Crystal Structures of Inorganic Oxoacid Salts Perceived as Cation Arrays: A Periodic-Graph Approach - Inorganic 3D Structures - page 32

Many other examples of such similarities are collected in [ 7 ] and a brief consider-
ation of inorganic oxysalts as cation arrays can be found in [ 8 ] .
O'Keeffe and Hyde [ 3 , 4 ] illustrated the eutaxy by many examples and consid-
ered this phenomenon as a result of mutual repulsion of cations. Further attempts to
interpret these experimental facts were undertaken by Vegas et al. [ 6 , 7 , 9 - 12 ] , by
extending the Zintl-Klemm concept to the cation arrays in oxides. It should be
recalled that the original Zintl concept [ 13 ] was conceived to explain the crystal
structures of compounds formed between highly electropositive atoms (A) and
main-group atoms (X). The resulting structure consists of an X-skeleton in which
the X atoms are bonded by directed covalent bonds, whose connectivity obey the
8- N rule (where N is the number of valence electrons of X). In this type of
compounds (the so-called Zintl-phases), it is assumed that all valence electrons of
the A atoms are formally transferred to the X atoms, forming so a negatively
charged X-skeletons known as Zintl polyanions. Because the X-skeletons adopt
the structure of the element, whose number of electrons is equal to N plus the
electrons transferred from A, Klemm [ 14 ] named the X atoms as pseudo-atoms.
Vegas [ 7 ] extended the Zintl-Klemm concept to oxides with complex oxoanions
[XO n ] and rationalized the structures of many ionic compounds.
The cation array model was then developed in [ 15 - 17 ] by applying the concept
of an infinite graph (net), which allows one to formally describe the cation arrays
and to analyze their geometrical-topological properties with strict computer algo-
rithms. Using the program package TOPOS [ 18 ] , we studied topological motifs in
all known crystal structures of inorganic salts of formulae M y [LO 3 ] z or M y [XO 4 ] z .
In them, the [LO 3 ] groups have either trigonal or trigonal-pyramidal geometry, and
the [XO 4 ] oxoanions are tetrahedral. The study revealed that more than 50% of the
structures followed the motifs of binary compounds A y X z . The eutaxy of those
arrays was evaluated by numerical criteria of uniformity, based on the Voronoi
partition of the crystal space.
Our aim, in this chapter, is to extend the analysis of the cation arrays, using novel
methods of crystal structure taxonomy. These methods are based on the concept of
underlying net derived from the periodic-graph approach and have been initially
developed to explore metal-organic frameworks [ 19 ] . We will show the general
applicability of these new tools that can be easily adjusted to describe the crystal
structures of any composition and bonding type.
2 Periodic-Graph Approach in Crystal Chemistry
2.1 Terminology
The term “topology” is often used in chemistry rather ambiguously [ 20 ]. Although
in most cases the crystal chemists admit that topology describes the properties
of connectivity of the crystal space, even the assertion that “the structures are