This section finishes with a consideration of the packing density of these structures. It is often necessary to state the direction in a crystal. A method is described which shows how to calculate the Miller index for a direction in a 2-D lattice. It is important to be able to identify the unit vectors in the lattice of the crystal, since the Miller index expresses direction in terms of ratios of these vectors. This method is easily extended to three dimensions.
Exercises allow the user to see if they have understood the method shown.
This section then looks at how to index planes in crystals and their lattices. Again an exercise page follows to check that this method has been understood. Finally the user is introduced to the four index Miller Bravais system for indexing planes and directions in hexagonal systems.