Geology Reference
In-Depth Information
Table 7.1
Co-ordination polyhedra
Range of radius ratio r
cation
/r
anion
Co-ordination number N
c
Co-ordination polyhedron
0.225 to 0.414
4
(
)
(
)
*
*
1
2
1
2
15 121
.
−
−
tetrahedron
0.414 to 0.732
6
(
)
(
)
1
2
1
2
−
−
2131
Octahedron
0.732 to 1.000
8
(
)
(
)
1
2
1
2
−
−
3141
Cube
>1.000
>12
Various
1
2
* The upper limit appropriate to co-ordination number
N
c
is given by
N
c
2
− .
1
maintaining the optimum bond length (Figure 7.1)
with all six anions. This will not be so if the central
sphere is smaller than 0.414
R
: it will 'rattle in the hole',
and the distance to some of the surrounding ions must
exceed the optimum bond length, violating the energy-
minimizing rule above. This electrostatically unstable
situation collapses into a new configuration in which
the cation is able to maintain the optimum bond length
with fewer surrounding anions. In practice this means
that a cation in this size range will occupy a
tetrahedral
site in preference to an octahedral one. A radius ratio of
less than 0.414 therefore implies
tetrahedral
(=four-fold)
co-ordination
of the cation (Table 7.1). For this reason
we find silicon (Si
4+
), with a radius ratio to oxide anion
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