JP4280830B2 - Measurement method of specific heat and thermal conductivity. - Google Patents

Description

  The present invention relates to a method for measuring specific heat and thermal conductivity, and more particularly to a method for simultaneously measuring specific heat and thermal conductivity under high pressure.

When a new solid material such as a new alloy or ceramic is newly obtained, understanding of the material begins by examining basic physical quantities or physical properties. In addition, even conventionally known substances have properties that have not been known so far in terms of properties at extremely low temperatures and ultrahigh pressures. In fact, CeCu ₂ Si ₂ is known as the first strongly correlated electron superconductor, and the superconducting transition temperature Tc rapidly rises from Tc = 0.7K to 2K under 2.5 GPa.

  In addition to Tc, the physical properties of solid substances are largely dependent on the electronic state. Conversely, if there is a transition point, it is presumed that the electronic state is changing there. Therefore, investigating basic physical quantities, such as electrical resistivity, specific heat, thermal conductivity, magnetic susceptibility, and magnetic susceptibility, under various atmospheres (pressure atmosphere, temperature atmosphere, etc.) is extremely important in researching physical properties. It is.

  However, although the measurement technology in a low-temperature atmosphere has progressed, there is a fact that basic physical quantity measurements under gigapascal-class ultra-high pressure, in particular, specific heat and thermal conductivity measurements have not progressed much. .

  For example, a heat insulation method and an alternating current method are known as methods for measuring specific heat. FIG. 22 shows an outline of the measurement apparatus for the heat insulation method. In the heat insulation method, first, a sample of several tens mg is put into a Teflon capsule together with a pressure transmission medium, and this is sealed in a piston cylinder type pressure cell, and a high pressure atmosphere is formed by a hydraulic press. In the measurement of specific heat, the piston cylinder type pressure cell is adiabatic and the heat capacity is obtained as C = ΔQ / ΔT from the temperature rise ΔT when the amount of heat ΔQ is added.

  The required heat capacity is the total heat capacity of the sample, Teflon cell, pressure transmission medium, and piston cylinder type pressure cell. Therefore, the heat capacity of the Teflon cell, pressure transmission medium, and piston cylinder type pressure cell is measured separately as a background. And subtract to obtain the heat capacity of the sample itself.

  Here, since the mass of the cell main body is as large as several tens of g compared with several tens of mg of the sample, this measurement method of subtracting the heat capacity as the background may naturally increase the error. In particular, when measuring under high pressure, this problem becomes more serious because the cell inevitably becomes larger and the background capacity to be subtracted also becomes larger. Therefore, a measurement limit is practically present, and at present, only a measurement value of less than 2 GPa can be obtained.

  On the other hand, the AC method has succeeded in measuring the abnormal specific heat under an ultra-high pressure of 20 GPa. However, although detailed explanation is omitted, since it is difficult to obtain an absolute value by the AC method, quantitative analysis such as entropy evaluation, which is also an important significance of specific heat measurement, cannot be performed, and the transition temperature depends on pressure. At present, the qualitative evaluation is limited to confirming sex.

  Moreover, the relaxation method is known as another method of specific heat measurement. The measurement outline of the relaxation method is shown in FIG. As shown in the figure, the relaxation method directly attaches a heat source and thermometer to the sample and creates a heat leak in the heat bath, resulting in a one-dimensional heat transfer problem and an increase or decrease in temperature due to heating or cooling. Is a method for determining the specific heat by measuring. Since the relaxation method is based on the assumption that all applied heat is transferred to the sample, the system is required to be vacuum (0 atm), and a pressure transfer medium that causes thermal diffusion is interposed. There is a problem that measurement (that is, measurement under high pressure) is impossible in principle.

As a method for measuring the thermal conductivity, for example, a steady method is known. FIG. 24 shows an outline of a measurement apparatus for the steady method. In the steady method, one end of an elongated sample having a cross-sectional area S [cm ² ] is fixed to a heat bath, the other end is heated by a heater, and a heat flow Q [W] is applied. The thermal conductivity is obtained from the temperature difference ΔT [K] generated between two points separated by cm] as κ [W / cmK] = (QS) / (ΔTL). Since the steady-state method is based on the assumption that a uniform heat flow is generated in the sample, the system is required to be vacuum (0 atm), and a pressure transmission medium that causes thermal diffusion is interposed. Measurement (ie measurement under high pressure) is not possible in principle. Also, other measurement methods for thermal conductivity have not yet been established for measurement under high pressure for the same reason as the steady-state method.

  An object of the present invention is to overcome such problems and to provide a method capable of simultaneously measuring not only specific heat but also thermal conductivity under high pressure.

  In order to achieve the above object, the specific heat and thermal conductivity measuring method according to claim 1 encloses a pressure transfer medium and a sample to be measured in contact with a heat source in a pressure vessel as a heat bath. , A measurement method for simultaneously measuring the specific heat and thermal conductivity of a sample under pressure, wherein the time change in temperature of at least three measurement points of one point on the heat source and two points not equivalent in terms of heat conduction on the sample Is measured in the process from the start or end of heating by the heat source to the steady state, and a numerical analysis model simulating this measurement system is constructed based on the unsteady heat conduction equation that also considers heat propagation in the pressure transfer medium. Using the model, the specific heat of the sample, the thermal conductivity, and the sample and heat source, so that the temperature change at the point corresponding to the measurement point draws the same temperature change curve as the actual temperature change at the measurement point. The thermal conductivity coefficient between And determining by performing value analysis.

  That is, according to the first aspect of the present invention, in consideration of the fact that the pressure transmission medium surrounds the periphery of the sample, the three-dimensional heat propagation from the sample or the heat source to the pressure transmission medium is performed by contacting the sample and the heat source. In addition, numerical analysis as an absolute value is possible by measuring at least three points in consideration of the above. At this time, the specific heat analysis of the sample can be performed based on the temperature rising curve or the temperature falling curve until reaching the steady state, and the specific heat of the sample can be analyzed from the three steady states.

  The specific heat and thermal conductivity measuring method according to claim 2 is the specific heat and thermal conductivity measuring method according to claim 1, wherein the sample is formed symmetrically, and the sample is placed in a pressure vessel. The arrangement of the heat source on the sample and the arrangement of the measurement points are symmetric along the sample.

  That is, in the invention according to claim 2, by making the system symmetrical, the unsteady heat conduction equation and the numerical analysis model corresponding thereto can be simplified, and the numerical analysis accuracy is improved.

  Further, the specific heat and thermal conductivity measuring method according to claim 3 is the specific heat and thermal conductivity measuring method according to claim 1, wherein the pressure vessel is cylindrical and the sample is processed into a cylindrical shape. The sample is disposed in the pressure vessel so that the center axis of the sample and the center axis of the sample coincide with each other, a heat source is joined to the center of the bottom surface of the sample, and the measurement point is provided on the center axis.

  That is, the invention according to claim 3 makes it possible to simplify the unsteady heat conduction equation and the numerical analysis model corresponding to this to a two-dimensional problem by making the system axially symmetric. Improvement is possible.

  Further, the specific heat and thermal conductivity measuring method according to claim 4 is the method of measuring specific heat and thermal conductivity according to claim 1, 2, or 3, wherein the numerical analysis method includes a finite element method and a finite difference method. Alternatively, the boundary element method is used.

  That is, the invention according to claim 4 enables efficient numerical analysis.

  As described above, according to the present invention, it is possible to provide a method capable of simultaneously measuring the specific heat and thermal conductivity of a sample even when thermal diffusion occurs from the sample to be measured. At this time, if the sample to be measured is a pressure transmission medium, the specific heat and thermal conductivity of the sample under high pressure can be measured simultaneously. In addition, since the temperature of the sample is directly measured as an absolute value instead of a method of subtracting the background, basically according to the present invention, there is no limitation on the atmospheric temperature (heat bath temperature) or the atmospheric pressure, and the specific heat or The thermal conductivity can be measured.

Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. In this example, CeRh ₂ Si ₂ was used, temperature was first measured by experiment, and then specific heat and thermal conductivity were determined by analysis from the obtained temperature change curve.

(Preparation of measurement sample)
The measurement sample was produced by arc melting of the raw material. The produced sample was confirmed by powder X-ray diffraction to be polycrystalline CeRh ₂ Si ₂ to be measured. Next, the measurement sample was shaped into a cylindrical shape having a diameter of 3.0 × a height of 1.0 mm. At the top and bottom surfaces, thermometers with a thermometer of 0.025 mmφ (manufactured by Nilaco) are attached as thermometers, and a heater for sample heating (a 350 Ω strain gauge (Kyowa Denshi Kogyo Co., Ltd.) is attached to the bottom surface. Made)).

  Subsequently, an outer layer of Cu—Be and an inner layer of NiCrAl having an inner diameter of 5 mmφ, a piston cylinder type pressure cell (made by R & D Support Co., Ltd.), Fluorinert 70 and Fluorinert 77 (both made by Sumitomo 3M Co., Ltd.) as pressure transmission media, Were mixed at a ratio of 1: 1, and a sample was sealed therein.

  A conceptual diagram of the measurement test is shown in FIG. In the measurement, the sample is directly heated by a heater, and the temperature change curve at that time is measured at a plurality of measurement points to observe a three-dimensional heat flow, and the specific heat and thermal conductivity of the pressure transfer medium. The specific heat and thermal conductivity of the sample were determined by estimating the effects of A GM refrigerator (R10 Refrigerator manufactured by ULVAC, Inc.) was used for cooling.

(Measurement procedure)
At the time of measurement, in order to determine parameters of an analysis model to be described later, blank measurement in which only a heater was immersed in a pressure transmission medium was first performed. This is because the influence of specific heat and thermal conductivity of florinate is so large that it cannot be ignored. The ambient temperature (heat bath temperature) was 40 K to room temperature from the lowest measured temperature of about 10 K, and the measurement pressure range was 0 GPa to 0.45 GPa.

  Next, a heater was attached to the bottom surface of the sample, and temperature changes from the heat bath temperature were measured at three measurement points: the heater, the center of the sample bottom surface (on the heater side), and the center of the sample top surface (on the side opposite to the heater). The measurement temperature range was from the lowest measurement temperature of about 10 K to 40 K and room temperature, and the measurement pressure range was 0 GPa to 0.45 GPa.

(Measurement result)
FIG. 2, FIG. 3 and FIG. 4 show the results of a blank test using only the heater. Among these, FIG. 2 shows the measurement results in vacuum, and FIGS. 3 and 4 show the measurement results when the pressure transmission medium is sealed. The temperature change curve measured in vacuum (see FIG. 2) and the temperature change curve when the pressure transmission medium is sealed (see FIG. 3 and FIG. 4) are the latter. The point that settles to the value is very different. Similarly, after the heating is stopped, the time until the temperature is relaxed and returned to the temperature of the hot bath is much shorter than that in the vacuum. Therefore, it was confirmed that the heat leak from the heater to the pressure transmission medium is quite large.

5, 6 and 7 show the measurement results of the temperature change of the sample. Among these, FIG. 5 shows the measurement results in vacuum, and FIGS. 6 and 7 show the measurement results when the pressure transmission medium is sealed. In the figure, the gray plot shows the temperature change ΔT _H of the heater, the black plot shows the temperature change ΔT ₁ on the heater side of the sample, and the white circle plot shows the temperature change ΔT ₂ on the opposite side of the heater. For the [Delta] T _H, coated in the middle of the copper leads some data is missing due to peeling.

The following can be seen from the curve when the pressure transmission medium is sealed, unlike in a vacuum.
(1) a temperature difference of about 0.1K to a temperature change of [Delta] T ₁ and [Delta] T _H occurs. The sample and the heater were bonded with an Ag-containing adhesive having the best possible heat conduction at the present stage, but actually a temperature difference occurs. Therefore, analysis considering thermal contact is indispensable.
(2) A slight temperature difference occurs between ΔT ₁ and ΔT ₂ . Therefore, the thermal conductivity of the sample can be calculated.

(Calculation of specific heat and thermal conductivity)
Next, specific heat and thermal conductivity are calculated based on the measurement results. However, in a pressure medium, it is necessary to simulate a temperature change at each measurement point in consideration of a three-dimensional heat flow. In this example, the specific heat and thermal conductivity of the sample and the pressure medium were used as parameters, and the temporal change in temperature at the measurement point was simulated by the finite element method. Furthermore, the parameters were optimized so that the experimental results and the simulation results matched.

First, the unsteady heat conduction equation in the cylindrical coordinate system is outlined for the three-dimensional microscopic region. A minute region in the cylindrical coordinate system (r, θ, y) can be approximately represented by a rectangular parallelepiped having dr, rdθ, dy on three sides, and the change in temperature T in unit time t of the minute region is a substance that occupies the region. The density of ρ, the specific heat C, the thermal conductivity κ, and when this substance is a heating element, the calorific value per unit time is Q,
C · (dT / dt) · (ρ · dr · rdθ · dy)
= Q + (amount of heat flowing in from the outside by heat conduction per unit time)-(amount of heat flowing out from the outside by heat conduction per unit time)
It can be expressed.

  When considering an axisymmetric heat transfer problem, there is no heat flow in the θ direction, so it is sufficient to consider the amount of heat flowing in or out per unit time in the r and y directions. The governing equation of is

となる。すなわち、対称性の良い軸対称な熱の流れを考える場合には、問題が２次元（ｒ、ｙ）に帰結できる。

It becomes. That is, when considering an axially symmetric heat flow with good symmetry, the problem can result in two dimensions (r, y).

To actually calculate the temperature at each coordinate point in consideration of the three-dimensional heat flow, the entire system is divided into several minute regions (elements), and ρ, C, κ and Q are given, and the solution of Equation 1 is obtained for each element. As a method for obtaining a solution, it is impossible to calculate analytically by combining equations of all elements, and in many cases, a numerical analysis method is used. Examples of numerical analysis methods include a difference method, a finite element method, and a boundary element method. In this embodiment, the finite element method is used.

(Creation of analysis model)
FIG. 8 is a schematic configuration diagram of an analysis model of the finite element method in the present embodiment. Among these, FIG. 8a shows a three-dimensional system in which the cylindrical sample bottom surface is arranged perpendicular to the axial direction, and FIG. 8b shows a state in which this is attributed to a two-dimensional problem in consideration of axial symmetry. It is explanatory drawing shown. For the analysis, ANSYS, a finite element method analysis program manufactured by Cybernet System Co., Ltd., was used.

In the analysis, the specific heat C (C _S , C _H , C _F ), thermal conductivity κ (κ _S , κ _H , κ _F ) of each of the sample S, the heater H, and the pressure transfer medium (Fluorinert) F, Density ρ (ρ _S , ρ _H , ρ _F ) and a thermal conductivity coefficient K as a thermal contact element between the heater and the sample were given as parameters. Since the measurement result to be analyzed is a change in temperature from the heat bath temperature, an atmospheric temperature of 0K was applied in the model. The meshing was done automatically, with a total of over 200 nodes. The meshing result is shown in FIG.

(simulation)
The state of temperature change numerically calculated by the finite element method based on Equation 1 is shown in FIGS. FIG. 13 shows a plot of the time dependence of the temperature change (heater temperature change ΔT _H , temperature change ΔT ₁ on the heater side of the sample, and opposite side ΔT ₂ ) at the point corresponding to the actually measured measurement point. It was. As is apparent from the figure, it was confirmed that the shape was almost the same as the temperature change curve obtained by actual measurement (see FIGS. 6 and 7).

(Calculation of specific heat and thermal conductivity of sample)
The temperature change based on the simulation is actually measured at each base temperature as a total of 10 parameters of C _S , C _H , C _F , κ _S , κ _H , κ _F , ρ _S , ρ _H , ρ _F , K. Work was done to optimize the temperature change curve. The simplex method was used for optimization. Specifically, the density ρ _S of the sample, the density ρ _{H of} the heater, the density ρ _{F of} the fluorinate, and the thermal conductivity κ _H of the heater are substituted in advance, and the specific heat C _H of the heater is also measured in advance in a vacuum. The measured value was used as being maintained even under pressure.

First, C _F and κ _F are analyzed from the measurement result of the temperature change of only the heater. First, so as to match the results of the simulation in "height" of the temperature change curve to determine the kappa _F. Subsequently, C _F is determined so that the simulation result matches the “curve” of the curve.

FIG. 14 is a diagram in which the temperature change curve obtained by the optimization is superimposed on the measurement result of the temperature change of only the heater at room temperature and normal pressure. As can be seen from the figure, it was confirmed that both curves matched well. The parameters obtained by the analysis were C _F = 925 (mJ / Kg) and κ _F = 0.83 (mW / cmK). On the other hand, the catalog values of the specific heat and thermal conductivity of florinate under room temperature and normal pressure are C _F = 1040 (mJ / Kg) (Florinert 70 and 77), κ _F = 0.71 (mW / cmK) (Florinert 70), κ _F = 0.63 (mW / cmK) (Fluorinert 77). The specific heat of florinate obtained from the analysis was slightly smaller than the catalog value, while the thermal conductivity was larger than the catalog value. This was measured in a state where 0.3 GPa was applied at room temperature in consideration of thermal contraction of the pressure transmission medium at the time of measurement at a low temperature, so that the specific heat was reduced by pressurization and the thermal conductivity was increased. It was confirmed that the derivation method according to the present invention could withstand practical use both qualitatively and quantitatively.

Next, the same analysis was performed on the temperature change curve in the low temperature region, and the temperature dependence of C _F and κ _F was obtained. Figure 15a, the temperature dependence of the specific heat C _F of the resulting Fluorinert, Figure 15b is a graph showing the temperature dependence of the resulting thermal conductivity kappa _F. FIG. 16 is experimental data showing the temperature dependence of the specific heat of florinate obtained by the adiabatic method in the range of ˜10 K and ˜0.64 GPa (Jin Mukai, 2000 Graduate School of Science, Nagoya University) (From master's thesis). FIG. 17 is a diagram in which FIGS. 15a and 16 are combined. When attention is paid to FIG. 17 and the known specific heat C _F by the adiabatic method near 0 kBar (1 kBar = 0.1 GPa) 10 K is read, it is about 38 (mJ / gK). On the other hand, the value of the specific heat C _F near 10 K of 0 GPa determined by this simulation is slightly different from about 22 (mJ / gK). However, considering that the reliability of the result of the heat insulation method and that the heater shape is not a perfect disk shape, the embodiment is not an ideal experimental situation, it can be said that both are roughly in agreement.

Next, the thermal conductivity coefficient K between the heater and the sample, the specific heat C _{S of} the sample, and the thermal conductivity κ _S of the sample were optimized from the measurement result of the temperature change of the sample. At this time, the specific heat C _F and the thermal conductivity κ _F of Fluorinert were used by calculating the values at the necessary temperature and pressure from the calibration formula obtained by the measurement of only the heater. FIG. 18 shows a result of 0.45 GPa and a heat bath temperature of 20K as an example of optimization. Regarding the analysis of the sample, first, pay attention to the “height” of the temperature change curve, and heat conduction so that the temperature measurement results at the three measurement points coincide with the calculation results by the finite element method in the range of 10 to 20 seconds. The coefficient K and the thermal conductivity κ _S of the sample were optimized. Subsequently, increasing of the temperature change curve descending portion is to optimize the specific heat C _S of the sample to match. As is clear from the figure, as in the case of only the heater, it was confirmed that the temperature change curve based on the parameters determined by this model and the actually measured temperature change curve matched very well. .

Next, the results of the specific heat _{C S} of the obtained sample CERH ₂ Si ₂ in the analysis in Figure 19. Incidentally, also shown a plot of the absolute value of the specific heat C _S at 0 atm measured by adiabatic method in the past. As shown in the figure, it is clearly observed that the antiferromagnetic transition temperature _TN near 36 K at 0 atm of CeRh ₂ Si ₂ is suppressed to about 30 K by pressurization. This behavior is in good agreement with the temperature-pressure phase diagram (see FIG. 20) obtained from electrical resistivity measurements in the past. From the viewpoint of the absolute value, it was confirmed that the temperature above the transition point, for example, 0.45 GPa at 40 K, which is not affected by the transition, was compared with the data obtained by the adiabatic method, so that they agreed very well. . Therefore, it can be said that the absolute value of the physical property value can also be derived according to the present invention.

FIG. 21 shows the analysis result of the thermal conductivity κ _S of CeRh ₂ Si ₂ . Regarding thermal conductivity, it is difficult to measure at normal pressure, and there is no comparable data for this material. However, since the features such as the absolute value and the slight increase in thermal conductivity κ _S at the magnetic transition point are consistent with those of other Ce compounds, the results are sufficiently reliable. I can say that.

  By using the present invention, for example, the behavior of a substance such as the seabed, the analysis of a planetary or stellar substance can be performed.

It is the figure which showed the conceptual diagram of the measurement test. It is the figure which showed the result of the blank test of only a heater (in a vacuum). It is the figure which showed the result of the blank test of only a heater (0GPa). It is the figure which showed the result of the blank test of only a heater (0.45GPa). It is the figure which showed the measurement result of the temperature change of a sample (in a vacuum). It is the figure which showed the measurement result of the temperature change of a sample (0GPa). It is the figure which showed the measurement result of the temperature change of a sample (0.45GPa). It is a schematic block diagram of the analysis model of a present Example. It is the figure which showed the meshing result. It is the figure which showed the mode of the temperature change numerically calculated by the finite element method based on Formula 1. FIG. It is the figure which showed the mode of the temperature change numerically calculated by the finite element method based on Formula 1. FIG. It is the figure which showed the mode of the temperature change numerically calculated by the finite element method based on Formula 1. FIG. It is the figure which showed a mode that the temperature change of the point corresponding to the measurement point of measurement was plotted. It is the figure which overlapped and drawn the temperature change curve obtained by optimization on the measurement result (circle mark) of the temperature change of only a heater under room temperature and normal pressure. It is the figure which showed the temperature dependence of the specific heat _CF and the thermal conductivity (kappa) _F of the fluorinate obtained by analysis. It is the experimental data which showed the temperature dependence of the specific heat of the fluorinate obtained by the heat insulation method in the range of -10K and -0.64GPa. It is the figure which synthesize | combined FIG. 15a and FIG. It is the figure which showed the result of 0.45 GPa and base temperature 40K as an example of optimization. It is a diagram showing temperature dependence of the specific heat _{C S} of the obtained sample CERH ₂ Si ₂ in the analysis. It is a temperature-pressure phase diagram of the antiferromagnetic transition temperature _TN obtained from electrical resistivity measurement. CeRh is a diagram showing an analysis result of the ₂ Si ₂ thermal conductivity kappa _S. It is the figure which showed the measuring device outline | summary of the heat insulation method. It is the figure which showed the measurement outline | summary of the relaxation method. It is the figure which showed the measurement outline | summary of the stationary method.

Claims (4)

A measurement method in which a pressure transfer medium and a measurement target sample in contact with a heat source are enclosed in a pressure vessel that is a heat bath, and the specific heat and thermal conductivity of the sample are simultaneously measured under pressure,
Measure the time change in temperature of at least three measurement points, one point on the heat source and two points that are not equivalent in terms of heat conduction on the sample, in the process from the start or end of heating by the heat source to the steady state,
A numerical analysis model simulating this measurement system is constructed based on the unsteady heat conduction equation that takes into account heat propagation in the pressure transfer medium,
Using the model, the specific heat of the sample, the thermal conductivity, and the relationship between the sample and the heat source so that the temperature change at the point corresponding to the measurement point draws the same temperature change curve as the actual temperature change at the measurement point. A method for measuring specific heat and thermal conductivity, characterized in that the thermal conductivity coefficient is determined by numerical analysis.   2. The specific heat according to claim 1, wherein the sample is formed symmetrically, and the arrangement of the sample in the pressure vessel, the arrangement of the heat source on the sample, and the arrangement of the measurement points are symmetric along the sample. And measuring method of thermal conductivity. The pressure vessel is cylindrical and the sample is processed into a cylindrical shape, and the sample is placed in the pressure vessel so that the central axis of the pressure vessel and the central axis of the sample coincide.
Join the heat source to the center of the bottom of the sample,
The method for measuring specific heat and thermal conductivity according to claim 1, wherein the measurement point is provided on a central axis. 4. The specific heat and thermal conductivity measuring method according to claim 1, 2, or 3, wherein a finite element method, a finite difference method, or a boundary element method is used as the numerical analysis method.

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