Electron Density Distributions in Derivative Crystals of α-Rhombohedral Boron

Abstract

Boron carbide (B 12 C 3 ) and boron phosphide (B 12 P 2 ) have the similar structures to α-rhombohedral boron (α-B 12 ) and are considered to be derivative crystals of it. The peculiar bonds in these two derivative crystals are visualized by MEM/Rietveld analysis, which involves a combination of the maximum entropy method (MEM) and Rietveld refinement for powder X-ray diffraction (XRD) data. The distinctive bending of bonds observed in α-B 12 is reversed by an insertion of other atoms. This bending arises from the conflict between the crystal structure of the rhombohedral lattice and the icosahedral structure of the B 12 cluster. Bond strength and interatomic distances are also varied by the insertion. In order to estimate the bond strength, we obtained the electron density height at each bond critical point, and compared it with the force constant, which is derived from the Raman shift.