Emissivity normal to the surface

In Section III.A.l we did not discuss the way the surface emission is excited. The radiative behavior of the surface shows that emission (normal to the surface) is observed as soon as the K = 0 state is prepared. This state may be prepared either by a short ( 0.2ps) resonant pulse, or by relaxation from higher, optically prepared excited states. It is obvious that the quantum yield of the surface emission will critically depend on the excitation, owing to intrasurface relaxation accelerated by various types of fission processes (see Fig. 2.8) and in competition with fast irreversible transfer to the bulk (3.30), which is also a surface relaxation, at least at very low temperatures. Thus, the surface excitation spectra provide key information both on the upper, optically accessible surface states and on the relaxation mechanisms to the emitting surface state K = 0. 

In addition to its variation with wavelength, the monochromatic emissivity of many surfaces is not isotropic and has directional properties. Experimental data on these properties, however, are scarce. Frequently used mean values are 6/e = 1.2 for polished metallic surfaces and e/e = 0.96 for insulators. Here e denotes the average hemispherical emissivity and en the emissivity normal to the surface. 

Table 10. Energetic positions of the 5p orbital states of adsorbed Xe as derived from photoemission. If not stated otherwise, the values are for the low coverage limit. The energies are referred to the Fermi level but the workfunction values for the clean substrates, (j)c, are also given. Abbreviations used T surface temperature, 6 coverage in monolayer units, F eenler of the Brillouin zone (electron emission normal to the surface plane)- see also Table 12.

Table 12. Band structure (dispersion) of the p valence levels of the noble gas monolayers obtained in angular resolved photoemission. The energies at T are referred to the Fermi level. If not explicitly given in the indicated reference, the positions Ff and band widths Ae were extracted from graphs of the dispersion curves. In this case the values are given with a sign. Abbreviations used 9 coverage in monolayer imits, F center of the Brillouin zone (electron emission normal to the surface plane). (Ad. = adsorbate)...

Figure 44, Contour map of the PUlIl) Auger emission intensity at 65 eV. Contours are drawn at 59r intervals. The center of the map corresponds to emission normal to the surface, and the edge to emission 70° from normal, as indicated by the scales. Coordinates are defined in Figure 43. (From Ref. 116.)...

The total enhancement, 3, of the intensity of the Raman emission from the molecule is directly proportional to the total average field enhancement normal to the surface of the sphere and inversely proportional to the distance the molecule is away from the surface of the sphere. For a molecule adsorbed on the surface 3 is given by ... 

The distribution of species normal to the surface can be obtained nondestructively by variation of the emission angle in XPS or AES (limited to a total depth of about 50 nm), by Rutherford backscattering spectrometry (applying only to elements with Z > 10) and by nuclear reaction analysis (Z < 20 only). Depth resolution in both RBS and NRA is in the range 5-50 nm. 

Table 5-4 illustrates values of emittance for materials encountered in engineering practice. It is based on a critical evaluation of early emissivity data. Table 5-4 demonstrates the wide variation possible in the emissivity of a particular material due to variations in surface roughness and thermal pretreatment. With few exceptions the data in Table 5-4 refer to emittances e normal to the surface. The hemispherical emittance eh is usually slightly smaller, as demonstrated by the ratio Ct/eri depicted in Fig. 5-12. More recent data support the range of emittance values given in Table 5-4 and their dependence on surface conditions. An extensive compilation is provided by Goldsmith, Waterman, and Hirschom (Thermophysicat Properties of Matter, Purdue University, Touloukian, ed., Plenum, 1970-1979). 

A few comments about the validity of tlie diffuse approximation are in order. Although real surfaces do not emit radiation in a perfectly diffuse manner as a blackbody does, they often come close. The variation of emissivity with direction for both electrical conductors and nonconductors is given in Fig. 12 26. Here 0 is tlie angle measured from the normal of the surface, and thus 0 = 0 for radiation emitted in a direction normal to the surface. Note that Sg remains nearly constant for about 0 < d0° for conductors such as metals and for 6 < 70° for nonconductors such as plastics. Therefore, the directional emissivity of a sur face in the normal direction is representative of the hemispherical emissivity of the surface. In radiatioit analysis, it is common practice to assume the surfaces to be diffuse emitters with an emissivity equal to the value in the normal (6 = 0) direction. 

The factor cos /3 that appears in (5.4) is a particularity of the definition of Lx the spectral intensity is not relative to the size dA of the surface element like in M(T), but instead to its projection dAp = cos/ dA perpendicular to the radiation direction, Fig. 5.5. It complies with the geometric fact that the emission of radiation for (3 = ir/2 will be zero and will normally be largest in the direction of the normal to the surface (3 = 0. An area that appears equally bright from all directions is characterised by the simple condition that Lx does not depend on... 

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. 

According to theory, the spectral emissivity e x n normal to the surface simply... 

Since frequently only the emissivity (, or e x n normal to the surface are determined in radiation experiments, and because the hemispherical total emissivity e is required for radiative exchange calculations, the ratio e/e], is of interest. For... 

Fig. 5.35 Ratio e/e n of the hemispherical total emissivity s to the emissivity s n normal to the surface as a function of s n. Right hand line Dielectrics from Table 5.5, left hand line Metals...

In contrast to dielectrics, the electromagnetic waves that penetrate metals are damped the extinction coefficient k in the complex refractive index n = n — ik is not equal to zero, but generally greater than n. For the spectral emissivity s Xn normal to the surface, the electromagnetic theory delivers the relationship... 

Table 5.6 Hemispherical total emissivity e, ratio e/e and product reT as functions of the (directional) total emissivity s n normal to the surface, for metals, calculated according to the simplified electromagnetic theory (n = k)...

Finally s A n from (5.84) with k = n can be developed into a power series of (1 jn) and by integrating over all wavelengths, the total emissivity s n normal to the surface can be calculated to be... 

A model for the unidirectional emission normal to the front surface of a semitransparent slab was developed by McMahon [8], The total emittance was found to be ... 

The identifier normal spectral emissivity indicates emittance normal to the surface and at a single wavelength (spectral). 

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