On the possibility of decomposition of integral spectra represented by a superposition of Gaussian, lorentz and pseudo-Voigt profiles

Abstract

The main objective of the work is to determine the minimum distance between the maxima of the elementary components, at which these peaks can be isolated from the integral spectrum by analyzing the identifier based on a combination of the first and second derivatives of the experimental data. The indicated dependencies were studied at various ratios of FWHM and intensities of the integral spectrum components. Following dependences of the distance Δλ at which two elementary components (ECs) are still distinguishable from the integral spectrum on the ratio of FWHMs Δλ = f(H₁/H₂) and on the intensity ratio Δλ = f(B₁/B₂) were obtained. The functions of Gauss, Lorentz and pseudo-Voigt with different contributions of the Lorentz and Gaussian components were studied as profiles representing the ECs. It was found that two Lorentzian profiles are distinguished from the integral spectrum at a distance between the maxima that is several times (3.55–4.36) smaller than one for a pair of Gaussian profiles. It is shown that with a slight increase in the contribution of the Lorentz component to the pseudo-Voigt function (up to 28 % in the case of the dependence Δλ = f(H₁/H₂) and 16 % in the case of Δλ = f(B₁/B₂)), a significant change in the form of these dependencies occurs, and a decrease in the values of Δλ, i.e. the distance at which two peaks, represented by the pseudo-Voigt functions, can be distinguished from the integral curve. The Discussion section provides an explanation of the practical application of the obtained data. It should be noted that the presented dependencies of Δλ = f(H₁/H₂) and Δλ = f(B₁/B₂) for two Gaussian, Lorentzian and pseudo-Voigt profiles with different contributions of the Lorentzian and Gaussian components were obtained for the first time.