“…In order to obtain consistent results, we computed µ Al(bulk) , µ N2 , µ AlN , µ O2 and µ Si(bulk) , employing the HSE functional. Similarly, we computed the formation enthalpies, ∆H f , of Al 2 O 3 and AlN, obtaining −17.91 eV and −3.55 eV, respectively, values that are on average 6% larger in modulus than the experimental ones [25,26]. Accordingly, we used in our calculations ∆H f (Si 3 N 4 ) = −5.10 eV, 6% larger in modulus than the corresponding experimental value [25].…”