Lorentz-type shape

It should be noted that the Raman-inactive soft mode is observed in the temperature region above Tc. A spectral shape completely different from that of the Lorentz-type peak function indicates the defect-induced Raman scattering (DIRS) in the paraelectric phase of ST018. When centrosymmetry is locally broken in the paraelectric phase, the nominally Raman-inactive soft mode is optically activated locally to induce DIRS in the soft mode. 

The interpretation of band progressions by the time dependent procedure is therefore identical with the Franck-Condon analysis and, in the low temperature limit, to the method of molecular distributions as well. The line shape function obtained on the basis of Eq. (52) (for E = hv) differs under this condition from that of Eq. (12) only in the line shape function of each vibrational member in the progression which in Eq. (52) is the delta function and in Eq. (12) has a Lorentz type distribution. 

Fig. 7.46 ESR spectra of PA films observed at 296 K (a) and 9 K (b). The circles show the theoretical line shape (Lorentz type). The figure is adapted from [50] with permission from the American Institute of Physics...

The experimental structure below 1 eV in Figures 1.10 and 1.11 corresponds to the free-electron behavior typically observed in metals. The lowest interband absorption starts to occur above 1.5 eV. In the non-noble (Cu) and noble metals (Ag, Au), Cooper et al. [18] indicated that the sharp rise in 2 at the lowest interband absorption edge is due to the fact that the transitions are from a very flat lower band to the Fermi surface and are not of the critical-point type. More strictly, these transitions occur between occupied states in band 5 and unoccupied states in band 6 as these cross the Fermi surface (5 —> 6 (Ep)) at the L point in the Brillouin zone. Here, the bands are numbered starting from the lowest band at a given k. Relatively poor agreement between the Lorentz line shape and the experiment observed at -1.5 eV in Figiues 1.10 and 1.11 may reflect this fact... 

There are generally three types of peaks pure 2D absorption peaks, pure negative 2D dispersion peaks, and phase-twisted absorption-dispersion peaks. Since the prime purpose of apodization is to enhance resolution and optimize sensitivity, it is necessary to know the peak shape on which apodization is planned. For example, absorption-mode lines, which display protruding ridges from top to bottom, can be dealt with by applying Lorentz-Gauss window functions, while phase-twisted absorption-dispersion peaks will need some special apodization operations, such as muliplication by sine-bell or phase-shifted sine-bell functions. 

Use the same series of data and follow the same procedure as before to try out the Lorentz-Gauss convert window type. There is one single parameter LB available to adjust the window. Set the initial value to LB = 0, increment and decrement its value in small steps and inspect the shape of the window using the interactive mode. Note that for LB > 0 the shape of the window is similar to the exponential window (signal-to-noise improvement) whereas for LB < 0 the window shape is similar to the sine-bell squared window. Try out a few values to enhance the signal-to-noise ratio and to improve the resolution, store the results and compare the spectra using the multiple display. 

For this type of isotherm, represents the maximum loading, which correlates with pore volnme among different adsorbents. The other isotherm parameters, and Po [no relation to the terms in Eqnations (14.4) or (14.5)], represent the characteristic parameter of the adsorbent and an affinity coefficient of the compound of interest, respectively. The characteristic parameter, A, defines the shape of the n versns e cnrve. The affinity coefficient, po, adapts the compound of interest to the characteristic cnrve. It is a fndge factoT that has been correlated to the ratio of molar volumes, parachors, or polarizabilities (via the Lorentz-Lorenz equation) of the componnd of interest to that of a reference component (e.g., benzene or n-heptane). These three methods are ronghly eqnivalent in accuracy. The molar volume version is = The only controversy is whether to nse the... 

In summary, the purpose of the Lorentz factor is to allow the comparison of an anisotropic intensity (in reciprocal space) calculated from a model with the obtained experimental intensities of samples whose symmetry (due to static or time-averaged disorientations) is generally different from that of the model [22]. It also takes into account the fact that only the intensity in reciprocal space that intersects the Ewald sphere can be observed experimentally [23]. Also, the time-averaged orientations may be related to the collimator type and the particle shape. This region in general has a well-defined shape, therefore only polynomial adjustments are made if necessary in order to avoid experimental noise. 

The default setting is Lorentz, i.e. a pure Lorentzian function. A single click on the upper arrow key switches immediately to a pure Gaussian function. The next click on the same arrow sets the peak to Baseline. If, beginning again with the Lorentzian type, the down arrow is clicked on instead, the band shape changes to 100% Lorentz + Gauss. In principle this band... 

ESR lines in solution can almost always be approximated by a Lorentz function. In the solid state the line-shape can in general be reproduced by a Gauss curve. In some instances a so-called Voigt profile can give a better approximation to the experimental line-shape. A Voigt line is a convolution of a Lorentz and a Gauss line. The shape is determined by the ratio ABi/ABg of the respective line-widths. The shapes of the 1st derivative lines of these types are given in Fig. 9.1. 

To determine the coordinates of these atoms, the intensities of about 300 structurally independent reflections of the hkO and Okf type were measured and anal3 ed. The reflection intensity was measured by the ionization method. The measurements were made on a spherical crystal of 0.51-mm diameter. The spherical shape was obtained by rolling [6]. Corrections were made for the absorption and for the Lorentz-polarization factor. 

In the literature, several EMTs have been reported. These EMTs originate from different assumptions of the shape, construction, number, and mutual orientations of the basic unit cells and various types of interactions between them (in addition to or instead of the Lorentz field — the long-range dipole-dipole field involved in the CMLL model). Rather than attempt to review this large body of theoretical work (see, e.g., Refs. [183, 195-197]), the results of only a few of them will be discussed. 

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