Wavelength-modulated diffraction: a new method for phase determination

Abstract

A new diffraction method has been developed in which the intensity of Bragg re¯ections is measured while changing continually the wavelength of the radiation over a range in the vicinity of the absorption edge of an atom contained in the crystal. It is shown that the intensity gradient with respect to the wavelength of the hkl re¯ection is in a simple relation to the real and imaginary parts of the structure factor of that re¯ection and, if the positions of the anomalously scattering atoms are known or properly assumed, the phase of F(hkl) can be derived by solving simultaneous linear equations. The procedure is particularly simple when the crystal is centrosymmetric. The method, called the wavelengthmodulated diffraction (WMD) method, is free from the problem of intensity scaling encountered in other methods of phase determination. Synchrotron radiation is most suited to WMD measurements. Suggestions on how to measure the intensity gradient are given and the possible errors involved are discussed.

5 Molecular structure from X-ray diffraction

“…Direct determination of values for phases (or of signs of phases for centrosymmetric crystals) can be derived from the intensity gradients of Bragg peaks collected with continuously varying wavelength provided by a synchrotron, 97 provided that the wavelength is in the region of the absorption edge of an anomalous scatterer present in the crystal. The method, called wavelength-modulated diffraction (MWD), is not subject to the inter-dataset scaling problems encountered in other methods such as MAD, but the optimum wavelength range for MWD may well be longer than that for a normal dataset; thus the number of phases or signs will usually be lower than the number of re£ections normally collected because the Ewald sphere is smaller for longer wavelengths.…”

Resonant Diffraction

“…The measurement of the intensity gradient of a reflection with respect to the energy also provides information on its phase free from the problem of intensity scaling. 63 As data collection from a large energy range is time-consuming, it was proposed to use energy dispersive optics to perform a simultaneous-MAD data collection 64,65 (Figure 10). Multiwavelength 2D-patterns must be analyzed by an ad hoc program to integrate reflections and normalize intensities 66 and to allow quantitative analysis.…”

“…Up to now, it was considered that it was better to improve the data accuracy at a few optimized energies (generally three) than to collect data at too many energies. , Nevertheless, with measurements at a large number of energies, the whole f a ‘/ f a ‘ ‘ loop can be used for the phasing power and the phase error is reduced. The measurement of the intensity gradient of a reflection with respect to the energy also provides information on its phase free from the problem of intensity scaling . As data collection from a large energy range is time-consuming, it was proposed to use energy dispersive optics to perform a simultaneous-MAD data collection , (Figure ).…”