Structural stability and electronic properties of β-tetragonal boron: A first-principles study

• β-tetragonal boron was thoroughly investigated using first-principles calculations.
• The lowest energy structure contains 192 atoms in an orthorhombic lattice.
• Another tetragonal structure with 192 atoms has a very close energy.
• The total energy per atom is between those of α- and β-rhombohedral boron.
• The band gap of the lowest energy structure is about 1.16 to 1.54 eV.

It is known that elemental boron has five polymorphs: α- and β-rhombohedral, α- and β-tetragonal, and the high-pressure γ phase. β-tetragonal (β-t) boron was first discovered in 1960, but there have been only a few studies since then. We have thoroughly investigated, using first-principles calculations, the atomic and electronic structures of β-t boron, the details of which were not known previously. The difficulty of calculation arises from the fact that β-t boron has a large unit cell that contains between 184 and 196 atoms, with 12 partially-occupied interstitial sites. This makes the number of configurations of interstitial atoms too great to calculate them all. By introducing assumptions based on symmetry and preliminary calculations, the number of configurations to calculate can be greatly reduced. It was eventually found that β-t boron has the lowest total energy, with 192 atoms (8 interstitial atoms) in an orthorhombic lattice. The total energy per atom was between those of α- and β-rhombohedral boron. Another tetragonal structure with 192 atoms was found to have a very close energy. The valence bands were fully filled and the gaps were about 1.16 to 1.54 eV, making it comparable to that of β-rhombohedral boron.

Electronic density distribution for the lowest-energy configuration (N=192) viewed from the 〈1 0 0〉 direction. Left: isosurface (yellow) at d=0.09 electrons/a.u.3 Right: isosurface (orange) at d=0.12 electrons/a.u.3Figure optionsDownload as PowerPoint slide