Line width maximum

Figure 8.13 Mechanical and dielectric loss tangent tan 8 and NMR absorption line width (maximum slope, in gauss) of polytrifluorochloroethylene (Kel-F) (41).

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. 

The recipe (5.58) is even more sensitive to the high-frequency dependence of kjj than similar criterion (5.53), which was used before averaging over kinetic energy of collisions E. It is a much better test for validity of microscopic rate constant calculation than the line width s j-dependence, which was checked in Fig. 5.6. Comparison of experimental and theoretical data on ZR for the Ar-N2 system presented in [191] is shown in Fig. 5.7. The maximum value Zr = 22 corresponding to point 3 at 300 K is determined from the rate constants obtained in [220],... 

To minimize experiment time, the highest possible source activity is desirable, with the constraint that the source line width should not increase sigiuficantly (maximum by a factor of 2-3) over the 9-12 months duration of the mission. Calculations and tests indicate an optimum specific activity for Co at 1 Ci per cm [42, 43], Sources of 350 mCi Co/Rh with a specific activity close to this value and extremely narrow source fine width (<0.13 mm s at room temperature), given... 

Table 7.8 Summary of results obtained for the four Os Mossbauer transitions studied. The absorber thickness d refers to the amount of the resonant isotope per unit area. The estimates of the effective absorber thickness t are based on Debye-Waller factors / for an assumed Debye temperature of 0 = 400 K. For comparison with the full experimental line widths at half maximum, Texp, we give the minimum observable width = 2 S/t as calculated from lifetime data.

Table 7.9 Summary of the results obtained from the Mossbauer spectra of the 36.2 and 69.6 keV y-rays of Os in absorbers of various osmium compounds containing d mg of is the full experimental line width at half maximum, 5 the isomer shift with respect to the source of Ir metal. 

Fig. 13.8 Dependences of the line width of Na atom emission on acoustic power for 2 M NaCl solutions with ethanol concentrations of 0.5 mM (asterisks), 1 mM (triangles) and 2 mM (closed circles). The Na line width without the addition of ethanol is denoted by open circles and has a maximum at 4.8 W...

The salient feature of the experimental results is the observation of a pronounced minimum in the Q(Q)/Q3 vs. z plot. It occurs at the same position, where the static structure factor in its Kratky representation exhibits its maximum. Furthermore, the reduced line width scales with the scaling variable z in the same way that the static structure factor does. Thus, the occurrence of the minimum is directly related to peculiarities of the star architecture. 

The probability of finding the system in the state vRjn> has an oscillatory time dependence. For off-resonance conditions, the system presents a line width at half maximum equal to 4 ll/fi. This matrix element can be expanded in a multipolar expansion, the first term being the electric dipole approximation [45, 152, 154],... 

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. 

Figure 4. Electric quadrupole spectrum of Te in pure Te at 4.8°K. Source, in Cu at 82°K. Total absorber thickness, 30.0 mg./sq. cm. of tellurium enriched in Te—i.e., Te/Te = 40.4%. Individual lines (A this doublet have a full width at half maximum of 0./3 cm./sec. Our experimental line widths for absorbers vary from 0.67-101 cm./sec.

One of the most striking features of the scattered spectrum for either neutrons or light in the vicinity of a phase transition is the appearance of a divergent elastic or quasielastic peak centred near zero frequency shift that lies entirely outside the quasiharmonic soft-mode description of the dynamics (Fleury Lyons, 1983). The first observation of a divergence in scattered intensity is due to Yakovlev et ai, (1956), who observed the phenomenon in the a-fi transition of quartz. The scattered intensity increases dramatically, sometimes by a factor of 10000 near and the maximum value of line width of the diverging feature is itself rather small ( 1 cm ). In Fig. 4.7, typical central peaks are shown for the purpose of illustration. 

He found a rough correlation of line width with decay times, namely, as the decay time decreased, the line widths increased. He points out, however, that these changes were only a maximum of 30 cm-1 for 2 per cent glasses. 

Load the proton spectrum of peracetylated glucose D NMRDATA GLUCOSE 1D H GH 002999,1R and expand a methyl resonance. From the Analysis pull-down menu choose the Linewidth option. With the cursor in Maximum Cursor mode, select a resonance line by clicking the left mouse button. With the cursor set on the top of the peak, click the right mouse button. A horizontal line indicates the intensity at half height and the corresponding line width (in Hz) will appear below the title bar. 

Multiple-pulse measurements were performed on both the LP and HP samples at 20° and — 80° C, and when no differences were noted, lower temperature measurements were performed only on the LP sample. Multiple-pulse spectra for the LP sample are illustrated in Figure 4 together with the eight-pulse spectrum of the reference used for the low-temperature measurements, Ca(OH)2. The lineshapes observed are quite broad, and the line center is a function of temperature. The line width was separated into three contributions by performing three related multiple-pulse measurements (I). These indicated that the main contributions to the linewidth came from both relaxation and second-order dipolar effects. The maximum possible field inhomogeneity Hamiltonian is estimated to be less than 16 ppm by this means, which indicates that the com-... 

The line widths recorded are the distances, in gauss, between the two maxima of the differential curve and thus represented the width of the absorption curve at the level of maximum slope. For a curve of Lorentzian shape, this width is equal to 0.577/T2, where T2 is the spin-spin or transverse relaxation time (12). Since the curves were not strictly Lorentzian (though they were so to well below the region of maximum slope) and in any case were not of identical shape, the recorded line widths do not have this exact theoretical significance, and small differences in width between two samples could be caused by shape differences rather than variations in relaxation phenomena. Nevertheless, since the conclusions drawn later from the observed line widths depend on major differences in level rather than subtle differences in numerical value, they should be perfectly valid. 

Fig. i.4. (a) Action of a radio-frequency field Bl on a nucleus precessing about direction B0. (b) NMR signal (Av1,2 is the half-maximum intensity line width). 

Since spin-spin relaxation reduces the life-time of a nucleus in a particular spin state to T2 g Tj, the half-maximum intensity line width is expressed more precisely by eq. (1.13), which accounts for spin-spin relaxation. 

By adding eqs. (1.13) and (1.14) one obtains the observed half-maximum intensity line width Avl/2(ohsy. 

Using the temperature dependence of NMR spectra, thermodynamic data of interconversions due to intramolecular mobility can be determined. If the coalescence temperature is known, the rate constant at Tc is calculated according to eq. (3.10). Often, Tc and (vA — vB) are not known exactly. In this case, a rough value for kr can be calculated by measuring the half maximum intensity line widths dv1/2(T, at temperatures near Tc and using eq. (3.11) [107, 108],... 

Very slow molecular motion (tc > 10 9 s/rad at B0 x 2.1 Tesla) leads to an increase in T, while T2 decreases (Fig. 3.20). The signals then broaden (line width at half-maximum intensity zlv1/2 1/7V). Therefore, the more sluggish macromolecules usually give poorly resolved 13C NMR spectra having a bandlike shape. 

---