Modulation functions of aperiodic crystals by the maximum entropy method in superspace

Abstract

The maximum entropy method (MEM) can be used to determine the electron density in the unit cell of periodic crystals from phased x-ray diffraction data. As a straightforward extension of this method, the MEM formalism can be applied to the generalized electron density in the unit cell of superspace describing the structures of aperiodic crystals. The principles of the MEM are discussed as they need to be modified for the application of the MEM to generalised electron densities in (3+d)-dimensional superspace (d is an integer). A critical discussion is given of the potential of the MEM for the determination of modulation functions of incommensurately modulated crystals and composite crystals as well as for the determination of atomic occupation domains of quasicrystals.