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Line width limiting

The line width limit with very fast exchange is (2/T2) where T2A = T2b = T2- Equation (42) merely gives the v mode signal in the absence of exchange, as in equation (15b) when wf 2 T2 < 1. Equation (43) is a very useful relation since, in the limit of very fast exchange, chemical shift changes can be determined by changes in pA and pH, the concentrations of species present in equilibrium. [Pg.204]

X-Ray photoelectron spectroscopy has been used to study diazenido com-plexes. " " Sample decomposition, problems with sample charing, and poor spectral resolution (range of chemically induced shifts vj. spectral line widths) limit the general utility of XPES. The diazenido ligand shows a large positive ligand shifts (RN = 1.6 eV, RNj = 0.6 eV)... [Pg.785]

The line width limit with very fast exchange is where =... [Pg.204]

Until the advent of lasers the most intense monochromatic sources available were atomic emission sources from which an intense, discrete line in the visible or near-ultraviolet region was isolated by optical filtering if necessary. The most often used source of this kind was the mercury discharge lamp operating at the vapour pressure of mercury. Three of the most intense lines are at 253.7 nm (near-ultraviolet), 404.7 nm and 435.7 nm (both in the visible region). Although the line width is typically small the narrowest has a width of about 0.2 cm, which places a limit on the resolution which can be achieved. [Pg.122]

A monochromator is useful not only for removing unwanted lines from the X-ray source but also for narrowing the otherwise broad lines. For example, each of the MgXa and AlXa doublets is unresolved and about 1 cY wide at half-intensity. A monochromator can reduce this to about 0.2 cY This reduction of the line width is very important because in an XPS specttum, unlike an ultraviolet photoelectron specttum, the resolution is limited by the line width of the ionizing radiation. Unfortunately, even after line narrowing to 0.2 cY... [Pg.292]

Figure 9.3 Doppler limited laser line with twelve axial modes within the line width... Figure 9.3 Doppler limited laser line with twelve axial modes within the line width...
Although more direct than photoresist, this method, limited to line widths of 250—380 p.m (10—15 mils) because of the limits of screen fabrication, is used primarily for low cost print-and-etch and plated PWBs (5). [Pg.125]

Figures 6.30 and 6.31 present the same information for saturated hydrocarbons. In Figure 6.30, the saturated liquid state is on the lower part of the curve and in Figure 6.31 it is on the upper part of the curve. Below T y, the line width changes, indicating that the liquid probably does not flash below that level. Note that a line has been drawn only to show the relationship between the points a curve reflecting an actual event would be smooth. Note that a liquid has much more energy per unit of volume than a vapor, especially carbon dioxide. Note It is likely that carbon dioxide can flash explosively at a temperature below the superheat limit temperature. This may result from the fact that carbon dioxide crystallizes at ambient pressure and thus provides the required number of nucleation sites to permit explosive vaporization. Figures 6.30 and 6.31 present the same information for saturated hydrocarbons. In Figure 6.30, the saturated liquid state is on the lower part of the curve and in Figure 6.31 it is on the upper part of the curve. Below T y, the line width changes, indicating that the liquid probably does not flash below that level. Note that a line has been drawn only to show the relationship between the points a curve reflecting an actual event would be smooth. Note that a liquid has much more energy per unit of volume than a vapor, especially carbon dioxide. Note It is likely that carbon dioxide can flash explosively at a temperature below the superheat limit temperature. This may result from the fact that carbon dioxide crystallizes at ambient pressure and thus provides the required number of nucleation sites to permit explosive vaporization.
The resolution of a monochromator is the smallest frequency interval the instrument can separate. The limiting resolution is the bandwidth measured at half height when scanning across an infinitely narrow intense source 22). As already mentioned, the broader excitation line width of Ar+ lasers (0.15 to 0.25 cm-1) compared to that of the He-Ne lasers (0.05 cm-1) means a lower resolution limit when the Ar+ laser is used as a Raman source. [Pg.314]

In the ultraslow exchange limit, O -4 1/T, the line shape becomes insensitive to the motion because the extra broadening is much smaller than the natural line width. [Pg.31]

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. 3.8. 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. 3.13. 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<jp from experimental HWHM y = yR + VdP-...
X-Ray diffraction has an important limitation Clear diffraction peaks are only observed when the sample possesses sufficient long-range order. The advantage of this limitation is that the width (or rather the shape) of diffraction peaks carries information on the dimensions of the reflecting planes. Diffraction lines from perfect crystals are very narrow, see for example the (111) and (200) reflections of large palladium particles in Fig. 4.5. For crystallite sizes below 100 nm, however, line broadening occurs due to incomplete destructive interference in scattering directions where the X-rays are out of phase. The two XRD patterns of supported Pd catalysts in Fig. 4.5 show that the reflections of palladium are much broader than those of the reference. The Scherrer formula relates crystal size to line width ... [Pg.133]

Another consideration is the natural line width and satellite structure of the x-ray line used. Titanium (TiKa=4510.9 eV) has seen limited use (12) for non-destructive depth profiling, but the observed spectra are complicated by the TiKa satellite structure and the large natural line width of 2.0 eV (13). [Pg.42]

Potzel et al. [60] used a Ga/ZnO single crystal source in combination with a single crystal absorber of natural ZnO and observed a resonance line width of 0.36 0.04 pm s for the 93.3 keV transition in Zn (at 4.2 K). This, after correction for finite absorber thickness, equals, within the limit of error, the minimum observable line width as deduced from the lifetime of 13.4 ps for the 93.3 keV state. The spectra observed by these authors are shown in Fig. 7.23. [Pg.260]

ESR line widths are also sensitive to processes that modulate the g-value or hyperfine coupling constants or limit the lifetime of the electron spin state. The effects are closely analogous to those observed in NMR spectra of dynamical systems. However, since ESR line widths are typically on the order of 0.1-10 G... [Pg.30]

On an intermediate scale, smaller than the workpiece, but larger than the features, is a regime in the range of tens to hundreds of micrometers that is influenced by convection. This is the same size range in which convectively controlled fine structure is observed in pattern formation studies. In this regime, Debecker et al. [139] treated mass-transfer limited deposition on a set of lines in the presence of flow. They defined a Peclet number based on the line width L, the flow velocity U0 and the distance B between electrodes. [Pg.184]

The recoilless nuclear resonance absorption of y-radiation (Mossbauer effect) has been verified for more than 40 elements, but only some 15 of them are suitable for practical applications [33, 34]. The limiting factors are the lifetime and the energy of the nuclear excited state involved in the Mossbauer transition. The lifetime determines the spectral line width, which should not exceed the hyperfine interaction energies to be observed. The transition energy of the y-quanta determines the recoil energy and thus the resonance effect [34]. 57Fe is by far the most suited and thus the most widely studied Mossbauer-active nuclide, and 57Fe Mossbauer spectroscopy has become a standard technique for the characterisation of SCO compounds of iron. [Pg.25]


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See also in sourсe #XX -- [ Pg.216 ]




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