Incommensurate modulations made visible by the Maximum Entropy Method in superspace

Abstract

Abstract This paper presents the application of the Maximum Entropy Method (MEM) to structure solution of incommensurately modulated structures within the superspace formalism. The basic principles of the MEM are outlined, and its generalization toward superspace is discussed. Possible problems in MEM reconstructions and their solutions are summarized. They include series-termination errors in the reconstructed electron density, the effect of insufficient constraints, and the effect of missing data. The use of the MEM in superspace is illustrated by three examples: the structure of the misfit-layer compound (LaS)1.14NbS2, the structure of the high-pressure phase III of bismuth, and the modulated structure of ammonium tetrafluoroberyllate. It is shown that the MEM is able to extract more information about the modulation functions than can be obtained by structure refinements. The MEM can also be used for the study of accurate charge densities of modulated structures. An illustration is given by the charge density of ammonium tetrafluoroberyllate.