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A new simultaneous measurement method for the measurement of the three thermoelectric properties with a film-type thermocouple probe was proposed. Seebeck coefficient was measured using the steady-state condi-tion of the differential method. The electrical resistivity was measured us-ing the four-probe method and the thermal diffusivity is measured using the periodic heating method. The effectiveness of the proposed method was verified using constantan as a reference material. After describing the effectiveness of the method, the measurement of three thermoelectric properties of Bi
_{0.3}Sb
_{1.7}Te
_{3}, which is a thermoelectric material, was per-formed.

Thermoelectric power generation is attracting attention as an unutilized energy utilization method. On the other hand, it has not been widely used because of its low energy conversion efficiency, toxic or rare components in its material and so on. Therefore, new thermoelectric materials are being actively developed to solve these problems. Technologies to evaluate these materials with high precision have become increasingly important. The thermoelectric material is evaluated using the dimensionless figure of merit ZT. ZT is expressed as

where S is the Seebeck coefficient, ρ is electrical resistivity, κ is thermal conductivity, and T is the absolute temperature. In evaluating the performance of thermoelectric materials, it is necessary to measure three physical property values S, ρ and κ. Conventionally, temperature dependency of these properties was measured separately in order to calculate ZT. In other words, it takes a great deal of time and effort to evaluate the performance of materials. Materials with nanostructures, which have been developed in recent years, are anisotropic, and there are reports that ZT greatly differ depending on the literature in spite of the same material ( [

Currently, there are several simultaneous measurement methods for two thermoelectric properties such as the Seebeck coefficient and electric resistivity, or the Seebeck coefficient and thermal conductivity. However, the number of previous studies of simultaneous measurement which can measure three thermoelectric properties are limited. Chaussy et al. ( [

As described above, in the temperature range above the room temperature, there is still no effective method of simultaneous measurement of thermoelectric properties. In this paper, a new simultaneous measurement method for three thermoelectric properties with film-type thermocouple probe has been proposed. At the beginning, the principle of the measurement and the original instrument is explained. In order to verify the proposed measurement method, constantan is used as a reference material. In addition, the result of the temperature dependence measurements of constantan is reported. Finally, the measurement result of Bi_{0.3}Sb_{1.7}Te_{3} is shown and discussed.

The principle of the simultaneous measurement for three thermoelectric properties will be explained using

1) The Seebeck coefficient (

The Seebeck coefficient measurement is conducted under the steady-state condition. By heating the one edge of the sample, a temperature gradient is generated along the longitude direction of the sample. From the temperature difference ΔT and the thermoelectromotiveforce ΔV_{th} between two measuring points, the relative Seebeck coefficient between the sample and the wire are obtained as the Equation (2).

The absolute Seebeck coefficient of the sample can be obtained by adding the absolute Seebeck coefficient _{sample-wire}.

2) Electrical resistivity (

Four-probe method is used as a measuring method for electrical resistivity. As the current I is applied to the installed leads to the sample, the voltage drop ΔV between any two points on the sample is measured. The electrical resistivity is obtained with the sample thickness t as the Equation (4).

where t is the sample thickness and f_{1} and f_{2} are shape correction factors ( [

where s, l and w are the probe pitch, the sample length and the sample width, respectively.

In order to eliminate the effect of thermoelectromotive force due to Joule heat, the polarity of the current is switched and the average value of the obtained voltage drops is used as ΔV in Equation (4).

3) Thermal diffusivity (

In the thermal diffusivity measurement, periodic heating is used. By heating periodically one end of the sample, the AC temperature is propagated along the longitude direction of the sample. Considering the one dimensional heat conduction equation with respect to the sample length direction x, the phase delay

where a is thermal diffusivity of the sample and f is the frequency of the AC temperature. In Equation (7), when x is a constant x_{1} and x_{2} and

In other words, by measuring the phase delay at the two points

In Equation (9), m is the distance between the center of the heater and the one sample edge as the

1) Film-type thermocouple probe

The photograph of film-type thermocouple probe proposed in this research is shown in

Components | Material | Size | |
---|---|---|---|

Base | Polyimide | 15 × 2 × t0.05 mm | |

Thermocouple | Chromel, Alumel | 50 | |

Lead wire | Constantan | 50 | |

Sensor’s pitch | - | 3 mm | |

Heater | Cu-Ni alloy | 6.3 × 2.8 mm (120 Ω) |

pairs of lead wires at both ends. The former are used for the measurements of the temperature and the voltage difference. The latter are used in order to apply the current to the sample. In addition, a strain gauge is used as a heater for heating the sample, and it is installed so that it can perform one-dimensional heating in the in-plane direction of the sample.

2) Simultaneous measurement device

perature measured between two thermocouples is measured using the lock-in amplifier. These three thermoelectric property measurements can be done automatically by switching the wiring using relays. Based on the measurement principle shown in the previous section, it is possible to measure thermoelectric properties of bulk material with the same setting. By placing the measuring part into a thermostatic chamber, the atmospheric temperature can be controlled to enable temperature dependency measurements.

In order to verify the effectiveness of this method, measurement of three thermoelectric properties at 293 K was carried out using constantan (Cu: 50% - 55%, Ni: 45% - 50%) as a reference sample. The sample size was 5 × 36 × t0.3 mm. The reason for choosing constantan as the reference sample here is that it is possible to verify the Seebeck coefficient measurement by using the thermoelectromotive force table ( [

Temperature dependence of thermoelectric properties was measured using this

Relative Seebeck coefficient | Electrical resistivity | Thermal diffusivity | ||||
---|---|---|---|---|---|---|

1st run | 2nd run | 1st run | 2nd run | 1st run | 2nd run | |

Measurement result | 59.4 μV/K | 58.8 μV/K | 0.468 μΩ・m | 0.466 μΩ・m | 6.63 mm^{2}/s | 5.99 mm^{2}/s |

Reference value | 60.5 μV/K ( [ | 0.486 μΩ・m ( [ | 6.34 mm^{2}/s ( [ | |||

Difference | −1.8 % | −2.8% | −3.7% | −4.1% | −4.5% | 5.5% |

measurement method. The measurement part was placed in a thermostatic chamber and the measurement was carried out while changing the temperature inside the thermostatic chamber at intervals of 10 K in the range of 283 to 343 K. The measurement results are shown in

Three thermoelectric properties of Bi_{0.3}Sb_{1.7}Te_{3} which was known a representative thermoelectric material were measured. The sample size was 4.5 × 35 × t1 mm. This Bi_{0.3}Sb_{1.7}Te_{3} was sinter prepared by a hot press method. The measurement was carried out by placing the apparatus in a thermostatic chamber and the absolute Seebeck coefficient of the sample was calculated by substituting the absolute Seebeck coefficient of chromel ( [

Seebeck coefficient | Electrical resistivity | Thermal diffusivity | |
---|---|---|---|

Measurement result | 183.3 μV/K | 9.44 μΩ・m | 1.01 mm^{2}/s |

Reference value | 182.8 μV/K ( [ | 10.7 μΩ・m ( [ | 0.88 mm^{2}/s ( [ |

Difference | 0.3% | 11.7% | 14.8% |

and 14.8% for the Seebeck coefficient, electrical resistivity and thermal diffusivity, respectively.

In the measurement of electrical resistivity and thermal diffusivity of Bi_{0.3}Sb_{1.7}Te_{3}, the cause of the large difference between the measurement result and the reference value will be considered.

1) Electrical resistivity

When a current I is applied to the thermoelectric material, heat absorption and heat generation occur by the Peltier effect at the junction between electrode and the material as an effect peculiar to the thermoelectric material. The heat quantity Q is expressed as

This heat generates a temperature gradient in the sample, and a thermoelectromotive force is generated. The thermoelectromotive force due to the Peltier heat cannot be canceled even if the polarity of the current is changed unlike thermoelectromotive force caused by Joule heat. This thermoelectromotive force is added to the drop voltage due to the resistance and it is measured to be larger than the actual resistance. As a solution, it is possible to measure in a short time after applying the current by utilizing the fact that the relaxation time of heat is significantly longer than that of the career. ( [

2) Thermal diffusivity

In the case of constantan, the difference between the measured value and the reference value was 4.5%. In the case of Bi_{0.3}Sb_{1.7}Te_{3}, however, it was a large value of 14.8%. This may be attributed to the difference in the value of thermal diffusivity between the two materials. While the thermal diffusivity of constantan is 6.34 mm^{2}/s ( [_{0.3}Sb_{1.7}Te_{3} is 0.88 mm^{2}/s ( [_{0.3}Sb_{1.7}Te_{3}, the AC temperature amplitude decayed at the thermocouple contact position. Therefore, by reducing the distance between the thermocouple contact position and the heater, it can be considered that the measurement is conducted more accurately. Thermoelectric materials are low-thermal conductivity materials like Bi_{0.3}Sb_{1.7}Te_{3} and it is considered that it is necessary to measure the temperature in the vicinity of the heater. However, since the sample has a finite thickness at a location close to the heater, one-di- mensional thermal conductivity does not hold true. Therefore, by solving the two-dimensional heat conduction equation, it may be possible to estimate the boundary between the position where one-dimensional thermal conductivity is established and the position till which it does not hold true, and it is also necessary to investigate the optimum position to contact the thermocouple.

A new measurement method for thermoelectric properties was proposed and the verification of this method using a film-type thermocouple probe was carried out using constantan. The difference between the physical property values and the reference value was within ±10%, indicating the soundness of the device. Further, three thermoelectric property values of Bi_{0.3}Sb_{1.7}Te_{3} were measured at a temperature of 323 K (thermal diffusivity measurement is 300 K), and the difference between the measured value and the reference value was as follows: the result was 0.3%, 11.7% and 14.8% for the Seebeck coefficient, electric resistivity and thermal diffusivity, respectively.

Part of this research funding was subsidized by strategic fundamental technology advancement support project. The author wish to acknowledge Kiyoshi Ogawa and Ryouzo Hiramatsu of Ozawa Science Co., Ltd. and Dr. Woosuck Shin of AIST cooperated in promoting this research.

Yamazaki, T., Ueno, A. and Nagano, H. (2017) Proposal and Verification of Simultaneous Measure- ment Method for Three Thermoelectric Pro- perties with Film-Type Thermocouple Probe. Journal of Electronics Cooling and Thermal Control, 7, 23-32. https://doi.org/10.4236/jectc.2017.72003