PHYSICAELSEVIER

PhysicaC 263 (1996) 309-312

Thermal conductivity of REBa2Cu307 (RE -- Y,Dy,Sm,Nd)superconducting oxides
M. Ikebe *, H. Fujishiro, K. Nakasato, K. Noto
Department of Materials Science and Technology, Faculty of Engineering, lwate University, 4-3-5 Ueda, Morioka 020, JapanAbstract
The thermal conductivity K was measured for 90 K phase oxide RE123 (RE = Y,Dy,Sm,Nd) sintered samples. The shiftof the K maximum toward lower temperatures in Nd123 and Sm123 was observed in comparison with Y123 and Dy123.
Based on the dominant phonon thermal carrier model, the shift of the K(T) maximum is explained as due to enhanced
phonon scattering by point defects caused by the migration of Nd and Sm ions into the Ba sites of RE123 compounds.

1. InWoducfion
Thermal conduction is an important and fundamental transport phenomenon of solids. In dielectrics
where electrical conduction is absent, the thermal
conductivity K offers valuable information concerning the state of the crystalline lattice through thephonon scattering. In metals and alloys, circumstances are a little bit complicated because the heatconduction is due to both electron (K e) and phonon(Kph) contributions. If the separation of Ke and /(phcan be suitably made, the information contained in
the thermal conductivity should surpass, in principle,
that contained in the electrical conductivity. In superconductors where the DC electrical conductivity diverges to infinity below To, the thermal conduction isalmost a unique measure to study the transport properties. With regard to the thermal conduction ofhigh-T~ superconductors, one recent problem in dispute is concerned with the origin of the observed* Corresponding author. Fax: + 81 196 21 6373.

characteristic enhancement below T~: phonons orelectrical carriers? In this paper we study the thermal
conductivity of REBa 2Cu 307 (RE123) superconductors with rare earth ions RE = Y, Dy, Sm and Nd.
Recently, it was reported that the transition temperature Tc and the critical current Jc are enhanced in
NdBaECU30 7 (Ndl23) and SmBaECU30 7 (Sm123)
in comparison with YBaECU30 7 (Y123) [1]. The
possibility of migration into a Ba site was suggested
for Nd and Sm ions which have a relatively large ionradius. Nd and Sm ions on Ba sites might act asvortex pinning centers in RE123 compounds. We
expected to get information on both the lattice disorder of the specimen and the phonon scattering byquasi-particles in this RE123 system.

2. Experimental procedure

REBa2Cu307 samples were prepared from stoichiometric mixtures of (RE)20 3, BaCO 3 and CuO
raw powders. The mixtures were calcined at 910°C
for 24 h in air. They were pressed into pellets andsintered at between 945°C and 965°C for 30 h in

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M. Ikebe et al. / Physica C 263 (1996) 309-312

flowing oxygen. The X-ray analyses confirmed thatall samples are of single RE123 phase. The thermal
conductivity measurement was made by a continuous
heat flow method with Au(0.07 at.%Fe)-chromel
thermocouples as thermometers. Measuring temperatures were varied between 10-150 K in a GM-cycle
He refrigerator [2].

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Fig. 2. Thermal conductivity K as a function of T. The maximumof K shifts toward lower temperatures in Nd123 and Sml23 and Kof these specimens is smaller in the high-temperature region(T > Tc). These facts suggest stronger phonon scattering by point
defects in Nd123 and Sm123.

Tc occurs at lower temperatures for Nd and Sm thanfor Y and Dy. In the following, this shift of themaximum K is analyzed based on the assumptionthat the thermal conduction is mainly due to phonons
over the entire temperature range of the presented
data.

4. Discussion

The heat transport in conductors is due to bothelectrons and phonons. In the normal state the electron contribution Ken can be estimated by using theWiedemann-Franz law ( = 8 m W / c m K for thepresent RE123). In the superconducting state, we
assume that Kes follows the theory proposed byKadanoff and Martin [5] which predicts the reductionof Ke below Tc because of the formation of Cooper
pairs. Taking account of the phonon scattering byvarious crystal defects and electrons, the phonon
conductivity is given by [6].

t °ff It 1f

O/0•A

•
.

''6t~Fig. 1 shows the temperature dependence of theelectrical resistivity p of RE123 compounds. The pvalue of each sample is 0.7-0.8 m O cm at room
temperature and is almost independent of the REions. These values are rather small for sintered materials. If the sintering process is not optimized, thesevalues easily become larger by 3 - 5 times. The insetin Fig. 1 shows the superconducting transition temperature in an expanded scale. Tc values of Nd123
and Sm123 are slightly higher than those of Y123
and Dy123. This tendency of T~ enhancement waspointed out by Yoo et al. [3,4] for melt-grown crystals.
Fig. 2 shows the thermal conductivity K as afunction of temperature T. We notice the characteristic enhancement below T~ common to all RE123
samples. However, K shows some peculiar features
which depend on RE ions: the maximum of K belowi•I60

O

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=O

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3. Experimental results|

E

fOo/T x 4ex

KPh =,3dnRT 3v2
M (gD3 "0(e x -1) 2 "rph d x ,(1)300(K)

Fig. 1. The electrical resisdvity p(T) vs. temperature T. The inset

shows the superconducting transition in an extended temperaturescale. Tc is enhanced in Nd123 and Sm123 specimens.

where d is the mass density, M the mass of 1 mole,n(= 13) the number of atoms composing RE123
compounds, R the gas constant, O o the Debye
temperature, v the average phonon velocity and x

311

M. lkebe et al./Physica C 263 (1996) 309-312

the reduced phonon frequency. The phonon relaxation time ~'ph is given by1--=-1 + s T Z x l + p T a x 4 + E T x g ( x ,"rby).

(2)%Here, % is the phonon relaxation time due to grainboundaries and s, p and E refer to the strength ofthe phonon scattering by sheet-like faults, point defects and electrons, respectively. The function
g(x, y ) = Tphn/Tph s stands for the ratio of thephonon-electron relaxation time in the normal andsuperconducting states as given by Bardeen, Rickayzen and Tewordt [7,8]. The values of g(x, y)
which depend on the energy gap through the parameter y = A(T)/kBT become smaller than 1 below Tc
in superconducting state because the Cooper pairs do
not take part in the phonon scattering.
Fig. 3 shows examples of the fitting curves for thephonon thermal conductivity Kph ( ~ - - K - Ke). The
parameters used and determined in the fitting process
are summarized in Table 1. We note two importantpoints. First, the shift of the maximum K toward
lower temperatures in Nd123 and Sm123 is causedby the enhanced point-defect scattering. If small
amounts of Nd and Sm are located at Ba sites asreported [1], then they will work as point defects atBa sites enhancing the point-defect scattering. The
shift of maximum K(T) is consistent with the migra-80.

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Table 1
Characteristic parameters of the REBa2Cu307
Sample

Y123

Dy123

Nd123

Sm123

To(K)
d(g/cm 3)
OD (K)
zt,- t (s- l)lb(ixm)p(K -4 s - t )s(K -~ s - t )E(K -t s - t )
A91
5.68
430
3.0X 10811.2456
2.7X106
6.9X108
0.26

92
6.12
430
1.6X 1082.1487
3.2X106
9.9X108
0.38

94
5.89
430
3.0X 10811.1884
2.7X106
7.4X1080.2894
6.21
430
3.1X 108
10.6711
2.1XI06
7.7X1080.29

tion of Nd and Sm ions into Ba sites. Secondly,
though the magnitude and the shape of the K(T)curve are somewhat different among RE123 compounds, the electron-phonon scattering term E isnearly constant irrespective of the RE ions. In otherwords, the electron-phonon coupling constantA(= 2a(t)/'rrv, where a is the lattice constant, ( t )the effective hopping matrix element of electrons [6])is not heavily influenced by RE ions, which seems
physically reasonable. Thus, the phonon conduction
model naturally explains the observed shift of themaximum K temperature without introducing any
special new assumption. If we try to explain thisshift of the K maximum on the basis of the electricalcarrier model [9], we need a reasonable explanation
for the change of the quasi-particle scattering rate
which depends on RE ions in the superconducting
state. The present experimental results seem to support our first assumption that phonons are the dominant thermal carriers over the entire temperature
range. It will be interesting to investigate the possible correlation between phonon scattering by point
defects and vortex pinning force Fp, because bothquantities are possibly related to RE ions on Ba sites.

References

20,0050
Temperature

100(K)

50Fig. 3. Examples of the fitting curves of K(T) based on E,q. (1).
The electrical component re(T) estimated by the WiedemannFranz law (in the normal state) and by the theory proposed byKadanoff and Martin (in the superconducting state) is also shown.

[1] M. Murakami, S.I. Yoo, T. Higuehi, N. Sakai, J. Weltz, N.
Koshizuka and S. Tanaka, Jpn. J. Appl. Phys. 33 (1994) L715.
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Jpn. 63 (1994) 3107.
[3] S.I. Yoo, N. Sakai, H. Takaichi, T. Higuchi and M. Murakami, Appl. Phys. Lett. 65 (1994) 633.
[4] S.I. Yoo, N. Sakai, H. Takaichi, T. Higuchi and M. Murakami, Physica C 235-240 (1994) 2781.

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M. lkebe et al./Physica C 263 (1996) 309-312[5] L.P. Kadanoff and P.C. Martin, Phys. Rev. 124 (1962) 670.
[6] L. Tewordt and T. W~lkhausen, Sol. St. Commun. 70(1989) 839.
[7] J. Bardeen, G. Rickayzen and L. Tewordt, Phys. Rev. 113(1959) 982.

[8] L. Tewordt, Phys. Rev. 129 (1963) 657.
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