Physica C 152 ( 1988) 247-250
North-Holland, Amsterdam
AC LOSSES AND CRITICAL CURRENT DENSITY OF SUF’ERCONDUCTING GdBa2Cuj0,_-x
M. CISZEK, J. OLEJNICZAK, E. TROJNAR, A.J. ZALESKI and J. KLAMUT
Institutefor Low Temperature and Structure Research, Polish Academy of Sciences, 53-529 Wroclaw, Prochnika Str. 95, Poland
A.J.M. ROOVERS and L.J.M. VAN DE KLUNDERT
University of Twente, Department ofApplied Physics, P.O. Box 217, 7500 AE Enschede, The Netherlands
Received 17 March 1988
Revised manuscript received 8 April 1988
Energy losses occurring in a cylindrical sample of Gd-Ba-Cu-0, subjected to an external AC magnetic field were examined.
The loss dependence on the amplitude of the magnetic induction exhibits two stages of flux penetration into the superconductor.
Critical current densitities for both stages of penetration were examined and an explanation for such behaviour is proposed.
Support for this point of view is obtained by measurements on pulverized sample material. All measurements were performed at
a temperature of 4.2 K and in absence of a background field.
Analysis of the data provides two critical current densities: an inter-granular critical current density at weak alternating mag-
netic fields and an intra-granular critical current density at higher magnetic fields. The intra-granular critical current density is at
least two orders of magnitude larger than the inter-granular one.
1. Introduction
The practical large-scale applications of high-T=
superconductors are strongly limited by the magni-
tude of the electrical current which can be lossless
transported through the material. The existing re-
sults concerning the critical current densities in
YBaZCu307 _-x samples are not too encouraging. The
critical current densities, obtained from critical cur-
rent measurements, are of the order of IO’ Am-‘,
which is at least two orders of magnitude too low for
practical applications. However, the critical current
derived from magnetization measurements proved
the potential applicability of the new superconduc-
tors [ l-5 1. The reason of this discrepancy between
the transport and magnetization J, values are most
probably weak links between the superconducting
regions in granular superconductors [ 6-91. The aim
of our experiments was too examine this phenome-
non and to estimate the values of the intrinsic and
extrinsic critical current densities.
2. Sample preparation
Superconducting specimens of Gd-Ba-Cu-0 were
prepared through the usual solid state reaction of fine
powders of pure Gd203, BaC03 and CuO. The mixed
powders were pressed into pellets and calcined for 8
hours at 940°C in air and then three times at 900°C
for 5 hours with intermediate grinding steps. Finally,
after pulverization, the powder was pressed into a
cylindrical rod of 5 mm in diameter and 11 mm in
length, at a pressure of approximately 11 kbar, and
heated at 900°C for several hours in a flowing
atmosphere.
The X-ray powder diffraction patterns indicated a
single phase orthorhombic-distorted structure, the
same as that of YBa2Cu307_-x samples. The resistive
transition, measured with a standard four-lead tech-
nique, had a midpoint of transition at 92.6 K and its
width was 2.4 K.
0921-4534/88/$03.50 0 Elsevier Science Publishers B.V.
( North-Holland Physics Publishing Division )
248 M. Ciszek et al. /AC Losses and critical current density of superconducting GdBaZCu307_,
3. AC loss measurements
3.1. Experimental technique
The sample, with a pick-up coil consisting of 100
turns of 20 pm copper wire wound directly on the
central part of the cylinder, was placed axially inside
a superconducting solenoid producing a sinusoidally
varying magnetic field.
For small amplitudes of the external magnetic in-
duction the losses were measured by means of a lock-
in amplifier technique. The hysteresis loops were
taken from the oscilloscope, where on the x and y
axis were plotted respectively the signals propor-
tional to the amplitude b, and the integrated voltage
from the pick-up coil.
For larger amplitudes of the applied field the losses
in the sample were determined using a computer-
controlled measuring system as previously described
in ref. [ lo]. The set-up was adjusted for the cylin-
drical shaped sample by replacing the installed pick-
up coil by one attached directly to the surface of the
sample.
3.2. Results
The dependence of the AC losses W on the am-
plitude of the alternating external magnetic induc-
tion b0 for the cylindrical shaped sample is shown in
fig. 1. The plot can be divided into three regions.
In the first one, the magnetic flux starts to pene-
trate into the sample, already for amplitudes b,, of
the order of 1 mT. The losses increase with approx-
imately the fourth power of the amplitude bO.
At a certain value of 15, the losses start to saturate
and remain nearly constant for some interval of the
amplitude of the magnetic induction. For this region
a frequency dependence of the losses can be noticed.
It means probably that eddy current losses, apart
from the hysteretic ones, play some role in the ma-
terial investigated.
In the third region of the plot in fig. 1, for the high-
est available values of b, in our experiment, the losses
are not dependent of the frequency, i.e. they are
purely hysteretic in nature. In this region the losses
exhibit a field dependence approximately as W- 62.
The hysteresis loops (O-b) for different values of
b. equal to 3, 7, 12, and 100 mT, observed on the
b. hT1
Fig. I. The dependence of AC losses of the cylindrical shaped
sample on the amplitude of the external magnetic induction for
different frequencies. The solid line with the slope n=4 corre-
sponds to calculations according to ref. [ 151 for cr= 1.1 x IO6
TAm-* and B,,=0.5 mT.
oscilloscope are presented in fig. 2. For low ampli-
tudes of the magnetic induction, the hysteresis loops
are typical for type-II superconductors. With in-
creasing b, the loop increases as well. However, from
a certain value of b. its enclosed area remains con-
stant. Further increase of the the amplitude b. does
not affect the area of the loops (the “plateau” region
in fig. 1); only straight line “tails” occur with steady
increasing length. From an amplitude of about 20
mT a further increase of the hysteresis loop area oc-
curs. This corresponds to the region where the losses
are proportional to the third power of the magnetic
field amplitude bo.
Figure 3 shows the result of the loss measurements
on pulverized GdBa2Cu307_-r The results coincide
with those of the cylindrical sample for large values
of the amplitude of the magnetic field b,, (the third
region in the plot of fig. 1). The “plateau” region
however has disappeared.
hf. Ciszek et al. /AC Losses and critical current density of superconducting GdBazCu30,_,
249
ba= 3 mT
Fig. 2. A set of magnetic hysteresis loops taken from an oscillo-
scope for different values of the amplitude of the external mag-
netic induction. The drawings are not in scale, 0 values are in
arbitrary units. The measurements are performed on the cylin-
drical shaped sample.
4. Discussion
From our point of view the existence of three dif-
ferent regions in the W(b,) dependence can be ex-
plained by assuming that the sample consists of grains
of material with high critical parameters intercon-
nected by weak links. When increasing the AC mag-
netic field amplitude bo, magnetic flux starts to
penetrate the weak links first. For small magnetic
field amplitudes the losses are proportional to the
fourth power of the amplitude of the magnetic field.
This can be explained by a strong field dependence
of the critical current density in the vicinity of zero
field. For amplitudes sufficiently high, the magnetic
field penetrates the weak links and drives them into
the normal state. It is seen as a “plateau” in fig. 1,
and as hysteresis loops with the same surface areas
but with longer “tails”. In this region the AC losses
are frequency dependent, which is characteristic for
normal metals. For higher amplitudes b. the AC
losses are connected with properties of the super-
conducting material inside the grains. For this region
I
IO2 :r
- ‘E
-5
IO’-=>
IO0 r
f
b. hT1
16" ’ ’ ’ ‘{ ’ ’ ’ ’ ’ ’ ’ L
1
10
100
Fig. 3. AC losses of pulverized GdBazCu,O,_, as a function of
the amplitude of an alternating magnetic field.
the magnetic field dependence of J, is rather weak
and its value is connected with flux pinning. Also for
this region the anisotropic properties of the material
within a grain may have a strong influence on the
critical current of the polycrystalline samples [ 6 1.
In the first region of the plot of fig. 1, the W( b,)
dependence can be described by using the Kim
model, in which the J,(B) dependence is written as
J, ( 1 B I ) = a ( B. + 1 B I). The value of the critical cur-
rent density can be estimated from the AC loss mea-
surements by fitting the parameters a! and B. using
the expressions derived by Foumet and Mailfert
[ 111. In ref. [ 111 loss calculations are presented us-
ing a slab model for different field dependences of
the critical current density. The best fit with the ex-
perimental data was obtained for the values
(Y= 1.1 X lo6 ATmm2 and L&=0.5 mT. The value of
the constant B,, supports our finding that the H,,
value is very low (it should be of the order of B.
[ 121) and that J, is very strongly field dependent.
The critical current density J, derived for these con-
stants equals about 2 x 10’ Amw2 for B= 0. The low
value of the constant Bo, equal to about 1 mT for a
250
M. Ciszek et al. /AC Losses and critical current density of superconducting GdBa2CuJ07_,
Y-Ba-Cu-0 compound, was also reported in ref.
[131.
For larger amplitudes of the applied magnetic field
the loss behaviour of the cylindrical shaped sample
corresponds to the one of the pulverized material.
Therefore it is plausible to assume that the magnet-
ization is dominated by shielding currents inside the
grains. If in the above-mentioned theory isolated
“grains” are considered the intra-granular critical
current density can be estimated. Calculation of the
critical current density from the loss measurements
requires that the size of the grains is known. From
our measurements the magnitude of the critical cur-
rent density is estimated to be 10’“-lO” AmW2, as-
suming a grain size in the order of micrometers [ 14 1.
For instance, assuming a grain size of 10 pm yields
a good fit for @=5x 10” ATme and Bo=0.5 T in
the third region of the plot in fig. 1.
5. Conclusions
The results of our experiments show a difference
between the intrinsic and extrinsic critical current
densities of at least two orders of magnitude. From
our explanation it is seen that to obtain larger ex-
trinsic critical current densities it is necessary to im-
prove the preparation technique in order to avoid
weak links between the grains and improve the con-
tacts between them. Therefore a further study to the
origin of those weak links is necessary.
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