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 105

8.509 ˚ ). Ru(1)O 4 tetrahedra - brown ,Ru(2)O 4 tetrahedra -

Fig. 8 (a) The structure of RuO 4 ( a ¼

8.595 ˚ ). Os(2)F 4 tetrahedra - grey , Os(1)(F/O) 4 tetrahedra
- red , F atoms - green , F/O atoms - yellow

pink . O atoms - blue .(b)OsF 2 O 2 ( a ¼

-He] 56 and [(Nb 3 ) 2 (Nb 3 ) 6 ][

to each of the eight Nb atoms to give [ C C -O] 32 .

Nb 3 is

-Ru(2).
For the OsF 2 O 2 structure, we take as parent the hypothetical Li 56 [Re 2 Re 6 ]N 32 .
Justification for this is that the compound Li 56 [Mn 2 Mn 6 ]N 32 does exist, and Re is in
the same group. We require 48 electrons to convert the 32 N atoms to 16 [

C -Ru, and so we have [ C -RuO 4 ] with both C -Ru(1) and C

C -O]

and16 [ C -F] atoms and the remaining 8 from the 56 Li atoms to convert the Re to

C -[Os(F 2 )(O 2 )]. The resulting structure

involves a body-centred cube comprising two Os(2)F 4 tetrahedra, the inscribed
icosahedron being formed by six Os(1)(F/O) 4 tetrahedra.

-Os. The nett result is [ C -He] 56 plus C

3.2.3 Sodalite and Danalite

Another substructure of Li 56 [V(1) 2 V(2) 6 ]N 32 is that of the sodalite type typified by
Na 8 [Al 6 Si 6 O 24 ](ClO 4 ) 2 [ 30 ] , derived from the hypothetical parent Na 56 [V(1) 2
V(2) 6 ]N 32 , where the V(2)N 4 tetrahedra correspond with SiO 4 tetrahedra, Na(2)N 4
tetrahedra with AlO 4 tetrahedra and V(1)N 4 tetrahedra with ClO 4 tetrahedra
(Fig. 9a, b ) .
In rationalizing this substructure, we begin with the parent structure,
Na 56 [P(1) 2 P(2) 6 ]N 32 (note the substitution of Li atoms by the Na atoms of the
original sodalite). First, we convert the 32 N atoms to 32[

-O] by the acceptance of
32 electrons from 32 Na atoms, leaving 24 Na atoms plus 32 [ C -Ne]. The formula
becomes Na 24 [

C

-O] 32 . Within the [P(1) 2 P(2) 6 ] group, we
now have 2P(1) atoms accept 2e each from Na to form 2[

C -Ne] 32 [P(1) 2 P(2) 6 ][ C

C -Cl], and we then

associate with 2[ C -Cl] eight of the 32[ C -O] atoms to form 2[ C -ClO 4 ]: the pseudo-

formula is now Na 20 [ C -Ne] 36 [[ C -ClO 4 ] 2 P(2) 6 ][ C -O] 24 , which we rewrite as

Na 14 [ -ClO 4 ] 2 . We need now to convert [Na 6 P(2) 6 ]

to [Al 6 Si 6 ], and this requires that the 6 P(2) atoms donate 1e each and the six Na
atoms accept 2e each, a net acceptance of 6e for the group, leading to a final
pseudo-formula Na 8 [

C -He] 36 [Na 6 P(2) 6 ][ C -O] 24 [ C

C -Ne] 42 [Al 6 Si 6 ][ C -O] 24 [ C -ClO 4 ] 2 , a neon-stuffed sodium

perchlorate sodalite.