Search for the boron quasicrystal by first-principle-calculation

Among quasicrystals, no semiconductor has been reported, and the existence of semiconducting quasicrystal is one of the major questions in the solid-state physics, and a semiconducting quasicrystal is expected to be a high performance thermoelectric material. First-principles calculations was performed on four real crystalline structures and hypothetical approximant crystalline and quasicrystalline structures, and total energies were calculated. The formation energy of the α-type 1/1-cubic approximant crystal was found to be very close to the estimated value based on the approximate equation using the formation energy and abundance ratio of α-prolate and α-oblate. From this, it is considered that the estimated value by the approximate equation is reliable, and it is estimated that the β-type 1/1-cubic approximant crystal and β-type quasicrystal have the almost the same formation energy as the α-tetragonal boron phase known as metastable phase. This suggests the possibility of formation of boron quasicrystal as a metastable phase. In addition, the electronic density of states was clarified in the α-type 1/1-cubic approximant crystal. As a result, it was shown that the α-type 1/1-cubic approximant crystal is a semiconductor having a band gap of about 0.25 eV, and it can be strongly expected that the boron quasicrystal is also a semiconductor.