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 116

coordinated by these O(2) atoms, and all the latter are thus accounted for: if we
draw these tetrahedra, it is clear that they can be considered as entities in their own
right and responsible for the lattice expansion from ~9.6 ˚ in Li 7 VN 4 to ~12 ˚ in
boracite. Figure 16c showsthisverywell.Andsowehavea1:1correspondence
between the two structures, as seen above, where the 24 B(1)O(2) 4 tetrahedra of the
unit cell in boracite correspond to the 24 MN 4 tetrahedra of Li 7 VN 4 comprising
6V(2)N 4 , 6Li(2)N 4 and 12Li(1)N 4 tetrahedra. We note also that the 32 B(2) atoms of
boracite are equivalent to the 32 N atoms of Li 7 VN 4 , i.e. 24 N(1) and 8 N(2).

-Phase of Li 7 V V N 4

4 The

b

This structure is also cubic [ 5 , 6 ], but its space group, P a 3(Z ¼ 8), is different from

that of the -phase. The lattice sites are given in Table 8 .

Moreover, this space group requires the formula to be written as Li 6 [LiV]N 4
since one Li atom and the V atom are ordered on two separate eightfold sites. In an
earlier publication on “stuffed” anti-bixbyite structures, we applied the EZKC [ 1 ]
by supposing that four of the six Li atoms donate four electrons to the four N atoms,
converting them to four (

g

-O) (pseudo-oxygen), and that the two remaining Li
atoms of this group transfer two electrons to the [LiV] group to create the [LiV] 2
group, with a total of eight electrons. These can then be formally distributed
as (Li 3 )

C

-Ti), where the symbol Li 3 implies the accep-
tance by Li of three electrons to give (

-C) and (V +1 ) ( C ( C

-C), and the symbol V +1

C implies the

donation by V of one electron to give ( C -Ti). The [LiV] group is now isoelectronic

with ( -CTi). The overall loss of six electrons by the six Li atoms outside the

square brackets is equivalent to the formation of six isoelectronic (

C

-He)
atoms; so the nett effect of all these electron transfers is the pseudo-compound,
C

C

-(He 6 CTiO 4 ), a hypothetical “C/Ti-stuffed sesquioxide, He 3 O 2 ”, or what is

essentially a V/Li-stuffed sesquinitride, Li 3 N 2 .
It is worth noting that alternative distributions of the eight electrons within the
square brackets are possible, leading to the following: [Li 2 V 0 ] [( C -B)V];

[Li 1 V 1 ] -Cr)]; and [Li 0 V 2 ]

C C C

[( -Be)( [Li( -Mn)]. The corresponding

pseudo-compounds would be C -(He 6 [BV]O 4 ), C -(He 6 [BeCr]O 4 )a d C -

(He 6 [LiMn]O 4 ), respectively.
Table 9 shows the fi ve possible subgroup pathways by which a doubled unit cell
with the s pa ce group

P a3 can be derived from the parent fluorite unit cell with space

group arnighausen Tree for Case 3, which is not quite

identical with that first published by Niewa et al . [ 6 ].

F m 3 m . Table 10 shows the B €

Table 8 The lattice sites
for

Atom Site x y z

b -Li 7 VN 4

V 8 c 0.3703 0.3703 0.3703

Li(1) 8 c 0.1250 0.1250 0.1250

Li(2) 24 d 0.1320 0.3830 0.1360

Li(3) 24 d 0.3570 0.3790 0.1141

N(1) 8 c 0.2610 0.2610 0.2610

N(2) 24 d 0.4858 0.2575 0.4786