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 110

Table 4 The two sets of like-
tetrahedra in the anti-fluorite-
type Li 7 VN 4

Set A Set B

V(1) 2-fold V(2) 6-fold

Li(3) 6-fold Li(1) 12-fold

Li(5) 24-fold Li(2) 6-fold

N(1) 24-fold Li(4) 8-fold

N(2) 8-fold N(1) 24-fold

N(2) 8-fold

Fig. 12 (a) Set A of the zinc-blende-type array in Li 7 VN 4 formed by the V(1)N 4 tetrahedra - grey ,
the Li(3)N 4 tetrahedra - yellow and the Li(5)N 4 tetrahedra - purple . (b) The set B of the zinc-
blende-type array in Li 7 VN 4 formed by the V(2)N 4 tetrahedra - red , the Li(2)N 4 tetrahedra -
green , the Li(4)N 4 tetrahedra - light blue , the Li(1)N 4 tetrahedra - brown

3.3 Substructures in the Space Group I 43 m

We now explore the space group I43 m, one of the four immediate precursor
supergroups to P43 n . Inspection of Table 2 can reveal the various equivalences
between the lattice sites, and these are summarized as follows:
The

P43 n sites are 2 a ,6 b ,6 c ,6 d ,8 e ,12 f and 24 i , and of these the 2 a ,6 b and 8e
sites are identical with the corresponding sites in I43 m . The 6 c and 6 d sites of P43 n

I43 m while the 12 f sites of P43 n are equivalent to

are equivalent to the 12 d sites in

P43 n has the y and z parameters nearly
the same in the case of Li 7 VN 4 , so that there is a close relationship between these
sites and the 24 g ( z, x, x ) sites of

I43 m . The general set, 24 i ,of the 12 e sites of

I43 m . This sets the stage for comparisons of the

P43 n with its precursor structures in I43 m . Li 7 VN 4 structure in

3.3.1 Al 6 Ca 4 O 13

I43 m and some First, is a comparison between the structure of Al 6 Ca 4 O 13 [ 39 ] in

P43 n (Fig. 13 ) . The equivalent atom sites for the drawings elements of Li 7 VN 4 in

below are indicated.
Here we have a thoroughly mixed-up situation in which the V(1)N(2) 4 tetrahedra
of Li 7 VN 4 correspond to the OCa 4 tetrahedra of Al 6 Ca 4 O 13 , and the 12-fold