Geology Reference
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(a)
(c)
(b)
(d)
Cation
Anion
Figure 7.3
Structures of simple binary compounds. Ions are depicted at one-tenth of the appropriate size to allow the
three-dimensional disposition to be seen. (a) Sodium chloride structure. (b) Caesium chloride (CsCl) structure. (c) Rutile
structure. (d) Fluorite structure.
(O
2-
) of 34/132 = 0.25, in tetrahedral co-ordination in
all silicate minerals (which are compounds of various
metals with silicon and oxygen).
A radius ratio larger than 0.414 does not prevent
the cation maintaining the optimum bond length with
six equidistant anions. The larger cation prevents the
anions remaining in contact with each other (they
cease to be strictly close-packed), but in view of their
mutual repulsion this will not reduce the stability of
the structure. Octahedral co-ordination is therefore
consistent with radius ratios above 0.414 (Table 7.1).
Na
+
is octahedrally co-ordinated in NaCl (radius ratio
110/172 = 0.64). Neutrality dictates that Na
+
and
Cl
-
ions must be equal in number (this is called an
'AB-compound'). It follows that each chloride ion must
also be octahedrally co-ordinated by Na
+
ions
(Figure 7.3a). This
sodium chloride structure
is shared by
the mineral galena (PbS).
In the mineral rutile (one of the
polymorphs
of TiO
2
),
the Ti
4+
: O
2-
radius ratio is 69/132 = 0.52, and accord-
ingly the Ti
4+
ion is octahedrally co-ordinated by O
2-
ions (Figure 7.3c). Because there are twice as many
O
2-
ions (the valency difference makes this an 'AB
2
'-
type compound), each O
2-
ion is found in three-fold co-
ordination, occupying the centre of a triangular
grouping of Ti
4+
ions.
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