Patterson selectivity by modulation-enhanced diffraction

Abstract

Modulation excitation spectroscopy is a powerful and well established technique for investigating the dynamic behaviour of chemical and physical systems. Recently, an expansion of this technique for diffraction was proposed and the theory deriving the diffraction response of a crystal subjected to a periodically varying external perturbation was developed [Chernyshov, van Beek, Emerich, Milanesio, Urakawa, Viterbo, Palin & Caliandro (2011).Acta Cryst.A67, 327–335]. The result of this is that a substructure composed of atoms actively responding to the stimulus may be separated out by analysing the diffraction signal at a frequency twice that of the stimulus. This technique is called modulation-enhanced diffraction. Here, a version of the theory dealing with the modulation of the site occupancies of a selected subset of atoms is formulated, and this is supported by experiments carried out at the Swiss–Norwegian Beam Lines at the ESRF, involving periodic variation of the xenon content of a polycrystalline zeolite as a function of temperature. The data analysis involves three steps: (i) data selection is carried out to mimic a linear response; (ii) phase-sensitive detection is applied to obtain contributions both from the responding part of the electron density associated with the Xe atoms and from the interference term; (iii) a phasing procedure is applied to both. A Patterson deconvolution technique has been successfully used to phase the demodulated diffraction patterns and obtain the active substructure.