Geology Reference

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(a)

(b)

Octahedron
with apices

lying at the centres of six

surrounding balls, showing

the largest sphere that can

be accommodated.

Tetrahedron
showing the

largest sphere that can be

accommodated in a tetra-

hedral site.

(c)

(d)

Figure 7.2
(a) Two layers in a close-packed array of spheres. The heavy lines show the co-ordination polyhedra of the

tetrahedral and octahedral interstitial voids between the spheres. (b) 3D model showing tetrahedral co-ordination of anions

around a small cation; the cation (ball bearing) can be seen nestling between the four anions. (c) Octahedral co-ordination

around a larger cation. (d) Octahedron with top anion layer removed to show the octahedrally co-ordinated cation within.

(Sources: Adapted from McKie & McKie 1974; K. d'Souza.)

The second type of hole in a close-packed array of

identical spheres is bounded by six neighbouring spheres,

whose centres lie at the six apexes of a regular
octahedron
1

(FigureĀ 7.2a,c,d). Such holes are called
octahedral sites
. In

terms of the size of the largest interstitial sphere that each

hole can accommodate (analogous to the glass marble in

FigureĀ 7.2d), octahedral sites are 'bigger' than tetrahedral

sites. Both are substantially larger than the cavity between

three adjacent spheres in the same layer.

In many ionic crystals the anions are assembled in a

more or less close-packed array, the cations occupying

some of the tetrahedral and/or octahedral sites

between them. The kind of site a given cation occupies

is determined by the value of the ratio
r
cation
:
r
anion
, known

as the
radius ratio
. Using three-dimensional trigonom-

etry, it is not difficult to show that, to fit exactly into an

octahedral site between six identical 'anion' spheres of

radius
R,
a 'cation' sphere must have a radius of 0.414
R
.

A cation in this position in a crystal is said to have
oct-

ahedral co-ordination
. However, the likelihood of a real ion

pair having a radius ratio of exactly 0.414 is negligible,

so we must consider the effect on the co-ordination

number if the radius ratio deviates from this value.

A radius ratio of exactly 0.414 allows the 'cation'

sphere to touch all of the surrounding spheres at once,

An octahedron (meaning 'eight sides') has six apexes (points)

but eight faces.

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