partially occupied sites vary greatly among the different samples. Hoard’s and Will’s forms are traditional $\alpha$-T boron, and the others are recently discovered forms. The lattice parameters $a_0$ and $c_0$ are compared by evaluating the difference from Hoard’s crystal in %. For Qin’s structure, the name ${\rm B_{50}}$ is only nominal and does not indicate the accurate composition.[]{data-label="tbl:alpha-tetra"}

Recently, motivated by a quest for pure $\alpha$-T boron, Hayami and Otani showed that B$_{52}$, with two occupied $4c$ sites, is the lowest-energy structure, and they suggested that pure $\alpha$-T boron exists in bulk form.[@Hayami10] Hereafter, when speaking of non-stoichiometry, we refer to ${\rm B_{52}}$ as the stoichiometric composition, for a reason which will be clear below. The deviation from stoichiometry is expressed as ${\rm B_{52+\delta}}$, with a small fractional number $\delta$. Incidentally, several articles reporting the synthesis of pure $\alpha$-T boron have been published.[@Ekimov11; @Ekimov11a; @Qin12; @Kurakevych12; @Kurakevych13; @Solozhenko13] These newly discovered $\alpha$-T forms should be seen as distinct from the traditional boron, because in most cases they were obtained by solid-state phase transformation from $\beta$-R boron. Thus they are very likely to be truly pure boron crystals. Unfortunately, the chemical compositions in the new $\alpha$-T borons are not well analyzed. 