Temperature Line-Broadening

Unsatisfactory features of these particular calculations are due to the limitations of the HF-RPA procedure to produce quantitatively correct spectroscopic patterns, and to the very small basis set that we adopted in order to carry out evaluations of several thousands of HF ground-electronic-state wave functions and their associated RPA spectra. Such a quantitative inadequacy of the computational model, however, does not alter the physical meaning of the conclusion that can be drawn the appearance of a single broad band in the optical spectrum of Na9 is simply a thermal broadening effect, which, in general, is particularly effective in the presence of several low-lying isomers or in the case of cluster structures characterized by low-frequency vibrations, accompanied by large nuclear displacements due to the low curvature of the BO surface. 

Another interesting T-averaged quantity is the set of principal moments of the inertia tensor, which in the case of the Na9 cluster has been computed using a selection based on HF energies (atomic coordinates in A). At temperatures values equal to 1, 100, 400, 600 and 1000 K, the principal moments turn out to be equal to (4.07 4.07 7.12), (4.07 4.09 7.14), (3.70 3.81 7.21), (3.57 3.71 7.23) and (3.47 3.65 7.27), respectively. Clearly, as the temperature increases, the shape of the cluster loses the symmetry inherent in the form preferred at low temperature, and the three principal moments become progressively more distinct. The present calculations, therefore, do not support the idea that the shape of melted clusters must necessarily be spheroidal. 

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Relaxation data for the methyl carbon could be measured only down to ca. -125°C below this temperature line broadening was too severe to obtain results. The near equal values observed for the Ti and Tip over much of the limited temperature interval is in accord with the methyl motion being on the high temperature side of the Ti-minimum. 

More recently, 13C-NMR studies have been used to investigate rotational isomerism. At lower temperatures line broadening is observable and below — 60 C furfural in dichloromethane shows two C-3 and two C=0 resonances the relative intensities and chemical shifts of which suggest a ratio of oxygen-cis to oxygen-trans isomers of 5 1, in conformity with the earlier work.362... 

Cas temperature This depends on the kinetic energy of the atoms and ions in the plasma. It can be determined from the Doppler peak broadening. This is however not completely straightforward, as the contributions of Doppler and temperature line broadening have to be separated by mathematical deconvolution. Together with the rotational temperature it is an indicator for the vaporisation and atomisation capability of a plasma. 

The pressure cell can be mounted in an insulating box for experiments requiring heating of the cell. Pressure measurements are reliable to temperatures up to about 300 C and perhaps to 400 C when the model is used. At higher temperatures, line broadening effects, very low fluorescent intensity levels, and a poor temperature correction all contribute to give an increasingly more unreliable pressure measurement. 

Figure C2.17.10. Optical absorjDtion spectra of nanocrystalline CdSe. The spectra of several different samples in the visible and near-UV are measured at low temperature, to minimize the effects of line broadening from lattice vibrations. In these samples, grown as described in [84], the lowest exciton state shifts dramatically to higher energy with decreasing particle size. Higher-lying exciton states are also visible in several of these spectra. For reference, the band gap of bulk CdSe is 1.85 eV.

Carbon Dioxide The contribution to the emissivity of a gas containing CO9 depends on gas temperature Tc, on the CO9 partial pressure-beam length product p L and, to a much lesser extent, on the total pressure P. Constants for use in evaluating at a total pressure of 101.3 kPa (1 atm) are given in Table 5-8 (more on this later). The gas absorptivity Ot equals the emissivity when the absorbing gas and the emitter are at the same temperature. When the emitter surface temperature is Ti, Ot is (Tc/Ti)° times , evaluated using Table 5-8 at T instead of Tc and at p LTi/Tc instead of Line broadening, due to... 

Most surface area measurements are based on the interpretation of the low temperature equilibrium adsorption of nitrogen or of krypton on the solid using the BET theory [33,269,276—278]. There is an extensive literature devoted to area determinations from gas adsorption data. Estimates of surfaces may also be obtained from electron micrographs, X-ray diffraction line broadening [279] and changes in the catalytic activity of the solid phase [ 280]. 

The ESR spectra of a large variety of sulfonyl radicals have been obtained photolytically in liquid phase over a wide range of temperature. Some selected data are summarized in Table 2. The magnitudes of hyperfine splittings and the observations of line broadening resulting from restricted rotation about the C—S bond have been used successfully in conjunction with INDO SCF MO calculations to elucidate both structure and conformational properties. Thus the spin distribution in these species is typical of (T-radicals with a pyramidal center at sulfur and in accord with the solid-state ESR data. 

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... 

Isomerization sets in at higher temperatures than 273 K as apparent from NMR line broadening. The reason for a preference for the particular (cis O, N1) isomer is not obvious neither the O/N alternative for organosilyl migration nor the position of the cis/trans equilibrium with respect to the N-C(=X) bonds is easily predictable. 

A very similar application of the modified Bloch equations was based in the work of Adams and Connelly.4 ESR spectra (Figure 5.8) of [Mo P(0 Me)3 2(MeC = CMc)Cp] show the expected triplet (two equivalent 31P nuclei) at 280 K, but only a doublet at 160 K. At intermediate temperatures, the lines broaden. The interpretation is that the alkyne undergoes a pendulum oscillation, which in the extrema diverts spin density from one or the other phosphite. Interestingly, the diamagnetic cation undergoes a similar motion on the NMR time scale, but then the alkyne undergoes a complete rotation. Thus, analysis of the effect leads to a measure of the rate of the oscillation. The... 

Vapor quenching provides a method of bridging the miscibility gap which exists in many alloy systems, and makes a range of novel alloys available for study. Such films, of course, would not be ideal for catalytic studies. They could not be used at high temperatures, and indeed the heat of reaction might be sufficient to induce a transformation to a more stable structure. In addition, characterization by X-ray diffraction would be difficult, even for the crystalline films, because of line broadening by the small crystallites. Nevertheless, alloy films which are metastable above room temperature can be prepared, and their high surface area would... 

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