Curve fitted spectrum

Figure 4.4 (a) A comparison of the 10th curve fitted spectrum (dotted curve) A/ith the 10th... 

Figure 3. XPS survey spectrum and Cls, Ols, and P2p high-resolution spectra after background subtraction and curve fitting of OOP powder pressed onto indium foil. The difference between the original and the curve fitted spectrum is shown.

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. 

Special attention was paid to the detection of residual Cu-fl quantities accompanying the metallic Cu. The relative amounts of Cu+1 and Cu were determined by curve-fitting the Cu (LMM) spectra using the Physical Electronics Version 6 curve-fitting program. The catalyst showed reduction of Cu+2 Into a mixture of Cu+1 and Cu after reduction In H2 at 250 C for one hour (Figure 6) as evidenced by the two resolved peaks In the Cu (LMM) spectrum at 568.0 and 570.3 eV which are characteristic of Cu and Cu+1, respectively, and by the disappearance of the Cu+2 2p satellite structure. It could be shown that less than 2%, If any, of the total Cu could be present In the +1 oxidation state during methanol formation. However, when the catalyst was briefly exposed to air (1 minute), a few percent of Cu+1 readily formed (7). Thus, any kind of oxidation environment has to be avoided between methanol synthesis and catalyst analysis. Otherwise, appreciable amounts of Cu+1 will be detected. 

Spectra of s.o. samples differed markedly from those of a.p. samples and were unaffected by a subsequent evacuation up to 673 K (Fig. 4, a). Spectra consisted of a composite envelope of heavily overlapping bands at 980-1070 cm-, with two weak bands at 874 and 894 cm-. Irrespective of the preparation method, the integrated area (cm- ) of the composite band at 980-1070 cm- was proportional to the V-content up to 3 atoms nm-2. An analysis of spectra by the curve-fitting procedure showed the presence of several V=0 modes. The relative intensity of the various peaks contributing to the composite band depended only on the V-content and did not depend on the method used for preparing the catalysts. Samples with V > 3 atoms nm-2 R-spectra features similar to those of pure V2O5 (spectrum 8 in Fig. 4, a). 

Fig. 5.14 Experimental (a, black curve), fitted (a, red) and simulated (b) NIS spectrum of the Fe (Ill)-azide complex obtained at the BP86ATZVP level (J = 20 K). Bar graphs represent the corresponding intensities of the individual vibrational transitions. The blue curve represents the fitted spectrum with a background line removed (taken from [63])...

Figure 9. Data reduction and data analysis in EXAFS spectroscopy. (A) EXAFS spectrum x(k) versus k after background removal. (B) The solid curve is the weighted EXAFS spectrum k3x(k) versus k (after multiplying (k) by k3). The dashed curve represents an attempt to fit the data with a two-distance model by the curve-fitting (CF) technique. (C) Fourier transformation (FT) of the weighted EXAFS spectrum in momentum (k) space into the radial distribution function p3(r ) versus r in distance space. The dashed curve is the window function used to filter the major peak in Fourier filtering (FF). (D) Fourier-filtered EXAFS spectrum k3x (k) versus k (solid curve) of the major peak in (C) after back-transforming into k space. The dashed curve attempts to fit the filtered data with a single-distance model. (From Ref. 25, with permission.)...

Therefore, the action spectrum for phototropism does not simply reflect the absorption spectrum of the active photoreceptor pigment itself, but instead, its absorption spectrum somehow modified by shading pigments. However, on this basis Thimann and Curry failed to calculate a curve fitting the experimental action spec-... 

Solid-state NMR spectroscopy was also used to examine the post reaction behavior of pTrMPTrA samples prepared in bulk as thin films, as described in the experimental. All of the spectra in this aging study required a minimum of 720 scans on approximately 50 mg of sample with a 100 s pulse delay to achieve adequate signal/noise. Under these conditions, reliable peak areas could be obtained from the curve fits of the carbonyl region. Figure 3 depicts the evolution of the solid state spectrum of the sample stored under N2 over time and upon heating. The area of the peak at 174 ppm for the carbonyl adjacent to the reacted double bond increases as the peak at 166 ppm for pendant unsaturation decreases. The results of the aging study are given in Table I. 

Figure 6. The XPS spectrum and Ni curve fit for a sample of Spanish sepiolite (loaded with 2%and calcined at 850°C) after reduction at 400°C/lh.

Van Gelder It depends what you are fitting it to. For an opsin it gives you a fit, but your data points have error in them that is not captured in the action spectrum. I know of no statistical means to rigorously do the DartnaU fit taking into account the curve fit used on the fluence curves. 

The analysis of any multicomponent resin or composite is greatly facilitated when the spectrum of that material is expressed by a linear combination of a finite set of pure component spectra. The entire process may be separated into three steps calculation of the number of species present, identification of each of those species, and curve fitting of the spectra of these species to the spectra of the composites7). The technique for determining the number of components in the mixture is called factor analysis or major component analysis and has been described in detail in a number of publications 28,29). Factor analysis is concerned with a matrix of data points. So, in matrix notation we can write the absorbance spectra of a number of mixtures as ... 

Quantitative measurements are carried out by use of a single frequency in the conventional i.r. spectrum, but, with digitized spectra and a computer, the entire frequency spectrum of each component in a mixture can be fitted by curve-fitting techniques using such methods as least-squares refinements,5 which can yield an indication as to the precision of the fit. 

Figure 25.8 (a) C Is spectrum recorded from the clean WC(0001) surface and after an oxygen exposure of 30 L. (b) W 4f7/2 core level spectra (dots) recorded, using a photon energy of 100 eV, from the clean WC(0001) surface and after oxygen exposures of 30 L, 100 L and 300 L. The solid lines through the data points show the results of a curve fitting procedure. The curves below each spectrum show the bulk (B), surface shifted (S) and chemically shifted... 

The N(ls) spectrum from this surface obtained at an exit angle of 15° (Fig. 12) shows the high binding energy component characteristic of amines that have been protonated by the oxide hydroxyls. The low intensity of the N(ls) spectra obtained at steeper exit angles prevented accurate curve fitting of these spectra. 

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