Chun-Hsiung Chao

Quantitative phase determination for macromolecular crystals using stereoscopic multibeam imaging

Without invoking anomalous dispersion and heavy-atom derivatives, it is demonstrated that it is possible to directly determine the phases of a large number of reflections collected in a short time from macromolecular crystals using a stereoscopic oscillation-crystal imaging technique, in a multibeam diffraction geometry, where two crystallographic axes in opposite directions are employed as the rotation axes. The intensity profiles (distributions) of the diffraction spots versus the varying tilt Bragg angle of the rotation axis in the two stereoscopically related images yield quantitative phase information. Many multiple diffraction profiles of tetragonal lysozyme and an unknown protein structure are obtained at the rate of 100 profiles per 30 min of X-ray exposure.

The phenomenon of polarization suppression of X-ray Umweg multiple waves in crystals

The phenomenon of the polarization suppression of X-ray Umweg multiple waves in Renninger scans [Renninger (1937). Z. Kristallogr. 97, 107–121] of crystals, showing intensity decrease due to properly chosen wavelength and polarization of incident radiation, is observed. That is, one of the participating wave components in the multiple-wave interference is reduced considerably so that the intensity of multiple diffraction is decreased. The condition for total suppression of the multiple-wave interaction in crystals is derived theoretically from the Born approximation and verified with exact dynamical calculation and experiments. Partial suppression of the strong Umweg interfered component is demonstrated using elliptically or linearly polarized synchrotron radiation. The suppressed multiple-wave intensity distribution reveals high sensitivity to X-ray reflection phase. This multiple-diffraction technique under partial polarization suppression provides an alternative way of enhancing the visibility of multiple-wave interference in crystals for direct phase determination.

Quasi-universality and scaling behaviour of three-wave X-ray interference in crystals: A novel way for the quantitative determination of X-ray reflection phases

Abstract A quasi-universal function describing the intensity distribution of three-wave X-ray interaction in single crystals is derived for the first time from X-ray dynamical theory under the Bethe approximation for inversion-symmetry related reflections. The intensity distributions of three-wave interference can be scaled down to this dimensionless universal function with proper scaling factors. A newly derived intensity-ratio formula provides a new way of analyzing three-wave diffraction data for direct quantitative determination of X-ray reflection phases of complex systems involving macromolecules.

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 C(25)H(25)NO(2) 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 A was deduced.

Anomalous Dispersion Behavior of Multiple-Wave X-Ray Diffraction at Absorption Edges

The effects of anomalous dispersion (resonance) on multiple reflection of x rays and their interference in crystals at atomic absorption edges are studied. Intensity ratios of two inversion-symmetry-related multiple diffractions at or near absorption edges exhibit highly phase-sensitive profiles with strong asymmetric characteristics, unlike those far from the edges. A new resonance perturbation Bethe approach is developed to explain this behavior. This leads to direct determination of the phase change for x-ray reflections at resonance.

Polarization Suppression of X-rayUmwegMultiple Waves in Crystals

The phenomenon of the polarization suppression of X-ray Umweg multiple waves in Renninger scans [Renninger (1937). Z. Kristallogr. 97, 107-121] of crystals, showing intensity decrease due to properly chosen wavelength and polarization of incident radiation, is observed. That is, one of the participating wave components in the multiple-wave interference is reduced considerably so that the intensity of multiple diffraction is decreased. The condition for total suppression of the multiple-wave interaction in crystals is derived theoretically from the Born approximation and verified with exact dynamical calculation and experiments. Partial suppression of the strong Umweg interfered component is demonstrated using elliptically or linearly polarized synchrotron radiation. The suppressed multiple-wave intensity distribution reveals high sensitivity to X-ray reflection phase. This multiple-diffraction technique under partial polarization suppression provides an alternative way of enhancing the visibility of multiple-wave interference in crystals for direct phase determination.