Japanese Journal of Applied Physics Vol. 45, No. 11, 2006, pp. 8805–8809 #2006 The Japan Society of Applied Physics
Development of Transient Measurement Method for investigating Thermoelectric Properties in High Temperature Region Shinichi F UJIMOTO, Hiromasa K AIBE, Seijirou SANO and Tsuyoshi K AJITANI1 Technology Research Center, Research Division, Komatsu Ltd., 1200 Manda, Hiratsuka, Kanagawa 254-8567, Japan 1 Department of Applied Physics, Graduate School of Engineering, Tohoku University, Aramaki Aoba, Aoba-ku, Sendai 980-8579, Japan (Received March 1, 2006; accepted August 21, 2006; published online November 8, 2006)
The measurement equipment based on a transient measurement method was fabricated to characterize Seebeck coefficient, resistivity, and thermal conductivity simultaneously from room temperature to 573 K. The rate of ambient heat flow was reduced by employing a thermal anchor and a thermal reflector at elevated temperatures, and a model for suitable corrections for compensating remaining errors in data evaluation was studied. Using n-type Bi2 Te3 -based samples, the comparison of thermoelectric properties with the results obtained using another commercial conventional measurement equipment was performed and showed a very good agreement. [DOI: 10.1143/JJAP.45.8805] KEYWORDS: thermoelectric properties, Bi2 Te3 , transient measurement method, Harman method
1.
Introduction
Thermoelectric energy conversion is widely recognized as a promising technology, and great effort has been devoted to the practical use of thermoelectric power generation using waste heat1) in recent decades. For heat waste recovery at moderate temperatures, Bi2 Te3 and its solid solutions are examples of the most promising thermoelectric materials not only around room temperature but also at high temperatures up to 573 K if their composition and carrier concentration are optimized. To optimize their composition, a reliable method is required for measurement at high temperatures. We fabricated the measurement equipment based on a transient measurement method2) to investigate the thermoelectric properties of Bi2 Te3 and its solid solutions with various compositions from room temperature to 573 K. Although this measurement method is similar to the Harman measurement method,3) it has a few fundamental differences. DC current is used for this measurement method, and by changing the polarity of electrical and thermal signals at the point where the current is switched off, thermoelectric properties are deduced using one identical specimen. The commercial method basically focuses on room-temperature characterization, and it is significantly difficult to investigate thermoelectric properties above room temperature. This is due to ambient heat flow whose rate becomes more significant with an increase in temperature. We improved this measurement method and reduced a thermal heat flow from outside as much as possible by employing a thermal anchor and a thermal reflector. Moreover, we compensated thermal conductivity by considering heat flows from ambient radiation, wires, air conduction, and air convection. 2.
Transient Measurement Method
The schematic of the apparatus is shown in Fig. 1. One end of the sample is soldered directly to a sufficiently large Ni-coated Cu plate. Thin wires of 0.254 mm diameter for current lead electrodes and thin thermocouples of 0.127 mm diameter are soldered on the other end of the sample and on the Ni-coated Cu plate as close as possible to the sample. The thermal anchor made of an insulator is placed between the Ni-coated Cu plate and a heater, and the wire and
thermocouple on the top of the sample pass through it. Moreover, the sample is covered with a thermal reflector that is connected directly to the Ni-coated Cu plate. These components are placed in vacuum. By employing this system, the rate of heat flow from the sample caused by air conduction, air convection, wire conduction or radiation is reduced. On measuring thermoelectric properties, DC current is applied to the sample. As a result of the Peltier effect, a temperature difference between the top and bottom of the sample of a few degree develops. After voltage and temperature become stable, the current is switched off, and voltage and temperature differences decrease in a characteristic manner. Then, the current is turned on in the opposite direction, and the same process is used. Using the voltages and temperatures of the top and bottom of the sample, Seebeck coefficient and resistivity are obtained. Also, thermal conductivity and figure of merit are deduced by thermal equation derivation, as shown in the next section. 3.
Analysis Model
The formulation of equations in the transient measurement method is described in detail by Buist.2) Thus, only the expressions of thermoelectric properties, certain equations related to the discussion in the next section, and the situations at which these equations are derived are explained here. For the evaluation of thermoelectric properties, the thermal model shown in Fig. 2 is used. When the current I is applied as shown in Fig. 2(a), the temperatures and heat flows on the top and bottom of the sample are expressed as ðTc ; Qc Þ and ðTh ; Qh Þ, respectively. When the reversed current I 0 is applied as shown in Fig. 2(b), the temperatures and heat flows on the top and bottom of the sample are expressed as ðTh0 ; Qh0 Þ and ðTc0 ; Qc0 Þ, respectively. Here, Seebeck coefficient, resistance, and thermal conduction are expressed as , R, and K, respectively. Then, the Seebeck coefficient , electrical resistivity , thermal conductivity , and figure of merit Z are given by ¼ 2Voa =Da w ;
ð3:1Þ
with w : thermopower of the wires ¼ ðVia Voa Þ=ðLIa Þ
ð3:2Þ
2LITa Voa =ðCD2a Þ
ð3:3Þ
¼
E-mail address: shinichi
[email protected]
8805
þ LITa w =ðCDa Þ
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Thermal Reflector Cu Current Wire
Thermocouple
Sample
Thin Thermocouple
Fig. 1. Schematic of apparatus based on transient measurement method.
Ni-Plated Cu Plate Thin Cu Thermal Anchor (Insulator) Current Wire Heater Block
(a)
QW ¼ KW ðTh0 Tc Þ
Qh’
Qc
Th’
Tc α Tc I
C ¼ 1 þ fðQW þ QRe þ QRi ÞL=ð2Da Þg
(b)
α Th’I’
RI 2 / 2
K(Th Tc)
I
RI 2 / 2
α Tc’I’
Qh
Th
Qc ’
QRi ¼ 4ðTh0 Tc ÞT 3 Ai
RI’ 2 / 2
T ¼ ðTh0 þ Tc Þ=2;
K(Th’ Tc’ )
α Th I
QRe ¼ 4ðTh0 Tc ÞT 3 Ae
I’
with KW : thermal conduction of wires; Ae : external surface area; Ai : internal surface area; : effective emissivity; : Stefan–Boltzmann constant. In our system, the correction factor is suppressed within 1.05 at most by employing the thermal anchor and reflector.
RI’ 2 / 2
Tc’
4. Fig. 2. Thermal modeling when direct current is applied in thermal equibrium: (a) for current applied in positive direction and (b) for current applied in negative direction.
Z ¼ 2CIa Voa =fITa ðVia Voa Þg ðCIa w =Da Þ=fITa ðVia Voa Þg;
ð3:4Þ
where Voa , Via , Da , Ia , ITa , and L are expressed as Voa ¼ ðVo þ Vo0 Þ=2 Via ¼ ðVi þ Vi0 Þ=2 Da ¼ ðTh Tc Þ þ ðTh0 Tc0 Þ Ia ¼ ðI þ I 0 Þ=2 ITa ¼ ðTc þ Th ÞI=2 þ ðTc0 þ Th0 ÞI 0 =2 L ¼ l=s; with s: cross section perpendicular to the current direction; l: length of the sample, where Vi or Vi0 is the voltage after temperature and voltage become stable when the current I or I 0 is applied, and Vo or Vo0 is the voltage immediately after the current I or I 0 is switched off, respectively. Moreover, C is a correction factor as a function of ambient heat flow. As the origins of heat flow, radiation, air convection, and air conduction are considered in ref. 2. Since the measurement is performed under vacuum conditions, air convection and air conduction are neglected in our system. On the other hand, wire conduction is considered in our system, though it is neglected in ref. 2. Then, the expression of C becomes
Experimental Setup
The thermoelectric properties of an n-type Bi2 Te3 -based sample are measured from 300 to 553 K. The sample is about 2:35 2:35 mm2 cross-section and 2.75-mm-tall rectangular parallelepiped. The longer the sample, the lower the specific contact resistance, but the larger the effect of heat flow caused by external factors, such as radiation and wire conduction. The contact resistance of the sample is shown in Fig. 3. It is measured using a 2:0 2:0 mm2 cross-section and 5.0-mm-tall rectangular parallelepiped sample whose cross-sectional surface is soldered to a Au/Ni-coated Cu block. Since a solder with a high melting point is easily oxidized, soldering does not succeed if an ordinary soldering iron is used. Therefore, soldering is carried out in nitrogen flow for a short time with a high-frequency heating furnace. The voltage probe is scanned along the direction of the length crossing the contact point. By extrapolating the resistance data of the sample and Cu block to the contact point and by reading the gap between two lines, a maximal contact resistance of 6:3 106 cm2 is obtained. As a result, the ratio of contact resistance to sample resistance in our setup is lower than 3%. However, the effect of the contact resistance becomes severe if soldering fails. The temperature dependences of the resistivity, Seebeck coefficient, and thermal conductivity of an n-type Bi2 Te3 -based sample for good and bad solderings are shown in Figs. 4(a)– 4(c). Filled or open circles indicate the data for good or bad soldering, respectively. The difference in contact resistance hardly affects Seebeck coefficient and thermal conductivity but considerably affects resistivity. In this case, the error of
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ρ (µΩ cm)
45 44 43 42 41 40 39 38 37 36 35
Resistance (mΩ)
Resistance (mΩ)
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35 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 Position (mm)
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500 good soldering
Bi2 Te 3 -based sample Au/Ni-plated Cu block
bad soldering
(a)
0
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
200
Position (mm) Fig. 3. Changes in resistance along direction of sample length crossing contact point. The cross-sectional surface of an n-type Bi2 Te3 -based sample is soldered to a Au/Ni-coated Cu block.
300 400 500 Temperature (K)
600
-200
Qrad ¼ KðTbottom Ttop Þ Qwire ¼ KðTbottom Ttop Þ Kwire ðTtop Trt Þ;
ð4:1Þ
where Qrad : outflow of effective radiation heat in the system; Qwire : outflow of wire conduction heat; Kwire : thermal conduction of the wires; Tbottom : bottom temperature of the sample; Ttop : top temperature of the sample; Trt : room temperature. Since the radiation heats affecting the sample only outflow from the sample, inflow from components such
-160 -140 -120
good soldering bad soldering
(b)
-100 200
300 400 500 Temperature (K)
600
30
25
-1
-1
κ (mW cm K )
resistivity ranges from 8 to 23% when temperature increases from 300 to 553 K. For solving this problem, cross-checking using another solder with a low melting point, such as Bi58 Sn42 , is effective. The contact resistance of the sample using the Bi58 Sn42 solder is too small to read the gap of resistance at the contact point. Next, the data obtained by the transient measurement and conventional methods are compared. The temperature dependences of the resistivity and Seebeck coefficient of an n-type Bi2 Te3 -based sample are shown in Figs. 5(a) and 5(b). Filled circles indicate the data obtained by the transient measurement method, and open circles indicate the data obtained by the conventional method using the commercial four-probe equipment Ozawa Science RZ-2001i. These data show a very good agreement. The temperature dependence of the thermal conductivity of an n-type Bi2 Te3 -based sample is shown in Fig. 6. Filled circles indicate the data obtained by the transient measurement method, and open circles indicate the data obtained by the laser flash method in Yamaguchi University using the specific heats calculated using the Debye model.4) Again these data show a good agreement, except for a small discrepancy particularly at high temperatures. Since the uncertainty in radiation correction is one of the major factors producing the uncertainty in the thermal conductivity in the transient measurement method, the temperature difference between the top and bottom of the sample is measured, and the effective emissivity in this system is calculated when the temperature of the sample is stable without current. At this point, heat balance is expressed as
α (µV/K)
-180
20
15 good soldering bad soldering
(c)
10 200
300 400 500 Temperature (K)
600
Fig. 4. Temperature dependences of resistivity, Seebeck coefficient, and thermal conductivity of n-type Bi2 Te3 -based sample for good and bad solderings: (a) resistivity, (b) Seebeck coefficient and (c) thermal conductivity.
as the reflector whose temperature is about Tbottom , and inflow from the radiation reflected to the sample, the term on the left-hand side of eq. (4.1) is expressed as 4 4 4 Qrad ¼ s As Ttop c Ac Tbottom C3 Ttop ;
where s : emissivity of the sample; c : emissivity of the components; As : surface area of the sample; Ac : constant
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ρ (µΩ cm)
-1
κ (mW cm K )
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20
1000
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500 Transient measurement method
Transient measurement method
(a)
Commercial equipment
Laser flash method
10
0 200
300 400 500 Temperature (K)
200
600
300 400 500 Temperature (K)
600
Fig. 6. Temperature dependence of thermal conductivity of n-type Bi2 Te3 -based sample. The specific heats obtained by the laser flash method data are analyzed using the Debye model.
-200 -180
α (µV/K)
20
-160 -140
With thermal reflector Without thermal reflector
-120
∆ T (K)
15 Transient measurement method
10
(b)
Commercial equipment
-100 200
300 400 500 Temperature (K)
600
5
Fig. 5. Temperature dependences of resistivity and Seebeck coefficient of n-type Bi2 Te3 -based sample: (a) resistivity and (b) Seebeck coefficient.
0 300
400
500
600
T top (K) including the surface area of the components; C3 : constant including s As , the reflectance of the components and angle factor. To simplify the equation, substitute s As ¼ C1 , c Ac ¼ C2 , and Tbottom Ttop ¼ T. Thus, Qrad ¼
4 C1 Ttop
4 C2 Tbottom
4 C3 Ttop :
4 4 4 4 Qrad ¼ AðC2 Tbottom þ C3 Ttop Þ ðC2 Tbottom þ C3 Ttop Þ
ð4:3Þ
Since 0 < C2 < ðC2 þ C3 Þ, the third term in brackets in eq. (4.3) has the relation 0 < C2 ð4T=Ttop Þ < ðC2 þ C3 Þð4T=Ttop Þ;
thus, Qrad has the relation 4 < Qrad ðA 1ÞðC2 þ C3 ÞTtop
ð4:2Þ
The temperature dependence of T is shown in Fig. 7. Filled circles indicate the data obtained with the thermal reflector, and open circles indicate the data obtained without 4 the thermal reflector. The outflow of radiation heat C1 Ttop using the data obtained without the thermal reflector is measured, and by subtracting the curve obtained using the thermal reflector from that obtained without the thermal 4 4 reflector, the inflow of radiation heat (C2 Tbottom þ C3 Ttop ) and then the outflow and inflow ratio of radiation heat 4 4 4 C1 Ttop =ðC2 Tbottom þ C3 Ttop ) (¼ A) are estimated. Thus, eq. (4.2) is rewritten as 4 : ðA 1Þ½C2 þ C3 þ C2 ð4T=Ttop ÞTtop
Fig. 7. Temperature dependence of T.
4 < ðA 1ÞðC2 þ C3 Þð1 þ 4T=Ttop ÞTtop :
ð4:4Þ
If the coefficient (A 1) is constant, the deviations of Qrad equivalents to (4T=Ttop ) and of Qrad are almost propor4 tional to Ttop . The temperature dependences of coefficients (A 1) and (A 1)(1 þ 4T=Ttop ) are shown in Fig. 8. These coefficients are almost constant at temperature higher than 400 K, and the deviation caused by (4T=Ttop ) is 4.6% at most when Ttop ¼ 550 K. Since the correction factor caused by radiation heat is 0.029 at this time, the error of thermal conductivity caused by radiation heat is 0.13%. On the other hand, the deviation from the constant value shown by a straight line in Fig. 8 increases with a decrease in temperature to values lower than 400 K, because the measurement of radiation heat in a relatively low temperature region has uncertainty as it is very small. However, since the correction factor caused by radiation heat in such a low temperature region is originally small (
