Acta Crystallographica Section A

Foundations of Crystallography

Volume 57, Part 4 (July 2001)

research papers

Acta Cryst. (2001). A57, 420-428 [ doi:10.1107/S0108767300018869 ]

Phase determination and extension using X-ray multiple diffraction and the maximum-entropy method

C.-M. Wang, C.-H. Chao and S.-L. Chang

Abstract: The extension of the phases of the structure factors of the organic crystal C₂₅H₂₅NO₂ from 77 starting individual phases using the maximum-entropy method is reported. These starting phases were determined from 90 experimental triplet phases calculated from 215 measured $\psi$ -scan three-beam and four-beam diffraction profiles obtained with a rotating-anode X-ray source, where the $\psi$ scans were around the reciprocal-lattice vectors of the 001, 002 and 003 reflections. The extension of the structure factors with phase values was carried out using the maximum-entropy method for 2040 measured two-beam Bragg diffraction intensities with 77 starting phases and the symmetry of the space group as the constraints. Use of structure-factor triplets as constraints for entropy maximization was also attempted. The minimum [chi] ² criteria were applied to the maximum-entropy extrapolation to discern the best phase set to be used as the new constraints for the next step of generating new phases. With this phase-extension procedure, more than 100 phases were determined and an electron-density map at 1.97 Å was deduced.

Keywords: maximum entropy; multiple diffraction; phase determination.