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Boron bulk crystals are marked by exceptional structural complexity andunusual related physical phenomena. Recent reports of hydrogenated$\alpha$-tetragonal and a new $\delta$-orthorhombic boron B$_{52}$ phase haveraised many fundamental questions. Using density functional theory calculationsit is shown that hydrogenated $\alpha$-tetragonal boron has at least two stablestoichiometric compositions, B$_{51}$H$_{7}$ and B$_{51}$H$_{3}$. Thermodynamicmodeling was used to qualitatively reproduce the two-step phase transitionreported by Ekimov et al. [J. Mater. Res. 31, 2773 (2016)] upon annealing,which corresponds to successive transitions from B$_{51}$H$_{7}$ toB$_{51}$H$_{3}$ to pure B$_{52}$. The so obtained $\delta$-orthorhombic boronis an ordered, low-temperature phase and $\alpha$-tetragonal boron is adisordered, high-temperature phase of B$_{52}$. The two phases are connected byan order-disorder transition, that is associated with the migration ofinterstitial boron atoms. Atom migration is usually suppressed in stronglybound, covalent crystals. It is shown that the migration of boron atoms islikely to be assisted by the migration of hydrogen atoms upon annealing. Theseresults are in excellent agreement with the above mentioned experiment and theyrepresent an important step forward for the understanding of boron andhydrogenated boron crystals. They further open a new avenue to control orremove the intrinsic defects of covalently bound crystals by utilizingvolatile, foreign atoms.

Hydrogenation, dehydrogenation of $\alpha$-tetragonal boron and its transition to $\delta$-orthorhombic boron