Physica C 392–396 (2003) 171–174
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Thermal conductivity of YBaCuO bulk superconductors
under applied ﬁeld: eﬀect of content and size of Y211 phase
Hiroyuki Fujishiro a,*, Hidekazu Teshima b, Manabu Ikebe a, Koshichi Noto aba
Faculty of Engineering, Iwate University, 4-3-5 Ueda, Morioka 020-8551, Japan
Advanced Technology Research Laboratories, Nippon Steel Corporation, 20-1 Shintomi, Futtsu, Chiba 293-8511, Japan

Received 13 November 2002; accepted 31 January 2003

Abstract
The temperature and magnetic ﬁeld dependence of the a-axis thermal conductivity ja of YBaCuO bulk superconductors has been measured as a function of the content and the size of Y2 BaCuO5 (Y211) impurity phase particles. In thespecimen with the high critical current density Jc the ja ðT Þ enhancement below the superconducting transition temperature Tc is drastically suppressed in comparison with that of the lower Jc specimens with smaller Y211 content or withlarger Y211 particle size. In the YBaCuO bulk system, Y211 particles are eﬃcient phonon scatterers as well as the main ﬂux
pinning centers and a clear correlation between the ﬂux pinning and the phonon scattering strength has been conﬁrmed.
 2003 Elsevier B.V. All rights reserved.
PACS: 74.72.)h; 51.20.+dKeywords: Thermal conductivity; YBaCuO; Magnetic ﬁeld; Critical current

1. Introduction
In the melt-processed REBaCuO bulk superconductors (RE: rare earth ions), RE2 BaCuO5(RE211) impurity phase particles are dispersed ﬁnely and uniformly in the REBa2 Cu3 O7 (RE123)
matrix phase by addition of platinum (Pt) metal[1]. The critical current density Jc is increased bythe dispersed RE211 particles which act as strong
ﬂux pinning centers. In this case, the number
density and the size of the RE211 particles are
essential to determine Jc . Recently, the higher Jc
than that for RE ¼ Y system, were realized for*

Corresponding author. Tel./fax: +81-19-621-6363.
E-mail address: fujishiro@iwate-u.ac.jp (H. Fujishiro).

RE ¼ Nd and Sm systems, where a part of the Nd
and Sm ions substituted for the Ba ions and produce the non-superconducting (or low-Tc ) phase[2]. Furthermore, new promising REBaCuO bulk
superconductors using RE ¼ Gd, (Sm,Gd) and(Nd,Eu,Gd) have been investigated, resulting in a
drastic improvement of Jc caused by the extremely
ﬁne and uniform RE211 phase particles [3–5]. The
REBaCuO bulks are promising materials from theview point of the superconductor application.
For the application of the bulk superconductors, thermal transport properties such as thethermal conductivity j and thermal diﬀusivity aare important to estimate the thermal stability andthe reliability as cryogenic apparatus. For example, the low thermal conductivity is desirable for0921-4534/$ - see front matter  2003 Elsevier B.V. All rights reserved.
doi:10.1016/S0921-4534(03)01104-3

H. Fujishiro et al. / Physica C 392–396 (2003) 171–174

2. Experimental
The YBaCuO bulk crystals were fabricated by
the modiﬁed quench and melt growth method[9,10] with various volume fractions and sizes of
the Y211 phase particles. The three specimens
were prepared with diﬀerent volume fraction X(%) and average particle size Z (lm) of the Y211
phase. We abbreviate the name of the threespecimens as #11(25%, 1 lm), #10(2%, 1lm) and#01(25%, 10 lm), respectively, where the X and Z
values are given in the parenthesis. The specimensof #11 and #10 were fabricated by the additionof Pt metal (0.5 wt.%) and the #01 specimen wasfabricated without the Pt addition. The specimens
were cut into a rectangular parallelepiped withthe a-axis directed along the longest edge. The
typical sizes of the specimens were 3.0 · 3.0 · 12.5mm3 . The a-axis thermal conductivity ja ðT Þ wasmeasured by a steady-state heat ﬂow method in
the temperature range of 10–300 K [11]. Theja ðT Þ measurement under the magnetic ﬁeld ofup to 10 T was performed using the cryocoolercooled superconducting magnet. The magnetic
ﬁeld dependence of the critical current density Jc
at 77 K was determined by the magnetization
measurement (B?ab-plane) on the basis of theBean-model.

3. Results and discussion
Fig. 1 shows the a-axis electrical resistivity qa of
the three specimens as a function of temperature
T . The inset shows the normalized magnetization
M. The superconducting transition temperature Tc
determined by resistivity and magnetization depends on both the volume fraction and the size ofY211 phase and the specimen #11(25%, 1 lm),
which is a standard product of Nippon SteelCorporation as a bulk superconductor, has thehighest Tc . qa of the specimen #10(2%, 1 lm) is thehighest and that of #01(25%, 10 lm) is the lowest.
These results suggest that the size of the Y211
particles may aﬀect the electron transport morestrongly rather than the net Y211 content.
Fig. 2 presents the magnetic ﬁeld dependence ofthe critical current density Jc at 77 K as a functionof the applied ﬁeld B. In zero magnetic ﬁeld, #11
specimen attained the highest Jc value of 6.07 · 104
A/cm2 and #10 showed the lowest value of 1.05 ·104 A/cm2 , while that of #01(2.2 · 104 A/cm2 ) wasintermediate. The reduction in Jc in the appliedﬁeld was somewhat consistent with the initial values of Jc i.e., the specimen with larger Jc showed
gentler ﬁeld dependence. In the applied ﬁeld of 0.5
T, for example, the Jc values of the #11, #01 and#10 were about 55%, 45% and 11% of the respective zero ﬁeld values. The large Jc values of#11 may reﬂect the strong ﬂux pinning caused by

1.5
Normalized M

the application to the power current leads of superconducting magnets. For the application as
bulk magnets as high as 2 T at 77 K, however,
the high heat conduction is indispensable to prevent the exudation of the trapped ﬂux caused by
the temperature rise. We have already reported thethermal transport properties of the several REBaCuO bulk superconductors [6–8]. The eﬀects of thecontent and the size of the RE211 phase particles
on the thermal transport properties, however, havenot been clariﬁed.
In this paper, we investigate the a-axis thermalconductivity ja ðT Þ of the YBaCuO bulk superconductors by varying the volume fraction andsize of the Y2 BaCuO5 (Y211) impurity phase under
the applied ﬁeld of up to 10 T and discuss the interrelation between the critical current density Jc
and the phonon scattering strength.

Resistivity ρ a (mΩc m )172

1#11(25%, 1µm)
#10(2%, 1µm)
#01(25%, 10µm)

0

#11
#10
#01-10.50085
90
Temperature (k)

95

100
200
Temperature (K)300

Fig. 1. The a-axis electrical resistivity qa of the three specimens(#11(25%, 1 lm), #10(2%, 1 lm) and #01(25%, 10 lm)) as afunction of temperature T . The normalized magnetization M isalso shown in the inset.

H. Fujishiro et al. / Physica C 392–396 (2003) 171–174
105Jc(A/cm 2 )77K, H//c
104103#11 (25%, 1µm)
#10 (2%, 1µm)
#01 (25%, 10µm)

1020123H (Tesla)

45Fig. 2. The magnetic ﬁeld dependence of the critical current
density Jc at 77 K for three specimens.

Thermal Conductivity κ a (mW/cmK)

the rich number of the Y211 ﬂux pinning centers.
In #01 specimen with larger Y211 particle size andin #10 with the smaller Y211 content, the number
density of the Y211 pinning center is not large
enough, which may deteriorate their Jc characteristics.
Fig. 3 shows the temperature dependence of thea-axis thermal conductivity ja ðT Þ in the zero ﬁeldfor three specimens. The electronic thermal conductivity je is also shown, which is estimated by
Wiedemann–Franz law above Tc using qab shownin Fig. 1. Below Tc , je is estimated based on theformula derived by Kadanoﬀ and Martin [12,13].
The contribution of the electronic part is relatively
small and the heat transport is overwhelmingly
due to phonons.
300#11(25%, 1µm)
#10(2%, 1µm)
#01(25%, 10µm)

200

100

κe00100
200
Temperature (K)300

Fig. 3. The temperature dependence of the a-axis thermal
conductivity ja ðT Þ under the zero ﬁeld. The estimated electronic
thermal conductivity je is also shown.

173

In superconductors below Tc , je is rapidly reduced with decreasing temperature, because theelectrons condense into the Cooper pairs which do
not carry entropy. On the other hand, the phonon
thermal conductivity jph is enhanced because theCooper pairs are ineﬀective in phonon scattering.
In Fig. 3, the ja ðT Þ enhancement in the #11
specimen below Tc is suppressed in comparison
with those of #01 and #10. The specimen #01
contains the same amount of the Y211 impurity
phase but the Y211 particle size (10 lm) is 10
times larger in comparison with those (1 lm) in#11. The number density n of the Y211 particles in#01 is smaller by 103 compared with that of #11.
The phonon wavelength is by far smaller than theY211 particle size of the present specimens. In
such a case, the phonon scattering cross section Sof a particle with radius r is pr2 which is 100 times
larger for the Y211 particles in #01. Then the total
phonon scattering probability ( ¼ nS) due to Y211
particles in #01 should be about 1/10 of that of#11. In #10, of which Y211 content is 1/12.5 of#11, the total scattering probability is estimated to
be also 1/12.5 of the #11 specimen. Thus the estimated phonon scattering probability due to theY211 phase particles is the largest in #11 and is
the smallest in #10. The thermal conductivity ja isthe smallest for #11 and is the largest for #10,
which strongly indicates that the variation of ja
enhancement between three specimens is controlled by the phonon scattering strength by theY211 particles. The ja values of the three specimens, in contrast, are in accord with each other inthe high temperature region (T P 140 K), where
the dominant phonon scattering mechanisms are
due to electrons and phonon–phonon scattering(Umklapp process) and the scattering by the Y211
particles becomes relatively unimportant [13].
As we have seen, the Y211 impurity phaseparticles play an important role for both the ﬂux
pinning and the phonon scattering below Tc By
comparing the Jc results in Fig. 2 and ja in Fig. 3,
we notice that the ja enhancement is more strongly
reduced in the specimen with higher Jc and this isnot a mere coincidence. This fact directly supportsthat the Y211 pinning centers are strongly scattering phonons at the same time. Then it is expected that the both Jc and the phonon scattering

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H. Fujishiro et al. / Physica C 392–396 (2003) 171–174

In summary, we found that the Y211 impurity
phase particles, which are the main ﬂux pinning
centers in the bulk YBaCuO superconductors, arealso quite eﬃcient phonon scattering centers at
low temperatures below Tc . Then the low temperature phonon thermal conductivity can be a usefullandmark for the ﬂux pinning strength. The obtained results suggest that we can further enhanceboth phonon scattering and ﬂux pinning by dispersing the ﬁner (0.1 lm) Y211 particles in theY123 matrix phase.

300κ a (mW/cmK)(a) #11(25%, 1µm )

200

0T
5T
10T

a-axisQab-planeB
100

Q//a-axis, B⊥ ab-plane0κ a (mW/cmK)(b) #10(2%, 1µm )

200

10000

Acknowledgements

0T
5T
10T

50

100
150
Temperature (K)200This work is partially supported by Japan Science and Technology Corporation under the Jointresearch Project for Regional Intensive in theIwate Prefecture on ‘‘Development of practicalapplications of magnetic ﬁeld technology for use in
the region and in everyday living’’.

Fig. 4. Magnetic ﬁeld dependence of ja ðT Þ for the (a) #11(25%,1 lm) and (b) #10(2%, 1 lm) specimens.

References
strength of the YBaCuO bulk superconductors canbe simultaneously enhanced if we can disperse
more ﬁne Y211 particles in the YBa2 Cu3 O7 superconducting phase.
Fig. 4(a) and (b) presents ja ðT Þ of the #11(25%,1 lm) and #10(2%, 1 lm) specimens in the appliedﬁelds. By application of ﬁelds, the phonon scattering by electrons partially recovers below Tc because of the normal-electron ( ¼ quasi-particle)
revival in the vortex core regions. Then the thermal conductivity ja is reduced in the superconducting state. By comparing Fig. 4(a) and (b), theja reduction eﬀect due to the applied ﬁeld seems tobe smaller for the #11 specimen. For #11, theeﬀect of the phonon scattering enhancement by
quasi-particles is relatively small because of thestronger phonon scattering by the Y211 particles.
Thus the behavior of ja in the magnetic ﬁeld also
supports that the heat conduction is mainly due tophonons and that the phonon scattering by theY211 particles are important at low temperatures
well below Tc .

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