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 111

Fig. 13 Comparison of a sub-array in Li 7 VN 4 (P43 n , a ¼ 9.606 ˚ ) with the structure of
Ca 4 Al 6 O 13 (I43 m . a ¼ 8.86 ˚ ). The former is shown in (a), with the V(1)N 4 tetrahedra - grey ,
V(2)N 4 tetrahedra - red and Li(2)N 4 tetrahedra - green . The latter structure is shown in (b) with
O(2)Ca 4 tetrahedra - grey , AlO(1) 4 tetrahedra - blue , Ca atoms - green , O(1) atoms - yellow .
(c) The sodalite-type framework in Ca 8 [Al 12 O 24 ]O 2 is outlined by the Al-Al bonds - blue :Al
atoms - dark grey . The OCa 4 tetrahedra are at the origins: O atoms - red , Ca atoms - green .
(d) The same framework formed by the Al atoms in Ca 8 [Al 12 O 24 ](WO 4 ) 2 : W atoms - blue ,Al
atoms - green , Ca atoms - dark grey

tetrahedral set, AlO(1) 4 ,ofAl 6 Ca 4 O 13 corresponds with the two 6-fold tetrahedral
sets, V(2)N(1) 4 and Li(2)N(1) 4 of Li 7 VN 4 . We note immediately that the patterns
of Figs. 13a, b (as depicted further in Fig. 13c) are the same as those in Figs. 9a, b : in
other words, these patterns conform to the sodalite-type framework, and we rewrite
the formula as Ca 8 [Al 12 O 24 ]O 2 to reflect this fact. The ultimate reason for the
formation of the sodalite-like network is that the six Ca atoms provide 12 electrons
to the Al atoms, converting them into

-Si, as occurs in other similar compounds.
In this context, the formula should be written as (Ca +2 ) 6 [Al 12 O 24 ] -12 (CaO) 2 , equiv-
alent to [

C

-Si 12 O 24 ](CaO) 2 .
From a purely crystallographic viewpoint, there is no doubt that the Ca 8 [Al 12 O 24 ]
O 2 structure is a substructure of Li 7 VN 4 , a fact that can only be rationalized
chemically on the basis that, in both compounds, a four-connected, sodalite-like
network is obtained. In the case of Li 7 VN 4 , the skeleton is III-V [

C -Ar] 6 [ C

C -BP], whereas in

Ca 8 [Al 12 O 24 ]O 2 the network is IV-IV, formed by -Si atoms, both structures being

related through the common sodalite-like framework. Indeed, there is a general
trend for many structures to form four-connected nets, characteristic of the Group 14
elements, these networks being rationalized by using the EZKC [40].

C