ICEC 15 Proceedings

New Method For Measuring Pinning Strength Inside Grains of HTCS Ceramics

Dang An +, Godelaine P-A + and Ausloos M*.

+ Mesures et Instrumentation, lnstitut Montefiore B28, University of Liege, Sart Tilman, B4000 Liege. * Physique du solide, Institut de Physique B5, University of Liege, Sart Tilman, B4000 Liege, Belgium.

We have designed a new setup and analysis route based on the Campbell's method for measuring the critical current in superconductors. Our model takes consideration of the ceramics granular nature, the existence of intergrain and intragrain currents. We obtain the variation of the pinning strength Pv as a function of pg, which is the radial position inside an average grain. We apply this scheme to Bil.7Pb0.3Sr2Ca2Cu3Ol0-y ceramics synthesized by a vitreous route. The intragrain critical current is 105A/cm 2 at 40K with zero DC magnetic field. Some important increase of the pinning strength is observed near the grain surface.

INTRODUCTION

In this communication, we present the latest results of the SUPRAS group in critical current measurements. It is important to increase the critical current of bulk Bil.7Pb0.3Sr2Ca2Cu3010-y, for many practical

applications. In effect, the pinning strength of BSCO is relatively low. This is mainly due to the lack of pinning centers in the bulk of the grains.

To reach this goal, we decided to use a material prepared by a so-called "glass route" [ 1]. Then, we tested the result by measuring the internal pinning strength inside the grain by a modified

Campbell's method.

CAMPBELL'S METHOD AND CERAMICS MODEL

We let a sample in a magnetic field composed of a de component and a small alternating superimposed signal.

We define the penetration depth p as the difference between the radius R of a homogeneous cylindrical sample and the position reached by the magnetic flux in the sample. This penetration is easily obtained by considering the flux modification as a function of the magnitude of the ac field fowing along the sample axis. We obtain the so-called Campbell's formula [3].

P - - 1 - 1 dhac R - 2 =l~ oR 2 ( 1 )

Ssupra is the signal measured and bac the magnitude of the applied ac field. The inverse graph hac(P) is known as the "flux profile".

To take into account the granular nature of the ceramics, we formulate a special model [2]. We observe that for a ceramics sample, the flux profile has a structure like a knee. With that flux profile, we can find both the critical current in the grains, Jcg, and the critical current in the weak links, Jcj.

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(dhac'~ R :c,= o - p ' /R) c2)

where p* is the intersection of the straight line fitted to the high hae(p) data values with the hae = 0 axis and

dha____~c l p* ( 2 _ L R ) J0-- R (3)

obtained from the small hac region. Furthemore, we are able to obtain fg, the grain superconducting fraction,

fg= (l -~'R*) 2 (4,

It 's important to note that it is possible to extract the flux profile inside the grains from the global flux profile. In other words, without crushing the sample, we can measure the penetration of the magnetic flux inside the grains. Hence , we can calculate the critical current of the grains as a function of the distance pg inside the grain.

1 - e / R (5) pg/Rg = 1 - 1 - p*/R

RESULTS

The flux profile for the Bil.7Pb0.3Sr2Ca2Cu3010.y sample was taken at 40K. In this measurement the DC- field is perpendicular to the at-field which is along the axis of the sample. The flux is measured with a small coil surrounding the sample and with a lock-in amplifier. In figure 1, la0hae is the magnitude of the at-field which is at most 3mT and p is the penetration depth inside the sample of radius R. We show four flux profiles with four DC-field ranging from 0 to 0.3 T. The knee structure is well seen. The slope in the low field region is proportional to the critical current in the weak links, Jcj and the slope in the high field region is proportional to the critical current in the grains, Jeg. The weak link critical current is greater than 600 A/cm 2 at low DC-field and larger than 100 A/cm 2 at relatively large DC-field. The grain critical current is in the range between 104 and 5 104 A/cm 2.

We see a curvature of the flux prof'de in the grain region after the knee. By using formula (5), we can look at the grains region. We conclude that higher the DC-field is, higher the ae-field penetration occurs (fig. 2). The derivative of these curves is proportional to the critical current Jog. Figure 3 shows the result where Jog is replaced by Pv, the pinning strength which is related to Jog by,

/'v = Jcz B (6)

where B is the DC flux density. Pv increases when the DC-field increases. More interesting, we should notice the very large rise of Pv near the grain surface. We can argue that the increase is due to the presence of SrCaCuO3 near the grain surfaces (due to the synthesis process [1]). These particules may act directly or indirectly as pinning centers.

Figure 4 shows the inverse of the pinning strength versus pg. We see that it is almost a straight line. So we can fit the data with a linear function,

]/Pv = k p g + c. (7)

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ICEC 15 Proceedings

We obtain the value of k and c for the three DC-fields (Table 1).

Table 1 Coefficients of the linear fit. De-field (T) k (m2/N) c (m3/N) 0.04 2.89 10 .3 3.76 10 -10 0.1 1.18 10 .3 2.70 10 -10 0.3 5.30 10 4 8.90 10 -11

These values of k and c decrease when the DC-field increases. The inverse of a straight line is an hyperbolic curve. Figure 3 shows a fit of the data with these k and c parameters.

CONCLUSIONS

We have demonstrated that a modification of the Campbell's method for measuring Je allows us to obtain the pinning strength inside the grains of superconducting ceramics. We applied this technique to a sample of Bil.7Pb0.3Sr2Ca2Cu3010-y prepared by a "glass route". The reinforcement of the pinning strength near the surface of the grains is clearly observed. This is due to the presence of SrCaCuO3 crystalline phase near the grain boundaries.

REFERENCES

2

3

Cloots R., Stassen S., Rulmont A., Godelaine P.A., Diko P., Duvigneaud P.H. and Ausloos M., Crystallization process in Pb-free or Pb-doped Bi2-xPbxSr2Ca2Cu3010-y glass system, J. Crystal Growth (1994) 135 496-504. Godelaine P. and Ausloos M., Effects ofintergrain and intragrain currents on flux profile in granular superconducting ceramics, Solid. State Comm. (1990) 76 785-788. Campbell A.M., The response of pinned flux vortices to low frequency fields, J. Phys. C (1969) 2 1492-1501.

2.5 -

"G 2.0 - --.

_= 1.5 - 1.o - 0.5 - 0.o 0.1

::i:;'; K / / ,', ".3 T ~ I I ~

l l l i

C.2 '=.,'5 5.4 :.5 ; .e : .7 F/R

Figure 1 The flux-profile hac as a function of p/R which is the normalized penetration depth inside the sample for different magnetic D e fields 0, 0.04, 0.1 and 0.3T.

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ICEC 15 Proceedings

2.~

2.C

g

v C.C4 T n ,7.1 T

" , "z

& ..... "F

~ 1 I f I

..... 1,2 2.:2 7 ,~ ~ , ° ~ .

F ~r~ir ' ~rr,;

Figure 2 The flux-profile hac as a function of the penetration depth pg inside an average grain (diameter

10l.tm) for different magnetic DC fields 0.04, 0.1 and 0.3T

6 -X 10 +9

a~ , 0.04 T

z~ 0.1 T

,._., 4 a 0.3 T

~ E z

n

2

C I I I

0.0 1.0 2.0 3.0 Pg~in. (jJ, m )

Figure 3 The pinning strengtht inside an average grain for 0.04, 0.1 and 0.3T

T

z

~k. '~

4 - X I "

, " " 4 T

z~ " . I T

" : T

" )

/

/ /

P

f

___L__ 2 _ 2 _L . . . . . . . . . J

" ~ I " I .~7 L . 7 L . , -

Figure 4 The inverse of the pinning strength inside an average grain for 0.04, 0.1 and 0.3T

832 Cryogen ics 1994 Vol 34 ICEC S u p p l e m e n t