A New Approach for Indexing Powder Diffraction Data Based on Whole-profile Fitting
and Global Optimization Using a Genetic Algorithm
Benson M. Kariuki*, Scott A. Belmonte#, Malcolm I. McMahon#, Roy L. Johnston*, Kenneth D. M. Harris* and
Richard J. Nelmes#
*School of Chemistry, University of Birmingham, Edgbaston,
Birmingham B15 2TT, U.K.
#Department of Physics and Astronomy, University of Edinburgh,
Edinburgh EH9 3JZ, U.K.
Article: J. Synchrotron Rad. 1999, 6, 87-92.
Abstract
This paper describes a new technique for indexing powder
diffraction data. The lattice parameters (unit-cell dimensions)
{a,b,c,alpha,beta,gamma} 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, R_wp
obtained following a Le Bail-type fit of the intensity profile.
To find the correct lattice parameters (i.e, the global minimum
in R_wp), a genetic algorithm has been used to explore the
R_ wp(a,b,c,alpha,beta,gamma) 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 R_wp). Examples are presented to
demonstrate the success and underline the potential of this new
approach for indexing powder diffraction data..
Write or e-mail me (roy@tc.bham.ac.uk) for a reprint.