Line-shape studies Lorentzian

The linewidth, or lineshape, is the third aspect of the ESR spectrum important in any study of radicals. The two most frequently encountered lineshapes observed are the Lorentzian and Gaussian. The Gaussian line-shape is observed when the line is the superposition of a large number of unresolved individual components, such a line being referred to as inho-mogeneously broadened. More important is the Lorentzian lineshape which is often observed for radicals in solution, when complications due to unresolved hyperfine splittings do not occur. The Lorentzian lineshape may be defined by... 

Early studies (Reimer et al., 1980) indicated a broad Gaussian component superimposed on a narrower Gaussian, but most recent studies (Reimer et al., 198 lb Carlos and Taylor, 1980,1982b Taylor and Carlos, 1980 Jefirey and Lowry, 1981) suggest that the narrow line has a Lorentzian shape. Microcrystalline films of Si H also exhibit a broad Gaussian superimposed on a narrower Lorentzian line (Kumeda et al., 1983). This fact demonstrates that the microstructure that gives rise to the two different sites exists in both the crystalline and amorphous forms. All studies confirm that the widths of the two lines are governed by the dipolar term [Eq. (3)] in the Hamiltonian. 

For the Pb/Pt(lll) system, some insight into the displacement mechanism was obtained by studying the temporal evolution of the Pb-(3xv/3) structure as CO was introduced to the solution. The inset to Fig. 1.18 a shows a rocking scan through the (4/6, 1/6, 0.2) position, where scattering from the (3xv/3) structure occurs. The solid line is a Lorentzian fit to the line shape which enables a coherent domain size of ca. 160 A to be calculated for this structure. The main part of Fig. 1.18 a shows the time dependence of the peak intensity after CO was introduced to the solution at r 200 s. The presence of CO in solution initially caused a large increase in the intensity due to the (3xi/3) phase. This could be due to displacement of Pb that is adsorbed on the Pt surface in defect... 

Fourier transform is in face the line shape one would observe directly in an actual resonance experiment. The width of the line corresponds to I/T2, where T2 is the characteristic transverse relaxation time. In many instances Gx(t) can be written as a simple exponential relaxation Gx(t) = expC-t/Tp), corresponding to a Lorentzian line shape. However, more complicated functional forms (the next simplest being Gaussian) are often used to fit the data, particularly in studies of/i diffusion and trapping in solids. 

Conclusive additional evidence for the metallic nature of PAni and its blends with PMMA is provided by electron spin resonance (ESR) studies with the observation of a Dysonian line shape [104]. In both cases, the asymmetry ratio (A/B) decreases with decreasing temperature. The observed changes in the line shape from Dysonian to Lorentzian are thus seen to be a manifestation of the variation with temperature of the electrical conductivity (Figure 1.46). The g value is calculated as 2.00191 + 0.00005. The g value, which is close to the fi-ee spin value, confirms that the spins are indeed polarons. 

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