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Pinning energies of oxygen deficient YBCO using time dependent AC susceptibility measurements
PHYSICA
Physica C 205 (1993) 266-270 North-Holland
Pinning energies of oxygen deficient YBCO using time dependent AC susceptibility measurements H.B. Sun, K . N . R . T a y l o r a n d G.J. Russell Advanced Electronic Materials Physics, University of New South Wales, PO Box 1, Kensington, NSW 2033, Australia
Received 21 September 1992 Revised manuscript received 23 November 1992
By observing the time decay of the AC susceptibility after an external field is removed from the sample, we have been able to determine the temperature dependence of the pinning energies in several oxygen deficient samples of YBCO. The time scale of the measurements extended from 100 ms to 2000 s and showed a very fast initial decay lasting for less than 1 s followedby a slower relaxation which continued for the rest of the observational period. The nature of the initial decay is still not understood; however, the longer time decay has a logarithmic form and has been used in the determination of the pinning energies.
I. Introduction Because of the relatively weak pinning effects in the high-temperature superconducting materials the magnetization relaxes quite rapidly after removing an external field. M a n y workers have used this characteristic to establish estimates o f the flux pinning energies in these materials by the measurement o f the time decay o f the remanent magnetic m o m e n t (see e.g. refs. [ 1-3 ] ) associated with the sample. Since the trapped field associated with the magnetization is known to affect the current-voltage characteristics of the mixed state, the decay can also be observed using conventional electrical measurements and pinning energy values have been obtained [4] which are comparable to those from magnetization studies. In the literature, there are several reports o f a two stage decay, involving an initially fast relaxation, whose nature is not understood, followed by a slower decay which is generally taken as logarithmic in time. With few exceptions [5], the magnetization measurement technique precludes observations at short decay times ( < 1 s) and the overall form of the magnetization relaxation has usually been made for minimum times considerably greater than this. In order to attempt to explore both short and long time decay processes, we have investigated the use
o f conventional AC susceptibility measurements for the observation of the relaxing magnetization. It is well known that the AC susceptibility is strongly dependent upon the presence o f external fields which are sufficiently strong as to penetrate the inter- and intragranular components of ceramic samples [ 6,7 ]. This sensitivity is associated with the density and distribution of the static flux within the sample and hence is related to the magnetization. In principle, therefore, it should be possible to determine the time decay o f this relaxation by the observation of the AC susceptibility (Z') as a function o f time after removing a magnetizing field. Preliminary measurements using this technique are described in the following.
2. Experimental The samples used in this work were part of a series of oxygen deficient YBa2Cu307_xwith x ~ 0.1, 0.2 and 0.3. The basic YBCO ceramics were prepared in a conventional manner, and the oxygen concentrations established by annealing [ 8 ]. The precise value o f x was determined using both X-ray and chemical methods, with a confirmatory calibration o f one of the samples using Rietveld fitting o f the neutron dif-
0921-4534/93/$06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved.
267
H.B. Sun et al. / Pinning energies of oxygen deficient YBCO
Table 1
-25
Sample
x (+0.02)
Tc (K)
Sma~
Tm~ (K)
U*( 30 K) (eV)
HB-1 HB-2 HB-3
0.05 0.20 0.35
93 63 52
0.007 0.01
61 42 -
0.64 0.31 0.15
-30
-35
fraction pattern. The characteristics of these samples are given in table I. The susceptibility was measured using a computer controlled AC susceptometer based on the n o r m a l balanced-secondary transformer system. The sample was located in one half o f the secondary coil and thermally coupled to the cold head o f a helium refrigerator through a copper peg extending into the coil. The DC fields were a p p l i e d using an external coil system, coaxial with both the sample a n d transformer axes. The m e a s u r e m e n t s were m a d e at a frequency o f 1 kHz a n d an AC field a m p l i t u d e o f 0.35 Oe. In operation, the sample was cooled to the base temperature (T~20K) in zero field and subsequently w a r m e d to the measuring temperature. The DC field was then a p p l i e d for a p p r o x i m a t e l y one minute during which time the AC susceptibility was measured continuously at a d a t a rate which dep e n d e d on the total t i m e range to be covered. The fastest rate used c o r r e s p o n d e d to 20 Hz while the longer times could be observed at either 3 Hz or < 1 Hz. A typical t i m e decay o f the susceptibility is shown in fig, l for d a t a acquired using the 20 Hz and 3 Hz d a t a rates. The fast decay is very obvious, as also is the change to the slower logarithmic relaxation. In the present work, we have restricted the observations to the second, longer time-scale process a n d have used a d a t a rate o f 3 Hz. Since the data collection occurs continuously, as the field is switched off, the measurements effectively c o m m e n c e at zerotime in the decay. The susceptibility m e a s u r e d after the r e m o v a l o f an a p p l i e d D C field o f H = 300 Oe, for three temperatures is plotted against the logarithm o f time in fig. 2 for one o f the samples used in the study. As m a y be seen, the relaxation o f the susceptibility was linear in In t during the observation interval. The width o f the curve (in AZ') arises because o f a small ( A T = _+0.1 K ) oscillation in the sample tempera-
o
-40
-45
I
-$0
100
5O
Time (See.) Fig. I. A typical time decay of the susceptibility showing both t h e fast and slow components of the relaxation for the x= 0.05 sample.
-50.5
• ''""
•
85K
e~
e~ O
-53.5
0
80K
. I I
em
70K
-$6.$ -2
I
I
t
I
O
2
4
6
lnt (see.) Fig. 2. The long term decay for the x= 0.05 sample after removing an applied field of H= 300 Oe, for several temperatures.
268
H.B. Sun et al. / Pinning energies of oxygen deficient YBCO
ture due to the resolution of the temperature controller. Figure 3 shows the normalized relaxation rate S= ( 1/Z~) ( d x ' / d ( l n t) ) derived from this data, as a function of temperature for the different samples. The ( d z ' / d ( l n t ) ) values are obtained directly from the slope of the results shown in fig. 2. In these results the relaxation rate passes through a peak with increasing temperature, the temperature of the peak corresponding to the temperature at which the field first fully penetrates the whole sample [ 9 ] and establishes the critical state. These penetration temperatures, along with the peak S values are shown in table l, the temperature of this peak shifting to lower temperatures with increasing oxygen deficiency, decreasing from ~ 60 K to ~ 40 K as the oxygen content decreases from 6.95 to 6.8. For the sample with x = 6 . 6 5 the flux lines have completely penetrated the sample at H = 300 Oe for all the measured temperatures and as a result this sample does not show a maximum in the temperature dependence of d z ' / d ( l n t). A second series of observations was carried out at a reduced field amplitude (0.17 Oe); however, the results were not significantly different from those de-
scribed above and are consequently not given in this publication.
3. D i s c u s s i o n
Before proceeding with the derivation of the pinning energies, it is worth establishing that the observed susceptibility is indeed directly proportional to the magnetization measured using normal magnetometer techniques. In the present AC susceptibility measurements, the field at the sample can be written H ( t ) = HDC + HAC sin o9t and the instantaneous magnetization is given by M=ZoHDc +HAc
~ [Xnsin no9t-X'/, cos no9t] ,
where n relates to the harmonic component of the fundamental frequency o9. Zo is the change in susceptibility caused by the DC field, which can be written 2n X0= (1/XHDc)
.I M(t) d(ogt) . o
For a fixed temperature Ti, Z~= ~= constant =Z' (Ti) and the detected signal Vs is proportional to the measured susceptibility Zm(t') at time t' where
0.018
2x
0.014
~ ¢ x-0.$5
Xm(t') = I/XHAc } M ( t ) sin ogt d(ogt) 0 2~x
0.010
/~
= 1/XHAc I Md(t) d(ogt) + Z ' ( T i )
t x-0.20
0
=CMd(t')+x'(Ti) • 0.006
0.002 20
I
I
I
30
40
50
I 60
I
I
70
80
90
Temperature(K) Fig. 3. The normalized relaxation rate of the three samples as a function of temperature.
Here Md(t) is the magnetization resulting from the DC field with Md (0) = ZoHDc at t = 0 ( the time when HDC is switched to zero) and C is a constant such that CMd (t') is the change in the observed susceptibility AX' at time t' after the application of the DC field. In the time period of the drive field (2~/o9), Md(t) can be considered constant and equal to Md(t'), and the signal decay is therefore directly proportional to the decay of the magnetization. The initial change Md(0) is taken in the following analysis as the initial magnetization Mi.
H.B. Sun et al. / Pinning energies of oxygen deficient YBCO
On this basis then, Z' can be replaced throughout by the magnetization M and S is now equivalent to (1/Mi) d M / d ( l n t ) so that the usual relationship U * = k T / [ - ( 1 / M i ) d M / d ( l n t) ] may be used to determine the average pinning potential U* from the data shown in fig. 2. The resulting temperature dependence of U* for the three samples is then plotted in fig. 4. These estimated values for the pinning energy in oxygen deficient material ( x = 6 . 6 5 ) are similar to the values of 100-500meV which have been reported by other workers [10]. The values for the sample with x = 6.95 are generally higher than those in the literature; however, this difference is probably related to the field dependence of U* [ 11 ] and the fact that relatively low fields are used in this work. The normalized relaxation rate in the temperature region below the peak temperature increases with temperature, while the decreasing normalized rate in the temperature region above the peak is associated with the small amount of pinned flux which is available to relax at these temperatures. Since the average pinning potential is calculated from the relationship U * = k T [ ( - 1 / M i ) d M / d ( l n t) ], U* increases 1.5
l.O --
$
269
sharply. Such increases in U* with temperature have also been reported by other authors [ 12-14]. Different models have been proposed to explain this effect. Hagen and Griessen [ 14] have modelled this dependence in terms of a distribution of U* in any particular sample, while Chaddah and Bhagwat [ 15 ] have predicted the rise of U* with T using the critical state model with a critical current density which decays exponentially with the field. In contrast, Chan and Liou [16 ] suggest that the anomalous increase of U* and the corresponding rapid decrease of the normalized relaxation rate are closely related to the irreversibility line. At temperatures above the irreversibility temperature the flux trapping is weak, and consequently is thought to be responsible for the reduction in the normalized relaxation rate, which in turn causes the increase of U*.
4. Conclusion We have shown that it is possible to use the time decay of the AC susceptibility to measure the effective pinning energies in a series of oxygen deficient YBCO samples. It is shown that this is directly proportional to the observation of magnetization decay and the pinning energy values obtained are comparable to those reported by other workers. Using this technique we hope to study the nature of the shortterm, fast decay of the magnetization which has been seen in other investigations and observed by ourselves in this work.
-g
0.5 --
l
/
t
References
x-0.20
n x-0.35
o.o 20
I
I
I
I
I
I
30
40
50
60
70
80
90
Temperature(K) Fig. 4. The temperature dependence of the effective pinning energy, U*, derived from the data of fig. 3.
[ 1 ] B.D. Biggs, M.N. Kunchur, J.J. Lin, S.J. Poon, T.R. Askew, R.B. Flippen, M.A. Subramanian, J. Gopalakrishnan and A.W. Sleight, Phys. Rev. B 39 (1989) 7309. [2]A. Tanaka, J. Crain and K. Niwa, Appl. Phys. Len. 57 (1990) 917. [3] M.P. Maley, J.O. Willis, H. Lessure and M.E. McHenry, Phys. Rev. B 42 (1990) 2639. [ 4 ] D.N. Matthews, G.J. Russell and K.N.R. Taylor, Physica C 171 (1990) 301. [ 5 ] Y.Y. Xue, L. Gao, Z.J. Huang, P.H. Hor and C.W. Chu, The Vortex State Below Ts Probed by Short-Time Relaxation (preprint).
270
H.B. Sun et al. / Pinning energies of oxygen deficient YBCO
[6] T. Ishida, R.B. Goldfarb, S. Okayasu, Y, Kazumata, J. Franz, T. Arndt and W. Schauer, The Series of Materials Science Forum, eds. John J. Pouch, Samuel A. Alterovitz and Robert R. Romanofsky (Trans. Tech. Publications, Aedermannsdorf, Switzerland). [ 7 ] Youngtae Kim, Q. Harry Lam and C.D. Jeffries, Phys. Rev. B43 (1991) 11404. [ 8 ] J.D. Jorgensen, B.W. Veal, A.P. Paulika, L.J. Nowicki, G.W. Crabtree, H. Claus and W.K. Kwok, Phys. Rev. B 41 (1990) 1863. [9] M. Xu, D. Shi, A. Umezawa, K.G. Vandervoort and G.W. Crabtree, Phys, Rev. B 43 ( 1991 ) 13049. [ 10] C.W. Hagen and R. Griessen, Studies of High Temperature Superconductors, ed. A.V. Narlikar, Vol. 3 (Nova Science, New York, 1989) p. 192.
[ 11 ] D.G. Shi and M.S. Boley, Supercond. Sci. Technol. 3 (1990) 285. [ 12 ] I.A. Campbell, L. Fruchter and R. Cabanel, Phys. Rev. Lett. 64 (1990) 1561. [13] Y. Xu, M. Suenga, A.R. Moodenbaugh and D.O. Welch, Phys. Rev. B 40 (1989) 10882. [14] C.W. Hagen and R. Griessen, Phys. Rev. Lett. 62 (1989) 2857. [15]P. Chaddah and K.V. Bhagwat, Phys. Rev. B 43 (1991) 6239. [ 16] V.K. Chan and S.H. Liou, Phys. Rev. B 45 (1992) 5547.
Physica C 205 (1993) 266-270 North-Holland
Pinning energies of oxygen deficient YBCO using time dependent AC susceptibility measurements H.B. Sun, K . N . R . T a y l o r a n d G.J. Russell Advanced Electronic Materials Physics, University of New South Wales, PO Box 1, Kensington, NSW 2033, Australia
Received 21 September 1992 Revised manuscript received 23 November 1992
By observing the time decay of the AC susceptibility after an external field is removed from the sample, we have been able to determine the temperature dependence of the pinning energies in several oxygen deficient samples of YBCO. The time scale of the measurements extended from 100 ms to 2000 s and showed a very fast initial decay lasting for less than 1 s followedby a slower relaxation which continued for the rest of the observational period. The nature of the initial decay is still not understood; however, the longer time decay has a logarithmic form and has been used in the determination of the pinning energies.
I. Introduction Because of the relatively weak pinning effects in the high-temperature superconducting materials the magnetization relaxes quite rapidly after removing an external field. M a n y workers have used this characteristic to establish estimates o f the flux pinning energies in these materials by the measurement o f the time decay o f the remanent magnetic m o m e n t (see e.g. refs. [ 1-3 ] ) associated with the sample. Since the trapped field associated with the magnetization is known to affect the current-voltage characteristics of the mixed state, the decay can also be observed using conventional electrical measurements and pinning energy values have been obtained [4] which are comparable to those from magnetization studies. In the literature, there are several reports o f a two stage decay, involving an initially fast relaxation, whose nature is not understood, followed by a slower decay which is generally taken as logarithmic in time. With few exceptions [5], the magnetization measurement technique precludes observations at short decay times ( < 1 s) and the overall form of the magnetization relaxation has usually been made for minimum times considerably greater than this. In order to attempt to explore both short and long time decay processes, we have investigated the use
o f conventional AC susceptibility measurements for the observation of the relaxing magnetization. It is well known that the AC susceptibility is strongly dependent upon the presence o f external fields which are sufficiently strong as to penetrate the inter- and intragranular components of ceramic samples [ 6,7 ]. This sensitivity is associated with the density and distribution of the static flux within the sample and hence is related to the magnetization. In principle, therefore, it should be possible to determine the time decay o f this relaxation by the observation of the AC susceptibility (Z') as a function o f time after removing a magnetizing field. Preliminary measurements using this technique are described in the following.
2. Experimental The samples used in this work were part of a series of oxygen deficient YBa2Cu307_xwith x ~ 0.1, 0.2 and 0.3. The basic YBCO ceramics were prepared in a conventional manner, and the oxygen concentrations established by annealing [ 8 ]. The precise value o f x was determined using both X-ray and chemical methods, with a confirmatory calibration o f one of the samples using Rietveld fitting o f the neutron dif-
0921-4534/93/$06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved.
267
H.B. Sun et al. / Pinning energies of oxygen deficient YBCO
Table 1
-25
Sample
x (+0.02)
Tc (K)
Sma~
Tm~ (K)
U*( 30 K) (eV)
HB-1 HB-2 HB-3
0.05 0.20 0.35
93 63 52
0.007 0.01
61 42 -
0.64 0.31 0.15
-30
-35
fraction pattern. The characteristics of these samples are given in table I. The susceptibility was measured using a computer controlled AC susceptometer based on the n o r m a l balanced-secondary transformer system. The sample was located in one half o f the secondary coil and thermally coupled to the cold head o f a helium refrigerator through a copper peg extending into the coil. The DC fields were a p p l i e d using an external coil system, coaxial with both the sample a n d transformer axes. The m e a s u r e m e n t s were m a d e at a frequency o f 1 kHz a n d an AC field a m p l i t u d e o f 0.35 Oe. In operation, the sample was cooled to the base temperature (T~20K) in zero field and subsequently w a r m e d to the measuring temperature. The DC field was then a p p l i e d for a p p r o x i m a t e l y one minute during which time the AC susceptibility was measured continuously at a d a t a rate which dep e n d e d on the total t i m e range to be covered. The fastest rate used c o r r e s p o n d e d to 20 Hz while the longer times could be observed at either 3 Hz or < 1 Hz. A typical t i m e decay o f the susceptibility is shown in fig, l for d a t a acquired using the 20 Hz and 3 Hz d a t a rates. The fast decay is very obvious, as also is the change to the slower logarithmic relaxation. In the present work, we have restricted the observations to the second, longer time-scale process a n d have used a d a t a rate o f 3 Hz. Since the data collection occurs continuously, as the field is switched off, the measurements effectively c o m m e n c e at zerotime in the decay. The susceptibility m e a s u r e d after the r e m o v a l o f an a p p l i e d D C field o f H = 300 Oe, for three temperatures is plotted against the logarithm o f time in fig. 2 for one o f the samples used in the study. As m a y be seen, the relaxation o f the susceptibility was linear in In t during the observation interval. The width o f the curve (in AZ') arises because o f a small ( A T = _+0.1 K ) oscillation in the sample tempera-
o
-40
-45
I
-$0
100
5O
Time (See.) Fig. I. A typical time decay of the susceptibility showing both t h e fast and slow components of the relaxation for the x= 0.05 sample.
-50.5
• ''""
•
85K
e~
e~ O
-53.5
0
80K
. I I
em
70K
-$6.$ -2
I
I
t
I
O
2
4
6
lnt (see.) Fig. 2. The long term decay for the x= 0.05 sample after removing an applied field of H= 300 Oe, for several temperatures.
268
H.B. Sun et al. / Pinning energies of oxygen deficient YBCO
ture due to the resolution of the temperature controller. Figure 3 shows the normalized relaxation rate S= ( 1/Z~) ( d x ' / d ( l n t) ) derived from this data, as a function of temperature for the different samples. The ( d z ' / d ( l n t ) ) values are obtained directly from the slope of the results shown in fig. 2. In these results the relaxation rate passes through a peak with increasing temperature, the temperature of the peak corresponding to the temperature at which the field first fully penetrates the whole sample [ 9 ] and establishes the critical state. These penetration temperatures, along with the peak S values are shown in table l, the temperature of this peak shifting to lower temperatures with increasing oxygen deficiency, decreasing from ~ 60 K to ~ 40 K as the oxygen content decreases from 6.95 to 6.8. For the sample with x = 6 . 6 5 the flux lines have completely penetrated the sample at H = 300 Oe for all the measured temperatures and as a result this sample does not show a maximum in the temperature dependence of d z ' / d ( l n t). A second series of observations was carried out at a reduced field amplitude (0.17 Oe); however, the results were not significantly different from those de-
scribed above and are consequently not given in this publication.
3. D i s c u s s i o n
Before proceeding with the derivation of the pinning energies, it is worth establishing that the observed susceptibility is indeed directly proportional to the magnetization measured using normal magnetometer techniques. In the present AC susceptibility measurements, the field at the sample can be written H ( t ) = HDC + HAC sin o9t and the instantaneous magnetization is given by M=ZoHDc +HAc
~ [Xnsin no9t-X'/, cos no9t] ,
where n relates to the harmonic component of the fundamental frequency o9. Zo is the change in susceptibility caused by the DC field, which can be written 2n X0= (1/XHDc)
.I M(t) d(ogt) . o
For a fixed temperature Ti, Z~= ~= constant =Z' (Ti) and the detected signal Vs is proportional to the measured susceptibility Zm(t') at time t' where
0.018
2x
0.014
~ ¢ x-0.$5
Xm(t') = I/XHAc } M ( t ) sin ogt d(ogt) 0 2~x
0.010
/~
= 1/XHAc I Md(t) d(ogt) + Z ' ( T i )
t x-0.20
0
=CMd(t')+x'(Ti) • 0.006
0.002 20
I
I
I
30
40
50
I 60
I
I
70
80
90
Temperature(K) Fig. 3. The normalized relaxation rate of the three samples as a function of temperature.
Here Md(t) is the magnetization resulting from the DC field with Md (0) = ZoHDc at t = 0 ( the time when HDC is switched to zero) and C is a constant such that CMd (t') is the change in the observed susceptibility AX' at time t' after the application of the DC field. In the time period of the drive field (2~/o9), Md(t) can be considered constant and equal to Md(t'), and the signal decay is therefore directly proportional to the decay of the magnetization. The initial change Md(0) is taken in the following analysis as the initial magnetization Mi.
H.B. Sun et al. / Pinning energies of oxygen deficient YBCO
On this basis then, Z' can be replaced throughout by the magnetization M and S is now equivalent to (1/Mi) d M / d ( l n t ) so that the usual relationship U * = k T / [ - ( 1 / M i ) d M / d ( l n t) ] may be used to determine the average pinning potential U* from the data shown in fig. 2. The resulting temperature dependence of U* for the three samples is then plotted in fig. 4. These estimated values for the pinning energy in oxygen deficient material ( x = 6 . 6 5 ) are similar to the values of 100-500meV which have been reported by other workers [10]. The values for the sample with x = 6.95 are generally higher than those in the literature; however, this difference is probably related to the field dependence of U* [ 11 ] and the fact that relatively low fields are used in this work. The normalized relaxation rate in the temperature region below the peak temperature increases with temperature, while the decreasing normalized rate in the temperature region above the peak is associated with the small amount of pinned flux which is available to relax at these temperatures. Since the average pinning potential is calculated from the relationship U * = k T [ ( - 1 / M i ) d M / d ( l n t) ], U* increases 1.5
l.O --
$
269
sharply. Such increases in U* with temperature have also been reported by other authors [ 12-14]. Different models have been proposed to explain this effect. Hagen and Griessen [ 14] have modelled this dependence in terms of a distribution of U* in any particular sample, while Chaddah and Bhagwat [ 15 ] have predicted the rise of U* with T using the critical state model with a critical current density which decays exponentially with the field. In contrast, Chan and Liou [16 ] suggest that the anomalous increase of U* and the corresponding rapid decrease of the normalized relaxation rate are closely related to the irreversibility line. At temperatures above the irreversibility temperature the flux trapping is weak, and consequently is thought to be responsible for the reduction in the normalized relaxation rate, which in turn causes the increase of U*.
4. Conclusion We have shown that it is possible to use the time decay of the AC susceptibility to measure the effective pinning energies in a series of oxygen deficient YBCO samples. It is shown that this is directly proportional to the observation of magnetization decay and the pinning energy values obtained are comparable to those reported by other workers. Using this technique we hope to study the nature of the shortterm, fast decay of the magnetization which has been seen in other investigations and observed by ourselves in this work.
-g
0.5 --
l
/
t
References
x-0.20
n x-0.35
o.o 20
I
I
I
I
I
I
30
40
50
60
70
80
90
Temperature(K) Fig. 4. The temperature dependence of the effective pinning energy, U*, derived from the data of fig. 3.
[ 1 ] B.D. Biggs, M.N. Kunchur, J.J. Lin, S.J. Poon, T.R. Askew, R.B. Flippen, M.A. Subramanian, J. Gopalakrishnan and A.W. Sleight, Phys. Rev. B 39 (1989) 7309. [2]A. Tanaka, J. Crain and K. Niwa, Appl. Phys. Len. 57 (1990) 917. [3] M.P. Maley, J.O. Willis, H. Lessure and M.E. McHenry, Phys. Rev. B 42 (1990) 2639. [ 4 ] D.N. Matthews, G.J. Russell and K.N.R. Taylor, Physica C 171 (1990) 301. [ 5 ] Y.Y. Xue, L. Gao, Z.J. Huang, P.H. Hor and C.W. Chu, The Vortex State Below Ts Probed by Short-Time Relaxation (preprint).
270
H.B. Sun et al. / Pinning energies of oxygen deficient YBCO
[6] T. Ishida, R.B. Goldfarb, S. Okayasu, Y, Kazumata, J. Franz, T. Arndt and W. Schauer, The Series of Materials Science Forum, eds. John J. Pouch, Samuel A. Alterovitz and Robert R. Romanofsky (Trans. Tech. Publications, Aedermannsdorf, Switzerland). [ 7 ] Youngtae Kim, Q. Harry Lam and C.D. Jeffries, Phys. Rev. B43 (1991) 11404. [ 8 ] J.D. Jorgensen, B.W. Veal, A.P. Paulika, L.J. Nowicki, G.W. Crabtree, H. Claus and W.K. Kwok, Phys. Rev. B 41 (1990) 1863. [9] M. Xu, D. Shi, A. Umezawa, K.G. Vandervoort and G.W. Crabtree, Phys, Rev. B 43 ( 1991 ) 13049. [ 10] C.W. Hagen and R. Griessen, Studies of High Temperature Superconductors, ed. A.V. Narlikar, Vol. 3 (Nova Science, New York, 1989) p. 192.
[ 11 ] D.G. Shi and M.S. Boley, Supercond. Sci. Technol. 3 (1990) 285. [ 12 ] I.A. Campbell, L. Fruchter and R. Cabanel, Phys. Rev. Lett. 64 (1990) 1561. [13] Y. Xu, M. Suenga, A.R. Moodenbaugh and D.O. Welch, Phys. Rev. B 40 (1989) 10882. [14] C.W. Hagen and R. Griessen, Phys. Rev. Lett. 62 (1989) 2857. [15]P. Chaddah and K.V. Bhagwat, Phys. Rev. B 43 (1991) 6239. [ 16] V.K. Chan and S.H. Liou, Phys. Rev. B 45 (1992) 5547.