Lorentz-Lorenz relation

It should be noted that also the refractive index in eq. (17) will change under pressure. This change can be estimated by the Lorenz local-field model, where the refractive index n is related to the atomic polarizability a p and the density of the material p by the Lorentz-Lorenz relation ... 

The relationship between the molar refraction RLL/ the refractive index n and the polarisability a is known as the molar Lorentz-Lorenz relation (1880), which reads... 

For an isotropic material the refractive index is given by the Lorentz-Lorenz relation (25)... 

Written in terms of the refractive index n = this relation is known as the Lorentz-Lorenz relation. Since electromagnetic radiation, if one ignores the magnetic component, is nothing but a time-varying electric field, it should come as no surprise later, in Chap. 16. when it is discovered that the dielectric and optical responses of insulators are intimately related. 

From the Lorentz-Lorenz relation for the usual case of k(v) = 1... 

The apparent oscillator strength is proportional to the integrated intensity under the molar absorption curve. To derive the formula, Chako followed the elassieal dispersion theory with the Lorentz-Lorenz relation (also known as the Clausius-Mosotti relation), assuming that the solute molecule is located at the center of the spherical cavity in the continuous dielectric medium of the solvent. Hence, the factor derived by Chako is also called the Lorentz-Lorenz correction. Similar derivation was also presented by Kortiim. The same formula was also derived by Polo and Wilson from a viewpoint different from Chako. 

For larger particle concentrations, the interactions between particles influence the electromagnetic properties. For interparticle distances much smaller than the wavelength, the Maxwell-Gamett model applies and leads to the Lorentz-Lorenz relation for the effective dielectric constant eff of the composite medium, which takes the form... 

We have seen that relaxor ferroelectric PLZT ceramics, with compositions (a/65/35) with 7frequency-dependent paraelectric (or relaxor) to long-range ferroelectric phase transition. PLZT (9.5/65/35) ceramics undergo this phase change around 5°C. However, no evidence of this phase change is seen in figure 13. This is likely because the specific refractivity of materials R, which is a measure of the electronic polarization, is unaffected by this particular phase transition. This refractivity constant is defined by the Lorentz-Lorenz relation ... 

A variation of the water adsorption isotherm method was then developed (Yeatman, 1994 Dawnay, 1995) called Molecular Probe Ellipsometry (MPE). In this technique, refractive index readings are made in dry nitrogen, and then in nitrogen saturated with an adsorbate solvent vapor. The porous structure is modelled as an effective medium according to the Lorentz-Lorenz relation, giving a relation between the measured film index f and the indices of the material in the pores and of the solid skeleton, p and s, respectively ... 

Table I. Refractive indices and vol% porosities (calculated from the Lorentz-Lorenz relation [18]) for B2 and AAB films as a function of aging time normalized by the gelation time. Mass fractal dimension values are for sols aged for comparable normalized aging times.

The second method of mass calculation is based on the Lorentz-Lorenz relation which can be presented in the most general case, i.e. when the deposited layer contains a mixture of substances, by the following equation ... 

Double films formed on InP were studied by applying ex situ ellipsometry after successive etching steps of the thermally formed oxide by an HF solution. From calculations based on a four-phase model (see Appendix A1 for treatment of two and more layers), the existence of an easily etched outer layer with smaller refractive index and a more durable inner layer with larger index was shown, which is consistent with XPS analysis. In the same work, in situ ellipsometry data was shown to be explained by the presence of a liquid layer when a microscopic model based on the Lorentz-Lorenz relation was used. Other ellipsometric studies of double films, such as double films of Si02 and Si3N4 on Si, have been reported. 

The refractive index, n, of an isotropic material is given hy the Lorentz—Lorenz relation... 

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