Multipopulation Genetic Algorithm for Determining Crystal Structures Using Powder Diffraction Data

Abstract

A method for the automatic determination of crystal structures using powder diffraction data by the multipopulation genetic algorithm is proposed. The advantage of using coevolution with exchange by better individuals over using evolution within a single genetic algorithm without interpopulation exchange is demonstrated. The process of searching for a structural solution using the multipopulation genetic algorithm is illustrated and analyzed by the example of the known Ca₂Al₃O₆F crystal structure (sp. gr. R3̄, a = 17.3237(1) Å, c = 7.0002(0) Å, Z = 6, and V = 1819.38(1) ų). The fitness functions for the best structural models and atomic position maps at different algorithm operation stages are plotted.