Page 133 - Geotechnical Engineering Soil and Foundation Principles and Practice

Soil Minerals
128 Geotechnical Engineering

6.3.4 Atomic Size and Coordination
The largest ions have a net negative charge because orbital electrons repel one
another. This also means that if an electron is lost, the size of an ion changes. The
2þ
diameter of a ferrous iron ion, Fe , is larger than that of its more positive alter
3þ
ego, ferric iron or Fe . Ion size also depends on the number of electron shells,
which increases downward in the periodic table.
4þ
A basic building block in many minerals is one silicon ion, Si , surrounded by
2
four oxygen ions, each having two negative charges as O . The oygen diameter is
˚
˚
2.6 A, and that of a silicon ion is 0.82 A, so one Si 4þ fits into holes between four
oxygens. The shape of this building block is that of a tetrahedron, and silica is said
to have a ‘‘tetrahedral coordination’’ with oxygen. Tetrahedral coordination is
shown at the top in Fig. 6.4.
In quartz, which is SiO 2 , each oxygen is shared by two tetrahedrons. This linkage
creates a continuous three-dimensional structure, which is the reason why quartz
is hard and has no natural cleavage direction: quartz crystals have flat faces
because they grow that way. Ionic substitutions can change and weaken the three-
dimensional structure, for example in feldspars, which are easier to weather than
quartz and have cleavage.

Because of its abundance in rocks and minerals and its large diameter compared
with positive ions, most of the Earth is composed of oxygen ions.

6.3.5 Other Coordinations

The outer ions in tetrahedral coordination can touch but not overlap, and if
separated far enough will allow room for more oxygen ions. These principles are
known as ‘‘Pauling’s rules,’’ and enabled him to work out the crystal structure
3þ
of mica. If aluminum, Al , substitutes for silicon, the diameter of an aluminum
˚
˚
ion is 1.0 A instead of 0.8 A for silicon, which spreads the structure sufficiently
to allow 6 oxygen ions instead of 4. The coordination number is 6, with oxygen
ions arranged as corners of an octahedron to give octahedral coordination, shown
at the middle in Fig. 6.4.

Pauling’s rules govern stable coordinations and establish that it is not
chemical composition but ionic sizes that control a crystal structure.
This means that certain ions having about the same diameter can substitute
others having approximately the same diameter without changing the crystal
structure or the mineral name. For example, some Mg 2þ can substitute for
Al 3þ without disrupting the crystal structure. Small changes in size are com-
pensated by ‘‘puckering’’ of the tetrahedral layer, as shown near the middle of
Fig. 6.4.

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