Linewidth broadening parameter

This applies most particularly to the linewidth broadening parameter, which can vary with the sample composition by up to an order of magnitude. The values for concomitant gases on the NH3 3,3 line range typically from 10 (He) to 205 (NH3) kHz Pa" (ref. 11, p. 364). This parameter reflects the different cross-sections experienced by the two molecules in collision. Its effect on the analytical... 

Although some correction must still be made for changes in the linewidth broadening parameter, the calculations required are much less detailed. In particular, practical measurements are much simplified by exploiting the insensitivity of the peak absorption coefficient to pressure (Section 1.2). This technique becomes especially effective if combined with the line profile integration described in the next section. 

The linewidth broadening parameter may be incorporated into the response function derived by Baker et al. (their Equations 9 and 12). It relates the area under the spectral line profile Area, measured at 2o), to the spectroscopic parameters and the ratio m of Equation 6.2 above through a term 5 = (1 +... 

Answer The data were Mated with an exponential multiplication [before Fourier transformation to improve the signal-to-noise ratio in the frequency spectrum ( 1.3.4). The line broadening parameter used was 1 Hz, forcing a rapid decay of the FID. This gives a greater. linewidth than is imposed by the field homogeneity and relaxation rates,... 

The main experimental information that usually can be deduced from ESR experiments in metals are the g-shift and the linewidth broadening. Both quantities can be measured as a function of an external parameter, like temperature or pressure. The g-shift corresponds to the Knight-shift in NMR experiments and yields information about the static susceptibility. This review nicely documents how the experimental results on the g-shifts in metals provide direct and detailed information on the band structure. The ESR linewidth in metals is determined by the spin-lattice relaxation time and has to be compared to l/T) as deduced from NMR results. The linewidth is determined by the density of states, but in addition yields detailed information on the low-frequency spectrum of spin fluctuations. This is of high relevance in the field of high-Tc superconductors and heavy-fermion compounds. 

Once the basic work has been done, the observed spectrum can be calculated in several different ways. If the problem is solved in tlie time domain, then the solution provides a list of transitions. Each transition is defined by four quantities the mtegrated intensity, the frequency at which it appears, the linewidth (or decay rate in the time domain) and the phase. From this list of parameters, either a spectrum or a time-domain FID can be calculated easily. The spectrum has the advantage that it can be directly compared to the experimental result. An FID can be subjected to some sort of apodization before Fourier transfomiation to the spectrum this allows additional line broadening to be added to the spectrum independent of the sumilation. 

The effect of a pressure of 80 and 150 MPa on the spin-state transition has been also studied [169], a series of spectra obtained at 150 MPa being shown in Fig. 32. The speetra show relaxation effects as line broadening and linewidth asymmetry. Calculated spectra were obtained in the same way as at ambient pressure. Rate constants for a number of temperatures are listed in Table 12, the parameter values resulting from an Arrhenius plot of the rate constants being listed in Table 13. In Fig. 33, the quantity 5g of Eq. (36) has been plotted as a... 

This chapter considers the distribution of spin Hamiltonian parameters and their relation to conformational distribution of biomolecular structure. Distribution of a g-value or g-strain leads to an inhomogeneous broadening of the resonance line. Just like the g-value, also the linewidth, W, in general, turns out to be anisotropic, and this has important consequences for powder patterns, that is, for the shape of EPR spectra from randomly oriented molecules. A statistical theory of g-strain is developed, and it is subsequently found that a special case of this theory (the case of full correlation between strain parameters) turns out to properly describe broadening in bioEPR. The possible cause and nature of strain in paramagnetic proteins is discussed. 

Qualitatively, all proposals indicate a linear dependence on ml (linewidth over a hyperfine pattern increases from low to high field or vice versa cf. Figure 9.4) plus a quadratic dependence on m, (outermost lines more broadened than inner lines). Multiple potential complications are associated with the lump parameters A, B, C, notably, their frequency dependence (Froncisz and Hyde 1980), partial correlation with g-strain (Hagen 1981), and low-symmetry effects (Hagen 1982a). The bottom line quantitative description of these types of spectra has been for quite some time, and still is, awaiting maturation. 

In contrast to the spin-lattice relaxation parameters, which remain invariant, a sijbstantial broadening of the resonant lines occurs upon crystallization. The effect is relatively modest for cis polyisoprene at 0°C and 57.9 MHz, where comparison can be made at the same temperature. Here there is about a 50% increase in the linewidths upon the development of 30% crystallinity. Schaefer (13) reports approximately 3- to 5-fold broader lines (but they are still relatively narrow) for the crystalline trans polyisoprene relative to the completely amorphous cis polyisoprene at 40°C and 22.5 MHz. It is interesting to note in this connection that for carbon black filled cis polyisoprene the line-widths are greater by factors of 5-10 relative to the unfilled polymer. 

The linewidth (corrected for instrumental effects) may also provide important chemical information of several types. For example, if the chemical environment of a resonant atom is not the same for all of the atoms in the sample, then a broadening of the observed resonance is expected. That is, the observed resonance is a sum of the contributions from each atom, the latter not all having the same Mossbauer parameters. Thus for a small catalyst particle, interesting particle size information might be contained in the linewidth due to the contribution from the surface atoms to the Mossbauer spectrum. The distribution (clustered or uniform) of resonant atoms throughout a multicomponent catalyst particle may also be reflected in the linewidth. 

Inhomogeneous broadening of the resonance lines can be related to distributions in the magnetic parameters M and K The corresponding contribution to the linewidth is [8] ... 

The collision halfwidth for a given transition is a function of temperature and the broadening species. In the present diode laser experiments, the temperature (and hence AVp) is known so that it is straightforward to infer values for the parameters a and AVq, and hence 2y, from the observed absorption linewidths. 

For the moment we shall consider the standard method for describing the Doppler-broadened linewidth—i.e. by using a simple lineshape parameter. By far the most common parameters used—called S and W—are defined... 

The spectral parameters were obtained by fitting the experimental EPR spectra using the WinSim package. In order to determine the hyperfine linewidth, the specific modulation amplitude of the CW detection mode had to be taken into account. To this end, the theoretical spectrum with optimized Lorentzian linewidth was used as a starting point. Then the theoretical spectrum with the same hyperfine parameters but a reduced Lorentzian linewidth was calculated and transformed taking into account the broadening due to the CW modulation technique. The reduced Lorentzian linewidth was varied until the best correlation between experimental and modulation-transformed theoretical spectrum was obtained. 

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