Rationalization of the Substructures Derived from the Three Fluorite-Related [Li6(MVLi)N4] Polymorphs: An Analysis in Terms of the "Bärnighausen Trees" and of the "Extended Zintl-Klemm Concept"

The crystallographic, group and subgroup relationships are explored for mixed transition metal nitrides of the type: Li₇M^VN ₄. The hypothetical parent M₈N₄ should have the anti-fluorite structure with the space group F m m. However, the corresponding mixed-cation nitride [Li₇V]N₄ is actually tri-morphic comprising one tetragonal phase SG: P4₂/nmc (α) and two cubic phases with space groups: Pa3̄ (β) and P4̄3n (γ), respectively. These three polymorphs are clearly subgroups arising from lowering of symmetry of the parent space group, Fm3̄m. Further decomposition of the pathways (or Bärnighausen Trees) reveals a rich variety of compounds derived from the subgroups and supergroups of the anti-fluorite parent structure. The most important outcome is that all the structures analysed in this work, which derive from the parent Fm3̄m space group of fluorite, can be identified as partial substructures in the three phases of Li ₇VN₄. All these substructures can be rationalized as pseudo-compounds by assuming the appropriate electron transfer between the atoms forming the nitride, following the extended Zintl-Klemm concept (EZKC) that implies charge transfer between atoms, even if they are of the same kind.