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RIAGNETIC SHIELDING BY SUF’ERCONDUCTING Y-Ba-Cu-O HOLLOW CYLINDERS
J. O. Willis, M. E. lv’lcHenry, M. P. Maley, and H. Sheinberg
Los Alamos National Laboratory, Los Alamos, NM 87545 USA
AMw.t
We have measured the magnetic field H’ at the center of
a hollow tube of sintered Y-Ba-Cu-O superconductor as a
function of applied field H, temperature, tube Ieng?h, and
tube wall thickness. The maximum field that can be
shielded H~h agrees with the value calculated from the
critical state mod using the measured critical current
density Jc. The maximum trapped field Htr in the tube upon
decreasing H to zero exceeds Hsh by
as much as a factor of
two, and large enhancements in Jc are observed in
decreasing field. These phenomena are identified with
intragranular flux pinning present only after H has
exceeded Hcl of the grains. Finite tube !ength does not
affect the Htr/Hsh ratio appreciably. Hsh depends
approximately on the square root of the wall thickness.
As a means of determining critical current density Jc
infe;mation on
a specimen in a contactless way, the “flux
tube” experiments of Kim et al.,1 first performed on
l’Jb-based superconductors in the 1960’s, is a classic
technique, A probe in the center of a hollow
superconducting tube measures the internal magnetic field
H’ as a function of the applied field H. The difference of
these values M = H’-H is attributed to supercurrent in ttlo
tube. In the critical state model, extremely useful for
analyzing such experiments, every region of a sample is
assumed to carry a critical currwt density determined only
by the local value of the magnetic field B in the sample. For
the case of the maximum shielcled field Hqh upon
increasing H from zgro for which H’ is zero, one obtains:
Hsh = k
W JC*COS(+,
(1)
where Hsh is in G, k =
0.4n G-cmA-l, w is tile wall thickness
in cm, JC* is the ave:age current density in Acre-2, and COS6?
is the opening half-angle of the tube. For a known
dependence of Jc on B, the internal field l{’ can be
calculated from (following Kim et al.):
k w = ‘i’ df3/Jc(B)
I
(2)
, 1+
T-he
gHHIJk)r, weak link nature2 of sintereci Y13a2Cu3(J/
(YI 23) might be expected to produce different features from
those commonly observed in the traditional hard type II
superconductors, and Cimberie et al.3 have reported new
phenomena in very short (diameter smaller than length)
cylinders. We report here on tube magnetization and
transport Jc measurements and attempt to interpret the data
in terms of a model that includes the granular aspects of
these new materials.
en~
Samples were prepared from commercial 4
YBa2Cu307 powder of average grain size 10 pm
cold-pressed to 50,000 psi (3.4 kbar) and then fired in
oxygen. The annealing cycle consists of a ramp to 9650C
at 2000 C/hour, holding at 9650C for 10 hours, cooling to
4000C at 250 C/hour, holding at 4000C for 20 hours, and
then cooling to room temperature at 250C/hour. The inside
diameter of the tube was bored out to 0.7 to 0.9 cm. Final
tube density was about 70°/0 of the theoretical 6.38 gcm-3.
The room temperature resistivity of this Ioaterial is about
2600 pfl-cm with a midpoint of 92 K, a 10 to 90% width of
2.5 K, and zero resistance near 89 K. dc susceptibility
measurements in a 100 Oe field showed a 93 K onset, a
74 K midpoint, and 95°/0 of 47r~ flux exclusion at 7 K. The
Meissner effect in 100 Oe was 24°/0 of 4XX at 7 K.
Magnetometer magnetization M vs. magnetic field H
loops were made at 7, 65, and 75 K. Hysteresis in these
data is indicative of intragranular critical currents. Values of
Jc determined using the Bean model,5 Jc = 15AM/R where
AMis the hysteresis in gauss, R is a typical parlicle size in
cm, and Jc is in Acre-2, are 1.8x106 at 7 K, 6.8x103 at 65 K,
and 3.4X1 03 at 75 K, all at H = O. Th9se values are similar
to those measured in single crystals6, although with a more
rapid fall off with increasing temperature.
The flux tube experiments were carried out using a
calibrated axial I +ali probe iri the ctrnier of ine noiiow
superconducting tube which is itself co~xial with a 2.5 cm
inner diameter by 10 or 15 cm long copper so{enold. The
Hall probe and tube wore both centered vertically wi!hin the
solenoid to t 1 mm. The external field H produced by the
solenoid was increased in steps with the Hall probe
determining the internal field H’ at each step. The field
range is ~. 1000 Oe, and the Hall probe resolution is
i 0.5 Oe. During the runs the experiment was irrtrnersed in
a bath of liquid N2 or liquid He to assure isothermal
conditions.
Transport critical current m[ asummen!s were made with
a short sample immersed in a cryogen and wi!h the cut rent
direction perpendicular to H. A 1 ~V criterion was used for
defining Jc; this corresponds to about 10 pV/cm or about
10-4 of the normal state resistance. Thq current is swept
and the voltage across the sample is monitored with a
nanovoltmeter. The contacts to the sample are made by
soldering Ag wires to plasma-sprayed Ag pads 0.2 cm in
diameter and n.01 cm thick. Contact resistivities are in the
10-8 Q-cm2 range and cause no observable joule heating.
Typical flux tube magnetization data are shown in Fig. 1
fo: a wbe of
0.9 cm inside diameler, 0.33 cm wall thickness,
and 5 cm long. The internal fie!d H’ remains iem up to an
applied field H equal to Hsh above which H’ climbs rapidly.
The value of Hsh for this tube is 28 Oe at 75 K,
corresponding to an average Jc of 69 Acre-2 using Eq. 1.
By using the measured transport JC(H) values, Eq. 2 can
be integrated and a value of 24 Oe is obtained, in
reasonable agreement with the directly measured Hsh. At
65 and 4 K Hsh and the magnitude of the hysteresis is
larger than at 75 K concomitant with increases in Jc at those
lower temperatures. The thickness dependence of Hsh is
roughly as ~w expected for a JC(H) that is proportional to
(H + HO)-l, where Ho is small, that is, a very rapid fall off of
Jc with H.
One remarkable feature of the data shown in Fig.
1 is tho
asymmetry in the shielding value Hsh and the larger
trapping field Htr upon reducing H from its maximum value
Hmax to 0. In addition, Htr monotonically increases with
Hmax. Figure 2 shows the ratio Ht+Hsh versus Hmax/H~h
for the same tuba as in Fig. 1. Clearly Ht+Hsh increases
and saturates at high Hmax to vaiues much greater than the
value of 1 expected from the ctitical state model,
We have considered several possible
exp!ma!ions for
this asymmetry. The first of these deals with finite length
corrections from the rnagngtic field distribution along the
tube. Because of the large field dependence of Jc,
demagnetizing effects might be expected to allow
significant flux penetration of the sample ends for H less
than or equal to H~h. To test this hypothesis, tubes of the
same wall thickness but different lengths with aspect ratios
(length to outside diameter) of 1.7 to 6,7 were meas~]red.
No qualitative differences were seen in the measurements.
i. e., both ils~l and I{tr are reduced for the shortor tl~bes, but
there always exists a large enhancement of t“{tr over tis~l
even for tubes with small demagnetizing factors (Iargo