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S tereographic projection

S tereographic projection. Representation of relationship of planes and directions in 3D on a 2D plane. Useful for the orientation problems. A line (direction)  a point. (100). http://courses.eas.ualberta.ca/eas233/0809winter/EAS233Lab03notes.pdf. A plane (Great Circle)  trace.

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S tereographic projection

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  1. Stereographic projection Representation of relationship of planes and directions in 3D on a 2D plane. Useful for the orientation problems. A line (direction) a point.

  2. (100)

  3. http://courses.eas.ualberta.ca/eas233/0809winter/EAS233Lab03notes.pdfhttp://courses.eas.ualberta.ca/eas233/0809winter/EAS233Lab03notes.pdf A plane (Great Circle)  trace

  4. Pole and trace http://en.wikipedia.org/wiki/Pole_figure

  5. Great circle Equal angle with respect to N or S pole

  6. Construction of latitude (Parallels) and longitude (Meridians) of Wulff net! http://www.quadibloc.com/maps/maz0202.htm

  7. Meridians: great circle Parallels except the equator are small circles

  8. Using a Wulff net: How to address the shorted distance between two locations? Connecting two points with the great circle!

  9. Measure the angle between two points: Bring these two points on the same great circle; counting the latitude angle.

  10. Angle between the planes of two zone circles is the angle between the poles of the corresponding

  11.  Finding the trace of a pole:

  12. Rotation of a projection about an axis in the projection plane

  13. Rotation about a direction (pole) that is inclined to the projection plane To rotate about the pole B1 by 40°

  14. Movement of pole when rotated along A axis for 35.3o. The (112) pole is brought to the center.

  15.  Determining Miller indices for poles: [001] [010] [100]

  16. Stereographic projection of different Bravais systems Cubic (001)

  17. How about a standard (011) stereographic projection of a cubic crystal? Start with what you know! What does (011) look like?

  18. [01] [100] [] (011) [] [11] [] 109.47o (011) 70.53o

  19. [011] [001] [01] [01] [100] [] (011) [001] [] 45o [011]

  20. [011] [111] [100] [100] [111] [01] 35.26o 70.53o [] (011) 111 [] [011] [011] [001] [01]

  21. 3a Trigonal Hexagonal [111] [0001] c 3a [110]

  22. Monoclinic Orthorhombic

  23.  Stereographic projections of non-cubic crystals: two stereographic projections is required (one for the surface normal (poles) and the other the directions).

  24. Two convections used in stereographic projection • (1) plot directions as poles and planes as • great circles • (2) plot planes as poles and directions as • great circles(plot the pole of the plane • and the great circles of the direction)

  25. Example:[001] stereographic projection; cubic (2) Zone axis B.D. Cullity

  26.  Applications of the Stereographic projections: (1) Representation of point group symmetry

  27. (2) Representation of preferred orientation (texture or fabric): e.g. A rolled sheet of polycrystalline cubic Metal. A {100} pole figure RD: rolling direction TD: transverse direction Successive levels of shading correspond to the contours of the orientations of plane normals and directions. {111} pole figure Showing the orientation of {111} planes {100} plane normals are spreading out toward the transverse direction

  28. Worthwhile reading: http://www.doitpoms.ac.uk/tlplib/stereographic/index.php http://folk.uib.no/nglhe/e-modules/Stereo%20module/1%20Stereo%20new.swf

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