JPH0765975B2 - Thermal diffusivity measurement method - Google Patents

Description

TECHNICAL FIELD The present invention relates to a method for measuring thermal diffusivity.

(Prior Art) Conventionally, there are two methods of irradiating an electromagnetic wave or particle beam on a flat plate sample having a constant thickness to measure the thermal diffusivity. One is instantaneous heating (flash method), and the other is constant heating (step method).

In the flash method, when a pulsed electromagnetic wave or particle beam such as laser light is uniformly irradiated over the entire surface of a flat plate sample having a constant thickness as shown in the third drawing, the laser light is absorbed by the sample and heats the sample. In the absence of loss, the temperature rise Θ ₁ curve on the backside of the sample rises according to the well known heat conduction equation:

Here, α is the thermal diffusivity of the sample l is the thickness of the sample t is the time after the laser irradiation, Θm is Θ ₁ when t → ∞, and by this relational expression, the Freeer number αt / l ² is used as the variable Θ
Fig. 4 shows the figure obtained by finding ₁ / Θm.

From Fig. 4, for example, obtain the free numerical value αt _0.5 / l ² = 0.1388 when the sample temperature rise reaches half the maximum temperature rise, and the sample temperature rise Θ ₁ becomes half of the maximum temperature rise Θm. The time to reach t _0.5 is measured, and the thermal diffusivity α is calculated from the following equation.

α = 0.13883l ² / t _0.5 (2) In addition, the specific heat c _p is the amount of heat absorbed by the sample is Q, and the weight of the sample is m. Required by.

Therefore, if the density ρ is known, the thermal conductivity λ is λ =
It can be calculated from α · C _P · ρ. On the other hand, in the step method, when light such as halogen light is uniformly irradiated over the entire surface of the sample in a step-like manner from t = 0 as shown in FIG. Below, the temperature of the back surface of the sample rises according to the following well-known heat conduction equation.

However, q is the energy absorbed by irradiation per unit time and unit area. The relation Θ ₂ λ / ql is calculated by this heat conduction equation using the Fourier number αt / l ² as a variable.

For example [alpha] t ₁ / l ₂ ² for theta ₂ to _{Θ (t 1), 2αt 1} / l to theta ₂ for ² and _{Θ 2 (2t 1), αt} 1 / l 2 and _{Θ 2 (2t 1) / Θ} 2
When the relationship of (t ₁ ) is illustrated, a graph as shown in FIG. 7 is obtained.

When t ₁ is specified, Θ ₂ (2t ₁ ) / Θ ₂ (t ₁ ) can be obtained experimentally, so from FIG. 7, α t ₁ / l ² = k at that value is obtained.
From this equation, the thermal diffusivity α can be obtained from α = kl ² / t ₁ (4).

Next, when t → ∞ in the equation (3), the value in Σ becomes zero, and at t → ∞, Becomes

Therefore, the equation (3) is illustrated and the slope of the curve is obtained. If the density ρ of the sample, the thickness 1 of the sample, the unit time, and the energy q absorbed and irradiated per unit area are known, the specific heat C _P can be obtained by substituting these and the gradient into the equation (5).

The thermal conductivity λ is obtained in the same manner as the Flash method.

(Problems to be Solved by the Invention) According to the above-mentioned flash method, the thermal diffusivity can be easily obtained, but since the sample is heated by irradiating light instantly, the sample having a poor thermal conductivity can be obtained. The temperature of the irradiated surface becomes extremely high. Therefore, it is difficult to accurately determine the thermal constants in the vicinity of the melting point and the transition point even in samples such as plastics and general samples.

On the other hand, the step method is less likely to damage the irradiated surface of the sample and is suitable for measuring a sample with poor thermal conductivity, but
If t ₁ is improperly selected, a considerable error may occur, and it requires considerable skill to find the thermal diffusivity.

An object of the present invention is to eliminate the disadvantages of each of the two conventional methods.

(Means for Solving Problems) In order to achieve the above-mentioned object, the present invention continuously irradiates an electromagnetic wave or particle beam having a constant energy on a surface of a flat plate sample having a constant thickness (l) from a certain point of time, A temperature rise curve on the back surface of the sample is recorded, the curve is differentiated with respect to time, and a time (t) from the time point when a differential value of a predetermined ratio is obtained with respect to a maximum differential value is obtained, and the step heating method is also used. The heat transfer equation of is differentiated with respect to time, and the Fourier value (αt / l ² ,
However, α: thermal diffusivity) is obtained, and the thermal diffusivity (α) is obtained from the Fourier numerical value, the time (t) and the thickness (l) of the sample.

(Operation) When the step method is used, the temperature rise curve on the back surface of the sample is a heat conduction type like the above equation (3). Differentiating this equation (3) Comparing this equation (6) 'with the equation obtained by dividing equation (1) by Θm, (dΘ ₂ / dt) (q / ρC _P l) on the left side of equation (6) ′ is represented by Θ
If replaced with / Θm, it becomes the same as the Flash method.
Since the denominator on the left side of the equation (6) 'is dΘ ₂ / dt when t is ∞ as is apparent from the equation (5), the left side of the equation (6)' is the differential value of temperature at a certain time and t. Is the differential value of the temperature at ∞ (in equation (6 '), if αt / = l ² = x and the left side is y, And y is a monotonically increasing function with respect to x. Therefore, when t is ∞, y takes the maximum value, and the differential value dθ ₂ / dt of the temperature when t is ∞ takes the maximum differential value and becomes the maximum differential value. ) And the ratio.

Therefore, similar to the Flash method, from Fig. 1 showing the equation (6) ', for example, the Fourier value αt _0.5 / l ² = 0.13 when the differential value of the temperature of the sample reaches half of the maximum differential value.
88 is calculated, and the time t _0.5 until the temperature differential value of the sample reaches half of the maximum differential value is measured, and the thermal diffusivity is calculated from the following equation α = 0.1388l ² / t _0.5 (2).

(Example) An example of the method of the present invention will be described with reference to the accompanying drawings.

As a sample, stainless steel (SUS304) having a thickness of 5 mm was used, and an energy of 0.5 W / cm ² was applied to one surface of the sample from a certain point using a halogen lamp as a heating source.

The differential ray of the temperature rise curve on the back surface of the sample at that time
Shown in the figure. This differential curve was obtained by software processing by a computer.

From this derivative curve, the time at the derivative value of 1/2 of the maximum derivative value was 0.96 seconds. So this 0.96 seconds and the thickness of the sample
0.5 cm was substituted into the equation (2) to calculate the thermal diffusivity α.

α = (0.1388 × 0.5 ² ) /0.96=0.036 cm ² / sec (Effect of the invention) As described above, a thick sample with low thermal conductivity is heated by step heating, and the analysis is performed using the same method as the flash method. By using, without damaging the irradiation surface of the sample,
In addition, the thermal diffusivity with a small error can be obtained relatively easily.

[Brief description of drawings]

FIG. 1 is a theoretical curve diagram of changes in differential value of temperature in the method of the present invention, FIG. 2 is a diagram showing a temperature rise differential value actual measurement curve of the back surface of the sample when step heating, and FIG. 3 is energy in the flash method. FIG. 4 is a diagram showing a time relationship, FIG. 4 is a diagram showing an energy time relationship in the step method, and FIG.
The figure shows the theoretical curve of temperature rise in the Flash method, No. 6
The figure is a theoretical curve diagram of temperature rise in the step method, and FIG. 7 is a diagram showing a curve used for data analysis in the step method.

Claims (1)

[Claims] 1. An electromagnetic wave or a particle beam having a constant energy is continuously irradiated on a surface of a flat plate sample having a constant thickness (l) from a certain point in time, and a temperature rise curve on the back surface of the sample is recorded to obtain the curve. Differentiating with respect to time, the time (t) from the time point when a differential value of a predetermined ratio is obtained with respect to the maximum differential value is obtained, and the heat conduction equation of the step heating method is differentiated with respect to time
The Fourier numerical value (αt / l ² , where α is the thermal diffusivity) with which the differential value of the predetermined ratio is obtained with respect to the maximum differential value of temperature is obtained, and the Fourier numerical value, the time (t) and the thickness of the sample are obtained. A method for measuring thermal diffusivity, which comprises obtaining the thermal diffusivity (α) from (l).