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 103

In favour of the hypothesis of a mixed valence compound is the existence of the
compound Ca 0.5 Pd 3 O 4 , which is a defective CaPd 3 O 4 -type structure with one half
of the Ca positions empty. In this way, we have the series CaPd 3 O 4 ,Ca 0.5 Pd 3 O 4 and
Pt 3 O 4 where the fully occupied Ca positions in CaPd 3 O 4 become empty in the
platinum oxide.
Then there is the alloy structure FeGeV 2 ( a

4.687 ˚ )[ 22 ] , shown below on the
left, with the corresponding metal-centred tetrahedra of Li 7 VN 4 ( a

¼

9.606 ˚ )
shown on the right (Fig. 6a, b ). The derivation is straightforward, i.e. if the Fe atom
donates one electron to each V atom, the compound becomes

¼

C -Cr 3 Ge (Cr 3 Si-type).

Fig. 6 (a) The structure of
FeGeV 2 ( a 4.687 ˚ ).

Ge atoms - grey ; Fe/V
atoms - red .(b)Li 7 VN 4
( a

¼

9.606 ˚ ). V(1)N 4
tetrahedra - grey , Li(2)N 4
tetrahedra - red

¼

3.2 Substructures in the Space Group P 43 n

3.2.1 Ag 3 PO 4

A furthe r search of the databases [ 17 , 18 ] reveals the compound Ag 3 PO 4 in space
group

43 n [ 23 ] : it has Ag atoms occupying the site 6 d (¼, 0, ½), which corre-
sponds to the Li(2) site in Li 7 VN 4 . The O atoms occupy the 8 e site, with coordinates
( x, x, x ) (with x

P

¼

0.1486). There are two other reported structures for Ag 3 PO 4
[ 24 , 25 ]. Both these determinations give the O sites as 8 e ( x, x, x ) (with x ~ 0.35).
We note that 0.35 is simply 0.5-0.15, and these determinations simply have the
effect of inverting the VO 4 tetrahedra at the origins (Fig. 6a ).
The topology of the Ag 3 PO 4 structure and the substructure V(1) 2 Li(2) 6 N 32 of
Li 7 VN 4 is the same. Figure 7a, b illustrates this: the grey V(1)N(2) 4 tetrahedra of
Li 7 VN 4 correspond to the actual PO 4 tetrahedra in Ag 3 PO 4 ,whiletheredLi(2)N 4
tetrahedra represent the Ag atoms, and are the reason for the much larger cell edge -
9.6064 ˚ for Li 7 VN 4 compared with 6.06 ˚ for Ag 3 PO 4 . Once again, inspection of
Fig. 7 reveals that the unit cell of Ag 3 PO 4 is actually comprised of a body-centred
cube of composition (PO 4 ) 2 in which is inscribed an icosahedron of composition Ag 6 .
The structures of both Li 7 PN 4 and Ag 3 PO 4 show another similarity when we
are comparing Ag atoms with the whole Li(2)N(1) 4 tetrahedra as pseudo-atoms.