A new approach for indexing powder diffraction data based on whole-profile fitting and global optimization using a genetic algorithm

Research output: Contribution to journalArticle


  • Scott A. Belmonte
  • Malcolm I. McMahon
  • Richard J. Nelmes

Colleges, School and Institutes

External organisations

  • University of Edinburgh


This paper describes a new technique for indexing powder diffraction data. The lattice parameters (unit-cell dimensions) {a,b,c,α,β,γ} define the parameter space of the problem, and the aim is to find the optimal lattice parameters for a given experimental powder diffraction pattern. Conventional methods for indexing consider the measured positions of a limited number of peak maxima, whereas this new approach considers the whole powder diffraction profile. This new strategy offers several advantages, which are discussed fully. In this approach, the quality of a given set of lattice parameters is determined from the profile R-factor, Rwp, obtained following a Le Bail-type fit of the intensity profile. To find the correct lattice parameters (i.e. the global minimum in Rwp), a genetic algorithm has been used to explore the Rwp(a,b,c,α,β,γ) hypersurface. (Other methods for global minimization, such as Monte Carlo and simulated annealing, may also be effective.) Initially, a number of trial sets of lattice parameters are generated at random, and this 'population' is then allowed to evolve subject to well defined evolutionary procedures for mating, mutation and natural selection (the fitness of each member of the population is determined from its value of Rwp). Examples are presented to demonstrate the success and underline the potential of this new approach for indexing powder diffraction data.


Original languageEnglish
Pages (from-to)87-92
Number of pages6
JournalJournal of Synchrotron Radiation
Issue number2
Publication statusPublished - 1 Mar 1999


  • Genetic algorithms, Indexing, Powder diffraction, Whole-profile fitting