RESUMEN
A collection of scholarly scripts dealing with the mathematics and physics of peak profile functions in X-ray powder diffraction has been written using the Wolfram language in Mathematica. Common distribution functions, the concept of convolution in real and Fourier space, instrumental aberrations, and microstructural effects are visualized in an interactive manner and explained in detail. This paper is the first part of a series dealing with the mathematical description of powder diffraction patterns for teaching and education purposes.
RESUMEN
In this study it is developed a model for the detailed and automatic study of the alpha-particle spectra coming from detection systems. The fitting of a typical shape of the alpha peak is performed by a Gaussian function for the right side of the peak and a sum of two Gaussian functions for its left tail. The model takes into account the entire spectrum background and, particular attention is posed to the analysis of overlapped peaks, background noise and peaks with low statistic counting. The effectiveness of the proposed model is supported by several tests.
RESUMEN
An algorithm based on moment estimation is presented to determine the initial parameters of the particle spectrum peak shape function for the iteration fitting procedure. The algorithm calculates the mean value, variance, and third-order central moment by using the spectrum peak data, solves the parameters of the fitting function, and then provides them as the initial values to the Levenberg-Marquardt algorithm to ensure convergence and optimized fitting. The effectiveness of the proposed algorithm was tested by gamma and alpha spectra. The algorithm can be used in automated peak curve fitting and spectral analysis.