Spectrum Gaussian lorentzian

When an element is present on the surface of a sample in several different oxidation states, the peak characteristic of that element will usually consist of a number of components spaced close together. In such cases, it is desirable to separate the peak into its components so that the various oxidation states can be identified. Curve-fitting techniques can be used to synthesize a spectrum and to determine the number of components under a peak, their positions, and their relative intensities. Each component can be characterized by a number of parameters, including position, shape (Gaussian, Lorentzian, or a combination), height, and width. The various components can be summed up and the synthesized spectrum compared to the experimental spectrum to determine the quality of the fit. Obviously, the synthesized spectrum should closely reproduce the experimental spectrum. Mathematically, the quality of the fit will improve as the number of components in a peak is increased. Therefore, it is important to include in a curve fit only those components whose existence can be supported by additional information. 

X-ray photoelectron spectroscopy (XPS) measurements were performed using a SSX-100 model 206 Surface Science Instrument Spectrometer operated at 10 kV, 12 mA with a monochromatized A1 Ka radiation (1486.6 eV). The catalysts were pressed into the samples holders of 6 mm and then introduced into the preparation chamber of the spectrometer. The Cu, Mosd, Co2p, Niap and Ou lines were recorded for each sample. All binding energies were referenced to the Cu level at 284.8 eV. Surface composition was determined from the peak intensities and the Scofield sensitivity factors provided by the instrument software. For spectrum deconvolution, a Shirley baseline was used and peaks were considered Gaussian/ Lorentzian ratio of 85/15. 

The sodium-23 MASNMR spectrum of a Na-Y zeolite at 132 MHz (11.7 Tesla) is shown in Figure la. As discussed below, the features of this spectrum arise from the presence of at least two separate NMR lines. A simulation of this spectrum, with symmetric lines of mixed Gaussian/Lorentzian character, is also shown in Figure la, along with the component lines of the simulation. Such a spectrum is difficult to simulate uniquely because of the overlap of the lines and the errors introduced into the spectrum as a result of spectral phasing and baseline correction. 

Figure 2.9 Residual optical absorption spectrum of y-irradiated sintered medical-grade Y-TZP (solid curve) and its Gaussian-Lorentzian deconvolution (dotted curves) (Dietrich, Heimann and Willmann, 1996).

Apart from the obvious variables of peak height and width, the type of bandshape needs to be considered. Ilie class of bandshape of an infrared spectrum depends on the type of sample. A choice of Gaussian, Lorentzian or a combination of these bandshapes, is usually considered. Figure 5.2f illustrates a typical. curve-fitting process. 

Figure 2. Survey and detailed XP spectra of Cls, Ols, P2p, S2p, and Zn2p of a commercial purified ZnDTP, frozen on sputtered gold and used as reference compound. In each detailed spectrum, the points are the original data the line between the points is the envelope of the model Gaussian-Lorentzian product functions (dotted lines) used in the curve-fitting routine. The P2p and S2p signals are fitted with two components to...

Fitting When dealing with real media, Raman spectra are the weighted sum of several contributions (bands), each of them described by a specific Gaussian-Lorentzian function. Thus, the whole experimental spectrum can be theoretically recomposed by a linear combination of Gaussian-Lorentzian functions, according to the formula ... 

Fig. 13 Isotopic line splitting of the V3 stretching vibration in single crystalline (see also Fig. 12(a)), after [108, 109], The origin of each absorption band is indicated by an isotopomer present in crystals of natural composition. While the absorption could be fitted by a Lorentzian band profile, the remaining peaks were dominated by the Gaussian contribution in the Voigt band shapes (solid lines below the spectrum). The sum result of fitting the isotopic absorption bands is inserted in the measured spectrum as a solid line...

Fig. IL The infrared absorption peak (solid line) of the ordered c(2 x 2) structure of CO on Cu(lOO) at 100 K. Shown also ate Lorentzian (dashed) and Gaussian (dash-dotted) distributions. The recorded first derivative spectrum is shown in the inset (Reproduced by permission from Ryberg. )...

Fig. 2. (a) Raw 300 MHz proton spectrum of a mixture of acetone and ethanol in deuteri-ochloroform (b) after reference deconvolution using the acetone signal as reference and an ideal lineshape of a 1 Hz wide Lorentzian and (c) after reference deconvolution with an ideal lineshape characterized by a negative Lorentzian width of 0.1 Hz and a Gaussian width of 0.4 Hz. The 0.1 Hz Lorentzian term represents the approximate difference in natural linewidth between the ethanol and acetone signals, and is responsible for the wings on... 

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