Surface Energy and Growth Mechanism of β-Tetragonal Boron Crystal

The surface energy of β-tetragonal (β-t) boron has been calculated from first principles to investigate how it affects nanoscale crystal growth. The results show that the surface energy of β-t boron is higher than that of α-tetragonal (α-t) boron, and lower than that of α-rhombohedral (α-rh) and β-rhombohedral (β-rh) borons. Although the cohesive energy of β-t boron is lower (more unstable) than that of α-rh and β-rh boron, β-t boron has the lowest total energy of all boron polymorphs in a region with a crystal size N = 216−512 (N: number of atoms). This explains why β-t boron can be obtained by gas-phase synthesis such as chemical vapor deposition (CVD) but not by liquid-phase synthesis because an appropriate number of atoms must be isolated to obtain the β-t structure. The real β-t crystal, which is much larger than this size, is probably obtained through nonequilibrium growth based on a small β-t nucleus. Since the surface energy of β-t boron is rather isotropic, it will probably not have a wire-like ...