JP2010204063A - Method and device for measuring specific heat capacity and hemispherical total emissivity of conductive sample - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To improve the accuracy of measuring results of the specific heat capacity and hemispherical total emissivity of a conductive sample of a high temperature by solving problems such as electromagnetic interference noise or the ununiformity of the sample temperature distribution. <P>SOLUTION: A measuring method includes a step of energizing and rapidly heating the conductive sample and making the sample reach a target temperature Tm, a step of varying the current immediately after reaching the target temperature, and calculating a plurality of values of X and Y corresponding to different currents using the relational expression (formulas 6) of X and Y based on the temperature change rate dT/dt immediately after it, current I flowing in the sample, and the measuring data of voltage drop V of the sample, and a step of calculating the specific heat capacity c<SB>p</SB>and hemispherical total emissivity ε<SB>t</SB>using formula 7. <P>COPYRIGHT: (C)2010,JPO&INPIT

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.
(1) Calorimetric method using classical pulse current heating technology (see Non-Patent Document 1)
(2) Calorimetry using feedback control pulse current heating technology (see Non-Patent Document 2)
(3) Calorimetric method using pulsed current heating technology considering the temperature distribution of the sample (see Non-Patent Documents 3 and 4)
The following is a brief introduction.

  The calorimetric method using the classic pulse current heating technique is a general method used when 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 near 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 surroundings is dominated by thermal radiation. The heat balance relationship per unit volume 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 calorimetric method using the feedback control pulse current heating technique described below is a method developed from the technique (1). The difference from the technology in (1) is that the sample temperature can be reduced only for a short time by using a semiconductor element such as a MOSFET for the current control switch and feedback control of the current using the sample temperature as a reference parameter as well as current ON / OFF. 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 method for measuring the specific heat capacity by the calorimetric method using the pulse current heating technique considering the temperature distribution of the sample described below is a method developed from the technique (1). The difference from the method (1) is that the temperature derived from the value of 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 by the technique of (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 electrical resistivity value, and the specific heat capacity is calculated by substituting the effective temperature into Equation [3-1] (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 performed (Non-patent Document 4).

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)
When a sample is rapidly heated by the pulse current heating method, the current flowing through the conductive sample often varies greatly with time. Changes in current over time can cause electromagnetic interference noise and can cause large errors in the measurement of the voltage drop across the sample and standard resistor.
FIG. 3 shows changes in the observed temperature T _p of the sample when the molybdenum sample is heated by pulse current (value observed at the center of the sample with a radiation thermometer) and the electrical resistivity. The two white lines in FIG. 3 indicate approximate curves for the electrical resistivity measurement results when the sample is heated and when the temperature is decreased. In this measurement, rapid heating was stopped after about 2 × 10 ⁵ μs after the start of heating, and the electrical resistivity (ρ _h and ρ _c ) at the time of temperature rise and fall immediately before and after that was compared. It turns out that there are systematic differences. Since the electrical resistivity should match if the temperature of the sample is the same, such a difference in electrical resistivity clearly indicates that some error is included in the measured voltage drop of the sample and the standard resistance. Watanabe and Matsumoto have reported that the error factor is a constant voltage noise that is always included in the measured value, such as an error in the zero point correction of the voltage drop measurement device (non- Patent Document 3). According to the report, it is assumed that the measured value of the voltage drop at both the temperature rise and the temperature drop always includes a constant voltage noise ΔV, and that ρ _h and ρ _c have the same magnitude, ΔV And the measurement result of the electrical resistivity is corrected using the derived ΔV.

However, as a result of performing the same measurement as the above-mentioned molybdenum on the carbon material, the present inventor found that the cause of the apparent discontinuity of the electrical resistivity immediately before and after the rapid heating was stopped was the time during which the current flowing through the sample was large. It came to the conclusion that it is electromagnetic interference noise that occurs only during rapid heating with changes. This is because, as a result of comparing the values of ρ _h and ρ _c of the carbon material measured by the present inventors with reliable literature values, ρ _c almost coincided with the literature values, but ρ _h was greatly different from the literature values. When causes a large error is included only in the [rho _h is assumed to steady voltage noise Watanabe and Matsumoto claims, will be too large voltage noise occurs constantly. On the other hand, since the magnitude of the electromagnetic interference noise is proportional to the magnitude of the time change of the current, it is sufficiently conceivable that only a large error is included in the measured value of electrical resistivity during rapid heating accompanied by a large time fluctuation of current. .
From the discussion so far, the specific heat capacity and the hemispherical total emissivity calculated by the equations [Equation 3-1], [Equation 3-2], and [Equation 5] using the measured values of I and V during rapid heating are used. May contain large errors due to electromagnetic interference noise. Further, in the specific heat capacity measurement method described in Non-Patent Document 3, the specific heat capacity is derived based on a false assumption that a steady voltage error is included in the measured voltage drop values of the sample and the standard resistor. Therefore, it is considered that a large error occurs when measuring a sample such as a carbon material measured by the inventor.

When measuring the total emissivity of the hemisphere according to [Equation 4], the voltage measurement value at the time of rapid heating is not used, so the problem of electromagnetic interference noise can be almost ignored. However, the following problems have been pointed out. FIG. 4 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 technique (2) described above (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, so it represents the effective temperature of the sample. Indicates not to.

  The discrepancy between the sample center temperature and the temperature coefficient of electrical resistivity shown in FIG. 4 indicates that the equation [Equation 4] used for calculating the hemispherical total emissivity by the technique (2) described above is not strictly established. Show. The method for measuring the total emissivity of the hemisphere described in Non-Patent Document 4 has been proposed as one solution to this problem. In order to calculate the total emissivity of the hemisphere, the specific heat capacity, the thermal conductivity, and the temperature of the sample There is a major limitation that the distribution and its change over time need to be measured.

(Solution Problems of the Present Invention)
The present invention improves the conventional measurement method of specific heat capacity and hemispherical total emissivity, solves the above-mentioned problems of electromagnetic interference noise and non-uniformity of sample temperature distribution with a low-cost apparatus, and conducts a conductive sample at a high temperature. It is an object to improve the accuracy of measurement results of specific heat capacity and hemispherical total emissivity.

In order to solve the above problems, the present invention provides the following measuring method and apparatus.
By energizing the conductive sample is rapidly heated, steps to reach the sample to the target temperature T _m, immediately after reaching the target temperature by changing the electric current, the current flowing through the temperature change rate dT / dt immediately, the samples I Calculating the X and Y values from the measurement data of the voltage drop V of the sample using the following relational expression:

(A in the formula is the effective surface area of the sample, σ _SB is the Stefan-Boltzmann constant, and T ₀ is the temperature around the sample.)
Approximate the X and Y values obtained by changing the current after reaching the target temperature to various values using the linear relationship shown in the following equation. the specific heat capacity and the hemispherical total emissivity of conductive samples comprising the step of calculating the specific heat capacity c _p and hemispherical total emittance epsilon _t the value of the linear expression of the slope and intercept of the derived X and Y Measuring method.

  The above specific heat capacity and hemispherical total emissivity measurement method is implemented, characterized by comprising means for automatically repeating a step of calculating a plurality of X and Y values by changing the current value after reaching the target temperature Device to do.

According to the present invention, a low-cost apparatus that does not have the temperature feedback control function required in the technique (2) described above eliminates the effects of electromagnetic interference noise and temperature distribution non-uniformity. The heat capacity and hemispherical total emissivity can be measured and the accuracy of measurement results can be easily improved by increasing the number of measurement points.
Further, according to the present invention, by evaluating whether or not a plurality of X and Y values calculated from a plurality of measurements at the same target temperature have a linear relationship, the presence or absence of a serious error in the measurement data can be determined. It is possible to self-check whether the feasible heat balance relational expression [Formula 1] has been established.

Typical apparatus for implementing the specific heat capacity and hemispherical total emissivity measurement method based on the calorimetric method using the classical pulsed heating technique Time course of typical sample temperature obtained in the measurement method of specific heat capacity and hemispherical total emissivity based on the calorimetric method using the classical pulse current heating technique Discontinuous change in electrical resistivity of specimen before and after rapid heating by pulsed heating Temporal change in electrical resistivity when the sample temperature is held constant by feedback control pulse current heating Schematic view of a superimposed plurality of time variation curve obtained by changing the value of the target temperature T _m gate voltage after reaching 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 implementing a plurality of different sample temperature change rate dT / dt under the same conditions X and Y The figure which plotted the value of X and Y obtained by the plurality of measurements of the carbon material actually performed on the XY plane

The outline | summary of the measuring method of the specific heat capacity and hemispherical total emissivity of the electroconductive sample concerning this invention is demonstrated.
The present invention, in order to reduce the effect of the two error factors described above, the specific heat capacity by using the measured data immediately after rapid heating heterogeneity of electromagnetic interference noise and the sample temperature distribution is small in the target temperature T _m c _p And to calculate the hemispherical total emissivity ε _t . Immediately after the sample is rapidly heated to the target temperature with a large current, the influence of the non-uniformity of the sample temperature distribution and the conduction heat loss can be almost ignored, so the equation [Equation 1] holds for the heat balance of the sample. The equation [Equation 1] can be modified as follows.

The above equation [Equation 8] indicates that a linear relationship is established between the values of X and Y calculated from the equations [Equation 9] and [Equation 10], respectively. Therefore, a linear expression of X and Y is approximately calculated by the least square method or the like for a plurality of X and Y values calculated by changing the current flowing through the sample to various values after reaching the target temperature, and the primary from the values of the slope and intercept of the approximate expression can be calculated specific heat capacity c _p and hemispherical total emittance epsilon _t at the target temperature T _m.

In order to implement the present invention, an apparatus that employs a semiconductor element such as a MOSFET as a current switch in the apparatus (see FIG. 1) that implements the technique (1) described above is required.
The measurement is performed according to the following procedure.
The sample was rapidly heated to the target temperature T _m, and by changing the gate voltage V _g to the MOSFET to a proper value, the current flowing through the sample I, voltage drop V corresponding to the sample, the temperature change rate dT / dt Each value is changed from the value immediately before the rapid heating is stopped. Then, repeating the measurement with different values of the target temperature T _m of a after reaching V _g, to calculate the values of the various X and Y.
For example, in the apparatus shown in FIG. 1, by providing means for automatically repeating the step of calculating the X and Y values by changing the current value after reaching the target temperature in order to obtain a plurality of X and Y values. To be implemented.
That is, the current flowing through the sample after reaching the target temperature may be of any magnitude, so that the gate voltages of the MOSFETs for adjusting the current are changed at a plurality of points at appropriate intervals to obtain I, V, and dT necessary for calculating X and Y. A device with a simple computer program function that repeats the measurement of / dt allows automatic measurement of specific heat capacity and hemispherical total emissivity.
FIG. 5 shows a schematic diagram when a plurality of sample temperature change curves obtained in the above-described plurality of measurements are superimposed. By calculating X and Y values corresponding to a plurality of measurements thus obtained and deriving a linear relationship between X and Y as shown in FIG. 6, _cp and ε _t at T _m can be calculated. .

The first advantage of the present invention is that a measurement error caused by using measurement data of the sample temperature, current, and voltage drop immediately after reaching the target temperature by rapid heating in which electromagnetic interference noise and non-uniformity of the sample temperature distribution can be almost ignored. Reduction.
The second advantage of the present invention is that it does not require the temperature feedback control function required in the technique (2) described above, and therefore can be implemented by a low-cost apparatus and is easy by increasing the measurement points of X and Y. In addition, the accuracy of the measurement results of specific heat capacity and hemispherical total emissivity can be improved. FIG. 7 shows a plurality of X and Y measurement results obtained by changing the value of the gate voltage after reaching the target temperature by the method of the present invention using a carbon material as a sample.
From this figure, the points where the value of X is around 8 are clearly deviated from the linear relationship, but these points are based on the measurement results when the gate voltage is set so that a considerably large rate of temperature increase occurs even after reaching the target temperature. This is a derived point. In this case, obviously, the current flowing through the sample greatly fluctuates in accordance with the change in the electrical resistivity of the sample accompanying a rapid increase in the sample temperature, and as a result, serious electromagnetic interference noise is included in the voltage measurement value. It shows that it has been. Such a deviation from the linear relationship between X and Y is caused by the deviation of the heat balance relationship of the sample from the ideal state represented by Equation [1]. Therefore, if a measurement error factor other than electromagnetic interference noise, such as sample contamination, occurs in any of the repeated measurements, the (X, Y) points obtained from that measurement are obtained from other normal measurements ( X, Y) point will deviate from the straight line formed.

Therefore, the third advantage of the present invention is that it is possible to evaluate other measurement errors such as serious electromagnetic interference noise and sample deterioration by evaluating whether or not the obtained (X, Y) points have a linear relationship. It is possible to self-check whether or not there is a heat balance and whether or not the heat balance relationship in which the present invention can be implemented, that is, whether the formula [Equation 1] is satisfied.
The fourth advantage of the present invention is that the current flowing through the sample after reaching the target temperature may be of any magnitude, so that the calculation of X and Y is performed by changing the gate voltage of the MOSFET for adjusting the current at multiple points at appropriate intervals. The specific heat capacity and hemispherical total emissivity can be automatically measured by a device having a simple computer program function that repeats the necessary I, V and dT / dt measurements.

Claims (2)

By energizing the conductive sample is rapidly heated, steps to reach the sample to the target temperature T _m, immediately after reaching the target temperature by changing the electric current, the current flowing through the temperature change rate dT / dt immediately, the samples I Calculating X and Y from the measurement data of the voltage drop V of the sample using the following relational expression:
(A in the formula 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.)
For the plurality of values of X and Y, using the fact that X and Y have the linear relationship shown in the following equation, the slope and intercept values of the approximated X and Y linear equations are derived. specific heat capacity and the measuring method of the hemispherical total emissivity of conductive samples comprising the step of calculating the specific heat capacity c _p and hemispherical total emittance epsilon _t.
  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 current value after reaching the target temperature. A device that performs the measurement method.