Wulff's network

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Wulff network with 10 ° distance between the circles

The Wulff network is an aid in creating a stereographic projection . It is named after the Russian crystallographer George V. Wulff (1863–1925).

properties

Generation of a Wulff network (arcs within the red circle) with a stereographic projection of a sphere from an equator point C onto the plane

The Wulff network is a stereographic projection of the great and small circles of a sphere from an equator point onto a plane through the north and south poles. The north pole is not in the center here, but at the top of the peripheral circle. Because in a stereographic projection circles on the sphere are reproduced as circles in the projection plane, all lines of the Wulff network represent circles. Usually an interval of 2 ° is chosen between the circles.

application

In crystallography , the Wulff network is used to describe the crystal morphology . For this purpose, a crystal with well-developed crystal faces is brought into the center of a large sphere and the lattice vectors [ uvw ] are mapped onto the surface of the sphere. The lattice vectors are the normals of the crystal faces. The points at which the surface normals meet the surface of the sphere are called surface poles. Usually the [001] -direction ( z -axis) of the crystal is placed on the north pole.

A stereographic projection with the help of the conformal Wulff network enables a distortion-free representation of the crystal in accordance with the law of constant angles for crystal surfaces.

literature

Web links