Analyzing diffuse scattering with supercomputers

Two new approaches to quantitatively analyze diffuse diffraction intensities
from faulted layer stacking are reported. The parameters of a probability-based
growth model are determined with two iterative global optimization methods: a
genetic algorithm (GA) and particle swarm optimization (PSO). The results are
compared with those from a third global optimization method, a differential
evolution (DE) algorithm [Storn & Price (1997). J. Global Optim. 11, 341–359].
The algorithm efficiencies in the early and late stages of iteration are compared.
The accuracy of the optimized parameters improves with increasing size of the
simulated crystal volume. The wall clock time for computing quite large crystal
volumes can be kept within reasonable limits by the parallel calculation of many
crystals (clones) generated for each model parameter set on a super- or grid
computer. The faulted layer stacking in single crystals of trigonal three-pointedstar-
shaped tris(bicylco[2.1.1]hexeno)benzene molecules serves as an example
for the numerical computations. Based on numerical values of seven model
parameters (reference parameters), nearly noise-free reference intensities of 14
diffuse streaks were simulated from 1280 clones, each consisting of 96 000 layers
(reference crystal). The parameters derived from the reference intensities with
GA, PSO and DE were compared with the original reference parameters as a
function of the simulated total crystal volume. The statistical distribution of
structural motifs in the simulated crystals is in good agreement with that in the
reference crystal. The results found with the growth model for layer stacking
disorder are applicable to other disorder types and modeling techniques, Monte
Carlo in particular.