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 121

4.2 Substructures in the Space Group Ia3

The site equivalences are given in Table 11 below.

Ta b le 11 Site equivale n ces between space gr o ups P a 3 and I a 3

Pa 3 Ia 3 Pa 3 Ia 3

( abc : x , y , z ) ( abc : x , y , z ) ( bac :¼ y , x ¼, z+ ¼) ( abc : x , y , z )

4 a +4 b 8 a 8 c 8 a

8 c 8 b 4 a +4 b 8 b

2 8 c 16 c 2 8 c 16 c

24 d 24 d 24 d 24 d

2 24 d 48 e 2 24 d 48 e

4.2.1 Anti-Bixbyite-Type Structure

In the light of what we have already discussed in the earlier paper mentioned above
[ 1 ], namely, that -Li 7 VN 4 is a “stuffed” anti-bixbyite structu re , it is immediately

obvious that the anti-bixbyite structure in space group

b

a 3, typified by such
compounds as Mg 3 N 2 ,Ca 3 N 2 ,Zn 3 N 2 ,Mg 3 P 2 ,Be 3 N 2 [ 47 ], is also a substructure
of

I

b -Li 7 VN 4 . The equivalent sites are collected in Table 12 .

Table 12 Equivalent sites for Mg 3 N 2 and b -Li 7 VN 4

Mg 3 N 2 b -Li 7 VN 4

Atom Site x y z Atom Site x y z

Mg 48 e 0.389 0.152 0.382 Li(2) 24 d 0.380 0.104 0.313

0.111 0.348 0.118 Li(3) 24 d 0.130 0.385 0.132

N(2) 8 b 0.250 0.250 0.250 N(1) 8 c 0.261 0.261 0.261

N(1) 24 d 0.500 0.250 0.522 N(2) 24 d 0.485 0.260 0.479

Drawings (Fig. 19a, b ) of the nitrogen-centred N(1)Mg 6 octahedra for Mg 3 N 2 ,
together with the N(2)Li(2) 6 and N(2)Li(3) 6 octahedra of b -Li7VN 4 , show the

virtually identical structures.

9.972 ˚ ): N(1)Mg 6 octahedra - Fig. 19 (a) The structure of the anti-bixbyite-type Mg 3 N 2 ( a ¼

9.6064 ˚ ): N(2)Li(2) 6 and N(2)Li
(3) 6 octahedra - blue , N(1) atoms - blue , Li(2) atoms - yellow , Li(3) atoms - light blue

blue , N(2) atoms - blue , Mg atoms - red .(b) b -Li 7 VN 4 ( a ¼