Geology Reference
In-Depth Information
discrete molecules like CO 2 . Instead ionic compounds
exist as solids or liquids ( condensed phases ), which
optimize their stability by packing oppositely charged
ions closely together in extended structures, or as ionic
solutions in which they are stabilized by being sur-
rounded by polar solvent molecules (Box  4.1). Ionic
compounds do not exist as gases.
ions should approximate to an equilibrium bond
length r o for the compound concerned (Box 7.1.), so
maximizing the attractive forces holding the struc-
ture together. Stretching a bond makes it less stable.
(c) Each cation should be surrounded by as many
anions as their relative sizes will allow. This achieves
the maximum degree of cation-anion attraction.
For the same reason, each anion needs to be closely
surrounded by as many cations as possible. The
number of oppositely charged nearest neighbours
surrounding an ion (in three dimensions) is called
its co-ordination number , an important parameter in
crystal chemistry.
Ionic crystals: stacking of spheres
in three dimensions
One can think of most ions as being spherically sym-
metric. The internal architecture of crystals like NaCl
can be understood in terms of stacking spheres of dif-
ferent sizes and different charges into regular three-
dimensional arrays. The potential-energy equation for
such an array will be the grand sum of (i) negative
terms representing the attractive force acting between
all pairs of oppositely charged ions in the structure,
and (ii) positive terms representing repulsion between
all pairs of similarly charged ions. There are three gen-
eral rules to observe for achieving maximum stabiliz-
ation (i.e. minimum potential energy):
These rules indicate that the atomic arrangement
found in a crystal of halite or fluorite is determined
primarily by the charge and the size of the constituent
ions. The charge can be predicted from the ion's
valency, but how can its 'size' be established?
Ionic radius
Because ions have fuzzy outlines (Figures 5.3, 5.4 and
7.1), we face a problem in defining precisely what we
mean by the 'radius' of an ion.
Nevertheless, when two oppositely charged ions
come into contact they establish a well-defined equilib-
rium bond length (Box  7.1.). The bond length can be
regarded as the sum of two hypothetical 'ionic radii',
one for each individual ion, as shown in Figure 7.1. It
will be clear that the 'radius' of an ion in a crystal rep-
resents not the actual size of the isolated ion (whatever
(a) Ions must obviously combine in proportions lead-
ing to an electrically neutral crystal. A halite crystal
contains equal numbers of Na + and Cl - ions, whereas
in fluorite (calcium fluoride) there must be twice as
many F - ions as Ca 2+ ions for the charges to cancel.
(b) The spacing (more precisely, the internuclear dis-
tance) between neighbouring oppositely charged
(a)
(b)
r Na-Cl
r Na +
r Cl -
Figure 7.1 Inter-nuclear distance r Na-Cl and ionic radii r Na + and r Cl for the ion pair Na + Cl - . (a) Electron density distributions of
the two ions. (b) Corresponding hard-sphere approximation.
 
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