l 0.05
III
aj
&j 0.02
en
om
Q)
~
Sample Lib
(Pb.Bi,-.)eSreCa,CileO.+6 Sample LIb
0.007l::-5.......'""!6'"0-~6l:5L...L.L...L.90u...L...L. .....9.L5.................. 10.L0................I.L05................Jll0
Ter.nperature T (K)
0.0060
60 100 120 140 160 160 200 220 240 260 260 300
Ter.nperature T (K)
Figure 1: The temperature dependence of the resistance of a single crystal sample LIb measured in the a - b plane.
0921-4526/90/$03.50
© 1990 -
Figure 2: The temperature dependence of the resistivity of the single crystal sample LIb in the a - b plane. Solid line represents the fit of the theoretical expression to the experimental data.
Elsevier Science Publishers B.V. (North-Holland)
J.J. Wnuk, L. W.M. Schreurs, P.J. T. Eggenkamp, P.J.E.M. van der Linden
1372
or rare earth) materials. However, the samples investigated were showing some peculiarities in the resistivity around the critical temperature leading to an ambiguity of the determination of Tc and the critical exponent in the formula for the excess conductivity. Below, we describe shortly results obtained from fitting the R(T) data of samples where these uncertainties were absent. The large anisotropy of the Bi-based compounds (our conservative estimates lead to a resistivity anisotropy ratio of 4 X 10 3 and values as high as 10 5 were reported (7» causes that the resistivity of the sintered samples is dominated by the a - b plane resistivity. Figures 2 and 3 show the fits of the theoretical formula to the resistance data of single crystal 2212 and sintered 2223 phases, respectively. The critical exponent in both cases is close to -1 fndicating two dimensional fluctuations of the order parameter. The fit is very good up to about 190 K and both the zero resistance criterion and the fit give practically the same value of the critical temperature. To check how other effects, smearing the transition temperature, disturb the fitting procedure, we have performed similar calculations for samples containing an appreciable amount of secondary phase (an example is shown in figure 4) and with grains connected by a normal material (2) (figure 5). The critical temperature coming from 0.08 , - - - - - , - - - . - - - . - - - - . , . - - - , . - - - - - ,
3°.06 Q)
o
...,~ 0.04
.!!l Ul
(Pb.Bi l _.).Sr.Ca.C U30 10+4 Sample 26WX
~0.02 0.00 100
105
110
115
120
Temperature T (K)
125
130
Figure 3: The temperature dependence of the resistance of ceramic sample 26WX with the theoretical fit of the excess conductivity (solid line).
---
0.06 30.05 Q)
(PbxBil_.).Sr.Ca.CU3010+4
~
Sample 18WX
00.04
20.03
.!!l
~ 0.02 0:: 0.01 0.00 75
80
85
90
95 100 105 110 115 120 125 130
Temperature T (K)
Figure 4: The temperature dependence of the resistance of ceramic sample 18WX with the theoretical fit of the excess conductivity (solid line).
the fit differs now from T(R = 0), but stays close to the one characterising the samples which did not undergo any additional treatment. Also the critical exponent is approximately the same. The last check has been done for a thin (100 nm) film of YBa2CU307_y leading to the critical exponent close to -1/2 (but only close to Tc ) and thus confirming the results of others (5). Concluding, the resistivity of the Bi-based compounds, both single crystals and ceramics, follows the theoretical model for the excess conductivity caused by two dimensional fluctuations of the superconducting order parameter.
Sample 977d 0.00 80
85
90
95
100 105
110
115 120 125 130
Temperature T (K)
Figure 5: The temperature dependence of the resistance of ceramic sample 977d containing an appreciable amount of Ag and the theoretical fit of the excess conductivity (solid line ). ACKNOWLEDGEMENTS The authors are greatly indebted to Dr. B. Dam from Philips Research Laboratories in Eindhoven for supplying them with thin films of YBCO compound. This work is part of the research programme of the Stichting voor Fundamenteel Onderzoek der Materie (F01v!) and was made possible by financial support from the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO). REFERENCES
(1) For a review see M. Tinkham in Introduction to Superconductivity, (McGraw-Hill, New York, 1975) ch. 7, pp. 251-256. ~) J.J. Wnuk, L.W.M. Schreurs, P.J.T Eggenkarnp, and P.J.E.M. van der Linden, to be published. (3) J.J. Wnuk, L.W.M. Schreurs, P.J.E.lvL van der Linden, and P.J.T. Eggenkamp, submitted to J. Crystal Growth. (4) W.A. Groen, D.M. de Leeuw, and L.F. Feiner, Physica C 165 (1990) 55. (5) F. Vidal, J.A. Veira, J. Maza, J ..J." Ponte, J. Amador, C. Cascales, M.T. Casais, and 1. Rasines, Physica C 156 (1988) 165. (6) W. Schnelle, E. Braun, H. Broicher, H. Weiss, H. Geus, S. Ruppel, M. Galffy, W. Braunisch, A. Waldorf, F. Seidler, and D. Wohlleben, Physica C 161 (1989) 123. (7) S. Martin, A.T. Fiory, R.M. Fleming, L.F. Schneemeyer, and J.V. Waszczak, Phys. Rev. Lett. GO (1988) 2194.
EXCESS ELECTRICAL CONDUCTIVITY IN Bi-Sr-Ca-Cu-O COMPOUNDS
J.J. WNUK, L.W.M. SCHREURS, P.J.T. EGGENKAMP, and P.J.E.M. van der LINDEN Research Institute for Materials, University of Nijmegen, Toernooiveld, NL-6525 ED Nijmegen, The Netherlands
We report on measurements of the resistivity of high quality (Bh-xPbxhSr2Ca2Cu301O+y ceramics and single crystals of the (Bil-xPbxhSr2CaCu20S+y phase. The resistivity is perfectly described by the theoretical expression for excess conductivity in the case of a two component order parameter fluctuating in two dimensions. The resistance data can be exactly fitted by one set of parameters starting from the critical temperature up to about 200 K.
1. INTRODUCTION The significant rounding of the resistance vs temperature, R(T), curve above the critical temperature, T c , in hightemperature superconductors, persistent even for the best samples, can be explained assuming thermodynamic fluctuations of the superconducting order parameter (1). As long as good quality samples of high T c materials were not accessible, this rounding could be explained by non-intrinsic effects like sample inhomogeneity or polycrystallinity. Having at our disposal high quality samples belonging to the 2212 and 2223 compounds of the Bi family, we tried to remove these ambiguities by fitting the theoretical formulae to the resistivity data of single crystal and sintered samples.
2. EXPERIMENTAL RESULTS AND ANALYSIS Sintered samples of the 2223 phase were obtained by the solid state reaction resulting in the composition (Bh-xPbxhSr1.92Ca2.Q7Cu2.S01O+y, with x=O.l (2). The lattice dimensions, a=b=0.542 nm, c=3.71 nm, were estimated from the powder X-ray diffraction patterns. The amount of secondary phases was lower than 5% in the best samples. Crystals of the composition (Bh-xPbx )2Srl.S3Cal.OSCu1.8S0s+y, x=0.15, and lattice dimensions a=0.538 nm, b=0.54 nm, c=3.08 nm, were grown by the self-flux method (3).
The temperature dependence of the resistance was measured by a standard dc four point method in an automated system. The temperature was measured with an accuracy better than 0.1 K. The samples were warmed up from liquid nitrogen to room temperature with a rate lower than 1 K/min. An example of the measured R(T) characteristics is shown in figure 1. The effects caused by the thermodynamic fluctuations of the order parameter are strongly enhanced in high-Tc superconductors due to a very small coherence volume (about 3 X 3 X 0.2nm 3 in Bi compounds connected with a hole density ofO.2/Cu per CU02 plane (4) leads to a smearing of the transition t:>.T ~ 30 - 40 K). The conductivity above T c in such case should follow a simple formula aCT) = aN(T)
+ t:>.a(T),
where the excess conductivity, t:>.a(T) = e(t _ 1)-(4-d)/2, t = T /Tc , depends on the dimensionality of the fluctuations, d=I,2,3 (1). aN is the 'normal' conductivity, which can be approximated by aN = (AT + B)-I. Attempts to check the applicability of the above formula to the conductivity of high-Tc superconductors have already been made (see 5,6 and references therein), indicating a difference in dimensionality of the fluctuations observed in BiSrCaCuO compounds compared to those of LaBaCuO, LaSrCuO or RBaCuO (R - Y 0.07 ._..0.06
S
C
0.10
.......0.05 Q)
gO.04
1l 0.03 aj
Q)
()
Q
1l 0.05
III
aj
&j 0.02
en
om
Q)
~
Sample Lib
(Pb.Bi,-.)eSreCa,CileO.+6 Sample LIb
0.007l::-5.......'""!6'"0-~6l:5L...L.L...L.90u...L...L. .....9.L5.................. 10.L0................I.L05................Jll0
Ter.nperature T (K)
0.0060
60 100 120 140 160 160 200 220 240 260 260 300
Ter.nperature T (K)
Figure 1: The temperature dependence of the resistance of a single crystal sample LIb measured in the a - b plane.
0921-4526/90/$03.50
© 1990 -
Figure 2: The temperature dependence of the resistivity of the single crystal sample LIb in the a - b plane. Solid line represents the fit of the theoretical expression to the experimental data.
Elsevier Science Publishers B.V. (North-Holland)
J.J. Wnuk, L. W.M. Schreurs, P.J. T. Eggenkamp, P.J.E.M. van der Linden
1372
or rare earth) materials. However, the samples investigated were showing some peculiarities in the resistivity around the critical temperature leading to an ambiguity of the determination of Tc and the critical exponent in the formula for the excess conductivity. Below, we describe shortly results obtained from fitting the R(T) data of samples where these uncertainties were absent. The large anisotropy of the Bi-based compounds (our conservative estimates lead to a resistivity anisotropy ratio of 4 X 10 3 and values as high as 10 5 were reported (7» causes that the resistivity of the sintered samples is dominated by the a - b plane resistivity. Figures 2 and 3 show the fits of the theoretical formula to the resistance data of single crystal 2212 and sintered 2223 phases, respectively. The critical exponent in both cases is close to -1 fndicating two dimensional fluctuations of the order parameter. The fit is very good up to about 190 K and both the zero resistance criterion and the fit give practically the same value of the critical temperature. To check how other effects, smearing the transition temperature, disturb the fitting procedure, we have performed similar calculations for samples containing an appreciable amount of secondary phase (an example is shown in figure 4) and with grains connected by a normal material (2) (figure 5). The critical temperature coming from 0.08 , - - - - - , - - - . - - - . - - - - . , . - - - , . - - - - - ,
3°.06 Q)
o
...,~ 0.04
.!!l Ul
(Pb.Bi l _.).Sr.Ca.C U30 10+4 Sample 26WX
~0.02 0.00 100
105
110
115
120
Temperature T (K)
125
130
Figure 3: The temperature dependence of the resistance of ceramic sample 26WX with the theoretical fit of the excess conductivity (solid line).
---
0.06 30.05 Q)
(PbxBil_.).Sr.Ca.CU3010+4
~
Sample 18WX
00.04
20.03
.!!l
~ 0.02 0:: 0.01 0.00 75
80
85
90
95 100 105 110 115 120 125 130
Temperature T (K)
Figure 4: The temperature dependence of the resistance of ceramic sample 18WX with the theoretical fit of the excess conductivity (solid line).
the fit differs now from T(R = 0), but stays close to the one characterising the samples which did not undergo any additional treatment. Also the critical exponent is approximately the same. The last check has been done for a thin (100 nm) film of YBa2CU307_y leading to the critical exponent close to -1/2 (but only close to Tc ) and thus confirming the results of others (5). Concluding, the resistivity of the Bi-based compounds, both single crystals and ceramics, follows the theoretical model for the excess conductivity caused by two dimensional fluctuations of the superconducting order parameter.
Sample 977d 0.00 80
85
90
95
100 105
110
115 120 125 130
Temperature T (K)
Figure 5: The temperature dependence of the resistance of ceramic sample 977d containing an appreciable amount of Ag and the theoretical fit of the excess conductivity (solid line ). ACKNOWLEDGEMENTS The authors are greatly indebted to Dr. B. Dam from Philips Research Laboratories in Eindhoven for supplying them with thin films of YBCO compound. This work is part of the research programme of the Stichting voor Fundamenteel Onderzoek der Materie (F01v!) and was made possible by financial support from the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO). REFERENCES
(1) For a review see M. Tinkham in Introduction to Superconductivity, (McGraw-Hill, New York, 1975) ch. 7, pp. 251-256. ~) J.J. Wnuk, L.W.M. Schreurs, P.J.T Eggenkarnp, and P.J.E.M. van der Linden, to be published. (3) J.J. Wnuk, L.W.M. Schreurs, P.J.E.lvL van der Linden, and P.J.T. Eggenkamp, submitted to J. Crystal Growth. (4) W.A. Groen, D.M. de Leeuw, and L.F. Feiner, Physica C 165 (1990) 55. (5) F. Vidal, J.A. Veira, J. Maza, J ..J." Ponte, J. Amador, C. Cascales, M.T. Casais, and 1. Rasines, Physica C 156 (1988) 165. (6) W. Schnelle, E. Braun, H. Broicher, H. Weiss, H. Geus, S. Ruppel, M. Galffy, W. Braunisch, A. Waldorf, F. Seidler, and D. Wohlleben, Physica C 161 (1989) 123. (7) S. Martin, A.T. Fiory, R.M. Fleming, L.F. Schneemeyer, and J.V. Waszczak, Phys. Rev. Lett. GO (1988) 2194.