Photon conductivity

Photon conductivity also adds to the total thermal conductivity. It comes from the electromagnetic radiation. This energy per unit volume is given by  

a is the Stefan-Boltzmann constant (1.37 x cal/cm s K ), n is the refractive index of the material, and c is the velocity of light (3 x 10 cm/s). The heat capacity contributed by the radiation is given by Equation 16.29. 

The velocity of movement of the radiation within the material is given by Equation 16.30. 

Substituting the values of Cr and v in Equation 16.26, we get the radiant energy conductivity as  

In this equation, 1, is the mean free path of the photons. The radiant energy transfer is negligible in opaque materials because 1 0. It is significant in the case of silicates and single crystals at moderate temperature levels, where Ij reaches macroscopic dimensions. 

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Amorphous materials have no long-range structural order, so there is no continuous lattice in which atoms can vibrate in concert in order for phonons to propagate. As a result, phonon mean free paths are restricted to distances corresponding to interatomic spacing, and the (effective) thermal conductivity of (oxide) glasses remains low and increases only with photon conduction (Figure 8.2). 

Berman, R. (1979) in The Properties of Diamond, edited by J.E. Field, Academic Press, London, p. 3. Discusses the thermal conductivity of diamond and the effect different impurities have on this property. Kingery, W.D., Bowen, H.K., and Uhlmann, D.R. (1976) Introduction to Ceramics, 2nd edition, Wiley, New York, pp. 583-645. A very detailed chapter on thermal properties. The discussion of photon conductivity and the thermal properties of glasses are covered in more depth than we do. 

Bouchet R, Siebert E (1999) Photon conduction in acid doped polybenzimidazole. Solid Stale Ion 118 287-299... 

There are three stages of the effect of temperature on the thermal conductivity of glass. From a very low value at 0 K, it increases rather rapidly as temperature is increased. After a certain increase, the value remains almost constant. At very high temperatures, it increases again rather sharply. This sharp increase is due to photon conductivity. 

The photon conductivity equation was given by Equation 16.31. The mean free path for photons (1,) is the inverse of the absorption coefficient (a). Absorption coefficient and refractive index are independent of temperature. But they depend on frequency. 

The mean free path for photon conductivity is fixed by absorption and scattering of photons. When materials have a low absorption coefficient, photon conduction becomes important at temperatures of the order of a few hundred degrees centigrade. The absorption coefficient depends on the wavelength. For a wavelength of 2 to 4 microns, the absorption coefficient is low. For higher values, it increases rapidly. 

The temperature dependence of photon conductivity depends on the integrated mean free path. This increase with temperature raised the power in the range of 3.5 to 5. 

For photon conductivity, boundary effects are found to predominate when the sample size is similar to the photon mean free path. Energy transfer between two boundaries can be identified by three separate processes ... 

The measured apparent photon conductivity includes the boundary effect because photon mean free paths range from 0.1 to 10 cm. Common sample sizes are also in this range. Let us consider a situation where the electromagnetic radiation does not interact with the material, and photon conduction is the only energy transfer process. In this situation, the temperature gradient in the material is independent of the rate of heat transfer. Increasing the ratio of the distance between the boundaries and the photon mean free path (d/1,) increases the apparent conductivity. 

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