Loss function dielectric

Fig. 24. Dielectric loss functions for Cs, CS7O, CS11O3 and CS3O from reflectivity data. (60) The absorption maxima yield approximate values for the plasma frequency...

The term 3(— l/e q, co)) is referred to as the dielectric loss function. Structures in this function can be correlated to bulk plasmon excitations. In the vicinity of a surface the differential cross section for inelastic scattering has to be modified to describe the excitation of surface plasmons. The surface energy loss function is proportional to 3(—l/e(, cu) + 1). In general, the dielectric function is not known with respect to energy and momentum transfer. Theoretical approaches to determine the cross section therefore have to rely on model dielectric functions. Experimentally, cross sections are determined by either optical absorption experiments or analysis of reflection energy loss spectra [107,108] (see Section 4.3). 

In 1991, A.S. Nowick and his coworkers discovered a new, second universality, which is ubiquitous in disordered ionic materials ( present in every plastic bag ) but becomes visible only at sufficiently low temperatures and/or high frequencies [30]. The phenomenon is also called Nearly Constant Loss (NCL) effect, since the dielectric loss function, e" oc ajv, appears to be virtually independent of both frequency and temperature, cf. Fig. 3. 

CEELS spectroscopy core electron energy loss lm(—1/ ) dielectric function dielectric loss function... 

Absent Fermi surface anisotropy or an appreciable contribution from interband transitions, the Raman scattering cross section in Eq. (8) corresponds to scattering from ordinary density fluctuations, and consequently is proportional to the dielectric loss function [56], [n(co) + 1]... 

This section considers reports of the frequency-dependent dielectric functions, primarily for polymers in nondilute solutions. By analogy with the treatment of the storage and loss moduli in Chapter 13, the two-parameter temporal scaling approach in that chapter leads to expectations for the dynamic dielectric and dielectric loss functions and their frequency dependences, including for the dynamic dielectric function... 

Figure 7.11 Frequency dependence of the dielectric loss function of cis-polyisoprenes in toluene at concentrations near 50 wt%, namely (x) 5 kDa, 52 wt% ( ) 14 kDa, 49 wt% (0) 32 kDa, 52 wt% and (O) 53 kDa, 52 wt%, using original measurements by Adachi, et a/. (31). Lines represent stretched exponentials, power laws, and their sums as described in the text.

These studies are based on the connection between the dielectric loss function and the dipole-dipole correlation function, Eq. 7.7, which on integration by parts shows... 

Figure 9.14 Real and imaginary parts of the dielectric function s and imaginary part of the dielectric loss functions —1 /e for in- (x) and out-of-plane (z) directions of one representative o-plane GaN film grown on r-plane sapphire surface. For clarity, the functions for directions y are given through the differences between those for directions (x) parallel to the GaN [1120] and (y) parallel to the GaN [1100] directions (cf. Color Plate XXX).

Figure 9.14 (p. 241) Real and imaginary parts of the dielectric function e and imaginary part of the dielectric loss functions —1 /s for in- (x) and out-of-plane (z) directions of one representative o-plane... 

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