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 118

Fro m all this, i t is clear that there are only two immediate supergroups of P a3,

viz. I a 3 and F m 3.

4.1 Substructures in the Space Group Pa 3

4.1.1 Molecular N 2 at 20 K

a 3 space group itself. A study of the
databases [ 16 , 17 ] reveals immediately the cry st al structure of molecular

We look first for substructures in the P

a

-N 2 at

20 K [ 44 ]; the N atoms occupy the site 8 c of P a 3, with coordinates 0.0530, 0.0530,

0.0530. The comparable component of b -Li 7 VN 4 is the Li(1)N 4 tetrahedron, thus
accounting for the greater cell edge of b -Li 7 VN 4 compared with that of N 2

5.661 ˚ ). In the N 2 structure, the N-N distance is 1.04 ˚ , whereas the
Li(1)-Li(1) distance in

( a ¼

-Li 7 VN 4 is 4.47 ˚ .
Figure 17a-g illustrates the molecular N 2 story. We note in particular that in
Fig. 17b the pairs of VN 4 tetrahedra, linked by brown lines, act like the N 2
molecules in Fig. 17a .
There are two important features arising here, one being that we can consider the
V atoms, belonging to Group 15, to be behaving as N 2 molecules, despite being at
the centres of VN 4 tetrahedra. Looked at differently, we have the electron count for
the VN 4 tetrahedra as 51, corresponding to

b

- (51) Sb, also in Group 15. And even
more surprising is the following: the eight LiN 4 tetrahedra have a total electron
count of 31 electrons each, and we can then allow each to accept two electrons from
the remaining Li atoms to form

C

-BN 4 tetrahedra, with an electron count of 33
each, just the count for As, also belonging to Group 15. Thus, both the LiN 4 and the
VN 4 tetrahedra are behaving structurally as

C

-Sb, respectively. In
addition, the complete set of V(1)N 4 and Li(1)N 4 tetrahedra (formed by combining
Fig. 17b, c ) give rise to the skeleton shown in Fig. 17d . As reported earlier [ 5 ] , this
array resembles the structure of high-pressure

C -As and C

g

-Si, drawn in Fig. 17e . This insight
led to the novel interpretation of the “stuffed” bixbyite structures reported by Vegas
et al. [ 1 ] in terms of the EZKC. As reported in that paper, the

g

-Si(Ge) structure is,
in fact, formed by two interpenetrating nets of the high-pressure, high-temperature
phase of nitrogen [ 45 ] (again, Group 15), in which there are no longer N 2 mole-
cules: instead, the N atoms form a 3D skeleton as shown in Fig. 17e .
A careful comparison of Fig. 17d-f can help to understand the process. Follow-
ing the 8-N rule, in -Si(Ge) (Fig. 17e ) each Ge atom forms four similar bonds

(2.40-2.48 ˚ ). If we assume that each Si atom accepts one electron, the resulting
N (Si 1

g

means pseudo, must be three-connected, forming thus
the 3D structure of nitrogen (Fig. 17e ) which results from the splitting of the two
equal nets that were forming the

¼ C (P)), where C

-Si(Ge) structure.
This can be clearly seen in Fig. 17f which represents the [VLi(1)] sub-array in

g

b -Li 7 VN 4 [ 1 ] . The network, C -[BV], as in the III-V compounds, should also be four-

3.91 ˚ ),

connected. However, the four ( C -B)-V distances are unequal (3 3.40; 1