Dissemination of IT for the Promotion of Materials Science (DoITPoMS)

DoITPoMS Teaching & Learning Packages The Stereographic Projection Use of the Wulff net in constructing a stereogram

# Use of the Wulff net in constructing a stereogram

There are a few important things to note about a stereogram. Any planes, whose poles lie upon a great circle, share a zone with any other plane whose pole is on that great circle. For example, in the cubic system, (100), (010), (100) and (010) all lie on the primitive circle. The primitive circle is a special case of a great circle. Therefore, if you are trying to plot the pole of a plane on a stereogram and you know which zone it lies in, the use of a Wulff net will enable you to draw it relatively straightforwardly

When drawing stereographic projections, brackets are not used when defining poles representing the normals to planes. Hence, the normals to the planes (100), (010), (100 ) and (010), etc. are written as 100, 010, 100 and 010 .

For cubic crystals, the normal to (hkl) planes is parallel to the vector [hkl], so that the pole representing the normal to the (hkl) set of planes is also the pole representing the vector [hkl]. While this is also true for particular directions of the plane normal to the (hkl) set of planes and vectors [hkl] for crystals of lower symmetry, such as the normal to the (010) planes of an orthorhombic crystal being parallel to [010], it is not generally true.

The following animation goes through the basics of using a Wulff net for cubic crystals where the centre of the stereogram is 001.