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 112

Further exploration in this space group yielded the structures of several alloys
(Cu 5 Zn 8 ,Fe 3 Zn 10 and La 6 Ni 6 P 17 ) and that of U 2 F 9 with atom sites quite closely
related to their counterparts in Li 7 VN 4 . But the site correspondences are not
sufficiently close, in our view, to claim these as genuine substructures.

3.4 Substructures in the Space Group Pn3n (222)

n 3 n , and of these
only two are of relevance here. These are the isostructural compounds Nd 5 Mo 3 O 16
and CdY 4 Mo 3 O 16 . Both are superstructures of fluorite, CaF 2 , and have the standard
MX 2 composition. This is in contrast to the compound,

There are very few entries in the data base for the space group P

-Li 7 VN 4 , which we have
described as an anti-fluorite superstructure M 2 X. The comparisons are interesting,
and shed new light on the whole issue of substructures. The reported structures have
the second origin, which puts this at the 8 c site, so we have transformed the
coordinates to refer to Origin 1, which then allows a direct comparison with those
of

g

g -Li 7 VN 4 . The equivalent sites are given in [ 13 ] (Table 5 ) .

Table 5 Site-equivalenc es
betwe e n space groups

P n 3 n P 43 n

P n 3 n

8 c !þ ¼, ¼, ¼ ! 8 e

and P 43 n

12 d !þ ¼, ¼, ¼ ! 6 c þ 6 d

12 e !þ ¼, ¼, ¼ ! 12 f

16 f !þ ¼, ¼, ¼ ! 8 e þ 8 e

48 i !þ ¼, ¼, ¼ ! 24 i þ 24 i

n 3 n to which are
added ¼, ¼, ¼. We have already identified CdY 4 Mo 3 O 16 as being a fluorite-type
superstructure, and if we now construct the B¨rnighausen tree (Table 6 ) relating
M 8 O 16 (fluorite) to the CdY 4 Mo 3 O 16 structure in

P43 n are those of This implies that the equivalent sites in P

n 3 n , and thence to the Li 7 VN 4 P

P43 n an interesting feature emerges: the cation and anion equivalences
of the Li 7 VN 4 substructure are those for a fluorite-related rather than an anti-
fluorite-related structure.

structure in

3.4.1 CdY 4 Mo 3 O 16

10.688 ˚ )in

In CdY 4 Mo 3 O 16 ( a 4[ 41 ], the four Cd atoms and

four Y atoms are in 8 c at (¼, ¼, ¼), with half occupancy for each: the equivalent
site in

¼ P n 3 n with Z ¼

g -Li 7 VN 4 is Li(4), close to (¼, ¼, ¼), and the other equivalents are: Mo in

12 d Li(1) in 12f . O(2),

in 16 f , and O(1), in 48 i , giving a total of 64 O atoms in the CdY 4 Mo 3 O 16 structure,
only half of which have their equivalents in the N atoms of Li 7 VN 4 : these unoccu-
pied sites are shown in Table 6 by fainter links. Missing from the Li 7 VN 4 structure
are the V(1), Li(3) and Li(5) atoms, exactly those of the type-A set discussed
above in relating the Li 7 VN 4 substructure to the sphalerite structure. Thus, both

V(2) þ Li(2) in 6 c and 6 d and the remaining Y in 12 e