J. Am. Ceram. Soc., 89 [7] 2301–2303 (2006)
DOI: 10.1111/j.1551-2916.2006.00979.x
r 2006 The American Ceramic Society

JournalThermoelectric Power in Nonstoichiometric Orthorhombic Titanium
OxidesIsao Tsuyumoto,w Taisuke Hosono, and Masataka Murata
Department of Environmental Chemistry, College of Environmental Engineering and Architecture, Kanazawa Instituteof Technology, Ishikawa 921-8501, Japan

Nonstoichiometric orthorhombic titanium oxides (TiOx; x 5
1.86–1.94) prepared by reducing the anatase titanium oxide in
H2 at 9501C are found to show large thermoelectric power.
Their Seebeck coefﬁcients are in the range 0.060 to 0.518
mV/K, and theoretical discussions are made based on theassumption that the electronic spin entropy dominating theentropy current is a main factor of the thermoelectric power.
The ﬁgure of merit for TiO1.94 at 701C is estimated at 0.195.
The nonstoichiometric orthorhombic titanium oxides, containing
no hazardous elements, are promising materials for thermoelectric power generation.

II. Experimental Procedure
According to our previous report,5 the orthorhombic titaniumoxides with the composition of TiOx (x 5 1.94, 1.88, and 1.86)
were prepared by reducing the anatase titanium oxide in H2 at
9501C for 1, 3, and 5 h, respectively. The O/Ti ratio x was determined by thermogravimetry from mass increase accompanied
by an oxidation from TiOx to TiO2 in air in the range 4301–
5701C. The anatase powder was pressed into pellets (j2.5mm  2–3 mm), and gold electrodes were coated on the top
and bottom surfaces and at the two points on the side using gold
paste (Tokuriki Chemical Corporation No. 8570, Japan). Reducing the cylindrical powder compacts in H2 at 9501C yielded
dark blue polycrystal pellets, whose relative densities were in therange 55%–64%.
The performance of thermoelectric materials is evaluated by ameasure of a material’s thermoelectric properties Z,

I. Introduction

T

HERMOELECTRIC effects of metal oxides have attracted muchattention since the middle of the 1990s. Various kinds ofmetal oxides, such as NaxCoO4, Ba1xSrxPbO3, and (ZnO)m
In2O3, have been found to exhibit high thermo-electromotive
force,1–3 and new theoretical approaches have been developed toderive thermoelectric properties in strongly correlated electron
systems.4–8 The thermoelectric oxides have been extensively investigated also from the viewpoint of applications in thermoelectric devices, which generate electric power from waste heat,because they have advantages in resistance to oxidation and toheat over the conventional thermoelectric alloys.9,10 From thepractical point of view, thermoelectric materials consisting of
nonhazardous and inexpensive elements are highly desirable.
Although titanium oxides, having the composition of
TinO2n1, where n is an integer above 2, have been well known
as Magneli phases,11–14 we have recently found new orthorhombic phases of titanium oxides with nonstoichiometric compositions of TiOx (x 5 1.85–1.94).15 The new orthorhombic phases
were obtained by reducing the anatase or the rutile TiO2 in H2 at
9501C, and the O/Ti ratio x can be controlled in the range 1.85–
1.94 by changing the reduction time from 1 to 5 h. Most of theconventional TinO2n1 (n 5 2–6) exhibit a semiconductor–-metaltransition at a critical temperature, and thus we have investigated the electrical and optical properties of the new orthorhombic phases ﬁrst.16 In the conductivity measurement we
discovered an unexpected thermoelectric property of the new
orthorhombic titanium oxides comparable to the other of thepreviously known thermoelectric oxides. It is believed that this is
the ﬁrst observation of thermoelectric effect for the Ti–O system.
In this study, we present the thermoelectric properties of the new
orthorhombic titanium oxides (TiOx, x 5 1.86, 1.88, and 1.94)
and give a theoretical discussion on the Seebeck coefﬁcient on
the basis of the spin-entropy current.

Z ¼ S 2 r1 k1(1)

where S is the Seebeck coefﬁcient, r is resistivity, and k is thermal conductivity.
In the present study, the Seebeck coefﬁcient and the resistivity
were measured at 251, 401, and 701C, in view of the application
to the waste heat recovery. The cylindrical pellet was sandwiched with two copper plates and its bottom was made to contact with a temperature-controlled hot plate. The temperature ofboth copper plates was measured with thermocouples type K,
and the thermoelectromotive force induced between the twoplates was measured by an HP34401A electrometer (HewlettPackard, Palo Alto, CA). The electromotive force was measured
as a function of the temperature difference in the range 0 to ca.
10 K. As for the measurement at 251C, the Seebeck coefﬁcient
was calculated from the slope of the ﬁtted line from 0 to ca. 10
K. On the other hand, as for the measurements at 401 and 701C,
the ﬁtted line from 0 to ca. 3 K was used to calculate the Seebeck
coefﬁcient. This is because the slope of the curves measured at
401 and 701C showed a slight decrease with increasing temperature difference.
The resistivity was measured for the same specimens used in the
Seebeck coefﬁcient measurement by the direct current four-probe
method. A constant current was made to ﬂow from two outside
electrodes using an R6144 current source (Advantest Corporation, Japan), and the electrical potential difference between thetwo inside electrodes induced by the constant current was measured using an HP34401A electrometer (Hewlett-Packard).
The thermal conductivity was measured for the larger pellets
prepared with the same condition using the laser ﬂash method(TC-7000, Ulvac-Riko Corporation, MA).

K. Kunihito—contributing editor

III. Results and Discussion
Figure 1 shows the relationship between thermoelectromotive
force and the temperature difference at 251C. The sign of theelectromotive force was plus on the higher temperature side, i.e.,

Manuscript No. 21080. Received October 18, 2005; approved January 19, 2006.
This work was ﬁnancially supported by the Nissan Science Foundation.
w
Author to whom correspondence should be addressed. e-mail: tsuyu@neptune.
kanazawa-it.ac.jp

2301

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Vol. 89, No. 7

Communications of the American Ceramic Society
2.5

Table I. The Seebeck Coefﬁcient (S, mV/K) of TiOx
(x 5 1.86, 1.88, and 1.94) at 251, 401, and 701C
251C

401C

701C

0.181
0.196
0.0600.199
0.237
0.1700.483
0.292
0.518emf (mV)

2

TiO1.86
TiO1.88
TiO1.94

1.5

This theory is extendable to the nonstoichiometric titaniumoxides, TiOx. The numbers of the conﬁgurations of Ti31 andTi41 are deﬁned as g3 and g4, respectively. Since Ti31 has one
3d-electron in three t2g orbitals, g3 is calculated at six by the
product of (2S11) and 3, where S ( 5 1/2) is the magnitude of
spin. Similarly, g4 is calculated at one because Ti41 has no 3delectron. The total number of the possible states g is expressed as

1

0.5

0
0

2

4
6
∆T (K)

810g ¼ g3NA M gM
4Fig. 1. Relationship between thermoelectromotive force and temperature difference at 251C. D: x 5 1.88, &: x 5 1.86.

the sign of the Seebeck coefﬁcient was minus, indicating that the
specimens were n-type semiconductor. The Seebeck coefﬁcients
estimated from the relationship by the least-squares method
at 251, 401, and 701C are summarized in Table I. The Seebeck
coefﬁcient of TiO1.94 at 701C was 0.518 mV/K. This value isgreater than that of the [(Ca, Sr, Bi)2CoO3]xCoO2 (0.14 mV/K),
which has been intensively investigated toward commercial
application.10 In most cases, the present orthorhombic titaniumoxides showed the Seebeck coefﬁcients to be greater than
0.1 mV/K.
Theoretical prediction of the Seebeck coefﬁcient based on the
Heikes formula in the Hubbard model is given as follows.17–19
The charge carrier transport in the thermoelectric effect isascribed to the difference of chemical potential due to thetemperature gradient, and the chemical potential is dependent
on the entropy current dominated by the electronic spin entropy.
On the basis of the assumption of the high-temperature limit of
the thermoelectric effect, the Seebeck coefﬁcient is expressed as
Q¼

m
qT

(2)

where m is the chemical potential and q is the charge of a carrier.
The chemical potential m is given by
 
m
qs
¼
T
qN E;V(3)

where s is the entropy of the system, and E and V are internalenergy and volume, respectively. The entropy s is expressed as
s ¼ kB ln g(4)where g is the degeneracy. By substituting Eq. (4) into Eq. (3),
we obtain


m
qln g
¼
T
qN E;V

where e is the elementary charge.

(7)

where M is the number of Ti41 and NA is the sum of Ti31 andTi41. By substituting Eq. (7) into Eq. (5), the Seebeck coefﬁcientof the nonstoichiometric titanium oxides is given by
Q¼



kB
g3 x
ln
e
g4 1  x(8)

where x ( 5 M/NA) is the ratio of Ti41.
The Seebeck coefﬁcients were calculated by applying Eq. (8)to TiOx. The ratio of Ti31 and Ti41 was estimated from theaverage valence of a titanium ion determined by the O/Ti ratio.
As shown in Table II, the Seebeck coefﬁcients of TiO1.94,
TiO1.88, and TiO1.86 predicted by Eq. (8) were 0.326, 0.254,
and 0.236 mV/K, respectively. These theoretical values were
found to be rather close to the experimental values at 701C in
Table I.
Here we should note that the theory above is based on theassumption of the high-temperature limit (B10 000 K). Although such agreement between the theoretical and the experimental values has also been reported for NaCo2O4, the fact thatthe theoretical values (B10 000 K) are near the experimental
ones at 701C (343 K) is said to be an anomalous behavior. The
agreement between these suggests that the system has a tendency
to exhibit various phase transitions by doping impurities. Actually, the NaCo2O4 system has been reported to show spin-density-wave, itinerant ferromagnetism, and superconductivity.20–22
From this analogy, it is probable that many intriguing physicalproperties of the nonstoichiometric titanium oxides (TiO2d) remain undiscovered, because there are few researches on thepresent nonstoichiometric titanium oxides. It is expected thatthe physical properties of the nonstoichiometric titanium oxides
will be a hot area of study from the viewpoint of fundamental
solid-state physics as well as for practical applications.
The ﬁgures of merit of the present nonstoichiometric titaniumoxides is evaluated as follows. The resistivity of TiO1.94 was
0.0646, 0.0590, and 0.0519 O  cm at 251, 401, and 701C, respectively. The temperature dependence was semiconductive, whichcorresponded to the negative sign of the Seebeck coefﬁcientsabove. The thermal conductivity of TiO1.86, TiO1.88, and TiO1.94(5)

Thus, the Seebeck coefﬁcient in the high-temperature limit isexpressed as
kB q ln g
Q¼
e qN

NA !
M!ðNA  MÞ!

(6)

Table II. The Theoretically Predicted Seebeck Coefﬁcient (S,mV/K) of TiOx (x 5 1.86, 1.88, and 1.94) at High-Temperature
Limit Based on Eq. (8)TiO1.86
TiO1.88
TiO1.94

Ti31 (%)

Ti41 (%)

g3/g4

x/(1x)Q (mV/K)

28
24
12

72
76
88

6
6
6

2.57
3.17
7.33

0.236
0.254
0.326

July 2006

Table III. The Measure of a Material’s Thermoelectric
Properties (Z,  105 K1) and the Figure of Merit (ZT) for
TiOx (x 5 1.86, 1.88, and 1.94) at 251, 401, and 701C
Z (  105 K1)

TiO1.86
TiO1.88
TiO1.942303

Communications of the American Ceramic Society

ZT

251C

401C

701C

251C

401C

701C

0.43
0.50
0.61

0.52
0.74
5.38

3.17
1.16
56.8

0.00130.00150.00180.00160.00230.017

0.01090.00400.195

was estimated at 1.0, 1.0, and 0.91 W  (m  K)1, respectively, at
251C. Table III shows the measure of a material’s thermoelectric
properties (Z) and the ﬁgure of merit (ZT). The ﬁgure of meritfor TiO1.94 at 701C reached ZT 5 0.195. This value is comparable to the other reported n-type materials, such as (ZnO)5(In0.97Y0.03)2O3,23 Ba1xSrxPbO3, and CaMnO3.25 It is thoughtthat the present nonstoichiometric titanium oxides have advantages over such thermoelectric materials with regard to environmental loading, because they contain no hazardous heavy
metals. Moreover, there is also a possibility of further improvement of performance by optimizing the synthetic condition. In
the present study, the polycrystal pellets were employed, aiming
at the practical applications, and therefore the performance
estimated above may be dependent on some qualities of eachpellet, such as porosity, grain size, and inhomogeneity. It canbe said that there still remains a need to clarify the theoreticalmechanism of thermoelectric oxides. The usage of the single
crystals would be more effective to provide theoretical details.

IV. Summary
It was found that the nonstoichiometric orthorhombic titaniumoxides (TiOx, x 5 1.85–1.94) obtained by reducing anatase TiO2
show a large thermoelectric effect. It is believed that this was theﬁrst observation of the thermoelectric effect with regard to the
Ti–O system. The Seebeck coefﬁcient of TiO1.94 at 701C was0.518 mV/K, and its ﬁgure of merit (ZT) was estimated at
0.195. This value is comparable to the other reported thermoelectric materials, and there is still a possibility that titaniumoxides with higher performance remain undiscovered. The experimental Seebeck coefﬁcients were compared with the theoretical values predicted by assuming that the entropy current
dominated by the electronic spin entropy determines the Seebeck coefﬁcient. Although the theoretical values were close to
the experimental ones, there appears to remain a need to formulate the theory to explain the thermoelectric effects of Ti–O
system. Further theoretical discussions would be possible by using single crystals of the nonstoichiometric orthorhombic titanium oxides. It can be said that thermoelectric power generation
using the nonstoichiometric orthorhombic titanium oxides has
advantages with regard to environmental load, not only because
they show high performance but also because they contain nohazardous elements.

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