Rationalization of the Substructures Derived from the Three Fluorite-Related [Li6(MVLi)N4] Polymorphs: An Analysis in Terms of the “Barnighausen Trees” and of the “Extended Zintl–Klemm Concept” - Inorganic 3D Structures - page 95

Table 2 The full Barnighausen Tree for Case 3

Notwithstanding, it is clear th at each pathway has one of the four immediate
supergroups of the space group 43 n (218), two kl as sengleiche a nd two trans la -

tionengleich e , as its immediate precursor: these are

P

43 m (217),

n 3 n (222), m 3 n

I P P

43 c (219), and each is a likely source for substructures within the

(223), and F

-Li 7 V V N 4 structure.
In Table 2 , the captions between the linked formatted tables define the nature
of the transition - k for klassengleiche and t for translationengleiche , with the
following number indicating the order, while those captions to the left of the tables
indicate both changes in unit cell size and how the Wyckoff sites of each subgroup
are derived from the immediate supergroup.
Table 2 illustrates just how we can use the group/subgroup relationships to
explore the existence of substructures in Li 7 VN 4 , and this inevitably brings to
the fore the question “what is a crystal structure?” Chemists have usually thought
of structure in terms of the chemical compound involved, and so we talk of “the
rock-salt structure”, “the fluorite structure”, etc. From the purely crystallographic
point of view, however, a structure is simply a set of occupied sites pertaining to the

g