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We have already seen simple crystal structures
- rocksalt, rutile and many metals - can be understood in terms of packing.
The atoms attract each other and pack together in the most efficient manner.
The crystal structures are controlled by the relative atomic sizes, which
limit the ways in which the atoms can be packed around each other. If all
atoms have the same size, then geometrical considerations show that each
atom can have twelve surrounding atoms as in the structure of metals; but
in rocksalt (sodium chloride) the greater size of the chloride ion
means that only six of these can pack round a sodium ion. Indeed, packing
considerations
like this can be used effectively to guide and rationalise many of the
structures adopted by crystals in which the atoms are bound by metallic
or electrostatic (ionic) forces.
More complex and less dense structures
are commonly adopted by crystals where the bonding has specific directional
requirements which is generally the case
with covalent bonding - that is bonding based on concentration of the electrons
between the nuclei. For these systems, an alternative approach is often
needed to understand and describe their structures: instead of packing
of spheres, we consider linking of polyhedra; that is, we describe
the crystal structure in terms of well defined simple geometrical constructs,
e.g. tetrahedra and octahedra with
atomic positions normally being associated with their corners and centres;
these are then linked together via their corners, edges or faces
to give the three dimensional crystal structure.
Tetrahedra and octahedra.
ReO3 possesses one of the simplest
but most elegant examples of this class of crystal architecture. It displays
the structure of the oxide of the rare metal rhenium, which is based on
octahedra in which six oxygen atoms surround a central rhenium atom; the
octahedra are then linked together via all their corners to give
a regular, symmetrical structure.
ReO3.
The open nature of the structure is apparent:
big voids are present between the octahedrally linked lattice structure
into which, as we will describe later, large atoms can be inserted. Indeed,
as we will learn, an important type of structure is based on the principle
of accommodating atoms in the voids of corner sharing octahedral networks.
The formation of MO6 octahedral (where M is a metal atom) dominates the
structural chemistry of the oxides of metals such as titanium, vanadium,
niobium, tantalum, molybdenum, tungsten and rhenium, which are grouped
together in the same region of the periodic table on the left.
MO6 elements.
MO6 octahedral containing these metals may share edges as well as
corners, as in the structure of TiO2 shown on
the left. Face sharing
is possible, but occurs to only a limited extent owing to the strong repulsions
between the positive charges of the closely spaced metal atoms in neighbouring
octahedra. Examples are largely limited to small clusters like that
on the left.
There is indeed a fascinating and
diverse structural chemistry based on small aggregates of
MO6 octahedra,
some of which are shown in this image.
Polyanion clusters based on octahedrally coordinated metal atoms.
Crystal structures fully exploit the architectural
possibilities of octahedral building blocks. The metal niobium forms oxide
structures containing blocks of corner shared
NbO6 octahedra, which in
turn are linked together by edges or faces as shown.
Nb2O5.
Moreover,
changes in chemical composition can cause restructuring of the octahedral
networks. Thus as the oxide material TiO2
loses oxygen (to form a "non-stoichiometric"
compound TiO2-x) sheets appear in
the structure in which face has replaced edge sharing.
Ti5O9.
The linking of tetrahedra leads
to an even bigger range of structures, although the structural principles
are in some ways more limited. Tetrahedra normally share only corners,
as the repulsion between the central atoms are too high in edge and face
shared structures; The image on the left shows examples of the very limited range
of structures which contain these latter energetically expensive modes
of linkage.
Corner sharing linkage of MO4 tetrahedra
is, however, the basis of the structural chemistry of the oxides of the
common and important elements aluminium, silicon and phosphorus. Thus
silicon dioxide forms a bewildering range of structures all of which are
based on SiO4 tetrahedral networks
in which all corners are shared. The most important is quartz,
a natural mineral and an important industrial material. Other structures
e.g. cristobalite and tridymite are adopted
by SiO2; and there exists an
enormous range of much more open networks
e.g. the clathrasils, examples of which are illustrated on the
left.
These may accommodate large organic molecules (and indeed their
synthesis in most cases requires the presence of such species). Further
discussion of these and related 'microporous' structures will follow later.
It seems, however, that despite the limitations imposed by the almost universal
adoption of corner sharing in tetrahedrally based structures, the tetrahedron
allows an even greater diversity of structural types than does the octahedron.
Tetrahedra sharing faces to form a helix.
SiO2 polymorphs
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