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

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 -scan three-beam and four-beam diffraction profiles obtained with a rotating-anode X-ray source, where the 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 χ² 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.