G. Kavei: Thermoelectric foam a component of waste-heat energy conversion to electric power
Available online at www.impj.ir
International Materials Physics Journal vol. 1 No.1 2013 22-27
Thermoelectric foam a component of waste-heat energy conversion to
electric power
G. Kavei1
Material and Energy Research Centre, P. O. Box 14155-4777, Tehran, Iran.
Abstract
A thermoelectric converter is a solid-state heat engine in which the electron gas serves as the
working fluid and converts a flow of heat into electricity. Widespread use of the
thermoelectric system requires not only improving the intrinsic energy-conversion efficiency
of the materials but also implementing recent advancements in the system architecture.
Thermoelectric foams with large pores and high surface area associated with a foam structure
as compared to its bulk counterpart, an efficient solution to extract the waste heat could be
foreseen. This study has been designed to fabricate and characterize thermoelectric foams.
No report was evolved in journals at (Bi0.25Sb0.75)2Te3 thermoelectric foam as widely as
extended search was carried out. Thermoelectric porous foam fabrication in replication mode
with powdered (Bi0.25Sb0.75)2Te3 compound and domestic salt powder using a hot die
pressing system was carried out. The structure and morphology formations were
characterized by X-Ray diffraction and scanning electron microscopy systems. Electrical and
thermal conductivities, Seebeck coefficient and relative density of foams were evaluated by
empirical assessment.
Keywords: Thermoelectric; Foam; Replica; Waste heat; Energy conversion.
1- E-mail, phone and fax: g-kavei@merc.ac.ir ; prof.kavei@hotmail.com ; Tel: +98 263 6204137,
Fax: +98 263 6201888.
1-Introduction
Waste heat is generated in a process of fuel
combustion or chemical reaction, which is then
“dumped” into the environment and not reused
for useful and economic purposes. The
mechanism to recover unused heat depends on
the temperature of waste heat gases and the
economics involved. Large quantities of hot gas
flux are generated from boilers, furnace and gas
turbine. If some of the waste heat could be
recovered, then a considerable amount of
primary fuel could be saved. The energy lost in
waste gases cannot be fully saved. However,
much of the waste heat could be reused and can
minimize losses. Porous foams of various
substances such as polymers, metals and
ceramics, exhibit particular physical and
mechanical properties that differ very much
22
from classical fully dense materials, [1-2].
Interesting combinations of these properties,
such as high thermal conductivity combined
with high gas permeability or relatively high
stiffness, in conjunction with very low specific
weight, offer the possibility for a new futureoriented multi-functional applications, e.g.
cooling and heating systems, heat exchangers or
fire protection, [3]. Thermal performance
improvement is basically a consequence of
enhancement of the effective thermal
conductivity in the binary packing and
transversely thermal dispersion increment due to
the decrease of porosity and increase of
tortuosity. Traditionally, tortuosity is the length
of the actual path line between two ports that the
fluid particle travels divided by the length of a
straight line between these ports. This path is
taken by a diffusion (Brownian) motion and is
independent of the net velocity, [4].
International Materials Physics Journal
Thermoelectric material (TM), on the other
hand, is a solid-state energy converter with a
combination of thermal, electrical, and semiconducting properties.
According to these
definitions TM is used to convert waste heat
into electricity or electrical energy directly into
cooling or heating energy. TM may also be
competitive with fluid-based systems, such as
two-phase air-conditioning compressors or heat
pumps, and may be used in smaller-scale
applications as an electrical-enclosure cooling
devices, [5]. However, heat as directly extracted
from bulk, gaseous and liquid media by
thermoelectric elements in a large surface area
(foam) will be more efficient than the extraction
of heat from a solid body. In this regard,
varieties of studies have been made in areas of
commercial foams, [6].
A computational model has been developed in
order to simulate the thermal and electric
behavior of thermoelectric generators [7]. This
model solves the nonlinear system of
thermoelectric and heat transfer equations, [8].
Nevertheless, given the renewable natural
energy resources, TM could play a significant
role to allow itself to be efficiently used in
conjunction with energy conversion processes.
Conventionally, thermoelectric modules have
been designed in bulk form of traditional
materials such as Bi2Te3, PbTe, SiGe etc. at
different ranges of temperature, [9]. The poor
chemical stability and brittle nature of Bi2Te3
material has narrowed down the processing of
foam structures. To avoid such inefficiency,
ternary compounds of high chemical stability
and mechanical strength may be used, [10].
Finding an optimal porosity with an increase
rate of electrical to thermal conductivities for a
given Thermoelectric Foam (TF) element is
feasible. This may improve ZT (the efficiency of
the thermoelectric generator). Large surface area
of foam structure may result in low Ohmic
electrical
contacts
to
the
fabricated
thermoelectric elements. Furthermore, the foam
has large surface area of physical contact with
hot or cold media with respect to solid
counterpart. High Seebeck coefficient of TM
foam has motivated working with foam
structures. This will make them as a favorite
element for efficient electric power generators.
This article describes the fabrication of porous
TF. Foam processing is based on the salt
replication method. A mechanically alloyed p
Int. Mat.Phys. J. Vol. 1 No. 1 September 2013
type (Bi0.25Sb0.75)2Te3 ternary compound is used
as raw material. Tentative investigation of the
thermal conductivity either measured directly,
[11] or calculated from electrical conductivity
values using the Wiedemann–Franz law for
open-celled porous TM, [7], makes possible to
compare bulk and foam properties. The study
has been focused on foam samples of 70%
porosity at different hot pressing temperatures
fabrication and characterization.
2- Experiment
2-1 Providing foam materials
Raw material (Bi0.25Sb0.75)2Te3 and domestic salt
(sodium chloride NaCl with 150–212µm
powder particle size and 99.0% purity) were
selected as items for foaming. The load was
ball-milled in a planetary ball-mill with stainless
steel cup for 20 h at a cup speed of 270 rpm.
The balls in a ball miller sphere of 17mm
diameter and the ratio of balls of the powder
weight is 10:1. Crystallite sizes were defined by
one of the methods reported in, [12-14]. Particle
sizes of the product powder were tested by
“Fritsch GmbH analysette 22”system, the size
population above 30% for NaCl was 4-8 µm and
above 25% of (Bi0.25Sb0.75)2Te3 6-8 µm with
flaky shape.
2-2 Fabricating thermoelectric foam
Thermoelectric foam was processed with mixed
milled TM (Bi0.25Sb0.75)2Te3 and NaCl powders.
The ratio of 2:1.5 weight of TM /NaCl was
calculated to obtain TF with a relative porosity
of 71%, (see Table 1). Foam with different
porosities processed on the ratio of raw and
replica substance weights. To calculate the
relative weights of TM /NaCl not only one can
change relative weights of TM/NaCl but also
one may do it by varying the particle size of
elementary material (TM) and replica material
(NaCl), [15].
The closed-cell foams were produced by mixing the
(Bi0.25Sb0.75)2Te3 powder with NaCl as a replica.
Mixed powder was charged into a hot-press mold
(high speed steel) with a dimension of 5×20×10mm
(volume cm-3). Foaming was made possible through
a controlled compression of a mixed powder the
force was exerted onto a cross section of 5x20mm.
So, the force direction (longitudinal direction)
introduced along 10mm length.
Hot pressing was performed at different
temperatures of 300, 400 and 500 °C under a
23
G. Kavei: Thermoelectric foam a component of waste-heat energy conversion to electric power
Table 1: Experiment and Theory values for a fabricated
typical 20x10x5mm3 foam.
(Bi0.25Sb0.75)2Te3 (gr.)
NaCl (gr.)
Volume Size (cm3)
2
1.5
1
71% Relative porosity
Ref.
29% Theoretical relative
density
5% Reside NaCl
Theory
2.14 Foam weight (gr.)
%30 Relative density
NaCl (gr.)
1.5
%70 Relative porosity
(Bi0.25Sb0.75)2Te3 (gr.)
2
Experiment
pressure of 500 MPa in Argon atmosphere for a
period of one minute. Compression was
repeated for several times at either temperature
to reach a high degree of compaction. This
procedure stops decomposition of the foam
whilst removing salt from foam. Foam
properties largely depend on a pressing time,
[15]
(a)
3. Results and Discussion
Morphology of the foam was examined by
scanning electron microscope (SEM) (Philips
XL30 Scanning Electron Microscope (SEM)
operating at 25 kV) to identify the formed
phases and micrograph of the surfaces. Fig. 1a
reveals dense mechanically alloyed powder
(Bi0.25Sb0.75)2Te3 prepared at 15 h ball mill.
Fig.1b shows morphology from TF surface with
a relative porosity of 70%. The images illustrate
dense structure, which is confirmed by intense
surface build up.
Crystalline phase evolution during foaming
were evaluated by the X-ray diffraction (XRD)
[Philips (30 kV and 25mA) diffractometer with
CuKα radiation (λ = 1.5405 Å)]. XRD was
performed with a step size of 0.02 and a time
per step of 1 s. The patterns were evaluated by
pure (Bi0.25Sb0.75)2Te3 patterns, [17]. Fig. 2
shows; a and b, XRD pattern from crystallized
(Bi0.25Sb0.75) 2Te3 raw and pure foam (raw foam
has been boiled in water for 2 hours to extract
(b)
Fig. 1: SEM microstructure of a) mechanically alloyed powder (Bi0.25Sb0.75)2Te3 prepared at 15 h ball mill, b)
morphology of TF surface with a relative porosity of 70% at 500˚C hot pressing temperature. The dense
structure of surface can be noticed in the image.
Hot-pressed sample was boiled in water for 2 h
in an attempt to remove NaCl from the raw
foam. This allows for a pure TF to be obtained.
Archimedes test was carried out for a
predetermined foam relative density. The
relative density of the foam with respect to its
bulk counterparts around 40%-30% has been
obtained, [16]. A sensible high value of relative
density indicates that about 5-7% NaCl was left
into the foam. (Bi0.25Sb0.75)2Te3 powder is
chemically stable against compression and any
applied heat up to 500 °C in the presence of
NaCl to bind particles.
24
pattern that has been taken NaCl crystals are
superimposed and screened up in (b). For foam
structure, it should be noted that the main peaks
for the NaCl crystal are at 27.5, 31.7, 45.5, 56.5,
66.5 and 75.5, 2θ degrees, [18].
The theory is based on the assumption that, if a
thermoelectric element is heated at one end a
temperature gradient may extend along the
element; this is due to the formation of the
electron/hole pairs at the hot end. As the pairs
recombined, heat streams toward the cold end.
A voltage, (Seebeck voltage), which drives the
hole/electron flow is appearing between the hot
International Materials Physics Journal
Int. Mat.Phys. J. Vol. 1 No. 1 September 2013
Fig. 2: a) XRD pattern of crystallized (Bi0.25Sb0.75)2Te3
raw foam. b) XRD patterns from pure foam (raw foam
has been boiled in water for 2 hours to extract NaCl) All
peaks were indexed for the (Bi0.25Sb0.75)2Te3 phase with
no presence of impurities. c) XRD pattern taken from
NaCl crystals are super positioned and screened over in a
pattern (b).
and cold ends of the TE element due to the
temperature gradient. Accurate measurement of
electrical transport parameters of the foam
requires good and clean surface contacts. As
there were large amounts of void on the
surfaces, the electrical contacts for the foams
were made by coating silver paint up to around
2 mm long, on both ends. Transport parameters
were measured at different temperature rates
listed in Table 2.
Table 2: Various physical parameters measured for the TF
module at different hot press temperatures.
Parameters
T1
T2
T3
(300°C (400°C) (500°C)
189
187
186
α (µV/K)
σ (Ω.cm) -1
95
106
120
ρ / ρ 0 (%)
30
30.5
31
0.33
0.34
0.38
1.03
1.09
1.09
κ (W.(mK)-1)
Z = α 2σ / κ ×10−3 ( K −1 )
4. Analysis of practical results
Effective thermal conductivity of porous metals
based on conduction in the solid materials was
studied by two different methods; namely,
numerical and analytical approaches, [19]. The
numerical approach considers a single unit cell
or periodic structures in order reduce the
computation time. The analytical approach
allows for an easy consideration of perturbations
in the pore arrangement. Numerical and
analytical concerned the finite element method
allows arbitrary pore geometries and
nonlinearities study (e.g. material or boundary
conditions). The basic idea of the finite element
method is the decomposition of a domain with a
complicated geometry into geometrically simple
elements, such that the governing differential
equation can be solved (approximately) for
these finite elements. The single element
solutions are then assembled to obtain the
complete system solution using given boundary
conditions. The assembly process uses
appropriate balance equations at the nodes
which are used to define the elements and serve
also as connection points between the elements.
Taking into the account of the above
classifications, the influence of radiation inside
the pores can be neglected, [19]. Furthermore,
the thermal conductivity of inclusion
atmosphere e.g. air, κ1 ≈ 0.025W/(m·K) , [20] is
typically several orders of magnitudes smaller
than the cell wall material e.g. TM, κs =
~1W/(m·K) , [21]. However, in order to
maintain the comparability of the results,
convection has been disregarded, inclusions can
be approximated as voids with no contribution
to the thermal conductivity of the structure (κ1 =
0). Consequently, only the thermal conduction
in the base material κs is considered for basic
studies.
A highly porous substance is mostly desired if it
has acceptable mechanical strength. Porosity
may also be found advantageous in conventional
thermoelectric modules although a high thermal
flux density creates problems. However, any
heat transfer through the pores can degrade the
thermoelectric figure of merit. The amount of
this degradation may be calculated, and it is
small enough to be accepted in practical
devices. Generally speaking, a thermoelectric
energy converter figure of merit is expressed by
the relation, [22-23].
Z=
(α B − α A ) 2
[(κ B ρ B )1/ 2 + (κ A ρ A )1/ 2 ]2
(1)
where α is the Seebeck coefficient, κ is the
thermal conductivity, ρ is the electrical
resistivity. Subscripts A and B denote both p and
n type legs.
Goldsmid, [7], presented an ideal model for a
porous thermoelectric element as Fig. 3. The
pores are assumed to be uniform and cubes of
edge length l are separated by the width of 2w
25
G. Kavei: Thermoelectric foam a component of waste-heat energy conversion to electric power
so, each cell consists of a cubic space
surrounded by a wall of thickness w. For l≈2w
the electrical and thermal flows are linear.
Since, the pores in actual foam will be quite
different from the model but it is valid with
good approximations.
Goldsmid, [7] calculated this ratio for the voids
filled with air, carbon dioxide and krypton. He
has shown how the figure of merit falls the same
as porosity factor p does in these three
instances. The porosity factor p was defined as a
ratio of an electrical conductivity in fully dense
material to that of porous material. Since,
electrical conductivity of gases related to TM
within the pores is insignificant:
p=
(1 + 2w) 2
(1 + 2 w) 2 − l 2
(4)
The figure of merit falls down to about 20% for
a porosity factor of 10 if the pores are filled with
air.
5. Conclusion
Fig.3: A model for thermal loss calculation in a porous
thermoelectric element.
For an application in which evacuated pore is
considered. Thermal conduction of the gas does
not disappear unless the mean free path of
molecules is much greater than the width of the
pore. Very high vacuum and interconnection
between the pores will assist in allowing
vacuum or any gas to penetrate throughout the
foam. Generally the pores containing a gas of
thermal conductivity κl, will normally be much
less than the thermal conductivity κs of TE with
thermal conductance K C (effective conductivity
of the porous material of each cell) is given by,
[24].
KC =
κ / κ p + (2w / l )
+
κ l[{1 + (2 w / l )} − 1]
1 + (2w / l )
(2)
The effective thermal conductivity is not only a
function of porosity and the thermal
conductivity of each phase, but is very sensitive
to the microstructure, [25]. The thermal
conductivity of the gas in the pores in
comparison with TM thermal conductivity was
negligible, thermal conductance per cell (Ks
conductance of the solid material) would be,
[26]:
2
κ l[{1 + (2 w / l )} − 1]
1 + (2 w / l )
(3)
KRel = K C / K s relative conductance is
analogous to the ratio of figure of merit Zp/ Zs
where Zp is the porous material figure of merit
to that Zs that belongs to a fully dense specimen.
26
References:
2
κl
Ks =
Foam structures are interested to replace bulk
thermoelectric elements in conventional module
designed for waste heat conversion to
electricity. High surface area of the voids in the
foam allows an efficient heat extraction as
compared to that of bulk materials.
(Bi0.25Sb0.75)2Te3 has been known as a high
efficiency thermoelectric compound to fabricate
a foam structured thermoelectric generator with
optimum quality. On a simple thermoelectric
foam module configuration with 70% porosity
one side of the module was heated up to about
400 °C as a result voltage difference between
two sides was observed.
[1] Ashby M.F., Evans A.G., Fleck N.A.,
Gibson L.J., Hutchinson J.W., Wadley H.N.G.,
"Metal foams: a design guide, Butterworth
Heinemann", Boston, 2000.
[2] Banhart J., "Manufacture, characterization
and application of cellular metals and metal
foams.", Prog Mater Sci., Prog Mater Sci.,
Vol.46(6), 559–632, 2001.
[3] Dias R.P., Fernandes C.S., Mota M.,
Teixeira J.A., Yelshin A., " Permeability and
effective thermal conductivity of bisized porous
media", International Journal of Heat and Mass
Transfer, Vol.50, 1295–1301, 2007.
[4] Carbonell R.G. and Whitaker S., "Heat and
Mass Transfer in Porous Media", Fundamentals
of Transport in Porous Media, Bear and
Corapcioglu, Eds. Martinus Nijhoff, 123–198,
1984.
International Materials Physics Journal
[5] Bell L.E., "Cooling, Heating, Generating
Power, and Recovering Waste Heat with
Thermoelectric
Systems",
Science,
Vol.321(5895), 1457-1461, 2008.
[6] van Setten B.A.A.L., Spitters C.G.M.,
Bremmer J., Mulders A.M. M., Makkee M.,
Moulijn J.A., "Stability of catalytic foam dieselsoot filters based on Cs2O, MoO3, and Cs2SO4
molten-salt catalysts", Applied Catalysis B:
Environmental, Vol.42(4), 337-347, 2003.
[7] Goldsmid H.J., "Porous Thermoelectric
Materials", Materials, Vol.2(3), 903-910, 2009.
[8] Rodŕguez A., Vián J.G., Astrain D.,
Martinez A. "Study of thermoelectric systems
applied to electric power generation", Energy
Conversion and Management, Vol.50(5), 1236–
1243, 2009.
[9] Scherrer H. and Scherrer S., "Bismuth
Telluride, Antimony Telluride and Their Solid
Solutions", Handbook on thermoelectric, CRC
Press , Boca Raton, FL, 211-238, 1995.
[10] Dharmasena K.P., Wadley H.N.G.,
"Electrical conductivity of open-cell metal
Foams", Journal of Materials Research,
Vol.17(3), 625-631, 2002.
[11] Kavei G., Zare Y., Seyyedi A., "Tentative
Design for Measurements of Absolute Value of
Thermal Conductivity of Semi-Conducting
Thermoelectric Elements: Material and Energy",
Journal of Thermoelectricity, No.2, 2008.
[12] Williamson G.K. and Hall W.H., "X-ray
line broadening from filled aluminum and
wolfram,Acta. Metall"., Vol.1, 22–31, 1953.
[13] Klug H.P. and Alexander L., "X-ray
Diffraction Procedures for Polycrystalline and
Amorphous Materials", 2nd Ed., John Wiley&
Sons, New York, USA, 618-709, 1974.
[14] Herrmann M. and Fietzek H.,
"investigation of the micro structure of energetic
crystals by means of x-ray powder diffraction",
Advances in X-ray Analysis, Vol.48, 52-58,
2005.
[15] Reddy E.S., Noudem J.G., Goupil C.,
"Open porous foam oxide thermoelectric
elements
for
hot
gases
and
liquid
environments", Energy Conversion and
Management, Vol.48(4), 1251-1254, 2007.
Int. Mat.Phys. J. Vol. 1 No. 1 September 2013
[16] Kavei G., "Novel method for power
generation from waste heat via thermoelectric
foam", Journal of Thermoelectricity, No.1, 3440, 2012.
[17] Kavei G., Karami M.A., "Thermoelectric
crystals Bi2Te2.88Se0.12 undoped and doped
by CdCl2 or CdBr2 impurities, fabricated and
characterized by XRD and Hall effect",
Materials Research Bulletin, Vol. 43, 239–243,
2008.
[18] Anthony J.W., Bideaux R.A., Bladh K.W.
Nichols M.C., "Handbook of Mineralogy",
Mineral Data Publishing, Tucson Arizona, USA,
by permission of the Mineralogical Society of
America, 1990.
[19] Fiedler T., Pesetskaya E., Öchsner A.,
Grácio J., "Calculations of the Thermal
Conductivity of Porous Materials", Materials
Science Forum, Volume Advanced Materials
Forum III, Vol.514–516, 754-758, 2006.
[20] Breitz W., Grote K.H., "Dubbel
Taschenbuch für den Maschinenbau", Springer
Verlag, Germany, 1997.
[21] Keawprak N., Sun Z.M, Hashimoto H.,
Barsoum M.W., "Effect of sintering temperature
on the thermoelectric properties of pulse
discharge sintered (Bi0.24Sb0.76)2Te3 alloy",
Journal of Alloys and Compounds, Vol.397,
236-244, 2005.
[22]
Ioffe
A.F.,
"Semiconductor
Thermoelements and Thermoelectric Cooling",
Infosearch; London, UK, 39, 1957.
[23] Anatychuk L.I., "The Physics of
Thermoelectricity", Academy of Science of
Ukraine, Institute of Thermoelectricity, Kiev,
1998.
[24] Fu X., Viskanta R., Gore J.P., "Prediction
of effective thermal conductivity of cellular
ceramics, Int. Comm. Heat Mass Transfer,
Vol.25(2), 151-160, 1998.
[25] Kaviany M., "Principles of Heat Transfer in
Porous Media", Springer, 686, 1991.
[26] Druma A.M., Alam M.K., Druma C.,
"Surface Area and Conductivity of Open-Cell
Carbon Foams", Journal of Minerals &
Materials Characterization & Engineering,
Vol.5(1), 73-86, 2006.
27