Lorentzian fitting

Figure Cl.5.2. Fluorescence excitation spectra (cps = counts per second) of pentacene in /i-teriDhenyl at 1.5 K. (A) Broad scan of the inhomogeneously broadened electronic origin. The spikes are repeatable features each due to a different single molecule. The laser detuning is relative to the line centre at 592.321 nm. (B) Expansion of a 2 GHz region of this scan showing several single molecules. (C) Low-power scan of a single molecule at 592.407 nm showing the lifetime-limited width of 7.8 MHz and a Lorentzian fit. Reprinted with pennission from Moemer [198]. Copyright 1994 American Association for the Advancement of Science.

Fig. 10. (a) Raman spectra (T = 300 K) of arc-derived carbons from a dc arc cobalt was absent (dotted line) and cobalt was present (solid line) in the carbon anode, (b) the difference spectrum calculated from (a), emphasbjng the contribution from Co-catalyzed nanolubes, the inset to (b) depicts a Lorentzian fit to the first-order spectrum (after ref. [27]). 

Figure 16. Rosch and Ratner spectral density (direct damping) Rosch and Ratner lineshapes (lines) Lorentzian fit (circles) Gaussian fit (black dots).

In Fig. 3.20, the experimental transition curves (circle, square, and diamond markers for LP0S. LP07, and LP06 modes, respectively) are plotted together with the Lorentzian fitting, while the fitting parameters are shown in Table 3.1. 

Table I. Parameters for Two Peak Lorentzians Fitted to Indochinite Spectra"...

Fig. 3 shows the combined Mg10+ data, and N5+ resonances obtained with the same 4 pg cm-2 foil. The magnesium resonance width is dominated by the natural width due to the 29.5 ps mean lifetime of the 2 3Pi state [24], A Lorentzian fit gave a FWHM in beam energy of 315(24) keV, consistent with the 326 keV expected from the natural width. The widths of the much narrower nitrogen... 

The values represent the average and standard deviations for the areas under the specified m/e TPD feature normalized by the area under the ml e = 34 peak obtained in six independent measurements. b The peak areas were determined by fitting the TPD curves using a combination of a Gaussian and a Lorentzian. Fits to the formulas for first and second order desorption kinetics were also attempted but did not provide significantly better statistical results. 

Fig. 12 Time-dependent wavenumber of the excited-state A (l) v(CO) IR band of [Re(im) (CO)3(phen)]+ in D20 black) and azurins with Re(CO)3(phen) chromophore attached to His83 red) and Hisl09 blue). Measured in D20 (pD = 7) after 400 nm, 150 fs laser pulse excitation. Exact IR band positions were determined by Lorentzian fitting. Reproduced with permission from [75]...

Fig. 26.7. Sequence of fluorescence-excitation spectra of the narrow spectral feature recorded with the single-mode laser, (a) Stack of 23 fluorescence-excitation spectra recorded at a scan speed of 0.2cm /s (5GHz/s) and an excitation intensity of 0.5 W/cm. The fluorescence intensity is indicated by the gray scale. The averaged spectrum is shown in the lower panel and features a linewidth of 1.8cm (FWHM). (b) Individual fluorescence-excitation spectra together with Lorentzian fits (solid line). Prom top to bottom the linewidths (FWHM) are 1.8cm , 0.7cm , 0.9cm and 1.1 cm , respectively. Adapted from [61]...

Figure 3.12 X-ray diffraction pattern in the glasses (the numbers correspond to the numbers in Table 3.4). Thin lines are Lorentzian fits. (After Sokolov et al., 1992).

Gaussian-Lorentzian fit. The left shoulder at 949cm-1 may be associated with ACP, the right shoulder at 971 cm-1 may originate from p-TCP (see Figure 7.9b) (Heimann and Vu, 1996). 

Figure 7.16 2D-1 H/31 P-CP-HETCOR NMR spectrum (a) and a Lorentzian fit of the cross-section of the HETCOR spectrum at the proton frequency of band L (b) of a plasma-sprayed hydroxyapatite coating incubated in r-SBF for 12 weeks (Heimann, 2007). For details see text.

Fig. 2.47. Unpolarized Raman spectrum of a frozen solution ofCeo in CS2at30 K. The solid line is a 3-Lorentzian fit to the experimental data. The highest frequency is assigned to the totally symmetric pentagonai-pinch Ag mode in The other two lines are assigned to the pentagonal-pinch mode in molecules containing one and two isotopes, respectively. The inset shows the evolution of these peaks as the solution is warmed [1548].

How much does this affect the resultant Fe /EFe ratios An example from Rancourt (1994a) serves to illustrate the effects. Spectra of three micas (two biotites and an annite) were fit with either multiple Lorentzian doublets or a Voigt-based quadrupole splitting distribution (QSD) of peaks. The Lorentzian fits yielded Fe /EFe ratios of 8.62, 22.17, and 18.79, while the QSD fits gave values of 10.60, 25.44, and 17.52 respectively, for the three samples. Based upon this author s considerable recent experience in fitting mica spectra both ways, these differences are typical. 

Results of wet chemical, Mossbauer, XPS, and XANES studies of micas are shown in Figure 10. Figure lOA shows a comparison of wet chemical results vs. Mossbauer data for trioctahedral micas in 15 of the papers cited here. With only a few outliers that can probably be explained by either impurities or experimental error by analysts, there is good agreement between the two data sets. This plot shows that despite the known problems with Lorentzian fits (as discussed earlier in this paper), data from the pre-QSD-fit literature can still be used with confidence if Fe VSFe results are the subject of interest, as long as the error bars on the older measurements are realistically quoted as 3 to 5% absolute. 

It has been found that IVR is in the statistical limit for a series of molecules with the general formula (0X3)37—C C—H, where 7 is C or Si and X is H, D, or F (Kerstel et al., 1991 Gambogi et al., 1993). The initially excited state is a fundamental or first overtone of the acetylenic C—H stretch. The spectra for the R 1) transitions of the fundamentals and the R 5) transitions of the overtones for 3,3-dimethylbutane, (CH3)3CC=CH, and (trimethylsilyl) acetylene (CH3)3SiC CH are shown in figure 4.16. The solid lines are Lorentzian fits, Eq. (4.34), to the spectra. In the statistical limit of intramolecular vibrational energy redistribution a Lorentzian line shape is... 

Figure 4.16 Left-hand side R(7) of the fundamental acetylenic C—H stretch rovibrational spectra of (CHjljCC CH (above) and (CHjljSiC CH (below). Right-hand side R(5) of the overtone acetylenic C—H stretch rovibrational spectra of (CH3)3CC H (above) and (CH3)3SiC CH (below). In all four cases the measured rotational line and a nonlinear least-squares fit to a single Lorentzian are shown in the upper traces, while residual of the Lorentzian fit and the zero line are shown in the lower traces. (For the sake of clarity upper and lower traces are staggered.) The residuals indicate a true Lorentzian line shape for the carbon compound as expected for the statistical regime of IVR. For the silicon compound the fit to a single Lorentzian is not as exact. The small residuals at the low-frequency side for Si compound (below) in both the fundamental and the overtone are likely due to two isotopes of Si with 4.67% and 3.1 % natural abundance or to a hot-band transition (Kerstel et al., 1991).

For the Pb/Pt(lll) system, some insight into the displacement mechanism was obtained by studying the temporal evolution of the Pb-(3xv/3) structure as CO was introduced to the solution. The inset to Fig. 1.18 a shows a rocking scan through the (4/6, 1/6, 0.2) position, where scattering from the (3xv/3) structure occurs. The solid line is a Lorentzian fit to the line shape which enables a coherent domain size of ca. 160 A to be calculated for this structure. The main part of Fig. 1.18 a shows the time dependence of the peak intensity after CO was introduced to the solution at r 200 s. The presence of CO in solution initially caused a large increase in the intensity due to the (3xi/3) phase. This could be due to displacement of Pb that is adsorbed on the Pt surface in defect... 

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