Supporting Information
High Thermoelectric Performance of All-Oxide
Heterostructures with Carrier Double-Barrier
Filtering Effect
Chunlin Ou,1† Jungang Hou,1,3† Tian-Ran Wei,2 Bo Jiang,1 Shuqiang Jiao,1 Jing-Feng
Li,2 Hongmin Zhu1,3*
1
School of Metallurgical and Ecological Engineering, University of Science and
Technology Beijing, Beijing, 100083, China.
2
State Key Laboratory of New Ceramics and Fine Processing, School of Materials
Science and Engineering, Tsinghua University, Beijing, 100084, China.
3
Tohoku University, 6-6-02 Aramaki-Aza-Aoba, Aoba-ku, Sendai, 980-8579, Japan
†
These authors contributed equally to this work.
*Corresponding author: hzhu@ustb.edu.cn
Figure Captions
Figure S1. Blue line: anodization with constant current up to 8V; red line: anodization
with constant 8 V voltage and illustration of the sketch of device used for anodization
process.
Figure
S2.
XRD
patterns
of
the
all-oxide
TiC0.5O0.5@TiOy-5wt.%TiO2
heterostructured sample with 8 V anodization.
Figure S3. The temperature dependence of the power factor (  2 ) for various
TiC0.5O0.5@TiOy-TiO2 heterostructured bulks.
Figure S4. XRD patterns of the various TiC1-xOx samples.
Figure S5. Seebeck coefficient and Lorenz number as functions of chemical potential.
Figure S6. Lattice thermal conductivity of the various all-oxide TiC1-xOx@TiOy-TiO2
heterostructures samples.
Figure S7. SEM fractographs of the various all-oxide TiC1-xOx@TiOy-5wt.%TiO2
heterostructures samples with 8 V anodization: (a) x=0.9, (b) x=0.8, (c), x=0.7, (d)
x=0.6.
Figure S8. The porosity and density of the bulk after SPS-treatment.
Figure S9. The temperature dependence of the power factor (  2 ) for
TiC1-xOx@TiOy-5wt.%TiO2 heterostructured bulks with 8 V anodization.
Figure S1 Blue line: anodization with constant current up to 8V; red line: anodization
with constant 8 V voltage and illustration of the sketch of device used for anodization
process.
Figure
S2.
XRD
patterns
of
the
all-oxide
heterostructured sample with 8 V anodization.
TiC0.5O0.5@TiOy-5wt.%TiO2
Figure S3. The temperature dependence of the power factor (  2 ) for various
TiC0.5O0.5@TiOy-TiO2 heterostructured bulks.
Figure S4. XRD patterns of the various TiC1-xOx samples.
Transport parameters’ were estimated for a representative sample 8V+5wt.%%tTiO2.
Chemical potential (or reduced Fermi energy)  was determined in the frame work of
the single parabolic band (SPB) model via:
S
where Fj ( )  

0
kB
e
  2    F 1

  

 1    F

x j dx
are the Fermi integrals. Here we assumed the
1  Exp  x   
acoustic phonon scattering dominates the carrier mobility which is commonly seen in
thermoelectric materials and then =0, and the Seebeck coefficient is
S

kB  2F1
  .

e  F0

For each measured Seebeck coefficient, we can deduce the corresponding chemical
potential. The Lorenz number L is also a function of chemical potential via the
equation:
2
 k  3F0 ( ) F2 ( )  4 F1 ( )
L B 
F02 ( )
 e 
2
Again the acoustic phonon scattering assumption was employed here. Using the
calculated  by S, we calculated each L accordingly. S and L as functions of  are
shown in Fig. S5
Figure S5 Seebeck coefficient and Lorenz number as functions of chemical potential
Lattice thermal conductivity L was obtained by subtracting the electronic part e
from the total :
 L     e    L T .
The mean free paths (MFP) of phonons were related to L via
1
3
 L = Cva l ,
where va is the average sound speed, l is the MFP of phonons and C is the heat
capacity per unit volume. va was obtained by
va   2 / vtrans 3  1/ vlongt 3  / 3
1/3
,
in which vtrans = 4450 m/s and vlongt = 7416 m/s are the transverse and longitudinal
sound speed measured by an ultrasonic instrument (Ultrasonic Pulser/Recever Model
5900 PR, Panametrics, USA) for a representative sample 8V+5wt.%%tTiO2. The heat
capacity was estimated by the Dulong-Petit law. All the parameters used in the
calculation are listed in TableS1.
Table S1 Parameters of the sample 8V+5wt.%%tTiO2
Parameter
Value
Notes
T (K)
373
S (V/K)
91
 (--)
2.8
L (10-8WK-2)
1.95
 (S/cm)
180
 (W/mK)
1.14
e (W/mK)
0.13
L (W/mK)
1.01
d (g/cm3)
3.75
measured at room temperature
Cp(J/gK)
0.81
estimated by Dulong-Petit law
C (J/cm3K)
3.04
va (m/s)
4922
l (nm)
0.2
measured at room temperature
Figure S6. Lattice thermal conductivity of the various all-oxide TiC1-xOx@TiOy-TiO2
heterostructures samples.
From Table S1 it is found that TCO has a considerably large sound velocity when
compared with several typical oxide thermoelectrics, such as BiCuSeO which has a
similar thermal conductivity but a much lower va (~2112 m/s).1 Large sound velocity
is a direct indication of large bulk modulus, suggesting rigid and hard bonding in TCO,
which is not commonly seen in good thermoelectric materials. The average MFP was
calculated as ~ 0.2 nm at 373 K, on the scale of atomic distances and several orders of
magnitude smaller than the grain size. Thus it is concluded that the low lattice thermal
conductivity in these materials should be ascribed to the ultralow MFP of phonons i.e.
the highly frequentcy scattering of phonons. It should be noted, however, in real cases
the MFP of phonons is a distribution of phonon energy or frequency, ranging from the
order of angstrom to that of micrometre. Especially, the semi-quantitative value in this
work is an average one obtained from thermal and elastic data, is an a preliminary but
efficient strategy for the explaination of the low electrical thermal conductivity over
the entire temperature range and a semiconducting electrical transport behaviour of
as-prepared TiC0.5O0.5@TiOy-TiO2 heterostructures.
Reference.
1. Li, F., Li, J. F., Zhao, L. D., Xiang, K.,Liu, Y., Zhang, B. P., Lin, Y. H., Nan, C. W.,
Zhu, H. M. Polycrystalline BiCuSeO oxide as a potential thermoelectric material,
Energy Environ. Sci. 5, 7188-7195 (2012).
Figure S7. SEM fractographs of the various all-oxide TiC1-xOx@TiOy-5wt.%TiO2
heterostructures samples with 8 V anodization: (a) x=0.9, (b) x=0.8, (c), x=0.7, (d)
x=0.6.
Figure S8. The porosity and density of the bulk after SPS-treatment.
Figure S9. The temperature dependence of the power factor (  2 ) for
TiC1-xOx@TiOy-5wt.%TiO2 heterostructured bulks with 8 V anodization.