Thermoelectric properties of Bi-doped Mg2Si semiconductors

Article abstract of DOI:10.1016/j.physb.2005.04.017

The thermoelectric properties of Bi-doped Mg₂Si (Mg ₂Si:Bi=1:x) fabricated by spark plasma sintering process have been characterized by Hall effect measurements at 300 K and by measurements of electrical resistivity (ρ), Seebeck coefficient (S), and thermal conductivity (κ) between 300 and 900 K. Bi-doped Mg₂Si samples are n-type in the measured temperature range. The electron concentration of Bi-doped Mg₂Si at 300 K ranges from 1.8×10¹⁹ cm ^-3 for the Bi concentration x=0.001 to 1.1×10²⁰ cm^-3 for x=0.02. The solubility limit of Bi in Mg₂Si is estimated to be about 1.3 at% and first-principles calculation revealed that Bi atoms are expected to be primarily located at the Si sites in Mg₂Si. The electrical resistivity, Seebeck coefficient, and thermal conductivity are strongly affected by the Bi concentration. The sample of x=0.02 shows a maximum value of the figure of merit, ZT, is 0.86 at 862 K.

Full text of DOI:10.1016/j.physb.2005.04.017

ARTICLE IN PRESS
Physica B 364 (2005) 218–224
www.elsevier.com/locate/physb
Thermoelectric properties of Bi-doped Mg Si semiconductors
2
Ã
Jun-ichi Tani , Hiroyasu Kido
Department of Electronic Materials, Osaka Municipal Technical Research Institute, 1-6-50 Morinomiya, Joto-ku, Osaka 536-8553, Japan
Received 25 February 2005; received in revised form 11 April 2005; accepted 11 April 2005
Abstract
The thermoelectric properties of Bi-doped Mg
been characterized by Hall effect measurements at 300 K and by measurements of electrical resistivity ðrÞ, Seebeck
coefficient (S), and thermal conductivity ðkÞ between 300 and 900 K. Bi-doped Mg Si samples are n-type in the
measured temperature range. The electron concentration of Bi-doped Mg Si at 300 K ranges from 1.8 Â 10 cm for
2
Si (Mg
2
Si:Bi ¼ 1:x) fabricated by spark plasma sinteringprocess have
2
1
9
À3
2
2
0
À3
the Bi concentration x ¼ 0:001 to 1.1 Â 10 cm for x ¼ 0:02. The solubility limit of Bi in Mg
2
Si is estimated to be
about 1.3 at% and first-principles calculation revealed that Bi atoms are expected to be primarily located at the Si sites
in Mg Si. The electrical resistivity, Seebeck coefficient, and thermal conductivity are strongly affected by the Bi
2
concentration. The sample of x ¼ 0:02 shows a maximum value of the figure of merit, ZT, is 0.86 at 862 K.
r 2005 Elsevier B.V. All rights reserved.
PACS: 72.20.Pa; 71.55.Ài
Keywords: Semiconductor; Thermoelectric material; Hall effect; Mg
2
Si; First-principles calculation
1
. Introduction
low thermal conductivity [1–4]. There have been
some attempts to dope additives into Mg (Si, Ge,
2
The intermetallic compounds such as Mg X
2
Sn) to control its semiconductingproperties. The
conduction types are p-type, produced by doping
with Agand Cu and n-type, produced by doping
with Sb and Al [2–7].
(
X ¼ Si, Ge, Sn) and their solid solutions are
semiconductors havingthe antifluorite structure
and have been proposed to be good candidates for
high-performance thermoelectric materials, be-
cause of their superior features such as its large
Seebeck coefficient, low electrical resistivity, and
For thermoelectric materials, a large Seebeck
coefficient, S, a small electrical resistivity, r, and a
small thermal conductivity, k, are required. These
quantities determine the so-called thermoelectric
2
Ã
figure of merit, Z ¼ S =rk. A low lattice thermal
Correspondingauthor. Tel.: +81 6 6963 8081;
fax: +81 6 6963 8099.
E-mail address: tani@omtri.city.osaka.jp (J. Tani).
conductivity and a high carrier mobility are
desirable for improvement of the figure of merit.
0921-4526/$ - see front matter r 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.physb.2005.04.017

ARTICLE IN PRESS
J. Tani, H. Kido / Physica B 364 (2005) 218–224
219
0
Vining [8] pointed out that a factor A ¼ ðT=300Þ
ratio of Mg Si:Bi ¼ 1:x) were added to each
2
Ã
3=2
Ã
ðm =meÞ mkph, where m is the carrier effective
charge. They were ground together, and then
heated in a graphite die (15 mm in diameter) at
1023–1053 K for 15 min at 30 MPa under a
2
mass, m is the mobility in cm /V s, and k is the
ph
lattice thermal conductivity in mW/cmK, is a
larger value of 3.7–14 for Mg (Si, Ge, Sn), as
compared with 1.2–2.6 for SiGe and 0.05–0.8 for
b-FeSi and therefore Mg (Si, Ge, Sn) system will
achieve higher ZT with further development.
Recently, Kajikawa et al. [9,10] and Umemoto
et al. [11] reported thermoelectric properties of
À3
vacuum of 1 Â 10 Torr by the SPS method with
2
a heatingrate of 60 K/min. The density of the
annealed samples was more than 99% of the
theoretical value.
2
2
X-ray diffraction by Cu Ka radiation of the
samples detected only the anti-fluorite type struc-
ture. The Hall coefficient (R ) was measured for
Mg Si fabricated by spark plasma sintering(SPS),
2
H
which is a novel process because it is reported that
the diffusion velocity becomes extremely large
even at low temperatures due to pulse electric field
1.5-cm-diameter, 0.1-cm-thick samples usingthe
Toyo Corporation Resitest 8320. The contacts
between the samples and lead Au wires were
formed by solderingwith In. The Hall effect was
measured at 300 K usingan alternatingcurrent
(AC) magnetic method, under an applied magnetic
field of 0.39 T at a frequency of 200 mHz. The
carrier concentration (n) of the samples was
superposed on DC. In case of Mg Si, SPS plays
2
two roles: (a) solid-state reaction process between
Mgand Si, (b) densification process in a short time
at relatively low temperatures, which would be
effective to suppress the volatilization of Mgas
well as dopants with low meltingpoint. Bi has a
low meltingpoint of 545 K [12] and belongs to
same Vb group as Sb, which is n-type dopant of
Mg Si. For Bi-doped Mg Si, a low thermal
determined by the factor 1/e|R |. The Seebeck
H
coefficient (S) was measured by the standard
technique usingPt electrodes in a He ga s atmo-
sphere in the temperature range of 300–900 K
usingan ULVAC ZEM-1S. The temperature
gradient across the length of the sample was about
5 K. The electrical resistivity ðrÞ was also measured
concurrently by the four-probe DC method. The
thermal diffusion coefficients of the samples were
measured by the conventional laser flash method
usinga thermal constant analyzer (ULVAC TC-
7000). The disk specimen was set in an electric
furnace and heated to 900 K under vacuum. After
the temperature was stabilized, the front surface of
the specimen was irradiated by a ruby laser pulse.
The temperature variation at the surface was
monitored with a Pt–Pt 13%Rh thermocouple
and an InSb infrared detector. The density was
measured by the Archimedes method. The thermal
conductivity was calculated from the experimental
thermal diffusivity as well as density values and
a previous reported specific heat capacity data
2
2
conductivity might be possible because Bi has a
larger radius than other n-type dopants such as Al
and Sb. However, to our knowledge, there has
been no research concerningthe thermoelectric
properties of Bi-doped Mg Si.
2
In this paper, the thermoelectric properties of
Bi-doped Mg Si fabricated by SPS process have
2
been characterized by Hall effect measurements at
3
00 K and by measurements of electrical resistiv-
ity, Seebeck coefficient, and thermal conductivity
between 300 and 900 K. Finally, an optimum
composition giving the largest ZT value in the
present system is determined. We have also
performed quantum-mechanical first-principles
calculations of Bi-doped Mg Si within density
2
functional theory to obtain information on the
preferential site occupation of Bi in Mg Si.
2
of nondoped Mg Si investigated by Riffel and
2
2
. Experiment and details of the calculations
Schilz [13].
In order to investigate geometrical structure of
Powders of high purity, Mg (499.9%), Si
Bi-doped Mg Si, density functional theory (DFT)
2
(
499.999%), and Bi (499.9%), were used as
startingmaterials. The Mgand Si were mixed in
:1 ratio and varyingan amount of Bi (the molar
calculations within the pseudopotential and gen-
eralized gradient approximations (GGAs) were
2
performed usingthe computer pro rg am
CASTEP

ARTICLE IN PRESS
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J. Tani, H. Kido / Physica B 364 (2005) 218–224
(Cambridge Serial Total Energy Package in
Cerius2, Accelrys Inc.) [14]. We constructed a
supercell containing48 atoms (Mg 32Si ) with the
16
at x ¼ 0:005 in the composition range
0:001 % x % 0:02. The mH of Bi-doped Mg Si is
2
2
larger than the reported values 41.5 cm /V s
¯
space group Fm3m and replaced one of the 48 sites
for 0.6 mol% Sb-doped Mg Si investigated by
2
of the Mgor Si atoms by Bi. We expanded the
valence electronic wave functions in a plane-wave
basis set up to an energy cutoff of 400 eV, which
converges the total energy of the unit cell to better
than 1 meV/atom. The Brillouin zone integrations
were preformed at the G point for the 48-atom unit
cell. The electron–ion interaction is described by a
Vanderbilt’s ultrasoft pseudopotentials [15]. The
lattice constant was determined through calcula-
tions for the primitive cell, usinga plane-wave
cutoff energy of 400 eV and the calculated value is
Kajikawa [9]. The carrier concentration of non-
1
7
À3
doped Mg Si is 4.3 Â 10 cm , while that of
2
1
9
À3
Bi-doped Mg Si is 1.8 Â 10 cm for x ¼ 0:001
2
2
0
À3
to 1.1 Â 10 cm for x ¼ 0:02. In the Bi-doped
Mg Si, the carrier concentration is almost propor-
2
tional to the dopingconcentration within the
composition range of 0:000 % x % 0:01. If Bi atom
is soluble in Mg Si, carrier concentration should
2
correspond to the Bi atom concentration. There-
fore, a solid solution of Bi-doped Mg Si exists at
2
least in the range of 0:000 % x % 0:01. However,
the carrier concentration for x ¼ 0:02 is much
lower than a value from a straight line in Fig. 1.
This fact suggests that Bi atoms are not completely
soluble for x ¼ 0:02. From the plot in Fig. 1, the
solubility limit is estimated to be 1.3 at%.
9
Mg Si [16]. The positions of the atoms within the
9.9% of the experimental value reported for
2
second nearest neighbors of the impurity were
allowed to relax under a constant volume condi-
tion by total energy minimization, until the
residual forces for the relaxed atoms were
There is no information on the preferential site
occupation of Bi in Mg Si. So, we performed
˚
o0.1 eV/A.
2
quantum-mechanical first-principles calculations
of Bi-doped Mg Si within density functional
2
3
. Results and discussion
theory to obtain information on the preferential
site occupation of Bi in Mg Si.
2
Table 1 lists the results of the Hall effect and
electrical resistivity measurements at 300 K of Bi-
doped Mg Si, compared to those of nondoped
2
Mg32Si16 þ Bi ! Mg31Si16Bi þ Mg,
(1)
(2)
Mg Si. The sign for R of nondoped and Bi-doped
2
Mg Si þ Bi ! Mg Si Bi þ Si.
H
16
15
3
2
32
Mg Si is negative, indicating that the conductivity
2
The energetic difference between reactions (1) and
2) is estimated:
is mainly due to electrons. The Hall mobility
ðm ¼ R =rÞ at 300 K of Bi-doped Mg Si is lower
(
H
H
2
2
than the value 204 cm /V s of nondoped Mg Si.
2
DEt ¼ fEtðMg Si16BiÞ þ mMgg
3
1
mH of Bi-doped Mg Si shows composition depen-
2
2
dence and shows the highest value of 92.4 cm /V s
À fE ðMg Si BiÞ þ m g.
ð3Þ
t
32 15
Si
Table 1
Electrical properties of Bi-doped Mg
2
Si (Mg
2
Si: Bi ¼ 1:x ð0:000 % x % 0:020Þ) at 300 K
x
Conduction type
Carrier concentration
À3
Mobility
2
(cm /V s)
Resistivity
(Ocm)
(at%)
(cm
)
17
19
19
19
19
20
À2
À3
À3
À3
À3
À4
0.0
0.1
0.3
0.5
1
2
N
N
N
N
N
N
4.3 Â 10
1.8 Â 10
3.1 Â 10
4.1 Â 10
8.5 Â 10
1.1 Â 10
204
7.14 Â 10
3.97 Â 10
2.22 Â 10
1.64 Â 10
1.16 Â 10
8.58 Â 10
85.7
91.5
92.4
63.5
64.0

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221
1
5
2
9
6
3
0
Table 2
The calculated total energies of Mg
2
Si perfect crystal, the Bi-
doped crystals, Si atom calculated from the Si crystal, and Mg
atom calculated from the Mgcrystal
1
Models
Total energy
(
eV)
Mg
2
Si
À2066.309
Mg31BiSi16
Mg32Si15Bi
Mg
À32234.84
À33106.15
À978.519
À108.728
Si
1
.3 at%
fore, the substitution at the Si sites is lower than
that for substitution at the Mgsites. Therefore, Bi
atoms are expected to be primarily located at the
Si sites in Mg Si. The n-type conduction can be
2
interpreted as a result indicatingthat Bi atoms (Vb
group) in Mg Si are substituted by Si atoms (IVb
0
1
2
3
2
Bi (at%)
group) and act as donors. Kajikawa et al. [9]
reported that Sb is estimated to be replaced to Si
site from the results of electron probe microana-
lysis (EPMA). Takinginto account that Bi is the
Fig. 1. Bi atom concentration (x) dependence of carrier
concentration (n) of Bi-doped Mg Si at 300 K.
2
The chemical potentials of mMg and mSi can be
varied within a range limited by the three
constraints:
same group Vb as Sb and Sb-doped Mg Si shows
2
same n-type behavior, this calculation result seems
reasonable.
Fig. 2 shows the temperature dependence of
mMg % mMg ðbulkÞ,
m % m ðbulkÞ,
(4)
(5)
(6)
the electrical resistivity ðrÞ of Bi-doped Mg Si,
2
as compared with that of nondoped Mg Si. r of
2
Si
Si
Bi-doped Mg Si decreases with increasing x. r of
2
Bi-doped Mg Si has an almost constant value
2
2
mMg þ m ¼ m
ðbulkÞ,
Si
Mg Si
2
at 300–380 K, but increases gradually with increas-
ingtemperature at 380–900 K. LaBotz et al. [1]
and Noda et al. [4] reported that the tempera-
ture dependence of mobility in Mg Si Ge
where mMg Si (bulk), the chemical potential of the
bulk Mg Si, is a constant value calculated as the
2
2
total energy per Mg Si unit formula. The forma-
2
2
x
1Àx
À3=2
tion energies were calculated under the two
extreme conditions, the Si-rich limit ðm
indicates m / T
and the acoustic lattice
¼
scatteringis the predominant mechanism. There-
fore, the increment of r at 380–900 K will be
explained by the decrease of mobility with
increasingtemperature. On the other hand, the r
Mg
1
=2ðm
À m
Þ
and m ¼ m
)
Mg Si ðbulkÞ
Si ðbulkÞ
Si
Si ðbulkÞ
2
and the Mg-rich limit (mSi ¼ mMg Si ðbulkÞÀ
2
2
total energies of the Mg Si perfect crystal, the Bi-
mMg ðbulkÞ and mMg ¼ mMg ðbulkÞ). The calculated
of nondoped Mg Si increases, reachinga max-
2
2
doped crystals, Si atom calculated from the Si
crystal (space group Fd3m, cubic structure), and
Mgatom calculated from the Mgcrystal (space
imum at 470 K, and then decrease with increasing
temperature. The decrease of r at high tempera-
tures is explained by a result that the intrinsic
conduction will occur due to the band gap of
0.77 eV [17,18].
group P6 /mmc, hexagonal structure) are shown in
3
Table 2. A comparison of the computed total
energies revealed that DE is 1.25 and 2.06 eV at
the Si-rich and Mg-rich limit, respectively. There-
Fig. 3 shows the temperature dependence of
the Seebeck coefficient (S) of Bi-doped Mg Si,
t
2

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J. Tani, H. Kido / Physica B 364 (2005) 218–224
0
1
0
1
0
Nondoped
0.1 at %
0.3 at %
0.5 at %
-100
-
1 at %
at %
-
-
-
-
200
300
400
500
10
2
-
2
3
4
1
1
1
0
Nondoped
.1 at %
0.3 at %
0
-
0
-600
0
1
2
.5 at %
at %
at %
-
700
-
0
-800
300
3
00
400
500
600
700
800
900
400
500
600
700
800
900
Temperature (K)
Temperature (K)
Fig. 3. Seebeck coefficient (S) of Bi-doped Mg
Mg Si as a
Si:Bi ¼ 1:x ð0:001%x%0:020Þ) and nondoped Mg
function of temperature.
2
Si
Fig. 2. Electrical resistivity ðrÞ of Bi-doped Mg
Mg Si as a
Si:Bi ¼ 1:x ð0:001%x%0:020Þ) and nondoped Mg
function of temperature.
2
Si
(
2
2
(
2
2
0
.12
.10
as compared with that of nondoped Mg Si.
2
Nondoped
.1 at %
The polarity of S for Bi-doped Mg Si is nega-
2
0
0
tive, indicatingthat the conductivity is mainly
due to electrons. At 300 K, the polarity of S is in
good agreement with the sign of R , and the
H
0.3 at %
0.5 at %
1
2
at %
at %
0.08
absolute value of S corresponds to the value of
S for
electron concentration. The absolute
x ¼ 0:003, 0.005, 0.01 and 0.02 increases with
increasingtemperature. The absolute S of non-
0.06
doped Mg Si as well as x ¼ 0:001, however,
2
0.04
increases, reachinga maximum at 470 and 750 K,
respectively and then decrease with increasing
temperature.
0
.02
.00
Fig. 4 shows the temperature dependence of
thermal conductivity ðkÞ of Bi-doped Mg Si, as
2
0
compared with that of nondoped Mg Si. k
300
400
500
600
700
800
900
2
decreases with increasingtemperature at
3
Temperature (K)
00–660 K, and shows a almost constant value
Fig. 4. Thermal conductivity (k) of Bi-doped Mg
(Mg Si:Bi ¼ 1:x ð0:001 % x % 0:020Þ) and nondoped Mg Si as
a function of temperature.
2
Si
above 660 K. At low temperatures, k depends
strongly on x and decreases with increasing x. The
k is the sum of the contributions arisingfrom the
lattice ðk Þ, and the electronic ðk Þ components.
2
2
ph
el
In order to understand the thermal conductivity
dependences of kph and k . We can calculate k
el
el
behavior of Bi-doped Mg Si, it is necessary
2
to determine the temperature and composition
usingthe Wiedemann–Franz law [19], kel ¼ L0sT
À8 2 2
(L , Lorentz number 2.45 Â 10 V /K , s,
0

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223
electrical conductivity, T, absolute temperature). It
is possible to calculate kph by subtracting kel from k.
Fig. 5 shows the temperature dependence of kph
and kel in the thermal conductivity of Bi-doped
Mg Si and nondoped Mg Si. k decreases with an
increase in x and temperature. However, kel
increases with an increase in x and temperature.
For x ¼ 0:001, the ratio of kel to kph at 300 K is
about 1/50, and it is about 1/15 at 860 K. For
x ¼ 0:02, the ratio of kel to kph at 300 K is about
2/13, and it is about 1/2 at 860 K. Therefore, the
thermal conductivity of Bi-doped Mg Si is mainly
2
influenced by k . The k of Bi-doped Mg Si and
2
2
ph
ph
ph
2
À1
nondoped Mg Si is proportional to T , indicating
2
that phonon–phonon interactions are the primary
source of thermal resistance. This mechanism is in
good agreement with an early work of nondoped
Mg Si investigated by LaBotz and Mason [20].
2
0.12
0.10
0.08
0.06
0.04
0.02
0.00
Fig. 6 shows the temperature dependence of ZT
of Bi-doped Mg Si, as compared with that of
2
Nondoped
nondoped Mg Si. The value of ZT increases with
2
increasingtemperature. An optimum composition
giving maximum ZT value in the present system is
0
0
0
1
2
.1 at %
.3 at %
.5 at %
at %
x ¼ 0:02. The value of Bi-doped Mg Si is 0.86 at
2
at %
862 K, which is 1.5 times larger than an earlier
result (ZT ¼ 0:57 at 856 K) reported for Al-doped
Mg Si by Umemoto et al. [14]. In case of Al-doped
2
Mg Si, the solubility limit of Al in Mg Si is around
2
2
0.15 at%, which is much lower than the solubility
limit of 1.3 at% of Bi in Mg Si and the carrier
2
concentration of 0.1 at. % Al-doped sample is
1
9
À3
reported to be 1.4 Â 10 cm at room tempera-
ture, which is one magnitude lower than Bi-doped
Mg Si. Therefore, the reason why the higher ZT is
300
400
500
600
700
800
900
2
(a)
Temperature (K)
0.020
0.015
0.010
0.005
0.000
1
.0
Nondoped
0
0
0
1
2
.1 at %
.3 at %
.5 at %
at %
Nondoped
.1 at %
0.3 at %
0.8
0
0
1
.5 at %
at %
at %
0.6
0.4
0.2
2 at %
0.0
300
300
400
500
600
700
800
900
400
500
600
700
800
900
(b)
Temperature (K)
Temperature (K)
Fig. 5. Carrier contribution ðkelÞ and lattice contribution ðkphÞ
in the thermal conductivity of Bi-doped Mg Si (Mg
Si:Bi ¼ 1:x
ð0:001 % x % 0:020Þ) and nondoped Mg Si.
Fig. 6. Dimensionless figure of merit (ZT) of Bi-doped Mg
(Mg Si as a
Si:Bi ¼ 1:x ð0:001 % x % 0:020Þ) and nondoped Mg
function of temperature.
2
Si
2
2
2
2
2

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J. Tani, H. Kido / Physica B 364 (2005) 218–224
achieved in Bi-doped Mg Si will be explained as
2
[2] E.N. Nikitin, V.G. Bazanov, V.I. Tarasov, Sov. Phys.
Solid State 3 (1962) 2648.
a result that the high carrier concentration is
obtained because of higher solubility limit of Bi in
Mg Si.
[
[
[
[
[
3] Y. Noda, H. Kon, Y. Furukawa, N. Otsuka, I.A. Nishida,
K. Masumoto, Mater. Trans. JIM 33 (1992) 845.
2
4] Y. Noda, H. Kon, Y. Furukawa, N. Otsuka, I.A. Nishida,
K. Masumoto, Mater. Trans. JIM 33 (1992) 851.
5] R.G. Morris, R.D. Redin, G.C. Danielson, Phys. Rev. 109
(
1958) 1909.
6] R.G. Morris, R.D. Redin, G.C. Danielson, Phys. Rev. 109
1958) 1916.
4
. Conclusions
(
The thermoelectric properties of Bi-doped
Mg Si fabricated by the spark plasma sintering
7] M.W. Heller, G.C. Danielson, J. Phys. Chem. Solids 23
(1962) 601.
2
process have been characterized by Hall effect
measurements at 300 K and by measurements of
electrical resistivity, Seebeck coefficient, and ther-
mal conductivity between 300 and 900 K. Bi-doped
[8] D.M. Rowe, CRC Handbook of Thermoelectrics, CRC
Press, New York, 1995, p. 277.
[
9] T. Kajikawa, K. Shida, S. Sugihara, M. Ohmori, T. Hirai,
Proceedings of the 16th International Conference on
Thermoelectrics (ICT’97), IEEE, 1997, p. 275.
Mg Si samples are n-type in the measured
2
[10] T. Kajikawa, K. Shida, K. Shiraishi, T. Ito, M. Ohmori, T.
Hirai, Proceedings of the 17th International Conference on
Thermoelectrics (ICT’98), IEEE, 1998, p. 362.
temperature range. The electron concentration
of Bi-doped Mg Si at 300 K ranges from
2
1
9
À3
[11] M. Umemoto, Y. Shirai, K. Tsuchiya, Proceedings of the
Fourth Pacific Rim International Conference on Advanced
Materials and Processing(PRICM4), The Japan Institute
of Metals, 2001, p. 2145.
1
0
.8 Â 10 cm
for the Bi concentration x ¼
20 À3
:001 to 1.1 Â 10 cm for x ¼ 0:02. The solubi-
lity limit of Bi in Mg Si is estimated to be about
2
1
.3 at% and first-principles calculation revealed
that Bi atoms are expected to be primarily located
[12] D.R. Lide, CRC Handbook of Chemistry and Physics,
8
4th ed., CRC Press, New York, 2003, pp. 4–132.
[
[
13] M. Riffel, J. Schilz, Proceedings of the 16th International
Conference on Thermoelectrics (ICT’97), IEEE, 1997,
p. 283.
at the Si sites in Mg Si. The electrical resistivity,
2
Seebeck coefficient, and thermal conductivity are
strongly affected by the Bi concentration. The
sample of x ¼ 0:02 shows a maximum value of ZT
is 0.86 at 862 K, which is 1.5 times larger than an
earlier result (ZT ¼ 0:57 at 856 K) reported for Al-
doped Mg Si. Therefore, Bi-doped Mg Si is a
14] CASTEP Users Guide, Accelrys Inc., San Diego, CA,
2001.
[
[
15] D. Vanderbilt, Phys. Rev. B 41 (1990) 892.
16] J.G. Barlock, L.F. Mondolfo, Z. Metall. 66 (1975)
6
05.
17] G. Busch, U. Winkler, Helv. Phys. Acta 26 (1953)
59.
[18] G. Busch, U. Winkler, Physica 20 (1954) 1067.
2
2
[
good candidate material for thermoelectric con-
version in the middle-temperature range.
3
[
19] See, for example, N. W. Ashcroft, N. D. Mermin, Solid
State Physics, Holt, Rinehart, & Winston, New York,
1976, p. 20, and references therein.
References
[
20] R.J. LaBotz, D.R. Mason, J. Electrochem. Soc. 110 (1963)
1
21.
[
1] R.J. LaBotz, D.R. Mason, D.F. O’Kane, J. Electrochem.
Soc. 110 (1963) 127.