JP2007005359A - Method of evaluating seebeck coefficient - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method of evaluating the Seebeck coefficient for solving the problems, wherein the shape of a sample is defined and that it takes time to stabilize a temperature difference in a conventional measurement of the Seebeck coefficient, because the Seebeck coefficient is calculated, based on the temperature difference generated by heating one end of a measurement sample and cooling the other end and thermal electromotive force. <P>SOLUTION: This method of evaluating the Seebeck coefficient has at least a process of applying a DC current to a portion between one end of a measurement sample and the other end, to obtain the temperature difference (dΔT/dt) generated between the one end and the other end in a unit time. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a method for evaluating the Seebeck coefficient, and particularly relates to a method suitable for evaluating the Seebeck coefficient of a thin film sample.

  Thermoelectric conversion elements using the Seebeck effect can convert thermal energy into electrical energy. Utilizing this property, it is possible to convert exhaust heat exhausted from industrial / consumer processes and mobile objects into effective electric power, and thermoelectric conversion elements are attracting attention as energy-saving technologies in consideration of environmental problems.

  Evaluation of the Seebeck coefficient is indispensable for the development of thermoelectric conversion materials used for thermoelectric conversion elements, and various measuring devices have been proposed (for example, see Patent Documents 1 to 3).

Conventionally, the Seebeck coefficient has been calculated based on a temperature difference and a thermoelectromotive force generated by heating one end of a measurement sample installed between a heater and a heat sink and cooling the other end.
JP 2004-165233 A Japanese Patent Laid-Open No. 7-324991 JP 9-222403 A

  In the conventional measurement of the Seebeck coefficient, the measurement sample must be placed between the heater and the heat sink, the size of the measurement sample is limited, and it is difficult to form a measurement sample of a predetermined size. In some cases, it was not possible to evaluate. In addition, when a temperature difference is applied to the measurement sample, it takes time for the temperature difference to stabilize, and it may take time to measure one sample.

  The present invention has been made in view of the above problems, and an object thereof is to provide a simple method for evaluating the Seebeck coefficient.

That is, the present invention
<1> A step of applying a constant direct current between one end and the other end of the measurement sample to obtain a temperature difference (dΔT / dt) generated between the one end and the other end per unit time. This is a method for evaluating the Seebeck coefficient.

  <2> The Seebeck coefficient evaluation method according to <1>, wherein an absolute value of the Seebeck coefficient is calculated from the following formula (1) using the dΔT / dt.

In the formula (1), alpha represents the Seebeck coefficient, I is represents the applied current value, T (*) is the temperature T _B of the other end with a temperature T _A of the end of the immediately preceding application of direct current An average value is represented, and C represents a heat capacity value of the measurement sample.

  <3> A plurality of the measurement samples are formed on the substrate so as to have substantially the same shape, and the Seebeck coefficients of the plurality of measurement samples are relatively compared based on the following formula (2) using the dΔT / dt. The evaluation method for the Seebeck coefficient according to <1>.

In the formula (2), alpha represents the Seebeck coefficient, I is represents the applied current value, T (*) is the temperature T _B of the other end with a temperature T _A of the end of the immediately preceding application of direct current Represents an average value.

  According to the present invention, a simple method for evaluating the Seebeck coefficient can be provided.

  Hereinafter, the evaluation method of the Seebeck coefficient of the present invention will be described in detail.

  In the evaluation method of the Seebeck coefficient according to the present invention, a constant direct current is applied between one end and the other end of a measurement sample, and a temperature difference (dΔT / dt) at least, and based on the obtained dΔT / dt value, the absolute value of the Seebeck coefficient can be calculated, and the relative comparison of the Seebeck coefficients of a plurality of measurement samples can be performed. is there.

  First, a method for calculating the absolute value of the Seebeck coefficient using the method for evaluating the Seebeck coefficient of the present invention will be described with reference to the drawings. The method for evaluating the Seebeck coefficient of the present invention utilizes the endothermic and exothermic phenomenon due to the Peltier effect that occurs when a constant direct current is applied to both ends of a measurement sample.

  FIG. 1 is a diagram for explaining the principle for calculating the absolute value of the Seebeck coefficient using the method for evaluating the Seebeck coefficient of the present invention.

As shown in FIG. 1, a measurement sample 1 is configured such that a conducting wire 2 is connected to its end A and end B and a direct current is applied by a direct current power source 3. The magnitude of the direct current applied to the measurement sample 1 is measured by an ammeter 5. When the switch 7 is turned on and a constant current I is applied to the measurement sample 1 from time t ₀ , heat absorption occurs at one end of the measurement sample 1 and heat release occurs at the other end of the measurement sample 1 due to the Peltier effect. Therefore, there is a temperature difference ΔT between the end A and the end B of the measurement sample 1 (assuming that the temperature of the end _A is T _A and the temperature of the end B is T _B , ΔT = | T _A −T _B |) Occurs.

FIG. 2 shows the relationship between the current I (FIG. 2A) and ΔT (FIG. 2B) with respect to the elapsed time from the time t ₀ . Constant current I is applied from time t ₀ to the measurement sample 1 as shown in Figure 2A. Further, as shown in FIG. 2B, ΔT rises linearly from a time t ₀ for a certain period (t ₁ ), but eventually reaches a certain value. In the present invention, the temperature difference (dΔT / dt) generated between the end A and the end B per unit time can be obtained from the slope between the times t ₀ and t ₁ .

If heat is generated at the end A when the constant current I is applied to the measurement sample 1, and heat is absorbed at the end B, the heat quantity q _A generated at the end A per unit time and the end B are absorbed. The quantity of heat q _B is represented by the following formulas (3) and (4), respectively.

  In the equations (3) and (4), α represents the Seebeck coefficient, I represents the applied current value, R represents the electric resistance value between the end A and the end B, and A represents the end Represents the cross-sectional area of the measurement sample 1 with respect to the direction of the current flowing between the part A and the end part B, l represents the distance between the end part A and the end part B, and κ represents the thermal conductivity of the measurement sample 1. .

The first item on the right side of the equations (3) and (4) is related to the Peltier effect, the second item is related to the Joule heat generation, and the third item is related to the heat conduction term caused by the temperature gradient. Since the three items are due to the temperature gradient, if the temperature of the sample 1 is uniform before the time t ₀ , the short time after energization is very small compared to the first and second items and is regarded as zero. be able to.

The temperature difference ΔT generated per unit time from time t ₀ is the sum of the temperature drop at the low temperature end and the temperature rise at the high temperature end.

  It can be expressed as.

  When formula (5) is modified, the following formula (6) is derived.

In Equation (6), T (*) is an average value ((T _A + T _B ) of the temperature T _A at the end _A and the temperature T _B at the end B immediately before application of a direct current (ie, t ₀ in FIG. 2). ) / 2).

  Here, when Expression (6) is modified, the following Expression (7) is established.

  Further, ΔT can be expressed as dΔT / dt because the amount of heat generated per unit time is taken into consideration. Therefore, the absolute value of the Seebeck coefficient α is calculated from the following equation (1) using dΔT / dt.

  The shape of the measurement sample 1 is not particularly limited, and is appropriately selected from a rectangular parallelepiped, a cylinder, a thin film, a thin film formed on an arbitrary substrate, and the like. Since it is desirable that the current density of the current flowing through the measurement sample 1 is uniform, the shape of the measurement sample 1 is preferably a rectangular parallelepiped or a cylinder.

The temperature T _B of the temperature T _A and the end B of the end portion A, for example, can be measured using a thermocouple or an infrared camera. The temperature measured using a thermocouple or an infrared camera is taken into a microcomputer, personal computer, etc., and dΔT / dt is calculated. In the present invention, the heat capacity and the like of the measurement sample can be measured by a known method.

  Next, a method of relatively comparing the Seebeck coefficients of a plurality of measurement samples using the Seebeck coefficient evaluation method of the present invention will be described with reference to the drawings. This method is effective for evaluating the Seebeck coefficient of a thin film-like measurement sample formed on a substrate.

FIG. 3 is a diagram for explaining the principle for relatively comparing the Seebeck coefficients of a plurality of measurement samples. As shown in FIG. 3, a thin film-like measurement sample 1 is formed on a substrate 9 provided with a pair of electrodes 11 (11 </ b> C, 11 </ b> D) so as to be in contact with the pair of electrodes 11. In the measurement sample 1, the lead wire 2 is connected to the electrode 11 </ b> C in contact with the end portion C and the electrode 11 </ b> D in contact with the end portion D, and a direct current is applied from the direct current power source 3. The magnitude of the direct current applied to the measurement sample 1 is measured by an ammeter 5. By turning on the switch 7 and applying a constant current I to the measurement sample 1 from time t ₀ , the temperature difference ΔT (between the end C and the end D of the measurement sample 1 is the same as in FIG. If the temperature of the end _C is T _C and the temperature of the end D is T _D , ΔT = | T _C −T _D |) is generated.

In this case, assuming that heat is released at the end _C and heat absorption at the end D, the amount of heat q _C generated at the end _C and the amount of heat q _D absorbed at the end D per unit time are respectively It is represented by the following formula (8) and formula (9).

  In Equations (8) and (9), κ ′ represents the thermal conductivity of the substrate 9, and A ′ represents the cross-sectional area of the portion of the substrate 9 where the heat flow moves from the high temperature side to the low temperature side.

  If the substrate is sufficiently thicker than the measurement sample, it can be considered that most of the heat flow flows from the high temperature side to the low temperature side through the substrate. Therefore, the cross-sectional area A ′ taking into account the thickness of the substrate and the thermal conductivity κ ′ of the substrate are applied to the three items on the right side of each equation.

Similar to the case of the equation (5), the temperature difference ΔT generated per unit time from the time t ₀ can be expressed by the following equation (10).

  However, C ′ represents the heat capacity of the surroundings including the measurement sample and the substrate of each of the heat generating part and the heat absorbing part.

  When the equation (10) is transformed, the following equation (11) is derived.

  Since ΔT is a temperature difference generated per unit time, that is, a time change of the temperature difference generated at both ends of the measurement sample, when expressed as dΔT / dt, the following formula (12) is obtained.

  It is difficult to calculate the Seebeck coefficient α by actually obtaining C ′ using the equation (12). Here, consider a case where a plurality of measurement samples 1 having substantially the same shape are formed on the same substrate as shown in FIG. When the substrate 9 is sufficiently thick as compared with the measurement sample 1, the contribution of the measurement sample 1 to C ′ is small and the contribution of the substrate 9 is almost the same, so that C ′ of each measurement sample is considered to be the same. be able to.

  Therefore, when comparing the Seebeck coefficients between measurement samples having substantially the same shape formed on the same substrate, comparison can be made using only dΔT / dt, T (*), and I. That is, the Seebeck coefficient α satisfies the relationship of the following formula (2).

  In the case where the Seebeck coefficients are relatively compared using the Seebeck coefficient evaluation method of the present invention, a plurality of measurement samples may be formed on the same substrate so as to have substantially the same shape as described above. Alternatively, as long as C ′ can be regarded as the same, measurement samples having substantially the same shape can be formed on a plurality of substrates, and the Seebeck coefficients can be compared between the measurement samples.

  EXAMPLES Hereinafter, although this invention is demonstrated further in detail using an Example, this invention is not limited by the following Example.

The Seebeck coefficient was measured using a measurement sample (Ba ₈ Ga ₁₅ Ge ₃₁ ) having dimensions of 2.5 × 2.5 × 10 mm. Lead wires were connected to both ends in the longitudinal direction of the measurement sample, and current was applied. The measurement sample had a density of 5.8 g / cm ³ , a mass of 0.36 g, a specific heat of 0.07 cal / g / K, and a thermal conductivity of 2.0 W / m / K. The current applied to the measurement sample was 1.0A.

  FIG. 5 shows the change of ΔT with respect to the elapsed time when 1.0 A is applied to the measurement sample. The temperature of the measurement sample was measured with an infrared camera (manufactured by Nippon Avionics Co., Ltd.), and the obtained image was taken into a personal computer, and PE PROFESSIONAL ver. Processing with 3.11 yielded FIG.

  As is apparent from FIG. 5, a constant value of dΔT / dt = 0.205 K / sec was exhibited for about 5 seconds after the current application. The Seebeck coefficient was calculated using this value. When a certain amount of time elapses after application, heat conduction due to the temperature gradient in the measurement sample, heat leakage to the lead wire or the like, heat radiation to the atmosphere, and the amount of heat generated by the measurement sample balance, and dΔT / dt Approaches 0 (that is, ΔT takes a constant value).

  Moreover, it was T (*) = 295 (K). Using these values, the Seebeck coefficient α = 40 (μV / K) was obtained from the equation (1). This value is measured by ULVAC-RIKO ZEM-2, which can implement the conventional method of calculating the Seebeck coefficient based on the temperature difference and thermoelectromotive force generated by heating one end of the measurement sample and cooling the other end. Value (approximately 50 μV / K).

It is a figure for demonstrating the principle for calculating the absolute value of a Seebeck coefficient. Current with respect to the elapsed time from the time t ₀ I is a graph showing the relationship (FIG. 2A) and [Delta] T (Figure 2B). It is a figure for demonstrating the principle for comparing the Seebeck coefficient of a some measurement sample relatively. It is a figure which shows the board | substrate with which the some measurement sample of substantially the same shape was formed. It is a figure which shows the change with respect to the elapsed time of (DELTA) T when applying an electric current to a measurement sample.

Explanation of symbols

1 Measurement Sample 2 Conductor 3 DC Power Supply 5 Ammeter 7 Switch 9 Substrate 11 Electrode

Claims (3)

  Seebeck coefficient having at least a step of applying a constant direct current between one end and the other end of the measurement sample to obtain a temperature difference (dΔT / dt) generated between the one end and the other end per unit time Evaluation method. The evaluation method of the Seebeck coefficient according to claim 1, wherein the absolute value of the Seebeck coefficient is calculated from the following formula (1) using the dΔT / dt.

In the formula (1), alpha represents the Seebeck coefficient, I is represents the applied current value, T (*) is the temperature T _B of the other end with a temperature T _A of the end of the immediately preceding application of direct current An average value is represented, and C represents a heat capacity value of the measurement sample. A plurality of the measurement samples are formed on the substrate so as to have substantially the same shape, and the Seebeck coefficients of the plurality of measurement samples are relatively compared based on the following formula (2) using the dΔT / dt. The evaluation method of Seebeck coefficient of 1.

In the formula (2), alpha represents the Seebeck coefficient, I is represents the applied current value, T (*) is the temperature T _B of the other end with a temperature T _A of the end of the immediately preceding application of direct current Represents an average value.

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