Miller indices are a notation system used to describe the orientation of crystal planes or directions in a crystal lattice. They were developed by William Hallowes Miller in the 19th century.
Miller indices are
the labels used to distinguish one set of parallel planes from another. It is a
set of three numbers h k l that defines
a set of parallel planes in a crystal. The following
procedure is generally followed to determine the Miller indices:
- Choose an origin;
- Find out the intercept that the first such plane makes with the three crystallographic axes;
- Obtain their reciprocals;
- Eliminate fractions
Indexing
procedure: a b c
Determine
intercepts: 3 2
1
Note their
reciprocals: 1/3
1/2 1
Clear fractions: 2 3
6
The major advantage
of the Miller indices is that it permits to express interplanar distance dhkl
of a set of hkl planes in terms of lattice parameters a, b, c, α, β and γ.
For a cubic crystal:
Miller indices are useful in crystallography because they provide a way to describe the orientation of crystal planes and directions in a way that is independent of the actual size of the crystal. They are also used in materials science and engineering to describe the structure of materials and their properties.
By understanding Miller indices, scientists can predict how crystals will grow and how they will respond to external forces such as stress and temperature. This knowledge is important in fields such as metallurgy, materials science, and solid-state physics.
