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Patterson in plane group p2

Learn how to derive coordinates in a plane group P2 using symmetry operators and Patterson mapping method. Discover the relationship between Patterson peaks, smiley faces, and crystallographic data.

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Patterson in plane group p2

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  1. Patterson in plane group p2 a (0,0) b SYMMETRY OPERATORSFOR PLANE GROUP P2 1) x,y 2) -x,-y

  2. Patterson in plane group p2 a (0,0) b (0.1,0.2) SYMMETRY OPERATORSFOR PLANE GROUP P2 1) x,y 2) -x,-y

  3. Patterson in plane group p2 (-0.1,-0.2) a (0,0) b (0.1,0.2) SYMMETRY OPERATORSFOR PLANE GROUP P2 1) x,y 2) -x,-y

  4. Patterson in plane group p2 (-0.1,-0.2) a (0,0) b (0.1,0.2) SYMMETRY OPERATORSFOR PLANE GROUP P2 1) x,y 2) -x,-y

  5. Patterson in plane group p2 (-0.1,-0.2) a (0,0) a (0,0) b b (0.1,0.2) SYMMETRY OPERATORSFOR PLANE GROUP P2 1) x,y 2) -x,-y PATTERSON MAP 2D CRYSTAL

  6. Patterson in plane group p2 (-0.1,-0.2) a (0,0) a (0,0) b b (0.1,0.2) SYMMETRY OPERATORSFOR PLANE GROUP P2 1) x,y 2) -x,-y PATTERSON MAP 2D CRYSTAL

  7. Patterson in plane group p2 (-0.1,-0.2) a (0,0) a (0,0) b b (0.1,0.2) What is the coordinate for the Patterson peak? Just take the difference between coordinates of the two happy faces. (x,y)-(-x,-y) or (0.1,0.2)-(-0.1,-0.2) so u=0.2, v=0.4 SYMMETRY OPERATORSFOR PLANE GROUP P2 1) x,y 2) -x,-y PATTERSON MAP 2D CRYSTAL

  8. Patterson in plane group p2 (-0.1,-0.2) a (0,0) a (0,0) b b (0.1,0.2) (0.2, 0.4) What is the coordinate for the Patterson peak? Just take the difference between coordinates of the two happy faces. (x,y)-(-x,-y) or (0.1,0.2)-(-0.1,-0.2) so u=0.2, v=0.4 SYMMETRY OPERATORSFOR PLANE GROUP P2 1) x,y 2) -x,-y PATTERSON MAP 2D CRYSTAL

  9. Patterson in plane group p2 a (0,0) b (0.2, 0.4) If you collected data on this crystal and calculated a Patterson map it would look like this. PATTERSON MAP

  10. Now I’m stuck in Patterson space. How do I get back to x,y, coordinates? a (0,0) b Use our friends, the space group operators. The peaks positions correspond to vectors between smiley faces. (0.2, 0.4) SYMMETRY OPERATORSFOR PLANE GROUP P2 1) x,y 2) -x,-y x y -(-x –y) 2x 2y symop #1 symop #2 PATTERSON MAP

  11. Now I’m stuck in Patterson space. How do I get back to x,y, coordinates? a (0,0) b Use our friends, the space group operators. The peaks positions correspond to vectors between smiley faces. (0.2, 0.4) SYMMETRY OPERATORSFOR PLANE GROUP P2 1) x,y 2) -x,-y x y -(-x –y) 2x 2y symop #1 symop #2 PATTERSON MAP set u=2x v=2y plug in Patterson values for u and v to get x and y.

  12. Now I’m stuck in Patterson space. How do I get back to x,y, coordinates? SYMMETRY OPERATORSFOR PLANE GROUP P2 1) x,y 2) -x,-y a (0,0) b x y -(-x –y) 2x 2y symop #1 symop #2 (0.2, 0.4) set u=2x v=2y plug in Patterson values for u and v to get x and y. v=2y 0.4=2y 0.2=y u=2x 0.2=2x 0.1=x PATTERSON MAP

  13. Hurray!!!! SYMMETRY OPERATORSFOR PLANE GROUP P2 1) x,y 2) -x,-y a (0,0) b x y -(-x –y) 2x 2y (0.1,0.2) symop #1 symop #2 set u=2x v=2y plug in Patterson values for u and v to get x and y. v=2y 0.4=2y 0.2=y u=2x 0.2=2x 0.1=x HURRAY! we got back the coordinates of our smiley faces!!!!

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