Thermal line broadening

A comparison between the measured ° and calculated second band of the photodetachment spectrum of N02 is shown in Fig. 1. The theoretical line spectrum has been generated by employing the linear vibronic-coupling model with parameters determined by ab initio calculations which are more accurate than those previously available. Subsequently, the line spectrum has been convoluted with Lorentzians of suitable width to account for the finite experimental resolution and thermal line broadening effects. The experimental spectral envelope is seen to be very well reproduced by the theory. The theory predicts, moreover, a sub-structure of vibronic lines under most of the peaks of the spectral envelope, which could not be resolved experimentally. 

Stress in crystalline solids produces small shifts, typically a few wavenumbers, in the Raman lines that sometimes are accompanied by a small amount of line broadening. Measurement of a series of Raman spectra in high-pressure equipment under static or uniaxial pressure allows the line shifts to be calibrated in terms of stress level. This information can be used to characterize built-in stress in thin films, along grain boundaries, and in thermally stressed materials. Microfocus spectra can be obtained from crack tips in ceramic material and by a careful spatial mapping along and across the crack estimates can be obtained of the stress fields around the crack. ... 

In all such circumstances the problem which presents itself is, in the first place, that of distinguishing between the different possible causes of line-broadening and then, if a definite verdict on this point can be given, to attempt quantitative interpretation in terms of this factor, be it crystal size, or the extent of the variation of lattice dimensions, or the periodicity of structural irregularities or thermal movements. 

For optical depth t 1 the observed interstellar molecular lines usually have a gaussian shape. This is to be expected, since collisional broadening, which causes the Lorentzian line profile, should be negligible and become important only at gas densities 1012 — 1014 cm- 3. If thermal motions of the molecules were the only source of line broadening the line half power width (i.e. the width between half power points) would be given by... 

Thus, the occurrence of broad C resonances under H high-power decoupling and MAS conditions should neither lead to the automatic conclusion of lack of crystallinity of the sample, nor be considered a nuisance in contrast line broadening mechanisms under MAS are a valuable source of information for the extraction of kinetic parameters and activation energies of thermally activated processes. It should also be mentioned that further line broadening effects may arise from interference between ooi and the MAS frequency, leading to so-called rotary-resonance recoupling of dipolar... 

Equation (3) has several other important implications which can be directly confirmed by finite-frequency probes. One example is the motion-narrowing effect in NMR experiments which is expected to disappear when l/r is below the chemical-shift-anisotropy (CSA) width. Indeed the NMR results of Tycko et al. [16] indicate that for a CSA width of 18.2 kHz the line broadens below 190 K and develops a powder pattern at lower temperature. This is in fair agreement with the 200 K calculated from Eq. (3). They also concluded that the thermal activation energy is around 260 meV below TV, again close to the values we calculated. The glassy dynamics can be probed by other experiments such as sound attenuation, microwave absorption, and thermal conductivity. In particular the characteristic temperature will depend on probe frequency. Such studies are essential to fully understand the low-temperature orientational dynamics. 

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