Deconvolution of X-ray Diffraction Profiles Using Genetic Algorithms and Differential Evolution

Some optimization problems arise when X-ray diffraction profiles are used to determine the microcrystalline characteristics of materials, like the detection of diffraction peaks and the deconvolution process necessary to obtain the pure diffraction profile. After applying the genetic algorithms to solve satisfactorily the first problem, in this work we propose two evolutionary algorithms to solve the deconvolution problem. This optimization problem targets the objective of obtaining the profile that contains the microstructural characteristics of a material from the experimental data and instrumental effects. This is a complex problem, ill-conditioned, since not only there are many possible solutions, but also some of them lack physical sense. In order to avoid such circumstance, the regularization techniques are used, where the optimization of some of their parameters by means of intelligent computing permits to obtain the optimal solutions of the problem.