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 114

Fig. 14 (a)The g -Li 7 VN 4 structure projected on (100). Li(4) atoms - light blue , V(2) + Li(2) - green
and brown , respectively, are connected to form the sodalite-like cage, Li(1) - red ,N(1)- dark blue ,N
(2) - blue . Note that the Li(4) atom sites deviate from the ideal positions (¼, ¼, ¼) corresponding to
the yellow atoms in (b). (b) The related structure of CdY 4 Mo 3 O 12 . Cd/Y sites - yellow , Mo sites -
green : these are connected to form the sodalite cage: Y atoms - blue , O atoms - red

Fig. 15 The sodalite-type
cage formed by the Mo atoms
in both CdY 4 Mo 3 O 16 and
Nd 5 Mo 3 O 12

complementary icosahedra like those existing in the A 15 structure of the Cr 3 Si type.
This is consistent with the existence of the A 15 structure in several Mo alloys such as
Mo 3 Zr and Mo 3 Ga. It is as if the pair Cd/Y occupying the Si sites in Cr 3 Si (the Zr sites
in Mo 3 Zr) serves as the catalyst allowing the interconversion of Mo 3 (Y/Cd) into C -

Mo 3 Zr ↔ C -Mo 3 In by the mutual transfer of only one electron between Cd and Y.

3.5 Substructures in Space Group F 43 c

Many compounds listed in the database have essentially the cubic boracite struc-
ture. Boracite itself, as reported in [ 42 ], has the formula Mg 3 B 7 O 13 Cl and is c u bic
above 538 K. The cell edge is 12.0986 ˚ with Z

¼ 8 and the s p ace group is F 43 c .

Table 7 shows how the atom sites of F 43 c relate to those of P 43 n .

What this means is that the coordinates of atoms in g -Li 7 VN 4 , with space group

P 43 n , are to be calculated from those of boracite by adding (¼, ¼, ¼) to the boracite

lattice sites. So we need to co m pare two drawings, one of the boracite structure
itself and that of

g -Li 7 VN 4 in P 43 n with the coordinate shifts indicated.