K Absorption index

Fig. 57. Harmotome. IR reflection spectra (a) reflectivity, (b) imaginary part of the dielectric function e , (c) real part of the dielectric function e , (d) imaginary part of the refractive index k (absorption index), (e) real part of the refractive index n [88S3],...

In contrast with other methods, spectra recorded by specular reflection show dispersion-like shaped bands because both the refractive index (n) and the absorption index (k) contribute to reflection. These can nevertheless be separated... 

In Mie s theory, the scattering diameter Qs and the absorption diameter QA are related to the particle size D, the wavelength A, and the optical constants of the material (refractive index n and absorption index k). 

Mie s Theory. Mie applied the Maxwell equations to a model in which a plane wave front meets an optically isotropic sphere with refractive index n and absorption index k [1.26]. Integration gives the values of the absorption cross section QA and the scattering cross section Qs these dimensionless numbers relate the proportion of absorption and scattering to the geometric diameter of the particle. The theory has provided useful insights into the effect of particle size on the color properties of pigments. 

The consequences of Mie s theory for absorption (i.e., for tinting strength) are now considered. Calculations from Mie s theory, using the relative refractive index n and the absorption index k, are given in Figure 8 [1.30]. The parameter a on the abscissa can once more be taken as a relative measure of the particle size. The following conclusions may be drawn ... 

With increasing absorption index k, the absorption of very small particles increases. 

The top curve in Figure 8 applies to pigments with a high absorption index k and low refractive index rt (e.g., carbon black) and shows that the optimal particle size lies below a given limit. 

The lowest curve applies to pigments with a small absorption index k and high relative refractive index n, as is usually the case with inorganic pigments (e.g., red iron oxide). Here, there is a distinct maximum [1.11], [1.16]. 

The absorption index, k, introduces an exponential decay in E (and E ) with increasing z (see eq. [3]). Recalling that the intensity, I, is related to the electric field amplitude E, according to I lE 2 it follows from eqs. [3] and [4] that... 

Fourier transform infrared microscopes are equipped with a reflection capability that can be used under these circumstances. External reflection spectroscopy (ERS) requires a flat, reflective surface, and the results are sensitive to the polarization of the incident beam as well as the angle of incidence. Additionally, the orientations of the electric dipoles in the films are important to the selection rules and the intensities of the reflected beam. In reflectance measurements, the spectra are a function of the dispersion in the refractive index and the spectra obtained are completely different from that obtained through a transmission measurement that is strongly influenced by the absorption index, k. However, a complex refractive index, n + ik can be determined through a well-known mathematical route, namely, the Kramers-Kronig analysis. 

The absorption index k is a characteristic function of the wave-length and obviously increases as the wave-length of an absorption peak is approached. Most polymers show no specific absorption in the visible region of the spectrum and are therefore colourless in principle. 

The considerations before refer to the non-absorbing case when and n are real quantities. In order to characterize the optical properties completely absorption must be included. This can be achieved by taking the optica] and dielectric functions to be complex quantities comprising two real figures each. The (real) refractive index n is complemented by the real absorption index k to constitute the complex refractive index... 

Figure 6.4-5 Simulated spectra of a strong oscillator (strength/ = 200 10 cm with resonance at t> real and imaginary part of the dielectric function = s + k", refractive index n and absorption index k, ellipsometric parameters A and ip, as well as reflectance R for the angles of incidence and the polarization states stated.

For the strong oscillator the n and k spectra are asymmetric. The shift of the k maximum away from the resonance frequency is particularly obvious. In such a case a reliable representation of the vibrational structure cannot be derived from transmittance spectra and thus, from the absorption index k alone. Another peculiarity of the strong oscillator is the spectral range where the (real) refractive index is below unity. This renders... 

Figure 6.4-14 Spectra of the refractive index n, the absorption index k, and the degree of (phase) polarization Ppi, of quartz glass as derived from ellipsometric measurements.

The above relationships (Figure 1.10) show that the optical pigment properties depend on the particle size D and the complex refractive index n = n (1 - i/c), which incorporates the real refractive index n and the absorption index k. As a result, the reflectance spectrum, and hence the color properties, of a pigment can be calculated if its complex refractive index, concentration, and particle size distribution are known [1.40]. Unfortunately, reliable values for the necessary optical constants (refractive index n and absorption index k) are often lacking. These two parameters generally... 

Fig. 17. The ratios of the integrated intensities of the laimnelar reflections R(h/h ) = ([S(h)/S(h )], — [S(h)/S(h )]2)/[S(h)/S(h )l2 for a reconstituted cytochrome oxidase membrane multilayer. The subscript 1 denotes the incident X-ray energy and the index 2 corresponds to an energy far from the absorption edge, h = 4, h = 2, 3, 5 and 6 at incident X-ray energies near the iron K-absorption edge ( ). The f dispersion is most significant with h = 2 and h = 6. There is no dispersion at wavelenghts near the Co K-absorption edge (O)- After Stamatoff et al.

Table 23 Refractive index, n, and absorption index, k, of the ordinary ray for sapphire in the ultra-violet spectral range, at 25°C, from [49, 50]...

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