Page 26 - Modern physical chemistry

1.11 Stability Conditions 15

in table 1.3 apply. By the way, because like charges repel, oppositely charged ones attract,
cations are much smaller than, while anions are much larger than, the corresponding iso-
electronic atoms.
When the radius of the smaller ion divided by the radius of the larger ion is between
0.9021 and 0.7321, each small ion can hold eight of the larger ones around itself without
squeezing them against each other and the cesium chloride lattice tends to fonn. When
the radius ratio is between 0.7321 and 0.4142, each small ion can hold six large ions
around itself without squeezing them against each other and the sodium chloride lattice
tends to fonn. When the radius ratio is between 0.4142 and 0.2247, each small ion can
only bond four large ions without squeezing them against each other and either the zinc
blende or the wurtzite lattice tends to form. The linear arrangement is observed in the
hydrogen bond.

Example 1.5
At what radius ratio do the anions begin to touch each other in the cesium chloride
structure?
Consider an electrolyte AB in which the ions are spherical, with

r + = radius of A + ,
A
r B - = radius ofB-.
Let rA- be large enough so that eight B- ions can be packed around it without touching
each other. Keep the oppositely charged ions in contact and decrease the radius of the
cation until the anions meet each other along each edge of the unit cube. If a is the length
of an edge of the cube, then

But each diagonal through the cube passes through one half of a B -, the A+, and one half
of another B-; consequently,

Now, eliminate a from these two equations,

-J3(2rB- )=2r A + +2r B -,

TABLE 1.3 Radius Ratios at which an Anion Touches Neighboring
Anions as well as Neighboring Cations

Number oJ Cation Radius
Lattice Anions around Arrangement Anion Radius
Structure One Cation about Cation when Anions Touch

Quasicrystal 12 Icosahedral 0.9021
Cesium chloride 8 Cubic 0.7321
Sodium chloride 6 Octahedral 0.4142
Zinc blende or 4 Tetrahedral 0.2247
wurtzite
- 3 Triangular 0.1547
- 2 Linear 0.0000