Comparison of the critical current density of a polycrystalline MgB2 superconductor by ac-

susceptibility and Bean's model

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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: intikhabansari@yahoo.com

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