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-pointed-star-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.