- Email: [email protected]
Estimation of magnetic relaxation property for CVD processed YBCO-coated conductors
Physica C 470 (2010) 1284–1287
Contents lists available at ScienceDirect
Physica C journal homepage: www.elsevier.com/locate/physc
Estimation of magnetic relaxation property for CVD processed YBCO-coated conductors Y. Takahashi a, M. Kiuchi a, E.S. Otabe a, T. Matsushita a,*, K. Shikimachi b, T. Watanabe b, N. Kashima b, S. Nagaya b a b
Faculty of Computer Science and Systems Engineering, Kyushu Institute of Technology, 680-4 Kawazu, Iizuka, Fukuoka 820-8502, Japan Chubu Electric Power Co., Inc., 20–1, Kitasekiyama, Ohdaka-cho, Midori-ku, Nagoya 459-8522, Japan
a r t i c l e
i n f o
Article history: Available online 16 May 2010 Keywords: YBCO tape IBAD/CVD Thickness dependence Flux creep-flow model Apparent pinning potential
a b s t r a c t Ion Beam Assist Deposition/Chemical Vapor Deposition(IBAD/CVD)-processed YBCO-coated conductors with high critical current density Jc at high magnetic fields are expected to be applied to superconducting equipments such as superconducting magnetic energy storage (SMES). For application to superconducting magnet in SMES one of the most important properties for superconductors is the relaxation property of superconducting current. In this paper, the relaxation property is investigated for IBAD/CVD-processed YBCO-coated conductors of the superconducting layer in the range of 0.18–0.90 lm. This property can be quantitatively characterized by the apparent pinning potential, U 0 . It is found that U 0 takes a smaller value due to the two-dimensional pinning mechanism at high magnetic fields for conductor with thinner superconducting layer. Although U 0 decreases with increasing thickness at low magnetic fields at 20 K, it increases at high magnetic fields. The results are theoretically explained by the model of the flux creep and flow based on the dimensionality of flux pinning. Scaling analysis is examined for the dependence of U 0 on the magnetic field, temperature and the layer thickness. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction Application of YBa2Cu3O7d (YBCO)-coated conductor is expected for various electric power devices because its critical current characteristics are much superior to those of Bi-2223 tapes at high temperatures and/or at high magnetic fields. Recently, attention is paid to Multiple-Stage Chemical Vapor Deposition (MS-CVD) method for fabrication process of coated conductors because of shorter fabrication time and lower cost than the Pulsed Laser Deposition (PLD) method [1]. It is expected that YBCO-coated conductors fabricated by this method are commonly used in the future. Superconducting magnetic energy storage (SMES) is one of electric power devices which may be used in power grid systems in the future. Since this device will be commonly used in the condition of stored energy, a decay of superconducting current is required to be suppressed severely. Hence, the apparent pinning potential, U 0 , a parameter associated with the decay of superconducting current is necessary to be investigated in detail. Since the flux creep phenomenon which determines U 0 depends appreciably on the thickness of superconducting layer, the thickness dependence of U 0 is investigated.
* Corresponding author. Tel.: +81 948 29 7663; fax: +81 948 29 7661. E-mail address: [email protected] (T. Matsushita). 0921-4534/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2010.05.094
Sometimes SMES is planned to be used at very high magnetic fields at low temperatures. However, the measurement of relaxation of current is not easy at high magnetic fields. If the dependence of U 0 on magnetic field and temperature is described in a form of scaling law, it may be useful for such cases of difficult measurement. In this paper, the thickness dependence of relaxation properties in CVD-processed YBCO-coated conductors is investigated, and analyzed using the flux creep-flow model [2]. In addition, scaling of U 0 for the dependence on magnetic field and temperature is examined.
2. Experiments The specimens were YBCO-coated tapes prepared by MultipleStage CVD (MS-CVD) process. The superconducting layer was deposited on Ion Beam Assist Deposition (IBAD)-processed substrate with Gd2Zr2O7 (GZO) inner layer and CeO2 cap layer [1]. The thickness of YBCO layer was varied in the range of 0.18– 0.90 lm. The specifications of these specimens are listed in Table 1. The DC magnetization and its relaxation were measured by using a SQUID magnetometer in a magnetic field up to 7 T parallel to the c-axis of the specimen over the temperature range of 20– 60 K. The critical current density was estimated from the DC magnetization using the Bean model:
1285
Y. Takahashi et al. / Physica C 470 (2010) 1284–1287
0.08
Table 1 Specifications of specimens. Specimen
Thickness d (lm)
Tc (K)
#1 #2 #3
0.18 0.45 0.90
87.9 89.5 88.5
6 Dm 2
dw ð3l wÞ
U0* [eV]
Jc ¼
0.07
ð1Þ
;
where Dm is the hysteresis of magnetic moment, d the thickness of the superconducting layer, and w and l are the width and the length of specimens (w < l), respectively. E–J characteristics were estimated from the relaxation measurement [3]. The magnetization M is magnetic moment per unit volume : Dm/wld. From the logarithmic relaxation rate of the magnetization, the apparent pinning potential U 0 was estimated:
d M U ¼ 0 : dlogt M 0 kB T
20 K exp.
0.06
#1 #2 #3 0.05
2
ð2Þ
The initial magnetization M0 was determined by extrapolating the relaxation curve from the time range of 102 103 s to t = 1 s. Fig. 1 shows the Jc–B characteristics of the three specimens at 20 and 60 K in the magnetic field regions of 0–6.5 T. The Jc decreases with increasing thickness in the entire region of magnetic field at 20 K and at low magnetic fields at 60 K. The decrease in the critical current density seems to be caused by the structural deterioration of superconducting layer in the specimens with increasing thickness [4]. On the other hand, Jc of the thinnest specimen rapidly decreased with increasing magnetic field at 60 K due to the strong influence of the flux creep. The magnetic field dependence of U 0 at 20 K obtained from the relaxation rate of the magnetization is shown in Fig. 2. It is found that U 0 decreases with increasing thickness at low magnetic field at 20 K. On the other hand, U 0 of the thinnest specimen rapidly decreases with increasing magnetic field. Such behavior of U 0 cannot be foreseen only from the Jc characteristics shown in Fig. 1.
4
6
B [T] Fig. 2. Magnetic field dependence of observed U 0 at 20 K. The lines are guide for eye.
current density takes a value determined only by the flux pinning and its temperature and magnetic field dependence is assumed as
m 2 T B J c0 ¼ A 1 Bc1 1 ; Tc Bc2
ð3Þ
where A, m, c are pinning parameters. The pinning potential U0 which determines the flux creep property is described in terms of Jc0 as: 1=2
U0 ¼ ¼
0:835g 2 kB J c0 3=2 1=4
ð2pÞ B 4:23g 2 kB J c0 d 2pB1=2
;
;
d > L;
d < L:
ð4Þ ð5Þ
3. Theory
In the above d is the thickness of the superconducting layer and L is the pinning correlation length given by
The critical current properties were analyzed using the flux creep-flow model [2]. In the virtual flux-creep free case, the critical
L¼
Jc [A/m2]
1010
60 K
2pl0 J c0
ð6Þ
"
# ðlog A log Am Þ2 f ðAÞ ¼ K exp ; 2r2
109
#1 #2 #3 10
1=2
Baf
with af denoting the flux line spacing. It should be noted that even if the pinning is in the three-dimensional case (d > L) at low magnetic fields for fairly thick superconductor, the pinning may change to the two-dimensional one at high magnetic fields due to the increase in L with decreasing Jc0. More detailed discussion of this mechanism is given in [5]. The parameter g2 is the number of flux lines in a flux bundle. In practical superconductors the flux pinning strength is statistically distributed widely [6]. Here it is simply assumed that only the parameter A which represents the pinning strength is distributed as
20 K
1011
8
0
2
4
6
B [T] Fig. 1. Magnetic field dependence of critical current density at 20 and 60 K in the magnetic field range of 0–6.5 T. The lines are guide for eye.
ð7Þ
where Am is the most probable value of A and r 2 is a parameter representing a distribution width and K is a normalization constant. The electric field E caused by the mechanism of flux creep and flow is calculated as a function of the current density J and averaged statistically with respect to the distributed A. The details of the theoretical calculation are described elsewhere [2]. The theoretical critical current density is determined from the obtained E–J curve
1286
Y. Takahashi et al. / Physica C 470 (2010) 1284–1287
0.08
4. Results and discussion
0.07
U0* [eV]
with the same electric field criterion of Ec = 109 V/m as done in experiments. The pinning parameters Am, r, m and c are determined so that the calculated E–J curves agree with the experiments. The obtained parameters are listed in Table 2.
The E–J curves of specimen #3 obtained from the relaxation of magnetization are shown in Fig. 3. The lines are the theoretical results of flux creep-flow model. The experimental results are explained well by the theory. Fig. 4 shows the theoretical results of U 0 at 20 K. Good agreement with experiments shown in Fig. 2 is obtained. Thus, the relaxation property is describable by the mechanism of flux creep and flow. Now the possibility of description of U 0 ðB; TÞ in the form of scaling law is examined. It is assumed for simplicity that the magnetic field dependence of U 0 can be approximated by quadratic function:
¼
U 0 peak ðTÞ
2
aðTÞ½B Bpeak ðTÞ ;
#1 #2 #3 0.05
11
0.15
#1 : function’s peak 0.1
#1 #2 #3
4.30 10 2.93 1011 1.79 1011
exp.
0.05 r2
c
m
5.70 103 5.90 103 6.20 103
0.57 0.59 0.60
1.9 1.9 1.9
6
Fig. 4. Magnetic field dependence of U 0 calculated by theoretical relaxation rate at 20 K. The lines are guide for eye.
Table 2 Pinning parameters of specimens at 20 K. Am
4
B [T]
ð8Þ
where a is unique parameter for each specimen. Fig. 5 shows the magnetic field dependence of U 0 for specimen #1 in the temperature range of 20–40 K. The lines are curves of the approximated quadratic function. The arrow shows the position of the peak. It is found that the peak moves to low magnetic field with increasing temperature. The peak field (Bpeak) and the peak value of U 0 ðU 0 peak ) are important parameters for description of U 0 ðB; TÞ. The obtained parameters are listed in Tables 3 and 4. The temperature dependences of U 0 peak and Bpeak are shown in Fig. 6a and b. The condition of pinning in specimen #1 is two-dimensional and that of specimen #3 is three-dimensional over the entire temperature region of 20–40 K. On the other hand, that of specimen #2 changes from three-dimensional to two-dimensional between 25 K and
Specimen
2
U0* [eV]
U 0 ðB; TÞ
20 K theo.
0.06
0
Eq.(8)
0
20 K 25 K 30 K 35 K 40 K
2
4
6
B [T] Fig. 5. Magnetic field dependence of U 0 in specimen #1 in the temperature region 20–40 K. The lines are approximated quadratic function of Eq. (8).
10−9
E [V/m]
Table 3 Scaling parameter (Bpeak) of specimens.
#3 20 K 1T 2T 3T 4T 5T 6T
10−10
Specimen
Bpeak(T) 20 K
25 K
30 K
35 K
40 K
#1 #2 #3
1.54 3.06 4.51
0.61 2.39 3.55
1.50 0.04 2.32
4.13 5.07 0.28
8.34 13.50 1.10
Table 4 Scaling parameter (U 0 Specimen
10
10
2
J [A/m ]
10
11
Fig. 3. E–J curves of specimen #3 obtained from the relaxation of magnetization. The lines are theoretical results of flux creep-flow model.
#1 #2 #3
U 0 peak
peak )
of specimens.
(eV)
20 K
25 K
30 K
35 K
40 K
7.79 102 7.70 102 7.62 102
9.63 102 9.45 102 9.71 102
1.12 101 1.13 101 1.14 101
1.40 101 1.43 101 1.32 101
1.82 101 2.05 101 1.53 101
1287
Y. Takahashi et al. / Physica C 470 (2010) 1284–1287 Table 5 Scaling parameter a of specimens.
(a) 0.2
d>L
d
Specimen
#1
2
a(eVT )
U0 peak*[eV]
#1 #2 #3
#2 3
0.6 10
0.5 10
#3 3
0.8 103
0.08
0.06
20
30
40
T [K]
−10
20 K exp. Eq.(8)
d
0
#1 #2 #3
Bpeak [T]
0.04
#1 #2 #3
0.02
(b) d>L
U0* [eV]
0.1
0
10
B [T] U 0
Fig. 7. Magnetic field dependence of at 20 K. Symbols and lines represent the experimental result and approximation of Eq. (8), respectively.
5. Summary
0
20
30
40
T [K] U 0 peak
Fig. 6. Temperature dependence of (a) and (b) Bpeak in the temperature region 20–40 K. The open and solid symbols show that the pinning is threedimensional and two-dimensional, respectively.
30 K. It is found that while U 0 peak increases linearly with increasing temperature in the three-dimensional pinning regime, its increase rises nonlinearly in the two-dimensional pinning regime. The value of U 0 peak does not depend on the layer thickness at low temperatures. The temperature dependence of Bpeak is similar to that of U 0 peak , while the value of Bpeak increases with increasing thickness at low temperatures. On the other hand, the parameter a listed in Table 5 does not precisely depend on the thickness. The experimental results of the apparent pinning potential are compared with the scaling formula of Eq. (8) at 20 K for three specimens in Fig. 7. This indicates that superconducting tape with thicker superconducting layer is better for high field performance. Thus, it is shown that the dependence of U 0 on magnetic field and temperature is generally expressed as in Eq. (8). It is found that the parameters U 0 peak and Bpeak change with the thickness of superconducting layer through the dimensionality of flux pinning. However, the phenomenon is complicated and more detailed analysis is necessary for exact understanding of the phenomenon. It is necessary to examine the relaxation property for other specimens, such as a series of coated conductors with less structural degradation.
The thickness dependence of the critical current and relaxation characteristics were investigated for IBAD/CVD YBCO-coated conductors. It is found that Jc decreases with increasing thickness in the magnetic field region 0–6.5 T at 20 K. In the same temperature, although U 0 decreases with increasing thickness at low magnetic fields. U 0 increases at high magnetic fields, the results were theoretically explained by the model of the flux creep and flow based on the dimensionality of flux pinning. Application of scaling law is examined for the dependence of U 0 on magnetic field and temperature. It was found that the scaling parameters behave in different manner depending on the dimensionality of flux pinning. For more precise understanding, the relaxation property additional experiments are necessary for different series of samples. Acknowledgements This work was supported by the New Energy and Industrial Technology Development Organization (NEDO) as the Technological Development of Yttrium-based Superconducting Power Equipment. References [1] M. Mori, T. Watanabe, N. Kashima, T. Muroga, S. Miyata, Y. Yamada, T. Izumi, Y. Shiohara, Physica C 445–448 (2006) 515. [2] M. Kiuchi, K. Noguchi, T. Matsushita, T. Hikata, K. Sato, Physica C 278 (1997) 62. [3] K. Himeki, M. Kiuchi, E.S. Otabe, T. Matsushita, S. Miyata, A. Ibi, Y. Yamada, Y. Shiohara, Physica C 468 (2007) 1674. [4] K. Himeki, M. Kiuchi, E.S. Otabe, T. Matsushita, K. Shikimachi, T. Watanabe, N. Kashima, S. Nagaya, Y. Yamada, Y. Shiohara, Physica C 469 (2009) 1457. [5] T. Matsushita, Flux Pinning in Superconductors, Springer, Berlin, 2006. p. 333. [6] T. Matsushita, T. Tohdoh, N. Ihara, Physica C 259 (1996) 321.
Contents lists available at ScienceDirect
Physica C journal homepage: www.elsevier.com/locate/physc
Estimation of magnetic relaxation property for CVD processed YBCO-coated conductors Y. Takahashi a, M. Kiuchi a, E.S. Otabe a, T. Matsushita a,*, K. Shikimachi b, T. Watanabe b, N. Kashima b, S. Nagaya b a b
Faculty of Computer Science and Systems Engineering, Kyushu Institute of Technology, 680-4 Kawazu, Iizuka, Fukuoka 820-8502, Japan Chubu Electric Power Co., Inc., 20–1, Kitasekiyama, Ohdaka-cho, Midori-ku, Nagoya 459-8522, Japan
a r t i c l e
i n f o
Article history: Available online 16 May 2010 Keywords: YBCO tape IBAD/CVD Thickness dependence Flux creep-flow model Apparent pinning potential
a b s t r a c t Ion Beam Assist Deposition/Chemical Vapor Deposition(IBAD/CVD)-processed YBCO-coated conductors with high critical current density Jc at high magnetic fields are expected to be applied to superconducting equipments such as superconducting magnetic energy storage (SMES). For application to superconducting magnet in SMES one of the most important properties for superconductors is the relaxation property of superconducting current. In this paper, the relaxation property is investigated for IBAD/CVD-processed YBCO-coated conductors of the superconducting layer in the range of 0.18–0.90 lm. This property can be quantitatively characterized by the apparent pinning potential, U 0 . It is found that U 0 takes a smaller value due to the two-dimensional pinning mechanism at high magnetic fields for conductor with thinner superconducting layer. Although U 0 decreases with increasing thickness at low magnetic fields at 20 K, it increases at high magnetic fields. The results are theoretically explained by the model of the flux creep and flow based on the dimensionality of flux pinning. Scaling analysis is examined for the dependence of U 0 on the magnetic field, temperature and the layer thickness. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction Application of YBa2Cu3O7d (YBCO)-coated conductor is expected for various electric power devices because its critical current characteristics are much superior to those of Bi-2223 tapes at high temperatures and/or at high magnetic fields. Recently, attention is paid to Multiple-Stage Chemical Vapor Deposition (MS-CVD) method for fabrication process of coated conductors because of shorter fabrication time and lower cost than the Pulsed Laser Deposition (PLD) method [1]. It is expected that YBCO-coated conductors fabricated by this method are commonly used in the future. Superconducting magnetic energy storage (SMES) is one of electric power devices which may be used in power grid systems in the future. Since this device will be commonly used in the condition of stored energy, a decay of superconducting current is required to be suppressed severely. Hence, the apparent pinning potential, U 0 , a parameter associated with the decay of superconducting current is necessary to be investigated in detail. Since the flux creep phenomenon which determines U 0 depends appreciably on the thickness of superconducting layer, the thickness dependence of U 0 is investigated.
* Corresponding author. Tel.: +81 948 29 7663; fax: +81 948 29 7661. E-mail address: [email protected] (T. Matsushita). 0921-4534/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2010.05.094
Sometimes SMES is planned to be used at very high magnetic fields at low temperatures. However, the measurement of relaxation of current is not easy at high magnetic fields. If the dependence of U 0 on magnetic field and temperature is described in a form of scaling law, it may be useful for such cases of difficult measurement. In this paper, the thickness dependence of relaxation properties in CVD-processed YBCO-coated conductors is investigated, and analyzed using the flux creep-flow model [2]. In addition, scaling of U 0 for the dependence on magnetic field and temperature is examined.
2. Experiments The specimens were YBCO-coated tapes prepared by MultipleStage CVD (MS-CVD) process. The superconducting layer was deposited on Ion Beam Assist Deposition (IBAD)-processed substrate with Gd2Zr2O7 (GZO) inner layer and CeO2 cap layer [1]. The thickness of YBCO layer was varied in the range of 0.18– 0.90 lm. The specifications of these specimens are listed in Table 1. The DC magnetization and its relaxation were measured by using a SQUID magnetometer in a magnetic field up to 7 T parallel to the c-axis of the specimen over the temperature range of 20– 60 K. The critical current density was estimated from the DC magnetization using the Bean model:
1285
Y. Takahashi et al. / Physica C 470 (2010) 1284–1287
0.08
Table 1 Specifications of specimens. Specimen
Thickness d (lm)
Tc (K)
#1 #2 #3
0.18 0.45 0.90
87.9 89.5 88.5
6 Dm 2
dw ð3l wÞ
U0* [eV]
Jc ¼
0.07
ð1Þ
;
where Dm is the hysteresis of magnetic moment, d the thickness of the superconducting layer, and w and l are the width and the length of specimens (w < l), respectively. E–J characteristics were estimated from the relaxation measurement [3]. The magnetization M is magnetic moment per unit volume : Dm/wld. From the logarithmic relaxation rate of the magnetization, the apparent pinning potential U 0 was estimated:
d M U ¼ 0 : dlogt M 0 kB T
20 K exp.
0.06
#1 #2 #3 0.05
2
ð2Þ
The initial magnetization M0 was determined by extrapolating the relaxation curve from the time range of 102 103 s to t = 1 s. Fig. 1 shows the Jc–B characteristics of the three specimens at 20 and 60 K in the magnetic field regions of 0–6.5 T. The Jc decreases with increasing thickness in the entire region of magnetic field at 20 K and at low magnetic fields at 60 K. The decrease in the critical current density seems to be caused by the structural deterioration of superconducting layer in the specimens with increasing thickness [4]. On the other hand, Jc of the thinnest specimen rapidly decreased with increasing magnetic field at 60 K due to the strong influence of the flux creep. The magnetic field dependence of U 0 at 20 K obtained from the relaxation rate of the magnetization is shown in Fig. 2. It is found that U 0 decreases with increasing thickness at low magnetic field at 20 K. On the other hand, U 0 of the thinnest specimen rapidly decreases with increasing magnetic field. Such behavior of U 0 cannot be foreseen only from the Jc characteristics shown in Fig. 1.
4
6
B [T] Fig. 2. Magnetic field dependence of observed U 0 at 20 K. The lines are guide for eye.
current density takes a value determined only by the flux pinning and its temperature and magnetic field dependence is assumed as
m 2 T B J c0 ¼ A 1 Bc1 1 ; Tc Bc2
ð3Þ
where A, m, c are pinning parameters. The pinning potential U0 which determines the flux creep property is described in terms of Jc0 as: 1=2
U0 ¼ ¼
0:835g 2 kB J c0 3=2 1=4
ð2pÞ B 4:23g 2 kB J c0 d 2pB1=2
;
;
d > L;
d < L:
ð4Þ ð5Þ
3. Theory
In the above d is the thickness of the superconducting layer and L is the pinning correlation length given by
The critical current properties were analyzed using the flux creep-flow model [2]. In the virtual flux-creep free case, the critical
L¼
Jc [A/m2]
1010
60 K
2pl0 J c0
ð6Þ
"
# ðlog A log Am Þ2 f ðAÞ ¼ K exp ; 2r2
109
#1 #2 #3 10
1=2
Baf
with af denoting the flux line spacing. It should be noted that even if the pinning is in the three-dimensional case (d > L) at low magnetic fields for fairly thick superconductor, the pinning may change to the two-dimensional one at high magnetic fields due to the increase in L with decreasing Jc0. More detailed discussion of this mechanism is given in [5]. The parameter g2 is the number of flux lines in a flux bundle. In practical superconductors the flux pinning strength is statistically distributed widely [6]. Here it is simply assumed that only the parameter A which represents the pinning strength is distributed as
20 K
1011
8
0
2
4
6
B [T] Fig. 1. Magnetic field dependence of critical current density at 20 and 60 K in the magnetic field range of 0–6.5 T. The lines are guide for eye.
ð7Þ
where Am is the most probable value of A and r 2 is a parameter representing a distribution width and K is a normalization constant. The electric field E caused by the mechanism of flux creep and flow is calculated as a function of the current density J and averaged statistically with respect to the distributed A. The details of the theoretical calculation are described elsewhere [2]. The theoretical critical current density is determined from the obtained E–J curve
1286
Y. Takahashi et al. / Physica C 470 (2010) 1284–1287
0.08
4. Results and discussion
0.07
U0* [eV]
with the same electric field criterion of Ec = 109 V/m as done in experiments. The pinning parameters Am, r, m and c are determined so that the calculated E–J curves agree with the experiments. The obtained parameters are listed in Table 2.
The E–J curves of specimen #3 obtained from the relaxation of magnetization are shown in Fig. 3. The lines are the theoretical results of flux creep-flow model. The experimental results are explained well by the theory. Fig. 4 shows the theoretical results of U 0 at 20 K. Good agreement with experiments shown in Fig. 2 is obtained. Thus, the relaxation property is describable by the mechanism of flux creep and flow. Now the possibility of description of U 0 ðB; TÞ in the form of scaling law is examined. It is assumed for simplicity that the magnetic field dependence of U 0 can be approximated by quadratic function:
¼
U 0 peak ðTÞ
2
aðTÞ½B Bpeak ðTÞ ;
#1 #2 #3 0.05
11
0.15
#1 : function’s peak 0.1
#1 #2 #3
4.30 10 2.93 1011 1.79 1011
exp.
0.05 r2
c
m
5.70 103 5.90 103 6.20 103
0.57 0.59 0.60
1.9 1.9 1.9
6
Fig. 4. Magnetic field dependence of U 0 calculated by theoretical relaxation rate at 20 K. The lines are guide for eye.
Table 2 Pinning parameters of specimens at 20 K. Am
4
B [T]
ð8Þ
where a is unique parameter for each specimen. Fig. 5 shows the magnetic field dependence of U 0 for specimen #1 in the temperature range of 20–40 K. The lines are curves of the approximated quadratic function. The arrow shows the position of the peak. It is found that the peak moves to low magnetic field with increasing temperature. The peak field (Bpeak) and the peak value of U 0 ðU 0 peak ) are important parameters for description of U 0 ðB; TÞ. The obtained parameters are listed in Tables 3 and 4. The temperature dependences of U 0 peak and Bpeak are shown in Fig. 6a and b. The condition of pinning in specimen #1 is two-dimensional and that of specimen #3 is three-dimensional over the entire temperature region of 20–40 K. On the other hand, that of specimen #2 changes from three-dimensional to two-dimensional between 25 K and
Specimen
2
U0* [eV]
U 0 ðB; TÞ
20 K theo.
0.06
0
Eq.(8)
0
20 K 25 K 30 K 35 K 40 K
2
4
6
B [T] Fig. 5. Magnetic field dependence of U 0 in specimen #1 in the temperature region 20–40 K. The lines are approximated quadratic function of Eq. (8).
10−9
E [V/m]
Table 3 Scaling parameter (Bpeak) of specimens.
#3 20 K 1T 2T 3T 4T 5T 6T
10−10
Specimen
Bpeak(T) 20 K
25 K
30 K
35 K
40 K
#1 #2 #3
1.54 3.06 4.51
0.61 2.39 3.55
1.50 0.04 2.32
4.13 5.07 0.28
8.34 13.50 1.10
Table 4 Scaling parameter (U 0 Specimen
10
10
2
J [A/m ]
10
11
Fig. 3. E–J curves of specimen #3 obtained from the relaxation of magnetization. The lines are theoretical results of flux creep-flow model.
#1 #2 #3
U 0 peak
peak )
of specimens.
(eV)
20 K
25 K
30 K
35 K
40 K
7.79 102 7.70 102 7.62 102
9.63 102 9.45 102 9.71 102
1.12 101 1.13 101 1.14 101
1.40 101 1.43 101 1.32 101
1.82 101 2.05 101 1.53 101
1287
Y. Takahashi et al. / Physica C 470 (2010) 1284–1287 Table 5 Scaling parameter a of specimens.
(a) 0.2
d>L
d
Specimen
#1
2
a(eVT )
U0 peak*[eV]
#1 #2 #3
#2 3
0.6 10
0.5 10
#3 3
0.8 103
0.08
0.06
20
30
40
T [K]
−10
20 K exp. Eq.(8)
d
0
#1 #2 #3
Bpeak [T]
0.04
#1 #2 #3
0.02
(b) d>L
U0* [eV]
0.1
0
10
B [T] U 0
Fig. 7. Magnetic field dependence of at 20 K. Symbols and lines represent the experimental result and approximation of Eq. (8), respectively.
5. Summary
0
20
30
40
T [K] U 0 peak
Fig. 6. Temperature dependence of (a) and (b) Bpeak in the temperature region 20–40 K. The open and solid symbols show that the pinning is threedimensional and two-dimensional, respectively.
30 K. It is found that while U 0 peak increases linearly with increasing temperature in the three-dimensional pinning regime, its increase rises nonlinearly in the two-dimensional pinning regime. The value of U 0 peak does not depend on the layer thickness at low temperatures. The temperature dependence of Bpeak is similar to that of U 0 peak , while the value of Bpeak increases with increasing thickness at low temperatures. On the other hand, the parameter a listed in Table 5 does not precisely depend on the thickness. The experimental results of the apparent pinning potential are compared with the scaling formula of Eq. (8) at 20 K for three specimens in Fig. 7. This indicates that superconducting tape with thicker superconducting layer is better for high field performance. Thus, it is shown that the dependence of U 0 on magnetic field and temperature is generally expressed as in Eq. (8). It is found that the parameters U 0 peak and Bpeak change with the thickness of superconducting layer through the dimensionality of flux pinning. However, the phenomenon is complicated and more detailed analysis is necessary for exact understanding of the phenomenon. It is necessary to examine the relaxation property for other specimens, such as a series of coated conductors with less structural degradation.
The thickness dependence of the critical current and relaxation characteristics were investigated for IBAD/CVD YBCO-coated conductors. It is found that Jc decreases with increasing thickness in the magnetic field region 0–6.5 T at 20 K. In the same temperature, although U 0 decreases with increasing thickness at low magnetic fields. U 0 increases at high magnetic fields, the results were theoretically explained by the model of the flux creep and flow based on the dimensionality of flux pinning. Application of scaling law is examined for the dependence of U 0 on magnetic field and temperature. It was found that the scaling parameters behave in different manner depending on the dimensionality of flux pinning. For more precise understanding, the relaxation property additional experiments are necessary for different series of samples. Acknowledgements This work was supported by the New Energy and Industrial Technology Development Organization (NEDO) as the Technological Development of Yttrium-based Superconducting Power Equipment. References [1] M. Mori, T. Watanabe, N. Kashima, T. Muroga, S. Miyata, Y. Yamada, T. Izumi, Y. Shiohara, Physica C 445–448 (2006) 515. [2] M. Kiuchi, K. Noguchi, T. Matsushita, T. Hikata, K. Sato, Physica C 278 (1997) 62. [3] K. Himeki, M. Kiuchi, E.S. Otabe, T. Matsushita, S. Miyata, A. Ibi, Y. Yamada, Y. Shiohara, Physica C 468 (2007) 1674. [4] K. Himeki, M. Kiuchi, E.S. Otabe, T. Matsushita, K. Shikimachi, T. Watanabe, N. Kashima, S. Nagaya, Y. Yamada, Y. Shiohara, Physica C 469 (2009) 1457. [5] T. Matsushita, Flux Pinning in Superconductors, Springer, Berlin, 2006. p. 333. [6] T. Matsushita, T. Tohdoh, N. Ihara, Physica C 259 (1996) 321.