On completion of this tutorial you should:
Understand the concept of a lattice plane;Be able to determine the Miller indices of a plane from its intercepts with the edges of the unit cell;Be able to visualise and draw a plane when given its Miller indices;Be aware of how knowledge of lattice planes and their Miller indices can help to understand other concepts in materials science.Before you start
You should understand the concepts of a
, Unit cell
, Crystal axes
, Crystal system
and the variations, Primitive
which make up the Bravais lattice
You might also like to look at the TLP on Atomic Scale Structure of Materials.
You should understand the concepts of vectors and planes in mathematics.
Miller Indices are a method of describing the orientation of a plane
or set of planes within a lattice in relation to the unit cell. They
were developed by William Hallowes Miller.
These indices are useful in understanding many phenomena in materials
science, such as explaining the shapes of single crystals, the form of
some materials' microstructure, the interpretation of X-ray diffraction
patterns, and the movement of a dislocation
, which may determine the mechanical properties of the material.
How to index a lattice plane
The next three animations take you through the basics of how to index
a plane. Click "Start" to begin each animation, and then navigate
through the pages using the buttons at the bottom right.