Page 131 - Geotechnical Engineering Soil and Foundation Principles and Practice

Soil Minerals
126 Geotechnical Engineering

A similar solution can be made for third-order and higher reflections. Note that diffraction
angles always are expressed in terms of 2 .

6.2.6 Defining Orientations of Crystal Planes

Planes in a crystal are defined on the basis of their relationships to crystallographic
axes. These axes may or may not be orthogonal. In rock salt or diamond, which
crystallize in the cubic system, the axes are at right angles. The smallest repeating
pattern is called a unit cell, which in this case has the shape of a cube.

Question: Can you identify a unit cell in Fig. 6.1?

The orientation of a crystalline plane is described by a ‘‘Miller index,’’ which is
the number shown on the plane orientations in Fig. 6.1. The most useful
Miller index in clay mineralogy is 001. The d 001 distance is the distance
˚
between repeating layers stacked like pages in a book. For mica, d 001 ¼ 10 A,so
˚
each layer in a mica crystal is 10 A thick, or about the diameter of three oxygen
atoms.

6.3 CLAY MINERALOGY

6.3.1 Atoms and Ions
For most minerals the use of the name ‘‘atom’’ for individual components is not
strictly correct because an atom has a neutral charge, which means that the
number of protons, each with a (þ) charge, equals the number of electrons, each
with a ( ) charge. Minerals for the most part are composed of ions, which are
atoms that either have a surplus or a shortage of electrons. This occurs when
one atom gives up an electron to another kind of atom in order to fill out a shell.
For example, a sodium atom, Na, readily loses an electron from its outer shell
þ

to chlorine, Cl, which needs one to fill its outer shell. The result is Na Cl ,
sodium chloride or rock salt. The linkage between sodium and chlorine is not a
true chemical bond, but an ionic attraction that is easily put off by an intruder

þ
such as water that has a high dielectric constant, so Na Cl readily dissolves in
water.

þ
Because the crystal structure of crystalline minerals such as Na Cl (the mineral
name is halite) is continuous and ionic attractions have no particular directional
orientation, there is no way to define a discrete molecule. In true molecules the
bonds are covalent, which means that instead of electrons being transferred they
are shared. Atoms of many gases, for example, pair off to make molecules such as
O 2 ,H 2 , and N 2 .

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