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Physica C 463–465 (2007) 478–481

Superconductivity of Ag-added composites of Hg-1223grained Bean model

M. Kubo a, T. Akune a, N. Sakamoto a,*, H.R. Khan b, K. Luders c

a Department of Electrical Engineering, Kyushu Sangyo University, 2-3-1 Matsukadai, 813-8503 Fukuoka, Japanb Institut von Ionenstrahl und Vakuum Technologie, 73728 Esslingen, Germany

c Freie Universitat Berlin, Institut fur Experimentalphysik, 14 Arnimallee, D-14195 Berlin, Germany

Available online 2 June 2007

Abstract

High-Tc ceramics tend to lower its quality by the aging effect. The main cause of the degradation is considered to originate in the linkregion among the superconducting grains. The preservation and recovery of superconductivity by reinforcement of the grain boundary isan important issue for high-Tc application.

A quantitative analysis of the contribution due to the grain and link is necessary and the grained Bean model is proposed, where thesuperconducting phases are immersed in the matrix link superconductor. Difference of the superconducting characteristics of the grain,the link and grain content factor give a variety of deformation on the AC susceptibility curves. Comparing the observed data with thenumerically computed model allows more clear insight between the grain and intergrain structure.� 2007 Elsevier B.V. All rights reserved.

PACS: 74.72; 74.25.Ha; 74.80.Bj

Keywords: Grained Bean model; AC susceptibility; Pinning penetration field

1. Introduction

High-Tc ceramics are textures of grain and interconnect-ing links as shown in Fig. 1. Sintered high-Tc superconduc-tors exhibit two type of properties. One is intrinsic to thesuperconductor and the other is characteristic of the cou-pling between either grains. In such materials, the couplingcomponent supports supercurrents and has its own effec-tive critical temperature Tc‘, critical current density Jc‘

and pinning penetration depth Bp‘. The situation is less cer-tain, but lack of stoichiometry at the grain boundaries andmicrobridges between grains give rise to normal precipi-tates and proximity-effect coupling and so on. The couplingregion has a weak superconductivity and the field pene-trates more freely through them compared to the grainregion. Then the surface field of the grain is determined

0921-4534/$ - see front matter � 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.physc.2007.05.042

* Corresponding author. Tel.: +81 92 673 5636; fax: +81 92 673 5091.E-mail address: saka@te.kyusan-u.ac.jp (N. Sakamoto).

by the coupling matrix superconductor. The intrinsicsuperconductors with high pinning penetration field Bpg

are considered to be immersed in the weak matrix withlow Bp‘.

Field distribution and magnetization in multi-phases arecalculated by Bean model [1]. Fourier integration of mag-netization is carried out numerically and gives rise to thereal part v 0 and the imaginary part v00 of AC susceptibili-ties. Measured results of Pb-doped [2,3] and Ag-addedHg-1223 superconductors [4] are compared with the simu-lated results to give the link characteristics.

2. Grained Bean model

Matrix superconductor with a penetration field Bp‘

determines the magnetic fields at the grain surface withthe penetration field Bpg as shown in Fig. 2. Field distribu-tion Boi outside the ith grain at a grain position Xi and field

Fig. 2. Field distribution Boi outside the grain and distribution Bi insidethe grain. Penetration fields are Bp‘ and Bpg for matrix and grain,respectively.

10—2 100 102—1

—0.5

00

0.1

0.2

χ ''

χ '

Ba / Bpl(0)

00.2

0.4

0.6

Bpg(0) = 1

Bpl(0) = 0.1

fg

0.8

1.0

Fig. 3. Computed AC susceptibilities as a function of AC field Ba

normalized by Bp‘(0). With decreasing the grain content fg, high field peakwith no link region (fg = 0) gradually shifts to low field peak with no grain(fg = 0).

Fig. 1. Texture of grains and interconnecting links. Bpg is the pinningpenetration field of grain with the diameter of 2dg. The distance betweengrains is 2dv.

M. Kubo et al. / Physica C 463–465 (2007) 478–481 479

inside Bi of ith grain with the grain size dgi are given byusing Bp‘, Bpg and Bean model as [1]

Boi ¼ Bo � Bp‘

X i

D

� �: outside the grain ð1Þ

Bi ¼ Boi � Bpg

xdgi

� �: inside the grain ð2Þ

where D is a half thickness of the superconductor, x is a po-sition inside the grain from the each grain surface as shownin the inset. Average of the magnetic flux density hBi in theincreasing period for both of the matrix and ng grains withgrain interval dvi is given by

Bh i ¼ Bo �Bp

2þXng

i¼1

dgi

dvi

� �mi ð3Þ

Grain magnetization mi is easily computed following mag-netization process of each grains. In the case of uniformgrain structure with constant grain size dg(=dgi for all i)and intergrain distance dv(=dvi for all i),

Bh i ¼ Bo �Bp

2þ fg

Xng

i¼1

mi; ð4Þ

where fg(=dg/dv) is the grain content factor. Then the mag-netization M of the superconductor at the field Bo for eachmagnetization processes is given by

M ¼ hBi � Bo ð5Þ

3. AC susceptibilities of the grained Bean model

The equations for the AC susceptibilities v 0 and v00 underan AC field Ba cosxt are derived from Fourier integrals ofthe magnetization. The fundamental Fourier componentsv01 and v001 are denoted as v 0 and v00 hereafter, and expressedas [5]

v0 ¼ 1

pBa

Z p

�pM cos xt dxt ð6Þ

v00 ¼ 1

pBa

Z p

�pM sin xt dxt ð7Þ

Numerical integration of Eqs. (6) and (7) is carried outand the results are shown in Fig. 3, where the imaginarypart v00 and the real part v 0 are plotted as a function ofthe amplitude of the superposed AC field Ba normalizedby a link penetration field at 0 K, Bp‘(0). When the contentfactor fg increases, new peak appears corresponding to thegrain magnetization and old peak at low field begins toshrink. The peak of v00 shifts smoothly from low link com-ponent to high grain one.

Temperature dependence of v 0 and v00 is obtained byintroducing the temperature variation of the penetration

0 0.5 1—1

—0.5

00

0.1

0.2χ

''χ

'

T / Tcg

Ba / Bpl(0) = 0.2Bpg(0) = 1.0

Bpl(0) = 0.1

fg0.10.20.4

0.60.8

Fig. 4. AC susceptibilities v 0 and v00 as a function of temperature T

reduced by the grain critical temperature Tcg. Parameters are the same inFig. 3 and Ba/Bp‘(0) = 0.2.

0.4 0.6 0.8 1—1

—0.5

00

0.1

0.2

χ ''

χ '

T / Tcg

Ba / Bpl (0) = 0.2

Bpg(0) = 1.0

Bpl(0) = 0.1

Tcl / Tcg

0.940.96

0.980.99

fg = 0.5

Fig. 6. Dependence of AC susceptibilities v 0 and v00 on reduced temper-ature T/Tcg with link critical temperatures Tc‘/Tcg of 0.94, 0.96, 0.98and 0.99.

0.5 1

Ba = 0.5 (mT)

Pb—02Ag—01

B = 1.0 (T)

T / Tcg (1T)

arbi

trary

f = 100 (Hz)

a

480 M. Kubo et al. / Physica C 463–465 (2007) 478–481

fields of Bp‘ and Bpg. If these Bp‘,g’s have a usual parabolicdependence of the form as

Bp‘;g ¼ Bp‘;gð0Þ 1� TT c‘;g

� �2( )

ð8Þ

where over the temperatures Tc‘ and Tcg the pinning effectfor the fluxoid motion disappears in the link and thegrain region, respectively. The AC susceptibilities arenumerically computed and plotted in Fig. 4 where theparameters are the same in Fig. 3 and AC field amplitudeBa/Bp‘(0) = 0.2. The peak of v00 decreases and the addi-tional peak is produced just below Tc‘. This means thatthe grain penetration field Bpg approaches Ba at rather hightemperature than the matrix penetration field Bpg.

At a fixed grain content of fg = 0.5 the effect of Bpg areshown in Fig. 5. The imaginary peaks decrease withincreasing Bpg and new peaks appear and coexist. This typeof double peaks are often observed in high-Tc materials [6].

0.6 0.8 1—1

—0.5

00

0.1

0.2

χ ''

χ '

T / Tcg

Ba / Bpl(0) = 0.2

Bpl(0) = 0.1

Bpg(0)

0.10.20.4

0.60.81.0

fg = 0.5

Fig. 5. Influence of Bpg on the temperature dependence of AC suscepti-bilities v 0 and v00 at a grain content of fg = 0.5.

0.6 0.8 1T / Tcg

arbi

trary

fg = 0.8

Tcl / Tcg = 1

Bpl(0) / Bpg(0)0.20.8

b

Fig. 7. (a) Temperature dependence of AC susceptibilities of Pb-02 andAg-01 sample. (b) Numerically computed AC susceptibilities as a functionof T/Tcg for Bp‘(0)/Bpg(0) of 0.2 and 0.8.

M. Kubo et al. / Physica C 463–465 (2007) 478–481 481

When the critical temperature of the link Tc‘ is lower thanthat of the grain Tcg, the peak related to the link appears ateven lower temperature as shown in Fig. 6. The doublepeak structure in the v00 curve is specifically indicated tooriginate in the cooperative work of the grain and the inter-connecting link.

4. Grain and link characteristics in Hg-1223 superconductors

The AC susceptibilities vs. temperature of Pb-02 (Hg0.8-Pb0.2Ba2Ca2Cu3O8+d) [2,3] and Ag-01 (Ag0.1(HgBa1.9Bi0.1-Ca2Cu3O8+d)0.9) [4] sample are shown in Fig. 7a. The valueof v 0 and v00 are normalized to coincide the lowest values ofv 0. Shift of curves to high temperature for Ag-added impliesan improvement of the superconducting properties. Thecomputed curves of the grained Bean model with theparameters of fg = 0.8, Tc‘/Tcg = 1 and Bp‘(0)/Bpg(0) = 0.2(Pb-02) and 0.8 (Ag-01) are plotted in Fig. 7b. With addi-tion of the Ag, Bpg is nearly constant but link penetrationfield Bp‘ increases. This tendency is the same at differentmagnetic fields and should be considered that Ag additionresults in strengthening the link quality.

5. Conclusions

Textures of grains and interconnecting links in high-Tc

superconductors are simulated by the grained Bean model,where the superconducting regions are divided two parts;grains and interconnecting links. A variety of characteris-tics, double peak in the imaginary part of AC susceptibilityand their movement, are shown in the computed results.Ag addition to Hg-1223 superconductors was reported toincrease the quality of the link.

References

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C 412–414 (2004) 430.[5] T. Matsushita, E.S. Otabe, B. Ni, Physica C 182 (1991) 95.[6] L. Fabrega, A. Sin, A. Calleja, J. Fontcuberta, Phys. Rev. B 61 (2000)

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