Miller indices are a standard mathematical notation describing planes in crystals, derived from where the plane intercepts each coordinate axis. In a specific material with a known lattice constant and crystal structure, this allows the calculation of angles and distances between planes and directions of interest.
Miller indices form a notation system in crystallography for lattice planes in crystal (Bravais) lattices. is marked by Miller indices. By convention, negative integers are written with a bar, as in 3 for −3. The integers are usually written in lowest terms, i.e. their greatest common divisor should be 1.
Position in a unit cell: coordinates measured along axes in units of corresponding cell dimensions. Each coordinate is thus 0 or a proper fraction, except that
Strukturbericht Notation System
The Strukturbericht system was developed in the early 1900s and is probably the most common naming system in older scientific articles Using Bravais Lattices to Identify Crystals
The best “casual” way of identifying crystals is by Bravais lattice Using Space Groups to Identify Crystals
Just like there are 14 ways to arrange 3D stuff by translation (Bravais lattices), there are 32 ways to arrange 3D stuff by reflection, rotation Summary Table
Putting everything together, here is a summary table for each common crystal structure, showing the Bravais lattice, prototype Final Thoughts
Unfortunately, there is no “best” way to name crystal structures. Each naming system is an attempt to abbreviate by removing information References and Further Reading
AFLOW libraryis a great resource for crystals. If you want to see the other crystallography-related articles I’ve written, here is this list 