Elpasolite-type superstructures in inverse perovskite nitrides

We present a range of inverse perovskite nitrides with an elpasolite-type superstructure. (Ca₃N_0.682(9))Sn and (Ca₃N_0.559(7))Pb are variants of the previously described (Ca₃N)Sn and (Ca₃N)Pb which contain less nitrogen and crystallize in $Fm\bar{3}m$. (Ba₃N_0.5)Sn and (Ba₃N_0.5)Pb resemble the previously reported perovskites (Ba₃N_x)Sn and (Ba₃N_x)Pb, but with both the superstructure and octahedral tilting, resulting in space group $R\bar{3}$. (Ca₃N_0.77(2))Si, (Ca₃N_0.669(6))Ge, (Sr₃N_0.5)Ge and (Ba₃N_0.5)Ge all crystallize in P2₁/n. Among these, only (Ca₃N_x)Ge has been previously described as (Ca₃N)Ge. (Ca₃N_0.77(2))Si is notably the first compound in which mutually isolated N³⁻ and Si⁴⁻ ions coexist. There also exists a version with composition (Ca₃N_0.86(6))Si, which crystallizes in the cubic perovskite aristotype structure with space group $Pm\bar{3}m$. Similarly, there are versions of (Sr₃N_0.5)Ge, (Ba₃N_0.5)Sn and (Ba₃N_0.5)Pb with elevated nitrogen contents, less strongly tilted octahedra and no apparent superstructure. Electronic structure calculations indicate a metallic nature of the title compounds, with rather narrow improper band gaps for the strontium and barium compounds.