WO2024116508A1

WO2024116508A1 - Peltier coefficient calculation method, program, and measurement system

Info

Publication number: WO2024116508A1
Application number: PCT/JP2023/031251
Authority: WO
Inventors: 康孝天谷; 顕次郎大川; 毅島崎; 憲彦坂本; 晋久金子
Original assignee: 国立研究開発法人産業技術総合研究所
Priority date: 2022-11-30
Filing date: 2023-08-29
Publication date: 2024-06-06

Abstract

In order to easily measure the Peltier coefficient of a sample, this Peltier coefficient calculation method comprises: (A) a step for measuring the temperature at both ends of a conductor sample of which a Peltier coefficient is to be measured by passing a direct current through the conductor sample, after making the conductor sample have a constant temperature; (B) a step for measuring the temperature at the end portions and the center of the conductor sample by passing an alternating current having an effective value equal to the direct current through the conductor sample; and (C) a step for calculating the Peltier coefficient by using the temperature at both ends of the conductor sample measured by passing the direct current through the conductor sample, the temperature at the end portions and the center of the conductor sample measured by passing the alternating current, an electrical resistance value of the conductor sample, and a value of the current passed through conductor sample.

Description

Peltier coefficient calculation method, program, and measurement system

The present invention relates to a technique for calculating the Peltier coefficient.

The mutual conversion of heat and electricity through the movement of electrons in a solid is called thermoelectric conversion, and research and development is being conducted on power supplies and electronic cooling components that use this principle to recycle waste heat as electricity. These technologies use the Seebeck effect, in which a voltage is generated according to the temperature difference applied to an object, and the Peltier effect, in which a heat flow is generated according to the direction of the voltage. The proportionality coefficient linking the temperature difference and voltage is called the Seebeck coefficient, and conversely, the proportionality coefficient linking voltage and heat flow is called the Peltier coefficient.

There has been great progress in the measurement technology of thermoelectric materials over the past 20 years. Until now, the reference material for the Seebeck effect has been supplied by NIST (National Institute of Standards and Technology) as high-purity iron (i.e., electrolytic iron) as part of its thermal property standards. However, in 2012, for the first time in about half a century, the supply of a more sophisticated semiconductor-type reference material began. This is because, in the race to develop highly efficient thermoelectric materials, data with poor reproducibility has become more common, and measurement technology has become increasingly important.

However, while the Seebeck effect is very frequently measured in the evaluation of the efficiency and physical properties of materials, the Peltier effect is rarely measured. This is because the measurement of the Seebeck effect requires the measurement of heat flow, whereas the temperature difference and voltage are sufficient to measure the Seebeck effect. Fortunately, a reciprocity has been theoretically shown in which the response coefficient is equal when the temperature difference drives the current (Seebeck effect) and when the voltage drives the heat flow (Peltier effect), so in many cases the Peltier effect is indirectly determined from the Seebeck effect. In other words, the accuracy of the Peltier effect reported so far is strongly dependent on the accuracy of the measurement of the Seebeck effect. However, in recent years, it has become clear that differences in measurement methods and materials can cause systematic deviations in the Seebeck effect, which has become a problem. In addition, more precise experimental verification of the reciprocity has been repeatedly called for in papers and other publications. To solve this problem, it is preferable to measure the Peltier effect independently of the Seebeck coefficient.

In light of this background, various techniques for measuring the Peltier coefficient have been developed. For example, Non-Patent Document 1 discloses a method for determining the Peltier coefficient from the heat flow of a sample when a temperature difference is applied and when it is electrically shorted and opened, and the current value flowing through the sample at that time. The advantage of this method is that it does not require measurement of the thermal conductivity or dimensions of the sample. However, it has a disadvantage in that it requires measurement of the heat flow flowing through the sample, which is more difficult to measure accurately than temperature measurement. In other words, since the heat flow generated by the heater is all flowed into the sample without leaking to the surroundings, the heater part of the measurement device generally has a complex and large-scale mechanism to prevent heat leakage. In addition, the temperature difference is measured to measure the heat flow, but multiple temperature measurements are performed with multiple thermometers, which is time-consuming for general physical property and device evaluation.

Non-Patent Document 2 also discloses a technology that derives a more general relationship between the Peltier coefficient and temperature, taking into account the parasitic thermal resistance of the electrodes, from thermal conduction analysis, making it possible to accurately determine the Peltier coefficient from temperature measurement. This method has the advantage of being able to determine the Peltier coefficient by temperature measurement rather than heat flow. However, since the temperature is measured at two locations on both ends of the sample, the information that can be obtained from the temperature measurement is limited, and the thermal conductivity and dimensions of the sample and current lead wire are included as unknowns in the measurement equation. Therefore, in order to measure the Peltier coefficient, not only is the temperature generated by the Peltier effect measured, but multiple measurement systems (synonymous with multiple measurement devices) with different measurement principles and boundary conditions are used. In particular, since the measurement of thermal conductivity requires the measurement of heat flow, problems similar to those in Non-Patent Document 1 may occur.

As such, conventional technology not only requires the use of large-scale measurement equipment to measure heat flow, but also introduces a system based on a different principle, which adds unknown quantities that affect the measurement system and the associated uncertainties. For example, when measuring thermal conductivity, the heat flow value and the amount of heat loss from the sample to the surroundings become new factors that must be considered, and the uncertainty involved becomes a major factor in the overall measurement of the Peltier coefficient.

Therefore, in one aspect, an object of the present invention is to provide a technique for easily measuring the Peltier coefficient of a sample.

The method for calculating the Peltier coefficient according to the present invention includes the steps of: (A) bringing a conductor sample, the object of which is to measure the Peltier coefficient, to a constant temperature, and then passing a direct current through the conductor sample to measure the temperature at both ends of the conductor sample; (B) passing an alternating current, the effective value of which is equal to the direct current, through the conductor sample to measure the temperature at the ends and center of the conductor sample; and (C) calculating the Peltier coefficient using the temperatures at both ends of the conductor sample measured by passing a direct current through the conductor sample, the temperatures at the ends and center of the conductor sample measured by passing an alternating current through the conductor sample, the electrical resistance value of the conductor sample, and the value of the current passed through the conductor sample.

FIG. 1 is a diagram for explaining the measurement principle. FIG. 2 is a diagram for explaining a temperature change when a direct current is passed through a conductor sample. FIG. 3 is a diagram for explaining a temperature change when an AC current is applied to a conductor sample. FIG. 4 is a diagram for explaining the configuration of the measurement system according to the embodiment. FIG. 5 is a diagram showing the measurement procedure. FIG. 6 is a diagram for explaining a preferred frequency band of an alternating current. FIG. 7 is a diagram for explaining a preferable range of the direct current. FIG. 8 is a diagram for explaining the effect of the correction term. FIG. 9 is a diagram for explaining the relationship between the correction value and the theoretical value of the correction value. FIG. 10 is a diagram illustrating an example of the configuration of the calculation unit.

[Measurement principle according to the embodiment of the present invention]
In this embodiment, an AC current and a DC current are applied to the sample to distinguish between Peltier heat and Joule heat, and the Peltier coefficient is calculated by measuring at least the temperature difference at both ends of the sample caused by the Peltier heat generated at the ends of the sample and the temperature rise at the center of the sample caused by the Joule heat. By adding one temperature measurement point at the center of the sample in this way, the thermal conductivity and sample size values can be eliminated from the unknowns included in the conventional measurement equation, and the same measurement system can be used. This makes it possible to perform measurements more easily than the conventional method using multiple measurement systems with different principles and boundary conditions. Furthermore, since major uncertain factors such as thermal conductivity and heat loss can be eliminated from the measurement system, high accuracy can be achieved. The principle will be described in detail below.

FIG. 1 shows a thermal analysis model for deriving the Peltier coefficient. As shown in FIG. 1, the left end of the sample is x=0, and both ends of the sample with length L are thermally connected to a heat bath block (heat sink) by current leads having thermal conductance Kw. The heat bath block is held at temperature Te. The length of the left current lead is _Lc , and the length of the right current lead is _Lh . When a direct current is applied to the sample, a heat flow generated by the Peltier effect flows to both ends of the sample by diffusion within the sample, generating a temperature gradient. That is, as shown in FIG. 1, heat absorption occurs near x=0, and heat generation occurs near x=L, so the temperature gradient in the sample is as shown in FIG. 2. Specifically, at x=0, the temperature is _T0 , which is lower than the temperature Te of the heat bath block, at x=L/2, the temperature is Te, and at x=L, the temperature is _TL , which is higher than the temperature Te. Here, the temperature difference ΔT _dc between both ends of the sample caused by the Peltier effect is expressed as follows:
ΔT _dc = T _L - T ₀

On the other hand, when an AC current is applied, the Peltier effect is cancelled out, the linear temperature gradient disappears, and a parabolic temperature distribution occurs due to the Joule effect. The temperature distribution in this case is as shown in FIG. 3. That is, at x=0, the temperature rises due to the Joule effect, so the temperature rises from the temperature Te of the heat bath block by ΔT _corr , which becomes T ₀ in this case. Similarly, at x=L, the temperature rises from Te by ΔT _corr , which becomes T _L in this case. Meanwhile, a parabolic temperature distribution occurs in the sample, and the temperature is highest at x=L/2, where T _L/2 =T ₀ +ΔT _ac . Note that T ₀ =T _L =Te+ΔT _corr .

(a) Analysis when DC current is applied When DC current is applied, the following relationship holds for the heat flow density _JQ flowing through the sample and the temperature T of the sample.

Here, a represents the cross-sectional area of the sample, Q [W] represents the heat flow, π [V] represents the Peltier coefficient of the sample, T [K] represents the temperature of the sample, I [A] represents the current density, κ [W/(mK)] represents the thermal conductivity of the sample, ρ [Ωm] represents the electrical resistivity of the sample, and the variable x [m] represents the coordinates of the sample. The thermal boundary conditions at x = 0 and x = L in FIG. 1 can be expressed as follows using the thermal conductance Kw of the current lead wire, since the heat flow is continuous. Note that the physical properties of thermal conductivity, Peltier coefficient, and electrical resistivity have finite temperature coefficients, and therefore generally become functions of position x in conductors with temperature gradients and heat generation, but are ignored in this analysis as the temperature gradient and Joule heat generation are sufficiently small. However, the verification experiments shown in the examples described later were also conducted under such conditions, and it is believed that those skilled in the art would understand this premise.
Kw(Te−T ₀ )=Q(0) (3)
Kw(T _L -Te)=Q(L) (4)

Next, since equation (2) can be easily integrated, we integrate it with respect to x and transform it using the heat flow density equation (1), and obtain the following equations for the heat flows Q(0) and Q(L) at both ends of the sample, x = 0 and x = L.

Here, the thermal conductance K and electrical resistivity R of the sample are defined as K = (κa)/L and the electrical resistivity R = (ρL)/a. Using the boundary conditions of equations (3) and (4), equations (5) and (6) can be expressed as follows:

This is a strict equation for the balance between electrical energy and thermal energy derived from the heat conduction equation. The left side represents heat generation due to the Peltier effect. The right side represents heat diffusion due to thermal conduction in the sample, Joule heat, and heat loss through the lead wires. In other words, it represents that the Peltier heat generated at both ends of the sample and the Joule heat generated inside the sample are equal to the heat flow due to thermal conduction in the sample and thermal conduction in the lead wires. Adding both sides of equations (7) and (8) and solving for the Peltier coefficient, we obtain the following equation.

Therefore, it can be seen that the Peltier coefficient π can be obtained by calculating the temperature difference between both ends of the sample, ΔT _dc = T _L - T ₀ , the DC current I, the thermal conductance K of the sample, and the thermal conductance Kw of the current lead wire. As such, in the conventional measurement equation, there are still other parameters that need to be measured in addition to the temperature gradient ΔT _dc of the sample.

(b) Analysis when AC current is applied The problem with equation (9) can be solved by measuring the temperature difference between the center and the end of the sample when AC current is applied to the sample. Here, we consider the temperature distribution occurring inside the sample. This temperature distribution can be easily obtained by solving equation (2), and the temperature distribution is as follows, with the temperatures at the ends of the sample being _T0 and _TL . Note that here too, the temperature dependence of electrical resistivity and thermal conductivity is ignored.

Then, by solving the boundary conditions of equations (3) and (4) as simultaneous equations with two unknowns, T ₀ and T _L can be obtained as follows:

Then, by substituting x=L/2 and x=0 into equation (10), the thermal conductances K and Kw of the sample and the current lead wire are expressed as follows using the temperatures of the center and ends of the sample.

Therefore, by substituting equations (12) and (13) into equation (9), the following equation is obtained.

In this way, if the temperature difference ΔT _dc between both ends of the sample caused by the Peltier effect when a direct current is applied and the temperature difference ΔT _ac between the temperature at the center of the sample and the temperature at the end of the sample caused by the Joule effect when an alternating current is applied can be obtained, the Peltier coefficient π can be obtained in a simple manner without separately measuring the thermal conductivity value or dimensional values of the sample. Furthermore, since major uncertain factors such as thermal conductivity and heat loss can be eliminated from the measurement system, high accuracy can be achieved in this respect.

In addition, RIΔT _dc /(8ΔT _ac ) in equation (14) represents the Peltier coefficient when there is no heat loss, and RIΔT _dc /(8ΔT _ac )×(2ΔT _ac )/ΔT _corr represents a correction term, which represents the Peltier heat lost due to heat loss.

Also in equation (9), KΔT _ac /I represents the Peltier coefficient when there is no heat loss, and KΔT _ac /I×K _w /(2K) represents a theoretical correction term, which represents the Peltier coefficient lost due to heat loss.

[Embodiment]
An example of the configuration of the measurement system according to the present embodiment is shown in Fig. 4. The measurement system according to the present embodiment includes a DC power source 11, an AC power source 12, a switch 13 for switching the current flowing through the conductor sample 100 between DC and AC, heat bath blocks 31 and 32 for maintaining the conductor sample 100 and the like at a constant temperature Te, a current lead wire 14 connecting the DC power source 11 and the AC power source 12 to one end of the conductor sample 100, a current lead wire 15 connecting the switch 13 to the other end of the conductor sample 100, a voltmeter 21 for measuring the voltage generated between both ends of the conductor sample 100, a temperature measurement unit 40 for measuring the temperatures of both ends and the center of the conductor sample 100, and a calculation unit 50 for calculating the Peltier coefficient based on the measurement results of the temperature measurement unit 40 and the like.

Heaters and thermometers (not shown) are attached to the heat bath blocks 31 and 32, and the temperature is controlled to be kept constant at Te. The calculation unit 50 may be used for this control. In order to avoid heat loss due to convection, it is preferable to place at least a part of the current leads 14 and 15, the conductor sample 100, and the heat bath blocks 31 and 32 in a vacuum environment. In order to suppress heat exchange between the conductor sample 100 and the outside due to radiation, it is preferable to cover the entire conductor sample 100 with a heat shield. The heat bath blocks 31 and 32 ensure that the temperatures of at least a part of the current leads 14 and 15 and the conductor sample 100 are also in thermal equilibrium at temperature Te. For this reason, the current lead 14 is in contact with the heat bath block 32 via the electrical insulating coating 16, and the current lead 15 is in contact with the heat bath block 31 via the electrical insulating coating 17. By using

current leads

14 and 15 with high thermal resistance, the value of the correction term in equation (14) becomes small, making it possible to obtain a highly accurate Peltier coefficient without the correction term. Heat bath blocks 31 and 32 are made of a metal such as copper.

The temperature measuring unit 40 includes a thermocouple 42 for measuring the temperature of one end of the conductor sample 100, a thermocouple 44 for measuring the temperature of the center of the conductor sample 100, and a thermocouple 46 for measuring the temperature of the other end of the conductor sample 100. The voltmeter 21 is used to measure the voltage generated across both ends of the conductor sample 100 when an alternating current is passed through it, and to obtain the electrical resistance R of the conductor sample 100. The calculation unit 50 is a calculation device such as a personal computer, and the main function is realized by a processor executing a program that calculates the Peltier coefficient using the entire formula (14) or the first term of formula (14).

Next, the calculation procedure of the Peltier coefficient by the measurement system according to this embodiment will be described with reference to FIG. 5. First, preparations for temperature measurement are made (step S1). As shown in FIG. 4, thermocouples are attached to both ends and the center of the conductor sample 100, and

current leads

14 and 15 are connected to both ends of the conductor sample 100. The current leads 14 and 15 are in contact with the heat bath blocks 31 and 32 via the electrical insulating

coatings

16 and 17. Furthermore, the conductor sample 100 and the like are placed in a vacuum environment, the heat bath blocks 31 and 32 are kept at a temperature Te, and the temperature of the conductor sample 100 is also kept at a temperature Te until it reaches thermal equilibrium. That is, even at this stage, the temperatures of the ends and center of the conductor sample 100 are measured to confirm whether they have reached temperature Te.

Thereafter, the switch 13 is connected to the DC power source 11 to pass a DC current through the conductor sample 100, and the temperature measuring unit 40 measures the temperatures at both ends of the conductor sample 100 (step S3). As a result, T ₀ and T _L are obtained, and ΔT _dc =T _L -T ₀ is obtained. After the measurement, the switch 13 is used to stop current from flowing through the conductor sample 100 from either power source, so that the conductor sample 100 returns to the temperature Te of the heat bath blocks 31 and 32.

Thereafter, the switch 13 is connected to the AC power source 12 to pass an AC current (the effective value of the AC current is the same as the DC current passed in step S3) through the conductor sample 100, and the temperature (T ₀ , T _L ) of the end portion of the conductor sample 100 and the temperature (T _L/2 ) of the center portion are measured by the temperature measuring unit 40 (step S5). The end portion of the conductor sample 100 may be both ends or one end. As described with reference to FIG. 3, the temperature T ₀ at x=0 and the temperature T _L at x=L when an AC current is passed are the same in principle, so either one may be used. In some cases, their average values may be calculated. This measurement provides ΔT _ac (=T _L/2 -T ₀ =T _L/2 -T _L ) and ΔT _corr (=T ₀ -Te=T _L -Te).

Furthermore, by connecting switch 13 to AC power source 12, an AC current (the effective value of the AC current is set to be the same as the DC current passed in step S3) is passed through conductor sample 100, i.e., in the same manner as in step S5, the voltage at the end of conductor sample 100 is measured by voltmeter 21 (step S7). The electrical resistance R of conductor sample 100 is obtained by dividing the measured voltage V by the passed current I.

Then, the calculation unit 50 calculates the Peltier coefficient based on the measurement results and outputs it to, for example, a display device or other output device (step S9). Since ΔT _dc is obtained in step S3, ΔT _ac and T _corr are obtained in step S5, and the electrical resistance R is obtained in step S7, the Peltier coefficient π is calculated by equation (14) by further using the flowing current I. Note that if the correction term is ignored, the Peltier coefficient π is calculated as RIΔT _dc /(8ΔT _ac ), so it is not necessary to calculate ΔT _corr .

By following the above procedure, the Peltier coefficient can be easily calculated by measuring the temperature at three points on the conductor sample 100. In this case, major uncertain factors such as the measurement of the dimensions of the conductor sample 100, thermal conductivity, and heat loss can be eliminated from the measurement system, so high accuracy is achieved from this perspective as well.

[Example]
The measurement system shown in FIG. 4 was used, and a polycrystalline sample of _Bi2Te3 , an n-type semiconductor material, was used as the conductor sample _100. The conductor sample 100, measuring 30 mm x 3 mm x 2 mm, was thermally connected to the heat bath blocks 31 and 32 by

current leads

14 and 15 having a thermal conductance Kw. A vacuum environment was used to prevent heat loss due to convection. The entire conductor sample 100 was covered with a heat shield to suppress heat exchange between the conductor sample 100 and the outside due to radiation. In this example, the effective value of the AC current was 25 mA, and the AC frequency was 62.5 Hz.

There is a characteristic frequency at which the Peltier heat decays and becomes sufficiently small, so in order to measure accurately, a specific frequency that is sufficiently higher than that characteristic frequency is selected. For this purpose, the temperature difference in the conductor sample 100 caused by the Peltier effect at both ends of the conductor sample 100 is measured at an appropriate range of frequencies, and the frequency for measurement is determined within a range in which the temperature difference is independent of frequency. Figure 6 shows an example of measurement. That is, the horizontal axis represents frequency, and the vertical axis represents the temperature difference [K] at both ends of the conductor sample 100. In this example, since the temperature difference is constant and independent of frequency at 1 Hz or higher, a frequency of 1 Hz or higher should be selected. Integer values such as 10 Hz and 100 Hz are also acceptable, but to avoid power supply frequency noise, selecting 62.5 Hz allows for more accurate measurement.

On the other hand, if the current value is too large, the Joule effect will cause an imbalance in the amount of heat absorbed and the temperature difference will no longer increase in proportion to the current. Therefore, a region of current that changes linearly is found, and the current value is set within that range. Figure 7 shows an example of a measurement. In Figure 7, the horizontal axis represents the DC current [mA], and the vertical axis represents the temperature difference [K] between both ends of the conductor sample 100. It can be seen that if the range is between -60 mA and +60 mA, the temperature difference changes in full proportion to the DC current.

Figure 8 shows the results of calculating the Peltier coefficient while intentionally changing the amount of heat loss from the conductor sample 100 by changing the length of the current leads 14 and 15. The horizontal axis of Figure 8 represents the thermal conductance [mW/K] of the current leads, the vertical axis represents the Peltier coefficient [mV], the black circles represent the Peltier coefficient calculated without the correction term, and the black squares represent the Peltier coefficient calculated using equation (14). Since the Peltier coefficient is a value specific to the sample, it is constant regardless of heat loss. However, as shown by the black circles, if the correction term is not taken into account, the Peltier coefficient increases as the thermal conductance of the current leads 14 and 15 increases. This is because the Peltier heat generated at the ends of the conductor sample 100 flows out through the current leads 14 and 15, reducing the temperature difference between both ends of the conductor sample 100. On the other hand, if the effect of the thermal conductance of the current leads 14 and 15 is corrected, it becomes almost independent of the heat loss from the current leads 14 and 15 and becomes constant, as shown by the black squares.

Also, whether the correction works correctly is verified. As can be seen from the two terms of formula (9), KΔT _ac /I×K _w /(2K), the theoretical value of the correction value can be obtained by further using the thermal conductance Kw of the current leads 14 and 15 and the thermal conductance K of the conductor sample 100. Therefore, the thermal conductivity and dimensions of the conductor sample 100 and the current leads 14 and 15 are accurately measured, and the correction value of the Peltier coefficient calculated from these values is shown by a solid line in FIG. 9. The horizontal axis of FIG. 9 represents the thermal conductance [mW/K] of the current leads 14 and 15, and the vertical axis represents the correction value [mV]. The correction value (i.e., the measured value) obtained from the correction term of formula (14) and the theoretical value of the correction value were approximately equal.

In this way, by using this embodiment, unlike conventional methods in which multiple measurement systems with different principles and boundary conditions are prepared, it is possible to obtain the Peltier coefficient by performing a composite measurement of temperature and electrical resistance value with a single measurement system. This is achieved by adding a single temperature measurement point at the center of the conductive sample and eliminating thermal conductivity and sample size values from the unknowns included in the conventional measurement equation. This makes it possible to eliminate thermal conductivity values and geometric shape values from the measurement equation, thereby achieving high measurement accuracy. In this case, the configuration of the measurement system and the measurement method are simple.

Although the embodiment of the present invention has been described above, the present invention is not limited to this. For example, the voltmeter 21 may also be connected to the calculation unit 50. Furthermore, the switching control of the switch 13 and the temperature control of the heat bath blocks 31 and 32 may also be performed by the calculation unit 50. Furthermore, the procedure shown in FIG. 4 may also be modified so as not to affect the measurement results. For example, to measure ΔT _corr , the temperature T ₀ =T _L =Te at the end of the conductor sample 100 before the AC current is passed is used, but the temperature measured in step S1 may be used, or the temperature may be measured at another timing without passing the current and the value may be used. The order in which the AC current and the DC current are passed may be interchanged. Furthermore, in order to avoid overestimating the electrical resistance R due to Peltier heat, the AC method in which the AC current is passed through the conductor sample 100 is used, but the method may be modified so as not to affect the measurement results. For example, a time-resolved measurement method in which a step-like current is passed through the conductor sample 100 and the voltage is measured before the Peltier heat is distributed throughout the sample may be used.

The calculation unit 50 described above is, for example, a computer device as shown in FIG. 10, in which the memory 2501, the CPU 2503, the hard disk drive (HDD) 2505, the display control unit 2507 connected to the display device 2509, the drive device 2513 for the removable disk 2511, the input device 2515, and the communication control unit 2517 for connecting to the network are connected by a bus 2519. The operating system (OS) and the application program for implementing the processing in this embodiment are stored in the HDD 2505, and when executed by the CPU 2503, are read from the HDD 2505 to the memory 2501. The CPU 2503 controls the display control unit 2507, the communication control unit 2517, and the drive device 2513 according to the processing contents of the application program to perform a predetermined operation. Data during processing is mainly stored in the memory 2501, but may be stored in the HDD 2505. In an embodiment of the present invention, an application program for carrying out the above-mentioned processes is distributed stored on a computer-readable removable disk 2511, and is installed from the drive device 2513 to the HDD 2505. It may also be installed to the HDD 2505 via a network such as the Internet and a communication control unit 2517. Such a computer device realizes the various functions described above by organic cooperation between the above-mentioned hardware such as the CPU 2503 and memory 2501, and programs such as the OS and application programs.

The above-mentioned embodiment can be summarized as follows:

The method for calculating the Peltier coefficient according to this embodiment includes the steps of: (A) bringing the conductor sample, the object of which is to measure the Peltier coefficient, to a constant temperature, and then passing a direct current through the conductor sample to measure the temperature at both ends of the conductor sample; (B) passing an alternating current, the effective value of which is equal to the direct current, through the conductor sample to measure the temperature at the ends and center of the conductor sample; and (C) calculating the Peltier coefficient using the temperatures at both ends of the conductor sample measured by passing a direct current through the conductor sample, the temperatures at the ends and center of the conductor sample measured by passing an alternating current through the conductor sample, the electrical resistance value of the conductor sample, and the value of the current passed through the conductor sample.

In this way, it is possible to calculate the Peltier coefficient by measuring the temperature without obtaining the size or thermal conductivity of the conductor sample, making it possible to easily obtain the Peltier coefficient of the sample. Furthermore, since uncertain factors based on thermal conductivity, etc. can be eliminated from the measurement system, the Peltier coefficient can also be obtained with high accuracy.

The above method may further include a step of measuring the temperature at the end of the conductor sample when no current is flowing through the conductor sample. In this case, in the step of calculating the Peltier coefficient, the temperature at the end of the conductor sample when no current is flowing may be further used to calculate the Peltier coefficient. By using the temperature at the end of the conductor sample when no current is flowing, it becomes possible to correct for heat loss. Specifically, it becomes possible to correct the Peltier coefficient using the correction term in equation (14).

In addition, in the step of calculating the Peltier coefficient, the difference in temperature at both ends of the conductor sample measured by passing a direct current through the conductor sample, and the difference in temperature between the center of the conductor sample measured by passing an alternating current and the end of the conductor sample measured by passing an alternating current may be calculated. Since ΔT _dc and ΔT _ac are obtained, at least the first term of formula (14) can be calculated.

Furthermore, in the step of calculating the Peltier coefficient, if the electrical resistance value of the conductor sample is represented as R, the value of the current passed through the conductor sample is represented as I, the temperature difference at both ends of the conductor sample measured by passing a direct current through the conductor sample is represented as ΔT _dc , and the temperature difference between the center of the conductor sample measured by passing an alternating current and the temperature at both ends of the conductor sample measured by passing an alternating current is represented as ΔT _ac , then:
The Peltier coefficient is
RIΔT _dc /(8ΔT _ac )
In this way, if the thermal resistance of the current lead wire is high, the Peltier coefficient may be calculated with sufficient accuracy using only the first term of equation (14).

The method may further include a step of measuring a temperature at an end of the conductive sample when no current is flowing through the conductive sample. In this case, when the difference between the temperature at the end of the conductive sample measured by flowing an AC current and the temperature at the end of the conductive sample when no current is flowing in the step of calculating the Peltier coefficient is expressed as ΔT _corr ,
2ΔT _ac /ΔT _corr
In this way, the Peltier coefficient can be calculated with higher accuracy by correcting the heat loss.

The program according to this embodiment causes a computer (or processor) to execute the steps of: (A) bringing the conductor sample, the object of which is to measure the Peltier coefficient, to a constant temperature, and then passing a direct current through the conductor sample to obtain the temperatures at both ends of the conductor sample; (B) passing an alternating current, the effective value of which is equal to the direct current, through the conductor sample to obtain the temperatures at the ends and center of the conductor sample; and (C) calculating the Peltier coefficient using the temperatures at both ends of the conductor sample measured by passing a direct current through the conductor sample, the temperatures at the ends and center of the conductor sample measured by passing an alternating current through the conductor sample, the electrical resistance value of the conductor sample, and the value of the current passed through the conductor sample.

The measurement system according to this embodiment also includes: (A) a heat bath mechanism (e.g., heat bath blocks 31 and 32) for maintaining a constant temperature of the conductor sample for which the Peltier coefficient is to be measured; (B) a temperature measurement unit (which may include, for example, a thermocouple) for measuring the temperature at both ends and the center of the conductor sample; (C) a DC power supply for passing a DC current through the conductor sample; (D) an AC power supply for passing an AC current through the conductor sample; and (E) a calculation unit (e.g., a computer or other information processing device) for calculating the Peltier coefficient using the temperatures at both ends of the conductor sample measured by the temperature measurement unit when a DC current is passed from the DC power supply to the conductor sample, the temperatures at the ends and the center of the conductor sample measured by the temperature measurement unit when an AC current having an effective value equal to the DC current is passed from the AC power supply to the conductor sample, the electrical resistance value of the conductor sample, and the value of the current passed through the conductor sample.

Claims

a step of setting a conductor sample, the Peltier coefficient of which is to be measured, at a constant temperature, and then passing a direct current through the conductor sample to measure the temperature at both ends of the conductor sample;
a step of passing an AC current having an effective value equal to that of the DC current through the conductor sample and measuring temperatures at an end and a center of the conductor sample;
calculating a Peltier coefficient using temperatures at both ends of the conductor sample measured by passing a direct current through the conductor sample, temperatures at the ends and center of the conductor sample measured by passing an alternating current through the conductor sample, an electrical resistance value of the conductor sample, and a value of the current passed through the conductor sample;
A method for calculating a Peltier coefficient, comprising:
The method further includes a step of measuring a temperature at the end of the conductor sample when no current is flowing through the conductor sample;
In the step of calculating the Peltier coefficient,
The method for calculating a Peltier coefficient according to claim 1 , further comprising the step of calculating the Peltier coefficient by further using a temperature at the end of the conductive sample in a state where no current is flowing.
In the step of calculating the Peltier coefficient,
2. The Peltier coefficient calculation method according to claim 1, further comprising the steps of: calculating a difference in temperature between both ends of the conductor sample measured by passing a direct current through the conductor sample; and a difference in temperature between a center portion of the conductor sample measured by passing the alternating current through the conductor sample and an end portion of the conductor sample measured by passing the alternating current through the conductor sample.
In the step of calculating the Peltier coefficient,
3. The method for calculating a Peltier coefficient according to claim 2, further comprising the step of calculating a difference between a temperature at the end of the conductive sample measured while the AC current is being passed and a temperature at the end of the conductive sample measured while the current is not being passed.
In the step of calculating the Peltier coefficient,
When the electrical resistance value of the conductor sample is represented as R, the value of the current passed through the conductor sample is represented as I, the temperature difference at both ends of the conductor sample measured by passing a direct current through the conductor sample is represented as ΔT dc , and the temperature difference between the center of the conductor sample measured by passing the alternating current and the temperature at both ends of the conductor sample measured by passing the alternating current is represented as ΔT ac ,
The Peltier coefficient is
RIΔT dc /(8ΔT ac )
The Peltier coefficient calculation method according to claim 3, wherein the Peltier coefficient is calculated using the following formula:
measuring a temperature at the end of the conductor sample when no current is flowing through the conductor sample;
In the step of calculating the Peltier coefficient,
When the difference between the temperature at the end of the conductive sample measured by passing the AC current and the temperature at the end of the conductive sample measured without passing the AC current is represented as ΔT corr ,
2ΔT ac /ΔT corr
The method for calculating a Peltier coefficient according to claim 5 , further comprising the steps of: calculating the Peltier coefficient by using:
a step of setting a conductor sample, the Peltier coefficient of which is to be measured, at a constant temperature, and then passing a direct current through the conductor sample to obtain temperatures at both ends of the conductor sample;
a step of passing an AC current having an effective value equal to that of the DC current through the conductor sample to obtain temperatures at an end and a center of the conductor sample;
calculating a Peltier coefficient using temperatures at both ends of the conductor sample measured by passing a direct current through the conductor sample, temperatures at the ends and center of the conductor sample measured by passing an alternating current through the conductor sample, an electrical resistance value of the conductor sample, and a value of the current passed through the conductor sample;
A program for causing a computer to execute the above.
a heat bath mechanism for keeping the temperature of the conductor sample to be measured constant;
a temperature measuring unit for measuring temperatures at both ends and a center of the conductor sample;
a DC power source for supplying a DC current to the conductor sample;
an AC power source that applies an AC current to the conductor sample;
a calculation unit which calculates a Peltier coefficient using the temperatures at both ends of the conductor sample measured by the temperature measurement unit when a DC current is passed through the conductor sample from the DC power source after the conductor sample has been kept at a constant temperature by the heat bath mechanism, the temperatures at the ends and center of the conductor sample measured by the temperature measurement unit when an AC current having an effective value equal to that of the DC current is passed through the conductor sample from the AC power source, an electrical resistance value of the conductor sample, and a value of the current passed through the conductor sample;
A measurement system having