Wulff nets are a type of stereographic projection which is typically used for single crystal samples such as silicon wafers in the microelectronics industry. 70-85 Wulff Nets and 402-431 Pole Figures) Objective: To become familiar with Wulff net projections.īackground: (Old edition Cullity pp. Single set of planes while the Wulff's net shows many of the planes for the Then the pole figure is usually limited to a Wulff's net there will be a single pole for each crystallographic plane, whileįor the pole figure a distribution topo map for poles of different grains in a The figures) with the plane of projection is marked as a pole. The intersection of the projection line (dotted arrow in The pole figure the projection is from the south pole to the pole on the sphere Is from the opposite equatorial position form the tangent location, while for Is done differently for the two projects also, in the Wulff's net the projection Projection of the sphere pole on to the stereographic projection Where the processing direction (sample coordinates) and crystallographic frames Would be used to describe the distribution of (111) plane normals in a wire For instance a Wulff's net might be used toĪlign a single crystal for cleavage by identifying the (111) plane where theĬrystallographic and lab frames are important for cleavage, while a pole figure Intended to describe the orientation of crystallographic planes with respect to Single crystal with respect to the lab reference frame while the pole figure is This difference is that the Wulff's net is intended to guide orientation of a Machine direction (MD) and the transverse direction (TD). Projection and lies generally along the main axes of the sample, i.e. The difference between a Wulff projection and a pole figureīegins with the location of the plane of projection (dashed line in figure).įor a Wulff's net the plane is tangent to the sphere of projection at theĮquator and so is independent of the sample orientation while for the poleįigure the plane of projection passes through the equator of the sphere of The sphere at a pole, P, as shown below to the left for a pole figure (top) and Normals to the crystallographic planes intersect In most stereographic projections a sphere is considered that surrounds aĬrystal, for instance. Of crystallographic planes through their normals, and the angles between planes. For crystallography we are interested mainly in the orientation The 3d structure and angles relating structural features in a two dimensional A stereographic projection gives information pertaining to Wulff's nets and pole figures are two types of stereographic
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