Crystal Structures of Inorganic Oxoacid Salts Perceived as Cation Arrays: A Periodic-Graph Approach - Inorganic 3D Structures - page 36

2.2 The Concepts of Structure Representation, Underlying Net,
and Packing Net

While the set of the net nodes is usually predetermined by the chemical composition
of the crystal (we do not consider here disordered, incommensurate structures or
quasicrystals), the net topology can be established in different ways. The problem
of determination of chemical bonding is one of the crucial points of crystallochem-
ical analysis. Depending on strength and type of bonding, different sets of bonds
can be assigned to the same crystal structure that will have different topologies on
the same set of nodes. Moreover, some atoms can be excluded from the analysis if
they do not form part of the structure under consideration.

2.2.1 The Concept of Structure Representation

One can introduce the concept of (crystal) structure representation as a subset of
atoms of the crystal structure as well as some topology specified on the subset, i.e.,
any structure representation is a net. Although an infinite number of representations
can be ascribed to the same crystal structure, the number of those with crystal-
lochemical sense is always finite and small. For example, one can consider the
following representations for the crystal structure of an M y (XO 4 ) z n H 2 O oxoacid

salt hydrate: (1) the whole structure including H-bonded water molecules, (2)
valence-bonded M y (XO 4 ) z framework or packing of oxygens with interstitial
cations; water molecules as well as H-bonds are ignored, (3) M y X z cation array
with direct contacts between first-neighbor cations. Note that in this last case,
oxygens and their bonds are excluded. The question about which of the several
representations is “the best” is meaningless because the goodness depends on the
goals of the investigation.
All chemically reasonable structure representations can be derived from the so-
called complete representation where all atoms and interatomic interactions, even
the weakest ones, are taken into account [ 22 ] . Any other representation can be
obtained from the complete one by some simplification procedure .A primary
simplified net can be derived from the complete one by applying the following
procedures: (1) removing the edges corresponding to the bonds to be ignored; (2)
removing some nodes (atoms) together with their edges (bonds); and (3) contracting
some multiatomic groups to their centroids or central atoms but maintaining the
structure connectivity. In case (3), all atoms of a multiatomic group are fused in the
center of the group giving their bonds to the center; we call this procedure
contraction . For instance, the crystal structure of Lu(ClO 4 ) 3 (Fig. 2a , see
Sect. 3.3.4 ) can be considered as a net of the Lu atoms and perchlorate anions
that are represented by only the Cl atoms after contracting oxygens (Fig. 2b ) . Thus,
the nodes of the primary simplified net (Lu and Cl) correspond to structural groups
of a given chemical compound (the Lu 3 þ cations and ClO 4 - anions), while the
nodes of the complete representation always correspond to atoms . Usually the