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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., Comment: 27 pages, 7 figures, 3 tables

Pseudo-cubic tetragonal boron, which may be another form of boron allotropes, has recently been discovered under high pressure and high temperature conditions. In this paper, the structure of pseudo-cubic tetragonal boron is studied by density-functional-theory (DFT) calculation. The structure is abnormal compared with other boron allotropes in many respects, making it difficult to comprehend. The lattice is very close to a cubic lattice, such that the icosahedra are largely distorted along the c-axis. Such distortions are normally not favorable for boron crystals; in fact, the present calculations supported this. The reported positions of partially occupied interstitial sites render the intericosahedral bonds unusually long or short, which were again not supported by the present calculations. Furthermore, the potential of involving impurities is unlikely in terms of the formation energy and lattice parameters. Therefore, the structure of pseudo-cubic tetragonal boron was not proven by calculation, despite this extensive study. Something may be overlooked in the present structural model, or something unusual may have happened in this structure, the solution of which is left as an open question.