Relative stability of α and β boron

Abstract

α and β rhombohedral boron are closely related structures with nearly identical stability. Unlike α, in which every site is fully occupied, β is characterized by partial occupancy and intrinsic disorder. Optimizing the site occupation yields a superstructure of β that we call β . Its energy is lower than α but its symmetry lower than β. The configurational entropy of partial occupation drives a β → β transition around room temperature. Comparing the vibrational density of states, we find that β has an excess of low frequency modes that are strongly localized around the partially occupied sites. The vibrational entropy of these low frequency modes adds to the configurational entropy of partial occupation to further stabilize the β structure compared to α.

On permittivity of a stacking nano-faulty film

“…Th e conclusion has been made that high eff ective permittivity of real β-B crystalline fi lms are caused by the presence of planar defects leading to their nano-scale inhomogeneity. It should be emphasized a correlation between experimentally obtained abrupt change in eff ective permittivity around room temperature and theoretically predicted [40,41] intrinsic structural phase transition in β-B, which takes place in same temperature region and changes pattern of the partially occupied (vacant) atomic sites.…”

Electronic Structure of Boron Flat Holeless Sheet

“…In addition, recently, a highly stable quasi-planar boron cluster B 36 of hexagonal shape with a central hexagonal hole [9], which is viewed as a potential basis for an extended 2-D boron sheet, and boron fullerene B 40 [10], which can be imagined as the fragment of a boron sheet wrapped into the sphere, were discovered experimentally. Photoelectron spectroscopy in combination with ab initio calculations have been carried out to probe the structure and chemical bonding of the B 27 − cluster [56].…”

“…Thus, if it were a stable structure, then intra-icosahedral bonds would be only partially covalent but also to some extent metallic. As for boron icosahedra constituting real crystals, it was clearly demonstrated, for example, for β-rhombohedral boron [22][23][24][25][26][27], that they are stabilized by the presence of point structural defects-vacancies and interstitials, in other words, both partially filled regular or irregular boron sites-at very high concentrations. For example, in the case of β-rhombohedral boron, the total effect of such a stabilization is to increase the average number of boron atoms inside the unit cell from the ideal value 105 ( Figure 2) to 106.7 [28], which leads to the saturation of the electron-deficient orbitals and a 5-or 6-coordination number for the majority of constituent boron atoms.…”

Elastic and thermodynamic properties of potentially superhard carbon boride materials

“…Tetragonal phases are intermediate between α and β-boron. The boundary temperature depends on the preparation method and has been estimated to be about 1500 K [16,17]. In the case of the B 50 allotropes, a B 192 structure may be more appropriate [18].…”

“…Their results were in good agreement with other existing first-principle calculations using the pseudopotential plane-wave method. Various attempts have been made to study the ground state and finite temperature properties of α-and β-boron using ab initio pseudopotentials method with LDA [15,16]. These have clarified the features of β-boron by comparing them to those of the α-boron phase.…”