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Effect of current on transport critical temperature of silver supported Bi2Sr2Ca1Cu2O8 thick films with Bi-free needle-like crystals
Effect of current on transport critical temperature of silver supported Bi2Sr2Ca Cu208 thick films with Bi-free needle-like crystals S. Patel New York State Institute on Superconductivity, State University of New York at Buffalo, Amherst, NY 14260, USA Received 29 October 1993; revised 13 May 1994 The four point d.c. method is generally used to measure the transport critical temperature Tc and critical current density Jc of superconducting films. This paper theoretically investigates the effect of the measurement current and limiting voltage on the Tc of silver supported Bi2Sr2CalCu2Os tapes with and without the Bi-free needle-like crystals. Results show that finite currents that drive the superconductor normal at the true Tc will lower the measured Tc by several per cent. Results also show that the measured T¢ is further lowered by the presence of the needle-like crystals and that this is a direct consequence of the reduced Jc of such films. The degree to which the measured Tc is lowered from the true Tc depends on crystal size, orientation and concentration. In general, small crystals at any orientation with respect to the current flow have little effect on the Tc, whereas large crystals can have a significant effect, particularly when using large measurement currents. High concentrations of small crystals are relatively insensitive to the Tc, whereas small concentrations of large crystals can have a significant effect. The additional decrease in Tc due to the crystals is typically between 0 and 2%. Although relatively insignificant, the effect can be a noticeable factor during process optimization.
Keywords: high T© superconductors; critical temperature; Bi-2212
Non-superconducting Bi-free needle-like crystals having a phase of the type (Sr,_x,Cax)CuyOz [e.g. (Sr,Ca)ECuO3, (Sr,Ca)CuO2 and (Sr,Ca)14CUE404d are sometimes formed in Bi2SrECa~Cu208 (Bi-2212) superconducting thick films fabricated by the partial-melt-growth technique pioneered by Heine et al. 1-6. These crystals have a length of 10500 ~m and a width of 1-30/xm depending on the phase s,5. The size and concentration of these crystals are very sensitive to the precursor materials and processing heat treatment parameters. Microscopic examinations indicate that the cross-section of these crystals can traverse the entire film thickness. Films with fewer and smaller crystals generally have a high transport critical current density j4.7. The inclusion of these crystals in the superconducting film impedes the current flow through the film thus lowering its J~. The effect of crystal size and orientation on this degradation in Jc has been previously modelled8. Because of the finite currents used in the measurements of the transport critical temperature Tc this degradation in J~ can result in a lower To. The Tc of a superconductor is measured by the four point method. A small constant d.c. current I flows through the
0011-2275/94/110947-06 © 1994Butterworth-HeinemannLtd
conductor between the outer contacts, and the potential drop V is continuously measured across the inner contacts while the temperature T of the conductor is lowered gradually from room temperature. When V reaches the noise level of the instrument or a predetermined threshold V]i~t, typically 10-50 nV, the conductor is considered to be superconducting and the temperature at which this occurs is considered to be the zero resistance To. To determine the true transport critical temperature Too an infinitesimal current should be used in the four point measurement. This infinitesimal current will not drive the superconductor normal at Tco and the corresponding J¢ at T~o will be zero. Large currents will drive the superconductor normal at T¢o and will register a V larger than Vlimito Only by lowering T will V = V,n,t, resulting in a Tc that is lower than T¢o9. Large constant d.c. currents are generally used when the resistivity of the substrate is much lower than the resistivity of the superconducting material at room temperature. This is generally done so as to register a V at room temperature that is several orders of magnitude greater than Vlirnit. 7rhis enables the measurements to show accurately the details o f the resistance-temperature (R-T) characteristics. For
Cryogenics 1994 Volume 34, Number 11 947
Effect of current on transport critical temperature: S. Pate/ example, in the T~ measurement of Bi-2212 thick films on silver, a relatively large constant current of 0.1-0.5A is used to register 100-500/zV at room temperature, because the initial room temperature current flows through the low resistance silver [Psilver(300K) ~ /22212(300K)]. The R - T characteristics of these films are typically as follows: as the film is cooled from room temperature the R - T behaviour is that corresponding to silver. Near the onset of T~ the resistance of the film becomes comparable to that of silver and current sharing between silver and the film occurs. Further decrease in T results in a rapid drop in the resistance, wherein the film resistance becomes substantially smaller than that of silver. Further lowering of T results in the film going superconducting at To. During the entire test, the current is maintained constant. These large currents will result in a slightly lower T~ since these currents would exceed the J~ of the film at/'co which is zero. The presence of Bi-free needle-like crystals in the Bi2212 film will result in an additional decrease in Tc because of the finite currents used in the measurement. This paper presents a theoretical model of the effect of current on the T~ of Bi-2212 films with and without Bi-free needle-like crystals. The model is extended to see the effect of crystal size, orientation and concentration on To.
corresponding to Vlimitused to determine T~. Also assumed in the analysis is that the superconducting properties of the Bi-2212 grains between the Bi-free crystals are similar to those of the grains in a Bi-2212 film with no Bi-free crystals, and that no current sharing occurs between the Bi2212 film and the substrate at T<--Tco.The objective of the formulations is to determine the extent to which these crystals, assumed insulating, can degrade the T¢ when using a finite current in the four point electrical transport measurement. Figure 2 shows schematically the R - T (or equivalently, V - T at constant I) behaviour in the vicinity of Tc of a Bi2212 film with and without the Bi-free crystals. Curve 1 is that of a film with no Bi-free crystals, which is obtained using an infinitesimal current density AJ (or equivalently a small current A/). Curve 2 is that of the same film but using a current density J such that J>AJ. Curve 3 is that of a Bi-2212 film with Bi-free defects using a current density similar to that of curve 2. T~o,Tc2 and To3 are the critical temperatures corresponding to the three curves, respectively, and represent the temperatures at which V = Vlimi t. If AJ is used instead of J for curves 2 and 3, then T~o = T¢2 = To3. Also shown in Figure 2 is the variation of J¢ of the Bi-2212 film with no Bi-free defects. At any T below/'co there exists a J~ and the corresponding I - V characteristics can be described by the power law equation.
Formulations, results and discussion To simplify the formulations, the effect of a single needlelike crystal on the current flow is investigated. Figure la shows schematically the two-dimensional representation of a film consisting of randomly orientated Bi-free crystals having random lengths. Figure lb shows a simple model representation of the film of Figure la used for this study. The formulations of the potential drop across the projected length of the crystal and the current density distribution above and below the crystals are derived in reference 8 and will be used in this text. In the analysis, it is assumed that the current-voltage (l-V) characteristic of the superconducting film is described by the power law equation and that the power law equation is valid down to voltage levels
~/ \
"/
/
x
/
x /
Effect of current on transport critical temperature The following section describes the effect of current on the Tc of Bi-2212 superconducting films void of Bi-free needlelike crystals. Referring to Figure 2, curve 2, increasing the constant d.c. current will result in a decrease in the measured T¢2. The amount of decrease in T¢2 from /'co will depend on the J¢(T) characteristics of the superconductor described by the following expression J¢(T) = J¢(0) 1 -
L
(1)
where J~(O) is the characteristic transport critical current density at T = 0. For T < 0.9Too the exponent m is ~ 1 and for 0.9Too < T < /'co, m varies typically between 1 and 2,
/ V orR)
=l
T~T¢o
®®
@
==
(a)
(b)
y
.¢ I
Vlimit
Yo
I 0
,-I~X XL
(c)
Figure 1 Schematic representation of: (a) Bi-2212 film showing Bi-free needleTlike crystals; (b) model representation of film shown in (a); and (c) the co-ordinate system
948
Cryogenics 1994 Volume 34, Number 11
xo3
Too
~ T
Figure2 R - T (or V-T at constant I) behaviour in the vicinity of To. Curves 1 and 2 represent the R - T b e h a v i o u r of a Bi-2212 film without the crystals and curve 3 that with crystals. Curve 1 represents the true R- Tbehaviour using an infinitesimally small current density AJ. Curves 2 and 3 represent the R-Tbehaviour using a current density J > AJ. Too, T¢2 and Tea are the critical temperatures corresponding to the three curves
Effect of current on transport critical temperature: S. Pate/ depending on the properties of the superconducting grains and the type of junctions (SNS, SiS, SNINS, etc.) generated between the adjoining grains ]°. For SNS junctions m = 2 and for SIS junctions m = 1 ll'12. For more complex junctions, such as SNINS, m takes on intermediate values 13. At T
-
F,
~
- LZ4T)J
[j _l
(2)
1.00
(a) in
= LJo(T)J
where: V is the potential drop across the voltage taps separated by a distance L and Vo is the value of voltage (or equivalently Eo = Vo/L is the value of electric field) used to define J~. The exponent n is a function of T whose value increases with decreasing T. The dependence of magnetic field on the exponent n is not addressed in this paper, although the same methodology can be applied. The exponent n is indicative of the quality of the superconductor, especially at temperatures well below Too where n is typically between 10 and 30. At temperatures near T~o, n 1, indicating a near ohmic dependence between current and voltage. For single crystal Bi-2212 the dependence of n on T is linear except in close proximity to T¢oTM. However, assuming linearity to T~o, this dependence can be described by the following expression n=l+k
Figure 3a shows the effect of J* on T* with m as a parameter, k = 29 and V* = 0.01. Increasing J* decreases T*. Also, for a given J*, T* decreases with increasing m. As mentioned earlier, m = 2 represents SNS type junctions and m = 1 represents SIS type junctions. Thus, conductors having SNS type junctions will measure a smaller Tc than conductors having SIS type junctions for similar d.c. currents. 7"* is relatively insensitive to small d.c. currents (J* < 10-4) when m = 1, and very sensitive to relatively large
1-
0.95 [-
\ 0.90
k=29, V*--O.O1
0.85 ......... 10-5
J*
1.00
.................
where k is a constant. The current I (or equivalently J) in Equation (2) represents the constant d.c. current used in the four point method. During the cool-down process, V will equal V,~t at T = Tc2, such that equation (2) will become
. . . . . . . . . .
F, 0.90
0.S$
Vo
[ -
J
,
(3) 0.95
V.~t
i0 "4
0.90
L~J
1.00
-
0.85
(4)
[j--~j
j
10 -4
-
t --
10"=
tO -s
j~t
1,00
(5)
Equation (5) represents the dependence of the measured To, namely To2, normalized with respect to T¢o, on the magnitude of the measuring d.c. current density. The ratio V* = Vli,~tlVo represents the relative accuracy to which measurements of T~ and J~ are made. J* = J/Jc(O) is indicative of the magnitude of the current used in the Tc measurement. For thick films on conducting substrates, such as Bi-2212 on Ag, the d.c. current used for measurement is typically 0.1-0.5 A and the critical current at 4.2 K is typically 100 A, depending on the quality and dimensions of the conductor. J* [or IlljO) .-~ I/Ic (4.2 K)] for such films will have a typical value in the 10-3-10 --2 range. For high quality superconducting thin films on single crystal substrates such as MgO, J* can be much smaller. T* = Tc2/Tco can be evaluated iteratively using Equation (3) with T = TeE and Equation (5) for any given J*, V*, k and m.
-
10-s
Substituting Equation (4) in (1) and rearranging, the following is obtained
T~---~= 1 - [[--~-o ]
0.95
v
]"(r~2)
0.95 @
[-
0.1 " 0.90
k=29, m=1.5 0.85
. . . . . . . .
104
|
. . . . . . . .
10 4
i
. . . . . . .
I0 "3
10 "2
J* Figure 3
(a) Variation of normalized critical temperature, T* = J/Jc(O), and m as a parameter. (b) Variation of 7-* = Tc=ITcowith J* = J/J¢(O), and k as a parameter. Inset shows v a r i a t i o n o f e x p o n e n t n w i t h T*. T~2/Tco, w i t h n o r m a l i z e d c u r r e n t density, J * =
(c) V a r i a t i o n o f 7"* =
Tc2/Tcow i t h
J* =
J/Jc(O), and
V* =
Vm~JVo
as a p a r a m e t e r
Cryogenics
1994 Volume
34, Number
11
949
Effect of current on transport critical temperature: S. Pate/ d.c. currents (J* > 10-3) particularly for m = 2, reducing the value of T* by 15%. For more complex type intergranular junctions T* will have intermediate values. Figure 3b shows the effect of J* on T* with k as a parameter, m = 1.5 and V* = 0.01. The inset in Figure 3b shows the variation of n with T* for several values of k. At T = T¢o the I - V behaviour is ohmic (n = 1), becoming nonohmic (n > 1) as T* decreases. The higher the value of n, the better the quality of the superconductor is and the closer the measured T~ will be to T¢o for a fixed d.c. current. Figure 3c shows the effect of J* on T* with V* as a parameter, m = 1.5 and k = 29. V* is indicative of the accuracy with which the measurements are made. The smaller the value of V*, the more accurate the measurements will be. Figure 3c shows that for a given J*, the more accurate the measurement (reducing V~m~t)the greater the decrease in T* is. Thus by reducing the accuracy, 7"* of a superconductor can be artificially improved, making 7"* closer to unity.
Effect of needle-like defects on transport critical temperature The above formulations showed the effect of the d.c. current on the measured T~ of a superconductor without the Bi-free needle-like crystals. This effect is made larger by the presence of such crystals in the Bi-2212 films. Referring to Figures 1 and 2 and the formulations given in reference 8, the voltage drop across a projected length XL of the crystal in a Bi-2212 film with and without Bifree needle-like crystals is given by Equations (6a) and (6b), respectively Yo [~1 V3(T) = EoALtan/3-i-i-n)
LJ~-~J°
T < r¢o
(6a)
V2(T) = EoXL
T < T~o
(6b)
where A L = ( l+xLtan/3]l-n-lyo J Jc(T) is the transport critical current density at a temperature T of the Bi-2212 film void of any Bi-free needle-like crystals. JLo is the fraction of J that flows in the region below the crystal [Equation (8b), reference 8]. It was shown in reference 8 that the J~ of the film with Bi-free crystals is lower than that of films without such crystals. This implies that at any given T and operating J, the potential drop for the film with crystals, V3(T), will be greater than the potential drop for a film without crystals, V2(T). According to Equation (1), Jc increases as T is decreased below T~o. Referring to Equation (6a) and Figure 2 it can be seen that by lowering T and consequently increasing the J~, and for the same operating J, V3 can be decreased and made equal to V2(T). If V2 and V3 correspond to Vlimit, then the corresponding temperatures are the critical temperatures. In equation form this can be written as (refer to Figure 2) V*
-
950
Vlimit Vo
-
V2(Tc2) Vo
-
-
-
V3(Tc3) Vo
-
-
Cryogenics 1994 Volume 34, Number 11
(7)
where Vo = E o X L is the value of the potential drop used to determine J~ at any given T from the I - V curve. The third term in Equation (7) is that of a film with no crystals and is represented by Equation (4). The last term in Equation (7) is that of a film with the Bi-free crystals. Using Equations (6a) and (7), and Equation (9) (reference 8) for the effective critical current density J¢ of a film with Bi-free needle-like crystals, the following can be obtained
p:c,>l
v* = L ~ J
(8)
LJdT~3)J
Substituting Equation (8) in (1) and rearranging, the following is obtained '
To--~= ] - [L-~o J
LJ~-~J
LJ~(~)J
J
(9)
Equation (9) can be computed iteratively for T* = Tc31Tco for any given value of V* = V~i,-~t/Vo,J* = J/Jc(O), m, k, and defect size (L¢ or XL), orientation (/3) and location (Yo). Figure 4a shows a plot of T*(x*)/T*(0) = [Tc3(X*)/ Tco]/[T~3(O)/T~o] as a function of crystal size parameter (size and orientation) x* = (XL/W)tan/3with m as parameter, k = 29, V* = 0.01, J* = 0.001 and y* = yo/w = 0.1. T*(x*)/T*(0) represents the critical temperature parameter with needlelike defects [Tca(X*)/Tj normalized to that without crystals [T~3(O)/Tco). [T~3(O)/T~o] is identical to Tc2/T~o. Thus T*(x*)/T*(0) gives the fractional change in T~ with the addition of the crystals in the film. As x* increases or the crystal size and/or orientation with respect to the net current flow direction increases, the Tc decreases. In the presence of x* = 0.8 crystals, this additional decrease in T~ varies from 0.5% for SIS type films (m = 1) to 2% for SNS type films (m = 2). For small x*, the additional decrease in the Tc is negligible. Figure 4b shows the corresponding variation of Jr as a function of x* which is described by Equation (9) (reference 8). The figure shows a substantial decrease in Jr as x* increases. This decrease increases with the value of the exponent m. For large crystals this decrease can be as much as 50%. The decrease in Jc is directly reflected in the change in T¢ shown in Figure 4a. It was shown in reference 8 that the location of the crystal, y* = yo/W, is relatively insensitive to J¢. The maximum value of x* is dictated by the value of y*. Referring to Figure lc, it can be shown by simple trigonometry that X*m~, = I--y*. In this paper, y* = yolw = 0.1 is used as the crystal location parameter in order to show the Tc effect for a wide range of x*. Figure 4c shows a plot of T*(x*)/T*(0) as a function of x* with k as a parameter, m = 1.5, V* = 0.01, J* = 0.001 and y* = 0.1. Although the T~ decreases, it is not very sensitive to the quality of the superconductor as indicated by the value of the exponent n or k. Although at low temperatures n has a significant effect on determining the quality, close to T~ the exponent takes on small values, as seen in the inset of Figure 3b. Figure 4d shows a plot of T*(x*)/T*(0) as a function of x* with V* as a parameter, m = 1.5, k = 29, J* = 0.001 and y* = 0.1. The effect of V* is similar to that shown in Figure 3c, indicating that the more accurate the measurements in terms of Vlimit, the greater will be the decrease in T~. Small crystals are insensitive to the accuracy of the measurements and will not show any further decrease in To, whereas large crystals will.
Effect of current on transport critical temperature: S. Pate/ i
i
i
1.01 t" u
"~
0.990
"*
k=29
'~
V*---0.01
0.980 0.975 0.0
~t
\
,,;~_~..1001 ~ 0.2
,.,=
~= 2.0 '
'
0.4
'
0.6
0.9 0.8
1.5
t0.985
(b)
0.8
0.7
m l.O
0.6
v.=0.0: 0.5 0.4 0.0
1.0
~ b 1.5
J*=O.001 y*=0.1
\ b
' 0.2
' 0.4
X*
' 0.6
2.0
' 0.8
1.0
X*
i
1.000 I
1.0001
.
.
.
.
.
.
.
id)
.
v*
0.995 * [..,
0.1
0.995
~
o.~o0~
0.01
k
,It
0.990
V*=0.01 J*=O.O01 y*=O.1
0.985 0.0
~ . ~ 29 ~ b 19 ~n 9
i.
|
0.2
0.4
|
I
0.6
0.985
|
0.8
1.0
X*
0.980 0.0
k=29
~, 0.001
J*=O.O01 y*=O.1 . 0.2
.
. 0.4
.
0.6
0.8
1.0
X*
(0 t
o.oool
f
\
-ooo,
~ 0.9-/ 0.96[
~t2L5
0.95~
V:__~.~O1
0.04I oo
:,
02
,
\
, 04
,
o6
0.01
x"
,0
X*
Figure 4
(a) Variation of normalized critical temperature, T*(x*)/T*(0), with crystal parameter, x ~ = (XL/W)tan~ = (~/w)sin/3, and m as a parameter. (b) Variation of normalized effective critical current density, Je(x*,T*)/Jc(O,T*), with crystal parameter x ~, and m as a parameter. (c) Variation of T*(x*)/T*(0) with x ~, and k as a parameter. (d) Variation of T*(x*)/7~(0) with x~, and V* as a parameter. (e) Variation of T*(x*)/T*(0) with x*, and J* as a parameter
Figure 4e shows a plot of 7"*(x*)/T*(0) as a function of x* with J* as a parameter, m = 1.5, k = 29, V* = 0.01 and y* = 0.1. J* is the relative magnitude of the current used in the Tc measurement. Increasing J* decreases the To, particularly high J* values for films with large x* where the additional decrease in Tc due to the crystals can be as large as 5%. Small crystals are relatively insensitive to J* and its effect on Tc is insignificant. The above analysis can be extended to the entire Bi-2212 film consisting of Bi-free needle-like crystals. The formulation for the voltage drop across the film VF of length L
containing N identical crystals is given by Equation (13) (reference 8) and the effective critical current density by Equation (14) (reference 8). Equation (9) can be used to compute the decrease in Tc of such a film. Figure 5 shows a plot of T*(N*)/T*(N* = 0) as a function of N* = NXLIL with m and J* as parameters and k = 29, V* = 0.01, y* = 0.1 and x* = 0.8. For a given x*, in this case x* = 0.8, the T¢ decreases as the number of crystals per unit length (N/L) increases. In Figure 5, x* = 0.8 was chosen since large values of x* have the greatest effect on Tc (Figure 4). Large values of x* imply short or long crystals with high orien-
Cryogenics 1994 Volume 34, Number 11
951
Effect of current on transport critical temperature: S. Pate/
p-~.g.-~'*'¢-¢~4.~~ ~'~. ~"~ ~ 0.98 | "~'=t ~"~ ~._ "tt.
1.0 ~" 1.5 ~ 2.0 1.0
0.96
"0.
0.00f 0.001
0.001 0.01
@
[-,
[-,
~
0.94
k=29 V*=0.01 y*=O.1 x*=0.8
0.92 0.90
I
0"3
"4,
I
......
'
I0 "=
. . . . . . . .
"~
'a "~ 1.5 "~ "~'~ "~, "~
0.01
2.0
0.01
'
lO'l
. . . . . . . .
=
i0 o
. . . . . . . .
i
lOl
N* Figure5 Dependence of T*(N*)/T*(0) on crystal concentration, N* = Nx,/L, with m and J* as parameters tation angles or long crystals with relatively small orientation angles. When using J* = 0.001, increasing the concentration of these high x* value crystals has a negligible effect on T~. When using J* = 0.01, increasing the concentration of these crystals results in a significant degradation in To. Furthermore, SNS type films (m = 2) show a higher sensitivity to concentration than SIS type films (m = 1). Equation (9) can be used to compute the additional decrease in T¢ with concentration for smaller values of x*. However, it was shown in reference 8 that there is little degradation in the J~ of films consisting of a high concentration of small crystals. It was also mentioned earlier that the decrease in Jo directly reflects the change in T~ (Figures 4a and b). Hence crystals with low values of x* (short defects and/or low orientation angles with respect to the current flow direction) with high concentrations will have a negligible effect on To.
Conclusions The effect of Bi-free needle-like crystal length, orientation and concentration in Bi-2212 films on the transport critical temperature was theoretically investigated. The effect of finite d.c. currents used in the four point transport measurements of superconducting films without crystals was also investigated. It was shown that finite currents (J*) and the accuracy of measurements (V*) can result in a T~ several
952 Cryogenics 1994 Volume 34, Number 11
per cent lower than the true critical temperature obtained using an infinitesimal current. Large d.c. currents and better accuracy in the voltage measurement will result in much lower Tc values than small d.c. currents and low accuracy voltage measurements. Films consisting of SNS type grain boundary junctions (m = 2) will show a lower Tc than SIS type junctions (m = 1) for similar d.c. currents. This degradation in the measured T¢ due to using finite currents is made larger by the presence of the Bi-free needle-like crystals. The degree of degradation in Tc is directly related to the degradation in J~ of the film due to the crystals, Short crystals with a small orientation with respect to the net current flow direction will show little effect on To, whereas long crystals can give a significant decrease in To, especially when using large measurement currents. High concentrations of small crystals (small x*) have relatively little effect on To, whereas small concentrations of large crystals (large x*) will lower the To. The additional decrease in T~ due to the crystals is typically between 0 and 2%. Although relatively insignificant, the effect can be a noticeable factor during process optimization.
References 1 Ray II, R.D. and Hellstrom, E.E. Physica C (1991) 175 255 2 Danusantoso, J. and Chald, T.K. AIP Conf Proc Vol 251: Superconductivity and its Applications (Eds Kao, Y.H., Coppens, P. and Kwok, H.S.) (1991) 345-356 3 Haugan, T., Ye, J., Chen, S., Li, S.S. etM. AlP ConfProc Vo1273: Superconductivity and its Applications (Eds Kwok, H.S., Shaw, D.T. and Naughton, MJ.) (1993) 609-615 4 Feng, Y., Hautanen, K.E., High, YJE., Larbalestier, D.C. et al. Physica C (1992) 192 293 5 Wu, C.T., Goretta, K.C., Lanagan, M.T., Biondo, A.C. et al. TMS Symp Proc: Processing of Long Lengths of Superconductors (Eds Balachandran, U., Collings,E.W. and Goyal, A.) (1993) 101-112 6 Heine, K., Tenbrink, J. and Thfiner, M. Appl Phys Lett (1989) 55 2441 7 Ye, J., Hwa, S., Patel, S. and Shaw, D.T. AlP ConfProc Vol 219: Superconductivity and its Applications (Eds Kao, Y.H., Coppens, P. and Kwok, H.S.) (1990) 524-530 8 Patti, S. Cryogenics (1994) 34 251 9 Goldschmidt, D. Phys Rev B (1989) 39 9139 10 Neuhans, W. and Winzer, K. Cryogenics (1992) 32 357 11 de Gennes, P.G. Rev Mod Phys (1904) 36 225 12 Ambegaokar, V. and Baratoff, A. Phys Rev Leu (1963) 10 486 and (1963) 11 104 13 Zhang, Q.Z., Takagi, Y., Atake, T. and Saito, Y. Physica C (1990) 169 451 14 Pradhan, A.K., Hazell, Sj., Hodby, J.W., Chen, C. et al. Solid State Commun (1992) 82 685
Keywords: high T© superconductors; critical temperature; Bi-2212
Non-superconducting Bi-free needle-like crystals having a phase of the type (Sr,_x,Cax)CuyOz [e.g. (Sr,Ca)ECuO3, (Sr,Ca)CuO2 and (Sr,Ca)14CUE404d are sometimes formed in Bi2SrECa~Cu208 (Bi-2212) superconducting thick films fabricated by the partial-melt-growth technique pioneered by Heine et al. 1-6. These crystals have a length of 10500 ~m and a width of 1-30/xm depending on the phase s,5. The size and concentration of these crystals are very sensitive to the precursor materials and processing heat treatment parameters. Microscopic examinations indicate that the cross-section of these crystals can traverse the entire film thickness. Films with fewer and smaller crystals generally have a high transport critical current density j4.7. The inclusion of these crystals in the superconducting film impedes the current flow through the film thus lowering its J~. The effect of crystal size and orientation on this degradation in Jc has been previously modelled8. Because of the finite currents used in the measurements of the transport critical temperature Tc this degradation in J~ can result in a lower To. The Tc of a superconductor is measured by the four point method. A small constant d.c. current I flows through the
0011-2275/94/110947-06 © 1994Butterworth-HeinemannLtd
conductor between the outer contacts, and the potential drop V is continuously measured across the inner contacts while the temperature T of the conductor is lowered gradually from room temperature. When V reaches the noise level of the instrument or a predetermined threshold V]i~t, typically 10-50 nV, the conductor is considered to be superconducting and the temperature at which this occurs is considered to be the zero resistance To. To determine the true transport critical temperature Too an infinitesimal current should be used in the four point measurement. This infinitesimal current will not drive the superconductor normal at Tco and the corresponding J¢ at T~o will be zero. Large currents will drive the superconductor normal at T¢o and will register a V larger than Vlimito Only by lowering T will V = V,n,t, resulting in a Tc that is lower than T¢o9. Large constant d.c. currents are generally used when the resistivity of the substrate is much lower than the resistivity of the superconducting material at room temperature. This is generally done so as to register a V at room temperature that is several orders of magnitude greater than Vlirnit. 7rhis enables the measurements to show accurately the details o f the resistance-temperature (R-T) characteristics. For
Cryogenics 1994 Volume 34, Number 11 947
Effect of current on transport critical temperature: S. Pate/ example, in the T~ measurement of Bi-2212 thick films on silver, a relatively large constant current of 0.1-0.5A is used to register 100-500/zV at room temperature, because the initial room temperature current flows through the low resistance silver [Psilver(300K) ~ /22212(300K)]. The R - T characteristics of these films are typically as follows: as the film is cooled from room temperature the R - T behaviour is that corresponding to silver. Near the onset of T~ the resistance of the film becomes comparable to that of silver and current sharing between silver and the film occurs. Further decrease in T results in a rapid drop in the resistance, wherein the film resistance becomes substantially smaller than that of silver. Further lowering of T results in the film going superconducting at To. During the entire test, the current is maintained constant. These large currents will result in a slightly lower T~ since these currents would exceed the J~ of the film at/'co which is zero. The presence of Bi-free needle-like crystals in the Bi2212 film will result in an additional decrease in Tc because of the finite currents used in the measurement. This paper presents a theoretical model of the effect of current on the T~ of Bi-2212 films with and without Bi-free needle-like crystals. The model is extended to see the effect of crystal size, orientation and concentration on To.
corresponding to Vlimitused to determine T~. Also assumed in the analysis is that the superconducting properties of the Bi-2212 grains between the Bi-free crystals are similar to those of the grains in a Bi-2212 film with no Bi-free crystals, and that no current sharing occurs between the Bi2212 film and the substrate at T<--Tco.The objective of the formulations is to determine the extent to which these crystals, assumed insulating, can degrade the T¢ when using a finite current in the four point electrical transport measurement. Figure 2 shows schematically the R - T (or equivalently, V - T at constant I) behaviour in the vicinity of Tc of a Bi2212 film with and without the Bi-free crystals. Curve 1 is that of a film with no Bi-free crystals, which is obtained using an infinitesimal current density AJ (or equivalently a small current A/). Curve 2 is that of the same film but using a current density J such that J>AJ. Curve 3 is that of a Bi-2212 film with Bi-free defects using a current density similar to that of curve 2. T~o,Tc2 and To3 are the critical temperatures corresponding to the three curves, respectively, and represent the temperatures at which V = Vlimi t. If AJ is used instead of J for curves 2 and 3, then T~o = T¢2 = To3. Also shown in Figure 2 is the variation of J¢ of the Bi-2212 film with no Bi-free defects. At any T below/'co there exists a J~ and the corresponding I - V characteristics can be described by the power law equation.
Formulations, results and discussion To simplify the formulations, the effect of a single needlelike crystal on the current flow is investigated. Figure la shows schematically the two-dimensional representation of a film consisting of randomly orientated Bi-free crystals having random lengths. Figure lb shows a simple model representation of the film of Figure la used for this study. The formulations of the potential drop across the projected length of the crystal and the current density distribution above and below the crystals are derived in reference 8 and will be used in this text. In the analysis, it is assumed that the current-voltage (l-V) characteristic of the superconducting film is described by the power law equation and that the power law equation is valid down to voltage levels
~/ \
"/
/
x
/
x /
Effect of current on transport critical temperature The following section describes the effect of current on the Tc of Bi-2212 superconducting films void of Bi-free needlelike crystals. Referring to Figure 2, curve 2, increasing the constant d.c. current will result in a decrease in the measured T¢2. The amount of decrease in T¢2 from /'co will depend on the J¢(T) characteristics of the superconductor described by the following expression J¢(T) = J¢(0) 1 -
L
(1)
where J~(O) is the characteristic transport critical current density at T = 0. For T < 0.9Too the exponent m is ~ 1 and for 0.9Too < T < /'co, m varies typically between 1 and 2,
/ V orR)
=l
T~T¢o
®®
@
==
(a)
(b)
y
.¢ I
Vlimit
Yo
I 0
,-I~X XL
(c)
Figure 1 Schematic representation of: (a) Bi-2212 film showing Bi-free needleTlike crystals; (b) model representation of film shown in (a); and (c) the co-ordinate system
948
Cryogenics 1994 Volume 34, Number 11
xo3
Too
~ T
Figure2 R - T (or V-T at constant I) behaviour in the vicinity of To. Curves 1 and 2 represent the R - T b e h a v i o u r of a Bi-2212 film without the crystals and curve 3 that with crystals. Curve 1 represents the true R- Tbehaviour using an infinitesimally small current density AJ. Curves 2 and 3 represent the R-Tbehaviour using a current density J > AJ. Too, T¢2 and Tea are the critical temperatures corresponding to the three curves
Effect of current on transport critical temperature: S. Pate/ depending on the properties of the superconducting grains and the type of junctions (SNS, SiS, SNINS, etc.) generated between the adjoining grains ]°. For SNS junctions m = 2 and for SIS junctions m = 1 ll'12. For more complex junctions, such as SNINS, m takes on intermediate values 13. At T
-
F,
~
- LZ4T)J
[j _l
(2)
1.00
(a) in
= LJo(T)J
where: V is the potential drop across the voltage taps separated by a distance L and Vo is the value of voltage (or equivalently Eo = Vo/L is the value of electric field) used to define J~. The exponent n is a function of T whose value increases with decreasing T. The dependence of magnetic field on the exponent n is not addressed in this paper, although the same methodology can be applied. The exponent n is indicative of the quality of the superconductor, especially at temperatures well below Too where n is typically between 10 and 30. At temperatures near T~o, n 1, indicating a near ohmic dependence between current and voltage. For single crystal Bi-2212 the dependence of n on T is linear except in close proximity to T¢oTM. However, assuming linearity to T~o, this dependence can be described by the following expression n=l+k
Figure 3a shows the effect of J* on T* with m as a parameter, k = 29 and V* = 0.01. Increasing J* decreases T*. Also, for a given J*, T* decreases with increasing m. As mentioned earlier, m = 2 represents SNS type junctions and m = 1 represents SIS type junctions. Thus, conductors having SNS type junctions will measure a smaller Tc than conductors having SIS type junctions for similar d.c. currents. 7"* is relatively insensitive to small d.c. currents (J* < 10-4) when m = 1, and very sensitive to relatively large
1-
0.95 [-
\ 0.90
k=29, V*--O.O1
0.85 ......... 10-5
J*
1.00
.................
where k is a constant. The current I (or equivalently J) in Equation (2) represents the constant d.c. current used in the four point method. During the cool-down process, V will equal V,~t at T = Tc2, such that equation (2) will become
. . . . . . . . . .
F, 0.90
0.S$
Vo
[ -
J
,
(3) 0.95
V.~t
i0 "4
0.90
L~J
1.00
-
0.85
(4)
[j--~j
j
10 -4
-
t --
10"=
tO -s
j~t
1,00
(5)
Equation (5) represents the dependence of the measured To, namely To2, normalized with respect to T¢o, on the magnitude of the measuring d.c. current density. The ratio V* = Vli,~tlVo represents the relative accuracy to which measurements of T~ and J~ are made. J* = J/Jc(O) is indicative of the magnitude of the current used in the Tc measurement. For thick films on conducting substrates, such as Bi-2212 on Ag, the d.c. current used for measurement is typically 0.1-0.5 A and the critical current at 4.2 K is typically 100 A, depending on the quality and dimensions of the conductor. J* [or IlljO) .-~ I/Ic (4.2 K)] for such films will have a typical value in the 10-3-10 --2 range. For high quality superconducting thin films on single crystal substrates such as MgO, J* can be much smaller. T* = Tc2/Tco can be evaluated iteratively using Equation (3) with T = TeE and Equation (5) for any given J*, V*, k and m.
-
10-s
Substituting Equation (4) in (1) and rearranging, the following is obtained
T~---~= 1 - [[--~-o ]
0.95
v
]"(r~2)
0.95 @
[-
0.1 " 0.90
k=29, m=1.5 0.85
. . . . . . . .
104
|
. . . . . . . .
10 4
i
. . . . . . .
I0 "3
10 "2
J* Figure 3
(a) Variation of normalized critical temperature, T* = J/Jc(O), and m as a parameter. (b) Variation of 7-* = Tc=ITcowith J* = J/J¢(O), and k as a parameter. Inset shows v a r i a t i o n o f e x p o n e n t n w i t h T*. T~2/Tco, w i t h n o r m a l i z e d c u r r e n t density, J * =
(c) V a r i a t i o n o f 7"* =
Tc2/Tcow i t h
J* =
J/Jc(O), and
V* =
Vm~JVo
as a p a r a m e t e r
Cryogenics
1994 Volume
34, Number
11
949
Effect of current on transport critical temperature: S. Pate/ d.c. currents (J* > 10-3) particularly for m = 2, reducing the value of T* by 15%. For more complex type intergranular junctions T* will have intermediate values. Figure 3b shows the effect of J* on T* with k as a parameter, m = 1.5 and V* = 0.01. The inset in Figure 3b shows the variation of n with T* for several values of k. At T = T¢o the I - V behaviour is ohmic (n = 1), becoming nonohmic (n > 1) as T* decreases. The higher the value of n, the better the quality of the superconductor is and the closer the measured T~ will be to T¢o for a fixed d.c. current. Figure 3c shows the effect of J* on T* with V* as a parameter, m = 1.5 and k = 29. V* is indicative of the accuracy with which the measurements are made. The smaller the value of V*, the more accurate the measurements will be. Figure 3c shows that for a given J*, the more accurate the measurement (reducing V~m~t)the greater the decrease in T* is. Thus by reducing the accuracy, 7"* of a superconductor can be artificially improved, making 7"* closer to unity.
Effect of needle-like defects on transport critical temperature The above formulations showed the effect of the d.c. current on the measured T~ of a superconductor without the Bi-free needle-like crystals. This effect is made larger by the presence of such crystals in the Bi-2212 films. Referring to Figures 1 and 2 and the formulations given in reference 8, the voltage drop across a projected length XL of the crystal in a Bi-2212 film with and without Bifree needle-like crystals is given by Equations (6a) and (6b), respectively Yo [~1 V3(T) = EoALtan/3-i-i-n)
LJ~-~J°
T < r¢o
(6a)
V2(T) = EoXL
T < T~o
(6b)
where A L = ( l+xLtan/3]l-n-lyo J Jc(T) is the transport critical current density at a temperature T of the Bi-2212 film void of any Bi-free needle-like crystals. JLo is the fraction of J that flows in the region below the crystal [Equation (8b), reference 8]. It was shown in reference 8 that the J~ of the film with Bi-free crystals is lower than that of films without such crystals. This implies that at any given T and operating J, the potential drop for the film with crystals, V3(T), will be greater than the potential drop for a film without crystals, V2(T). According to Equation (1), Jc increases as T is decreased below T~o. Referring to Equation (6a) and Figure 2 it can be seen that by lowering T and consequently increasing the J~, and for the same operating J, V3 can be decreased and made equal to V2(T). If V2 and V3 correspond to Vlimit, then the corresponding temperatures are the critical temperatures. In equation form this can be written as (refer to Figure 2) V*
-
950
Vlimit Vo
-
V2(Tc2) Vo
-
-
-
V3(Tc3) Vo
-
-
Cryogenics 1994 Volume 34, Number 11
(7)
where Vo = E o X L is the value of the potential drop used to determine J~ at any given T from the I - V curve. The third term in Equation (7) is that of a film with no crystals and is represented by Equation (4). The last term in Equation (7) is that of a film with the Bi-free crystals. Using Equations (6a) and (7), and Equation (9) (reference 8) for the effective critical current density J¢ of a film with Bi-free needle-like crystals, the following can be obtained
p:c,>l
v* = L ~ J
(8)
LJdT~3)J
Substituting Equation (8) in (1) and rearranging, the following is obtained '
To--~= ] - [L-~o J
LJ~-~J
LJ~(~)J
J
(9)
Equation (9) can be computed iteratively for T* = Tc31Tco for any given value of V* = V~i,-~t/Vo,J* = J/Jc(O), m, k, and defect size (L¢ or XL), orientation (/3) and location (Yo). Figure 4a shows a plot of T*(x*)/T*(0) = [Tc3(X*)/ Tco]/[T~3(O)/T~o] as a function of crystal size parameter (size and orientation) x* = (XL/W)tan/3with m as parameter, k = 29, V* = 0.01, J* = 0.001 and y* = yo/w = 0.1. T*(x*)/T*(0) represents the critical temperature parameter with needlelike defects [Tca(X*)/Tj normalized to that without crystals [T~3(O)/Tco). [T~3(O)/T~o] is identical to Tc2/T~o. Thus T*(x*)/T*(0) gives the fractional change in T~ with the addition of the crystals in the film. As x* increases or the crystal size and/or orientation with respect to the net current flow direction increases, the Tc decreases. In the presence of x* = 0.8 crystals, this additional decrease in T~ varies from 0.5% for SIS type films (m = 1) to 2% for SNS type films (m = 2). For small x*, the additional decrease in the Tc is negligible. Figure 4b shows the corresponding variation of Jr as a function of x* which is described by Equation (9) (reference 8). The figure shows a substantial decrease in Jr as x* increases. This decrease increases with the value of the exponent m. For large crystals this decrease can be as much as 50%. The decrease in Jc is directly reflected in the change in T¢ shown in Figure 4a. It was shown in reference 8 that the location of the crystal, y* = yo/W, is relatively insensitive to J¢. The maximum value of x* is dictated by the value of y*. Referring to Figure lc, it can be shown by simple trigonometry that X*m~, = I--y*. In this paper, y* = yolw = 0.1 is used as the crystal location parameter in order to show the Tc effect for a wide range of x*. Figure 4c shows a plot of T*(x*)/T*(0) as a function of x* with k as a parameter, m = 1.5, V* = 0.01, J* = 0.001 and y* = 0.1. Although the T~ decreases, it is not very sensitive to the quality of the superconductor as indicated by the value of the exponent n or k. Although at low temperatures n has a significant effect on determining the quality, close to T~ the exponent takes on small values, as seen in the inset of Figure 3b. Figure 4d shows a plot of T*(x*)/T*(0) as a function of x* with V* as a parameter, m = 1.5, k = 29, J* = 0.001 and y* = 0.1. The effect of V* is similar to that shown in Figure 3c, indicating that the more accurate the measurements in terms of Vlimit, the greater will be the decrease in T~. Small crystals are insensitive to the accuracy of the measurements and will not show any further decrease in To, whereas large crystals will.
Effect of current on transport critical temperature: S. Pate/ i
i
i
1.01 t" u
"~
0.990
"*
k=29
'~
V*---0.01
0.980 0.975 0.0
~t
\
,,;~_~..1001 ~ 0.2
,.,=
~= 2.0 '
'
0.4
'
0.6
0.9 0.8
1.5
t0.985
(b)
0.8
0.7
m l.O
0.6
v.=0.0: 0.5 0.4 0.0
1.0
~ b 1.5
J*=O.001 y*=0.1
\ b
' 0.2
' 0.4
X*
' 0.6
2.0
' 0.8
1.0
X*
i
1.000 I
1.0001
.
.
.
.
.
.
.
id)
.
v*
0.995 * [..,
0.1
0.995
~
o.~o0~
0.01
k
,It
0.990
V*=0.01 J*=O.O01 y*=O.1
0.985 0.0
~ . ~ 29 ~ b 19 ~n 9
i.
|
0.2
0.4
|
I
0.6
0.985
|
0.8
1.0
X*
0.980 0.0
k=29
~, 0.001
J*=O.O01 y*=O.1 . 0.2
.
. 0.4
.
0.6
0.8
1.0
X*
(0 t
o.oool
f
\
-ooo,
~ 0.9-/ 0.96[
~t2L5
0.95~
V:__~.~O1
0.04I oo
:,
02
,
\
, 04
,
o6
0.01
x"
,0
X*
Figure 4
(a) Variation of normalized critical temperature, T*(x*)/T*(0), with crystal parameter, x ~ = (XL/W)tan~ = (~/w)sin/3, and m as a parameter. (b) Variation of normalized effective critical current density, Je(x*,T*)/Jc(O,T*), with crystal parameter x ~, and m as a parameter. (c) Variation of T*(x*)/T*(0) with x ~, and k as a parameter. (d) Variation of T*(x*)/7~(0) with x~, and V* as a parameter. (e) Variation of T*(x*)/T*(0) with x*, and J* as a parameter
Figure 4e shows a plot of 7"*(x*)/T*(0) as a function of x* with J* as a parameter, m = 1.5, k = 29, V* = 0.01 and y* = 0.1. J* is the relative magnitude of the current used in the Tc measurement. Increasing J* decreases the To, particularly high J* values for films with large x* where the additional decrease in Tc due to the crystals can be as large as 5%. Small crystals are relatively insensitive to J* and its effect on Tc is insignificant. The above analysis can be extended to the entire Bi-2212 film consisting of Bi-free needle-like crystals. The formulation for the voltage drop across the film VF of length L
containing N identical crystals is given by Equation (13) (reference 8) and the effective critical current density by Equation (14) (reference 8). Equation (9) can be used to compute the decrease in Tc of such a film. Figure 5 shows a plot of T*(N*)/T*(N* = 0) as a function of N* = NXLIL with m and J* as parameters and k = 29, V* = 0.01, y* = 0.1 and x* = 0.8. For a given x*, in this case x* = 0.8, the T¢ decreases as the number of crystals per unit length (N/L) increases. In Figure 5, x* = 0.8 was chosen since large values of x* have the greatest effect on Tc (Figure 4). Large values of x* imply short or long crystals with high orien-
Cryogenics 1994 Volume 34, Number 11
951
Effect of current on transport critical temperature: S. Pate/
p-~.g.-~'*'¢-¢~4.~~ ~'~. ~"~ ~ 0.98 | "~'=t ~"~ ~._ "tt.
1.0 ~" 1.5 ~ 2.0 1.0
0.96
"0.
0.00f 0.001
0.001 0.01
@
[-,
[-,
~
0.94
k=29 V*=0.01 y*=O.1 x*=0.8
0.92 0.90
I
0"3
"4,
I
......
'
I0 "=
. . . . . . . .
"~
'a "~ 1.5 "~ "~'~ "~, "~
0.01
2.0
0.01
'
lO'l
. . . . . . . .
=
i0 o
. . . . . . . .
i
lOl
N* Figure5 Dependence of T*(N*)/T*(0) on crystal concentration, N* = Nx,/L, with m and J* as parameters tation angles or long crystals with relatively small orientation angles. When using J* = 0.001, increasing the concentration of these high x* value crystals has a negligible effect on T~. When using J* = 0.01, increasing the concentration of these crystals results in a significant degradation in To. Furthermore, SNS type films (m = 2) show a higher sensitivity to concentration than SIS type films (m = 1). Equation (9) can be used to compute the additional decrease in T¢ with concentration for smaller values of x*. However, it was shown in reference 8 that there is little degradation in the J~ of films consisting of a high concentration of small crystals. It was also mentioned earlier that the decrease in Jo directly reflects the change in T~ (Figures 4a and b). Hence crystals with low values of x* (short defects and/or low orientation angles with respect to the current flow direction) with high concentrations will have a negligible effect on To.
Conclusions The effect of Bi-free needle-like crystal length, orientation and concentration in Bi-2212 films on the transport critical temperature was theoretically investigated. The effect of finite d.c. currents used in the four point transport measurements of superconducting films without crystals was also investigated. It was shown that finite currents (J*) and the accuracy of measurements (V*) can result in a T~ several
952 Cryogenics 1994 Volume 34, Number 11
per cent lower than the true critical temperature obtained using an infinitesimal current. Large d.c. currents and better accuracy in the voltage measurement will result in much lower Tc values than small d.c. currents and low accuracy voltage measurements. Films consisting of SNS type grain boundary junctions (m = 2) will show a lower Tc than SIS type junctions (m = 1) for similar d.c. currents. This degradation in the measured T¢ due to using finite currents is made larger by the presence of the Bi-free needle-like crystals. The degree of degradation in Tc is directly related to the degradation in J~ of the film due to the crystals, Short crystals with a small orientation with respect to the net current flow direction will show little effect on To, whereas long crystals can give a significant decrease in To, especially when using large measurement currents. High concentrations of small crystals (small x*) have relatively little effect on To, whereas small concentrations of large crystals (large x*) will lower the To. The additional decrease in T~ due to the crystals is typically between 0 and 2%. Although relatively insignificant, the effect can be a noticeable factor during process optimization.
References 1 Ray II, R.D. and Hellstrom, E.E. Physica C (1991) 175 255 2 Danusantoso, J. and Chald, T.K. AIP Conf Proc Vol 251: Superconductivity and its Applications (Eds Kao, Y.H., Coppens, P. and Kwok, H.S.) (1991) 345-356 3 Haugan, T., Ye, J., Chen, S., Li, S.S. etM. AlP ConfProc Vo1273: Superconductivity and its Applications (Eds Kwok, H.S., Shaw, D.T. and Naughton, MJ.) (1993) 609-615 4 Feng, Y., Hautanen, K.E., High, YJE., Larbalestier, D.C. et al. Physica C (1992) 192 293 5 Wu, C.T., Goretta, K.C., Lanagan, M.T., Biondo, A.C. et al. TMS Symp Proc: Processing of Long Lengths of Superconductors (Eds Balachandran, U., Collings,E.W. and Goyal, A.) (1993) 101-112 6 Heine, K., Tenbrink, J. and Thfiner, M. Appl Phys Lett (1989) 55 2441 7 Ye, J., Hwa, S., Patel, S. and Shaw, D.T. AlP ConfProc Vol 219: Superconductivity and its Applications (Eds Kao, Y.H., Coppens, P. and Kwok, H.S.) (1990) 524-530 8 Patti, S. Cryogenics (1994) 34 251 9 Goldschmidt, D. Phys Rev B (1989) 39 9139 10 Neuhans, W. and Winzer, K. Cryogenics (1992) 32 357 11 de Gennes, P.G. Rev Mod Phys (1904) 36 225 12 Ambegaokar, V. and Baratoff, A. Phys Rev Leu (1963) 10 486 and (1963) 11 104 13 Zhang, Q.Z., Takagi, Y., Atake, T. and Saito, Y. Physica C (1990) 169 451 14 Pradhan, A.K., Hazell, Sj., Hodby, J.W., Chen, C. et al. Solid State Commun (1992) 82 685