Relative stability of α and β boron

Abstract

α and β rhombohedral boron are closely related structures with nearly identical stability. Unlike a, 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 β.