Crystallographic Notation and Stereograms
Surfaces and thin films course
Prepared as a project by Monika Fleischer with John Venables,
CPES, University of Sussex, Brighton, UK.
Planes and directions of a crystal can be represented on a Stereogram,
Measurement of angles can be performed with a Wulff net.
If the stereogram
and the net are reproduced at exactly the same size, angles between directions or plane normals
can be read off graphically. Most of this work would now be done using algebra, as given below, or
using computer programs or databases, some of which are listed referenced at the end of this page.
Great and small circles on the sphere project into circles on the stereogram.
Angular relationships are preserved and can be measured along great circles using
the Wulff net.
Properties of Stereograms
Stereographic projection of surface planes
In many cases, one needs to be able to read stereograms to plot and interpret
data, such as surface energies as a function of crystallographic plane orientation. For
surfaces and thin films, the structure and reconstructions of particular surface planes can
be important. There are several web-based sources which are useful, which we are
currently searching. To get an idea of the power of these tools, try
Some of the oldest books are the best on this topic, so try
A. Kelly and G.W. Groves (1970) Crystallography and crystal defects (Longman), chapters 1-3.
Latest version of this document 12th November 2009, ex 20th Jan 2006.