Determination of phase stability of elemental boron

Boron is an important element, used in applications from superhard materials to superconductors. Boron exists in several forms (allotropes) and, surprisingly, it was not known which form (α or β) is stable at ambient conditions. Through experiment, we quantify the relative stability of α-boron and β-boron as a function of temperature. The ground-state energies of α-boron and β-boron are nearly identical. For all temperatures up to 2000 K, the complicated β-boron structure is more stable than the simpler α-boron structure at ambient pressure. Below 1000 K, β-boron is entropically stabilized with respect to α-boron owing to its partially occupied sites, whereas at higher temperatures β-boron is enthalpically stabilized with respect to α-boron. We show that α-boron only becomes stable on application of pressure.