36 STRUCTURE AND BONDING
This then is the limiting radius ratio for six nearest neighbours—
when the anion is said to have a co-ordination number of 6. Similar
calculations give the following limiting values:
- For eight nearest neighbours (a co-ordination number of 8)
the radius ratio r"*"/r" must not be less than 0.73.
- For six nearest neighbours (a co-ordination number of 6) the
radius ratio r+/r~ must not be less than 0.41.
- For four nearest neighbours (a co-ordination number of 4) the
radius ratio r+/r~ must not be less than 0.225.
These values enable many structures to be correctly predicted;
discrepancies arising mainly from the false assumption that ions
behave entirely as rigid spheres. Some examples are given in Table 2.7.
Table 2.7
RADIUS RATIOS IN TYPICAL CRYSTAL STRUCTURES
0.73 > ryr > 0.41 r+/r~ > 0.73
Rock salt Rutile Caesium chloride Fluorite
Compound r+/r Compound r+/r Compound r+/r Compound r+/r
NaCl 0.52 TiO 2 0.49 CsCl 0.93 CaF 2 0.73
KBr 0.68 PbO 2 0.60 CsBr 0.87 SrF 2 0.83
MgO 0.46 MnF 2 0.59 Csl 0.78 CeO 2 0.72
Examples of two crystal structures* for each co-ordination number
are included in the table.
BONDING BY ELECTRON SHARING—COVALENCY
There are many compounds which do not conduct electricity when
solid or fused indicating that the bonding is neither metallic nor
ionic. Lewis, in 1916, suggested that in such cases bonding resulted
from a sharing of electrons. In the formation of methane CH 4 for
example, carbon, electronic configuration Is^2 2s^2 2p^2 , uses the four
electrons in the second quantum level to form four equivalent
- Fluorite. CaF 2. and rutile. TiO 2. are minerals; in CaF 2. each Ca2+ is surrounded
by eight F ions, each F by four Ca~* ions, while in TiO, the corresponding
co-ordination numbers are 6 and 3. 'Co-ordination number' is generally referred to
the cation.
