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 104

Fig. 7 Comparison of the
structures of Ag 3 PO 4 and
Li 7 (P,V)N 4 . The structure of
Ag 3 PO 4 , viewed along [100]
( a ¼ 6.06 ˚ ). Ag atoms -
red ,PO 4 tetrahedra - grey .
Compare with the Li 7 VN 4
( a ¼ 9.606 ˚ ) represented
in Fig. 6b

The composition of the equivalent pseudo-structure in the isomorphic Li 7 PN 4 cell
is then simply [P(1)N 4 ] 2 [P(2)N 4 ] 6 . We can easily transform the 2 P(1)N 4 tetrahedra
to 2 P[ -O] 4 by donation from Li atoms of one electron to each N atom in

each P(1)N 4 tetrahedron, and so we have the required phosphate groups. The
sub-array then becomes [P(1)O 4 ] 2 [P(2)O 4 ] 6 , leaving 18 Li atoms as “stuffing”.
Now the electron count for each

C

-[P(2)O 4 ] tetrahedron is 47, corresponding to
the element Ag, so the sub-array can now be written as

C

C -Ag 6 (PO 4 ) 2 , with the

observed structure.
It should be added that the existence of the complementary substructure

C -Li 3 PO 4 could be seen as normal because another alkali phosphate, Na 3 PO 4 ,is

isostructural with the HT-phase of Ag 3 PO 4 [ 23 ]. Both compounds have a cation
array of the BiF 3 type which, surprisingly, is also adopted by several alkali-metal
pnictides, such as the HP-phase of Na 3 As [ 26 ] . Surprisingly, this structure is
preserved in the HT-phase of Na 3 AsO 4 [ 27 ]. Thus, in the same manner that
Na 3 As, Na 3 AsO 4 ,Na 3 PO 4 and HT-Ag 3 PO 4 are related by their common BiF 3 -type
structure, the existence of a (Li/Na) 3 PO 4 phase with the Ag 3 PO 4 structure should
not be discarded. In fact, it is implicit in Li 7 PN 4 and g -Li 7 VN 4 .

3.2.2 RuO 4 and OsO 2 F 2

Figure 4d depicts both the tetrahedral pairs V(1)N 4 /Li(2)N 4 and V(1)N 4 /V(2)N 4 .The
arrangement of the first pair is also the topological equivalent of one form of
the structure of RuO 4 [ 28 ] , shown in Fig. 8a , while that of the second pair represents
the OsO 2 F 2 structure [ 29 ] . All the Li atoms are now missing from the depicted Li 7 VN 4
substructure, a total of 56; so we have an alternative description of the full structure as
“Li-stuffed RuO 4 -type”. In this compound, the body-centred cube comprises two
Ru(1)O 4 tetrahedra with six Ru(2)O 4 completing the inscribed icosahedron.
Again, we can rationalize this RuO 4 -type structure: we take as the parent
Li 56 [(M V )] 8 N 32 structure the compound Li 56 [Nb 2 Nb 6 ]N 32 . The Li atoms donate
one electron to each of the 32 N atoms, converting them to

C -O, and three electrons