EXPERIMENTAL-EVIDENCE FOR THE EXISTENCE OF NONNUCLEAR MAXIMA IN THE ELECTRON-DENSITY DISTRIBUTION OF METALLIC BERYLLIUM - A COMPARATIVE-STUDY OF THE MAXIMUM-ENTROPY METHOD AND THE MULTIPOLE REFINEMENT METHOD

The electron-density distribution (EDD) of metallic beryllium has been derived from the structure factors of Larsen and Hansen [(1984), Acta Cryst. B40, 169-179] using the maximum entropy method (MEM). Subseque nt topological analysis reveals non-nuclear maxima (NNM) in the EDD. P lots of the gradient field of the electron density illustrates this fi nding. A possible critical-point network for the hexagonal close-packe d (h.c.p.) structure of beryllium is suggested. It is thus demonstrate d that it is possible to obtain detailed topological information about the electron density in metallic beryllium without the use of a struc tural model. In order to test the findings of the MEM, the same set of structure factors were analysed using the multipole refinement method (MRM). Use of the MRM also reveals NNM. The results of the two differ ent approaches to electron-density analysis are contrasted and discuss ed. Expressed within the framework of the theory of atoms in molecules , our results suggest that the h.c.p. structure of beryllium has no Be atoms directly bonded to other Be atoms. The structure is held togeth er through a three-dimensional network of bonds between the NNM and Be atoms as well as between different NNM. The topological analysis thus reveals that the beryllium structure has important interactions conne cting Be atoms of different basal plane layers. The breaking of these interactions when forming a surface may explain the abnormally large e xpansion of the inter-layer distance in the beryllium surface structur e.