
In the topological approach to modeling the structure of minerals, polyhedra
such 
. 
as
tetrahedra, octahedra, and cubes are used to represent the coordination of
the 
. 
larger, close packed atoms around the smaller atoms nestled in their
interstitial voids. 
. 
Tetrahedra represent the AX_{4} coordination groups, octahedra
the AX_{6} groups, cubes 
the
AX_{8} groups, and so on. 
The relationship of coordination number to radius ratio represents an ideal
which 
. 
presumes that the larger close packed atoms remain in contact and are not
pushed 
. 
apart by the insertion of an atom that is too large for the size of their
void space. This 
. 
is
often not the case in reality and thus radius ratios can only serve as a
rough guide 
. 
to
the microstructure of an extended atomic framework. Fortunately there
is a range 
. 
of
radius ratios within which the coordination can still be accommodated if the
atoms 
are
permitted to deviate somewhat from a close packed arrangement (diamond being 
an
exceptional case of this). Notice that it is permitted for an
interstitial atom to be 
. 


Radius ratio 
Coordination number 
Type of void 
.225
 .414 
4 
tetrahedral 
.414
 .732 
6 
octahedral 
.732
 1.0 
8 
cubic 
. 


Table 4  Range of radius ratios for different coordination
groups of atoms 




slightly larger than the void it fills but not smaller than it. That
is, in the vast majority 
of
cases the interstitial atom must remain in contact with the surrounding
close 
packed atoms and not "rattle" around loosely between them. 
This situation bodes well for the topological/polyhedral approach which is
meant 
to
model the coordinations of atoms not their absolute interatomic distances
or 
their specific radius ratios. Furthermore all general purpose atomic
modeling 
systems, all polyhedral models in general, and the Polymorf system in
particular 
depend on slight accommodations being allowed for structures that deviate
slightly 
from the ideal structure that is represented by the model. By adopting
this 
convention representative examples of the various mineral groups or
synthetic 
compounds whose structures approach the ideal can be modeled to show the
general 
type of structure characteristic of the group. It is understood that
individual members 
of
the group may deviate more or less from this ideal. 
In that spirit the models shown in this presentation are meant to be
representative 
of
general types of structures with the knowledge that deviations from the
ideal are 
more often the norm than the exception. 
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40  Structure matters  Atomic coordination 
