N at the $2b$ site.

A clearer contrast between pure and C/N-containing forms is found in the occupation of the $2a$ site. $\Delta E_{f}$ of the pure form is large (3.80 eV), while that of the latter one is small (0.3 eV), so that for the pure form there are practically no $2a$-site atoms. Again, if recently discovered $\alpha$-T forms are pure ones, the present results for the site occupancies are consistent with the experiment, as seen in Table \[tbl:alpha-tetra\].

The different site occupations, [*i.e.*]{}, $4c$ in the pure form and $8h$, $8i$, and $2a$ in the impurity-containing forms, provide a useful guideline for identifying impurities. From the site occupations, we can say that at least Ekimov’s $\alpha$-T boron is not a traditional $\alpha$-T form. To identify it as pure $\alpha$-T boron, however, we may need further evidence, because here the term ’impurity-containing form’ is used in a restricted sense,, referring to C- or N-impurities, only. We cannot exclude the existence of other impurities. Further assessments of Ekimov’s $\alpha$-T boron are made below.

### Valence filling {#sec:valenc-filling}

Let us now consider to vary the composition $n$ in B$_{50+n}$ (hereafter, B$_{50+n}$ is also designated as B$_{50}+ n$B$_{s}$ to indicate $n$ atoms 