Crystal Structures of Inorganic Oxoacid Salts Perceived as Cation Arrays: A Periodic-Graph Approach - Inorganic 3D Structures - page 38

(isolated), 1-coordinated (terminal), or 2-coordinated (bridge) nodes; the procedure
removes isolated and terminal nodes and contracted bridge nodes converting them
into edges as shown in Fig. 2c .

2.2.2 The Concept of Underlying Net

After the simplification, we obtain an underlying net of the crystal structure [ 31 ] ,
i.e., the net that describes the method of connection of the structural groups. If all
crystal structures under consideration were simplified in the same way, their
underlying nets can be used to find resemblances in their topological organization
irrespective of chemical composition, geometrical and topological features of the
structural groups.

2.2.3 The Concept of Packing Net

The underlying net is derived from the complete representation; so it is always
based on the topology of the crystal structure as a whole. This means that edges in
this net corresponds to chains of the bonds involving contracted atoms; for instance,
the bonds Lu-Lu in Fig. 2b conform to the chains Lu-O-Cl-O-Lu. However, it
could be insufficient if the eutaxy of the cation array should be studied since some
first-neighbor cations in the array could not be linked by such chains. To resolve
this problem, we can consider a packing net (cf. [ 32 ] ), where the edges between the
cations are assigned by geometrical, not topological reasons. The assignment
criteria could be some range of interatomic distances, or, more precisely, the
shape of the Voronoi polyhedra of the cations [ 32 ] . In particular, in the Lu cation
array of Lu(ClO 4 ) 3 , there are six additional long (8.11 ˚ ) Lu-Lu contacts (the
Voronoi polyhedron of any Lu atom has 6 12 faces), and the corresponding

packing net is f.c.c. (fcu) that allows one to treat the array as a distorted cubic close
packing (Fig. 2d ).
Thus, cation array can be considered as an underlying or packing net; in most
cases these nets coincide with each other and, more rarely, the underlying net is a
subnet of the packing net. The opposite case (the packing net is a subnet of the
underlying net) can occur only in structures with prolonged, not spherical poly-
atomic ions [ 16 ] . Studying both kinds of net gives the comprehensive and objective
information about the topology of the cation array.
The approach described above has an important advantage over the traditional
visual analysis: it can be made into an algorithm and implemented in a computer
program that makes the crystallochemical analysis universal, objective, and fast.
With such a program one does not need even to look at the crystal structure; the
conclusions about the structure topology, its taxonomy, and comparison with other
compounds can be made in an automatic mode.

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