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High-temperaturethermoelectric
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ImpactFactor:1.32·DOI:10.1016/j.physb.2004.06.033

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ARTICLE IN PRESS

Physica B 352 (2004) 18–23

High-temperature thermoelectric properties of
Ca1Àx Prx MnO3Àd ð0pxo1Þ
Bach Thanh Conga,*, Toshihide Tsujib, Pham Xuan Thaob, Phung Quoc Thanha,
Yasuhisa Yamamurab
b

a
Faculty of Physics, Hanoi University of Science, 334 Nguyen Trai, Hanoi 844, Viet Nam
School of Materials Science, JAIST, 1-1 Asahidai, Tatsunokuchi, Ishikawa 923-1292, Japan

Received 2 June 2004; accepted 15 June 2004

Abstract
Ca1ÀxPrxMnO3Àd (x=0, 0.05, 0.15, 0.1, 0.2, 0.4, 0.67; d=0.02) samples were prepared by a solid-state reaction
method. X-ray diffraction analysis showed that all samples prepared were of single phase with orthorhombic structure.
Electrical resistivity measurements from room temperature to 1300 K showed that a metallic conducting tendency
dominated at high temperatures. The hopping nature of the charge carriers was well interpreted in the framework of
polaron theory. The Seebeck coefficient was measured in the same temperature interval, and its concentration
dependence was analyzed using the high-temperature (HT) thermopower theory proposed by Marsh–Parris. The
thermal conductivity and the figure of merit of the prepared samples were also compared with those of other similar
perovskite compounds. The observed figure of merit of the sample with x=0.15 was Z=1.5 Â 10À4 KÀ1 at T=1100 K,
indicating a good potential for application as a HT thermoelectric material.
r 2004 Elsevier B.V. All rights reserved.
PACS: 72.20.Pa; 72.80.Ga
Keywords: Thermoelectric properties; Ca1ÀxPrxMnO2.98 perovskite; Electrical conductivity; Seebeck coefficient; Thermal conductivity

1. Introduction
Perovskite compounds with chemical formula,
A1ÀxA’xBO3 (where A is a rare earth metal, A’ is
an alkaline earth metal, and B is a transition metal
like Mn or Co), have attracted much attention of
researchers by their interesting physical phenom*Corresponding author. Tel.: +84-45582216; fax: +8448589496.
E-mail address: (B.T. Cong).

ena. The current interest is concentrated not only

on colossal magnetoresistance (CMR) and magnetocaloric effects (see for example Ref. [1]), but also
on thermoelectric properties. Manganese perovskites, with various substitutions for calcium,
Ca1Àx Ax MnO3 ; are considered as promising new
materials for high-temperature (HT) thermoelectric energy conversion with a sufficiently large
power factor and figure of merit over the wide
temperature range 600–900 C [2]. Recently, some
authors in this field examined Ca1Àx Dyx MnO3

0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.physb.2004.06.033


ARTICLE IN PRESS
B.T. Cong et al. / Physica B 352 (2004) 18–23

work [3]. The oxygen content in all samples was
determined to be ðO=Ca1Àx Prx MnÞ ¼ 2:98 by the
oxidation-reduction method (the oxygen deficiency
is d ¼ 0:02). The obtained samples were identified
by X-ray diffraction using a RIGAKU RINT2500 V. The electrical conductivity was carried out
in air in the temperature range 300–1273 K, using
a four-point probe method. The Seebeck coefficient was calculated from the linear gradient DV/
DT from the measured thermoelectromotive force
and temperature difference, in the same temperature range. The thermal diffusivity of the samples
was measured by a laser flash method using a
ULVAC TC-7000. The thermal conductivity, l,
was calculated using the method given in Ref. [3].

3. Results and discussion
The quality of the prepared samples was

checked by X-ray powder diffractometry. Fig. 1
shows the X-ray diffraction (XRD) patterns for all
samples, taken at room temperature. The powder
XRD patterns show a single phase of the
Ca1Àx Prx MnO3Àd solid solution over the whole
Pr-doping concentration. The crystals have an
orthorhombic structure belonging to the same

x = 0.67

x = 0.40
Intensity (abr.units)

(0pxp0:2) [3] and found the figure of merit of
Z ¼ 1:63 Â 10À4 KÀ1 for x ¼ 0:2 at 1273 K. The
aim of this contribution is to investigate the HT
thermoelectric properties of Ca1Àx Prx MnO3
(0pxo1). This system has the specific feature
( and Ca2+
that the ionic radii of Pr3+ (1.179 A)
(
(1.180 A) are almost the same [4]. It is well known
that the transport properties of perovskites depend
strongly on the average size of the A cation (/
rAS) and the concentration of carriers x. The
Ca1Àx Prx MnO3 solid solutions can exist in the
whole concentration interval 0pxp1; and are
suitable for studying the role of charge carriers in
transport phenomena. Most HT thermoelectric
investigations were performed in the electrondoping region (xo0:5; where the concentration

of Mn3+ is less than that of Mn4+) and it is
interesting to extend this to another, hole doping,
region. According to Ref. [4], the magnetic phase
diagram for Ca1Àx Prx MnO3 at low temperature
(o300 K) has the specific feature that the CMR
effect exists in both electron- and hole-doping
regions, around xB0.9 and xB0.3, respectively.
The other rare-earth mixed-valence systems like
Sr1Àx Prx MnO3 and Sr1Àx Smx MnO3 have not this
symmetric behavior. Inside and close to CMR
concentration intervals, the electrical conductivity
is sufficiently large, and then the HT power factor
of Ca1Àx Prx MnO3 can also be expected to be large.
The structure of Ca1Àx Prx MnO3 was studied using
X-ray diffraction by Pollert et al. [5] and using
neutron diffraction by Jirak et al. [6]. In their work
[6], it was shown that for 0:6pxp0:7 the Seebeck
coefficient of this material changes sign from
negative to positive when the temperature becomes
low enough. The HT behavior of these materials
above room temperature is the subject of the
present study.

19

x = 0.20
x = 0.15
x = 0.10

2. Experimental

Ca1Àx Prx MnO3Àd (x ¼ 0; 0.05, 0.15, 0.1, 0.2,
0.4, 0.67) perovskite samples were prepared by a
solid-state reaction method using as starting
materials powders of CaCO3, MnO2, and Pr2O3
with high purity. The sample preparation method
was similar to the one described in our previous

x = 0.05
x=0
20

40

60

80

100

120

2 (degree)

Fig. 1. X-ray diffraction patterns for Ca1Àx Prx MnO2:98
(x ¼ 0 À 0:67) samples.


ARTICLE IN PRESS
B.T. Cong et al. / Physica B 352 (2004) 18–23

20

Table 1
Lattice constants of Ca1Àx Prx MnO2:98 (x=0À0.67) samples
Samples
CaMnO3
Ca0.95Pr0.05MnO3
Ca0.9Pr0.1 MnO3
Ca0.85Pr0.15 MnO3
Ca0.8Pr0.2 MnO3
Ca0.6Pr0.4 MnO3
Ca0.33Pr0.67 MnO3

(
b (A)

(
c (A)

( 3
V (A)

5.273
5.279
5.280
5.295
5.306
5.321
5.381
5.452

5.267
5.264
5.278
5.292
5.305
5.318
5.377
5.426

7.451
7.448a
7.462
7.480
7.495
7.512
7.568
7.661

206.922
207.947
209.622
210.965
212.580
218.947
228.611

Data taken from Ref. [7].

Ca1-xPrxMnO2.98

ρ (x 10-2 Ω.cm)

8

60

x=0
x=0.05
x=0.10
x=0.15
x=0.20
x=0.40
x=0.67 (right axis)

6

40

20

4

ρ (x 10-2 Ω.cm)

a

(
a (A)

0
2
-20
0
200

400

600

800

1000

1200

1400

T (K)

Fig. 2. Electrical resistivity of Ca1Àx Prx MnO2:98 (x ¼ 0 À 0:67).

space group Pnmb, and the lattice constants are
given in Table 1.
Fig. 2 shows the temperature dependence of the
electrical resistivity, r, of the prepared samples in
the temperature range from room temperature to
1273 K. Samples with x ¼ 0; 0.2, 0.4, 0.67 show a
typical semiconducting behavior in the investigated temperature region. Low doping with
praseodymium (x ¼ 0:05; 0.1, 0.15) causes an

essential decrease of resistivity and its value does
not change much with increasing temperature.
Further doping with Pr (x > 0:15) leads to an
increase of the resistivity again. There are several
concepts used for the interpretation of conducting
phenomenon in perovskites. The temperature
dependence can be described using the small

polaron model given by Mott [8]. According to
this theory, the resistivity is expressed by,


r
Ea
¼ C exp
;
T
kB T
where C is given by
C¼

kB
expð2gRÞ:
Ne2 a2 xð1 À xÞnph

Here, e is the absolute value of the electron
charge, N is the number of ion sites per unit cell
volume (Mn sites), a is an average intersite
distance for polaron hopping obtained from the
relation a=(1/N)1/3, g is the electron wave function

decay constant, nph is the optical phonon frequency, x is the fraction of available sites occupied
by small polarons (assumed equal to the Mn3+
concentration), and Ea is an activation energy for
hopping conduction.
By plotting log(r/T) as a function of 1/T, one
can determine the activation energy, Ea, in the
temperature range from 300 to 700 K, as seen in
Fig. 3a. Fig. 3b shows the activation energy of
doped samples as a function of x in the
Ca1Àx Prx MnO2:98 solid solutions.
A tendency of the activation energy to increase
with increasing doping Pr concentration (x) is seen
in Fig. 3b. This increase indicates that an increase
of the Mn3+ concentration is favorable for the
formation of polarons in this temperature interval.
The well-observed jump of Ea at xB0:2 indicates
that the small polaron is more stabilized for
xX0:2:
Fig. 4 shows the temperature dependence of the
Seebeck
coefficient
for
Ca1Àx Prx MnO2:98
(x ¼ 0 À 0:67), and reveals that the dominating
electrical carriers at room temperature are electrons for all samples except for x ¼ 0:67:
At high temperatures, the conducting character
is n-type for the whole system (including both
electron- and hole-doping samples). This is an
interesting feature of HT behavior in comparison
with the symmetric property at temperatures

below room temperature [6], where n- (or p-)
conducting type prevails in the case of xo0:5 (or
x > 0:5). The dominating electron conducting
character shows that the carrier mobility rather
than their concentration governs HT transport


ARTICLE IN PRESS
B.T. Cong et al. / Physica B 352 (2004) 18–23

21

0

-2.5
Ca1-xPrxMnO2.98

-3.5

x=0
x=0.05
x=0.10
x=0.15
x=0.20
x=0.40
x=0.67

-50
α (µVK-1)

log[ρ/T (K-1Ω cm)]

-3.0

-100
Ca1-xPrxMnO2.98

-4.0
-200

-4.5
-250
200

-5.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

600

800
1000
T (K)

1200

1400

Fig. 4. Temperature dependence of the Seebeck coefficient, a,
for Ca1Àx Prx MnO2:98 (x ¼ 0 À 0:67) sintered bodies.

the HT limit, assuming that the energies of the
Jahn–Teller (DJT ) and the Coulomb interaction
(U) are smaller than the thermal energy
ðDJT ; U5kB TÞ:


kB
3 À r0 À x
a ¼ À ln
:
r0 À 1 þ x
e

0.15

Ea (eV)

400

103/T (K-1)

(a)

0.10

0.05

0.1

(b)

x=0
x=0.05
x=0.10
x=0.15
x=0.20
x=0.40
x=0.67

-150

0.2

0.3

0.4
x

0.5

0.6

0.7

Fig. 3. (a) log(r/T) vs. TÀ1 for Ca1Àx Prx MnO2:98
(x ¼ 0 À 0:67). (b) Activation energy, Ea, as a function of
doping Pr concentration for Ca1Àx Prx MnO2:98 (x ¼ 0 À 0:67) in
the temperature range from 300 to 700 K.

behavior. The Seebeck coefficients of the small
polaron conduction system at HT can be interpreted by Marsh and Parris’s theory [9], developed
for a strong coupling system. This theory is
applied for the case that the B-site transition
metal of perovskite ABO3 has the number of
electron, n, in the 3d manifold, 3pnp5: We used
the following formula for the Seebeck coefficient in

Here, r0 is the number of eg electrons per Mn3+
site, and x is the doping concentration. The
comparison between theoretical and experimental
values for the concentration dependence of Seebeck coefficient is shown in Fig. 5. A good
agreement is observed for r0 ¼ 1:3: The HT theory
[9] appears to describe our experiments well.
Fig. 6 demonstrates the temperature dependence
of the thermal conductivity, l. The contribution
from the electronic thermal conductivity, le, is
calculated by using Wiedemann–Franz’s law as

given in Ref. [3]. For all samples the phonon
contribution lph=lÀle is much more important
than the electronic one.
Fig. 7 shows the temperature dependence of the
power factor, sa2 ; calculated from the measured
Seebeck coefficient and the electrical conductivity
s ¼ rÀ1 : The power factor increases as the
temperature increases, and reaches the value of
2.43 Â 10À4 WmÀ1 KÀ2 for the electron-doping
compound (xo0:5) with x ¼ 0:15 at 1200 K. This
quantity is sufficiently small for the hole-doping
samples with x > 0:5 (for x ¼ 0:67; power factor is
near zero).


ARTICLE IN PRESS
B.T. Cong et al. / Physica B 352 (2004) 18–23

22

ρ0 = 1.3

2.5

0

-100
Ca1-xPrxMnO2.98

-200

2.0
(x 10-4 W m-1K-2)

α (µVK-1)

ρ0 = 1.05

573 K
873 K
1073 K
1273 K

-300

1.0

2

0=1.3

1.5

Ca1-xPrxMnO2.98
x=0
x=0.05
x=0.10
x=0.15
x=0.20
x=0.40

x=0.67

0=1.05

0.5

-400
0.0 0.1

0.2 0.3 0.4

0.5 0.6 0.7 0.8 0.9 1.0
x

0.0

Fig. 5. The concentration dependence of the Seebeck coefficient
for Ca1Àx Prx MnO2:98 (x ¼ 0 À 0:67).

Ca1-xPrxMnO2.98

3.5

200

400

600

800

1000

1200

1400

T (K)

Fig. 7. Temperature dependence of the power factor, sa2,
obtained from the measured Seebeck coefficient and electrical
conductivity data.

e

x=0
x=0.05
x=0.10
x=0.15
x=0.20
x=0.40
x=0.67

2.5
2.0

1.5
1.2

1.5

Z (x 10-4 K-1)

(W m-1 K-1)

3.0

1.0
0.5
0.0
200

0.9
0.6
0.3

400

Fig. 6. Thermal
(x ¼ 0 À 0:67).

600

800
1000
T (K)

conductivity,

l,

1200

1400
0.0

of

Ca1Àx Prx MnO2:98

200

400

600

800

1000

1200

1400

T (K)

Fig. 8. Figure of merit, Z, of Ca1Àx Prx MnO2:98 as a function of
temperature.

The temperature dependence of the figure of

merit, Z, in this system is plotted in Fig. 8. Z
increases with increasing praseodymium fraction
from 0 to 0.15. A doping level x > 0:15 leads to a
strong reduction of Z. This quantity is near zero
for x ¼ 0:6:

room temperature. In view of application as a
high-temperature thermoelectric material, the
large figure of merit of Z ¼ 1:5 Â 10À4 K À1 for x ¼
0:15 at T ¼ 1100 K indicates good possibilities.

4. Conclusions

Acknowledgements

Ca1Àx Prx MnO3Àd perovskite compounds were
prepared and their thermoelectric properties were
investigated in the high-temperature region. It was
shown that the observed HT transport properties
are much different from those in the region below

The author (B.T. Cong) thanks the JAIST-HUS
collaboration program for supporting his short
visit at JAIST, where a part of this work was done.
The help of the VNU Asia Research Center is also
acknowledged.


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B.T. Cong et al. / Physica B 352 (2004) 18–23

References
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23

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