Thermal Diffusivity Measurement in Solids by means of the Photoacoustic Technique
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Thermal Diffusivity Measurement in Solids by means of the Photoacoustic Technique José B. Rojas-Trigos, A. Calderón and E. Marín Centro de Investigación en Ciencia Aplicada y Tecnología Avanzada, del Instituto Politécnico Nacional. Av. Legaria # 694 Col. Irrigación, C.P. 11500, México D.F. México ABSTRACT We report thermal diffusivity measurements for samples of silicon, gallium arsenide and cupper by means of the photoacoustic technique in a heat transmission configuration in order to obtain a comparison between the results obtained with the use of the conventional RG-model and our SP-model (based in a square periodical heat source) in the fitting process to the experimental data. Our results show that our SP-model is accurate to obtain a good fitting with the experimental data and it improves notably the results obtained with the RG-model. INTRODUCTION The Photoacoustic (PA) technique is a non destructive test widely used for thermal characterization of solids because it’s relative low cost and easy implementation; but despite the goodness of it, still there are some issues that make the PA technique to be less effective than it can be. In this technique, the Rosencwaig and Gersho model (RG-model) [1] has been widely used during more than 30 years and nowadays [2,3]. This theoretical model is based on the solutions of the heat equation considering a heat source with a sinusoidal modulation in time, and even when several authors add to the original model corrections involving other physical effects [4,5], the basic consideration of sinusoidal modulation is hardly touched [6]. This consideration approaches to the experimental conditions; however the real experimental setup normally uses a heat source obtained when a chopped light beam normally impinges on the surface of the sample. In this paper we report an experimental comparison between the thermal diffusivity obtained with the use of the RG-model and our model (SP) based in a square periodical heat source. The PA technique in a heat transmission configuration is considered, with an open photoacoustic cell (OPC) detection [2, 3]. The monochromatic radiation normally impinges on the surface of the sample and the radiation is modulated on intensity by a mechanical chopper with a variable frequency , producing a square periodical heat source on the sample surface. If the sample is considered optically opaque, the absorption of the radiation occurs only on the surface of the sample.
Figure 1 Schematic draw of an open Photoacoustic cell (OPC) used in PA detection. After solving the one-dimensional heat diffusion equation with a square periodical heat source, for a superficial absorption, and considering an adiabatic expansion in the PA gas chamber, we obtained the following expression for the gas pressure fluctuations [7]:
P
C0 Sinc(n / 2)ei (n / 2 ) f nN n Cosh(2 n ) Cos(2 n )
(1)
Where
Tan n ; Tanh n
n arcTan
(2)
n nf / f c
(3)
And C0
P0 g l0 s l g T0
;
ܵ݅݊ܿሺݖሻ ൌ
ܵ݅݊ሺߨݖሻൗ ߨݖ
Here, C0 is a constan
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