JP5414068B2 - Method and apparatus for measuring specific heat capacity and hemispherical total emissivity of conductive samples - Google Patents

Description

  The present invention relates to a method and apparatus for measuring the specific heat capacity and hemispherical total emissivity of a conductive sample at high temperatures.

For the measurement of the specific heat capacity and the hemispherical total emissivity of a conductive sample at a high temperature, a measurement method based on the following calorimetric method has been conventionally employed.
Prior art (1): Calorimetric method using classical pulsed heating technology (see Non-Patent Document 1)
Prior art (2): calorimetric method using feedback control pulse current heating technology (see Non-Patent Document 2)
Prior art (3): calorimetric method using pulsed current heating technique considering temperature distribution of sample (see Non-Patent Documents 3 and 4)
Prior art (4): a calorimetric method using a pulse current heating technique characterized in that the operation of changing the heating rate at the target temperature is performed a plurality of times (see Patent Document 1)
The following is a brief introduction.

Prior art (1) is a general method used in measuring the specific heat capacity and hemispherical total emissivity of a conductive sample at a high temperature of 1500 K or higher. A schematic of a typical apparatus used to carry out this method is shown in FIG. In this method, a pulsed large current is passed through a sample through a battery to heat the sample instantaneously. Then, the current I flowing through the sample, the voltage drop V in the sample, and the temperature T of the sample are continuously measured. The value of I is calculated from the measured value of the voltage drop across a standard resistor connected in series with the sample, and the value of T is determined by measuring with a radiation thermometer. The temperature distribution around the center of the sample heated rapidly from room temperature is uniform within a short time, and it can be assumed that the heat transfer from the sample to the environment is dominated by heat radiation. Is expressed by the following equation [Equation 1].
Where m is the effective mass of the sample corresponding to the region for measuring the V described above, c _p is the specific heat capacity of the sample, A is the effective surface area of the sample corresponding to the above-mentioned m, epsilon _t the hemispherical total emissivity of the sample , Σ _SB is the Stefan-Boltzmann constant, and T ₀ is the temperature around the sample.

In the measurement, a temperature change as shown in FIG. 2 is observed, but even if the current is stopped and the sample is being cooled, it is assumed that the temperature distribution of the sample is kept uniform if it is immediately after the start of cooling. Assume that [Equation 1] holds. Based on this assumption, the heat balance equations at the target temperature T _m at the time of temperature rise (subscript h) and at the time of temperature fall (subscript c) are respectively expressed by the following equations [Equation 2].
Then, equation [Expression 2-1], can be calculated by the following equation [Expression 3] the specific heat capacity _{c p} and hemispherical total emittance epsilon _t by simultaneous equation [number 2-2.

The prior art (2) is an example of a method developed from the prior art (1). The difference from the prior art (1) is that not only the current ON / OFF by using a semiconductor element such as a MOSFET for the current control switch, but also the sample temperature is reduced for a short time by feedback control of the current using the sample temperature as a reference parameter. It has a function of keeping the temperature constant. Can be considered a left side zero of the Equation 1 in the case of the sample was held in a steady state of the target temperature T _m This feature hemispherical total emittance epsilon _t can be calculated by the following equation [Expression 4].
Further, the specific heat capacity can be calculated from the obtained hemispherical total emissivity and the temperature change during heating by the following equation [Formula 5].

The prior art (3) is also an example of a method developed from the prior art (1). The difference from the prior art (1) is that the temperature derived from the value of the electrical resistivity is used as the temperature of the sample during cooling and the time change rate thereof, not the value measured by the radiation thermometer. The reason for using the temperature derived from the electrical resistivity is that when rapid heating is completed and the sample is cooled, the temperature distribution of the sample becomes nonuniform rapidly due to the effect of conduction heat loss, so only a part of the sample surface is used. This is because the temperature indicated by the radiation thermometer that observes the difference between the effective temperature and deviation considering the temperature distribution of the entire sample. The specific implementation method of specific heat capacity according to the prior art (3) is that the electrical resistivity measurement based on the four-terminal method principle is continued even during cooling by passing a slight current after reaching the target temperature T _m by rapid heating. Then, an effective temperature is calculated from the obtained electric resistivity value, and the specific heat capacity is calculated by substituting the effective temperature into the formula [Equation 3-1] (see Non-Patent Document 3).

  The method of measuring the total emissivity of the hemisphere by the calorimetric method using the pulse current heating technique considering the temperature distribution is a method developed from the technique (2). This method takes into account the effects of enthalpy reduction and conduction heat loss corresponding to the effective temperature fluctuation calculated from the electrical resistivity value measured simultaneously while maintaining the sample temperature constant by current feedback control. The hemispherical total emissivity is calculated by the analysis (see Non-Patent Document 4).

The prior art (4) is an example of a method developed from the prior art (1). The difference from the prior art (1) is that an electric heating experiment in which the heating rate of the sample is changed at the target temperature is performed a plurality of times.
In the prior art (4), by energizing the conductive sample is rapidly heated, steps to reach the sample to the target temperature T _m, by changing the electric current immediately after reaching the target temperature, immediately after the temperature change rate dT / calculating X and Y from the measurement data of dt, current I flowing through the sample, and voltage drop V of the sample using the following relational expression:
Where A is the effective surface area of the sample, σ _SB is the Stefan-Boltzmann constant, T _m is the target temperature, and T ₀ is the temperature around the sample.
By using the fact that X and Y have a linear relationship represented by the following expression for the plurality of X and Y values, a ratio is calculated from the slope and intercept values of the approximately derived X and Y linear expressions. specific heat capacity and the measuring method of the hemispherical total emissivity of conductive samples comprising the step of calculating the heat capacity c _p and hemispherical total emittance epsilon _t.

Japanese Patent No. 45289954

A. Cezairliyan, J.L.McClure, and C.W.Beckett: J.Res.National Bureau of Standards, Vol. 75C, 7 (1971). T. Matsumoto and A. Cezairliyan: Int. J. Thermophys. Vol. 18, 1539 (1997). H. Watanabe: Rev. Sci. Instrum., Vol. 77, 036110 (2006). H. Watanabe and T. Matsumoto: Rev. Sci. Instrum., Vol. 76, 043904 (2005).

(Problems of conventional technology)
FIG. 3 shows a measured value of the electrical resistivity ρ _av of the molybdenum sample when the sample temperature T _p is kept constant at the target temperature (1507 K) by the above-described conventional technique (2) (see Non-Patent Document 4). ). From this figure, it is recognized that the value of the electrical resistivity depending on the temperature changes with time even though the sample temperature is kept constant. This indicates that the temperature distribution is becoming non-uniform due to conduction heat loss through a holder for supplying current in contact with the sample and a probe for measuring voltage drop. In other words, the temperature measured by the radiation thermometer, which is an observation parameter, only shows the temperature in a part of the center of the sample to be observed, and the temperature distribution of the entire sample is not uniform. Indicates not to.

  The discrepancy between the sample center temperature and the temperature coefficient of the electrical resistivity shown in FIG. 3 indicates that the temperature distribution of the sample rapidly becomes non-uniform after the rapid energization heating is stopped. In the above-described conventional techniques (1) and (2), since the data after the rapid energization heating stop is used, there is a problem with the nonuniformity of the sample temperature distribution. Prior art (3) was proposed as one solution to this problem, but in order to calculate the total emissivity of the hemisphere, it is necessary to measure the specific heat capacity, the thermal conductivity, the temperature distribution of the sample, and its change over time. There is a big limitation that there is. Regarding the prior art (4), the heating rate after reaching the target temperature can be maintained at a relatively large value to avoid the non-uniformity of the sample temperature distribution, but there are the following problems.

  In the prior art (4), a large current is passed through the sample using a large-capacity battery or capacitor, the sample is rapidly heated from room temperature to a predetermined target temperature within 1 second, and the current is changed when the target temperature is reached. Let As shown in FIG. 4, a plurality of heating experiments are performed by discretely changing the current that flows after reaching the same target temperature, and the sample temperature, temperature change rate, sample voltage drop after reaching the target temperature in each heating experiment, and Measure the current. Then, the specific heat capacity and the hemispherical total emissivity can be derived from the above measured values at a plurality of sets of target temperatures according to the analysis method described in Patent Document 1. In this method, when measuring the specific heat capacity and the hemispherical total emissivity at one temperature, it is only necessary to repeat the heating experiment that is completed in 1 second or less, but the specific heat capacity and the hemispherical total in a wide temperature range are repeated. In order to measure the emissivity at a plurality of temperatures, it is necessary to repeat the heating experiment very often, and there is room for improvement in terms of measurement efficiency. In addition, since a current control function for changing the value of the current flowing through the sample immediately after reaching the target temperature is required, there is a problem that the cost of the apparatus is higher than that of the apparatus that implements the prior art (1).

(Solution Problems of the Present Invention)
The present invention relates to a specific heat capacity and hemispherical total emissivity measurement method of a conductive sample based on a calorimetric method using rapid energization self-heating, and a specific heat capacity at an arbitrary temperature in a wide temperature range with a low-cost apparatus. And improving the measurement efficiency by measuring the total emissivity of the hemisphere in a short time and improving the accuracy and reliability of measured values by eliminating the problem of non-uniform sample temperature distribution and electromagnetic interference noise. To do.

In order to solve the above problems, the present invention provides the following measuring method and apparatus.
(1) by applying a current to the conductive sample rapidly energizing self-heating, the sample to reach from any temperature of the hot target temperature T _m of the flow rate of heating of the sample at the target temperature T _m dT / dt, the samples A step of calculating X and Y from the measurement data of the current I and the voltage drop V of the sample using the following relational expression:
Where A is the effective surface area of the sample, σ _SB is the Stefan-Boltzmann constant, T _m is the target temperature, and T ₀ is the temperature around the sample.
The step of calculating the plurality of sets of X and Y by repeating the above steps by changing the heating rate discretely by changing the current passed through the sample, and for the plurality of X and Y values, The step of calculating the specific heat capacity c _p and the hemispherical total emissivity ε _t from the slope and intercept value of the approximately derived linear equation of X and Y using the linear relationship shown in the following equation is included. A method for measuring a specific heat capacity and a hemispherical total emissivity of a conductive sample.
(2) The specific heat capacity according to claim 1, further comprising means for automatically repeating a step of calculating a plurality of X and Y values by changing a heating rate in the rapid energization self-heating. A device that implements the emissivity measurement method.

  In the present invention, in order to avoid the non-uniformity of the temperature distribution of the sample, which is a problem in the prior arts (1) and (2), the temperature, voltage drop, and current value of the sample during rapid energization heating with a relatively constant temperature distribution. Is used for analysis. Further, the current feedback control function required in the prior art (2) and the current for changing the current value at the same time as the target temperature is reached during the rapid energization heating required in the prior art (3) and (4). With a low-cost device that does not have a control function, it is possible to measure the specific heat capacity and the hemispherical total emissivity while eliminating the influence of non-uniformity in temperature distribution. In addition, there is a concern that a significant error may occur in voltage drop and current measurement due to electromagnetic interference noise during rapid energization heating, but in the present invention, a plurality of X and Y values at the target temperature have a linear relationship. By evaluating whether or not it has, it is possible to self-check whether or not there is a serious error due to electromagnetic interference noise in the measurement data and whether the heat balance relational expression [Equation 1] that can implement the present invention is established. Furthermore, in the present invention, unlike all of the above four types of conventional technologies, the specific heat capacity and the hemispherical total emissivity at an arbitrary temperature in a wide temperature range from the starting temperature to the ending temperature of the sample are set to about 1 second. It can be efficiently derived by conducting the current heating experiment a plurality of times.

Typical apparatus for implementing specific heat capacity and hemispherical total emissivity measurement methods based on the calorimetric method using rapid energization self-heating technology Time course curve of typical sample temperature obtained by the prior art (1) Time course curve of electrical resistivity and temperature at the center of the sample after reaching the target temperature obtained by the conventional technique (2) Schematic diagram when temperature and time change curves obtained in a plurality of energization self-heating experiments are characterized in that the gate voltage value is changed after reaching the target temperature obtained by the prior art (4) Schematic diagram when temperature and time change curves obtained in a plurality of energization self-heating experiments conducted to derive X and Y values at an arbitrary temperature in a wide temperature range obtained by the technology of the present invention are superimposed. Schematic diagram of a specific heat capacity and the calculation method of the hemispherical total emissivity using the value of the target temperature T _m was obtained from measurements obtained by realizing the heating rate dT / dt to a plurality of different under the same conditions X and Y

The outline | summary of the measuring method of the specific heat capacity and hemispherical total emissivity of the electroconductive sample which concerns on this invention is demonstrated.
The present invention utilizes the measurement data during rapid self-heating of the sample with good uniformity of the sample temperature distribution, and the specific heat capacity at any temperature in a wide temperature range from the start temperature to the end temperature of the sample. The object is to accurately and efficiently derive c _p and the hemispherical total emissivity ε _t .
If by flowing a c _p large current rapidly energized heating the sample, the influence of nonuniformity and conductive heat loss of the sample temperature distribution for heat balance of the sample for substantially negligible formula [Number 1] is established. The equation [Equation 1] can be modified as follows.

The above equation [Equation 10] indicates that a linear relationship is established between the values of X and Y calculated from the equation [Equation 11], respectively. Therefore, a linear expression of X and Y is approximately calculated by a least square method or the like for a plurality of X and Y values calculated by discretely changing the current flowing through the sample during heating to various values. The specific heat capacity c _p and the hemispherical total emissivity ε _t at the target temperature T _m in the temperature range from the start temperature to the end temperature of the energization self-heating can be calculated from the slope and intercept value of the linear approximation formula, The soundness of the measurement can be evaluated from the presence or absence of linearity between them.

The present invention can be implemented by a low-cost apparatus (see FIG. 1) used when implementing the above-described prior art (1).
The measurement is performed according to the following procedure.
The sample held at the temperature T ₀ is subjected to rapid energization self-heating to an arbitrary temperature T _max by flowing a large current using an apparatus as shown in FIG. At that time, the sample temperature, the voltage drop of the sample, and the current value are continuously measured. As one follows the varying the value of the variable resistor in the current circuit, to a value different from the time of heating was conducted gate voltage V _g of the MOSFET during conduction self-heating above if you are using MOSFET as a current switch The sample is rapidly heated and self-heated rapidly at a heating rate dT / dt different from the previous time. In this way, the measurement with the heating rate dT / dt changed discretely is repeated, and X and Y at the target temperature T _m between the temperatures T ₀ and T _max measured under different dT / dt conditions. Is calculated.

FIG. 5 shows a time change curve of the sample temperature obtained by a plurality of energizing self-heating experiments performed by the above procedure. By providing means for changing the current I flowing during heating in each energizing self-heating experiment, a plurality of Xs at the target temperature T _m between temperatures T ₀ and T _max measured under different dT / dt conditions The value of Y can be derived in a short time.
Since the current flowing through the sample during each energization self-heating experiment may be arbitrarily large as long as it is discretely different, the variable resistance in the current circuit is automatically changed in the example of the apparatus embodying the present invention shown in FIG. If a MOSFET is used as a mechanical mechanism or current switch, measure the T, I, and V required to calculate X and Y by changing the gate voltage of the MOSFET that adjusts the current at multiple intervals. the device with a simple computer program functions to repeat, it is possible to automatically measure the specific heat capacity and hemispherical total emissivity of the target temperature T _m of a in the temperature range leading to completion temperature from the starting temperature of the energization self-heating experiment.
The values of X and Y at the target temperature T _m calculated from a plurality of current self-heating experiment as shown in FIG. 5, c in T _m by deriving a linear approximation of X and Y as shown in FIG. 6 _p and ε _t can be calculated.

The first advantage of the present invention is a reduction in measurement error by using only measurement data of sample temperature, current, and voltage drop during rapid energization self-heating where the non-uniformity of the sample temperature distribution can be almost ignored.
The second advantage of the present invention is that the current value is discretely changed during the temperature feedback control function required in the above-described prior art (2) and the rapid energization self-heating required in the prior art (4). With a low-cost device that does not have the current control function, it is possible to measure the specific heat capacity and the total emissivity of the hemisphere while eliminating the influence of non-uniform temperature distribution.

The third advantage of the present invention is that by evaluating whether or not the obtained (X, Y) points have a linear relationship, measurement errors caused by serious electromagnetic interference noise or sample alteration can be reduced. It is possible to self-check whether or not there is a heat balance relationship in which the present invention can be implemented, that is, whether the formula [Equation 1] has been established.
The fourth advantage of the present invention is that a mechanical resistance that automatically changes the variable resistance in the current circuit can be used as long as the current flowing through the sample during each energization heating experiment is discretely different. If a MOSFET is used for the mechanism or current switch, a simple computer program that repeats the T, I, and V measurements necessary to calculate X and Y by changing the gate voltage of the MOSFET that adjusts the current at appropriate intervals The specific heat capacity and hemispherical total emissivity at an arbitrary temperature in a wide temperature range from the start temperature to the end temperature of the electric heating can be automatically measured in a short time by a device having a function.

Claims (2)

By applying a current to the conductive sample rapidly energizing self-heating, the sample exceeds the target temperature T _m is reached to any temperature, the current flowing through the heating rate of the sample at the target temperature T _m dT / dt, the samples I, Calculating X and Y from the measurement data of the voltage drop V of the sample using the following relational expression;
Where A is the effective surface area of the sample, σ _SB is the Stefan-Boltzmann constant, T _m is the target temperature, and T ₀ is the temperature around the sample.
The step of calculating the plurality of sets of X and Y by repeating the above steps by changing the heating rate discretely by changing the current passed through the sample, and for the plurality of X and Y values, The step of calculating the specific heat capacity c _p and the hemispherical total emissivity ε _t from the slope and intercept value of the approximately derived linear equation of X and Y using the linear relationship shown in the following equation is included. A method for measuring a specific heat capacity and a hemispherical total emissivity of a conductive sample.
The specific heat capacity and hemispherical total emissivity according to claim 1, further comprising means for automatically repeating a step of calculating a plurality of X and Y values by changing a heating rate in the rapid energization self-heating. A device that implements the measurement method.