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 122

-Li 7 VN 4 , written as Li 6 [LiV]N 4 , involves only the
Li 6 N 4 components; the two eightfold sites occupied by [LiV] are absent, and the
sites of these in the

The Mg 3 N 2 substructure in b

-Li 7 VN 4 s tr ucture correspond with those of the cation
vacancies in the 16 c sites of the

b

a 3 space group, as we have already discussed in
an earlier paper [ 1 ]. If we were to assume the transfer of the six valence electrons of
the [LiV] group, one to each of the remaining six Li atoms, these would then
become

I

C -Be, leaving [ C -HeKr] as the stuffing in the pseudo-compound C -Be 3 N 2 ,

with the anti-bixbyite structure, just like in -Be 3 N 2 itself [ 47 ].

Moreover, as also discussed in that earlier paper, this 16 c site is the site of the
Si atoms in the high-pressure

a

b b

-Si phase; so this -Si structure is yet another substruc-

b

ture of -Li 7 VN 4 , and we have already discussed in some detail why this should be so.

4.2.2 The Rare-Earth C-Type Structure

The database for this space group also lists a large number of oxides with the
bixbyite-type structure, typified by the C-type rare-earth oxides, e.g. Y 2 O 3 . The
setting chosen by Paton and Maslen [ 48 ] , with Y in site 8 b at 0.25, 0.25, 0.25, as
opposed to the original Geller setting of Mn in site 8 a (0, 0, 0) in his determination
of the bixbyite structure [ 49 ] , allows a direct comparison between the oc cu pied
sites in C-type Y 2 O 3 (SG a 3 (see

Table 12 ). This comparison is shown in Table 13 and Fig. 20a, b to demonstrate in
a simple way the structure/anti-structure relationship.

I a 3) and those of b -Li 7 VN 4 in space group P

Table 13 C orresponding atom sites in Y 2 O 3 and b -Li 7 VN 4

Y 2 O 3 in Ia 3 b -Li 7 VN 4 in Pa 3

Y(1) 8 e 0.25, 0.25, 0.25 N(1) 8 c 0.2609, 0.2609, 0.2609

Y(2) 24 d 0.50, 0.25, 0.533 N(2) 24 d 0.4850, 0.2600, 0.4790

O 48 e 0.111, 0.346, 0.122 Li(2) 24 d 0.1300, 0.3850, 0.1320

0.389, 0.154, 0.378 Li(3) 24 d 0.3800, 0.1040, 0.3630

These data simply demonstrate the structure/anti-structure relationship. Inspection
of Fig. 20a, b seemstoindicatethattheYsites,redinFig. 20a , match the Li(2) and Li(3)

Fig. 20 (a) The Y 2 O 3 structure viewed near [100]. Y atoms - red , O atoms - blue .(b) The anti-
bixbyite structure formed by the Li(2), Li(3) and N atoms of b -Li 7 VN 4 ( a ¼ 9.606 ˚ ). N atoms -

red , Li(2) and Li(3) atoms - blue