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

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

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

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

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

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

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

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Patterson in plane group p2 (0,0) a b a b (0.1,0.2) (-0.1,-0.2) SYMMETRY OPERATORS FOR PLANE GROUP P2 1) x,y 2) -x,-y PATTERSON MAP 2D CRYSTAL 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 (0.2, 0.4)

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

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

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

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

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

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3.7 Translations. A) Translation: when we SLIDE a figure to a different location. Transformation: an operation that maps or moves a figure onto an image.

3.7 Translations. A) Translation: when we SLIDE a figure to a different location. Transformation: an operation that maps or moves a figure onto an image.

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