  Boron bulk crystals are marked by exceptional structural complexity and
unusual related physical phenomena. Recent reports of hydrogenated
$\alpha$-tetragonal and a new $\delta$-orthorhombic boron B$_{52}$ phase have
raised many fundamental questions. Using density functional theory calculations
it is shown that hydrogenated $\alpha$-tetragonal boron has at least two stable
stoichiometric compositions, B$_{51}$H$_{7}$ and B$_{51}$H$_{3}$. Thermodynamic
modeling was used to qualitatively reproduce the two-step phase transition
reported by Ekimov et al. [J. Mater. Res. 31, 2773 (2016)] upon annealing,
which corresponds to successive transitions from B$_{51}$H$_{7}$ to
B$_{51}$H$_{3}$ to pure B$_{52}$. The so obtained $\delta$-orthorhombic boron
is an ordered, low-temperature phase and $\alpha$-tetragonal boron is a
disordered, high-temperature phase of B$_{52}$. The two phases are connected by
an order-disorder transition, that is associated with the migration of
interstitial boron atoms. Atom migration is usually suppressed in strongly
bound, covalent crystals. It is shown that the migration of boron atoms is
likely to be assisted by the migration of hydrogen atoms upon annealing. These
results are in excellent agreement with the above mentioned experiment and they
represent an important step forward for the understanding of boron and
hydrogenated boron crystals. They further open a new avenue to control or
remove the intrinsic defects of covalently bound crystals by utilizing
volatile, foreign atoms.
