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 AX4 coordination groups,  octahedra the AX6 groups, cubes
the AX8 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



.414 - .732



.732 - 1.0






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 inter-atomic 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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Page  40 -  Structure matters - Atomic coordination

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