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Stereographic Projection

Stereographic Projection. equator plane. Stereographic Projection I. 1. Place the crystal in the center of a sphere. The c axis is vertical, the b axis points to the East. Up (N). 2. Draw the normal to each face. Displace the normal, until it intersects the center C of the sphere.

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Stereographic Projection

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  1. Stereographic Projection

  2. equator plane Stereographic Projection I 1. Place the crystal in the center of a sphere. The c axis is vertical, the b axis points to the East. Up (N) 2. Draw the normal to each face. Displace the normal, until it intersects the center C of the sphere 3. Mark the intersection D of the normal N with the sphere. D 4. Connect the intersection point D with the south pole S of the sphere. W E P C 5. The intersection P of the connecting line DS with the equatorial plane (eqp) of the sphere represents the stereographic projection of the face. Down (S) http://www.iucr.org/iucr-top/comm/cteach/pamphlets/11/index.html

  3. equator plane equator plane Stereographic Projection II Up (N) Up (N) W W E E O O Down (S) Down (S) The intersection line of the expanded face with the sphere is than projected into the equatorial plane by connecting each point of the intersection with the south pole. The intersection of these connecting line with the equatorial plane represents the projected face. Instead of the normal to a face, the face itself can be projected onto the equatorial plane. The face is first expanded in order that it intersects the projection sphere. The expanded face is than moved until it goes through the center of the sphere.

  4.  Spherical coordinates Position of a point on a sphere co-latitude 90°- latitude N (0°) longitude The normal of a face are indicated by the spherical coordinates and  of its normal. E (0°) S

  5. Stereographic net I Stereographic or Wulff net = - 90° or 270°  = 90° N small circles great circles primitive circle  = 0° = 180°  = 90° = 0°  = 90° G W E In order to plot the stereographic projection of a plane, the longitudes and latitudes have to be projected onto the equatorial plane. The longitudes become great circles, the latitudessmall circles. S = 90°  = 90°

  6. Stereographic net II Using the Wulff net = 60°  = 40° Example: 1. 2. E E  = 60° Draw the primitive circle (equator) on the tracing paper and mark the East direction Put a mark at 60° on the primitive circle

  7. Stereographic net III Using the Wulff net (cont.) E 4. 3.  = 40° E  = 60°  = 40°  = 60° Rotate the tracing paper counter-clockwise by 60° around the net center and mark the 40° position along the W-E line by a dot. Rotate the tracing paper back clockwise by 60°. The dot represents the stereo- graphic projection of the point with spherical coordinates  = 40°and = 60°

  8. Stereographic projection of an forsterite crystal I Stereographic projection of an orthorhombic crystal: Forsterite c face (hkl)  a (100) 90.0° 90.0° b (010) 90.0° 0.0° c (001) 0.0° 0.0° m (210) 90.0° 22.8° d (101) 51.5° 90.0° k (031) 63.3° 0.0° e (212) 72.8° 22.8° k d e e m m b a 1. Fix the axes on the Wulff net according to standard settings. For orthorhombic crystals, the c-axis is perpendicular to the primitive circle, the a-axis parallel to N-S pointing to the south, and the b-axis parallel to W-E pointing to east. 2. Mark all face poles using the angles and . e e d

  9. (001) c (031) (010) b (212) (210) (101) (100) a Stereographic projection of an forsterite crystal II Stereographic projection of the forsterite crystal:

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