JP2019024044A - Thermoelectric property measuring apparatus and thermoelectric property measuring method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a thermoelectric physical property measuring device and a thermoelectric physical property measuring method for measuring the Seebeck coefficient S with higher accuracy. SOLUTION: In the thermoelectric property measuring device 1 of the present invention, a power source 14 for applying a potential difference VA between one end 12a and the other end 12b of a measurement object 12 and a temperature between the one end 12a and the other end 12b. The temperature difference generating unit 16 for adding a difference, the current meter 13 for measuring the current value flowing between the one end 12a and the other end 12b, and the power supply 14 between the one end 12a and the other end 12b. When the first current value ΔIV measured by the current meter 13 and the temperature difference ΔT between the one end 12a and the other end 12b are added by the temperature difference generating unit 16 when the potential difference VA is applied. In addition, a calculation unit 20 for obtaining a Seebeck coefficient S using the second current value IT measured by the current meter 13 is provided. [Selection diagram] Fig. 1

Description

  The present invention relates to a thermoelectric property measuring apparatus and a thermoelectric property measuring method.

The Seebeck coefficient S as the thermoelectric property is obtained when the temperature difference ΔT = Th−Tc (Th: temperature of the high temperature part, Tc: temperature of the low temperature part) is given to both ends of the measurement object. Conventionally, the generated electromotive force is defined as Δv using the following equation.
S = Δv / ΔT (1)
When obtaining the Seebeck coefficient S, a temperature difference ΔT is given to both ends of the measurement object, and an electromotive force Δv generated at both ends of the measurement object is measured with a voltmeter, and is calculated using the above equation (1). (For example, refer to Patent Document 1).

JP 2004-165233 A

However, the method for directly obtaining the Seebeck coefficient S from the electromotive force Δv has the following problems.
A voltmeter is used to measure the electromotive force Δv. The ideal condition when measuring the voltage between two points of the measurement object with the voltmeter is that no current flows inside the voltmeter, that is, the point between the two points is an open end. By increasing the internal resistance of the voltmeter, the current value can be reduced in a state close to the open end. However, the current value cannot be made completely zero. Therefore, there is a limit to the measurement accuracy of the electromotive force Δv, and therefore there is a limit to increasing the accuracy of the calculation of the Seebeck coefficient S based on the equation (1).

  An object of the present invention is to provide a thermoelectric property measuring apparatus and a thermoelectric property measuring method capable of obtaining Seebeck coefficient S, that is, thermoelectric property with higher accuracy.

The present invention provides the following in order to solve the above problems.
(1) A power source for applying a potential difference between one end and the other end of the measurement object, a temperature difference generating unit for applying a temperature difference between the one end and the other end, and between the one end and the other end A first current value measured by the ammeter when the potential difference is applied between the one end and the other end by the power source, and generation of the temperature difference A thermoelectric property measuring apparatus comprising: a calculation unit that obtains a Seebeck coefficient using a second current value measured by the ammeter when a temperature difference is applied between the one end and the other end by a unit.

(2) The computing unit sets the first current value to ΔI _V , the second current value to ΔI _T , a potential difference applied between the one end and the other end by the power source to ΔV _A , and the temperature the temperature difference applied between the other end and the one end by the difference generating unit when the [Delta] T, and, the Seebeck coefficient S, S = with _{(ΔI T · ΔV a) /} (ΔI V · ΔT) You may ask.

(3) The calculation unit generates the first current value as ΔI _V , the second current value as ΔI _T , a potential difference applied between the one end and the other end by the power source as ΔV _A , and generation of the temperature difference. ΔT is a temperature difference applied between the one end and the other end by the unit, l is a length from the one end to the other end of the measurement object, and A is a cross-sectional area orthogonal to the length direction. Then, the electrical conductivity L ₁₁ is obtained using L ₁₁ = (l / A) × (ΔI _V / ΔV _A ), and the thermoelectric coefficient L ₁₂ is calculated as L ₁₂ = (l / A) (ΔI _T / ΔT), and the Seebeck coefficient S may be determined using S = L ₁₂ / L ₁₁ using the electrical conductivity L ₁₁ and the thermoelectric coefficient L ₁₂ .

(4) A voltmeter that measures a voltage between the one end and the other end of the measurement object is provided, the length from the one end to the other end of the measurement object is l, and the length Using a current ΔI _V ⁽²⁾ measured by the ammeter when a potential difference ΔV _A is applied between the one end and the other end by the power source, where A is a cross-sectional area perpendicular to the direction. The electrical conductivity L ₁₁ ⁽²⁾ is obtained from the following formula,
L ₁₁ ⁽²⁾ = (l / A) (ΔI _V ⁽²⁾ / ΔV _A )
Using the voltage ΔV _V measured by the voltmeter when the potential difference ΔV _A is applied between the one end and the other end by the power source, and the current ΔI _V ⁽⁴⁾ measured by the ammeter The electrical conductivity L ₁₁ ⁽⁴⁾ is obtained from the following formula,
L ₁₁ ⁽⁴⁾ = (l / A) (ΔI _V ⁽⁴⁾ / ΔV _V )
Using the electrical conductivity L ₁₁ ⁽²⁾ and the electrical conductivity L ₁₁ ⁽⁴⁾ , the contact resistance r is obtained from the following equation:
^{_{r = R (2) -R (}} 4) = (1 / L 11 (2) -1 / L 11 (4)) (l / A)
Using the voltage value ΔI _T ⁽²⁾ measured by the ammeter when the temperature difference ΔT is applied between the one end and the other end by the temperature difference generator, a thermoelectric coefficient is obtained from the following equation: Find L ₁₂ ^{(2)
_{L 12 (2) = (l}} / A) (ΔI T (2) / ΔT)
The thermoelectric coefficient L ₁₂ ⁽²⁾ is corrected using the contact resistance r, and the thermoelectric coefficient L ₁₂ ⁽⁴⁾ is obtained from the following equation:
L ₁₂ ⁽⁴⁾ = {(R ⁽⁴⁾ + r) / R ⁽⁴⁾ } L ₁₂ ⁽²⁾
The Seebeck coefficient S may be obtained from the following equation using the electrical conductivity L ₁₁ ⁽⁴⁾ and the thermoelectric coefficient L ₁₂ ⁽⁴⁾ .
S = L ₁₂ ⁽⁴⁾ / L ₁₁ ⁽⁴⁾

In another aspect, the present invention provides the following in order to solve the above problems.
(5) A temperature difference generating unit that adds a temperature difference between one end and the other end of the measurement object, an ammeter that measures a current value flowing between the one end and the other end, and an arithmetic unit. The arithmetic unit is configured to generate a second current value measured by the ammeter as ΔI _T when the temperature difference is applied between the one end and the other end by the temperature difference generating unit, and to generate the temperature difference. ΔT is a temperature difference applied between the one end and the other end by the unit, l is a length from the one end to the other end of the measurement object, and A is a cross-sectional area orthogonal to the length direction. Then, the thermoelectric coefficient L ₁₂ is obtained using L ₁₂ = (l / A) (ΔI _T / ΔT).
Thermoelectric property measuring device.

As a further aspect, the present invention provides the following to solve the above problems.
(6) A power source for applying a potential difference between one end and the other end of the measurement object, a temperature difference generating unit for applying a temperature difference between the one end and the other end, and between the one end and the other end An amperemeter for measuring a current value flowing through the voltmeter, a voltmeter for measuring a voltage between the one end and the other end of the measurement object, and a calculation unit. When a potential difference ΔV _A is applied between the one end and the other end by the power source when the length l from the one end to the other end and the cross-sectional area A orthogonal to the length direction are set. And using the current ΔI _V ⁽²⁾ measured by the ammeter, the electrical conductivity L ₁₁ ⁽²⁾ is obtained from the following equation:
L ₁₁ ⁽²⁾ = (l / A) (ΔI _V ⁽²⁾ / ΔV _A )
Using the voltage ΔV _V measured by the voltmeter when the potential difference ΔV _A is applied between the one end and the other end by the power source, and the current ΔI _V ⁽⁴⁾ measured by the ammeter The electrical conductivity L ₁₁ ⁽⁴⁾ is obtained from the following formula,
L ₁₁ ⁽⁴⁾ = (l / A) (ΔI _V ⁽⁴⁾ / ΔV _V )
Using the electrical conductivity L ₁₁ ⁽²⁾ and the electrical conductivity L ₁₁ ⁽⁴⁾ , the contact resistance r is obtained from the following equation:
^{_{r = R (2) -R (}} 4) = (1 / L 11 (2) -1 / L 11 (4)) (l / A)
Using the voltage value ΔI _T ⁽²⁾ measured by the ammeter when the temperature difference ΔT is applied between the one end and the other end by the temperature difference generator, a thermoelectric coefficient is obtained from the following equation: Find L ₁₂ ^{(2)
_{L 12 (2) = (l}} / A) (ΔI T (2) / ΔT)
The thermoelectric coefficient L ₁₂ ⁽²⁾ is corrected using the contact resistance r, and the thermoelectric coefficient L ₁₂ ⁽⁴⁾ is obtained from the following equation:
L ₁₂ ⁽⁴⁾ = {(R ⁽⁴⁾ + r) / R ⁽⁴⁾ } L ₁₂ ⁽²⁾
Thermoelectric property measuring device.

As another aspect, the present invention provides the following in order to solve the above problems.
(7) When a potential difference is applied between one end and the other end of the measurement object, a first current value that flows between the one end and the other end is measured, and between the one end and the other end A thermoelectric property measuring method for measuring a second current value flowing between the one end and the other end when a temperature difference is applied to the first and second Seed's coefficients using the first current value and the second current value.

(8) The first current value is ΔI _V , the second current value is ΔI _T , the potential difference applied between the one end and the other end is ΔV _A , and the one end and the other end are When the added temperature difference is ΔT, the Seebeck coefficient S may be obtained using S = (ΔI _T · ΔV _A ) / (ΔI _V · ΔT).

(9) The first current value is ΔI _V , the second current value is ΔI _T , and the potential difference applied between the one end and the other end is ΔV _A , and the one end and the other end are added. When the temperature difference is ΔT, the length from the one end to the other end of the measurement object is l, and the cross-sectional area perpendicular to the length direction is A, the electrical conductivity L ₁₁ is L _11. = (L / A) (ΔI _V / ΔV _A ), the thermoelectric coefficient L ₁₂ is determined using L ₁₂ = (l / A) (ΔI _T / ΔT), and the electric conductivity L ₁₁ , The Seebeck coefficient S may be obtained using S = L ₁₂ / L ₁₁ using the thermoelectric coefficient L ₁₂ .

In another aspect, the present invention provides the following in order to solve the above problems.
(10) A power source for applying a potential difference between one end and the other end of the measurement object, a temperature difference generating unit for applying a temperature difference between the one end and the other end, and between the one end and the other end In a thermophysical property measuring apparatus, comprising: an ammeter for measuring a current value flowing through the voltmeter; and a voltmeter for measuring a voltage between the one end and the other end of the measurement object. When the potential difference ΔV _A is applied between the one end and the other end by the power source when the length l to the other end and the cross-sectional area A orthogonal to the length direction are taken, the ammeter Using the current ΔI _V ⁽²⁾ measured by the following equation, the electrical conductivity L ₁₁ ⁽²⁾ is obtained from the following equation:
L ₁₁ ⁽²⁾ = (l / A) (ΔI _V ⁽²⁾ / ΔV _A )
Using the voltage ΔV _V measured by the voltmeter when the potential difference ΔV _A is applied between the one end and the other end by the power source, and the current ΔI _V ⁽⁴⁾ measured by the ammeter The electrical conductivity L ₁₁ ⁽⁴⁾ is obtained from the following formula,
L ₁₁ ⁽⁴⁾ = (l / A) (ΔI _V ⁽⁴⁾ / ΔV _V )
Using the electrical conductivity L ₁₁ ⁽²⁾ and the electrical conductivity L ₁₁ ⁽⁴⁾ , the contact resistance r is obtained from the following equation:
^{_{r = R (2) -R (}} 4) = (1 / L 11 (2) -1 / L 11 (4)) (l / A)
Using the voltage value ΔI _T ⁽²⁾ measured by the ammeter when the temperature difference ΔT is applied between the one end and the other end by the temperature difference generator, a thermoelectric coefficient is obtained from the following equation: Find L ₁₂ ^{(2)
_{L 12 (2) = (l}} / A) (ΔI T (2) / ΔT)
The thermoelectric coefficient L ₁₂ ⁽²⁾ is corrected using the contact resistance r, and the thermoelectric coefficient L ₁₂ ⁽⁴⁾ is obtained from the following equation:
L ₁₂ ⁽⁴⁾ = {(R ⁽⁴⁾ + r) / R ⁽⁴⁾ } L ₁₂ ⁽²⁾
Using the electrical conductivity L ₁₁ ⁽⁴⁾ and the thermoelectric coefficient L ₁₂ ⁽⁴⁾ , the Seebeck coefficient S is obtained from the following equation.
S = L ₁₂ ⁽⁴⁾ / L ₁₁ ⁽⁴⁾
Thermoelectric property measurement method.

As a further aspect, the present invention provides the following to solve the above problems.
(11) a second current value [Delta] I _T flowing between the end and the other end upon application of a temperature difference ΔT between the one end and the other end of the measurement object is measured, the said measurement object When the length from one end to the other end is 1 and the cross-sectional area orthogonal to the length direction is A, the thermoelectric coefficient L ₁₂ is L ₁₂ = (l / A) (ΔI _T / ΔT) Thermoelectric properties measurement method obtained using

As another aspect, the present invention provides the following in order to solve the above problems.
(12) A power source for applying a potential difference between one end and the other end of the measurement object, a temperature difference generating unit for applying a temperature difference between the one end and the other end, and between the one end and the other end In the physical property assumption apparatus comprising: an ammeter that measures a current value flowing through the voltmeter; and a voltmeter that measures a voltage between the one end and the other end of the measurement object; from the one end of the measurement object to the other When the potential difference ΔV _A is applied between the one end and the other end by the power source when the length l to the end and the cross-sectional area A orthogonal to the length direction are set, the ammeter Using the measured current ΔI _V ⁽²⁾ , the electrical conductivity L ₁₁ ⁽²⁾ is obtained from the following equation:
L ₁₁ ⁽²⁾ = (l / A) (ΔI _V ⁽²⁾ / ΔV _A )
Using the voltage ΔV _V measured by the voltmeter when the potential difference ΔV _A is applied between the one end and the other end by the power source, and the current ΔI _V ⁽⁴⁾ measured by the ammeter The electrical conductivity L ₁₁ ⁽⁴⁾ is obtained from the following formula,
L ₁₁ ⁽⁴⁾ = (l / A) (ΔI _V ⁽⁴⁾ / ΔV _V )
Using the electrical conductivity L ₁₁ ⁽²⁾ and the electrical conductivity L ₁₁ ⁽⁴⁾ , the contact resistance r is obtained from the following equation:
^{_{r = R (2) -R (}} 4) = (1 / L 11 (2) -1 / L 11 (4)) (l / A)
Using the voltage value ΔI _T ⁽²⁾ measured by the ammeter when the temperature difference ΔT is applied between the one end and the other end by the temperature difference generator, a thermoelectric coefficient is obtained from the following equation: Find L ₁₂ ^{(2)
_{L 12 (2) = (l}} / A) (ΔI T (2) / ΔT)
The thermoelectric coefficient L ₁₂ ⁽²⁾ is corrected using the contact resistance r, and the thermoelectric coefficient L ₁₂ ⁽⁴⁾ is obtained from the following equation:
L ₁₂ ⁽⁴⁾ = {(R ⁽⁴⁾ + r) / R ⁽⁴⁾ } L ₁₂ ⁽²⁾
Thermoelectric property measurement method.

  ADVANTAGE OF THE INVENTION According to this invention, the thermoelectric property measuring apparatus and thermoelectric property measuring method which can obtain | require Seebeck coefficient S, ie, a thermoelectric property, with higher precision can be provided.

It is a block diagram explaining the thermoelectric property measuring apparatus in 1st Embodiment. It is a flowchart which shows how to obtain | require Seebeck coefficient S by 1st Embodiment. It is a flowchart which shows how to obtain | require Seebeck coefficient S by 2nd Embodiment. It is a graph which shows the result of having measured electric current value (DELTA) I by changing electric potential difference (DELTA) _VA in each temperature difference (DELTA) T. L ₁₂ for each of the temperature difference ΔT from the y-intercept of the graph of FIG. 4 _is a graph showing a result of calculating the L ₁₁ from the slope. FIG. 5 shows the result of obtaining the Seebeck coefficient S from the values of L ₁₁ and L _{12 in} FIG. 5, the horizontal axis of (a) is the temperature difference ΔT, and the horizontal axis of (b) is the average temperature. The data of the I-V _A graph is fitted by linear regression. (A) is when ΔT is 2K, and (b) is when ΔT is 0.4K.

(First embodiment)
(Description of thermoelectric property measuring apparatus 1)
FIG. 1 is a block diagram illustrating a thermoelectric property measuring apparatus 1 according to a first embodiment of the present invention. The thermoelectric property measuring apparatus 1 of this embodiment is an apparatus for obtaining the Seebeck coefficient S as a thermoelectric property, and includes a measuring unit 10 and a calculating unit 20 as shown in the figure.

  The measurement unit 10 includes a sample placement unit 11 on which a measurement target of the Seebeck coefficient S (hereinafter referred to as a sample 12) is placed, and one end 12a and the other end 12b of the sample 12 placed on the sample placement unit 11. Is connected to the first circuit C1. In the first circuit C1, an ammeter 13 and a first switch S1 provided between the one end 12a of the sample 12 and the ammeter 13 are arranged.

The wiring portion extending from the ammeter 13 to the first switch S1 side in the first circuit C1 branches in two directions. One of the branches is provided with a first terminal a, the other of the branches is provided with a second terminal b, and a power source 14 is disposed between the second terminal b and the ammeter 13. .
The first switch S1 can be switched between the first terminal a and the second terminal b on the ammeter 13 side. When the first switch S1 is connected to the first terminal a side, the first circuit C1 is connected from the one end 12a of the sample 12 to the other end 12b through the ammeter 13 without passing through the power source 14. When the first switch S1 is connected to the second terminal b side, the first circuit C1 is connected from one end 12a of the sample 12 to the other end 12b through the power source 14 and the ammeter 13.

The measurement unit 10 also includes a second circuit C2 that connects one end 12a and the other end 12b of the sample 12. The second circuit C2 includes a voltmeter 15 and a gap between the other end 12b of the sample and the voltmeter 15. And a second switch S2 provided in.
Furthermore, the measurement unit 10 also includes a temperature difference generation unit 16 that adds a temperature difference between the one end 12a and the other end 12b of the sample 12.

Calculating unit 20 is described later in detail, when the potential difference [Delta] V _A is applied between one end 12a and the other end 12b of the sample 12 by the power source 14, ammeter 13 one end 12a and the other end 12b measured by when the temperature difference ΔT is added, measured by the ammeter 13 at one end between a first current value [Delta] I _V flowing between, the temperature difference generating unit 16 and one end 12a and the other end 12b of the sample 12 with using a second current value [Delta] I _T flowing between the 12a and the other end 12b, it performs computation for obtaining the Seebeck coefficient S, and the like.

(Calculation method of Seebeck coefficient S)
In general, the Seebeck coefficient S is calculated using the following formula (1) by giving a temperature difference ΔT to both ends of the sample 12 and measuring the electromotive force Δv generated at both ends of the sample 12.

S = Δv / ΔT (1)

  However, in this embodiment, the Seebeck coefficient S is not calculated using the above equation (1). Hereinafter, a method for obtaining the Seebeck coefficient S according to the present embodiment will be described.

FIG. 2 is a flowchart showing how to obtain the Seebeck coefficient S according to the first embodiment.
[1] First, the sample 12 is mounted on the sample mounting portion 11 (step S1).
In the present embodiment, the sample 12 that is the measurement target of the Seebeck coefficient S is rectangular, and the length l between the one end 12a and the other end 12b and the cross-sectional area A in the direction orthogonal to the length direction are constant. is there. However, the present invention is not limited to this, and the Seebeck coefficient S can be calculated even if the cross-sectional areas A are different in the length direction.

[2] determining the electrical conductivity _{L 11} (step S2)
Electrical conductivity L ₁₁ is a physical quantity representing how much current easily flows (and ease of the electrical conduction in the material) when a potential difference to the object. Electrical conductivity L ₁₁ is a potential difference [Delta] V _A across the sample 12, to measure the current value [Delta] I _V flowing through the sample 12, using these values obtained from the following equation (2). At this time, a temperature difference may not be given to both ends of the sample 12 (ΔT = 0).

L ₁₁ = (l / A) (ΔI _V / ΔV _A ) (2)

Here, when measuring the electrical conductivity L _11, by the measuring method, and a case may not include the effects of contact resistance r. In this embodiment, the contact resistance r is a resistance generated at the contact portion when the sample 12 is brought into contact with the wiring configuring the first circuit C1 and the second circuit C2.
In computing the Seebeck coefficient S with higher accuracy, it is necessary to determine the electrical conductivity of L ₁₁ the influence of the contact resistance r was eliminated.

[2-1] The electric conductivity L ₁₁ ⁽²⁾ including the influence of the contact resistance r is obtained by the two-terminal method (step S2-1).
The electric conductivity L ₁₁ ⁽²⁾ including the influence of the contact resistance r by the two-terminal method is obtained as follows.
First, the first switch S1 is connected to the second terminal b, and the second switch S2 is turned OFF. The power supply 14 to ON, the state in which [Delta] V _A is applied to the first circuit C1. In this state, the current value ΔI _V ⁽²⁾ flowing through the ammeter 13 is measured.
Information on the length l of the sample 12 and the cross-sectional area A of the sample 12 is input to the calculation unit 20. Using these values and the current value ΔI _V ⁽²⁾ measured as described above, the calculation unit 20 calculates the electrical conductivity L ₁₁ ⁽²⁾ using the following equation (2-1). .

L ₁₁ ⁽²⁾ = (l / A) (ΔI _V ⁽²⁾ / ΔV _A ) (2-1)

[2-2] An electric conductivity L ₁₁ ⁽⁴⁾ not including the influence of the contact resistance r is obtained by the four-terminal method (step S2-2).
The electric conductivity L ₁₁ ⁽⁴⁾ not including the influence of the contact resistance r by the four-terminal method is obtained as follows.
First, the first switch S1 is connected to the second terminal b, and the second switch S2 is turned on. The power supply 14 to ON, the state in which [Delta] V _A is applied to the first circuit C1. In this state, the voltage ΔV _V is measured by the voltmeter 15 and the current value ΔI _V ⁽⁴⁾ is measured by the ammeter 13.

Similar to the electrical conductivity L ₁₁ ⁽²⁾ , the computing unit 20 uses the voltage ΔV _V and the current value ΔI _V ⁽⁴⁾ measured as described above to calculate the electric power according to the following equation (2-2). The conductivity L ₁₁ ⁽⁴⁾ is calculated.

L ₁₁ ⁽⁴⁾ = (l / A) (ΔI _V ⁽⁴⁾ / ΔV _V ) (2-2)

Note that the order of step S2-1 and step S2-2 may be reversed.

[3] Obtain contact resistance r (step S4)
Next, the arithmetic unit 20 uses the following equation (3), and electric determined by the two-terminal measuring method conductivities _L ^{11 (2),} electrical conductivity _L ¹¹ was determined by four-terminal measurement method ⁽⁴⁾ Then, the contact resistance r is calculated.

r = R ⁽²⁾ -R ⁽⁴⁾ = (1 / L ₁₁ ⁽²⁾ -1 / L ₁₁ ⁽⁴⁾ ) (l / A) (3)

[4] thermoelectric coefficient (thermoelectric response factor, thermoelectric response function, thermoelectric constants) determining the L ₁₂ (step S4)
Next, the arithmetic unit 20 obtains the thermoelectric coefficient _{L 12.} Thermoelectric coefficient L ₁₂ is a physical quantity that indicates how much current easily flows when applying a temperature difference to the object. Thermoelectric coefficient _{L 12} is not providing a potential difference at both ends of the sample 12 (ΔV _A = 0), giving a temperature difference ΔT across the sample 12 by using the temperature difference generating unit 16, a current value [Delta] I _T flowing through the sample 12 Measured and obtained from the following equation (4).

L ₁₂ = (l / A) (ΔI _T / ΔT) (4)

When measuring the thermoelectric coefficient L ₁₂ Again, the measurement method, and a case may not include the effects of contact resistance r. To more accurately calculating the Seebeck coefficient S, it is necessary to determine the thermoelectric coefficient L ₁₂ without the influence of the contact resistance r.

[4-1] The thermoelectric coefficient L ₁₂ ⁽²⁾ including the influence of the contact resistance r is obtained by the two-terminal method (step S4-1).
The thermoelectric coefficient L ₁₂ ⁽²⁾ by the two-terminal method is obtained as follows.
A temperature difference ΔT is added to both ends of the sample 12.
Then, the first switch S1 is connected to the first terminal a, and the second switch S2 is turned OFF. In this state, ΔI _T ⁽²⁾ flowing through the ammeter 13 is measured.

Then, the arithmetic unit 20 calculates thermoelectric coefficient _L ^{12 (2)} using the following equation (4-1).

^{_{L 12 (2) = (l}} / A) (ΔI T (2) / ΔT) ··· (4-1)

[4-2] Calculation of thermoelectric coefficient L ₁₂ ⁽⁴⁾ not including the influence of contact resistance (step S4-2)
The thermoelectric coefficient L ₁₂ ⁽²⁾ is corrected by the following equation (4-2) using the contact resistance r obtained as described above, and the thermoelectric coefficient L ₁₂ ⁽⁴⁾ not including the influence of the contact resistance r is obtained.

L ₁₂ ⁽⁴⁾ = {(R ⁽⁴⁾ + r) / R ⁽⁴⁾ } L ₁₂ ⁽²⁾ (4-2)

[5] Calculation of Seebeck coefficient S (step S5)
Next, using the electrical conductivity L ₁₁ ⁽⁴⁾ and the thermoelectric coefficient L ₁₂ ⁽⁴⁾ determined as described above, the calculation unit 20 calculates the Seebeck coefficient S from the following equation (5).

S = L ₁₂ ⁽⁴⁾ / L ₁₁ ⁽⁴⁾ (5)

The calculation unit 20 also calculates the electric conductivity L ₁₁ ⁽⁴⁾ and the thermoelectric coefficient L ₁₂ ⁽⁴⁾ obtained as described above by the following equation (6) as the power factor PF that is the generated power per unit temperature. It can be obtained using.

PF = (L ₁₂ ⁽⁴⁾ ) ² / L ₁₁ ⁽⁴⁾ (6)

This measurement is

J = L ₁₁ × E + L ₁₂ (−dT / dx) (7)

This is possible as long as J is the current density, E is the electric field, and l is the length of the sample 12. In order for Equation (7) to hold, it is important not to make dT / dl too large. This is because if dT / dl is large, nonlinearity appears in the JE curve. Moreover, when it becomes a condition where Formula (7) is not materialized, it can be confirmed whether there was no problem in a measurement by confirming the linearity of a JE curve. Note that dT / dx indicates a temperature gradient in the length direction of the sample 12.

(Second Embodiment)
In the first embodiment, the Seebeck coefficient S is obtained in consideration of the influence of the contact resistance r. However, since the influence of the contact resistance r is slight as described above, the contact resistance r can be ignored. FIG. 3 is a flowchart showing how to obtain the Seebeck coefficient S according to the second embodiment.
The thermoelectric property measuring apparatus of the second embodiment performs only two-point measurement with the configuration of only the first circuit C1 of the first embodiment. Since each part is the same as that of the first embodiment, the same reference numerals are given and description thereof is omitted.

[1] First, the sample 12 is mounted on the sample mounting portion 11 (step S21).
[2] determining the electrical conductivity _{L 11} (step S22)
The first switch S1 is connected to the second terminal b. The power supply 14 is turned on so that ΔV is applied to the first circuit C1. Measuring a current value [Delta] I _V flowing through the ammeter 13 in this state. Calculation unit 20 uses the current value [Delta] I _V, calculates the electric conductivity _{L 11} by the following equation (2).

L ₁₁ = (l / A) (ΔI _V / ΔV) (2)

[3] obtaining a thermoelectric coefficient _{L 12} (step S23)
Next, determine the thermoelectric coefficient _{L 12.} Thermoelectric coefficient L ₁₂ is not providing a potential difference at both ends of the sample 12 ([Delta] V = 0), giving a temperature difference ΔT across the sample 12 by using the temperature difference generating unit 16, measures the current [Delta] I _T flowing through the sample 12 To do. Calculation unit 20 uses the current value [Delta] I _T, calculates the thermoelectric coefficient _{L 12} by the following equation (4).

L ₁₂ = (l / A) (ΔI _T / ΔT) (4)

[4] Calculation of Seebeck coefficient S (step S24)
Next, using the electrical conductivity L ₁₁ and the thermoelectric coefficient L ₁₂ obtained as described above, the calculation unit 20 obtains the Seebeck coefficient S from the following equation.

S = L ₁₂ / L ₁₁ (5)

It should be noted that substituting equations (2) and (4) into equation (5) yields the following.

S = (ΔI _T · ΔV) / (ΔI _V · ΔT) (5-2)

Therefore, the arithmetic unit 20, the electric conductivity L _11, without calculating the thermoelectric coefficient L _12, directly from the current value [Delta] I _V and the current value [Delta] I _T, it is possible to obtain the Seebeck coefficient S.
Further, the arithmetic unit 20 can also obtain the power factor PF by the following formula (6) using the electrical conductivity L ₁₁ and the thermoelectric coefficient L ₁₂ obtained as described above as in the first embodiment.

PF = (L ₁₂ ) ² / L ₁₁ (6)

(Effect of embodiment)
[1] As described above, conventionally, the Seebeck coefficient S is obtained by the equation (1) S = Δv / ΔT using the electromotive force Δv measured by a voltmeter.
However, according to the present embodiment, as described above, the Seebeck coefficient S is expressed by the equation (5) S = L ₁₂ / L ₁₁ or the equation (5-2) S = (ΔI _T · ΔV) / (ΔI _V · ΔT). It is expressed as follows.
Here, for example, in the case of B2911A, Precision Source / Measure Unit, which will be described later, the minimum measurement resolution as an ammeter is 10 fA, and the minimum measurement resolution as a voltmeter is 100 nV.
Therefore, if measures against noise or the like are appropriately performed, the system of the Seebeck coefficient S calculated using the measured current value according to the equation (5-2) is the voltage value measured according to the conventional equation (1). towards the current measurement in compared to Seebeck coefficient S obtained are guaranteed ¹⁰⁷ times more accurate.
Therefore, according to the present embodiment, the Seebeck coefficient can be obtained with high accuracy as compared with the case where Δv measured by the voltmeter is used as a value directly used when obtaining the Seebeck coefficient S as shown in equation (1). Can do.

In the first embodiment, when calculating L ₁₁ ⁽⁴⁾ , the following equation:
L ₁₁ ⁽⁴⁾ = (l / A) (ΔI _V ⁽⁴⁾ / ΔV _V ) (2-2)
As shown in FIG. 6, ΔV _V which is a measured value of the voltmeter 15 is used. However, L ₁₁ ⁽⁴⁾ is the following equation for determining the contact resistance r:
^{_{r = R (2) -R (}} 4) = (1 / L 11 (2) -1 / L 11 (4)) (l / A)
Is used to assign to.
The contact resistance r is the following formula:
L ₁₂ ⁽⁴⁾ = {(R ⁽⁴⁾ + r) / R ⁽⁴⁾ } L ₁₂ ⁽²⁾ (4-2)
Since the L ₁₂ but is intended to be used to improve the accuracy for obtaining the ^_(4), the contact resistance r is very small compared to the resistance of sample 12 was determined by the 4-terminal method R ^(4), the formula ( The influence of the contact resistance r in 4-2) is not large in the first place.
In this embodiment, in order to obtain the Seebeck coefficient S with higher accuracy, the influence of the contact resistance r is taken into consideration, and ΔV _V which is a measured value of the voltmeter 15 used when obtaining the contact resistance r having a small influence. Even if some errors are included, the influence on the measurement of the Seebeck coefficient S is very small compared to the above equation (1).
Therefore, the Seebeck coefficient S can be determined with higher accuracy than in the case of using the equation (1).

  Further, since the resolution of the Seebeck coefficient S is improved by improving the measurement accuracy of the Seebeck coefficient S, it is possible to measure, for example, the distribution of the Seebeck coefficient in a plane in one material.

[2] According to the present embodiment can be obtained thermoelectric coefficient L ₁₂ also without using the measurement value measured by the voltmeter. Therefore, according to this embodiment can be obtained thermoelectric coefficient L ₁₂ also accurate.

[3] Furthermore, not only the Seebeck coefficient S but also the power factor PF of the thermoelectric material can be made highly accurate.

Hereinafter, examples of actually measuring thermoelectric properties using the thermoelectric property measuring apparatus 1 of the second embodiment will be described. In the thermoelectric property measuring apparatus 1 of the example, B2911A manufactured by Keysight, Inc., a precision source / measure unit was used as the ammeter 13 and the power supply unit 14. This unit can measure by switching between 2-terminal measurement and 4-terminal measurement. The performance of this unit is shown below.
Minimum power resolution: 10 fA / 100 nV
Minimum measurement resolution: 10 fA / 100 nV
Maximum output: 210 V, 3 A DC / 10.5 A pulse In addition, the temperature difference generator 16 can perform heating control (Th) by a temperature controller and constant temperature control (Tc) at room temperature by water cooling. As a thermoelectric material as a sample for measuring thermoelectric properties, Mg ₂ Si of 2 × 2 × 11.6 mm was used.

The thermoelectric property measurement using the thermoelectric property measuring apparatus 1 was performed as follows.
The sample 12 is placed on the sample placement unit 11, the first switch S1 is connected to the second terminal b, the power source 14 is turned on, and the potential difference _VA is applied to the first circuit C1 while the temperature difference generation unit 16 is applied. Was used to give a temperature difference ΔT to both ends of the sample 12.
In the embodiment, to measure the current value ΔI by changing the potential difference [Delta] V _A to the temperature difference ΔT constant. The temperature difference ΔT to be constant is 8 steps of 2, 3, 4, 5, 6, 7, 8, 9K. The measurement results are shown in FIG.

As shown in the figure, the slope of the ΔI−ΔV _A straight line is substantially constant regardless of the temperature difference ΔT, but as the temperature difference ΔT increases, the ΔI−ΔV _A straight line translates downward in the figure, ie, y The intercept (ΔI intercept, ΔI when ΔV _A = 0) is small.

As described above, L ₁₁ and L ₁₂ are expressed by Expression (2) L ₁₁ = (l / A) (ΔI _V / ΔV) and Expression (4) L ₁₂ = (l / A) (ΔI _T / ΔT). Therefore, L ₁₁ was calculated from the slope of the graph of FIG. 4 and L ₁₂ was calculated from the y-intercept at each temperature difference ΔT. The result is shown in FIG. Incidentally, formula (2), [Delta] _V and [Delta] I _T is in (4), in the embodiment, simultaneously measured, expressed in [Delta] I.

FIG. 6 shows the result of obtaining the Seebeck coefficient S from the values of L ₁₁ and L ₁₂ in FIG. The horizontal axis in FIG. 6A is the temperature difference ΔT, and the horizontal axis in FIG. 6B is the average temperature. Similar results are obtained in (a) and (b).
In the embodiment, the temperature difference ΔT is generated by clamping the low temperature portion of the sample 12 to a room temperature of 18.7 ° C. and controlling the heating on the heater side. For example, when ΔT = 2 ° C., the average temperature is (18.7 + 20.7) /2+273.15=2922.85K.

  As shown in FIG. 6, in the vicinity of the average temperature of about 293 to 296K, the Seebeck coefficient S of the example was about −350 to −325 μV / K.

The accuracy can be further improved by performing linear regression processing on the measurement data.
7A and 7B are obtained by fitting the data of the I-V _A graph by linear regression. FIG. 7A shows the case where ΔT is 2K, and FIG. 7B shows the case where ΔT is 0.4K.
As shown in the figure, the data point has variations such as noise. Further, L ₁₂ expressed by the equation (4) L12 = (l / A) (ΔI _T / ΔT) has a small temperature difference ΔT. since the change of [Delta] I _T is also reduced in the vicinity of the y-intercept, accurate calculation of L ₁₂ it becomes difficult.
In such a case, the accuracy of the y-intercept and inclination can be improved by performing linear regression processing. In general, the error (ERR) has a relationship of ERR∝1 / √ (number of measurements). For example, when 2500 points are measured, there are points, so that it is possible to obtain 50 times the accuracy compared to the case where one y-intercept is measured.

A conventional Seebeck coefficient evaluation apparatus also performs an averaging process, but only one voltage is obtained for a certain temperature difference, and the accuracy is improved by repeating this measurement a plurality of times. Therefore, it is common to perform the number of times less than 2500 measurement points.
In the example, for a certain temperature difference, 2500 points of current density were measured under each electric field while changing the applied electric field. In the embodiment, the measurement at 2500 points is performed once, but the accuracy can be further improved by performing the measurement at 2500 points a plurality of times. In addition, since the number of measurement points is a problem in the setting of the instrument, the accuracy can be improved by utilizing a measuring instrument that can obtain more points or a plurality of measuring instruments.
Incidentally, the standard error obtained during the linear regression process is the accuracy of this measurement. The standard error is as shown in the following results. In the example, the measurement is performed 2500 times.

Thus, according to this embodiment, the standard error of the slope a of the IV line is on the order of 10 ⁻⁵ , the standard error of the I intercept (V = 0) b is on the order of 10 ⁻⁸ , and 0.4K Even with such a small temperature difference, the standard error was extremely small, and the slope a and I intercept b could be obtained with high accuracy.

DESCRIPTION OF SYMBOLS 1 Thermoelectric property measuring apparatus 10 Measuring part 11 Sample mounting part 12 Sample 12a One end 12b Other end 13 Ammeter 14 Power supply 15 Voltmeter 16 Temperature difference generation part 20 Calculation part C1 1st circuit C2 2nd circuit a terminal b terminal r contact resistance

Claims (12)

A power source for applying a potential difference between one end and the other end of the measurement object;
A temperature difference generator for adding a temperature difference between the one end and the other end;
An ammeter for measuring a current value flowing between the one end and the other end;
When the potential difference is applied between the one end and the other end by the power source, the first current value measured by the ammeter and between the one end and the other end by the temperature difference generator A calculation unit for obtaining a Seebeck coefficient using a second current value measured by the ammeter when a temperature difference is added to
Thermoelectric property measuring apparatus comprising: The computing unit is
ΔI _V , the first current value,
ΔI _T , the second current value,
The potential difference applied between the one end and the other end by the power source is ΔV _A , and
When the temperature difference applied between the one end and the other end by the temperature difference generator is ΔT,
The Seebeck coefficient S is determined using S = (ΔI _T · ΔV _A ) / (ΔI _V · ΔT).
The thermoelectric property measuring apparatus according to claim 1. The computing unit is
ΔI _V , the first current value,
ΔI _T , the second current value,
_A potential difference applied between the one end and the other end by the power source is expressed as ΔV _A ,
The temperature difference applied between the one end and the other end by the temperature difference generator is ΔT,
When the length from the one end to the other end of the measurement object is l, and the cross-sectional area perpendicular to the length direction is A,
The electrical conductivity L ₁₁ is determined using L ₁₁ = (l / A) × (ΔI _V / ΔV _A ),
The thermoelectric coefficient L ₁₂ is determined using L ₁₂ = (l / A) (ΔI _T / ΔT),
Using the electrical conductivity L ₁₁ and the thermoelectric coefficient L ₁₂ , the Seebeck coefficient S is determined using S = L ₁₂ / L ₁₁ .
The thermoelectric property measuring apparatus according to claim 1. A voltmeter for measuring a voltage between the one end and the other end of the measurement object;
When the length from the one end to the other end of the measurement object is l, and the cross-sectional area perpendicular to the length direction is A,
Using the current ΔI _V ⁽²⁾ measured by the ammeter when a potential difference ΔV _A is applied between the one end and the other end by the power source, the electrical conductivity L ₁₁ ^{(2 )}
L ₁₁ ⁽²⁾ = (l / A) (ΔI _V ⁽²⁾ / ΔV _A )
Using the voltage ΔV _V measured by the voltmeter when the potential difference ΔV _A is applied between the one end and the other end by the power source, and the current ΔI _V ⁽⁴⁾ measured by the ammeter The electrical conductivity L ₁₁ ⁽⁴⁾ is obtained from the following formula,
L ₁₁ ⁽⁴⁾ = (l / A) (ΔI _V ⁽⁴⁾ / ΔV _V )
Using the electrical conductivity L ₁₁ ⁽²⁾ and the electrical conductivity L ₁₁ ⁽⁴⁾ , the contact resistance r is obtained from the following equation:
^{_{r = R (2) -R (}} 4) = (1 / L 11 (2) -1 / L 11 (4)) (l / A)
Using the voltage value ΔI _T ⁽²⁾ measured by the ammeter when the temperature difference ΔT is applied between the one end and the other end by the temperature difference generator, a thermoelectric coefficient is obtained from the following equation: Find L ₁₂ ^{(2)
_{L 12 (2) = (l}} / A) (ΔI T (2) / ΔT)
The thermoelectric coefficient L ₁₂ ⁽²⁾ is corrected using the contact resistance r, and the thermoelectric coefficient L ₁₂ ⁽⁴⁾ is obtained from the following equation:
L ₁₂ ⁽⁴⁾ = {(R ⁽⁴⁾ + r) / R ⁽⁴⁾ } L ₁₂ ⁽²⁾
Using the electrical conductivity L ₁₁ ⁽⁴⁾ and the thermoelectric coefficient L ₁₂ ⁽⁴⁾ , the Seebeck coefficient S is obtained from the following equation.
S = L ₁₂ ⁽⁴⁾ / L ₁₁ ⁽⁴⁾
The thermoelectric property measuring apparatus according to claim 1. A temperature difference generator that adds a temperature difference between one end and the other end of the measurement object;
An ammeter for measuring a current value flowing between the one end and the other end;
An arithmetic unit,
The computing unit is
When a temperature difference is applied between the one end and the other end by the temperature difference generating unit, a second current value measured by the ammeter is expressed as ΔI _T ,
The temperature difference applied between the one end and the other end by the temperature difference generator is ΔT,
When the length from the one end to the other end of the measurement object is l, and the cross-sectional area perpendicular to the length direction is A,
The thermoelectric coefficient L ₁₂ is determined using L ₁₂ = (l / A) (ΔI _T / ΔT).
Thermoelectric property measuring device. A power source for applying a potential difference between one end and the other end of the measurement object;
A temperature difference generator for adding a temperature difference between the one end and the other end;
An ammeter for measuring a current value flowing between the one end and the other end;
A voltmeter for measuring a voltage between the one end and the other end of the measurement object;
An arithmetic unit,
The computing unit is
When the length l from the one end to the other end of the measurement object and the cross-sectional area A orthogonal to the length direction,
Using the current ΔI _V ⁽²⁾ measured by the ammeter when a potential difference ΔV _A is applied between the one end and the other end by the power source, the electrical conductivity L ₁₁ ^{(2 )}
L ₁₁ ⁽²⁾ = (l / A) (ΔI _V ⁽²⁾ / ΔV _A )
Using the voltage ΔV _V measured by the voltmeter when the potential difference ΔV _A is applied between the one end and the other end by the power source, and the current ΔI _V ⁽⁴⁾ measured by the ammeter The electrical conductivity L ₁₁ ⁽⁴⁾ is obtained from the following formula,
L ₁₁ ⁽⁴⁾ = (l / A) (ΔI _V ⁽⁴⁾ / ΔV _V )
Using the electrical conductivity L ₁₁ ⁽²⁾ and the electrical conductivity L ₁₁ ⁽⁴⁾ , the contact resistance r is obtained from the following equation:
^{_{r = R (2) -R (}} 4) = (1 / L 11 (2) -1 / L 11 (4)) (l / A)
Using the voltage value ΔI _T ⁽²⁾ measured by the ammeter when the temperature difference ΔT is applied between the one end and the other end by the temperature difference generator, a thermoelectric coefficient is obtained from the following equation: Find L ₁₂ ^{(2)
_{L 12 (2) = (l}} / A) (ΔI T (2) / ΔT)
The thermoelectric coefficient L ₁₂ ⁽²⁾ is corrected using the contact resistance r, and the thermoelectric coefficient L ₁₂ ⁽⁴⁾ is obtained from the following equation:
L ₁₂ ⁽⁴⁾ = {(R ⁽⁴⁾ + r) / R ⁽⁴⁾ } L ₁₂ ⁽²⁾
Thermoelectric property measuring device. Measuring a first current value flowing between the one end and the other end when a potential difference is applied between the one end and the other end of the measurement object;
Measuring a second current value flowing between the one end and the other end when a temperature difference is applied between the one end and the other end;
A thermoelectric property measuring method for obtaining a Seebeck coefficient using the first current value and the second current value. ΔI _V , the first current value,
ΔI _T , the second current value,
_A potential difference applied between the one end and the other end is expressed as ΔV _A , and
When the temperature difference applied between the one end and the other end is ΔT,
The Seebeck coefficient S is determined using S = (ΔI _T · ΔV _A ) / (ΔI _V · ΔT).
The thermoelectric property measuring method according to claim 7. ΔI _V , the first current value,
ΔI _T , the second current value,
_A potential difference applied between the one end and the other end is expressed as ΔV _A ,
ΔT, the temperature difference applied between the one end and the other end
When the length from the one end to the other end of the measurement object is l, and the cross-sectional area perpendicular to the length direction is A,
The electrical conductivity L ₁₁ is determined using L ₁₁ = (l / A) (ΔI _V / ΔV _A ),
The thermoelectric coefficient L ₁₂ is determined using L ₁₂ = (l / A) (ΔI _T / ΔT),
Using the electrical conductivity L ₁₁ and the thermoelectric coefficient L ₁₂ , the Seebeck coefficient S is determined using S = L ₁₂ / L ₁₁ .
The thermoelectric property measuring method according to claim 7. A power source for applying a potential difference between one end and the other end of the measurement object;
A temperature difference generator for adding a temperature difference between the one end and the other end;
An ammeter for measuring a current value flowing between the one end and the other end;
A voltmeter for measuring a voltage between the one end and the other end of the measurement object;
In a thermophysical property measuring apparatus comprising:
When the length l from the one end to the other end of the measurement object and the cross-sectional area A orthogonal to the length direction,
Using the current ΔI _V ⁽²⁾ measured by the ammeter when a potential difference ΔV _A is applied between the one end and the other end by the power source, the electrical conductivity L ₁₁ ^{(2 )}
L ₁₁ ⁽²⁾ = (l / A) (ΔI _V ⁽²⁾ / ΔV _A )
Using the voltage ΔV _V measured by the voltmeter when the potential difference ΔV _A is applied between the one end and the other end by the power source, and the current ΔI _V ⁽⁴⁾ measured by the ammeter The electrical conductivity L ₁₁ ⁽⁴⁾ is obtained from the following formula,
L ₁₁ ⁽⁴⁾ = (l / A) (ΔI _V ⁽⁴⁾ / ΔV _V )
Using the electrical conductivity L ₁₁ ⁽²⁾ and the electrical conductivity L ₁₁ ⁽⁴⁾ , the contact resistance r is obtained from the following equation:
^{_{r = R (2) -R (}} 4) = (1 / L 11 (2) -1 / L 11 (4)) (l / A)
Using the voltage value ΔI _T ⁽²⁾ measured by the ammeter when the temperature difference ΔT is applied between the one end and the other end by the temperature difference generator, a thermoelectric coefficient is obtained from the following equation: Find L ₁₂ ^{(2)
_{L 12 (2) = (l}} / A) (ΔI T (2) / ΔT)
The thermoelectric coefficient L ₁₂ ⁽²⁾ is corrected using the contact resistance r, and the thermoelectric coefficient L ₁₂ ⁽⁴⁾ is obtained from the following equation:
L ₁₂ ⁽⁴⁾ = {(R ⁽⁴⁾ + r) / R ⁽⁴⁾ } L ₁₂ ⁽²⁾
Using the electrical conductivity L ₁₁ ⁽⁴⁾ and the thermoelectric coefficient L ₁₂ ⁽⁴⁾ , the Seebeck coefficient S is obtained from the following equation.
S = L ₁₂ ⁽⁴⁾ / L ₁₁ ⁽⁴⁾
Thermoelectric property measurement method. A second current value [Delta] I _T flowing between the end and the other end was measured when applying a temperature difference ΔT between the one end and the other end of the measurement object,
When the length from the one end to the other end of the measurement object is l, and the cross-sectional area perpendicular to the length direction is A,
The thermoelectric coefficient L ₁₂ is determined using L ₁₂ = (l / A) (ΔI _T / ΔT).
Thermoelectric property measurement method. A power source for applying a potential difference between one end and the other end of the measurement object;
A temperature difference generator for adding a temperature difference between the one end and the other end;
An ammeter for measuring a current value flowing between the one end and the other end;
A voltmeter for measuring a voltage between the one end and the other end of the measurement object;
In a physical property assumption device comprising:
When the length l from the one end to the other end of the measurement object and the cross-sectional area A orthogonal to the length direction,
Using the current ΔI _V ⁽²⁾ measured by the ammeter when a potential difference ΔV _A is applied between the one end and the other end by the power source, the electrical conductivity L ₁₁ ^{(2 )}
L ₁₁ ⁽²⁾ = (l / A) (ΔI _V ⁽²⁾ / ΔV _A )
Using the voltage ΔV _V measured by the voltmeter when the potential difference ΔV _A is applied between the one end and the other end by the power source, and the current ΔI _V ⁽⁴⁾ measured by the ammeter The electrical conductivity L ₁₁ ⁽⁴⁾ is obtained from the following formula,
L ₁₁ ⁽⁴⁾ = (l / A) (ΔI _V ⁽⁴⁾ / ΔV _V )
Using the electrical conductivity L ₁₁ ⁽²⁾ and the electrical conductivity L ₁₁ ⁽⁴⁾ , the contact resistance r is obtained from the following equation:
^{_{r = R (2) -R (}} 4) = (1 / L 11 (2) -1 / L 11 (4)) (l / A)
Using the voltage value ΔI _T ⁽²⁾ measured by the ammeter when the temperature difference ΔT is applied between the one end and the other end by the temperature difference generator, a thermoelectric coefficient is obtained from the following equation: Find L ₁₂ ^{(2)
_{L 12 (2) = (l}} / A) (ΔI T (2) / ΔT)
The thermoelectric coefficient L ₁₂ ⁽²⁾ is corrected using the contact resistance r, and the thermoelectric coefficient L ₁₂ ⁽⁴⁾ is obtained from the following equation:
L ₁₂ ⁽⁴⁾ = {(R ⁽⁴⁾ + r) / R ⁽⁴⁾ } L ₁₂ ⁽²⁾
Thermoelectric property measurement method.

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