Electron density distribution in germanium from X-ray powder data by the maximum entropy method

Abstract

The electron density distribution map of germanium has been drawn using the maximumentropy method (MEM) with 11 independent structure factors and one combined structure factor, which were determined by the powder pattern decomposition from X-ray data. The R factor was 0.5% for the final MEM density map, though we used the powder data. The result indicates that the bonding electron with a level of 0.3 e Å −3 is clearly visible in the map even though no forbidden reflection is included in the analysis. This is the first observation of the bonding electron from powder X-ray diffraction data. Both the observed and calculated structure factors agreed well with previous measurements, where available. The structure factor F(222)e − M for the 222 forbidden reflection at room temperature calculated from the maximum-entropy map is −1.056 and it shows good agreement with those measured by the integrated intensity using a nearly perfect single crystal.