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between smiley faces. SYMMETRY OPERATORS. FOR PLANE GROUP P2. 1) x,y. 2) -x,-y. x y -(-x y) ... back the coordinates. of our smiley faces!!!! (0,0) a. b (0.1, ... – PowerPoint PPT presentation

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Title: Patterson%20in%20plane%20group%20p2

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 u0.2, v0.4
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 u0.2, v0.4
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 Im 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 Im 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 u2x v2y plug in Patterson values for u
and v to get x and y.
12
Now Im 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 u2x v2y plug in Patterson values for u
and v to get x and y.
v2y 0.42y 0.2y
u2x 0.22x 0.1x
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
symop 1 symop 2
(0.1,0.2)
set u2x v2y plug in Patterson values for u
and v to get x and y.
v2y 0.42y 0.2y
u2x 0.22x 0.1x
HURRAY! we got back the coordinates of our
smiley faces!!!!