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 96

underlying symmetry of a particular space group, regardless of the chemical nature
of the occupancy . At issue in this context is the question whether or not any
particular, derived substructure makes chemical sense. The pure crystallographer
might take the view that this question is irrelevant.

3 The Gamma Phase of Li 7 V V N 4

-Li 7 V V N 4 , space group The lattice sites occupied in the cubic compound g P 43 n , are

listed below (see also Table 2 ):
Li(1) in 12 f at ( x , ½, ½): Li(2) in 6 d at (¼, 0, ½): Li(3) in 6 b at (0, 0, ½).
Li(4) in 8 e at ( x, x, x ): Li(5) in24 i at ( x , y, z ): V(2) in 6 c at (¼, ½, 0).
V(1) in 2 a at (0,0,0): N(1) in 8 e at ( x, x, x ) and N(2) in 24 i at ( x, y, z ).

The actual arithmetic data are given in Table 2 .
Hence, the question then arises as to whether there are some compounds in

43 n
or in its immediate supergroups whose atoms occupy some of the above sites, and if
so, whether there is a rational chemical argument as to why there should be this
correspondence.

P

3.1 Substructures in the Space Group Pm 3 n

3.1.1 The A 15-Type Structure

We begin this discussion by recalling the comment by Schnick and Luecke [ 11 ]
on the structure of the isomorphic compound, Li 7 PN 4 , as determined by them:
“ ... distribution of P atoms in the cubic unit cell of Li 7 PN 4 ( a ¼ 936.48(3) pm)

resembles a ” The

archetypal A 15 structure is that of the alloy Cr 3 Si, and indeed the arrangements of
P atoms in Li 7 PN 4 and of V atoms in

b -tungsten analogous arrangement (A15-type) as illustrated ...

-Li 7 V V N 4 conform to th e A15 type. This
compound, Cr 3 S i (and many like it), crystallizes in the S.G.

g

m 3 n , which immedi-

P

43 n in Cases 10 and 12 of Table 1 . The Cr atoms are in site 6 c at
(¼, 0, ½) and the Si atoms ar e in site 2 a at (0, 0, 0). However, these sites correspond
to the sites 2 a and 6 d of

ately precedes P

43 n , occupied by V(1) and Li(2), respectively, not V(1)
and V(2) as implied by Schnick and Luecke [ 11 ] . Nevertheless, as we shall see, the
V(1) and Li(2) arrangement is complementary to that of V(1) and V(2). The
complete table of site equivalences, as given in [ 13 ] , is shown in Table 3 .
Thus, the pattern of the Cr 3 Si structure is present in the structures of both

P

g -Li 7 VN 4 and Li 7 PN 4 , although these latter patterns are considerably expanded

with respect to the actual Cr 3 Si structure: this derives from the fact that the cell edge
of Cr 3 Si is approximately half that of -Li 7 VN4. Nevertheless, the patterns are the

same, despite the bond lengths being very different, as is seen in identical views
(near the [100] projection) in Fig. 1a, b , where the respective linkages define
icosahedra in the same orientation. If we now depict the V(2) linkages in

g

g -Li 7 VN 4