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 97

Table 3 Site equivalence s
betwe e n space groups P

Pm 3 n P 43 n

m 3 n

2 a 2 a

and P 43 n

6 b 6 b

6 c 6 d

6 d 6 c

8 e 8 e

12 f 12 f

24 j 24 j

4.666 ˚ ). Cr atoms - green ,Si
atoms - grey , Cr-Cr bonds - blue , d(Cr-Cr) centring the faces are 2.28 ˚ , d(Cr-Cr) interfacial bonds
are 2.79 ˚ .(b) Partial structure of Li 7 VN 4 ( a

Fig. 1 (a)The A 15 structure of the Frank-Kasper phase Cr 3 Si ( a ¼

9.6064 ˚ ) showing the pattern formed by Li(2)
atoms - green , and V(1) atoms - grey . Li(2)-Li(2) bonds - orange . d(Li-Li) interfacial bonds are
5.88 ˚ . d(Li-Li) centring the faces are 4.80 ˚ .(c) The pattern formed by the V(1) and V(2) atoms in
Li 7 VN 4 .V(1)atoms- grey ,V(2)atoms- red . V(2)-V(2) bonds - yellow . d(V-V) interfacial bonds
are 5.88 ˚ : d(V-V) centring the faces are 4.80 ˚ .(d)theCr 3 Si-type structure formed by the sub-array
of the Li(2)N(1) 4 tetrahedra - green and the V(1)N 4 tetrahedra - grey in Li 7 VN 4 ( a ¼ 9.606 ˚ ). N(1)
atoms - blue ,N(2)atoms- yellow

¼

in a precisely identical view , it is apparent that these also form an icosahedron,
but one rotated by 90 with respect to the others. This is shown in Fig. 1c . Both
icosahedra are centred by the V(1) atom, and we conclude that, in either orientation,
both structures involving the pairs V(1)/Li(2) and V(1)/V(2) constitute substruc-
tures of the Cr 3 Si (A15) type (as listed in Section 3).
It emerges from an inspection of Fig. 1a that the unit cell of Cr 3 Si comprises a
body-centred cube of composition Si 2 in which is inscribed an icosahedron of