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 109

5.903 ˚ ). Zn atoms - red , S atoms - light blue , Zn-Zn
bonds - red , S-S bonds - light blue . (b) Partial structure of

Fig. 11 (a) The zinc-blende structure ( a ¼

-Li7VN4 showing the ZnS-like
arrangement formed by the V(1)N4 tetrahedra - grey , the Li(3)N4 tetrahedra - red and the Li(4)N4
tetrahedra - light blue

g

the odd situation in which a LiN 4 tetrahedron equates to both a zinc atom on the one
hand and a sulphur atom on the other. Now the electron count for the LiN 4 tetrahe-
dron is 31, and the donation of one electron gives a count of 30, equivalent to Zn.
Thus, the four Li(4)N 4 tetrahedra, when donating one electron each become equiva-
lent to four Zn atoms. Acceptance of three electrons by the three Li(3)N 4 tetrahedra
plus one electron by the V(1)N 4 tetrahedra gives a total count of 34 and 52 electrons
respectively, which are those for the elements Se and Te. Recall that ZnSe and ZnTe
crystallize in the same space group as ZnS.
Another possible chemical rationalization of the ZnS (sphalerite) substructure
exists: we consider as parent compound, Li 56 [P(1) 2 P(2) 6 ]N 32 , isostructural with
g -Li 7 VN 4 . The P(1)N 4 tetrahedra have a total of 43 electrons, but if we were to convert

these to -[P(1)O 4 ] with the acceptance of 4 electrons from the Li atoms, we have a

total of 47 electrons per tetrahedron, equivalent to

C

C -Ag. Again, converting the LiN 4

C C

tetrahedra to -[LiO] 4 tetrahedra, with 35 electrons, this is equivalent to -Br. The

C

resulting -[AgBr] is isoelectronic to the zincblende CdSe [ 37 ] so that an additional

transfer of one electron from

C C C

-[LiO] 4 to -[P(1)O 4 ], is required to get the -[CdSe].

We must also recall that a zincblende phase has been reported for AgI [ 38 ] .
An alternative approach would be to ignore the cell-size differences and simply
compare the various tetrahedra. There are two sets of atoms in Li 7 VN 4 (Table 4)
Table 4 corresponding to the two types of tetrahedra that were discussed in an
earlier paper on the bixbyite structure [ 4 ].
We have drawn these two separate situations in the [111] projection (Fig. 12 ) to
better illustrate the two sets of MN 4 tetrahedra, type - A and type - B, as discussed in
that bixbyite paper. Each of the drawings shown above represents the zinc
blende structure. Set A is simply Set B-stuffed blende-type; Set B is Set A-stuffed
blende-type.
It is a matter of choice as to which of these two quite different representations is
the more appropriate.