Optical properties of mixed crystalline solutions

Now we shall discuss some features of the electromagnetic wave spectrum in mixed crystalline solutions using the equations for the dielectric constant tensor of the solution derived in the mean polarizability approximation. We know that the effects of concentration broadening of absorption spectra are lost in this approximation. However, Onodera and Toyozawa (16), Dubovsky and Konobeev (17), Hoschen and Jortner (18), and Hong and Robinson (19), who have actually studied the corrections to the mean polarizability approximation, have shown that 

Moreover, the mean polarizability approximation can yield highly accurate results for dispersion and optical anisotropy of crystalline solutions outside the absorption band. This is due to the fact that the concentration broadening in crystals of this type (with only van der Waals interactions between the molecules) does not affect the integral oscillator strength of a transition. The mean polarizability approximation served as the basis for the procedure developed by Obreimov for the analysis of the composition of multicomponent systems as applied to a wide variety of isotopic mixtures, both liquid and crystalline (for the details, see (20)). 

Let us illustrate the mean polarizability approximation by applying it to the spectrum of a binary mixture of isotopically related molecules in a cubic crystal. In this case eqn (5.12) gives 

In deriving eqn (5.59) we have used the fact that the polarizabilities of the different isotopic molecules are given by eqn (5.9) and differ from one another only in the values of the resonance frequencies. Equation (5.59) enables us to determine the shift of the absorption lines of the mixture as a function of its composition in the given approximation. The dependence of the frequencies of the longitudinal waves on the composition of the mixture can be found from the equation e(w) = 0. Using eqn (5.58) we find that these frequencies satisfy the equation 

In a similar way we can find the dependence, for instance, of the frequency of the surface waves, on the composition of the mixture (from the condition e(w) = —1) and many other parameters of the mixture that are determines by its dielectric constant. 

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