JPH08261967A - Measuring method and device for thermal constant using laser flash method - Google Patents

Abstract

PURPOSE: To accurately and efficiently determine the thermal constants of an unknown layer in a multi-layer material by comparing the temperature response on the back face side obtained when a laser flash is radiated from the surface side of the multi- layer material and the theoretical temperature response including thermal diffusivity, specific heat, and Biot number as variables. CONSTITUTION: The temperature response on the back face side obtained when a laser pulse is radiated from the surface of a multi-layer material containing one layer having unknown thermal diffusivity (α) and specific heat (c) is fed to a computer. It is compared with the theoretical temperature response F(α, c, h, t) or F'(α, c, h, p) including the thermal diffusivity α, specific heat (c), and Biot number (h) of the surface and back face of an unknown layer in the material set from documentary records as variables and calculated as a function of the time (t) or Laplace variable (p) of the temperature response. The thermal diffusivity α, specific heat (c), and Biot number (h) are set when the deviation R between the functions E(t) and E'(p) using the time (t) and variable (p) of the actual temperature response as variables becomes the minimum deviation Rm, then the thermal constants such as the Biot number (h), specific heat (c), and thermal diffusivity α of the unknown layer can be obtained.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for measuring a thermal constant using a laser flash method and an apparatus therefor capable of accurately determining a thermal diffusivity, a specific heat and a thermal constant such as Biot number of a sample.

[0002]

2. Description of the Related Art The laser flash method is a method that has rapidly spread in recent years as a method for measuring the thermal diffusivity and specific heat of a homogeneous material, and requires a small amount of measurement sample compared to other methods.
The feature is that highly accurate measurement values can be obtained over a wide temperature range. In this method, the sample surface is irradiated with a pulse generated by a laser, the back surface temperature of the sample is measured using a radiation thermometer, and the thermal diffusivity and specific heat of the sample are obtained from the data of the temperature response characteristics. It is a thing.

When there is an unsteady heat flow inside a one-dimensional material, it is described by the equation δT / δt = α · (δ ² T / δx ² ). T is temperature, α is thermal diffusivity, x is a one-dimensional coordinate variable, and the solution of T can be obtained by setting initial conditions and boundary conditions. The thermal diffusivity α in this equation is defined by α = κ / (C _p · ρ) = κ / c, and C _p , ρ,
c is a constant pressure specific heat, density, and heat capacity per unit volume (hereinafter referred to as specific heat). Therefore, if the constant pressure specific heat and density of the measurement sample are known, the thermal conductivity κ of the sample can be obtained using the thermal diffusivity α. Then, in recent years, an attempt has been made to apply such a laser flash method to a multilayer material to obtain an unknown thermal diffusivity in the multilayer material.
Satisfactory results have not been obtained due to problems such as the accumulation of calculation errors due to repeated calculations many times because the calculation formulas are complicated. Here, the method for analyzing the thermal diffusivity of a single layer material is described.

A general method for measuring the thermal diffusivity in the laser flash method is required to match the theoretical solution to the measured value data of the back surface temperature of the measured sample. That is, the theoretical temperature response T of the backside temperature of the sample by the one-dimensional heat conduction equation
Assuming a thermal diffusivity α, which is an unknown number in one layer in the multilayer material, a specific heat c, and a Biot number h which is a parameter related to heat loss, respectively, when the laser pulse is Q (t), the time t is used. Can be strictly shown by the relational expression of T = F (α, c, h, t), and T = F (α, h, t) in the case of a single layer material. However, the theoretical temperature response F (α, c, h, t) is replaced with the actual back surface temperature response E.
In order to obtain the unknowns α and h under the condition of matching the pattern according to (t), an implicit function including a trigonometric function and an exponential function is included in the formula, and actual numerical calculation is extremely difficult. Specifically, a method of simplifying the calculation is used by using an approximate value for a specific variable and limiting the data used for the calculation to only the data within a specific region.
Currently, as a method of analyzing the thermal diffusivity by such a laser flash method, the half-value arrival time t as shown below is used.
_{The 1/2} method, the area method, and the method of analyzing the specific heat are known, such as the method of measuring the temperature rise of the measurement sample to obtain the specific heat.

Half-value arrival time method The half-value arrival time t _1/2 is the time required for the temperature to rise from the initial temperature value to half the maximum rising temperature T _m on the temperature response curve on the back surface of the material. Is. Then, using the half-value arrival time t _1/2 until the temperature rises to half the maximum rise temperature T _m on the temperature response curve, it is established that there is no heat loss, and α ₀ = 1. 36975L ²
The thermal diffusivity α ₀ by the half-value reaching time method is calculated from the expression / (π ² · t _1/2 ). Here, L is the thickness of the measurement sample. The maximum temperature rise _Tm is obtained by extrapolating the decay curve after the temperature rises to the pulse irradiation time. Then, the heat loss correction coefficient K is obtained from the product of the relaxation coefficient k of the decay curve (the reciprocal of the time constant τ of the decay curve) and the half-value arrival time t _1/2, and the heat loss correction coefficient K is divided by the half value. The corrected thermal diffusivity α is calculated by multiplying the thermal diffusivity α ₀ by the value arrival time.

Area method A method for obtaining a thermal diffusivity α by calculating a deviation R between an average temperature in a specific section area set in the temperature response and an average temperature obtained from a theoretical formula. Extrapolating the subsequent temperature response decay curve to the laser pulse irradiation time as the maximum rise temperature T _m , using the time constant τ of the decay curve, the Biot number h as a function of the thermal diffusivity α, and the deviation R Is expressed, and then the thermal diffusivity α is calculated by the conditional expression R = 0 for the deviation R.

The method of irradiating a measurement sample with a fixed amount of laser flash and measuring the temperature rise value ΔT of the measurement sample to calculate the specific heat of the measurement sample is performed by the following procedure. (A) Measurement of Absorbed Energy Q After a glassy carbon plate is attached to a plate (usually a sapphire plate or the like) having a known specific heat at room temperature with silicon grease, a laser pulse is applied to absorb the absorbed energy Q.
To measure. The weight and specific heat of each are known, and the absorbed energy Q is expressed by the following equation from the measured value of the temperature rise value ΔT ′. Q = (M ₁ C ₁ + M ₂ C ₂ + M ₃ C ₃ ) ΔT ′ where M ₁ , M ₂ and M ₃ are the weights of glassy carbon, silicon grease and sapphire, respectively.
C ₁ , C ₂ , and C ₃ are the specific heats of glassy carbon, silicon grease, and sapphire, respectively. (B) Measurement of specific heat of sample at room temperature Next, at room temperature, a temperature rise value ΔT is measured by irradiating a laser pulse with a laser pulse in the same manner as in (a) of attaching a glassy carbon plate to a sample with silicon grease. If the emissivities of the glassy carbons are equal, the absorbed energies become equal and the following equation holds. _{Q = (M 1 C 1 +} M 2 C 2 + M s C s0) · ΔT where, M _s is the weight of the sample, C _s0 is the specific heat of the sample at room temperature. Therefore, the specific heat C _s0 of the sample at room temperature is given by the following equation using the Q obtained in (a). C _s0 = (Q · ΔT ⁻¹ −M ₁ C ₁ −M ₂ C ₂ ) / M _s (c) Measurement of specific heat of sample at high temperature Temperature rise value at room temperature and high temperature by irradiating laser pulse on sample alone Measure ΔT ₀ and ΔT ₁ , respectively.
At this time, Q ′ = C _s0 M _s ΔT ₀ , Q ″ = C _s1 M _s ΔT
_1, when the absorbed energy of the sample is not altered by the temperature Q '= Q "becomes, than this specific heat of the sample is given by the following _{equation. C s1 = C s0 ΔT 0} / ΔT 1 laser pulse absorption rate of If the sample is small, a material having a high absorptivity (such as carbon spray) is applied to the sample for measurement.

[0008]

However, in the above-described method of analyzing thermal diffusivity and specific heat in the laser flash method, since a single layer material is targeted, an unknown thermal diffusivity or specific heat in a multilayer material should be obtained. In such a case, when the above method is applied, the calculation becomes extremely complicated, and the calculation error accumulates, the elements intervening the calculation error increase, and it becomes extremely difficult to obtain a highly accurate value. As shown in FIG. 2, the intensity distribution of the laser pulse is represented as Q (t) as a function of time t, and by irradiating the laser pulse from the front surface side of the multilayer material, its temperature response E on the back surface side is shown. (T) is obtained. FIG. 3 is a cross-sectional view of a multilayer material consisting of n sheets, in which the thermal diffusivity α in the i-th layer, the specific heat c and the Biot number h on the front and back surfaces of the multilayer material are unknown, and the thickness of the layer and the remaining layers All thermal constants and thicknesses for

Then, such a theoretical temperature response T on the back surface side is strictly expressed as T = F (α, c, h, t), and is represented by the thermal characteristic values α, c, h of the multilayer material. The deviation between the theoretical temperature response T and the temperature response E can be calculated by giving a specific numerical value. The smaller the deviation, the higher the degree of conformity between the theoretical temperature response T and the temperature response E, and the higher the accuracy of the values of α, c, and h set at this time. That is, F is greater than F (α, c, h, t) shown in FIG.
The deviation of (α ', c', h ', t) from the temperature response E (t) is larger, and therefore (α, c, h) is (α',
It is a numerical value with higher accuracy than h ', c'). However, the theoretical temperature response T = F (α, c, h, t) in the multilayer material
Since the equation of is complicated, it is extremely difficult to exactly obtain such a minimum value of the deviation by mathematical analysis means.

Further, the method of irradiating a measurement sample with a fixed amount of laser flash and measuring the temperature rise value ΔT of the measurement sample to calculate the specific heat of the measurement sample has the following problems. is there. (B) The measurement condition is that the pulse energy does not change with repeated irradiation, but there is no guarantee. (B) The absorption rate of the sample needs to be constant with respect to temperature, but there is no guarantee. In addition, the coating material that raises the absorbed energy needs to be constant in the absorbed energy without deteriorating up to a high temperature, but there is no guarantee for this. (C) Since the absolute value of the temperature rise value is required, measure with a thermocouple. When the sample is ceramics or the like, it is attached to the sample with an adhesive, and the temperature at which this adhesive functions is usually 100.
It is up to about 0K, and the specific heat cannot be measured at temperatures higher than that. (D) Installation of this thermocouple is complicated and requires skill. Usually, a fast response is required to measure the thermal diffusivity, and the absolute value of the temperature is not required, so it is measured by a radiation thermometer.When measuring the specific heat, the absolute value of the temperature is required. It is necessary to measure in pairs. Therefore, when obtaining the thermal conductivity, it is necessary to measure twice.

The present invention has been made in view of the above circumstances, and it is possible to accurately and efficiently determine unknown thermal diffusivity, specific heat and other thermal constants in one layer of a multilayer material, and An object of the present invention is to provide a method for measuring a thermal constant using a laser flash method and an apparatus for the same, which are less affected by environmental conditions of measurement.

[0012]

A method according to the above-mentioned object.
The method for measuring the thermal constant using the laser flash method described is a temperature response on the back surface side obtained by irradiating a laser flash from the front surface side of a multilayer material including one layer whose thermal diffusivity and specific heat are unknown, and the thermal diffusivity. , Specific heat, and the theoretical temperature response including Biot number as a variable, the thermal diffusivity, specific heat,
And a Biot number.

According to a second aspect of the present invention, there is provided a method for measuring a thermal constant using a laser flash method, wherein the thermal diffusivity, the specific heat, and the Biot number are the same as those in the first method. By setting one of them as A, the other as B, and the other as C, the initial values of A and B are set, and C that minimizes the deviation between the temperature response and the theoretical temperature response on the back surface of the multilayer material is obtained. A first step of setting the deviation as an initial value of the minimum deviation, a second step of setting new A and B of the multilayer material in the vicinity of A and B giving the minimum deviation, and The third step of obtaining C and the deviation from A and B at which the deviation between the theoretical temperature response and the back surface temperature response of the multilayer material is minimized is compared with the deviation and the minimum deviation. If it is large, from the second step When the deviation becomes less than or equal to the minimum deviation after repeating three steps, the deviation is newly set as the minimum deviation, the second to third steps are repeated, and the minimum deviation reaches the vicinity of the minimum value. And a fourth step of outputting the thermal diffusivity, the specific heat, and the Biot number.

According to a third aspect of the present invention, there is provided a method for measuring a thermal constant using a laser flash method, wherein each of the thermal diffusivity, the specific heat and the Biot number is the same as the method for measuring a thermal constant using the laser flash method. The initial value is set, the deviation between the theoretical temperature response including the initial value and the back surface temperature response is obtained, and the thermal diffusivity, specific heat, biot number, and deviation are set to the thermal diffusivity, specific heat, and biot number, respectively. And a first step of setting deviation, a second step of setting a new A in the vicinity of the A by setting one of the set thermal diffusivity and the specific heat to A and the other one to B, and the setting. The calculated A and the B that minimizes the deviation between the theoretical temperature response including the set Biot number and the backside temperature response are used to obtain B, and the Biot number is updated by the thermal diffusivity and specific heat. Set the number of biot and set A The third step of determining the thermal diffusivity, the specific heat, and the Biot number by repeating the calculation step until the vicinity of the minimum deviation value in the above-mentioned state, and the theoretical temperature response and the temperature response including the thermal diffusivity, the specific heat, and the Biot number Then, it is determined whether the minimum deviation has reached the minimum value, and if it has not reached the minimum value, the above steps 2 to 3 are repeated. When the deviation reaches the minimum value, And a fourth step of outputting the thermal diffusivity, specific heat, and Biot number at that time.

According to a fourth aspect of the present invention, there is provided an apparatus for measuring a thermal constant using a laser flash method, wherein a temperature of a rear surface obtained by irradiating a laser flash from a front surface side of a multi-layered material including one layer whose thermal diffusivity and specific heat are unknown. Measurement of the thermal constant of the multilayer material using the laser flash method for determining the thermal diffusivity, the specific heat, and the Biot number by comparing the response and the theoretical temperature response including the thermal diffusivity, the specific heat, and the Biot number as variables. A device, wherein one of the thermal diffusivity, the specific heat, and the Biot number is A, the other one is B, and the other is C, and the initial values of A and B are set, and First calculation means for obtaining C which minimizes the deviation between the temperature response and the theoretical temperature response and setting the deviation as an initial value of the minimum deviation, and the new deviations A and B of the multilayer material In the vicinity of A and B And a second calculation for obtaining a C and a deviation that minimize the deviation between the theoretical temperature response and the back surface temperature response of the multilayer material from A and B of the multilayer material. If the deviation is larger than the minimum deviation by comparing with the minimum deviation, the first and second calculations are repeated, and when the deviation becomes the minimum deviation or less, the deviation is newly set as the minimum deviation. The second calculating means to be set and whether or not the minimum deviation has reached the vicinity of the minimum value are determined. If not, the first and second calculations are repeated to bring the minimum deviation value to the vicinity of the minimum value. Outputs the thermal diffusivity, specific heat, and Biot number when it reaches the third
And a computing means of.

According to a fifth aspect of the present invention, there is provided a device for measuring a thermal constant using a laser flash method, wherein a temperature of a rear surface obtained by irradiating a laser flash from a front surface side of a multilayer material including a single layer whose thermal diffusivity and specific heat are unknown. Measurement of the thermal constant of the multilayer material using the laser flash method for determining the thermal diffusivity, the specific heat, and the Biot number by comparing the response and the theoretical temperature response including the thermal diffusivity, the specific heat, and the Biot number as variables. An apparatus, wherein each initial value of thermal diffusivity, specific heat, and Biot number is set, a deviation between a theoretical temperature response including the initial value and a back surface temperature response is obtained, and the thermal diffusivity, specific heat, and Biot number are obtained. , And deviation are respectively set thermal diffusivity, set specific heat, set Biot number and set deviation, and one of the set thermal diffusivity and specific heat is A, and the other one is B, New in the vicinity of A Calculating the second calculation means for setting, A set by the second calculation means, and B for minimizing the deviation between the theoretical temperature response including the set Biot number and the back surface temperature response, and the calculation The Biot number is updated by the resulting thermal diffusivity and specific heat to determine a new set Biot number, and the above calculation is repeated until the vicinity of the minimum deviation value in the state where A is fixed is reached.
A third computing means for determining the Biot number and a deviation between the theoretical temperature response and the temperature response including the thermal diffusivity, the specific heat and the Biot number obtained by the third computing means are obtained, and the deviation is near the minimum value. A fourth calculation means for determining whether or not
When the deviation obtained by the calculation means of 1 does not reach the vicinity of the minimum value, a new A set in the direction of giving a smaller minimum value is input to the second calculation means,
When it reaches the vicinity of the minimum value, it has a fifth calculation means for outputting the thermal diffusivity, the specific heat, and the Biot number at that time.

Here, the deviation between the theoretical temperature response and the back surface temperature response is the forward squared deviation which is the sum of the squares of the difference between the two, and the inverse squared which is the sum of the squares of the differences of the respective reciprocals. deviation,
It can be applied to a logarithmic square deviation obtained by summing squares of respective logarithmic differences, and a deviation formed by a combination thereof. Further, the respective measurement data and the theoretical temperature response data may be subjected to the Laplace transform for arithmetic processing, or the actual data may be used for the arithmetic processing. The difference and the difference are so-called absolute values of the difference. Further, the specific allowable value, the specific reference value, and the allowable reference value are determination values for updating the deviation and the like, and are values that are appropriately set according to the allowable limit of the required calculation error. . When the deviation reaches the vicinity of the minimum value, it means that the difference before and after the update remains within the predetermined allowable reference value range even if the update calculation of the deviation is repeated.

[0018]

The theoretical temperature response T of the back surface of the sample by the one-dimensional heat conduction equation is calculated by the thermal diffusivity α in one layer of the multilayer material, the specific heat c, and the Biot number h which is a parameter related to the heat loss in the front and back surfaces of the multilayer material. When set respectively, time t
Alternatively, as a function of the Laplace variable p, T = F (α, c,
h, t) or T = F '(α, c, h, p). In the method for measuring a thermal constant using the laser flash method according to any one of claims 1 to 3, the theoretical temperature response F (α, c, h, t) or F '(α, c,
h, p) and the function E (t) having the time t of the actually obtained temperature response as a variable or the function E '(p) having the Laplace variable p as a variable, the thermal diffusivity α is used as an index. ,
By the Biot's number h and the specific heat c will sequentially set to a value near that giving the minimum deviation R _m, performs updating of minimum deviation R _m, determined Biot number h, specific heat c and the true value of the thermal diffusivity α Can be obtained.

In the method of measuring the thermal constant using the laser flash method according to the second aspect, any one of the thermal diffusivity, the specific heat and the Biot number is A, the other one is B, and the other is C.
, One or more values of A and B are set in the vicinity of A and B that give the minimum deviation, and C and the deviation that minimize the deviation are obtained for the combination of A and B, and the minimum deviations are By comparing and updating A and B in the direction that gives the smallest smaller deviation sequentially, when the minimum deviation reaches the vicinity of the minimum value, the thermal diffusivity, the specific heat, and the Biot number are output. It is possible to accurately and promptly obtain a desired value by appropriately selecting two unknowns from the above, depending on the situation. In the following description, the specific heat is assigned as A, the Biot number and the thermal diffusivity are assigned as B and C, respectively. The procedure for obtaining the thermal diffusivity α and the specific heat c will be described in detail below based on the flow chart shown in FIG.

First, the specific heat c and the Biot number h, which are unknowns in one layer in a multilayer material as shown in FIG. 3, are appropriately determined from literature values and the like, and respective initial values c ₀ and h ₀ are set ( S-1). Then, the respective initial values (c ₀ , h ₀ ) set in S-1 are set to the theoretical temperature response F (α, c, h,
t) or F ′ (α, c, h, p), and the value of α that minimizes the square deviation R from the actual temperature response E (t) or E ′ (p) is δR. It is calculated by setting / δα = 0. Here, the expression δR / δα = 0 is a one-dimensional equation of the form g (α) = 0 including only α as a variable,
This root α can be precisely obtained by a numerical analysis method such as Newton's method. The initial value of the thermal diffusivity α thus obtained is α ₀ , and the initial value of the deviation R is R
₀ , the set of these initial values (R ₀ , α ₀ , c ₀ ,
h ₀ ) is set as a set of temporary minimum values (R _m , α _m , _cm , h _m ) (S-2).

Then, the set of minimum values (R _m , α _m , _cm ,
For h _m ), a new set of values (c _i , h _i ) is set near the point on the two-dimensional plane represented by ( _cm , h _m ) (S-3). Then, the values of c _i and h _i are set to the theoretical temperature response F (α, c, h, t) or F ′ (α, c, h,
p), and the actual temperature response E (t) or E '
The value of α that minimizes the squared deviation R from (p) is δR
It is calculated by setting / δα = 0. The value of the thermal diffusivity α obtained at this time is α _i and the value of the deviation R is R _i , and these pairs (R _i , α _i , h _i , c _i ) are set (S−
4). In S-5, R already set as the minimum value
_{When m} is compared with R _i obtained in S-4, R _i is R
When _m is greater than returns to S-3, when R _i is smaller than R _m is the minimum value by the R _m = R _i R _m
Is updated with R _i at that time (S-6). After S-6, the preset allowable reference value ε is compared with the minimum value R _m (S-7), and when the minimum value R _m is larger than the allowable reference value ε, the process returns to S-3, When it is smaller than the allowable reference value ε, the set of minimum values at that time (R _m , α _m , c
_m , h _m ) is regarded as desired α, c, h and is output (S
-8), End all the procedures for obtaining the thermal diffusivity α and the specific heat c in the multilayer material.

[0022] or less to the an example of a method of setting h _i, c _i of S-3. Fix the number of bios. The specific heat is sequentially changed to obtain the thermal diffusivity and the deviation, the magnitudes of the deviations are compared, and the specific heat is moved in the direction of giving the smaller deviation. The amount of transfer of this specific heat becomes smaller as it approaches the minimum deviation value when the Biot number is fixed. By this procedure, the specific heat, the thermal diffusivity, and the deviation for one Biot number are obtained. Change the setting value of Biot number, and execute the procedure of.
By comparing the magnitude of the deviation determined for each Biot number, the Biot number is moved in the direction of giving a smaller deviation. The movement amount of the Biot number is reduced as it approaches the minimum deviation value. By this procedure, the Biot number, the specific heat and the thermal diffusivity that give the minimum deviation value are obtained. In the above procedure, it is possible to set a plurality of Biot numbers and specific heats respectively. In this case, the Biot number and specific heat setting intervals ΔX are set to be smaller as the deviation minimum value is approached.

In addition to the above, in the determination of S-7, one of the thermal diffusivity, the specific heat, the Biot number or the deviation is X _i , and the value at that time is X _m , and | (X _i −X _m ) /
The determination may be performed under the condition that X _m | <ε or | X _i −X _m | <ε.

In the method for measuring the thermal constant using the laser flash method according to the third aspect, either the thermal diffusivity or the specific heat can be set first. Hereinafter, a case where the specific heat is set first to obtain the heat constant will be described. After setting a new specific heat in the vicinity of the specific heat that gives the minimum deviation, the Biot number is updated based on the relational expression determined by the specific heat and the value of the thermal diffusivity that gives the minimum deviation,
The desired values of α, c, and h can be accurately and quickly obtained using only the specific heat c as a variable. This measurement procedure will be described in detail below with reference to the flow chart shown in FIG. First, the specific heat c and the thermal diffusivity α of an unknown layer in a multilayer material are appropriately determined as initial values c ₀ and α ₀ with reference to literature values (S-1). The thermal diffusivity may be obtained by using the relationship between t _1/2 and the average thermal diffusivity when there is no radiation loss. Then, the initial value h ₀ of the Biot number h is calculated from the relational expression h ₀ = f (t _1/2 , τ) using the time constant τ obtained from the temperature response curve and the value of the half value arrival time t _1/2. The calculation is performed (S-2), and the initial values are set as the set specific heat, the set thermal diffusivity, and the set Biot number, respectively. Above S-1, S-2
Thus, the first step is completed. This initial value setting method is not limited to the measuring method described in claim 3. Subsequently, by setting a new specific heat c _i in the vicinity of the set specific heat (S-3), and terminates the second process. Then, the S-
2, the theoretical temperature response F (α, c, h, t) of the value (c _i , h ₀ ) set in S-3, or F ′ (α, c, h, p) obtained by Laplace transforming this. ), The value of α that minimizes the deviation R from the actual temperature response E (t) or E ′ (p) is obtained by δR / δα = 0, and this is obtained by α _i (S-4).

In S-5, the set c _i ,
And the value of α _i are used to obtain the updated Biot number h _i by the formula h _i = g (α _i , c _i ) (S-5). Where h
The update of _i can be calculated based on the following formula, for example. c _av = (Σ (ρ _j · C _pj · Δl _j )) / l _n α _av = l _n / ((Σ (Δl _j / (ρ _j · C _pj · α _j ))) · c _av ) β _{0i = l n / (sqrt (α} av · τ) h i = β 0i · ((sinβ 0i) -1 - (tanβ 0i) -1) _{where, ρ j · C pj · Δl} j, l n respectively, first The density in the j layer, the specific heat at constant pressure, the thickness of the j-th layer, and the thickness of all layers, c _av is the average value of the heat capacity per unit volume of the multilayer material, α _av is the average thermal diffusivity of the multilayer material, and Σ is The sum of each term from the first layer to the n-th layer, which is the last layer, is to be shown.Next, the respective values (thermal diffusivity, Biot number, deviation) obtained in S-4 and S-5. Is determined by comparing the difference between any of the above and each of the already set values or the ratio of each of the values of the difference based on the allowable reference value (S-6), and the determination condition is satisfied until the determination condition is satisfied. S-4, S
-5 is repeated until the desired thermal constant (thermal diffusivity,
A Biot number, specific heat) pair is obtained, and the third step is finished here. The thermal diffusivity used in S-6 is the thermal diffusivity of the unknown layer or the average thermal diffusivity of all or a part of the layers including the unknown layer.

In S-7, the thermal diffusivity, specific heat,
Then, the deviation between the theoretical temperature response including the Biot number and the temperature response is obtained, and the ratio or difference between the specific heat or the deviation and the set specific heat and the set deviation and the set specific heat and the set deviation are calculated (S -8), when the ratio or difference is larger than the specific allowable value, the process returns to S-3 and S-3 to S-7 are repeated, and when the ratio or difference becomes less than or equal to the specific allowable value, The thermal diffusivity, the specific heat, and the Biot number at the time point are output (S-9), and the fourth step ends and the whole procedure ends.

An example of the method of setting the specific heat in S-3 is shown below. First, when the specific heat set value is changed, the Biot number, thermal diffusivity and deviation are obtained for each specific heat. The magnitude of this deviation is compared, and the next specific heat is set in the direction that gives the smaller deviation. The amount of change in the specific heat is reduced as it approaches the minimum deviation value. It is also possible to set a plurality of specific heats in the above procedure. In this case, the specific heat setting interval Δc is reduced as it approaches the minimum deviation value.

In the determination of S-8, in addition to this, one of the thermal diffusivity and the Biot number is set as X, and | (X _i −X _m ) / X
_The determination may be performed under the condition that _m | <ε or | X _i −X _m | <ε. When a plurality of specific heats are set in S-3, the thermal diffusivity, the Biot number, and the deviation are obtained for each specific heat by S-4, S-5, and S-6. Select the specific heat that gives the smallest deviation from
At 8, the same judgment is made. If the conditions are not satisfied, a plurality of new specific heats are set in S-3 so as to give smaller deviations.

In the apparatus for measuring thermal constants using the laser flash method according to claim 4, the thermal diffusivity, the specific heat,
And one of the Biot numbers is A, the other one is B and the other is C, and the initial values of A and B are set to minimize the deviation between the temperature response and the theoretical temperature response on the back surface of the multilayer material. And a new calculation means for setting the deviation as an initial value of the minimum deviation, and new A and B for the multilayer material.
Is set in the vicinity of A and B that give the minimum deviation, and C that minimizes the deviation from the theoretical temperature response and the back surface temperature response of the multilayer material from A and B of the multilayer material.
And a second calculation for obtaining the deviation, and comparing the deviation with the minimum deviation. If the deviation is larger than the minimum deviation, the first and second calculations are repeated to obtain the minimum deviation. When it becomes the following, it is determined whether or not the deviation is newly set as the minimum deviation, and whether or not the minimum deviation reaches the vicinity of the minimum value. When the minimum deviation value reaches the vicinity of the minimum value by repeating the calculation of, the third calculation means for outputting the thermal diffusivity, the specific heat, and the Biot number is included, and therefore the theoretical temperature response time function F (α , C, h, t), or F '(α, c, h, p), which is the Laplace transform form of this, and the temperature response E (t) actually obtained, or the deviation R between E' (p) as an index, by sequentially setting the a and B in the vicinity of a value giving the minimum deviation R _m Performing updating of minimum deviation R _m, unknown Biot number, can be determined by the configuration of a simple calculation means the true value of the specific heat and thermal diffusivity. And the first
The third calculation means is a computer configured to perform actual calculation according to a preset program.

In the apparatus for measuring thermal constants using the laser flash method according to claim 5, initial values of thermal diffusivity, specific heat and Biot number are set, and the theoretical temperature response and the back surface including the initial values are set. A first computing means for obtaining a deviation from the temperature response, the thermal diffusivity, the specific heat, the Biot number, and the deviation being the set thermal diffusivity, the set specific heat, the set Biot number, and the set deviation, respectively, and the set heat. Either the diffusivity or the specific heat is A,
Second computing means for setting a new A in the vicinity of A with the other one as B, A set by the second computing means, and a theoretical temperature response and a temperature response including a set Biot number. B that minimizes the deviation of B is calculated, the Biot number is updated by the thermal diffusivity and specific heat obtained from the calculation result, and a new set Biot number is determined, and the deviation is close to the minimum deviation value when A is fixed. The third calculation means for determining the thermal diffusivity, the specific heat, and the Biot number by repeating the calculation until reaching, and the theoretical temperature response and the back surface including the thermal diffusivity, the specific heat, and the Biot number obtained by the third calculation means. Fourth calculating means for determining a deviation from the temperature response and determining whether the deviation has reached the vicinity of the minimum value, and when the deviation calculated by the fourth calculating means does not reach the vicinity of the minimum value. Gives a smaller minimum Fifth calculating means for inputting a new A set in the direction to the second calculating means and outputting the thermal diffusivity, specific heat and Biot number at that time when the value reaches the vicinity of the minimum value. , And the Biot number is updated on the basis of the thermal diffusivity and the specific heat, and the time function F (α, c, h, t) of the theoretical temperature response or F ′ (α, c, h, p) and the temperature response E (t) actually obtained or E ′ (p) as an index, the specific heat c is sequentially set in the vicinity of the value giving the minimum deviation R _m , By updating the minimum deviation R _m , the unknown biot number,
The true values of the specific heat and the thermal diffusivity can be obtained by repeating the simple calculation calculation means.

[0031]

Embodiments of the present invention will now be described with reference to the accompanying drawings to provide an understanding of the present invention. Here, FIG. 1 is a block diagram of a laser flash device to which a thermal constant measuring method using the laser flash method according to an embodiment of the present invention is applied, and FIG. 2 shows a thermal constant measuring method using the laser flash method. FIG. 3 is an explanatory view of a laser flash method using a multilayer material, FIG. 4 is a flow chart of a direct method in a method of measuring a thermal constant using the laser flash method, and FIG. 5 is a thermal constant using a laser flash method. Flow chart of the time constant method of the measurement method, FIG. 6 is a diagram showing the calculation error of the time constant method when the thickness of the unknown layer in the multilayer material consisting of three layers is changed, and FIG. 7 is the laser flash method. Fig. 8 shows the flow chart of the direct method in the method of measuring thermal constants.
It is a figure which shows the calculation error of the direct method when changing the thickness of the unknown layer in the multilayer material which consists of layers.

First, an apparatus for measuring thermal diffusivity, specific heat, and thermal constants such as the Biot number using the laser flash method according to the embodiment of the present invention shown in FIG. 1 will be described. This is an apparatus for measuring an unknown thermal constant in a single layer contained in the multilayer material 10 by using a laser pulse generator as a measurement sample. The laser pulse generator can generate a pulse with an arbitrary waveform as necessary, and simplifies the calculation by selecting a special waveform according to the range of the physical property value of the multilayer material 10 and the analysis method of the thermal constant, It is also possible to improve the measurement accuracy in the area. The temperature response on the back surface of the sample is measured with a temperature measuring device such as a radiation thermometer or a thermocouple.

The waveform signal of the laser pulse applied to the multilayer material 10 is taken into the laser pulse detecting device via the half mirror 11 provided between the multilayer material 10 and the laser pulse generator. It is also possible to measure the pulse waveform by measuring the leaked light in the optical path of the laser light. Then, the signal data from the temperature measuring device and the laser pulse detection device are loaded into a computer, and the calculation processing for determining the thermal constants such as the thermal diffusivity, the specific heat and the Biot number is performed based on the signal data, and the data and the calculation are performed. It is entirely configured so that the results can be displayed on an output device connected to a computer.

Multilayer Material 10 Using Laser Flash Method
In order to analyze thermal characteristics such as thermal diffusivity or specific heat of
First, the theoretical temperature response when the multilayer material 10 is irradiated with the laser pulse Qf (t) is obtained. Here, f (t) uses a standardized function with the integral value in the entire time domain being 1. This analysis can be performed on the Laplace space obtained by conversion by the Laplace transform, and the theoretical solution of the temperature response can be obtained as follows.

First, assuming that the multilayer material 10 is composed of n layers, the thermal diffusivity α _i , the constant pressure specific heat C _pi , the density ρ _i and the thickness ΔL _i in the _{i-th layer} are determined. Therefore, the thermal conductivity k _i
Is represented by k _i = α _i · C _pi · ρ _i . Further, the thickness L _i from the surface to the boundary between the i-th layer and the (i + 1) -th layer is L _i =
ΔL ₁ + ΔL ₂ + ... + ΔL _i . The heat conduction equation in the i-th layer in the laminated composite material is δT _i (x,
t) / δt = α _i · δ ² T _i (x, t) / δx ² , the initial condition is T _i (x, t) = 0, and the boundary condition is T _i (L _i , t). = T _{i + 1} (L _i , t) and k _i · δT _i (L _i , t) / δx = k _{i + 1} · δT
_{i + 1} (L _i , t) / δx, respectively. Therefore, by applying the Laplace transform to these, and letting the Laplace variable be p, the above heat conduction equation is δ ² T _i (x,
p) / δx ² = (p / α _i ) · T _i (x, p),
Further, the boundary condition is T _i (L _i , p) = T _{i + 1} (L _i ,
p), and k _i · δT _i (L _i , p) / δx = k _{i + 1} ·
δT _{i + 1} (L _i , p) / δx, respectively.
Then, the same operation is sequentially applied from the first layer to the final n-th layer to obtain a set of Laplace-transformed heat conduction equations for the entire multilayer material 10.

As described above, the general solution of the heat conduction equation in the i-th layer is T _i (x, p) = A _i exp (r _i
X) + B _i exp (−r _i · x) However, r _i is r _i = sqrt (p / α _i ), and A _i ,
B _i is an integration constant. Then, the i-th layer and the (i + 1) -th layer
From the boundary conditions of the layers, the integration constants A _i , B of the temperature equation of the i-th layer
_i and the integration constants A _{i + 1} and B _{i + 1} of the temperature equation of the (i + 1) th layer
Equation 1 can be obtained by obtaining the relationship of Where G
_{i and i + 1} are matrices represented by Equation 2. Therefore, the coefficient of the first layer temperature and the coefficient of the n-th layer temperature have a relationship represented by Expression 3. The same analysis was performed using the conditions of heat input and heat dissipation on the front and back surfaces, and finally the temperature response in the nth layer,
That is, the sample back surface temperature Ts is given by Equation 4, and the relational expression T = F ′ (α, c, h, p) including three variables (thermal diffusivity α _i , specific heat c _i , Biot number h) in the equation Represented by (However, it is assumed that the front side value h ₀ of the Biot number and the back side value h ₁ are equal. H = h ₀ = h ₁ ).

[0037]

[Equation 1]

In the following, using Equation 4 which is a basic equation giving the theoretical temperature response on the back surface of the sample, the partial differential with respect to the thermal diffusivity α, the specific heat c or the Biot number h with respect to the square deviation R from the temperature response is calculated. The procedure for obtaining the thermal diffusivity α, the specific heat c or the Biot number h satisfying the equation obtained by setting it to zero by the Newton method will be described. The thermal diffusivity α, the specific heat c or the Biot number h of the layer with unknown thermal properties is represented by a variable x, and Δx = − (δR / δx) / (δ ² R / δx
² ) is obtained, and x is updated by x _new = x + Δx.
By repeating this procedure, x that satisfies δR / δx = 0, that is, the thermal diffusivity α, the specific heat c or the Biot number h can be obtained.

As described above, the thermal diffusivity α and the heat capacity per unit volume (ρ · C _p ) appear in the theoretical temperature response of each layer. Therefore, what is directly required is the thermal conductivity which is the product of these two thermal characteristic values (α, c), and if the density is known, the constant pressure specific heat is also required. However, in analysis, it is also possible to treat the density of the layer with unknown thermal properties as a constant and the constant pressure specific heat as a variable, and after the calculation is completed, multiply the constant pressure specific heat by the density to obtain the heat capacity per unit volume. In this numerical analysis method, it is assumed that a one-dimensional heat conduction equation is established, the Biot numbers on the front and back surfaces of the sample are equal, and that all the thermal characteristic values except the i-th layer and all the layer thicknesses are known. Calculation shall be performed under the conditions. Furthermore, when applying the time constant method shown below,
It is assumed that the relational expression between the thermal conductivity λ _i of each layer and the overall thermal conductivity λ in the steady state of the multilayer material is approximately satisfied.

In the case of the multilayer material 10 as shown in FIG. 3, the unknown variables are three variables of the thermal diffusivity α of the thermal property unknown layer, the specific heat c, and the Biot number h as unknown variables, and h = g.
This variable (α, c, h) can be determined by reducing the variable by one by the relational expression of (α, c) and by minimizing the deviation between the theoretical temperature response and the temperature response.

(Calculation of time constant τ) In the case of a single layer material having a thickness L, the characteristic time t ₀ is t ₀ = L ² / (π ² · α ₀ ).
In the time domain t satisfying t >> m · t ₀ , where m is a constant, the second and subsequent terms (n ≧ 1) in Equation 5 become negligibly smaller than the first term. , T (L, t) / T _m = A ₀ exp (−a ₀ ·.
t) ∫exp (a ₀ · t ′) f (t ′) dt ′ can approximate the theoretical solution of the backside temperature. Where A ₀
= 2β ₀ ² / (β ₀ ² + 2h + h ² ), a ₀ = β ₀ ² · α / L
²

[0042]

[Equation 2]

Therefore, when the logarithm of the temperature response data is plotted against time and the time constant τ is obtained from the slope thereof, the time constant τ can be regarded as equal to the reciprocal of a ₀ . That is, τ = 1 / a ₀ = L ² / (β ₀ ² · α), and assuming that this relationship holds for the average thermal diffusivity α _{av of the} multilayer material 10, α _av = α and τ = 1 / a ₀ = L ² / (β ₀ ²
・ Α _av ) is obtained.

For monolayer materials, t for the eigenvalue β _n
an (β _n ) = 2h · β _n / (β _n ² −h ² ) The biot number h is obtained as a function of β _{0 from} the equation and h ₀ = β ₀ · (by selecting a positive value for h. 1 / sin β ₀ -1
/ Tan β ₀ ) can be obtained. Since this relationship holds for the multilayer material 10 as well, β
₀ is given by β ₀ = L / sqrt (α _av · τ) using the average thermal diffusivity α _av of the multilayer material 10 and the time constant τ. That is, the Biot number h can be expressed as a function of the average thermal diffusivity α _av and the time constant τ as described above, and the average thermal diffusivity α _av of the multilayer material 10 is the unknown thermal diffusivity in the multilayer material 10. α
And the specific heat c, the total h = g
It is possible to set the Biot number h as (α, c).

The unknown thermal constant contained in any one layer of the multilayer material 10 can be measured by the direct method and the time constant method shown below. In the direct method, three variables to be obtained (thermal diffusivity α, specific heat c, Biot number h) are directly set to minimize the square deviation R between the theoretical temperature response and the temperature response (α, c, h) to reach the optimal solution,
The time constant method is to obtain the time constant τ after a sufficient time has elapsed from the characteristic time of the sample after laser irradiation, and the thermal diffusivity α and the Biot number h have a specific relationship via the time constant τ. Is a method of reducing variables by using. That is, α,
In this method, one variable is subtracted by the relational expression established between c and h to reach the minimum square deviation R.

Here, the deviations are (a) forward square deviation I, (b) forward square deviation II, and
Each deviation R such as (C) inverse square deviation I, (D) inverse square deviation II, and (E) logarithmic square deviation can be appropriately adopted. (B) R = Σ (Q · T _j −E _j ) ² (b) R = (ΣE _j ² ) · (ΣT _j ² ) − (ΣE _j · T _j ) ² (c) R = Σ {(1 / (Q · T _j ))-(1 / E _j )} ² (d) R = (Σ1 / E _j ² ) · (Σ1 / T _j ² ) − {Σ1 / (E _j · T _j )} ² (E) R = Σ {ln (Q · T _j ) −ln (E _j )} ²

Here, Q is the total energy absorbed in the sample of the laser pulse irradiating the multilayer material 10. When the above-mentioned deviations are calculated, the characteristics are as follows. (B) It is a general definition. Substitution of Q obtained by δR / δQ = 0 into the equation (a) and elimination of Q is used as the deviation. (B) δR / δQ using equation (a) which is a general deviation
This is a deviation obtained by substituting Q obtained by = 0 into the equation (a) and setting the numerator portion as zero, and has an advantage that the calculation equation is simpler than that of the equation (a). (C) Since the variables are concentrated in the denominator of the theoretical temperature, the calculation formula can be simplified by using the reciprocal. δR / δQ = 0
Substituting Q obtained by the equation into (C) and eliminating Q is used as the deviation. (D) It is the deviation obtained by substituting Q obtained from δR / δQ = 0 into Eq. (C) using Eq. (C) and setting the numerator as zero, and comparing it with (C). This has the advantage of simplifying the formula. (E) The minimum value can be easily determined by using the logarithmic square deviation. Substituting Q obtained by δR / δQ = 0 into the equation (E) and eliminating Q is used as the deviation. In addition, when adopting the Laplace transform format in the equations (a) to (e), a plurality of Laplace variables p are set, and the temperature response data is Laplace transformed to the plurality of set p. _Let E _j be obtained and apply these to the equations (a) to (e).

(Measurement Method of Thermal Constant by Time Constant Method) The procedure of the measurement method by the time constant method is shown below. Calculation of initial value of average thermal diffusivity α _av The time required to rise from the center of gravity of the laser pulse heat input curve to half the maximum temperature rise value T _m is calculated according to the usual half-value arrival time t _1/2 method. The initial value α _av of the average thermal diffusivity is calculated from the above. Alternatively, the specific heat of the layer whose thermal constant is unknown,
The thermal diffusivity may be set, and the initial value of the average thermal diffusivity α _av of the multilayer material may be calculated based on the thermal diffusivity. Here, the average specific heat c _av and the average thermal diffusivity α _av of the multilayer material are given by the following equations. c _av = (Σρ _i C _i Δl _i ) / l _n α _av = l _n / ((ΣΔl _i / (ρ _i C _i α _i )) · c _av ) where Δl _i is a multi-layer material composed of n layers The thickness of the i-th layer (= l _i −l _i−1 , and the total thickness of the multilayer material l _n
Is l _n = ΣΔl _i .

Calculation of time constant τ In the time domain in which an approximate expression based only on the first term of the time-space theoretical solution of the sample back surface temperature when sufficient time has elapsed after the laser pulse heat input, assuming a monolayer material, The time constant τ is calculated from the decay of the measured sample temperature. Calculating average thermal diffusivity of Biot number initial value h ₀ alpha _av, when obtaining the initial value h ₀ of Biot number from constant τ and eigenvalue equation. Initial setting of specific heat Set multiple specific heats for layers with unknown thermal constants. Calculation of thermal diffusivity of a layer whose thermal constant is unknown by Newton's method The square deviation R of the theoretical temperature response and the measured temperature of the back surface of the multilayer material 10 obtained by using laser pulses for a plurality of specific heats
Is used to update the thermal diffusivity of the layer with unknown thermal constant by the Newton method. The average thermal diffusivity and the Biot number of the multilayer material 10 are updated using the updated thermal diffusivity. Then, iterative calculation is performed using these values and repeated until Δα / α becomes sufficiently small.

Determination of minimum value of squared deviation R and resetting of plural specific heats The squared deviation is calculated from the specific heat c calculated above, the thermal diffusivity α, and the Biot number h, and the specific heat giving the minimum value is obtained. . Ratio Δc / c between a plurality of specific heat intervals Δc and c
Until the value becomes sufficiently small, the specific heat is reset near the specific heat that gives the minimum value, and this is repeated. In the above procedure, a plurality of specific heats c are set, and the corresponding thermal diffusivity α is obtained by the Newton method, but the thermal diffusivity α may be replaced by the specific heat c. That is, a method may be used in which a plurality of thermal diffusivities α are set and the specific heat c corresponding thereto is obtained by the Newton method.
In this case, since the specific heat c is an algebraic equation, the root may be analytically obtained.

FIG. 6 shows the calculation results when the thickness of the unknown layer in the multi-layered material 10 consisting of three layers obtained by the time constant method is changed. (A) shows the case where the lowermost third layer contains an unknown thermal constant, and (b) shows an example where the second layer which is an intermediate layer contains an unknown thermal constant. As is clear from the figure, it is understood that the calculation error, that is, the measurement error can be kept within a range of approximately ± 1% or less in both cases (a) and (b).

(Measurement Method of Thermal Constant by Direct Method) The direct analysis method is the above-mentioned least square method for the deviation R represented by three independent variables of the thermal diffusivity α, the specific heat c, and the Biot number h. And Newton's method are applied to obtain the thermal diffusivity α, the specific heat c, and the Biot number h that satisfy the minimum value of the deviation R. Two examples of this procedure are shown below.

Direct Method 1 A procedure for obtaining a desired thermal constant by simultaneously setting a plurality of Biot numbers according to FIG. 7 will be described below. An initial value c _{0 of the} specific heat is set (S-1). A plurality of biot numbers are set (S-2). For each Biot number, the thermal diffusivity α and the specific heat c that give the minimum value R _j of the square deviation R are determined by the following procedure. -1 minimum for each specific heat set
The thermal diffusivity that gives the minimum value R _j of the deviation R is obtained by applying the multiplication method and the Newton method (S-3) and (S-4). Alternatively, it is also possible to set a plurality of thermal diffusivities in S-3 and obtain a specific heat with a minimum deviation R. -2 The deviation R obtained for each combination of specific heat and thermal diffusivity is compared, and the specific heat that gives the minimum value R _j is selected (S-
5), (S-6). -3 A plurality of new specific heats are set in the vicinity of the specific heat having the minimum value in the direction of reducing the deviation R (S-3),-
Repeat from 1. The values are α and c when Δc / c becomes sufficiently small.

The Biot number which gives the minimum value R _j of the deviation R is obtained by the following procedure. -1 The deviation R is found for the combination of the thermal diffusivity and the specific heat obtained by each Biot number and process, and the minimum value R of the deviation R is obtained.
_The number of bios giving _i is selected (S-7). -A plurality of new Biot numbers are set in the vicinity of the Biot number giving the minimum value R _i in the direction of making the deviation R smaller (S-
2), carry out the process. The values are h, α, and c when Δh / h becomes sufficiently small (S-8). The desired values h _m , α _m , and _cm are output. (S-
9) In the above procedure for obtaining the minimum value of the deviation R, the Biot number, the specific heat and the thermal diffusivity are equivalent independent variables, and therefore the same holds true even if the variables are exchanged. For example, a method may be used in which a plurality of Biot numbers are set among a plurality of specific heats and a thermal diffusivity that gives a minimum value is obtained. Further, the thermal diffusivity, the specific heat and the Biot number which give the minimum value of the deviation R can be obtained by the Newton method for a plurality of variables.

Direct Method 2 First, the specific heat c and the Biot number h, which are unknowns in one layer in the multilayer material 10 as shown in FIG. 3, are appropriately determined, and respective initial values c ₀ and h ₀ are h−. (c on the c-plane
₀ , h ₀ ) points. The initial values (c ₀ , h ₀ ) set above are substituted into theoretical temperature responses F (α, c, h, t) and F ′ (α, c, h, p) to obtain a theory including the unknown α. Temperature response F (α, c ₀ , h
₀ , t), F '(α, c ₀ , h ₀ , p) and the actual temperature response E (t), E' (p) the minimum value of the deviation R is δR / δα = 0. And obtain.

The value of α satisfying the expression δR / δα = 0 is obtained by the above-mentioned least squares method and the numerical analysis method such as the Newton method. The initial value of the thermal diffusivity α obtained at this time is α ₀ and the initial value of the deviation R is R ₀ , and the set of these initial values (R ₀ , α ₀ , c ₀ , h ₀ ) is set to a temporary minimum value set. (R _m ,
α _m , _cm , h _m ). A new set of values (c ₁ , h) near the point on the two-dimensional plane represented by the set of minimum values (c _m , h _m ) = (c ₀ , h ₀ ).
₁ ) is set. To set this new point, an operation such as designating a circle within a preset reference radius by a random number method with the point on the two-dimensional plane as a center point may be calculated and processed on a computer. it can. The accuracy can be improved by gradually reducing the reference radius. Furthermore, it is also possible to set a plurality of new update values in the direction in which the deviation or the difference between the updated heat constants becomes smaller by using a plurality of sets of heat constants that have already been set.

The values of c ₁ and h ₁ are calculated as the theoretical temperature response F
(Α, c, h, t), F ′ (α, c, h, p), and the theoretical temperature response F (α, c ₁ , h ₁ ,
t), F '(α, c ₁ , h ₁ , p) and the actual temperature response E
The value of α that minimizes the deviation R from (t) and E ′ (p) is obtained by setting δR / δα = 0. The value of the thermal diffusivity α obtained at this time is α ₁ , and the value of the deviation R is R ₁ , and these pairs (R ₁ , α ₁ , h ₁ , c ₁ ) are determined. Next, R _m (=
If R ₁ is larger than R _m by comparing R ₀ ) and R ₁ , the above-mentioned set of minimum values (c _m , h _m ) = (c ₀ , h
Reset a new (c ₂ , h ₂ ) pair near ₀ ).
R ₁ is a is smaller than R _m updates the minimum value R _m by the R _m = R _1. Then, by repeating the above operation until the minimum value R _m becomes smaller than the preset allowable reference value ε, the minimum value R _m is gradually decreased so that the minimum value R _m becomes smaller than the allowable reference value ε. The minimum value set (R _m , α
_m , _cm , h _m ) is output as the desired α, c, h.
The above operation is executed by computing the temperature response data obtained using the laser flash method by the computer into which the program of the above operation procedure is input.

FIG. 8 shows calculation results when the thickness of the unknown layer of the multi-layered material 10 consisting of three layers obtained by the direct method 2 is changed. (A) shows an example where the second layer, which is an intermediate layer, contains an unknown thermal constant, and (b) shows a case where the third layer, which is the bottom layer, contains an unknown thermal constant. As is clear from the figure, in both cases (a) and (b), the calculation error, that is, the measurement error, satisfies the range of the generally required measurement accuracy.

Although the embodiments of the present invention have been described above, the present invention is not limited to these embodiments, and changes in conditions without departing from the gist of the present invention are all within the scope of the present invention. For example, in the present embodiment, the case where the theoretical temperature response and the data of the temperature response are Laplace-transformed and processed is described, but the data may be processed in a normal time space. Further, as the deviation between the theoretical temperature response and the temperature response applied to the present invention, a forward square deviation, an inverse square deviation, a logarithmic square deviation, or the like having different characteristics can be adopted as necessary. Furthermore, the unknown values of the thermal diffusivity, the specific heat, and the Biot number included in the equation of the deviation between the theoretical temperature response and the temperature response are 3
Since the two variables are mathematically equivalent,
The use of a relational expression in which each variable is arbitrarily exchanged in the relational expression as described in the above embodiment is also considered to be within the scope of the present invention.

[0060]

In the method and apparatus for measuring the thermal constant in the laser flash method according to the first to fifth aspects, the theoretical temperature response and the reality obtained by setting the thermal diffusivity α, the specific heat c, and the Biot number h are set. By comparing the deviation with the temperature response of, the value of the unknown value can be updated efficiently one after another, and the value of the unknown value that asymptotically satisfies the measured data of the actual temperature response can be determined with high accuracy. As described above, the unknown thermal constant in the multilayer material can be obtained based on the measured data of the relative temperature response without requiring the absolute value of the temperature response. Further, using the deviation between the theoretical temperature response and the actually obtained temperature response as an index, for example, the Biot number h and the specific heat c are sequentially set in the vicinity of the value giving the minimum deviation R _m , and the minimum deviation is updated. The true values of the unknown Biot number, the specific heat and the thermal diffusivity can be obtained by the configuration of the simple iterative calculation means, and the arithmetic processing by the computer can be performed at high speed.

Particularly, in the method for measuring the thermal constant using the laser flash method according to the second aspect, the deviation R is obtained by using the thermal diffusivity, the specific heat and the Biot number as variables, and α is taken to give the minimum value of the deviation. , C, h values can be obtained accurately and quickly. Further, in the method for measuring a thermal constant using the laser flash method according to claim 3, the initial value of the Biot number is based on the relationship between the time constant in the temperature response and the value of the half value arrival time t _1/2. Since it can be set in the vicinity of the true value in advance, the number of calculations can be significantly reduced, and the desired thermal constant does not diverge.

Further, in the thermal constant measuring device using the laser flash method according to the fourth aspect, the deviation R between the theoretical temperature response and the actually obtained temperature response is used as an index, for example, the Biot number h and the specific heat c. are sequentially set in the vicinity of a value giving the minimum deviation R _m, performs updating of minimum deviation R _m, unknown Biot number, can be determined by the configuration of a simple calculation means the true value of the specific heat and thermal diffusivity Since it is not necessary to measure the absolute temperature, it is possible to measure up to a high temperature range using a radiation thermometer that can measure the sample temperature without touching the sample, and it is affected by the environmental conditions of measurement. Less is. Further, in the thermal constant measuring device using the laser flash method according to claim 5, since the Biot number is updated based on the thermal diffusivity and the specific heat, the theoretical temperature response and the actually obtained temperature response are the deviation R as an index, the thermal diffusivity α or specific heat c are sequentially set in the vicinity of a value giving the minimum deviation R _m, performs updating of minimum deviation R _m, unknown Biot number, specific heat and thermal diffusivity Since the true value can be obtained by repeating a small number of arithmetic calculation means, the calculation error can be reduced.

[Brief description of drawings]

FIG. 1 is a configuration diagram of a laser flash device to which a method for measuring a thermal constant using a laser flash method according to an embodiment of the present invention is applied.

FIG. 2 is an explanatory diagram of a thermal constant measurement method using a laser flash method.

FIG. 3 is an explanatory diagram of a laser flash method using a multilayer material.

FIG. 4 is a flow chart of a direct method in a thermal constant measurement method using a laser flash method.

FIG. 5 is a flow diagram of a time constant method in a method for measuring a thermal constant using a laser flash method.

FIG. 6 is a diagram showing a calculation error of the time constant method when the thickness of an unknown layer in a multilayer material including three layers is changed.

FIG. 7 is a flow chart of a direct method in a method for measuring a thermal constant using a laser flash method.

FIG. 8 is a diagram showing a calculation error of a direct method when the thickness of an unknown layer in a multilayer material including three layers is changed.

[Explanation of symbols]

 10 Multilayer material 11 Half mirror

Claims (5)

[Claims] 1. A temperature response on the back surface side obtained by irradiating a laser flash from the front surface side of a multilayer material including one layer whose thermal diffusivity and specific heat are unknown, and the thermal diffusivity, specific heat and Biot number are included as variables. A method for measuring a thermal constant using a laser flash method, characterized in that the thermal diffusivity, the specific heat, and the Biot number are obtained by comparing with a theoretical temperature response. 2. The thermal diffusivity, the specific heat, and the Biot number are set to A, the other one is set to B, and the other is set to C.
And a first step of setting B as an initial value to obtain C that minimizes a deviation between the back surface temperature response and the theoretical temperature response of the multilayer material, and setting the deviation as an initial value of the minimum deviation. The new A and B of the multi-layer material are given by A
And a second step of setting in the vicinity of B, and a third step of obtaining C and a deviation that minimize the deviation between the theoretical temperature response and the back surface temperature response of the multilayer material from A and B of the multilayer material, The deviation is compared with the minimum deviation, and if the deviation is larger than the minimum deviation, the second to third steps are repeated, and when the deviation is less than or equal to the minimum deviation, the deviation is newly set as the minimum deviation. And a fourth step of outputting the thermal diffusivity, the specific heat, and the Biot number when the minimum deviation reaches the vicinity of the minimum value by repeating the second step to the third step. A method for measuring a thermal constant using the laser flash method described. 3. Initial values of thermal diffusivity, specific heat, and Biot number are set, and a deviation between a theoretical temperature response including the initial values and a back surface temperature response is obtained, and the thermal diffusivity, specific heat, and Biot number. , And a deviation as a set thermal diffusivity, a set specific heat, a set Biot number, and a set deviation, respectively, and A is set as one of the set thermal diffusivity and specific heat, and the remaining one is set as B, B is obtained by a second step of setting a new A in the vicinity of, and a step of calculating B that minimizes the deviation between the theoretical temperature response including the set A and the set Biot number and the temperature response, The Biot number is updated by the A and B to define a new set Biot number, and the calculation step is repeated until the vicinity of the minimum deviation value in the state where the A is fixed is reached to determine the thermal diffusivity, specific heat and Biot number. A third step, the thermal diffusivity, the specific heat, and The deviation between the theoretical temperature response including the Biot number and the temperature response is obtained, and it is determined whether or not the deviation has reached the vicinity of the minimum value. If the deviation has not been reached, the second step to the third step are repeated, The method for measuring a thermal constant using the laser flash method according to claim 1, further comprising a fourth step of outputting the thermal diffusivity, the specific heat, and the Biot number at the time when the deviation reaches the vicinity of the minimum value. 4. A temperature response on the back surface side obtained by irradiating a laser flash from the front surface side of a multilayer material including one layer whose thermal diffusivity and specific heat are unknown, and thermal diffusivity, specific heat, and Biot number are included as variables. Comparing with a theoretical temperature response, the thermal diffusivity, specific heat, and a device for measuring the thermal constant of the multilayer material using a laser flash method to determine the Biot number, the thermal diffusivity, the specific heat, and the Biot number of By setting one of them as A, the other as B, and the other as C, the initial values of A and B are set, and C that minimizes the deviation between the temperature response and the theoretical temperature response on the back surface of the multilayer material is obtained. Then, the first calculation means for setting the deviation as an initial value of the minimum deviation and the new A and B of the multilayer material are given as A giving the minimum deviation.
And a second calculation to set C and the deviation from the theoretical temperature response and the back surface temperature response of the multilayer material that are the minimum, from the first calculation set in the vicinity of B and B. The deviation is compared with the minimum deviation, and when the deviation is larger than the minimum deviation, the first and second calculations are repeated, and when the deviation is equal to or smaller than the minimum deviation, the deviation is determined. Second calculating means newly set as the minimum deviation, and it is judged whether the minimum deviation has reached the vicinity of the minimum value. If the minimum deviation has not been reached, the first and second calculations are repeated to determine the minimum deviation value. An apparatus for measuring a thermal constant using a laser flash method, comprising: a third calculation means for outputting a thermal diffusivity, a specific heat, and a Biot number when reaching the vicinity of the minimum value. 5. The temperature response on the back surface side obtained by irradiating a laser flash from the front surface side of a multilayer material including one layer whose thermal diffusivity and specific heat are unknown, and the thermal diffusivity, specific heat and Biot number are included as variables. A device for measuring the thermal constant of the multilayer material using the laser flash method for obtaining the thermal diffusivity, the specific heat, and the Biot number by comparing the theoretical temperature response with each of the thermal diffusivity, the specific heat, and the Biot number. The initial value is set, the deviation between the theoretical temperature response including the initial value and the back surface temperature response is obtained, and the thermal diffusivity, specific heat, biot number, and deviation are set to the thermal diffusivity, specific heat, and biot number, respectively. And a first calculation means for setting a deviation, and a second calculation means for setting a new A in the vicinity of the A by setting one of the set thermal diffusivity and the specific heat to A and the other one to B. And set by the second computing means A and B which minimize the deviation between the theoretical temperature response including the set Biot number and the backside temperature response are calculated, and the Biot number is updated by the thermal diffusivity and the specific heat obtained from the calculation result. The third computing means for determining the set Biot number and repeating the above calculation until the vicinity of the minimum deviation value in the state where A is fixed to determine the thermal diffusivity, the specific heat, and the Biot number; Fourth computing means for determining a deviation between the theoretical temperature response including the obtained thermal diffusivity, specific heat, and Biot number and the back surface temperature response, and determining whether the deviation has reached the vicinity of the minimum value; When the deviation obtained by the calculating means has not reached the minimum value, a new A which is set in the direction of giving a smaller minimum value is input to the second calculating means and reaches the vicinity of the minimum value. When Thermal diffusivity, the specific heat, and the measurement apparatus of the thermal constants used a laser flash method, characterized in that it comprises a fifth calculating means for outputting the Biot's number.