Line width contributions

Since these terms are proportional to tr, they increase with decreasing temperature.1 There are several line-width contributions, included in oc0, which do not depend on m,-. These include magnetic field inhomogeneity and the spin rotation interaction, the latter increasing with 1/tr and thus with increasing temperature. These and other line-width effects have been studied in some detail and are discussed elsewhere.13... 

NMR spectroscopy has been used for qualitative and quantitative analysis. All characteristics of a signal (chemical shift, multiplicity, line-width, coupling constants, and relative intensity) contribute analytical information. Chemical shifts provide information on the chemical environment of the nuclei. The multiplicity gives important stereochemical information. Line width contributes... 

High-resolution spectroscopy used to observe hyperfme structure in the spectra of atoms or rotational stnicture in electronic spectra of gaseous molecules connnonly must contend with the widths of the spectral lines and how that compares with the separations between lines. Tln-ee contributions to the linewidth will be mentioned here tlie natural line width due to tlie finite lifetime of the excited state, collisional broadening of lines, and the Doppler effect. 

Another feature of the spectrum shown in Figure 10.19 is the narrow width of the absorption lines, which is a consequence of the fixed difference in energy between the ground and excited states. Natural line widths for atomic absorption, which are governed by the uncertainty principle, are approximately 10 nm. Other contributions to broadening increase this line width to approximately 10 nm. 

Figure 2.5 shows, for a sample in the gas phase, a typical absorption line with a HWHM (half-width at half-maximum) of Av and a characteristic line shape. The line is not infinitely narrow even if we assume that the instmment used for observation has not imposed any broadening of its own. We shall consider three important factors that may contribute to the line width and shape. 

K, to optimize the energy resolution by reducing the contribution of thermal broadening to the line-width, and lead is, of course, superconducting at that temperature. 

We are interested in the effect of chemical exchange on line width, its usual manifestation. The total relaxation frequency contributing to line width is... 

Fig. 3.8. The Q-branch Raman width alteration with condensation of nitrogen. The theoretical results for the strong (A) and weak (B) collision limits are shown together with experimental data for gaseous [89] ( ) and liquid nitrogen [145] ( ) (point a is taken from the CARS experiment of [136]). The broken curves in the inset are A and B limits whereas the intermediate solid curve presents the rotational contribution to line width at y = 0.3. The straight line estimates the contribution of vibrational dephasing [143], and the circles around it are the same liquid data but without rotational contribution.

Fig. 3.13. Density-dependence of the Qo, branch line width y of methane (the dashed line is for pure vibrational dephasing, supposed to be Unear in density), (o) experimental data (with error bars) [162] Top part rotational contribution yR and its theoretical estimation in motional narrowing limit [162] (solid line) the points were obtained by subtraction of dephasing contribution y

Fig. 3.15, The CARS spectrum rotational width versus methane density for various values of parameter y (1) y = 0, (2) y = 0.3, (3) y = 0.5, (4) y = 0.7, (5) y = 0.75, (6) y = 0.9, (7) y = 0.95, (8) y = 1. Curves (4) and (6) are obtained by subtraction of the dephasing contribution from the line width calculated taking account of vibrational broadening. The other dependences are found assuming purely rotational broadening (vibrational relaxation neglected).

It is important from a practical viewpoint to predict the shear viscosity of mixtures from those of pure melts. For alkali nitrate melts, a linear dependence has been found between the reorientational line width obtained by Raman measurements and the ratio of temperature divided by shear viscosity.For NO3 ions, the depolarized Raman scattering from 1050cm" total stretching vibrational mode (Al) has a contribution to the line width L, which is caused by the reorientational relaxation time of the Csv axis of this ion. The Stokes-Einstein-Debye(SED) relation establishes a relation between the shear viscosity r of a melt and the relaxation time for the reorientation of a particle immersed in it ... 

The shapes of both /w and 7hv lines are assumed to be represented by simple Lorentzians. For a totally symmetric vibration with a low polarization ratio as in the present case, the vibrational and reorientational relaxation times Tv and can be determined from the half-widths of the isotropic and anisotropic spectra. Since the value of /hv is much smaller than that of /w for the 1050 cm" line, the contribution of /gv to the isotropic intensity can be neglected ... 

In the past two decades, 129Xe NMR has been employed as a useful technique for the characterization of the internal void space of nanoporous materials. In particular, the xenon chemical shift has been demonstrated to be very sensitive to the local environment of the nuclei and to depend strongly on the pore size and also on the pressure [4—6], Assuming a macroscopic inhomogeneity resulting from a distribution of adsorption site concentrations, 129Xe NMR spectra of xenon in zeolites have been calculated, and properties such as line widths, shapes as well as their dependence on xenon pressure can be reproduced qualitatively. A fully quantitative analysis, however, remains difficult due to the different contributions to the xenon line shift. (See Chapter 5.3 for a more detailed description of Xe spectroscopy for the characterization of porous media.)... 

Sensitivity of chemical shift analysis is determined by the spectral resolution of the XPS system. The resolution of a typical XPS system without a monochromator is 1.0 eV. This corresponds to the intrinsic line width of Al Ka or Mg Ka radiation. The analysing system contributes only little to the overall resolution. This resolution is sufficient to determine the binding energies of most core levels within 0.1 eV. Considerable improvement of the resolution down to 0.3 eV can be achieved by use of a monochromator. The higher resolution has to be paid for by a loss in intensity which, however, is no problem in modern instruments. 

A fraction of these radicals will contribute to energy absorption at a magnetic field between H and H + dH. This fraction depends on the individual line width AH as well as on the distance from resonance Hr — H. 

The fraction may be written as the function f(Ht — H, AH), where Hr is the resonance field, or center of the individual line. It should be pointed out that the resonance field is itself a function of orientation. Perhaps this concept can best be clarified by the illustration in Fig. 12. We are trying to determine the total energy absorption at the magnetic field H. One radical, oriented so that its absorption is centered at HIlt contributes to the absorption at H. It is clear that the extent of the contribution depends upon the value of Hr — H and upon the line width AH. Another orientation, corresponding to resonance at Hti, contributes less while a third orientation, with resonance at HT contributes a negligible amount at H. 

The 113Cd Ti values estimated for the various peaks varied from 10 to 50 ms and obeyed the qualitative dependence upon 1/R6 (R = Mn-Cd distance) of the dipolar relaxation mechanism expected to be operative. The broad line widths were also shown to have significant contributions from the T2 relaxation induced by Mn++, with both dipolar and contact terms contributing. The 113Cd shifts of the peaks assigned to different shells were measured as a function of temperature, and observed to follow a linear 1/T dependence characteristic of the Curie-Weiss law, with slopes proportional to the transferred hyperfine interaction constant A. 

The broadening due to the analyzer depends on the energy at which the electrons travel through the analyzer and the width of the slits between the energy filter and the actual detector. The analyzer contribution to the line width becomes irrelevant at low pass energies, however, at the cost of intensity. 

The second contribution to the line-width is Doppler broadening. While the transition energy AE may be constant, the frequency and therefore the energy of radiation increases if the molecule is approaching the source and decreases if the molecule is receding from the source. In terms of energy... 

For maximum ENDOR enhancement, the Zeeman modulation amplitude has to be about one half of the width of the EPR line which is saturated at an extremum of its first derivative. However, in an EPR spectrum with line widths of typically 1 mT this Zeeman modulation contributes 20 kHz to the width of a proton ENDOR line. It turns out that in many cases a remarkably better resolution of the spectra may be obtained with a single coding in which only the rf field is modulated. 

It is important to note that Eqs. (9)-(12) are valid only for very fast exchange. If the exchange is somewhat slower ( moderately fast exchange), there will be an exchange contribution to the line width, and Eq. (10) for the ligand resonance2 will be replaced by... 

Fig. 14.7 Additional contributions to the line widths of signals in the presence (triangles) or absence (diamonds) of exchange. The middle...

The analysis of a full tilt series of 2H NMR spectra not only allows the determination of the unique bond angle for a deuteriated methyl group, but also provides an internal check for the consistency of the spectral interpretation. In particular, simulations provide a means for the analysis of line-broadening effects, which arise from the sample mosaic spread as well as the intrinsic line width of the nuclear transition and instrumental factors. When line shapes are fitted to a full tilt series of spectra in a concerted manner and are also compared with the powder spectrum of an unoriented sample, the different contributions can be discerned. In that way an intrinsic line width of around 2 kHz is found for the spectra shown here, together with a mosaic spread between 8° and 10° for the three samples. 

An interesting application of the motional narrowing concept arises in the double NMR technique BS). In this technique the contribution to the NMR line width of nuclei (A) in a solid by the dipolar fields of dissimilar nuclei (B) may be removed by application of a sufficiently strong rf field at the resonance frequency of the B nuclei. With Hib A/Ib, A/Ia where AH is the line width, flipping of B nuclei by the Hib field will cause fluctuations in the dipolar fields of B nuclei at the A nuclei which are rapid compared to T2a and hence cause narrowing of the NMR line of the A nuclei. This effect has been observed in several different solids of the AB type 5S,6A). 

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