JP6127019B2 - Method for measuring thermal diffusivity of translucent materials - Google Patents

Description

  The present invention relates to a method for measuring the thermal diffusivity of a translucent material in which the energy of heating light applied to the surface reaches the back surface due to both heat transfer phenomena of diffusion heat transfer and radiation heat transfer. Here, examples of the semi-transparent material include a heat insulating material and ceramics, and a porous (porous) material in which a radiation heat transfer phenomenon occurs in addition to a normal heat conduction phenomenon.

As a method for measuring the thermal diffusivity of a material, for example, the laser flash method described in Patent Document 1 has been frequently used in recent years. In this method, for example, a sample having a diameter of about 10 mm and a thickness of several millimeters (hereinafter also referred to as a measurement sample) is prepared from a material whose thermal diffusivity is to be obtained, and the surface of this sample is shortened with laser light (heating light). Comparison of backside temperature measurement data obtained by measuring the temperature of the backside of the sample when irradiated for a long time, and the theoretical formula of the backside temperature indicating the theoretical temporal change in backside temperature when the sample surface is irradiated with laser light Then, the thermal diffusivity of the sample is obtained by analysis.
At this time, the necessary condition that the sample should satisfy is the condition of the sample when the theoretical formula of the back surface temperature is derived.

The theoretical formula of the back surface temperature of the sample used in the conventional laser flash method is the unsteady one-dimensional heat conduction equation shown in the equation (1), the initial condition shown in the equation (2), the equations (3) and (4) It can be obtained by solving under the boundary conditions shown below. Here, conditions that the sample should satisfy when the back surface temperature theoretical formula is derived are shown below.
(I) From the front surface to the back surface of the sample, a one-dimensional heat conduction equation of equation (6) obtained by modifying equation (1) is established based on the Fourier equation of equation (5).
(Ii) The energy of the laser light applied to the sample surface is absorbed by the sample surface.

Therefore, the conditions to be satisfied by the sample in the measurement by the laser flash method are the homogeneous, dense and opaque material from the condition (i) above, and the surface is opaque from the condition (ii) above. It is a simple material.
Moreover, as a back surface temperature theoretical formula compared with the back surface temperature measurement data obtained by measuring, the time-space solution shown in the formulas (7) to (9) and the Laplace shown in the formulas (10) and (11) are used. A spatial solution is used. Note that (7) in _{a n} is (8) in the formula, beta _n in (9), defined respectively.

  Where q is the heat flux, k is the thermal conductivity, T is the temperature, x is the coordinate (distance entering the sample surface from the inside), t is the time, ρ is the density, c is the specific heat, α is the thermal diffusivity, L is the sample thickness, h is the number of bioses representing the radiation loss from the front and back surfaces of the sample, and p is the Laplace variable. Q is the amount of heat input per unit area of the sample surface by laser light irradiation, f (t) is a function normalized with the integral value in the entire time region as 1, and Qf (t) is the laser light. It becomes energy per unit time unit area absorbed by the sample surface by irradiation.

The measurement of the thermal diffusivity using the laser flash method described above has many advantages such as simplicity of measurement and the ability to measure for a short time. For this reason, the present situation is that it is widely applied even to materials in which the conditions to be satisfied by the measurement sample are not satisfied in the measurement by the laser flash method.
For example, when the thermal diffusivity of a translucent material such as a translucent material or a heat insulating material is measured, a blackened film or a metal film is formed on the front and back surfaces of the manufactured measurement sample to make it non-translucent. Since most of the translucent materials such as heat insulating materials are inhomogeneous materials, when measuring this thermal diffusivity, further increase the thickness of the measurement sample to such an extent that it can be regarded as approximately homogeneous and dense. To measure.

JP-A-8-261967

  As described above, when an opaque film such as a blackening film is applied to the front and back surfaces of a sample made of a translucent material and the thermal diffusivity (thermal conductivity) is measured by a light irradiation method such as a laser flash method, When the temperature is low, radiant heat transfer is suppressed and the heat conduction is mainly diffusion heat transfer, so that a correct thermal diffusivity (thermal conductivity) can be obtained. Here, diffusion heat transfer is heat conduction by a heat flux (Fourier equation) proportional to the temperature gradient, and radiant heat transfer is heat conduction in which a material in the sample emits and absorbs electromagnetic waves. .

  In order for the above measurement to be established, the heat conduction of the sample must satisfy the above one-dimensional heat conduction equation, initial conditions, and boundary conditions. The bundle increases and it becomes a situation that cannot be ignored compared to the heat flux by diffusion heat transfer. For this reason, when the thermal diffusivity of a translucent material is measured and analyzed by the conventional laser flash method, the measured thermal diffusivity is affected by the radiation heat transfer phenomenon, and the measured thermal diffusivity is the original thermal diffusivity (thermal conductivity). A larger value was shown, and the measurement error was large.

The present invention has been made in view of such circumstances, and an object thereof is to provide a thermal diffusivity of a translucent material capable of accurately measuring the thermal diffusivity of diffusion heat transfer even when a radiant heat transfer phenomenon occurs. To do.

The method for measuring the thermal diffusivity of the translucent material according to the present invention in accordance with the above object is a method for measuring the thermal diffusivity of the translucent material in which heat transfer from the front surface to the back surface is caused by diffusion heat transfer and radiation heat transfer. And
An opaque material in which heat transfer is caused by diffusion heat transfer is closely arranged on the front and back surfaces of the measurement sample prepared from the translucent material, the surface of one of the opaque materials is irradiated with heating light, and the other opaque material A first step of measuring the temperature of the back surface to obtain back surface temperature measurement data indicating a temperature change of the back surface;
The diffusion including a thermal diffusivity , an absorption coefficient, and a refractive index of the translucent material as variables, and showing a theoretical time change of the temperature of the back surface of the opaque material when the surface of the opaque material is irradiated with heating light. A second step of determining the thermal diffusivity of the translucent material by comparing the heat transfer and the back surface temperature theoretical formula using the radiant heat transfer with the back surface temperature measurement data.

In the method of the thermal diffusivity of the translucent material according to the present invention, the backside temperature theoretical formula further, a Biot number of the previous SL opaque material, including as a variable, it is preferable to determine the number of the displacement in the second step .

  In the method for measuring the thermal diffusivity of a translucent material according to the present invention, the back surface temperature theoretical formula is a Laplace space formula of a one-dimensional heat conduction equation, and the back surface temperature measurement data is measured on the back surface of the measured opaque material. A temperature change is preferably Laplace converted.

In the method for measuring the thermal diffusivity of a translucent material according to the present invention, the variable can be determined from a condition that minimizes a square deviation between the back surface temperature theoretical formula and the back surface temperature measurement data.
Here, the condition for minimizing the square deviation can be obtained as all independent variables.
Further, the condition for minimizing the square deviation is obtained by using an additional condition in which the measured decay time constant obtained from the temperature decay region of the back surface temperature measurement data and the time constant obtained from the back surface temperature theoretical equation are the same value. be able to.

  Since the method for measuring the thermal diffusivity of the translucent material according to the present invention uses the back surface temperature theoretical formula using diffusion heat transfer and radiant heat transfer, for example, when a phenomenon of radiant heat transfer occurs in a high temperature region. However, the thermal diffusivity of the translucent material can be obtained with high accuracy.

In particular, since the backside temperature theoretical formula including refractive index and absorption coefficient of the translucent material as a variable, to consider the factors that affect these radiation heat transfer, the thermal diffusivity of the translucent material, determined more accurately be able to.
Further, when the back surface temperature theoretical formula further includes the number of bios of the opaque material as a variable, the thermal diffusivity of the translucent material at a high temperature can be obtained with high accuracy. This is because, at high temperatures, the energy radiated from the front and back surfaces of the sample cannot be ignored, and the bio number representing this phenomenon (proportional to the product of the emissivity of each opaque material and the steady temperature T ₀ ³ ) cannot be ignored. The high temperature is a temperature range in which the radiant heat transfer phenomenon cannot be ignored, and is, for example, 800K or more, and the upper limit is not particularly limited.

(A) is explanatory drawing of the measuring apparatus which applies the measuring method of the thermal diffusivity of the translucent material which concerns on one embodiment of this invention, (b) is explanatory drawing of the heat transfer model of a measurement sample. It is a graph which shows the boundary of diffusion heat transfer heat conduction and radiation heat transfer heat conduction. (A), (b) is a graph which shows the dependence of the absorption coefficient on the constant A of the radiant heat transfer temperature equation of the back surface temperature theoretical formula and the constant B of the diffusion heat transfer temperature equation at temperatures of 300K and 2000K, respectively. is there. It is an analysis flowchart which shows the procedure at the time of determining a thermal diffusivity and a bio number using the measuring method of the thermal diffusivity of the translucent material which concerns on one embodiment of this invention. It is an analysis flowchart which shows the procedure at the time of determining a thermal diffusivity and an absorption coefficient or a refractive index using the measuring method of the thermal diffusivity of the translucent material. It is an analysis flowchart which shows the procedure at the time of determining a thermal diffusivity, an absorption coefficient or a refractive index, and a bio number using the measuring method of the thermal diffusivity of the translucent material. It is an analysis flowchart which shows the procedure at the time of determining a thermal diffusivity, an absorption coefficient, and a refractive index using the measuring method of the thermal diffusivity of the translucent material. It is an analysis flowchart which shows the procedure at the time of determining a thermal diffusivity and a bio number using the measuring method of the thermal diffusivity of the translucent material which concerns on other embodiment of this invention. It is an analysis flowchart which shows the procedure at the time of determining a thermal diffusivity, a bio number, an absorption coefficient, or a refractive index using the measuring method of the thermal diffusivity of the translucent material. It is an analysis flowchart which shows the procedure at the time of determining a thermal diffusivity, an absorption coefficient, a refractive index, and a bio number using the measuring method of the thermal diffusivity of the translucent material.

Next, embodiments of the present invention will be described with reference to the accompanying drawings for understanding of the present invention.
First, a measurement apparatus 10 that applies a method for measuring the thermal diffusivity of a translucent material according to an embodiment of the present invention will be described with reference to FIGS. 1 (a) and 1 (b).

  The measurement apparatus 10 irradiates a laser beam (an example of heating light) on the surface side of a measurement sample (hereinafter also simply referred to as a sample) 11 made from a translucent material in which heat transfer is caused by diffusion heat transfer and radiation heat transfer. A device for obtaining a thermal diffusivity of a translucent material, a laser beam generator 12 for generating laser beam, and a half mirror 14 for distributing the generated laser beam so as to be directed to the laser beam detector 13 and the measurement sample 11, respectively. And a temperature measuring unit 15 for measuring a temperature change on the back surface of the measurement sample 11.

Here, as described above, the translucent material is, for example, a heat insulating material or ceramics, or a porous material in which a radiant heat transfer phenomenon occurs in addition to a normal heat conduction phenomenon. In addition, the material in which the radiant heat transfer phenomenon occurs means a material in which the following phenomenon occurs in the manufactured measurement sample.
-A material that emits and absorbs electromagnetic waves in a sample, and has a change in electromagnetic wave radiation proportional to the product of absorption coefficient μ, refractive index square n ² , and temperature T (electromagnetic wave) The phenomenon of radiation and absorption does not occur in transparent materials, but occurs in translucent materials). Here, the temperature T is a temperature increment that rises from the steady temperature T ₀ by irradiation with heating light (laser light).
-It is a material that has multiple reflection phenomenon between both end faces of the sample.
The measurement sample 11 produced using this translucent material has a diameter of about 10 mm and a thickness of several millimeters, for example, but various shapes and dimensions can be changed according to measurement conditions.

On the front and back surfaces (both end surfaces in the thickness direction) of the measurement sample 11, plate materials 16 and 17 made of an opaque material in which heat transfer is caused only by diffusion heat transfer are disposed in close contact to form a three-layer material 18. A black film (for example, a thin plate of a ceramic material such as carbon) or a metal film (for example, a thin plate of a metal material such as platinum) can be used for the plate members 16 and 17.
As described above, by bringing the plate material 16 into close contact with the surface of the measurement sample 11, the energy of the laser light irradiated on the surface of the plate material 16 can be absorbed by 100% on the surface. Furthermore, the absorbed heat can be supplied to the measurement sample 11 according to the diffusion heat transfer.
On the other hand, by bringing the plate material 17 into close contact with the back surface of the measurement sample 11, the heat passing through the measurement sample 11 can be received and moved according to diffusion heat transfer. It can be obtained as a solution of the heat conduction equation.

Even when the measurement sample 11 sandwiched between the two plates 16 and 17 described above, that is, the three-layer material 18 is held in a high-temperature atmosphere, the laser light generation unit 12 has thermal energy exceeding the thermal fluctuation of the atmosphere. For example, a ruby laser oscillator that can be injected into the surface of the three-layer material 18 can be used. The size of the three-layer material 18 is, for example, a dimension that can approximate one-dimensional heat conduction.
The laser beam detector 13 detects the heating waveform (laser beam waveform) of the laser beam generated from the laser beam generator 12.
The half mirror 14 is formed of a base material having a material with extremely low laser light absorption and extremely high transparency. For example, a coating layer that reflects a predetermined amount of laser light from incident laser light and allows the remaining part to pass therethrough may be provided on the surface of the substrate.

Therefore, the optical axis of the light receiving part is adjusted so that the laser light generated from the laser light generating part 12 is reflected by the half mirror 14 and reaches the light receiving part (not shown) of the laser light detecting part 13. Thus, a part of the laser light emitted from the laser light generator 12 can be incident on the laser light detector 13 and the heating waveform of the laser light can be measured.
Further, by matching the optical axis of the half mirror 14 with the central axis of the three-layer material 18 (along the thickness direction), the surface of the three-layer material 18 can be irradiated with the laser beam that has passed and heated. it can. Thereby, when the surface of the three-layer material 18 is irradiated with laser light, the temperature change of the back surface of the three-layer material 18 can be expressed by an unsteady one-dimensional heat conduction equation.

  The temperature measurement unit 15 needs to have a function capable of measuring the temperature change of the back surface of the three-layer material 18 irradiated with the laser light at high speed and with high accuracy. For example, a temperature detection sensor such as a thermocouple or a radiation thermometer A temperature measuring device with can be used.

  Further, the measuring device 10 obtains back surface temperature measurement data from the back surface temperature theoretical formula indicating the theoretical time change of the back surface temperature of the three-layer material 18 and the signal output from the temperature measuring unit 15, and detects the laser beam. The back surface temperature change behavior (theoretical back surface temperature data) obtained from the signal output from the unit 13 and the back surface temperature theoretical equation is applied to the back surface temperature change behavior obtained from the back surface temperature measurement data, and the back surface temperature theoretical equation is changed. The calculation processing unit 19 for determining the thermal diffusivity, the absorption coefficient and the refractive index of the measurement sample 11 included in the measurement sample 11 and the number of bios of the plates 16 and 17, respectively, and the back surface temperature theory obtained by the calculation processing unit 19 And an output device 20 for displaying the equation, back surface temperature measurement data, thermal diffusivity, absorption coefficient, refractive index, and bio number.

The arithmetic processing unit 19 has a function for obtaining a back surface temperature theoretical expression indicating a theoretical time change of the back surface temperature of the three-layer material 18, and a Laplace conversion of a signal (back surface temperature signal) output from the temperature measuring unit 15 is performed on the back surface. Function for obtaining temperature measurement data, the back surface temperature theoretical formula (theoretical back surface temperature data) and the back surface temperature measurement data square deviation is obtained, and the thermal diffusion of the measurement sample 11 in the three-layer material 18 from the condition that the square deviation is minimized. And a function of determining the heat absorption coefficient and refractive index, and the number of bios of the plate members 16 and 17 (see, for example, Japanese Patent Laid-Open No. 2012-2758).
The arithmetic processing unit 19 can be formed by installing a program that expresses each function described above in a computer.
For the output device 20, for example, a display device for a computer and a printing device can be used.

Then, the measuring method of the thermal diffusivity of the translucent material which concerns on one embodiment of this invention is demonstrated, referring Fig.1 (a).
First, the measurement sample 11 is produced from the translucent material to be measured. Then, on the front and back surfaces of the measurement sample 11, plate materials 16 and 17 made of an opaque material whose heat transfer is only diffusion heat transfer are arranged in close contact with each other to form a three-layer material 18.

Here, for the opaque material constituting the plate material 16 arranged in close contact with the front surface side of the measurement sample 11 and the plate material 17 arranged in close contact with the back surface side, for example, a ceramic material such as carbon or a metal material such as platinum Can be used.
Further, the plate members 16 and 17 are baked by depositing a ceramic material or a metal material on the front and back surfaces of the measurement sample 11 or by applying a fine powder of a ceramic material or a metal material on the front and back surfaces of the measurement sample 11. Further, it can be formed by carbon spray. Thereby, formation of a board | plate material and contact | adherence to the front and back of the measurement sample 11 of a board | plate material can be performed simultaneously.

Next, the three-layer material 18 is set in a sample holder provided in a sample chamber (not shown) of the measuring apparatus 10 and the atmosphere in the sample chamber is adjusted (for example, in a vacuum state).
In addition, with respect to one plate material 16, density ρ ₁ , specific heat c ₁ , thermal diffusivity α ₁ , thermal conductivity k ₁ , thickness dl ₁ , and emissivity ε ₁ are used as variables, and density ρ _{2 is} measured for measurement sample 11. , Specific heat c ₂ , thermal diffusivity α ₂ , thermal conductivity k ₂ , thickness dl ₂ , square of refractive index n ² , and absorption coefficient μ, and the density ρ ₃ and specific heat c for the other plate material 17. ₃ , the thermal diffusivity α ₃ , the thermal conductivity k ₃ , the thickness dl ₃ , and the emissivity ε ₃ are used as variables, and the sample temperature T ₀ before laser light irradiation is used as a variable. ) And input to the arithmetic processing unit 19.

Subsequently, the temperature in the sample chamber is controlled to be a preset measurement temperature, and when the temperature of the three-layer material 18 reaches the measurement temperature and is stabilized, the laser beam is emitted from the laser beam generator 12 to the half mirror 14. Fire towards.
Here, the emitted laser light reaches the half mirror 14, a part of the light amount of the laser light is reflected by the half mirror 14 and enters the laser light detection unit 13, and the waveform of the laser light is obtained. Data is input to the arithmetic processing unit 19. Further, the remaining laser light transmitted through the half mirror 14 reaches the surface of the three-layer material 18 and heats the surface.

When the surface of the three-layer material 18 is heated by the laser light, the thermal energy injected into the surface of the one plate material 16 is conducted toward the back surface of the three-layer material 18, and therefore the temperature of the back surface of the three-layer material 18. Gradually rises. However, since heat dissipation from the front surface, side surface, and back surface of the three-layer material 18 also occurs at the same time, the temperature of the back surface of the three-layer material 18 gradually decreases after passing through the maximum temperature.
The temperature change at this time is measured by, for example, the temperature measurement unit 15 including a radiation thermometer, and the obtained measurement value is input to the arithmetic processing unit 19. The arithmetic processing unit 19 records the input measurement value and performs Laplace conversion of the measurement value to create and record the back surface temperature measurement data T _m (p) (the first step).

In the arithmetic processing part 19, the back surface temperature theoretical formula in Laplace space is calculated | required based on the model shown in FIG.1 (b). Hereinafter, this model will be described.
After the temperature of the three-layer material 18 is set to the temperature (steady temperature) T ₀ , the surface of the plate material 16 that is the first layer (hereinafter also simply referred to as the first layer) is irradiated with laser light, and the plate material that is the third layer The back surface temperature of 17 (hereinafter also simply referred to as the third layer) is measured.
Here, the change in temperature from the temperature T ₀ and T. The surface coordinates of the first layer and x = 0, the back surface coordinates of the third layer and x = L _3, the first layer and the measurement sample 11 of the second layer (hereinafter, referred to simply as the second layer) and The interface coordinates are x = L ₁ and the interface coordinates of the second layer and the third layer are x = L ₂ .

From the surface of the first layer, there is energy emission of λ ₁ T ₁ (0, t) toward the outside, and from the back surface of the third layer, energy emission of λ ₃ T ₃ (L ₃ , t) is emitted. It is assumed that it is facing outside. Further, at the interface x = L ₁ , there is λ ₁ T ₁ (L ₁ , t) energy radiation from the first layer to the second layer, and at the interface x = L ₂ , λ from the third layer to the second layer. ₃ T ₃ (L ₂ , t) energy is emitted.
Here, in order to distinguish the radiant energy from the surface of the first layer to the outside and the radiant energy from the back surface of the first layer to the second layer, u ₀ is added to the radiant energy from the surface to the outside. Similarly, for the third layer, u ₁ is added to the radiant energy from the back surface (x = L ₃ ) to the outside. When the front and back surface emissivities of the first layer and the third layer are equal , u ₀ and u ₁ are set to 1.

As described above, the variables used are the density ρ ₁ , the specific heat c ₁ , the thermal diffusivity α ₁ , the thermal conductivity k ₁ , the thickness dl ₁ , and the emissivity ε ₁ for the first layer, as described above. , Density ρ ₂ , specific heat c ₂ , thermal diffusivity α ₂ , thermal conductivity k ₂ , thickness dl ₂ , refractive index square n ² , absorption coefficient μ, density ρ ₃ , specific heat c for the third layer ₃ , thermal diffusivity α ₃ , thermal conductivity k ₃ , thickness dl ₃ , emissivity ε ₃ , and sample temperature (steady temperature) T ₀ before laser light irradiation.
Therefore, the following relationship holds.
dl ₁ + dl ₂ = L ₂
dl ₁ + dl ₂ + dl ₃ = L ₃

Further, constants λ ₁ and λ ₃ relating to radiation from the front and back surfaces are expressed as follows.
λ ₁ = 4ε ₁ σT ₀ ³
λ ₃ = 4ε ₃ σT ₀ ³
The constant λ ₂ related to the radiation from the inside of the second layer is expressed as follows.
λ ₂ = e ₁ n ² σT ₀ ³
Incidentally, e ₁ described above is a constant (for example, there are e ₁ = 4 [pi, considered somewhat varies depending upon the vertical how the model of the radiation and absorption, are also like e 1 ₌ 32/3.) Be , Σ is a Stefan Boltzmann constant. Further, the attenuation of the back surface temperature of the three-layer material is defined as a time constant τ.
From the above, the unit volume inside the measurement sample 11 which is the second layer and the energy q _ν emitted per unit time are given by the equation (12).

Next, the back surface temperature theoretical formula T (L ₃ , p) in the Laplace space will be described.
The back surface temperature theoretical formula T (L ₃ , p) in the Laplace space is expressed by the following equation (13) showing the theoretical time change of the back surface temperature when the surface of the three-layer material 18 is irradiated with laser light.
Here, since the measurement sample 11 is made of a material in which heat transfer is caused by diffusion heat transfer and radiant heat transfer, the back surface temperature theoretical formula T (L ₃ , p) is expressed by the radiant heat transfer of the formula (14). It is expressed as the sum of the general temperature equation T _rad (L ₃ , p) and the diffusion heat transfer temperature equation T _dif (L ₃ , p) of the equation (15). A in the equation (14) and B in the equation (15) are constants.
Further, T _s (L ₃ , β) on the right side of the equations (14) and (15) is represented by the equation (16). In addition, the coefficient of k ₁ r ₁ k ₂ βk ₃ r ₃ of the right-hand side molecule in the equation (16) is the energy Qf (t) per unit area absorbed on the surface of the three-layer material 18 by irradiation with laser light. Is a Laplace transform. Here, Q represents the amount of heat input per unit area, and t represents time.

Note that β ₁ and β ₃ used in the above equations (14) and (15) are represented by equations (17) and (18), respectively, and r ₁ and r ₃ used in equation (16) are Respectively, it is expressed by the equations (19) and (20).

  Furthermore, the constants A and B used in the equations (14) and (15) are expressed by the equations (21) and (22), respectively.

Μ _c used in the above equations (21) and (22) is an absorption coefficient that becomes a boundary between radiative heat transfer and diffusion heat transfer.
Therefore, when the absorption coefficient μ is smaller than this value μ _c , the radiant heat transfer is mainly conducted, whereas when the absorption coefficient μ is larger than this value μ _c , the diffusion heat transfer is mainly conducted. . The absorption coefficient μ _c that defines the boundary between the two heat conductions is given by the optical thickness formula (23) shown in FIG. In FIG. 2, the left side from the line of the equation (23) is radiant heat transfer heat conduction, and the right side is diffusion heat transfer heat conduction. The optical thickness is represented by the product of the absorption coefficient μ and the thickness L (= dl ₂ ).
In this equation (23), e ₂ is a constant. Further, by using the absorption coefficient mu _c of this boundary, the Laplace variable _{p c} used in (21) and (22), shown in equation (24).

The constant e ₂ described above is given by equation (25) when one-dimensional heat conduction and one-dimensional radiation are established.
When the radiation into the second layer at the interface between the first layer and the second layer has a Lambertian surface characteristic emitted three-dimensionally, the constant e ₂ is a constant different from the equation (25). However, it should be set according to the characteristics of each surface. This Lambertian surface is a surface where the radiation intensity from the surface becomes I ₀ cos (θ), where θ is the angle from the interface vertical direction. I ₀ is the vertical radiation intensity.
The same applies to the interface between the second layer and the third layer.

Next, the constant A (that is, the equation (21)) used in the above equation (14) and the constant B that is used in the equation (15) (that is, the equation (22)) will be described.
The constant A is used for the radiant heat transfer temperature equation T _rad (L ₃ , p), and the constant B is used for the diffusion heat transfer temperature equation T _dif (L ₃ , p).
Here, FIGS. 3A and 3B show the absorption coefficient dependence of both constants A and B at temperatures T = 300K and T = 2000K, respectively.
FIG. 3 (a), (b), the with the absorption coefficient mu is increased, the mu = mu _c, the constant (coefficient) A is from 1 0, also constant (coefficient) B from 0 It can be seen that 1 changes respectively. Note that this change slightly differs depending on the temperature.

Next, the analysis method will be described.
The analysis method includes a direct method and a time constant method. First, an outline of the analysis method will be described.
As described above, when the back surface temperature theoretical formula is obtained by the arithmetic processing unit 19, the arithmetic processing unit 19 uses the back surface temperature theoretical formula T _th (theoretical back surface temperature data) and the back surface temperature measurement data T _m to obtain (26) A square deviation formula R expressed by the formula is created.
The sum of the square deviations is created by setting a plurality of Laplace variables p, and is the sum of the square deviations of the back surface temperature theoretical formula T (L ₃ , p) and the back surface temperature measurement data T _m (p). Indicated. In the formula (26), i is i = 1, 2, 3; 1 is the first layer (plate material 16), 2 is the second layer (measurement sample 11), and 3 is the third layer (plate material 17). ) Respectively.

Next, the physical property values of the second layer are analyzed with the physical property values and thicknesses of the first layer and the third layer being known.
In this analysis, the specific heat c ₂ , the density ρ ₂ , and the thickness dl ₂ of the second layer are known, the thermal diffusivity α ₂ , the absorption coefficient μ, the square of the refractive index n ^{2 of} the second layer, and The bio numbers h representing the heat loss from the front and back surfaces of the sample (the first layer and the third layer) are respectively analyzed.
The bio number h is equal to the physical properties and emissivities of the first layer and the third layer, and the thermal conductivities k ₁ and k ₃ and emissivities ε ₁ and ε _{3 of} the first layer and the third layer are the same. Is expressed by the equation (27). Thus, analyzing the bio number h is the same as analyzing the emissivities ε ₁ and ε ₃ of the first layer and the third layer.

First, the direct method will be described.
Here, as a variable to be analyzed (independent variable), a combination of Expressions (28) to (33) is examined.

  The analysis flow of the direct method for each combination of analysis variables described above is shown in FIGS. Specifically, FIG. 4 shows an analysis flow for equation (28), FIG. 5 shows an analysis flow for equations (29) and (30), and FIG. 6 shows an analysis flow for equations (31) and (32). FIG. 7 shows an analysis flow for Expression (33).

First, the procedure of the analysis flow of the thermal diffusivity α ₂ and the bio number h will be described with reference to FIG.
(A1) A variable other than the thermal diffusivity of the second layer is fixed, and only the thermal diffusivity is used as a variable to calculate a thermal diffusivity that gives a minimum square deviation.
(A2) A variable other than the thermal diffusivity and the number of bios is fixed to set a plurality of bio numbers, the calculation of (a1) is performed for each bio number, and then the biometric is reduced in the direction in which the square deviation becomes smaller. The number is reset and the above calculation (a1) is performed. By repeating this procedure, the thermal diffusivity and the bio number that minimize the square deviation are obtained.
Thereby, the thermal diffusivity α ₂ and the bio number h are obtained.

Next, the procedure of the analysis flow of the thermal diffusivity α ₂ and the absorption coefficient μ or the square n ² of the refractive index will be described with reference to FIG.
Here, after calculating (a1) above, the number of bios in (a2) above is changed to the square of the absorption coefficient or refractive index, and then calculating (a2) above.
Thereby, the thermal diffusivity α ₂ and the absorption coefficient μ or the square n ^{2 of the} refractive index are obtained.

Subsequently, the procedure of the analysis flow of the thermal diffusivity α ₂ and the bio number h and the absorption coefficient μ or the square n ² of the refractive index will be described with reference to FIG.
Here, after the above calculations (a1) and (a2) are sequentially performed, the second coefficient of the absorption coefficient or refractive index of the second layer is set as a third variable, and a plurality of these variables are set. Then, the calculation of (a2) is performed for each third variable, and then the third variable is reset in a direction in which the square deviation is reduced, and the calculation of (a2) is performed. This procedure is repeated (the above (a3)).
As a result, the thermal diffusivity α ₂ , the bio number h, and the third variable (that is, the absorption coefficient μ or the square n ^{2 of the} refractive index) that minimize the square deviation are obtained.

Finally, the procedure of the analysis flow of the thermal diffusivity α ₂ , the absorption coefficient μ, and the square n ² of the refractive index will be described with reference to FIG.
Here, after performing the calculation of (a1), the absorption coefficient of the second layer is set as the second variable, and the square of the refractive index is set as the third variable, so that (a2) and (a3) By performing the same calculation, the thermal diffusivity α ₂ , the absorption coefficient μ, and the square n ² of the refractive index are obtained.
In FIG. 7, the analysis method is shown in the order of the thermal diffusivity α ₂ , the absorption coefficient μ, and the refractive index square n ^2. However, the method is not limited to this, and for example, the thermal diffusivity It is also possible to analyze α ₂ , the refractive index square n ² , and the absorption coefficient μ in this order.

Next, the time constant method will be described.
Here, as a variable to be analyzed, a combination of the above-described Expression (28), Expression (31), Expression (32), and Expression (34) is examined.

After a while after the laser beam irradiation, the sample temperature becomes substantially the same in the measurement sample, the radiation heat transfer in the second layer is suppressed, and the laser beam is emitted with a radiation loss according to the number of bios from the front and back surfaces of the sample. Energy absorbed by irradiation is lost. Decay time constant in the course of sample temperature decays gradually This radiation loss is considered from the above discussion, substantially the same as the decay time constant in the case of the absorption of electromagnetic waves in the sample radiation phenomenon is no diffusion heat transfer only .
An example of the analysis flow of the time constant method based on this inference is shown in FIGS. Specifically, FIG. 8 shows an analysis flow for equation (28), FIG. 9 shows an analysis flow for equations (31) and (32), and FIG. 10 shows an analysis flow for equation (34).

First, the procedure of the analysis flow of the thermal diffusivity α ₂ and the bio number h will be described with reference to FIG.
(B1) Calculate the initial value of the bio number based on the initial value of the thermal diffusivity of the second layer, the time constant (measured decay time constant) obtained from the temperature decay region of the back surface temperature measurement data, and the time constant theoretical formula. .
(B2) Calculate the thermal diffusivity of the second layer that minimizes the square deviation based on the initial value of the bio number, with the square of the refractive index of the second layer and the absorption coefficient fixed.
(B3) The biodiffusivity is updated by substituting the thermal diffusivity obtained by the calculation into a time constant expression described later. Then, this bio number is substituted into the above-described equation (27), and the emissivities ε ₁ and ε ₃ of the first layer and the third layer are updated.
(B4) Based on the updated number of bios, the thermal diffusivity is calculated in (b2) above, and the thermal diffusivity and the bio number are calculated by repeatedly calculating the bio number in (b3) above. Ask.
Thereby, the thermal diffusivity α ₂ and the bio number h are obtained.

Next, the procedure of the analysis flow of the thermal diffusivity α ₂ and the bio number h and the absorption coefficient μ or the square n ² of the refractive index will be described with reference to FIG.
The above calculations (b1) to (b4) are sequentially performed.
(B5) A plurality of squares (or absorption coefficients) of the refractive index of the second layer are set as third variables, and the above calculations (b2) to (b4) are performed for each third variable. The thermal diffusivity and the bio number that minimize the square deviation with respect to the third variable are obtained. Then, a third variable is newly set in the direction in which the square deviation is reduced, and the calculation of repeating (b2) to (b4) above is performed, and the third variable that minimizes the square deviation, the thermal diffusivity And the number of bios.
Thereby, the thermal diffusivity α ₂ , the bio number h, and the third variable are obtained.

Finally, the procedure of the analysis flow of the thermal diffusivity α ₂ , the absorption coefficient μ, the refractive index square n ² , and the bio number h will be described with reference to FIG.
The above calculations (b1) to (b5) are sequentially performed.
(B6) The absorption coefficient (or the square of refractive index) of the second layer, which is a variable not taken up in the calculations of (b1) to (b5) above, is set as a fourth variable, and a plurality of the fourth variables are set. The calculation of the above (b2) to (b5) is performed for each fourth variable, and the thermal diffusivity, the bio number, and the third to minimize the square deviation for each fourth variable. Find a variable. Then, a fourth variable is newly set in the direction in which the square deviation is reduced, and the above calculation (b2) to (b5) is repeated, and the fourth variable, the thermal diffusivity, in which the square deviation is minimized. Find α ₂ , the bio number h, and the third variable.
In FIG. 10, the analysis method is shown in which the third variable is the refractive index squared and the fourth variable is the absorption coefficient. However, this variable is reversed, that is, the third variable is the absorption coefficient. It is also possible to analyze the fourth variable as the square of the refractive index.

Here, the time constant formula will be described.
In the following, 1) when the absorption coefficient is small and the expression (35) is established, 2) when the absorption coefficient is large and the expression (36) is established, and 3) the radiant heat transfer to the inside of the sample can be ignored, and the three-layer opaque body Each time constant expression when the time constant is established is described. The above 1) and 2) are time constant expressions to be used when the respective conditions are satisfied, and 3) is a time constant expression to be used regardless of the absorption coefficient.

  First, the following variables are defined by equations (37) and (38).

1) When the absorption coefficient is small and the expression (35) is satisfied The time constant τ is expressed by the following expressions (39) to (43) using f ₀ , s ₀ , s _1cosh , and s _1sinh shown below. .

  Here, when the radiation loss to the outside is small, an approximate expression (44) is obtained as a time constant expression.

2) When the absorption coefficient is large and Expression (36) is satisfied The time constant τ is expressed by Expressions (45) to (48) using f, s ₀ , and s ₁ shown below.

3) When radiant heat transfer to the inside is negligible When the radiant heat transfer to the inside is negligible, the time constant equation of a three-layer material in which each layer shown below is opaque can be used. Note that this equation also holds approximately for a translucent body after the sample has been heated and the temperature of the entire sample has reached equilibrium.

  Here, when the measurement temperature is low and the radiation loss from the front and back surfaces of the sample is small, the above equation (49) can be approximated to the equation (50).

  By the above method, the thermal diffusivity of the translucent material in which the energy of the laser light irradiated on the front surface reaches the back surface can be obtained by both the heat transfer phenomenon of diffusion heat transfer and radiation heat transfer (the second step). ).

Then, the effectiveness of the measuring method of the thermal diffusivity of the translucent material which concerns on one embodiment of this invention is demonstrated.
In the following, analysis results when the above-described equation (35) is satisfied with a small absorption coefficient and when the above-described equation (36) is satisfied with a large absorption coefficient are shown. Here, when the absorption coefficient has a value in the vicinity of the boundary of the optical thickness shown in the equation (23) (that is, the equation (51)), this approximation does not hold, and the temperature of the equation (13) described above is not established. A similar analysis will be performed using the equation. In addition, although the analysis result in this case is not described, the thermal diffusivity of the second layer and other analyzes can be performed in the same procedure.

1) When the absorption coefficient is small and formula (35) or formula (52) holds

When the absorption coefficient is small and the optical thickness satisfies the condition μdl ₂ << e ₂ , the theoretical formula of the back surface temperature of the measurement sample can be approximated by the equation (35) or (52). Here, when the absorption coefficient is small, the coefficient A can be approximated to 1 as shown in FIGS. 3 (a) and 3 (b) (that is, equation (53)).

  First, the theoretical data used for the analysis is shown in Table 1.

The analysis results using the direct method are shown in Tables 2 and 3, and the analysis results using the time constant method are shown in Table 4, respectively. Table 2 shows the analysis results when the combinations of variables are (α ₂ , h), (α ₂ , h, n ² ), (α ₂ , h, μ), and Table 3 shows (α ₂ , μ) and (α ₂ , μ, n ² ). Table 4 shows analysis results when the combination of variables is (α ₂ , h), (α ₂ , h, μ).
Here, in the analysis, ε ₁ = n ² = ε ₃ = 0.8.

2) When the absorption coefficient is large and (36) or (54) holds

When the absorption coefficient is large and the optical thickness satisfies the condition μdl ₂ >> e ₂ , the theoretical formula of the back surface temperature of the measurement sample can be approximated by the expression (36) or (54). Here, when the absorption coefficient is large, the coefficient B can be approximated to 1 as shown in FIGS. 3 (a) and 3 (b) (that is, equation (55)).

  First, the theoretical data used for the analysis is shown in Table 5.

The analysis results using the direct method are shown in Table 6, and the analysis results using the time constant method are shown in Table 7, respectively. Tables 6 and 7 show the analysis results when the combinations of variables are (α ₂ , h), (α ₂ , h, n ² ), (α ₂ , h, μ), respectively.
Here, in the analysis, ε ₁ = n ² = ε ₃ = 0.8.

The analysis results shown in Tables 2 to 4 and Tables 6 and 7 show errors with respect to the true values of the thermal diffusivity α ₂ , the bio number h, the absorption coefficient μ, and the square n ² of the refractive index. However, it seems that the accuracy is not enough. However, this is an analysis result when using a very small amount of data of about 400 points. In a normal measurement, for example, measurement and analysis using a data amount of about 9000 points are performed. Therefore, it is considered that analysis with higher accuracy becomes possible.
Therefore, it can be seen that by using the method for measuring the thermal diffusivity of the translucent material of the present invention, the thermal diffusivity of diffusion heat transfer can be accurately measured even when a radiant heat transfer phenomenon occurs.

As described above, the present invention has been described with reference to the embodiment. However, the present invention is not limited to the configuration described in the above embodiment, and the matters described in the scope of claims. Other embodiments and modifications conceivable within the scope are also included. For example, a case where the method for measuring the thermal diffusivity of a translucent material of the present invention is configured by combining some or all of the above-described embodiments and modifications is also included in the scope of the present invention. For example, a configuration in which a translucent liquid is put in an opaque container (opaque material) in which only the heat conduction phenomenon is diffusion heat transfer, and an opaque material lid similar to the container is covered so as to be in contact with the translucent liquid.
Moreover, in the said embodiment, although the case where a laser beam was used as a heating light was demonstrated, electromagnetic waves, such as visible light and infrared light, can also be used, for example, and a heating plate is made into 3 layer material. It is also possible to apply a method of contacting the surface.

And in the said embodiment, when calculating | requiring the variable which gives the minimum value of a square deviation in the analysis of a thermal diffusivity, several corresponding variables are set in the direction where a square deviation becomes small, and a square deviation is calculated. However, the method of newly setting the corresponding variable in the direction in which the value of the square deviation becomes smaller has been described, but the present invention is not limited to this method, and for example, the Newton method may be used.
Furthermore, since the physical property values to be used include those showing the wavelength dependence of electromagnetic waves (emissivity, absorption coefficient, refractive index squared), it is preferable to perform an averaging process by wavelength as necessary. .

  Note that the above-described theoretical formula of the back surface temperature is an expression applicable even when the absorption coefficient is 0, and can also be applied to a transparent material. Further, the present invention is also applicable when the absorption coefficient is large and the heat transfer is only diffusion heat transfer. Furthermore, in the back surface temperature theoretical formula, by setting the thicknesses of the first layer and the third layer to 0, the present invention can be applied to the physical property analysis of a single-layer translucent body.

10: Measuring device, 11: Measurement sample, 12: Laser light generating unit, 13: Laser light detecting unit, 14: Half mirror, 15: Temperature measuring unit, 16, 17: Plate material (opaque material), 18: Three-layer material , 19: arithmetic processing unit, 20: output device

Claims (6)

The heat transfer from the front surface to the back surface is a method for measuring the thermal diffusivity of a translucent material generated by diffusion heat transfer and radiation heat transfer,
An opaque material in which heat transfer is caused by diffusion heat transfer is closely arranged on the front and back surfaces of the measurement sample prepared from the translucent material, the surface of one of the opaque materials is irradiated with heating light, and the other opaque material A first step of measuring the temperature of the back surface to obtain back surface temperature measurement data indicating a temperature change of the back surface;
The diffusion including a thermal diffusivity , an absorption coefficient, and a refractive index of the translucent material as variables, and showing a theoretical time change of the temperature of the back surface of the opaque material when the surface of the opaque material is irradiated with heating light. A second step of determining the thermal diffusivity of the translucent material by comparing the heat transfer and the back surface temperature theoretical formula using the radiant heat transfer with the back surface temperature measurement data. A method for measuring the thermal diffusivity of transparent materials. In the method of the thermal diffusivity of the translucent material according to claim 1, wherein the back surface temperature theoretical formula further, a Biot number of the previous SL opaque material, including as a variable, to determine the number of the displacement in the second step A method for measuring the thermal diffusivity of a translucent material.   3. The method of measuring the thermal diffusivity of a translucent material according to claim 1 or 2, wherein the back surface temperature equation is a Laplace space equation of a one-dimensional heat conduction equation, and the back surface temperature measurement data is the measured opaque material. A method for measuring the thermal diffusivity of a translucent material, characterized in that the temperature change on the back surface of the material is Laplace converted.   4. The method of measuring a thermal diffusivity of a translucent material according to claim 3, wherein the variable is determined from a condition that minimizes a square deviation between the back surface temperature theoretical formula and the back surface temperature measurement data. A method for measuring the thermal diffusivity of a translucent material.   5. The method of measuring a thermal diffusivity of a translucent material according to claim 4, wherein the condition for minimizing the square deviation is to obtain all the variables as independent variables. Method.   5. The method for measuring the thermal diffusivity of a translucent material according to claim 4, wherein the condition for minimizing the square deviation is an actually measured decay time constant obtained from a temperature decay region of the back surface temperature measurement data and the back surface temperature theoretical formula. A method for measuring the thermal diffusivity of a translucent material, characterized in that it is obtained by using an additional condition that makes the time constant obtained from Eq.

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