JP5610529B2 - Specific heat measurement method and thermal conductivity measurement method - Google Patents

Description

  The present invention relates to a specific heat measurement method and a thermal conductivity measurement method.

  In the field of physical physics, the electrical, magnetic, thermal, and other properties of solids are measured, the interrelation between these properties is clarified, and the properties of materials are understood. A phase transition phenomenon is one of them, and a specific heat measurement experiment is generally performed to observe a superconducting transition, a magnetic phase transition, a structural phase transition, and the like. When the temperature dependence of the specific heat is measured, the specific heat radiates at the transition point if the phase transition is the first order, and a discontinuous jump occurs in the specific heat at the transition point if the phase transition is the second order. Thus, measurement of specific heat is the most effective means for confirming the evidence of phase transition and determining the transition temperature and determining the order of the transition. However, since the specific heat is basically a temperature differential of the amount of heat, the specific heat measurement experiment has a difficulty that an error becomes large. Further, in general, heat measurement is characterized in that it takes longer time than electricity or magnetic measurement.

 Specific heat measurement methods can be broadly classified into two methods, adiabatic methods and thermal relaxation methods. Since the present invention is a kind of thermal relaxation method, the thermal relaxation method will be described below. Non-patent document 1, pages 92 to 94 and non-patent document 2 describe the specific heat measurement technique using the thermal relaxation method. In the thermal relaxation method, after the sample is loosely thermally bonded to a heat bath having a large heat capacity via a thermal bond, the sample is heated to raise the temperature to be higher than that of the heat bath, and after heating is turned off. Specific heat can be measured from the cooling rate and the thermal conductivity of the thermal combination.

Conventionally, the most commonly used configuration in the thermal relaxation method is as shown in FIG. In this measurement system, a thermometer is installed in a sample (mass m, volume V), and the sample is loosely thermally coupled to a heat bath via a thermal coupling body having a thermal conductivity K (constant). The atmosphere is evacuated so that no heat escapes through the part other than the thermal coupling body. The temperature of the heat bath is controlled to the temperature T ₀ by balancing the amount of heat that escapes to the low temperature heat source by controlling the amount of heat applied to the heat bath from the heat bath heater. Then, as shown in FIG. 2, a small amount of heat is given to the sample by the heater, the temperature of the sample is slightly increased by ΔT ₀ , and then the heating is stopped, and the temperature increase ΔT is relaxed by the following equation toward T _0. Then, the relaxation time τ is measured, and the specific heat c at the temperature T ₀ is obtained from the relational expression of c = τK / m or c = τK / V. It should be noted that the width of ΔT ₀ is so narrow that the temperature dependence of the heat transfer degree K can be ignored within the temperature range and can be regarded as constant.

Then slightly raise the temperature T ₀ of the thermal bath by heat bath heater, perform the same measurements. Thus in to each temperature was measured 1 point specific heat slightly raising the temperature T _0, go repeat the same measurement, measurement is carried out over a predetermined temperature range.

An important problem in this measurement method is that, since the conventional thermal relaxation method obtains the specific heat based on the above equation, it is necessary to calculate the thermal conductivity of the thermal coupling body during thermal relaxation as a constant K. Since thermal conductivity that is generally a strong temperature dependence, reduced to the temperature rise [Delta] T ₀ from T ₀ only (e.g. 0.1 K), measured by regarding the temperature of the entire thermal coupling body and substantially uniform is performed. Therefore, for example, in order to measure the specific heat of 4K to 40K, it is necessary to repeat this measurement 360 times. As a result, the measurement takes a long time of 2 to 3 days, and the data becomes discrete.

The measurement of the thermal conductivity by the conventional steady method is performed with the configuration of FIG. One end of the sample is brought into thermal contact with a high temperature hot bath equipped with a thermometer and a heater, and the other end is brought into thermal contact with a low temperature hot bath whose temperature is controlled to T ₀ by the hot bath heater. If there is a large thermal resistance at the thermal contact portion between the both ends of the sample and the high temperature heat bath and low temperature bath heat, two thermometers may be installed near the both ends on the sample. Next, the atmosphere is evacuated so that heat does not flow out of the high temperature heat bath through parts other than the sample. Then, the temperature of the high temperature heat bath is slightly higher than that of the low temperature heat bath by ΔT ₀ , and a heat flow with a constant heat flow rate dQ / dt is generated in the sample. At this time, the thermal conductivity κ at that temperature can be calculated by the following equation.

 Here, S is the cross-sectional area of the cross section perpendicular to the heat flow of the sample, and L is the length of the sample. This equation is described on page 55 of Non-Patent Document 1.

Then, the temperature T ₀ of the low-temperature heat bath slightly higher by the heat bath heater, moves to the next measurement temperature, the same measurement as above. This is repeated to measure the thermal conductivity κ in a predetermined temperature range.

An important problem in this measurement is that, like the specific heat measurement, ΔT _{0 is set} to be small (for example, 0.1 K), the heat flow rate dQ / dt is made constant, and the heat conductivity κ is assumed to be constant, so that the measurement is performed from 4K to The measurement in the temperature range of 40K takes a long time of 2 to 3 days, and the data becomes discrete.

Shunichi Kobayashi, Yoichi Otsuka, Low Temperature Technology (2nd edition), The University of Tokyo Press, 1987 Mitsuharu Nagasawa, Precise measurement of specific heat in the medium and low temperature range of small organic conductor single crystals, Tokyo Denki University Research Institute Annual Report, No. 28 (2008)

JP-A-6-201490 JP 2006-64413 A

  As described above, when the specific heat is measured in a wide temperature range by applying heat to the sample once with a heater as in the conventional thermal relaxation method, since the measurement points are discrete, there is no difference between one measurement point and the next measurement point. When a phase transition point is located between them, there is a risk of missing a specific heat peak or jump based on the phase transition. FIG. 4 is an example of the measurement result of the magnetic specific heat measured by Tatsukazu Hamasaki with a physical property measuring device (PPMS) published on page 153 of the 22nd line of the Kyushu Sangyo University Faculty of International Studies in 2002. In FIG. 4, it appears that there is a magnetic phase transition point at the arrow, but it is not so clear due to the low data density. Also from this measurement result, it can be seen that when the conventional relaxation method is used, it takes time, so that the measurement interval is wide and the data becomes discrete. Further, in the conventional relaxation method, it takes at least 20 to 30 minutes to measure the specific heat at one point. Therefore, in order to measure in the wide temperature range of 2 to 16 K shown in FIG. Needed.

  An object of the present invention is to provide a specific heat measurement method capable of continuously measuring the specific heat of a sample over a wide temperature range in a short time, instead of measuring one point at a time by repeating heating and cooling. It is in.

  Another object of the present invention is to have the same configuration as this specific heat measurement method, and continuously measure the thermal conductivity of the sample in a wide temperature range in a short time without measuring one point at a time as in the conventional steady-state method. It is in providing the thermal conductivity measuring method which can be measured automatically.

In the specific heat measurement method of the present invention, the specific heat is measured from the relaxation rate of the temperature when the sample is thermally relaxed through a thermal bond having a known thermal conductivity κ. First, a sample having an unknown specific heat c is thermally coupled to a heat bath having a temperature _TL via a thermal coupling body having a known temperature dependence function κ (T) of thermal conductivity κ. And stopping the heating after heating the sample up to a maximum temperature T _H of the predetermined temperature range. Thereafter, the temperature T of the sample is measured as a function of time t until the temperature of the sample reaches the minimum temperature _TL within a predetermined temperature range. Further, the time differential dT / dt of the temperature T is obtained from the measurement result of the temperature T of the sample versus the time t. Then, the time differential dQ / dt of the heat flow Q flowing through the thermal coupling body in the process from the maximum temperature _TH to the minimum temperature _TL is obtained based on the following equation.

  In the above formula, L is the length of the thermal coupling body, and S is the cross-sectional area of the cross section in the direction perpendicular to the heat flow of the thermal coupling body. In the present invention, using the results of the time derivative dT / dt of the temperature of the sample and the time derivative dQ / dt of the heat flow Q, the heat capacity C of the sample is obtained by the equation C = (dQ / dt) / (dT / dt). The specific heat c is obtained by dividing the heat capacity C by the amount of material of the sample (such as mass m or volume V or number of moles M).

  The specific heat measurement method of the present invention is essentially different from the conventional thermal relaxation method in that the conventional thermal relaxation method obtains the specific heat based on the above equation while keeping the thermal conductivity of the thermal coupling constant. In the invention, the specific heat is measured after the heat flow rate dQ / dt is obtained based on the above-mentioned equation, assuming that the thermal conductivity of the thermal coupling body is temperature dependent. As a result, a much wider temperature range can be measured with a single thermal relaxation compared to the conventional thermal relaxation method, and continuous data can be obtained, so that specific heat peaks and jumps are not missed.

  Note that the time difference ΔT / Δt of the temperature T is obtained instead of the time derivative dT / dt of the temperature T, and the heat capacity C of the sample is calculated as C = (dQ / dt) using the result of the time differentiation dQ / dt of the heat flow Q. It is also possible to obtain the specific heat c by obtaining it by the equation of / (ΔT / Δt) and dividing this heat capacity C by the amount of material of the sample (mass m or volume V or mole number M or the like).

  The integral in the above formula may be obtained by numerical integration or by analytical integration. Ideally, the thermometer and the heater are installed directly on the sample. However, if it is difficult to install the thermometer and the heater directly because the sample is small, it may be installed on the sample stage on which the sample is placed. In this case, it is necessary to subtract the heat capacity of the sample stage + thermometer + heater from the measured heat capacity. In addition, you may make it measure temperature by measuring the temperature of a sample indirectly like a thermography thermometer. The sample may be heated indirectly such as by light irradiation. Furthermore, the thermometer and the heater may be constituted by a single resistor. In this case, since the ratio of the heat capacity of the part other than the sample to the heat capacity of the sample is reduced, the accuracy is improved.

In the thermal conductivity measuring method of the present invention, the thermal conductivity of the sample is measured in a predetermined temperature range (T _{L to} T _H ) in a vacuum atmosphere. First, a material whose temperature dependency of the heat capacity C is known is thermally coupled to a heat bath having a temperature _TL via a sample whose temperature dependence function κ (T) is unknown. And stopping the heating after heating the material to a maximum temperature T _H of the predetermined temperature range. Thereafter, the temperature T of the material is measured as a function of time t until the temperature of the material reaches a minimum temperature _TL within a predetermined temperature range. Further, the time differential dT / dt of the temperature T is obtained from the measurement result of the temperature T of the material versus the time t. Then obtained by equation maximum temperature _{T H} of the hot bath temperature _{T L} of the time derivative of the heat flow Q flowing through the sample in the process leading to the dQ / dt = C (dT / dt). Next, the obtained time derivative dQ / dt is substituted into the following equation, and the temperature dependence κ (T) of the thermal conductivity of the sample is measured.

  In the above formula, L is the length of the thermal coupling body, and S is the cross-sectional area of the cross section perpendicular to the heat flow of the thermal coupling body.

Note that the time difference ΔT / Δt of the temperature T is obtained instead of the time derivative dT / dt of the temperature T, and the time difference ΔQ / Δt = C (ΔT of the heat flow Q flowing through the sample instead of the time derivative dQ / dt of the heat flow Q. / Δt) may be obtained, and the obtained time difference ΔQ / Δt may be substituted into the following equation to obtain the temperature dependence κ (T) of the thermal conductivity of the sample.

  According to the measurement method of the present invention, since the heat transfer coefficient can be measured as continuous data, a slight change or a sudden change in the heat conductivity is not overlooked. The time required for the measurement can be as long as several days in the conventional stationary method, whereas the measurement can be completed in about 50 minutes, for example.

It is a schematic diagram showing the specific heat measurement system by the conventional thermal relaxation method. It is a schematic diagram showing the specific heat measurement principle by the conventional thermal relaxation method. It is a schematic diagram showing the thermal conductivity measuring method by the conventional stationary method. Conventional thermal relaxation method is the temperature change of the specific heat of the measured _{Ni 0.71 Mn 0.29 C l2 · 2H} 2 O with. It is a schematic diagram showing the specific heat measuring system for enforcing the specific heat measuring method of this invention. It is a schematic diagram showing the specific heat measurement principle by this invention. It is the schematic of the structure of the measurement system for enforcing the specific heat measuring method of this invention. It is a cooling curve when the ferromagnetic ErNi is cooled from 40K to 3.7K. A bending point based on a large change in specific heat can be seen at 10.5K. It is the temperature dependence of the specific heat of ErNi obtained from FIG. A specific heat peak based on the ferromagnetic transition is observed at 10.5K. It is the absolute temperature dependence of the specific heat of lead measured based on this invention. A small specific heat jump based on the superconducting transition is observed at 7.2K. FIG. 10 is a diagram in which a value obtained by dividing the specific heat of lead in FIG. 9 by the square of the absolute temperature is plotted against the square of the absolute temperature in order to make it easy to see the jump of the specific heat. It is the schematic of the structure of the measurement system for enforcing the thermal conductivity measuring method of this invention. It is a figure showing a temperature change when the material 21 cools through a stainless steel sample. It is the temperature dependence of the thermal conductivity of the stainless steel sample obtained from FIG.

  Embodiments of a specific heat measurement method and a thermal conductivity measurement method of the present invention for measuring specific heat in a predetermined temperature range will be described below in detail with reference to the drawings. FIG. 5 is a diagram showing an outline of the configuration of a specific heat measurement system for carrying out the specific heat measurement method of the present invention. In FIG. 5, the member indicated by reference numeral 1 is a sample whose specific heat c is unknown, and the member indicated by reference numeral 2 is a thermometer that measures the temperature of the sample 1. The member denoted by reference numeral 3 is a thermal coupling body whose temperature dependence function κ (T) of the thermal conductivity κ is known. A member denoted by reference numeral 4 is a heat bath thermally coupled to the sample 1 through the thermal coupling body 3. The member indicated by reference numeral 5 is a heater made of a resistor that can uniformly heat the sample 1, and the member indicated by reference numeral 6 is a hot bath heater that heats the hot bath 4. The heat bath 4 is thermally coupled to a low temperature heat source 7. As the low-temperature heat source 7, a cryogenic cryocooler (GM refrigerator) that generates refrigeration by repeatedly compressing and expanding helium gas can be used.

First, a heat bath 4 having a temperature T _L is prepared, and a predetermined temperature range T _{L to} T _H (where T _L <T _H ) to be measured is set. Next, as shown in FIG. 5, a sample 1 with an unknown heat capacity C (T) is applied to a thermal coupling body 3 with a known temperature dependence function κ (T) of thermal conductivity κ (the cross-sectional area perpendicular to the heat flow is It is heat-bonded loosely to the heat bath 4 via the heat flow direction). Then, the atmosphere of the sample 1 in terms of the thermal insulation in the vacuum, heating was stopped after heating the sample 1 to a maximum temperature T _H of the predetermined temperature range, then the temperature of the sample 1 is the temperature T _L of the heat bath During the cooling to the temperature t, the temperature T of the sample 1 is measured and recorded with respect to the time t by the thermometer 2 as shown in FIG. Next, the time differential dT / dt of the temperature T is obtained from the measurement result of the temperature T of the sample 1 versus time t. However, the time differential dT / dt in FIG. 6 expresses the width of dT and dt large for easy viewing.

Further, the length of the thermal coupling body 3 is L, the cross-sectional area of the cross section perpendicular to the heat flow of the thermal coupling body 3 is S, the temperature dependence function of the thermal conductivity of the thermal coupling body is κ (T), and the temperature T _H The time derivative dQ / dt of the heat flow Q flowing through the thermal coupling body 3 in the cooling process from the temperature _TL to the temperature _TL is obtained based on the following equation (3). The following formula (3) is described on page 57 of Non-Patent Document 1. At this time, the temperature integration of the thermal conductivity κ (T) of the thermal coupling body may be numerically integrated using the value of κ (T) measured at each temperature in advance by experiments. Alternatively, in the case of a pure metal such as copper, it is theoretically known that the thermal conductivity at a low temperature is expressed by κ (T) = AT, where A is a constant. It may be integrated analytically.

The following equation (3) is inherently established in a steady state, and an error occurs when the temperature of the sample is changing. However, if the temperature change of the sample is slow, an error is caused even in the steady state. It turns out to be small enough to be ignored. Of course, this calculation is performed before the calculation of specific heat.

Then, the time differential dT / dt of the measured temperature T and dQ / dt calculated by the above equation (3) are substituted into the following equation (4) to obtain the specific heat c (T).

  Here, m is the mass of the sample. The volume V or the number of moles M may be used instead of the mass m in the above formula (4).

  The specific heat measurement method of the present embodiment is essentially different from the conventional thermal relaxation method in that the conventional thermal relaxation method obtains the specific heat based on the above equation (1) while keeping the thermal conductivity of the thermal conjugate constant. On the other hand, in this embodiment, the specific heat is measured after obtaining the heat flow rate dQ / dt based on the above equation (3) on the premise that the thermal conductivity of the thermal coupling body is temperature dependent. As a result, a much wider temperature range can be measured with a single thermal relaxation as compared with the conventional thermal relaxation method. For example, the time required to measure the temperature range of 4K to 40K takes about 2 to 3 days in the conventional relaxation method, but according to the present invention, it can be completed in about 30 minutes. . In addition, according to the present embodiment, the specific heat data obtained is not discrete data but continuous data, so even a very small specific heat peak associated with the phase transition phenomenon can be detected with extremely high accuracy. It becomes possible.

The process of calculating the specific heat from the measurement data may be performed in real time during the measurement, or may be performed collectively after all the data has been collected. Although the predetermined temperature range is arbitrary, the temperature range can be a wide range within which the thermal conductivity of the thermal coupling body has temperature dependence and cannot be regarded as constant. This is a feature of the method of the embodiment and is essentially different from the conventional thermal relaxation method. For example, as a typical example, at a temperature T _L of the heat bath 4 is 4K, the maximum temperature T _H is determined temperature range so that the order of 40K, when to using thermal coupling body 3 of stainless steel, the thermal conductivity is temperature Since it changes 15 times from 0.25 W / m · K at 4 K to 4.5 W / m · K at a temperature of 40 K, the thermal conductivity cannot be considered constant. This temperature range is set much larger than the thermal relaxation range of about 0.1 K in the conventional thermal relaxation method.

  Note that the time difference ΔT / Δt of the temperature T is obtained instead of the time derivative dT / dt of the temperature T, and the heat capacity C of the sample is calculated as C = (dQ / dt) using the result of the time differentiation dQ / dt of the heat flow Q. It is also possible to obtain the specific heat c by obtaining it by the equation of / (ΔT / Δt) and dividing this heat capacity C by the amount of material of the sample (mass m or volume V or mole number M or the like).

FIG. 7 is a diagram showing an outline of an example of an actual configuration of a specific heat measurement system for carrying out the specific heat measurement method of the present invention. In FIG. 7, the same members as those shown in FIG. 5 are given the same reference numerals as the constituent members shown in FIG. 5 plus the number of ten. The member denoted by reference numeral 11 is a sample whose specific heat c (T) is unknown, and the sample 11 is placed on the upper surface of a copper sample stage 18 having high thermal conductivity in thermal contact with a small amount of grease. Yes. The sample stage 18 in this example has a size of 6 × 6 × 0.1 mm ³ . On the lower surface of the sample stage 18, a ruthenium oxide resistance thermometer 12 that indirectly measures the temperature of the sample 11 via the sample stage 18 and a heater 15 made of a ruthenium oxide resistor are fixed. The sample stage 18 is coupled to a large copper heat bath 14 by a stainless steel thermal coupling body 13 having a known temperature dependence function κ (T) of thermal conductivity. The thermal coupling body 13 is composed of four stainless rods having a diameter of 0.1 mm and a length of 6 mm. The heat bath 14 has a cylindrical shape, and the sample stage 18 is installed on the opening of the heat bath 14 by the thermal coupling body 13. A hot bath heater 16 made of a manganin resistor is wound around the hot bath 14. The heat bath 14 is connected to a second stage 17 of a cryogenic mechanical small refrigerator (GM refrigerator) that generates refrigeration by repeatedly compressing and expanding helium gas. The second stage 17 of the refrigerator constitutes the low-temperature heat source 7 of FIG. A copper radiation shield 19 that prevents the temperature of the sample 11 from rising due to thermal radiation from the surroundings is disposed on the heat bath 14 so as to surround the sample. In FIG. 7, the radiation shield 19 is depicted as being transparent for easy understanding.

 In the present embodiment, both the resistance thermometer 12 and the heater 15 are ruthenium oxide resistors. The resistance thermometer 12 uses a resistor whose resistance value changes with temperature as a temperature sensor. Since these need not be used at the same time, it is a matter of course that only one resistor that serves both as a thermometer and a heater may be disposed on the lower surface of the sample stage 18.

In the present embodiment, first, the sample 11 whose specific heat c (T) is unknown is connected to the heat bath 14 via the thermal coupling body 13 whose temperature dependence function κ (T) is known. And stopping the heating after heating the sample 1 to a maximum temperature T _H of the predetermined temperature range by using a heater 15. Thereafter, while the temperature of the sample 11 is cooled to the temperature _TL of the heat bath 14, the temperature T of the sample is measured using the thermometer 12 at predetermined time intervals. Further, the length of the thermal coupling body 13 is L, the cross-sectional area is S, the temperature dependence function of thermal conductivity is κ (T), and the heat flow Q flowing through the thermal coupling body 4 in the process from the temperature _TH to the temperature _TL is shown. The time derivative dQ / dt is obtained based on the above equation (3). Since the temperature dependence function κ (T) of the thermal conductivity κ is already known for the thermal coupling body 13, the calculation of the time derivative dQ / dt of the heat flow Q can be performed before the temperature measurement.

  The temperature dependence κ (T) of the thermal conductivity of each substance is described, for example, on page 56 of Non-Patent Document 1.

  In this embodiment, the specific heat of the sample is continuously measured over the predetermined temperature range based on the equation (4). As a result, even a very small specific heat peak associated with the transition phenomenon can be detected with extremely high accuracy. The time required for the measurement takes about one day in the conventional relaxation method, whereas according to the present invention, the measurement of the specific heat in a predetermined temperature range can be completed in about 30 minutes, for example.

  Actually, the measured heat capacity includes the heat capacity of the sample stage, heater, thermometer, etc. (referred to as an adder) on which the sample is placed. Subtract from the measured value.

  In the measurement of the present invention, when recording temperature T vs. time t in an analog manner such as a pen recorder, continuous measurement is performed. However, in the case of digital recording, recording is performed at predetermined sampling time intervals. Therefore, the differential dT / dt is replaced with a difference ΔT / Δt obtained by dividing the temperature change ΔT by a finite sampling time interval Δt.

The predetermined temperature range is arbitrary, but it is a feature of the present invention that the thermal conductivity of the thermal coupling body is temperature-dependent within that temperature range and is not regarded as constant. This is essentially different from the thermal relaxation method. For example, as a typical example, at a temperature T _L of the thermal bath is 4K, T _H is determined temperature range so that the order of 40K, when to using thermal coupling of stainless, 0 thermal conductivity at a temperature 4K It changes 15 times from 25 W / m · K to 4.5 W / m · K at a temperature of 40 K and cannot be regarded as constant. This temperature range is set much larger than the typical thermal relaxation range of about 0.1 K in the thermal relaxation method.

Next, the results of actual measurement of specific heat using the specific heat measurement method of the present embodiment will be described. In FIG. 8, 37.2 mg of ErNi alloy, which is a magnetic regenerator material for cryogenic temperature, is used as the sample 11, a stainless steel wire is used as the thermal coupling body 13, the temperature of the heat bath T _L = 3.7 K, and the maximum temperature T _H. = The relationship between the change in temperature T and time t when the sample 11 is heated and relaxed to 40K is digitally recorded at a time interval of 2 seconds. FIG. 9 shows the relationship between the specific heat c (T) and the temperature T obtained using the equations (3) and (4) based on FIG. However, since the temperature is recorded digitally, the difference ΔT / Δt is used instead of the differential dT / dt in the equation (4). As is clear from FIG. 9, the measured specific heat clearly shows a ferromagnetic magnetic phase transition as a large peak at 10.5K. The time taken to obtain the measurement result of FIG. 9 is about 30 minutes. The curve in this graph is actually a set of points, but it can be regarded as a continuous curve because the measurement points are closely spaced. Since the graph is represented by a substantially continuous curve in this way, a small specific heat peak or jump is not overlooked.

Further, FIG. 10 shows the result of measuring specific heat by using the same method as ErNi between T _H = 12K and T _L = 3.7K using 73.0 mg of lead (Pb) as the sample 11 (the absolute value of specific heat c and absolute value). (Relationship with temperature T). There is a superconducting transition point at the position of the arrow in FIG. In order to make the data in FIG. 10 locally enlarged and easy to see, the specific heat c divided by the square of the absolute temperature T (c / T ² ) was re-plotted against the square of the absolute temperature T (T ² ). Things are displayed in FIG. From FIG. 11, the jump of specific heat based on the superconducting transition can be clearly seen. The time required to obtain the measurement result of FIG. 10 was only about 6 minutes.

  From the above test results, according to the embodiment of the present invention, the specific heat can be measured in a short time, and the existence of a very small specific heat jump that cannot be seen between the data points by the conventional relaxation method. It can be seen that the specific heat can be measured with high accuracy and precise data density so that the above can be confirmed. The amount of the sample can also be measured with a minute amount of several tens mg.

  Next, an embodiment of the thermal conductivity measuring method of the present invention will be described with reference to FIG. FIG. 12 is a diagram showing an outline of the configuration of a thermal conductivity measurement system for carrying out the thermal conductivity measurement method of the present invention. In FIG. 12, a member denoted by reference numeral 21 is a material whose temperature dependence function C (T) of heat capacity is known. In this embodiment, 1.10 g of copper is used as the material 21. The material 21 is arbitrary, but a material such as copper or silver that has no abnormalities such as phase transition within a predetermined temperature range and whose heat capacity changes smoothly with respect to temperature is desirable. This is because if there is a phase transition, there is a rapid change in temperature in the vicinity of the transition point, which has a considerable effect on the measurement result. Further, it is desirable that the thermal conductivity of the material 21 is large so that the temperature of the entire material 21 is uniform. If the cooling rate of the material 21 is too slow, the rate of heat escaping through parts other than the sample 23 increases, and the error increases. On the contrary, if the cooling rate of the material 21 is fast, the degree of non-equilibrium becomes large, such as a temperature gradient in the material 21, and the error in the following equation (5) or (6) for obtaining the temperature dependent function κ (T) increases. . Since the cooling rate is determined by the balance between the heat capacity of the material 21 and the thermal conductivity of the sample 23, it is preferable to adjust the cross-sectional area S and the length L of the sample 23 so as to obtain an appropriate cooling rate.

Also in the present embodiment, ruthenium oxide is used as the thermometer 22 for measuring the temperature of the material 21. The stage 28 is a copper stage on which the material 21 is placed. The stage 28 is installed at the opening of the heat bath 24 by a sample (thermal coupling body) 23 whose temperature dependence κ (T) of thermal conductivity is unknown. The sample 23 is a stainless rod having a length of 6 mm and a cross-sectional area of 3.1 × 10 ⁻² mm ² (when converted to one). The heat bath 24 and the second stage (temperature 3.7K) 27 of the GM refrigerator are the same as those shown in FIG. The heater 25 is an electric heater that can uniformly heat the material 21 and is composed of a ruthenium oxide resistor. Since the thermometer 22, the heater 26, and the stage 28 on which the material 21 is placed are all smaller in size than the material 11, the heat capacity can be ignored. The member denoted by reference numeral 26 is a hot bath heater, and the member denoted by reference numeral 29 is a radiation shield.

In a specific thermal conductivity measurement method using the configuration of FIG. 12, first, the temperature of the heat bath 24 is set to a temperature T _L, and a predetermined temperature range T _{L to} T _H to be measured (T _L <T _H ) Set. The sample 23 whose thermal conductivity is to be measured needs to be processed into an elongated shape with a constant cross-sectional area. One end of the sample is thermally coupled to the heat bath 24, and the other end is thermally coupled to the material 21 having a high thermal conductivity through a stage 28 equipped with a heater 25 and a thermometer 22. The temperature dependence function C (T) of the heat capacity of the material 21 on the stage 28 to which the heater 25 and the thermometer 22 are attached is obtained in advance from another experiment. And the atmosphere of the sample 23 in terms of the thermal insulation as a vacuum, heating is stopped after the temperature of the material 21 is heated by the heater 25 to a maximum temperature T _H of the predetermined temperature range. Then, the temperature T of the material 21 is measured with respect to time until the temperature of the material 21 reaches the temperature _{TL of the} heat bath. Then, a time differential dT / dt of the temperature T is obtained from the measurement result of the temperature T of the material 21 versus time t. Further, the time differential dQ / dt of the heat flow Q flowing through the sample 23 in the process from the maximum temperature _TH to the temperature _TL of the heat bath 24 is obtained by the equation dQ / dt = C (T) (dT / dt). By substituting this dQ / dt into the following equation (5), the temperature dependence κ (T) of the thermal conductivity of the sample is measured.

  Here, L represents the length of the sample, and S represents the cross-sectional area of the sample. The above equation (5) can be obtained by differentiating both sides of the above equation (3) with respect to the temperature T to obtain dQ / dt.

As with the specific heat measurement, the recording of temperature T vs. time t is continuous when analog recording such as a pen recorder is performed, but when digital recording is performed, recording is performed at predetermined sampling time intervals. Therefore, the differential d (dQ / dt) / dT in the equation (5) is replaced with the difference Δ (ΔQ / Δt) / ΔT. In this case, the time difference ΔT / Δt of the temperature T is obtained instead of the time derivative dT / dt of the temperature T, and the time difference ΔQ / Δt of the heat flow Q flowing through the sample instead of the time derivative dQ / dt of the heat flow Q = C (ΔT / Δt) may be obtained, and the obtained time difference ΔQ / Δt may be substituted into the following equation (6) to measure the temperature dependence κ (T) of the thermal conductivity of the sample.

 In the thermal conductivity measurement method of the present embodiment, the thermal conductivity is measured on the assumption that the heat capacity of the material 21 connected to the heat bath 24 via the sample (thermal coupling body) 23 is known.

 The thermal conductivity measurement method of the present embodiment is essentially different from the conventional steady-state method in that the conventional steady-state method assumes that the thermal conductivity of the entire sample is constant by setting the temperature difference across the sample small. Whereas the measurement is performed by calculation, in this measurement method, it is assumed that the temperature difference between both ends of the sample is set large and the thermal conductivity of the sample is temperature-dependent, based on the above formula (5) or (6). This is the point at which the rate is measured. As a result, in the measurement in the temperature range of 4K to 40K, for example, the conventional measurement results in 360-point discrete data as measured at 0.1K increments, whereas the measurement method of the present embodiment provides continuous data. It can be measured as data. Further, the time required for the measurement can be completed in about 50 minutes, while the conventional steady-state method takes a long time of several days.

In this case as well, the predetermined temperature range is arbitrary, but the temperature range can be set so wide that the thermal conductivity of the sample cannot be considered constant. For example stainless steel used as a sample 23, the temperature _{T L} of the heat bath 24 is 4K, the maximum temperature _{T H} defines the temperature range to be approximately 40K, the thermal conductivity of 0.25 W / m · K at a temperature 4K 15 times from 4.5 W / m · K at a temperature of 40K. However, in the measurement method of the present embodiment using the above formula (5) or (6), the temperature dependence of the thermal conductivity is measured even when the thermal conductivity changes significantly as described above. can do.

In this embodiment, stainless steel is used as the sample 23, and the time change of the temperature when the material 21 is cooled from T _H = 36K to T _L = 4K is measured and recorded at intervals of 2 seconds as shown in FIG. . From FIG. 13, ΔQ / Δt was calculated from the equation dQ / dt = C (T) (dT / dt), and the result of calculating the thermal conductivity by substituting it into the equation (6) is shown in FIG. Show good agreement.

 From this measurement result, according to this Embodiment, a measurement result can be shown as substantially continuous data. On the other hand, in the measurement using the conventional steady method, discrete measurement data is obtained. Therefore, according to the present embodiment, even when there are small discontinuities and inflection points in the temperature dependence graph of thermal conductivity, the temperature of the thermal conductivity of the sample 23 can be detected with higher accuracy than the conventional method. The dependence κ (T) can be measured continuously.

  According to the present invention, specific heat and thermal conductivity can be measured as continuous data rather than discrete data. Therefore, even a very small specific heat peak associated with the transition phenomenon can be detected with very high accuracy without overlooking it. Further, the time required for the measurement takes about 1 day to several days in the specific heat measurement by the conventional thermal relaxation method and the thermal conductivity measurement by the steady method, but according to the present invention, the predetermined time is within a few tens of minutes. Measurement of specific heat and thermal conductivity in the temperature range can be completed.

DESCRIPTION OF SYMBOLS 11 Sample 12,22 Thermometer 13 Thermal coupling body 14,24 Heat bath 15,25 Heater heater 16,26 Heat bath heater 17,27 Second stage of GM refrigerator 18 Sample stage 19,29 Radiation shield 21 Material 23 Sample (heat Combined)
28 stages

Claims (12)

A specific heat measurement method for measuring specific heat of a sample in a predetermined temperature range (T _{L to} T _H ) in a vacuum atmosphere,
The sample having an unknown specific heat c is thermally coupled to a heat bath having a temperature _TL via a thermal coupling body having a known temperature-dependent function κ (T) of thermal conductivity κ.
The maximum temperature T _H of the predetermined temperature range the heating was stopped after heating the sample,
Thereafter, the temperature T of the sample is measured as a function of time t until the temperature of the sample reaches the lowest temperature _TL in the predetermined temperature range,
From the measurement result of the temperature T of the sample versus time t, the time derivative dT / dt of the temperature T is obtained,
A time derivative dQ / dt of the heat flow Q flowing through the thermal coupling body in the process from the highest temperature _TH to the lowest temperature _TL is obtained based on the following equation:

However, in said formula, L is the length of the said heat coupling body, S is the cross-sectional area of the cross section of the direction perpendicular | vertical to the heat flow of the said heat coupling body,
Using the results of the time derivative dT / dt of the temperature of the sample and the time derivative dQ / dt of the heat flow Q, the heat capacity C (T) of the sample is expressed as C (T) = (dQ / dt) / (dT / dt ), And the specific heat c (T) is obtained by dividing the heat capacity C (T) by the substance amount of the sample. A specific heat measurement method for measuring specific heat of a sample in a predetermined temperature range (T _{L to} T _H ) in a vacuum atmosphere,
The sample having an unknown specific heat c is thermally coupled to a heat bath having a temperature _TL via a thermal coupling body having a known temperature-dependent function κ (T) of thermal conductivity κ.
The maximum temperature T _H of the predetermined temperature range the heating was stopped after heating the sample,
Thereafter, the temperature T of the sample is measured at predetermined time intervals until the temperature of the sample reaches the lowest temperature _TL in the predetermined temperature range.
From the measurement result of the temperature T versus time t of the sample, a time difference ΔT / Δt of the temperature T is obtained,
A time derivative dQ / dt of the heat flow Q flowing through the thermal coupling body in a process in which the temperature of the sample reaches from the maximum temperature _TH to the minimum temperature _TL is obtained based on the following equation:

However, in said formula, L is the length of the said heat coupling body, S is the cross-sectional area of the cross section of the direction perpendicular | vertical to the heat flow of the said heat coupling body,
Using the result of the time difference ΔT / Δt of the temperature of the sample and the time derivative dQ / dt of the heat flow Q, the heat capacity C (T) of the sample is expressed as C (T) = (dQ / dt) / (ΔT / Δt ), And the specific heat c (T) is obtained by dividing the heat capacity C (T) by the substance amount of the sample.   The specific heat measurement method according to claim 1, wherein the integral in the equation is obtained by numerical integration.   The specific heat measurement method according to claim 1, wherein the integral in the equation is obtained by analytical integration.   The specific heat measurement method according to claim 1 or 2, wherein the temperature of the sample is measured by a thermometer installed on a sample stage on which the sample is placed, and the sample is heated by a heater installed on the sample stage.   The specific heat measurement method according to claim 5, wherein the thermometer and the heater are configured by one resistor. A thermal conductivity measurement method for measuring thermal conductivity of a sample in a predetermined temperature range (T _{L to} T _H ) in a vacuum atmosphere,
A material having a known temperature-dependent function C (T) of the heat capacity C is thermally coupled to a heat bath having a temperature _TL via a sample whose temperature-dependent property κ (T) is unknown.
The maximum temperature T _H of the predetermined temperature range the heating was stopped after heating the material,
And then measuring the temperature T of the material as a function of time t until the temperature of the material reaches a minimum temperature _TL in the predetermined temperature range,
From the measurement result of temperature T versus time t of the material, a time differential dT / dt of the temperature T is obtained,
Determined by the equation of the maximum temperature _{T H} of the hot bath temperature _{T L} of the time derivative of the heat flow Q flowing through the sample in the process leading to the dQ / dt = C (T) (dT / dt),
Substituting the obtained time derivative dQ / dt into the following equation to obtain the temperature dependence κ (T) of the thermal conductivity κ of the sample,

However, in the above formula, L is a length of the thermal coupling body, and S is a thermal conductivity measuring method which is a cross-sectional area of a cross section in a direction perpendicular to the heat flow of the thermal coupling body.
A thermal conductivity measurement method for measuring thermal conductivity of a sample in a predetermined temperature range (T _{L to} T _H ) in a vacuum atmosphere,
A material having a known temperature-dependent function C (T) of the heat capacity C is thermally coupled to a heat bath having a temperature _TL via a sample whose temperature-dependent property κ (T) is unknown.
The maximum temperature T _H of the predetermined temperature range the heating was stopped after heating the material,
Thereafter, the temperature T of the sample is measured at predetermined time intervals until the temperature of the material reaches the minimum temperature _TL in the predetermined temperature range,
From the measurement result of the temperature T of the material versus time t, a time difference ΔT / Δt of the temperature T is obtained,
Determined by the equation of the maximum temperature T _H of the hot bath temperature T _L time difference of the heat flow Q flowing through the sample in the process leading to ΔQ / Δt = C (T) (ΔT / Δt),
Substituting the obtained time difference ΔQ / Δt into the following equation to obtain the temperature dependence κ (T) of the thermal conductivity κ of the sample,

However, in the above formula, L is a length of the thermal coupling body, and S is a thermal conductivity measuring method which is a cross-sectional area of a cross section in a direction perpendicular to the heat flow of the thermal coupling body.   The thermal conductivity measurement method according to claim 7 or 8, wherein the integral in the equation is obtained by numerical integration.   The thermal conductivity measurement method according to claim 7 or 8, wherein the integral in the equation is obtained by analytical integration.   The thermal conductivity measurement method according to claim 7 or 8, wherein the temperature of the sample is measured by a thermometer installed on a sample stage on which the sample is placed, and the sample is heated by a heater installed on the sample stage.   The thermal conductivity measuring method according to claim 11, wherein the thermometer and the heater are configured by a single resistor.

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