Mathematical Methods for the Analysis of Polycrystal Phase Evolutions

Two methods for an automatic analysis of the temporal evolution of a multiphase polycrystalline sample are described: * The Upeak method, analyzing the spectra formally, i.e., carrying the peak search in them, and so describing the evolution in terms of spectral peaks, or having made additionally the autoindexing of the found peaks, preparing the crystallographic information for the Rietveld analysis. * The Rietveld method, using an already available crystallographic information about the phase reflections, and describing the unit cell and atomic characteristics of each phase, and the mutual phase contributions to the total intensity for each item of the analyzed sequence of neutron scattering spectra. The paper describes difficulties of an automatic analysis securing the convergence of a non-linear and at the same time non-stationary fitting. The evolution of the polycrystalline compound CuFe2O4 with the temperature T in the range from 300 to 500 degrees Celsius illustrates the performance of the methods.