Lorenz function

The most intense 826-cm band is broader than the other bands. The broadened band suggests a frequency distribution in the observed portion of the surface. Indeed, the symmetric peak in the imaginary part of the spectrum is fitted with a Gaussian function rather than with a Lorenz function. The bandwidth was estimated to be 56 cm by considering the instrumental resolution, 15 cm in this particular spectrum. This number is larger than the intrinsic bandwidth of the bulk modes [50]. 

Methods of measurement Burnett expansion, ref. 40 modified Burnett expansion, refs. 38, 78, 84, 121 Buckingham expansion, ref. 62 equation of state, refs. 45, 46, 55, 79, 82, 91, 99, 101, 103, 119, 122 expansion plus equation of state, refs. 58, 120 nsity balance, ref. 55 LL, Lorentz-Lorenz function measured. 

Rm is the molar refraction or Lorentz-Lorenz function, and As, Ba, Cb, are the refractivity virial coefficients. The rigorous derivation of the statistical mechanical equations for / m> Ab, and Bb, corresponding to equations (5)—(11), is complicated by the variation of the electric field... 

To calculate micelle size and diffusion coefficient, the viscosity and refractive index of the continuous phase must be known (equations 2 to 4). It was assumed that the fluid viscosity and refractive index were equal to those of the pure fluid (xenon or alkane) at the same temperature and pressure. We believe this approximation is valid since most of the dissolved AOT is associated with the micelles, thus the monomeric AOT concentration in the continuous phase is very small. The density of supercritical ethane at various pressures was obtained from interpolated values (2B.). Refractive indices were calculated from density values for ethane, propane and pentane using a semi-empirical Lorentz-Lorenz type relationship (25.) Viscosities of propane and ethane were calculated from the fluid density via an empirical relationship (30). Supercritical xenon densities were interpolated from tabulated values (21.) The Lorentz-Lorenz function (22) was used to calculate the xenon refractive indices. Viscosities of supercritical xenon (22)r liquid pentane, heptane, decane (21) r hexane and octane (22.) were obtained from previously determined values. 

E. Variation of the Lorentz-Lorenz Function with. Density. . 346... 

It is seen that the effect of the variation of the polarizability is of the same order of magnitude as the effect of statistical fluctuations in the dipole moments / described by the functions S2. For the highest frequencies which may be considered within the approximation introduced into the calculation, the correction to the Lorentz-Lorenz function is about 15 per cent larger than the corresponding correction for the static case, (i.e., to the Clausius-Mossotti function). A similar qualitative behavior may be expected for other noble gases under the same conditions. 

From Tables 3, 5, and 6 it is seen that refractions change in some inverse manner with the wave-length A of the light by which they are measured the variations originate, of course, in the refractive indices entering the Lorentz-Lorenz function (1). Since 1827, a number of equations have been developed to describe dispersions of refractive indices n (Wood, 1934, and Partington, 1953, give historical and other details) of these, those due to Cauchy (9) and Sellmeier (10) appear to be best known and most used... 

The density dependence of the refractive index is given by the Lorentz-Lorenz function... 

Measurements of the refractive index, , of a gas at different pressures also provide information on the second virial coefficient since similar equations are obtained to the above, but with replacing e. The Lorentz-Lorenz function is given by ... 

To examine the validity of the WFL relation, values of the ratio of the experimental to theoretical values for the Lorenz function (Z/Lo), for temperatures close to the melting point, were compared and L/Lq was found to be close to unity for most metals and the small deviations may be due to measurement uncertainties [68]. At lower temperatures, and for some metals, significant deviations from the theoretical Lorenz munber were found and attempts to modify the WFL relation were made [69, 70]. Even larger discrepancies occurred when using the WFL relation for alloys, because electron-electron interactions, electron-phonon interactions, as well as lattice contributions, need to be considered [71]. These limiting effects vanish at melting because the crystal structure is destroyed and the WFL relation becomes a reasonable tool for determining thermal conductivities for liquid metals and alloys. 

One more experimental method of characterizing the metallic state is to compare the volumes and refractions (R) of solids. As the refractive indices of metals are very great, the Lorentz-Lorenz function (Eq. 2.18) is close to 1 and V. According to the Goldhammer-Herzfeld [127, 128] criterion, V- R when a dielectric converts into a metal. As the measure of bond metallicity, the ratio... 

In inorganic crystals atoms have higher and, as follows from Table 11.3 and the polarizabilities of clusters (Table 11.6), their refractions must be lower than in the molecular state. Because the Lorentz-Lorenz function approaches 1 when n oo, and metals have very high RIs (at X = 10 (.im, Cu has n = 29.7, Ag 9.9, Au 8.2, Hg 14.0, V 12.8, Nb 16.0, Cr 21.2, etc [147]), we assumed that R = V foi solid metals [148], These refractions of metals, Rm (Table 11.5, lower lines) in some cases are close to the additive values [13,14]. Rm cannot be applied directly to calculate molar refractions of crystalline inorganic compounds because of the differences in Nc, but can be used [149] to calculate refractions of metals for such Nc as they have in the structures of their compounds, using the formula... 

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