Polymorf - Knowhwere- Atomic coordination

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	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 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