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Alpha irradiation of Bi-2212 superconductor
PHYSICA® ELSEVIER
Physica C 267 (1996) 303-307
Alpha irradiation of Bi-2212 superconductor S.K. Bandyopadhyay a, Pintu Sen a, p. Barat a, Udayan De a, K. Mandal b, S.K. Kar b, C.K. Majumdar b., a Variable Energy Cyclotron Centre, 1 / A F , Bidhan Nagar, Calcutta 700 064, India S.N. Bose National Centre for Basic Sciences, JD Block, Sector-Ill, Salt Lake, Calcutta 700 091, India
Received 3 October 1994; revised manuscript received 17 June 1996
Abstract
Single crystals of Bi2Sr2CaCu2Os+x(Bi-2212) with T~ of 80 K have been subjected to irradiation with 40 MeV a-particles from a Variable Energy Cyclotron at various doses up to 2 × 1015 alpha particles/cm 2. T~ decreases after irradiation. From the analysis of excess conductivity, it has been found that the interlayer coupling strength J decreases with the increase of irradiation dose. This decrease is due to a decrease in oxygen concentration. Keywords: Bi-2212 single crystal; a-irradiation; Oxygen "knockout; Interlayer coupling
1. I n t r o d u c t i o n High T~ copper oxide superconductors are more sensitive to radiation damage than the conventional low Tc ones. Some aspects of the mechanism of damage in the former [1-4] are also different from those in the latter. These differences originate from the structural arrangements and defects possible in high T~ superconductors. The compounds are based on layered structures: often a mismatch between bond lengths in various layers causes structural modulation. In particular, in Bi2Sr2CaCu2Os+ x (henceforth referred to as Bi-2212), the presence of small Bi 3+ ion causes tensile stress in the B i - O layer [5,6] and excess oxygen is intercalated in the B i - O layer causing an incommensurate modulation [7,8]. The accommodation of excess oxygen depends on annealing conditions. Samples quenched rapidly in air * Corresponding author. Fax: + 91 33 334 3477.
have very little of excess oxygen, while those cooled very slowly during annealing incorporate a lot of excess oxygen. This oxygen, like that in C u - O - C u chain in YBa2Cu3OT_x, is labile and is vulnerable to knock-out by a nuclear collision during ion bombardment. In alpha bombardment displacements occur for heavier ions also, and in quantitative explanation of the change in resistivity these must be considered. The change in Tc has, however, been correlated mostly with the change in oxygen content. We had earlier observed an increase in Tc of polycrystalline Bi-2212 due to irradiation by 20 MeV a-particles [9]. The initial Tc(R = 0) was 65 K; it increased by several degrees, but annealing the irradiated sample in oxygen reduced its Tc again towards the original value. We explained our observation as follows. The plot of critical temperature versus excess oxygen content is typically bell-shaped [10]. Since the original unirradiated sample had excess oxygen compared to samples with the highest Tc, oxygen knock-out
0921-4534/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved PH S0921-4534(96)00385- l
304
S.K. Bandyopadhyay et al./ Physica C 267 (1996) 303-307
caused an increase in Tc, and then annealing of the irradiated sample in oxygen caused its subsequent decrease. To confirm the above explanation, we wanted to examine the effect of a-irradiation on Bi-2212 samples with the highest Tc or on samples on the left hand side of the bell shaped curve. In this paper, we report the work of 40 MeV a-irradiation on single crystals of Bi-2212 with Tc(R = 0) of 80 K. We also include excess conductivity analysis for the single crystal before and after irradiation.
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2. Experimental details Polycrystalline samples of Bi-2212 were prepared by the usual solid state reaction [11] starting with the nitrates of the respective elements; the 2212 phase was confirmed by X-ray diffraction (XRD). Single crystals were prepared by the alkali halide flux method [12], starting with polycrystalline Bi-2212. Crystals obtained were of various sizes (2 mm x 2 mm to 8 mm X 4 ram, thickness 25-30 IX), and were free from needle growth. They were characterized by XRD in Philips PW1710 diffractometer. XRD of the crystals revealed all the characteristic 001 reflections. (Fig. l a). The microstructure was examined thoroughly at different positions of various crystals with Hitachi 52300 Scanning Electron Microscope (SEM) and showed dendritic growth free from needle-like structures usually attributed to CuO impurities [13]. Cationic compositions determined at various points with KEVEX instruments 3600-0388 Energy Dispersive X-Ray Analyzer (EDX) were fairly uniform. Critical temperatures Tc were found from resistivity measurement by the four probe method using Keithley 182 digital nanovoltmeter in a Leybold Refrigerator Cryostat Type 10-300. Tc(R = O) was 79 K. After annealing in oxygen at 400°C followed by slow cooling, Tc increased to 80 K. All our unirradiated samples were chosen to have Tc(R = 0) of 80 K, within our maximum possible error of 0.2 K. Irradiation was done with 40 MeV a-particles obtained from the Variable Energy Cyclotron in Calcutta. The range of a-particles in Bi-2212 is about 250 Ix. The single crystals were of lower thickness, 25 Ix to 30 Ix, so a-particles would pass through them. Details of the irradiation are given in
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's'~ ( t n D e g r e e s ) Fig. 1. X-ray diffraction patterns: (a) unirradiated single crystal; (b) irradiated single crystal (dose: 2 × 1015 e t / c m 2 ) .
our earlier work [13]. Single crystals were subjected to doses of 2 X 1014, and 2 X 1015 ot/cm 2. The irradiated samples were examined by XRD. Their T~ was measured by resistivity method.
3. Results and discussions XRD of the irradiated crystals (Fig. lb) showed a slight reduction of the c-parameter. S. Matsui et al. [14] have observed that the c-parameter for Bi-2212 films irradiated with 200 keV Ne-ions decreases up to a dose of 10 is ions/cm 2 and then increases. Ruault et al. [15] have observed a phase transition (orthorhombic to perovskite phase) in Bi2(Ca,Sr)2.6Cu20 . (Bi-2212 with Sr, Ca deficiency) films irradi-
305
S.K. Bandyopadhyay etal./Physica C 267 (1996) 303-307 5
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Fig. 2. Plot of resistivity of single crystals, irradiated and unirradiated.
The sample of Tc = 65 K had excess hole concentration as shown by the Hall coefficient [16] and it was on the right hand side of the bell shaped curve, i.e., in a region overdoped with oxygen. On the other hand, the present unirradiated single crystal for which Tc increased to 80 K after annealing in oxygen is on the left or oxygen deficient side of the curve. So the decrease in T~ by 40 Mev alpha irradiation is consistent with knock out of oxygen. We have also analyzed the excess conductivity [17] from the data on resistivity of the unirradiated crystal and the crystal irradiated at a dose of 2 × 1015 o t / c m 2 for estimating the interlayer coupling strength. Here the resistivity data is not complicated by granular effect as in polycrystalline samples [16]. From standard definition, excess conductivity is given as 80=
ated with 50 keV He ions and interpreted their observation in terms of a partial breakdown of the layered structure. In our sample, we do not get any indication of the development of another phase in XRD. In single crystals of 2 5 - 3 0 IX thickness, each 40 MeV a-particle deposits very little energy (4.5 keV/IX) so that the deposited energy does not cause any breakdown of structure, while a 50 keV or-particle deposits more energy (118 keV/i.L) in films causing a change in structure. Resistivities of the crystals were measured in the ab plane (Fig. 2). We note that Pab of the irradiated single crystal is higher than that of the unirradiated one and d p / d T of the irradiated crystal is also higher. Tc of the single crystal has decreased with irradiation by a-particles: Tc = 77 K for 2 x l0 n4 ot/cm 2 and Tc = 74 K for 2 x 1015 o t / c m 2. Resistivity increases with dose; the increase is due to radiation induced defects such as displacements in O ions and production of Bi, Sr, Ca and Cu vacancies and due also to decrease in carrier concentration. Monotonic increase in resistance with dose was also observed earlier in the u-irradiation of polycrystalline Bi-2212 with Tc = 65 K [9]. The increase in Tc for the sample with Tc = 65 K and the decrease in the present case of Bi-2212 single crystals of Tc = 80 K are consistent with the bell shaped curve of T~ versus excess oxygen or hole content.
0.m - 0.n ~- 1 / p m -- 1 / p n ,
where the subscripts m and n refer to the measured and normal values, respectively, of conductivity 0. and resistivity p. It is well known that the relationship between resistivity and temperature above 2Tc is linear. In the absence of any quantitative model for the determination of Pn for oxide superconductors, the normal resistivity Pn at low temperature is obtained by extrapolating the pn versus T data fitted at high temperature (200 K to 300 K) according to an expression p~(T) = a + bT. The parameters a and b were obtained by a least squares fit [17]. Aslamazov and Larkin (AL) first derived an expression [18] for the fluctuation induced excess conductivity 80--3
~:-~,
(1)
where A = e2/16 h d, A = e2/16 h ~ ( 0 ) ,
h = 1.0 for 2D system, A = 0.5 for 3D system.
Here d is the characteristic thickness for a 2D system and ~(0) is the coherence length at T-- 0 K. Also
Tmf is the mean field transition temperature. Lawrence and Doniach also derived an expression for fluctuation induced excess conductivity for layered superconductors [19,20], their analysis predict-
306
S.K. Bandyopadhyay et a l . / Physica C 267 (1996) 303-307 0.008 Irr 0.006
T
0.004 0.002 -Unlrradloted
0.000
~
70
75
80
85
90
95
100
T-
Fig. 3. Plot of (Btr)- l/x versus temperature T. The intersection of the linear fit with the x-axis gives the mean field transition
temperature T~me.
ing a transition from 2D to 3D behaviour. Within a certain range of temperature, both the expressions fit the experimental data. For simplicity the AL expression will be used here. The indirect Maki-Thompson contribution is also ignored, because of the large inelastic scattering rate and the small phase breaking time ( ~ 10-14 s). The value of T~mf is crucial for the proper analysis of excess conductivity data. It can be estimated by several methods [17]. We determine TcmY by carefully extrapolating the linear part of the (Bo') -1/~ versus T curve near Tc and in the 2D
region. The value of A used here are 1.15 for the unirradiated sample and 1.12 for the irradiated sample; these have been determined by the derivative technique originally proposed by Testardi et al. [21] and later used in [17]. The plot of (Btr) -1/~ versus T is shown in Fig. 3. The intersection of the linear fit with the x-axis gives Tmf = 81.8 K for the unirradiated and 74.5 K for the irradiated sample. In Fig. 4, we have plotted in Btr against In 8. We observe a distinct change in slope in both cases. For the unirradiated sample A changes from 1.15 (2D-like behaviour) to 0.55 (3D-like behaviour) at a crossover temperature TO= 84.3 K. For the irradiated sample, similar change is also observed A = 1.12 to A = 0.67 at a crossover temperature TO= 76.3 K. The interlayer coupling constant J is related to the crossover temperature TO by
4J= (To- Tcmf)/Tcmf
(2)
From this equation J comes out to be 7.8 × 10 -3 for the unirradiated crystal and 5.9 X 10 -3 for the irradiated crystal. The lower value of J in the case of
irradiated sample is a reflection of the lower hole content or lower carrier concentration.
4. Conclusion We have irradiated Bi-2212 single crystals of 0) 80 K and found a decrease in T~, which could be explained by knock out or displacement of oxygen by the a-particles. Analysis of excess conductivity of the single crystal, before and after irradiation, shows a decrease in interlayer coupling on irradiation, which can be attributed to the same cause.
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10
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8 . ~ 6. b
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4.
Acknowledgements 2.
0 -8
I
I
t
-6
-4
-2
0
h(~) Fig. 4. Plot of In Btr versus In e. The change of slope occurs at the crossover temperature TO.
The authors would like to thank the Department of Science and Technology, Government of India, for the financial support in the project of superconductivity (SBR No. 39), and the Alexander von Humboldt Foundation, Bonn, Germany, for the Leybold Cryogenerator 10-300.
S.K. Bandyopadhyay et a l . / Physica C 267 (1996) 303-307
References [1] A. Hofmann, H. Kronmuller, N. Moser, R. Reisser, P. Schule, H. Jager and F. Dworschak, in: Proc. Inter. Meeting on Advanced Materials (MRS) (Tokyo, 1988). [2] J. Geerk, G. Linker, O. Mejen, C. Politis, F. Ratzel, R. Smithley, B. Strehl and G.C. Xiong, Z. Phys. 13 67 (1987) 507. [3] H. Kupfer, 1. Apfelstedt, W. Sahaver, R. Fluckiger, R. Meier-Hirmor, H. Wuhl and H. Schevrer, Z. Phys. B 69 (1987) 167. [4] N. Moser, A. Hofmann, P. Schule, R. Henes and A.K. Kronmuller, Z. Phys. B 71 (1988) 37. [5] H. Zhang and H. Sato, Physica C 214 (1993) 265. [6] S.B. Samanta, P.K. Dutta, V.P.S. Awana, E. Gmelin and A.V. Narlikar, Physica C 178 (1991) 171. [7] J.M. Tarascon, W.R. McKinnon, Y. LePage, K. Remsehnig, R. Ramesh, R. Jones, G. Pleizier and G.W. Hull, Physica C 172 (1990) 13. [8] Y. LePage, W.R. Mckinnon, J.M. Tarascon and P. Barboux, Phys. Rev. B 40 (1989) 6810. [9] S.K. Bandyopadhyay, P. Barat, S.K. Kar, Udayan De, P. Mandal, B. Ghosh and C.K. Majumdar, Solid State Commun. 82 (1992) 397. [10] C. AIlgeier and J.S. Schilling, Physica C 168 (1990) 499.
307
[11] N. Knauf, J. Harnischmaker, R. Muller, R. Borowski, B. Roden and D. Wohlleben, Physica C 173 (1991) 414. [12] S.C. Gadkari, K.P. Muthe, K.D. Singh, S.C. Sabharwal and M.K. Gupta, J. Crystal Growth 102 (1990) 685. [13] S.K. Bandyopadhyay, P. Barat, Pintu Sen, Udayan De, A. De, P.K. Mukhopadhyay, S.K. Kar and C.K. Majumdar, Physica C 228 (1994) 109. [14] S. Matsui, H. Matsutera, T. Yoshitake and T. Satoh, Appl. Phys. Lett. 53 (1988) 2096. [15] M.O. Ruault and M. Gasgnier, Mater. Science Engineering B 5 (1989) 57. [16] P. Mandal, A. Poddar, B. Ghosh and P. Choudhury, Phys. Rev. B 43 (1991) 13102. [17] A. Poddar, P. Mandal and S. Das, J. Phys. Condens. Matter 7 (1995) 1351; P. Mandal, A. Poddar and S. Das, J. Phys. Condens. Matter 6 (1994) 5689. [18] L.G. Aslamazov and A.I. Larkin, Sov. Phys. - Sol. State 10 (1968) 875. [19] W.E Lawrence and S. Doniach, in: Proc. 12th Inter. Conf. on Low Temperature Physics (Kyoto, 1970), ed. E. Xanada (Keigaku, Tokyo, 1971) p. 361. [20] C.J. Lobb, Phys. Rev. B 36 (1987) 3930. [21] L.R. Testardi, W.A. Reed, P.G. Hohenberg, W.H. Hammerle and G.F. Breenert, Phys. Rev. 181 (1969) 800.
Physica C 267 (1996) 303-307
Alpha irradiation of Bi-2212 superconductor S.K. Bandyopadhyay a, Pintu Sen a, p. Barat a, Udayan De a, K. Mandal b, S.K. Kar b, C.K. Majumdar b., a Variable Energy Cyclotron Centre, 1 / A F , Bidhan Nagar, Calcutta 700 064, India S.N. Bose National Centre for Basic Sciences, JD Block, Sector-Ill, Salt Lake, Calcutta 700 091, India
Received 3 October 1994; revised manuscript received 17 June 1996
Abstract
Single crystals of Bi2Sr2CaCu2Os+x(Bi-2212) with T~ of 80 K have been subjected to irradiation with 40 MeV a-particles from a Variable Energy Cyclotron at various doses up to 2 × 1015 alpha particles/cm 2. T~ decreases after irradiation. From the analysis of excess conductivity, it has been found that the interlayer coupling strength J decreases with the increase of irradiation dose. This decrease is due to a decrease in oxygen concentration. Keywords: Bi-2212 single crystal; a-irradiation; Oxygen "knockout; Interlayer coupling
1. I n t r o d u c t i o n High T~ copper oxide superconductors are more sensitive to radiation damage than the conventional low Tc ones. Some aspects of the mechanism of damage in the former [1-4] are also different from those in the latter. These differences originate from the structural arrangements and defects possible in high T~ superconductors. The compounds are based on layered structures: often a mismatch between bond lengths in various layers causes structural modulation. In particular, in Bi2Sr2CaCu2Os+ x (henceforth referred to as Bi-2212), the presence of small Bi 3+ ion causes tensile stress in the B i - O layer [5,6] and excess oxygen is intercalated in the B i - O layer causing an incommensurate modulation [7,8]. The accommodation of excess oxygen depends on annealing conditions. Samples quenched rapidly in air * Corresponding author. Fax: + 91 33 334 3477.
have very little of excess oxygen, while those cooled very slowly during annealing incorporate a lot of excess oxygen. This oxygen, like that in C u - O - C u chain in YBa2Cu3OT_x, is labile and is vulnerable to knock-out by a nuclear collision during ion bombardment. In alpha bombardment displacements occur for heavier ions also, and in quantitative explanation of the change in resistivity these must be considered. The change in Tc has, however, been correlated mostly with the change in oxygen content. We had earlier observed an increase in Tc of polycrystalline Bi-2212 due to irradiation by 20 MeV a-particles [9]. The initial Tc(R = 0) was 65 K; it increased by several degrees, but annealing the irradiated sample in oxygen reduced its Tc again towards the original value. We explained our observation as follows. The plot of critical temperature versus excess oxygen content is typically bell-shaped [10]. Since the original unirradiated sample had excess oxygen compared to samples with the highest Tc, oxygen knock-out
0921-4534/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved PH S0921-4534(96)00385- l
304
S.K. Bandyopadhyay et al./ Physica C 267 (1996) 303-307
caused an increase in Tc, and then annealing of the irradiated sample in oxygen caused its subsequent decrease. To confirm the above explanation, we wanted to examine the effect of a-irradiation on Bi-2212 samples with the highest Tc or on samples on the left hand side of the bell shaped curve. In this paper, we report the work of 40 MeV a-irradiation on single crystals of Bi-2212 with Tc(R = 0) of 80 K. We also include excess conductivity analysis for the single crystal before and after irradiation.
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4000
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2000
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i
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2. Experimental details Polycrystalline samples of Bi-2212 were prepared by the usual solid state reaction [11] starting with the nitrates of the respective elements; the 2212 phase was confirmed by X-ray diffraction (XRD). Single crystals were prepared by the alkali halide flux method [12], starting with polycrystalline Bi-2212. Crystals obtained were of various sizes (2 mm x 2 mm to 8 mm X 4 ram, thickness 25-30 IX), and were free from needle growth. They were characterized by XRD in Philips PW1710 diffractometer. XRD of the crystals revealed all the characteristic 001 reflections. (Fig. l a). The microstructure was examined thoroughly at different positions of various crystals with Hitachi 52300 Scanning Electron Microscope (SEM) and showed dendritic growth free from needle-like structures usually attributed to CuO impurities [13]. Cationic compositions determined at various points with KEVEX instruments 3600-0388 Energy Dispersive X-Ray Analyzer (EDX) were fairly uniform. Critical temperatures Tc were found from resistivity measurement by the four probe method using Keithley 182 digital nanovoltmeter in a Leybold Refrigerator Cryostat Type 10-300. Tc(R = O) was 79 K. After annealing in oxygen at 400°C followed by slow cooling, Tc increased to 80 K. All our unirradiated samples were chosen to have Tc(R = 0) of 80 K, within our maximum possible error of 0.2 K. Irradiation was done with 40 MeV a-particles obtained from the Variable Energy Cyclotron in Calcutta. The range of a-particles in Bi-2212 is about 250 Ix. The single crystals were of lower thickness, 25 Ix to 30 Ix, so a-particles would pass through them. Details of the irradiation are given in
~ 12
20
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2500 , - -
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's'~ ( t n D e g r e e s ) Fig. 1. X-ray diffraction patterns: (a) unirradiated single crystal; (b) irradiated single crystal (dose: 2 × 1015 e t / c m 2 ) .
our earlier work [13]. Single crystals were subjected to doses of 2 X 1014, and 2 X 1015 ot/cm 2. The irradiated samples were examined by XRD. Their T~ was measured by resistivity method.
3. Results and discussions XRD of the irradiated crystals (Fig. lb) showed a slight reduction of the c-parameter. S. Matsui et al. [14] have observed that the c-parameter for Bi-2212 films irradiated with 200 keV Ne-ions decreases up to a dose of 10 is ions/cm 2 and then increases. Ruault et al. [15] have observed a phase transition (orthorhombic to perovskite phase) in Bi2(Ca,Sr)2.6Cu20 . (Bi-2212 with Sr, Ca deficiency) films irradi-
305
S.K. Bandyopadhyay etal./Physica C 267 (1996) 303-307 5
m
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~
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i
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105 140 175 Temperature (K)
210
Fig. 2. Plot of resistivity of single crystals, irradiated and unirradiated.
The sample of Tc = 65 K had excess hole concentration as shown by the Hall coefficient [16] and it was on the right hand side of the bell shaped curve, i.e., in a region overdoped with oxygen. On the other hand, the present unirradiated single crystal for which Tc increased to 80 K after annealing in oxygen is on the left or oxygen deficient side of the curve. So the decrease in T~ by 40 Mev alpha irradiation is consistent with knock out of oxygen. We have also analyzed the excess conductivity [17] from the data on resistivity of the unirradiated crystal and the crystal irradiated at a dose of 2 × 1015 o t / c m 2 for estimating the interlayer coupling strength. Here the resistivity data is not complicated by granular effect as in polycrystalline samples [16]. From standard definition, excess conductivity is given as 80=
ated with 50 keV He ions and interpreted their observation in terms of a partial breakdown of the layered structure. In our sample, we do not get any indication of the development of another phase in XRD. In single crystals of 2 5 - 3 0 IX thickness, each 40 MeV a-particle deposits very little energy (4.5 keV/IX) so that the deposited energy does not cause any breakdown of structure, while a 50 keV or-particle deposits more energy (118 keV/i.L) in films causing a change in structure. Resistivities of the crystals were measured in the ab plane (Fig. 2). We note that Pab of the irradiated single crystal is higher than that of the unirradiated one and d p / d T of the irradiated crystal is also higher. Tc of the single crystal has decreased with irradiation by a-particles: Tc = 77 K for 2 x l0 n4 ot/cm 2 and Tc = 74 K for 2 x 1015 o t / c m 2. Resistivity increases with dose; the increase is due to radiation induced defects such as displacements in O ions and production of Bi, Sr, Ca and Cu vacancies and due also to decrease in carrier concentration. Monotonic increase in resistance with dose was also observed earlier in the u-irradiation of polycrystalline Bi-2212 with Tc = 65 K [9]. The increase in Tc for the sample with Tc = 65 K and the decrease in the present case of Bi-2212 single crystals of Tc = 80 K are consistent with the bell shaped curve of T~ versus excess oxygen or hole content.
0.m - 0.n ~- 1 / p m -- 1 / p n ,
where the subscripts m and n refer to the measured and normal values, respectively, of conductivity 0. and resistivity p. It is well known that the relationship between resistivity and temperature above 2Tc is linear. In the absence of any quantitative model for the determination of Pn for oxide superconductors, the normal resistivity Pn at low temperature is obtained by extrapolating the pn versus T data fitted at high temperature (200 K to 300 K) according to an expression p~(T) = a + bT. The parameters a and b were obtained by a least squares fit [17]. Aslamazov and Larkin (AL) first derived an expression [18] for the fluctuation induced excess conductivity 80--3
~:-~,
(1)
where A = e2/16 h d, A = e2/16 h ~ ( 0 ) ,
h = 1.0 for 2D system, A = 0.5 for 3D system.
Here d is the characteristic thickness for a 2D system and ~(0) is the coherence length at T-- 0 K. Also
Tmf is the mean field transition temperature. Lawrence and Doniach also derived an expression for fluctuation induced excess conductivity for layered superconductors [19,20], their analysis predict-
306
S.K. Bandyopadhyay et a l . / Physica C 267 (1996) 303-307 0.008 Irr 0.006
T
0.004 0.002 -Unlrradloted
0.000
~
70
75
80
85
90
95
100
T-
Fig. 3. Plot of (Btr)- l/x versus temperature T. The intersection of the linear fit with the x-axis gives the mean field transition
temperature T~me.
ing a transition from 2D to 3D behaviour. Within a certain range of temperature, both the expressions fit the experimental data. For simplicity the AL expression will be used here. The indirect Maki-Thompson contribution is also ignored, because of the large inelastic scattering rate and the small phase breaking time ( ~ 10-14 s). The value of T~mf is crucial for the proper analysis of excess conductivity data. It can be estimated by several methods [17]. We determine TcmY by carefully extrapolating the linear part of the (Bo') -1/~ versus T curve near Tc and in the 2D
region. The value of A used here are 1.15 for the unirradiated sample and 1.12 for the irradiated sample; these have been determined by the derivative technique originally proposed by Testardi et al. [21] and later used in [17]. The plot of (Btr) -1/~ versus T is shown in Fig. 3. The intersection of the linear fit with the x-axis gives Tmf = 81.8 K for the unirradiated and 74.5 K for the irradiated sample. In Fig. 4, we have plotted in Btr against In 8. We observe a distinct change in slope in both cases. For the unirradiated sample A changes from 1.15 (2D-like behaviour) to 0.55 (3D-like behaviour) at a crossover temperature TO= 84.3 K. For the irradiated sample, similar change is also observed A = 1.12 to A = 0.67 at a crossover temperature TO= 76.3 K. The interlayer coupling constant J is related to the crossover temperature TO by
4J= (To- Tcmf)/Tcmf
(2)
From this equation J comes out to be 7.8 × 10 -3 for the unirradiated crystal and 5.9 X 10 -3 for the irradiated crystal. The lower value of J in the case of
irradiated sample is a reflection of the lower hole content or lower carrier concentration.
4. Conclusion We have irradiated Bi-2212 single crystals of 0) 80 K and found a decrease in T~, which could be explained by knock out or displacement of oxygen by the a-particles. Analysis of excess conductivity of the single crystal, before and after irradiation, shows a decrease in interlayer coupling on irradiation, which can be attributed to the same cause.
Tc(R =
10
o
/" Irradiated o unirradiated
8 . ~ 6. b
co v cD
4.
Acknowledgements 2.
0 -8
I
I
t
-6
-4
-2
0
h(~) Fig. 4. Plot of In Btr versus In e. The change of slope occurs at the crossover temperature TO.
The authors would like to thank the Department of Science and Technology, Government of India, for the financial support in the project of superconductivity (SBR No. 39), and the Alexander von Humboldt Foundation, Bonn, Germany, for the Leybold Cryogenerator 10-300.
S.K. Bandyopadhyay et a l . / Physica C 267 (1996) 303-307
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