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 93

and Ta. Compounds of this composition are not altogether unexpected since a dimer
of Li 3 AlN 2 would have the composition Li 6 [Al III ] 2 N 4 , which is isoelectronic with
Li 6 [Li I P V ]N 4 . Moreover, it is worth noting that if a tetramer of the anti-fluorite
structure, Li 2 O, were written as Li 7 [Li]O 4 , we could apply the EZKC to have each
O atom donating one electron to the single Li atom, yielding Li 7 [Li 4 ][O +1 ] 4 ; i.e.
Li 7 [( -N) V ]( -N) 4 , which is the N analogue of the known phosphorus, vanadium,

manganese, niobium and tantalum compounds, Li 6 [Li I M V ]N 4 . Our conclusion to
that paper stated that “

C C

a given compound might result from multiple resonance
structures, which implies a partial delocalization of electrons. When these are
distributed over all the atoms, the electron-count requirements for each structure
are fulfilled.” What we did not recognize at that time was that, in fact, the space
group of each of the resonance str u ctures discussed was a subgroup of the parent
anti-fluorite-type space group, F

...

m 3 m . In this chapter, we now extend this concept
of substructures by exploring crystallographic group/subgroup relationships.

2 Group/Subgroup Relationships: The Barnighausen Tree

The compound Li 7 VN 4 is tri-morphic, and Niewa et al. [ 6 ] have described in some
detail the high-temperature preparation of the alpha (tetragonal), beta (cubic) and
gamma (cubic) polymorphs from the starting materials Li 3 N and VN. Juza and
co-workers [ 7 , 8 ] had reported both the cubic -phases as early as 1959;

these were subsequently explored in more detail by a number of crystallographers
(see below). The

b - and g

8, and
its crystal structure has been explored recently in terms of the EZKC [ 1 ] . The
compounds Li 6 [LiNb]N 4 [ 9 ] and Li 6 [LiTa]N 4 [ 10 ] are both isostructural with
b

b -phase crystallizes in the space group P a 3, with Z ¼

-Li 7 V V N 4 phase is also cubic ( 8, and the

isostructural compounds Li 7 Mn V N 4 [ 7 ] and Li 7 P V N 4 [ 11 ] have been reported. The
tetragonal

-Li 6 [LiV]N 4 . The g P 43 n )with Z ¼

a

4 2 / nmc , Z

¼

2) was first identified by Niewa et al. [ 6 ] .
These same workers have studied the thermal behaviour and phase transitions
between the three phases of Li 7 VN 4 , which seem to be related by reconstructive
phase transitions because the observed transitions occurred only very slowly,
although the differences in lattice energy must be quite small. They also point out
that the three space groups involved are not related directly through a “B

-phase ( P

arnighausen
Tree” [ 6 , 12 ] - a defining property for reconstructive phase transitions. However,
all three compounds have s pa ce groups which are subgroups of the parent anti-
fluorite-type space group

€

m 3 m .
Perhaps, the most fascinating aspect of these and many other observations is
that so many structures derive from the parent fluorite-type or anti-fluorite-type
structures. Niewa et al. [ 6 ] have already published three pathways (“B

F

arnighausen
Trees”) by which the three polymorphs of Li 7 V V N 4 are derived from the parent
anti-fluorite-type structure of Li 2 O. Now, thanks to the recent publication of
International Tables for Crystallography, Vol. A1 [ 13 ], it has become relatively

€