Phase stability in α - aaanβd -rhombohedral boron

Phase stability in α - and β-B has been investigated by using first-principles quasiharmonic phonon calculations. It is found that the defect-free α-B is more stable than the defect-free β-B at lower temperatures up to the predicted 1388 K. It is revealed that the defect-free β-B is mechanically unstable at high temperatures (above 1840 K), indicated by the appearance of imaginary phonon modes, which can be suppressed by introducing defects, e.g., the extra B atoms. This discovery is consistent with the experimental observations that defects occur commonly in β-B.