Emissivities of real bodies

According to 5.3.2.1, the radiation properties of an opaque body are determined by its directional spectral emissivity e x = e x(A, f3,(p,T). In order to determine this material function experimentally numerous measurements are required, as the dependence on the wavelength, direction and temperature all have to be investigated. These extensive measurements have, so far, not been carried out for any substance. Measurements are frequently limited to the determination of the emissivity e x n normal to the surface (/ = 0), the emissivities for a few chosen wavelengths or only the hemispherical total emissivity e is measured. 

In addition to incomplete radiation measurements, the strong dependence of the results on the condition of the surface is a further difficulty. Impurities also play a role, alongside roughness. Even a very thin film of water or an oxide layer can completely change the radiation behaviour compared to the base material alone. It is therefore no surprise that the emissivities measured by various researchers often differ significantly. Unfortunately, in the description of the experiments the surface properties were inexactly or incompletely characterised, which frequently occurs due to the lack of quantitative measures for surface properties. The emissivities presented in Tables B12 and B13 of the Appendix must therefore be taken to be relatively uncertain. 

In view of the experimental difficulties a theory for radiation properties is desirable. The classical theory of electromagnetic waves from J.C. Maxwell (1864), links the emissivity e x with the so-called optical constants of the material, the refractive index n and the extinction coefficient k, that can be combined into a complex refractive index n = n — ik. The optical constants depend on the temperature, the wavelength and electrical properties, in particular the electrical resistivity re of the material. In addition, the theory delivers, in the form of Fresnel s equations, an explicit dependence of the emissivity on the polar angle / , whilst no dependence on the circumferential angle ip appears, as isotropy has been assumed. 

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