ELSEVIER

Physica B 219&220 (1996) 163-165

Thermal conductivity and diffusivity of Nd2-xCexCuO4
H. Fujishiro*, M. Ikebe, M. Yagi, M. Matsukawa, H. Ogasawara, K. Noto
Faculty of Engineering, lwate University, 4-3-5, Ueda, Morioka 020, Japan

Abstract

The thermal conductivity to(T), thermal diffusivity ~(T) and electrical resistivity p(T) of sintered Nd2-xCexCuO,~(0 ~< X ~< 0.2) were measured for 'annealed' materials, p(T) decreased with increasing Ce concentration and only thesample of X = 0.2 showed metallic behavior. The thermal conductivity showed maximum near X = 0.15, at which thesuperconductivity occurred. Taking account of the phonon-phonon interaction, ~c(T) was analyzed based on theTewordt and W61khausen (TW) theory. The phonon scattering by electrons was confirmed to be very small up to
X = 0.15 and it became discernible only for X = 0.2.

1. Introduction

2. Experimental

Nd2 xCexCuO4 (NCCO) belongs to the T'-phasestructure with C u - O squares in which the electron-doped
superconductivity can be realized for 0.15 ~< X ~< 0.18.
This structure makes a contrast with that of the T-phasewith Cu O octahedrons such as a hole-doped
La2-xSrxCuO4 (LSCO). The thermal conductivity ofNCCO was reported for sintered materials [1,2] andsingle crystals [3,4]. Larger to(T) values and the maximum of ~(T) near 30 K are characteristics of NCCO incomparison to LSCO. In this paper, we report the thermal conductivity to(T) and diffusivity c~(T) of the sintered
Nd2 xCexCuO4 (0 ~ X ~ 0.2) whose electrical properties were controlled by heat treatments in Ar. The
phonon scattering mechanisms were analyzed based on
the Tewordt and W61khausen (TW) theory [5]. It was
found that the phonon scattering by carriers was ineffective up to X = 0.15 in this system and the measured ~c(T)can be reproduced by varying the boundary and point
defect scattering under a unified phonon-phonon scattering strength.

Nd2-xCexCuO4 (0 ~< X ~< 0.2) samples were prepared from stoichiometric mixtures of Nd203, CeO2 andCuO raw powders. The mixtures were calcined twice at
900°C for 21 h in air. They were pressed into pellets andsintered at ll00°C for 18 h in air. These samples are
named 'as-sintered' samples. Subsequently, they wereheat-treated at 910°C for 18 h in flowing Ar gas and werenamed 'annealed' samples. The X-ray diffraction analyses
showed that all samples exhibited the single T'-phase.
The density of each sample was higher than 93% of theideal density. ~c(T) and ~(T) were measured from 10 to150 K under an identical experimental setup with a fully
automated measuring system [6]. x(T) was measured bya steady-state heat flow method and e(T) was measured
by an arbitrary heating method which was one of nonsteady state methods.

* Corresponding author.

3. Results and discussion

The annealing process in Ar is expected to create
the electron carriers, and at the same time, introduce
the scattering centers due to oxygen deficiency in the0921-4526/96/$15.00 :~ 1996 Elsevier Science B.V. All rights reserved
SSDI 0 9 2 1 - 4 5 2 6 ( 9 5 ) 0 0 6 8 3 - 4

164

H. Fujishiro et al./Physica B 219&220 (1996) 163 165

samples. The Ce substitution for Nd site also creates theelectron carriers and may also act as scattering centers.
Thus, p ( T ) and ~c(T) of the samples are to be changed by
the carrier doping and the scattering effects. The temperature dependence of the electrical resistivity of 'annealed'samples is shown in Fig. i. p ( T ) decreased with increase
in Ce concentration and only the sample of X = 0.2
showed metallic behavior, p ( T ) decreased by annealing
process except for X = 0.15. The annealing sample ofX =0.15 showed the superconducting transition at
To = 20 K.
The temperature dependence of the thermal conductivity of 'annealed' samples is shown in Fig. 2. ~(T) increased with increase in temperature and exhibited amaximum near 30K; it then gradually decreased withfurther increase in temperature. The maximum ~¢ value
increased with increase in Ce concentration up toX = 0.15; it then decreased for the sample of X = 0.2.
~(T) for the samples of 0 ~< X ~<0.1 decreased by annealing in Ar. Since the electronic contribution for ~c,which isestimated by the Wiedemann-Franz law, is very small forall samples, the measured K(T) is nearly the phonon
thermal conductivity and can be analyzed using the following TW formulation [-5]:3 d n R T ~ v ~ ~D/T

I< =M(93400

I''Eg''

I

annealedsamples
X=O300

X=O.05AA•

X=0.1
X=0.15
X=0.2':

200-"OC0l-,,oEA

100'~~. . . . . ,. . . . . . .

".".%".%%*YI--

0nnnn0lnnnn

|

50100

Temperature(K)n.

n.

150

Fig. 2.Temperature dependence of thermal conductivity of 'annealed' samples with various Ce concentrations.

400m

E0g.

.

mU

•nn

m|

ui

m

n

x=015

annealed samples(u=2 5x1011)•• " .-.-.

300._>

x4 e ~(ex _ 1)2 Zoh dx,

200

(1)
e-

where d is the mass density, n ( = 7) the number of atoms
per mole, M the molar weight of the sample, R the gas
constant, v ( = 5 0 0 0 m / s ) the sound velocity, Oo( = 450 K) the Debye temperature and x ( = hoJ/kB T) isthe reduced phonon frequency. The phonon relaxation
time Zph is assumed to obey Matthiessen's rule:

r~h~ = Zbl + z~l + z6~ + z~=rb

1+ p T 4 x 4 + Uxexp( -- @ p l a T ) + E T x .

(2)s'. pl;s

10 4

X~" 103

=O.

05~

Ug
X=0.1

.__.

X=O. 15~"~ 101
IX

X=0.2•

10~0IIIII I
100

Temperature

I200
(K).

.

.

s300

Fig. 1. Temperature dependence of electrical resistivity of 'annealed' samples with various Ce concentrations.

o0100/-° ;z7.~%_%%_%_%_~.

elIIII|

50''''l100.

.

,

,

50

Temperature (K)Fig. 3. The measured (symbols) and calculated (lines) thermal
conductivity data of 'annealed' samples of X = 0, 0.15 and 0.2.

Here, Tb is the phonon relaxation time due to grainboundaries and p, U and E refer to the strength of thephonon scattering by point defects, other phonons andcharge carriers, respectively, a is a constant which varies
the effectie Umklapp cutoff temperature. We tried severalmodels for the phonon-phonon interaction term rt5
The function U x e x p ( - O D / a T ) ( a = 1.8), which isa standard form at relatively low temperatures [7], wasfound to result in the best fit for all samples undercommon U and a values.
The measured and calculated ~:(T) data of 'annealed'samples (X = 0, 0.15 and 0.2) are shown in Fig. 3. For thesamples of 0 ~< X ~< 0.15 in which electron carriers arevery few, the calculated ~c(T) can fully reproduce themeasured ~:(T) without the parameter E. On the other
hand, for the sample of X = 0.2 with increased electron

H. Fujishiro et al./Physica B 219&220 (1996) 163 165
Table 1
Summary of fitting parameters analyzed by TW theory undera unified U ( = 2.5 x 1011 (s-l)) value

A=oSampler~l(s-1)

p ( K 4s-1)

E ( K ls-1)

g

X = 0 (S)X = 0 (A)X = 0.05 (S)X = 0.05 (A)X = 0.1 (S)X = 0.1 (A)X = 0.15 (S)X = 0.15 (A)X = 0.2 (S)X =0.2 (A)

6.5 × l0 s6.5 x 108
5.2 x l0 s
5.2 x l08
1.0 x 108
1.0 × 108
9.4 × 107
9.4 × 107
9.4 × l0 T
9.4× 10v

19492470
2617
4711
1675
1780
1790
1555
2544
2167

00000000
4,7 x 106
4,7 x 106.>

Note: S and A show the 'as-sintered' and 'annealed', respectively.

301 '165

|

i=I

=|

m

"annealed" samples

Ix=o I•

20

X=0.15?

(/I.=_QPEGI
el-3050

I

I
Temperature (K)
III|II

IlO050Fig. 4. Temperature dependence of the thermal diffusivity of the'annealed' samples of X = 0 and 0.15.

Acknowledgements
carriers, the best fit ~c(T) was possible by i n t r o d u c i n g also
the p a r a m e t e r E, the scattering due to carriers. The
values of the fitting p a r a m e t e r s determined in this study
are s u m m a r i z e d in Table 1. The crystal grain size in thesamples increases with increase in Ce c o n c e n t r a t i o n up toX = 0.1, a n d then saturates for X = 0.15 a n d 0.2 (fromthe s c a n n i n g electron microscope (SEM) observation). Ce
c o n c e n t r a t i o n dependence of ~b 1 is consistent with theS E M observation.
Finally, the t e m p e r a t u r e dependence of the t h e r m a ldiffusivity of the 'annealed' samples (X = 0 a n d 0.15) iss h o w n in Fig. 4. :t(T) increases gradually with decrease intemperature. ~(T) for the sample of X = 0.15 was largert h a n t h a t for X = 0 at low temperatures. This reflects thedecrease of the n u m b e r of p h o n o n scattering centers at
X = 0.15 a n d m a y be correlated with the a p p e a r a n c e ofsuperconductivity.

The a u t h o r s wish to t h a n k T o m o y u k i N a i t o
T o h o k u University for his i m p o r t a n t contribution.

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[3] H. Ogasawara et al., Physica C 235-240 (1994) 1399.
[4] J.L. Cohn and M.S. Osofsky, Phys. Rev. B 46 (1992) 12053.
1-5] L. Tewordt and T. W61khausen, Solid State Commun. 70(1989) 839.
[6] H. Fujishiro, M. Ikebe, T. Naito and K. Note, Cryo. Eng. 28(1993) 582 [in Japanese].
[7] P.G. Klemens, in: Solid State Physics, Vol. 1 (AcademicPress, New York, 1958) p. 1.