|
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. |
Back to
Knowhere |
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Page
40 - Structure matters - Atomic coordination |
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