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Comparison of the critical current density of a polycrystalline
MgB2 superconductor by ac-
susceptibility and Bean's model
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IOP PUBLISHING PHYSICA SCRIPTA
Phys. Scr. 84 (2011) 065701 (5pp)
doi:10.1088/0031-8949/84/06/065701
Comparison of the critical current densityof a polycrystalline
MgB2 superconductorby ac-susceptibility and Beans modelIntikhab A
Ansari, M Shahabuddin and Nasser Saleh AlzayedDepartment of Physics
and Astronomy, College of Science, PO Box 2455, King Saud
University,Riyadh-11451, Saudi Arabia
E-mail: [email protected]
Received 1 March 2011Accepted for publication 12 October
2011Published 8 November 2011Online at
stacks.iop.org/PhysScr/84/065701
AbstractIn this paper, the critical current density measured
from the real part of ac-susceptibility is inagreement with that
calculated from Beans formula at constant frequency ( f = 98 Hz) in
thetemperature range 3038 K for a pure MgB2 sample. The temperature
dependence of theimaginary part of ac-susceptibility ( T ) shows
the shifts in absorption peaks towards thelower temperature when
the applied field is increased. Scanning electron microscopy
imagesconfirmed the synthesis of a good sample and agglomerates
with fine grains.
PACS numbers: 74.25.Ld, 74.70.Xa, 75.30.Cr
(Some figures in this article are in colour only in the
electronic version.)
1. Introduction
Since the discovery of the MgB2 superconductor [1], a greatdeal
of effort has been made to improve its superconductingproperties
[25]. In addition to a high transition temperatureTc, other
parameters such as critical current density athigher fields Jc(H)
and irreversibility field Hirr are importantfactors for MgB2 that
make it a promising material forindustrial applications. Jc can be
determined from both theintra-granular pinning and the
inter-granular connectivity.
A great number of reports demonstrate that a
stronginter-granular current network is found in a MgB2sample [69].
In the case of magnetization measurements ofgrain agglomerates,
Bugoslavsky et al [6] have revealed thatwithin these microscopic
structures, inter- and intra-grainJcs are equivalent in value.
Additionally, other reports [8, 9]elucidate that high
superconducting homogeneity and stronginter-granular current flow
were present in high-densitysamples, as determined by
magneto-optical studies. Eventhough the Jc of pure MgB2 drops
abruptly in high magneticfields due to weak pinning centres as can
be seen in moststudies [10], measuring the Jc with varying
amplitude ofapplied field is important for practical applications.
A limitednumber of reports are available for the determination ofJc
with varying amplitude of applied field Ba for other
superconductors [1113]. However, no experimental resultson Jc as
a function of temperature T with varying Ba in MgB2have been
reported yet. Therefore, it is necessary to enhancethe grain
connectivity to improve the field dependence ofJc [14].
In this paper, a homemade ac susceptometer was used todetermine
the real and imaginary parts of ac-susceptibility asa function of
temperature for a pure MgB2 superconductorwith varying amplitude of
ac-applied field. Furthermore, wehave determined and compared the
result of the critical currentdensity Jc as a function of reduced
temperature derived fromthe real and imaginary parts of
ac-susceptibility and Beansformula. We have found that the Tc of
the MgB2 sampleremains at 37 K, while the inter-grain Jcs are
greatly improvedby applying the ac applied field. The loss peaks
observed inthe imaginary part of the ac-susceptibility curves refer
to thecoupling between neighboring grains (inter-grain behavior)and
are shifted to the lower temperature region on increasingthe ac
applied magnetic field. These particular peaks show themaximum
hysteresis loss due to inter-grain motion of vortices.The x-ray
diffraction (XRD) pattern shows the confirmationof MgO impurity.
The complete ac-susceptibility experimentwas done at a constant
frequency of f = 98 Hz in thetemperature range 3038 K.
0031-8949/11/065701+05$33.00 Printed in the UK & the USA 1
2011 The Royal Swedish Academy of Sciences
-
Phys. Scr. 84 (2011) 065701 I A Ansari et al
20 30 40 50 60 700
20
40
60
80
100
120
*
* MgO# Mg
# (111)(10
2)(11
0)
(002)
(101)
(100)
(001)
Pure MgB2
Inte
nsity
(a. u
.)
2 (degree)
Figure 1. XRD pattern of a pure MgB2 superconductor.
2. Experimental details
The synthesis of pure MgB2 was done by the solid statereaction
method with the help of Mg and amorphous Bpowders (purity is
greater than 99%). The stoichiometricratios of these materials were
mixed well and ground bythe ball milling method. Furthermore, the
mixed powderwas turned into pellets using a 10 ton hydraulic
press.In addition, the sample was slab-shaped with dimensions10 mm
10 mm 2 mm. These pellets were encapsulated inan Fe tube and kept
at high vacuum up to 105 torr. Finally,sintering was carried out in
the furnace up to 750 C. After 3 h,the furnace was switched off and
we found a polycrystallineand porous compound of pristine MgB2.
The room temperature XRD patterns of the MgB2sample were
recorded within the 2 = 2070 range usingCu K radiation. A homemade
ac susceptometer was usedfor the measurement of real and imaginary
components ofac susceptibility as a function of temperature for a
pureMgB2 superconductor with varying amplitude of ac-appliedfield.
We have cut the parent sample in slab form withdimensions 10 mm 3
mm 2 mm for the measurement ofac susceptibility. The grain
morphologies and microstructureswere studied by scanning electron
microscopy (SEM) with aJEOL JSM-6360.
3. Results and discussion
XRD of the samples was carried out using Cu K radiationwithin
2070 2 values. The XRD plot for the samplesynthesized in the
present study is shown in figure 1. Smallamounts of MgO and
unreacted Mg are seen in the pattern,which are marked by the
symbols and #, respectively,as shown in figure 1. Due to the highly
reactive nature ofMg with oxygen, the impurity phase MgO might
arise duringthe sintering process. No other impurities except MgO
andunreacted Mg are seen in the XRD plot of the MgB2 sample.We have
determined the a- and c-axis parameters and findvalues 3.0825 and
3.5219 , respectively, using PowderXsoftware. These lattice
parameters are in agreement withprevious reports [15, 16].
-1.0
-0.8
-0.6
-0.4
-0.2
0.0(a)
(b)
35 36 37
0.2 A/cm 0.4 A/cm 0.8 A/cm 2.0 A/cm 4.0 A/cm 8.0 A/cm 20 A/cm 28
A/cm 40 A/cm
'(a
.u.)
T (K)
-0.03
0.00
0.03
0.06
0.09
0.12
0.15
0.18
0.21
34 35 36 37 38
0.2 A/cm 0.4 A/cm 0.8 A/cm 2.0 A/cm 4.0 A/cm 8.0 A/cm 20 A/cm 28
A/cm 40 A/cm
'' (a.
u.)
T (K)Figure 2. (a) The real component of ac susceptibility of a
pureMgB2 sample. (b) The imaginary component of ac susceptibility
ofa pure MgB2 sample showing peak shifts at lower temperatures.
The real and imaginary parts of ac susceptibility behaveas given
below [17] for a slab-shaped sample with penetrationdepth xc under
an applied ac field:
=
y/2 1, for 06 y 6 1,1pi
[( y2 1
)cos1(1 2y)
+
(1 + 4
3y 4
3y2
)(y 1)1/2
], for 16 y,
(1)
=
2y/3pi, for 06 y 6 1,1
3pi
(6y 4
y2
), for 16 y.
(2)
Here we use the auxiliary variable
y = xcR= Ba
0 Jc R.
The variables 0 and R are the permeability of free space andthe
half-thickness of the sample, respectively. We can measurethe
transition temperature Tc from the onset of Tc with thehelp of
figure 2(a). The imaginary part of ac susceptibility inequation (2)
shows different peaks at a particular temperatureTp for different
amplitudes of applied field Ba for pure
2
-
Phys. Scr. 84 (2011) 065701 I A Ansari et al
Table 1. Peak temperature and transition temperature for the
pureMgB2 sample for inter- and intra-granular regions with
different acapplied magnetic fields.
Ba T interc T intrac Tp(A cm1) (K) (K) (K)0.2 37.29 37.38
37.120.4 37.27 37.36 37.040.8 37.20 37.32 36.982.0 37.15 37.28
36.924.0 37.02 37.24 36.858.0 36.94 37.16 36.7320.0 36.81 37.08
36.5628.0 36.73 37.03 36.4840.0 36.71 36.98 36.39
MgB2. Equations (1) and (2) fit the calculated results of
acsusceptibility better than Beans model.
Beans model reveals how the superconducting materialpins the
flux vortices [18]. The flux density gradient in thecritical state
takes the following relation:
Bx
=0 Jc(B). (3)Therefore, the superconducting sample is
characterized by thecritical current density Jc.
Let us assume that Jc is independent of the ac magneticfield, in
this case Bd Ba because Jc(B) Jc(Bd + Ba). Thesample is placed in
the external magnetic field Bext = Bd +Bac. Here Bd and Ba
represent the static and ac components,respectively. Whenever the
applied ac magnetic field Bac =Ba cos(t) acquires the maximum
value, the ac flux densityyields the following form:
B(x, 0)= Ba0 Jcx . (4)For the boundary condition B(x,0)= 0, we
obtain the form
Jc = Ba0x
. (5)
The applied field cannot penetrate the sample in the depth
xc = Ba0 Jc
. (6)
Due to robust nonlinearity of the currentvoltage relation,higher
harmonics will emerge in the sample, showinganharmonicity in the
pick-up coil voltage [19]. Let us nowtake the simplest case when
the flux pinning is only involvedin the fluxoid motion. Assume that
the sample is slab-shaped;then Jc can be determined by knowing that
the maximumof is reached at a peculiar value of ac-field
penetrationdepth [20]: xc =
2 R, so that
Ba =
20 Jc R. (7)
By using varying ac field amplitudes Ba, we can find Jc withthe
help of equation (7).
We have determined the transition temperature Tc fromthe
measurements of the real part of ac susceptibility ( ) fordifferent
ac applied magnetic fields (as shown in figure 2(a))and observed
the suppression in Tc as we increase the appliedfield as shown in
table 1. We have calculated the values
Figure 3. Critical current density as a function of
reducedtemperature as calculated by equations (1), (2) and (8).
of T interc and T intrac (for table 1) as per figure 2 of
[11].The ac applied magnetic field significantly broadens
thetransitions to the superconducting state. This means that
theinter-granular junctions are not very strong for the
sample.Figure 2(b) exposes the imaginary part of ac-susceptibility(
); one can note that the absorption peaks are shifted tolower
temperatures when the ac applied field increases and itswidth
broadens subsequently. At the maximum value of peakat a given
temperature, the ac field amplitude Ba penetrates thesample and the
critical current induced by the magnetic fieldsis equal to the
critical current density, Jc. From equation (7),we obtain the
following relation in the case of the slab-shapedsample:
Jc = Ba20 R
. (8)
We have calculated the critical current density as a functionof
reduced temperature as shown in figure 3 [2124] by usingBeans model
[25] (equation (8)).
The lnJc versus ln(1 T/Tc) plot shows the criticalcurrent
density of a pure MgB2 sample calculated fromthe real and imaginary
part of ac-susceptibility, and Beansmodel by using equations (1),
(2) and (8), respectively(as shown in figure 3). In this figure,
the critical currentdensity determined from the real part is in
agreement withthat calculated from Beans formula. The different
valuesof Jc were calculated near the transition temperature. Ata
higher reduced temperature, the critical current densitycalculated
from the real part is approximately equivalent tothat calculated
from Beans model.
From flux creep theory [26], the calculated currentdensity can
be expressed as
Jc( )= Jc(0)[
1 TTc
]p, (9)
where Jc(0) is a critical current density at zero magnetic
field,while the parameter p is used to indicate the pinning
forceestimation. For example, for the compound Bi2Sr2Ca2Cu3Ox ,p
was estimated at 1.95. Ciszek et al [27] fitted the best Jc at10 K
for exponent p = 2.152.6 for pure and C-substituted
3
-
Phys. Scr. 84 (2011) 065701 I A Ansari et al
32 34 360
1000
2000
3000
4000
5000
6000
0.00 0.05 0.10 0.15
2
4
6
8
Ba = 0.2 A/cm
Ba = 0.4 A/cm
Ba = 0.8 A/cm
Ba = 2.0 A/cm
Ba = 4.0 A/cm
Ba = 8.0 A/cm
Ba = 20 A/cm
Ba = 28 A/cm
Ba = 40 A/cmln
(J
c( ' ))
(1-T/Tc)
Ba = 0.2 A/cm
Ba = 0.4 A/cm
Ba = 0.8 A/cm
Ba = 2.0 A/cm
Ba = 4.0 A/cm
Ba = 8.0 A/cm
Ba = 20.0 A/cm
Ba = 28.0 A/cm
Ba = 40.0 A/cm
J c (A
/cm2 )
T (K)Figure 4. Critical current density as a function of
temperature withvarying applied field. The inset shows the ln(Jc(
)) versus(1 T/Tc) plot for a pure MgB2 sample with varying ac
appliedmagnetic field.
0 10 20 30 40
36.4
36.6
36.8
37.0
37.2
Ba(A/cm)
T p(K
)
Figure 5. Plot of peak temperature versus applied field of
theimaginary part of ac susceptibility for a pure MgB2 sample.
MgB2 single crystals, respectively. A higher value of pindicates
a lower pinning strength in the sample. Jc( ) asa function of T (as
shown in figure 4) is calculated fromfigure 2(a). The inset of
figure 4, showing Jc as a function ofreduced temperature (1 T/Tc),
has been used to calculatethe value of exponent p in equation (9).
The value of phas been found between 3.3 and 6.2 for the applied ac
fieldranging from 0.2 to 40 A cm1, respectively. This indicatesthat
the pinning strength of the pure MgB2 sample reducesas we increase
the amplitude of the ac field. When thesuperconductor finds full
magnetization the Jc value can becalculated from Beans model or ac
susceptibility.
Figure 5 shows the variation of peak temperature Tp asa function
of applied ac magnetic field, Ba. The range ofthe applied field is
0.240 A cm1 at a constant frequencyof f = 98 Hz. This figure
clearly shows the lowering ofTp as we increase the applied ac field
that elucidates theattribute of greater voids and disorders. Since
the realresponse of the sample to an applied ac magnetic field
isdetermined, the magnetodynamics can be calculated by usingthe
complex susceptibility ( + ). We have measured the
(a)
(b)Figure 6. SEM micrographs of the pure MgB2 samples with
(a)1000 times and (b) 10 000 times magnification.
peak temperature Tp from the imaginary part that is out ofphase.
The imaginary part is associated with energy lossesor,
equivalently, the energy absorbed by the sample from theac
field.
Figures 6(a) and (b) show the typical results of
amicrostructural analysis of pure MgB2 samples with
differentmagnifications. These SEM images confirm the
porouspolycrystalline nature of the sample. This sample consistsof
larger grains from 5m to as large as 10m andagglomerates of fine
grains. The SEM images are only shownto observe the origin of
disorder or MgO impurity becausethe polycrystalline nature of pure
MgB2 does not require anyevidence. No relationship between Jc and
microstructure ismentioned in this paper because we have not
substituted anyimpurity in pristine MgB2.
4. Conclusions
The result of the XRD plot shows the synthesis of a goodsample
with minimal impurities of unreacted Mg and MgO.This is confirmed
by the agreement of lattice parameters fromprevious reports. The
transition temperature Tc calculatedfrom the real part and the peak
temperature determined
4
-
Phys. Scr. 84 (2011) 065701 I A Ansari et al
from the imaginary part of ac susceptibility are shifted tolower
temperature as we increase the ac applied field. Jc(T )increases
with varying ac applied field as we enhance thetemperature. The
critical current density determined from thereal part of ac
susceptibility at T interc is very much similar tothat calculated
from Beans formula at Tp. From the study ofJc( ) as a function of
temperature, we observe a relativelylarge value of exponent p which
indicates large decay ofcurrent as a function of temperature. This
shows the weakpinning of the MgB2 sample near the transition
temperature.The SEM images confirm that grains are uniformly
distributedin the lattice of the MgB2 matrix.
Acknowledgments
This work was supported by the NPST program of King
SaudUniversity, project nos 08-ADV397-2 and 09-ADV846-2.
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5
1. Introduction2. Experimental details3. Results and
discussion4. ConclusionsAcknowledgmentsReferences