Modulation Functions of Aperiodic Crystals Determined by the Maximum Entropy Method

The Maximum Entropy Method (MEM) can be used for the reconstruction of the electron density in the unit cell from phased structure factors [1]. The maximum entropy density map ( ) may provide information about disorder and anharmonic temperature movements. If an informative prior density is employed, MEM may be used to derive the electron density in the chemical bond. The MEM can also be applied to the electron density in the n-dimensional (nD) unit cell of the superspace description of aperiodic crystals [2]. We have thus shown that MEM in superspace may provide a model-independent, quantitatively correct determination of the shapes of the modulation functions of incommensurately modulated crystals and incommensurate composite crystals [3]. All procedures have been implemented into a computer program BayMEM, that can be used for a Maximum Entropy analysis of both periodic and aperiodic crystals. In this contribution the features and problems of the MEM will be discussed, and selected applications of BayMEM will be presented [4].