STRUCTURE AND BONDING 35
and is a major factor in determining the nature of an ionic com-
pound. We shall discuss this further in Chapter 3.ARRANGEMENT OF IONS IN THE CRYSTAL LATTICE
The electrostatic attraction between ions is independent of direction.
X-ray diffraction studies show that a crystal lattice can be repre-
sented as made up of spherical ions, each ion having a characteristic
radius almost independent of the crystal lattice in which it is found.
For simple ions the charge on them determines the balance between
the numbers of anions and cations whilst the radii determine the
way in which the ions pack together in the lattice, this packing
always occurring in such a way that, if possible, ions of like charge
do not louch' each other. Figure 2.4 shows a cross-section through
an octahedral structure (the central ion having six nearest neigh-
bours) in the limiting conditions in which the cations and anions
are touching. The values of the radius ratio can be obtained by
simple trigonometry.
Figure 2.4, Limiting conditions for cation-anion contact (octahedral structure)If r+ and r are the radii of the cation and anion respectively
then by applying Pythagoras's theorem to triangle ABC we find that
CA^2 - AB^2 + BC^2i.e.
Hence
(r- + r+)^2 = (r~)^2 + (r')^2 - 2(r~)^2
r" 4- r+ = r~/J2 = 1.414 r""r+ = 0.414 r~
r+/r- = 0.414