Wulff net crystallography

  • How do you use a Wulff net?

    A zone on a Wulff net is represented by a great circle.
    All positions on this great circle represent the poles of planes lying within that zone.
    Therefore, to plot poles of planes within a zone, we need to rotate the Wulff net until a great circle lines up between the required poles..

  • What is a Wulff net diagram?

    Wulff net, or stereographic net, is a stereographic projection of the longitude and latitude curves on a sphere, which can be drawn as two series of circles with their centers and radii as shown in Fig..

  • What is the difference between the Wulff net and the Schmidt net?

    The Schmidt net is often used to sketch out the Lambert azimuthal projection for these purposes.
    Conversely, the Wulff net ("equal-angle projection") is used to plot crystallographic axes and faces..

  • What is the formula for the Wulff net?

    The formula is simple and follows directly from the construction of the projection: AO = tan (w/2).
    For the small circles of the stereonet, a always equals 90 because the circles are centered on the pole.
    Thus, a circle of latitude l has radius 90-l.
    The distance to its center is 1/cos r= 1/sin l..

  • What is the great circle on the Wulff net?

    A zone on a Wulff net is represented by a great circle.
    All positions on this great circle represent the poles of planes lying within that zone.
    Therefore, to plot poles of planes within a zone, we need to rotate the Wulff net until a great circle lines up between the required poles..

  • What is the use of Wulff net?

    This can be used to place planes and poles of planes on a stereogram with great accuracy.
    It allows the maintenance of angular truth, while still being easy to draw..

  • What is the Wulff net stereographic projection?

    If we consider rather more of each, we can project them downwards as before using the principle of projection to construct a stereographic projection of planes which are two degrees apart.
    This creates the Wulff Net.
    This can be used to place planes and poles of planes on a stereogram with great accuracy..

  • A zone on a Wulff net is represented by a great circle.
    All positions on this great circle represent the poles of planes lying within that zone.
    Therefore, to plot poles of planes within a zone, we need to rotate the Wulff net until a great circle lines up between the required poles.
  • Stereographic projection provides a means of representing different planes and directions of a crystal in two dimensions.
    It allows measurement of angles between planes and directions.
  • The Schmidt net is often used to sketch out the Lambert azimuthal projection for these purposes.
    Conversely, the Wulff net ("equal-angle projection") is used to plot crystallographic axes and faces.
The following animation goes through the basics of using a Wulff net for cubic crystals where the centre of the stereogram is 001.
Wulff net, or stereographic net, is a stereographic projection of the longitude and latitude curves on a sphere, which can be drawn as two series of circles with their center and radius shown in Figure 3. Here r is the radius of the sphere of a stereogram. The coordinate (x, y) is on the longitude or latitude circles.

How do you manipulate a Wulff net?

The first allowed manipulation is a simple rotation about the north pole of our stereographic projection (the center of the projection)

The second allowed manipulation is a simple rotation about the north pole of the Wulff net

This involves moving poles along the lines of latitude

How is the Wulff net constructed?

Having understood how the projection is constructed, we can now look at how it is examined using the Wulff Net

The net is a projection of a collection of great and small circles, which represent lines of latitude (small circles) and lines of longitude (great circles) on the sphere, as seen here:

How to construct a stereogram using a Wulff net?

In order to construct stereograms with the help of the Wulff net it is most convenient to work on tracing paper over the net

To plot a point at a given angle from the N -pole (equivalent to construction (i)) one simply uses the scale along either of the graduated diameters of the net

Pole figure of a diamond lattice in 111 direction. A Wulff net is used to read a pole figure. The stereographic projection of a trace is an arc. The Wulff net is arcs corresponding to planes that share a common axis in the (x, y) plane.
Wulff net crystallography
Wulff net crystallography
Georg Wulff, Georgy Wulff or Yuri Viktorovich Vulf was a pioneer Russian crystallographer.

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