The Measurement of Thermal Diffusivity in Conductor and Insulator by Photodeflection Technique

The purpose of this study is to estimate thermal diffusivities of high thermal diffusivity bulk material as well as low thermal diffusivity bulk material by using many types of fluid such as Ethyl alcohol and water. This method is studied by measuring amplitude and phase of photodeflection signal in various frequency modulations. The experimental setup consists of two laser lines: 1) a pump laser beams through a modulator, varied frequency, controlled by lock-in amplifier and focused on sample surface by lens. 2) a probe laser which parallels with the sample surface and is perpendicular to the pump laser beam. The probe laser deflection signal is obtained by a position sensor which controlled by lock-in amplifier. Thermal diffusivity is calculated by measuring the amplitude and phase of the photodeflection signal and compared with the thermal diffusivity of a standard value. The thermal diffusivity of SGG agrees well with the literature but the thermal diffusivity of Cu is less than the literature value by a factor of ten. The experiment requires further improvement to measure the thermal diffusivity of Cu. However, we succeed in using ethyl alcohol as the coupling medium instead of CCl4 which is highly toxic.


Introduction
Thermal diffusivity, one of the most important parameter of the thermal characterization of materials, is scientific and industrial interest. There are several photothermal methods such as photoacoustic, photothermal reflection, etc. which have been successfully used for measuring thermal diffusivity. Photodeflection or mirage technique, which is nondestructive and noncontact, is also the powerful and highly precise method to determine thermal diffusivity. Nowadays, photodeflection is usually used to measure high diffusivity of thin film materials [1]. In the past, to improve the sensitivity of deflection signal they used Carbon Tetrachloride (CCl 4 ) as the coupling medium. CCl 4 is known to be highly toxic [2] and evaporates easily.
In this paper we propose a method which permits to determine thermal diffusivity of high thermal diffusivity bulk material as well as low thermal diffusivity bulk material by using many types of fluid such as Ethyl alcohol and water. This method is studied by measuring amplitude and phase of photodeflection signal in various frequency modulations.

Theory
There are 3 layers which are fluid (f), sample (s) and backing (b), to determine the temperature at the sample surface. We have to solve the heat diffusion equation in various media where the heat can propagate. These calculations are run by Rosencwaig and Gersho in 1976 [3] for the case of a photoacoustic detection have been extended to the case of mirage detection by several researches [4]

Experimental set-up
The experimental setup is described in figure 3. There power I 0 =14 mW, 532 nm of wavelength modulator driver (AOM) which is controlled by lock sample surface by 75 mm focal length double µm. The second, a He-Ne gas laser probe beam, 632.8nm of wavelength, 0.14 mW of power, is focused by 25.4 mm focal length d the pump beam, is approximately 0.64 Figure 1. Geometry of the 1.D system the geometry shown in figure 1, as schematically outlined, an intensity beam generates a periodic thermal wave propagates across the sample. In our model, only sample layer can absorb the incident pump beam with an absorption coefficient α. We measurement in order to determine one layer of sample [5 modulated sample surface temperature ( ) at = 0: thermal diffusion length in the region i. and is thermal diffusivity thermal conductivity respectively. is the distance between the sample surface and probe beam. calculation of probe beam deflection is based on the schematic of figure 2.

= − ∫
is the width of the pump beam. Where n is the refractive index of the fluid | |) can be written as: are the real and imaginary part of T s respectively.
Equation (3) is for general sample case. In case the sample is thermally thin ( + )( ). The equation (3) can be written as [6]: The experimental setup is described in figure 3. There are 2 laser lines. The first, a pump of wavelength, is modulated in various frequency by acousto modulator driver (AOM) which is controlled by lock-in amplifier as SR830 then focused beam at the sample surface by 75 mm focal length double-convex lens. The diameter of the pump beam Ne gas laser probe beam, 632.8nm of wavelength, 0.14 mW of power, is ocused by 25.4 mm focal length double-convex lens. The diameter of the probe beam, intersects with the pump beam, is approximately 0.64 µm. It is paralleled the sample surface through the fluid and is thermal diffusivity and is the distance between the sample surface and probe beam. The s. The first, a pump laser beam, a , is modulated in various frequency by acousto-optic ier as SR830 then focused beam at the convex lens. The diameter of the pump beam is 1.06 Ne gas laser probe beam, 632.8nm of wavelength, 0.14 mW of power, is The diameter of the probe beam, intersects with paralleled the sample surface through the fluid and

Result and Discussion
We proved our calculation of equation (3) which was calculation as in equation (4). According to comparing with reference's calculation. The slope of g ( ≪ 1) and optically opaque ( In the other hand, in figure 5, the SGG.

Figure 3. Experimental set
We cannot see the laser beams directly but we observed the amplitude in amplifier. If the probe beam overlaps the pump beam, the amplitude will be highest n case that we measured them at the same frequency. The probe laser deflection signal is by a position sensor as quadrant photodiode with amplifier circuit related to the lock amplifier measure the deflection of probe beam. Computer reads the amplitude and phase signal from in amplifier for plotting the graph amplitude versus square root of frequency The sample uses as Sigradur type G (SGG), Copper (Cu). Their thermal diffusivity and their thickness Cu = 11.1×10 −1 cm 2 s -1 , -l SGG = 1.9 mm, -l Cu = 0.25 mm. In the case of acking media is ethyl alcohol. Its thermal diffusivity is D f =D In the case of Cu, the fluid and backing media is water, its thermal diffusivity is . The skimming distance (x 0 ) is 36 µm for SGG and 18 µm for Cu. To determine the thermal have to know properties of SGG and Cu which show in Table 1 (3) which was corrected by compar calculation as in equation (4). According to figure 4, it shows our SGG's theoretical calculation with reference's calculation. The slope of graphs are similar because SGG ) and optically opaque ( ≫ 1). Therefore, we are quite sure that our calculation is correct. In the other hand, in figure 5, the slope of graphs are different because Cu is not thermally thin like , it shows the experimental results and theoretical properties. We found that the trends of varying thermal diffusivities are ×10 -2 cm 2 s -1 which are slightly different. The Experimental results are cm 2 s -1 . The experimental results and theoretical variation for  thermal diffusivity of Cu properties diffusivity is different. There is the results because of electricity frequency noise since thermal diffusion length of Cu which its thickness is 0.25 mm. experimental results are in micro voltage range the precise experimental result. The thermal diffusivity of SGG and Cu variation of photothermal signal obtained from experiment is slightly different from value of literature. selected the coupling medium from the dn / dT value, which used to b prohibited in Thailand. Therefore, be used in Cu's case because the coated by black ink in order to reduce some reflection. So, if we use the on the copper surface will dissolve. experimental results are inaccurate because we can black ink causes discrepancy. thermal diffusivity of Cu properties are shown in figure 7. We found that the trend of varying th the noise at frequency at 50, 100, 150, 200 Hz. W because of electricity frequency noise. We obtained values for frequency range since thermal diffusion length of Cu which its thickness is 0.25 mm. We pres micro voltage range which is too little amount so it is The experimental results are correspond with D and Cu from the experiment and literature are given in Table 2. of SGG and Cu are shown in figure 8. In the case of SGG, t obtained from experiment is slightly different from value of literature. In the case of Cu, t from the dn / dT value, which used to be Carbon tetrachloride but it is prohibited in Thailand. Therefore, Ethyl alcohol is needed instead. However, the because the Ethyl alcohol is a good solvent. Moreover, the surface of copper is coated by black ink in order to reduce some reflection. So, if we use the Ethyl alcohol on the copper surface will dissolve. We hypothesized that the Thermal diffusivity of Cu experimental results are inaccurate because we cannot use Ethyl alcohol as coupling medium heoretical Variation of general in equation (3)  We presuppose that the so it is very hard to obtain D = 1.22×10 -1 cm 2 s -1 . iterature are given in Table 2. Phase In the case of SGG, the value In the case of Cu, the authors e Carbon tetrachloride but it is is needed instead. However, the Ethyl alcohol cannot is a good solvent. Moreover, the surface of copper is Ethyl alcohol, the ink coated hermal diffusivity of Cu values of coupling medium and that 's theoretical Variation of general in equation (3) vs specific case  Table 2.
Material SGG Cu

Conclusion
In this paper we succeed in theoretical calculation can be widely using. Our calculation of SGG). It means that our experiment frequency measurement of photothermal deflection alcohol as the coupling medium instead of CCl is the first time Ethyl alcohol is used as a coupling medium in photodeflection technique time photodeflection technique has been set to measure thermal diffusivities of materials in Thailand. The frequency measurement is easier t sample. Therefore, this success can reduce experimental set