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Fasproblemet
• Tungmetallderivat (MIR, SIR)
• Anomalous dispersion
• Patterson kartor
Vektorrepresentation av strukturfaktorer
Vektorrepresentation av strukturfaktorer
SIR
Multiple isomorphous replacement
MIR
Friedels Lag (hkl = -h –k –l)
Anomalous dispersion
Anomalous dispersion
Patterson map
• Karta över vektorer mellan par av atomer• För varje topp finns det två atomer, visar
atomer relativt till varandra ej relativt till enhetscellen
• Varje atom bildar ett par (och vektor) med varje annan atom, dvs i en enhetscell med N atomer finns det N2 vektorer.N self vectors och n(n-1) andra vektorer
• Intensitetet på toppen proportionell mot produkten av det ingående atomparet
Patterson in plane group p2
(0,0) ab
SYMMETRY OPERATORSFOR PLANE GROUP P21) x,y2) -x,-y
Patterson in plane group p2
(0,0) ab
(0.1,0.2)
SYMMETRY OPERATORSFOR PLANE GROUP P21) x,y2) -x,-y
Patterson in plane group p2
(0,0) ab
(0.1,0.2)
(-0.1,-0.2)
SYMMETRY OPERATORSFOR PLANE GROUP P21) x,y2) -x,-y
Patterson in plane group p2
(0,0) ab
(0.1,0.2)
(-0.1,-0.2)
SYMMETRY OPERATORSFOR PLANE GROUP P21) x,y2) -x,-y
Patterson in plane group p2
(0,0) ab
a(0,0)b
(0.1,0.2)
(-0.1,-0.2)
SYMMETRY OPERATORSFOR PLANE GROUP P21) x,y2) -x,-y
PATTERSON MAP2D CRYSTAL
Patterson in plane group p2
(0,0) ab
a(0,0)b
(0.1,0.2)
(-0.1,-0.2)
SYMMETRY OPERATORSFOR PLANE GROUP P21) x,y2) -x,-y
PATTERSON MAP2D CRYSTAL
Patterson in plane group p2
(0,0) ab
a(0,0)b
(0.1,0.2)
(-0.1,-0.2)
SYMMETRY OPERATORSFOR PLANE GROUP P21) x,y2) -x,-y
PATTERSON MAP2D CRYSTAL
What is the coordinate for thePatterson peak? Just take thedifference between coordinates ofthe two happy faces.(x,y)-(-x,-y) or (0.1,0.2)-(-0.1,-0.2)so u=0.2, v=0.4
Patterson in plane group p2
(0,0) ab
a(0,0)b
(0.1,0.2)
(-0.1,-0.2)
SYMMETRY OPERATORSFOR PLANE GROUP P21) x,y2) -x,-y
PATTERSON MAP2D CRYSTAL
What is the coordinate for thePatterson peak? Just take thedifference between coordinates ofthe 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)
Patterson in plane group p2
a(0,0)b
PATTERSON MAP
(0.2, 0.4)
If you collected data on this crystaland calculated a Patterson mapit would look like this.
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 vectorsbetween smiley faces.
SYMMETRY OPERATORSFOR PLANE GROUP P21) x,y2) -x,-y
x y-(-x –y)2x 2y
symop #1symop #2
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 vectorsbetween smiley faces.
SYMMETRY OPERATORSFOR PLANE GROUP P21) x,y2) -x,-y
x y-(-x –y)2x 2y
symop #1symop #2
set u=2x v=2y plug in Patterson valuesfor u and v to get x and y.
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 OPERATORSFOR PLANE GROUP P21) x,y2) -x,-y
x y-(-x –y)2x 2y
symop #1symop #2
set u=2x v=2y plug in Patterson valuesfor u and v to get x and y.
u=2x0.2=2x0.1=x
v=2y0.4=2y0.2=y
Hurray!!!!
SYMMETRY OPERATORSFOR PLANE GROUP P21) x,y2) -x,-y
x y-(-x –y)2x 2y
symop #1symop #2
set u=2x v=2y plug in Patterson valuesfor u and v to get x and y.
u=2x0.2=2x0.1=x
v=2y0.4=2y0.2=y
HURRAY! we got back the coordinatesof our smiley faces!!!!
(0,0) ab
(0.1,0.2)
Vektorrepresentation av strukturfaktorer
Vektorrepresentation av strukturfaktorer
Vektorrepresentation av strukturfaktorer
Vektorrepresentation av strukturfaktorer
Patterson map
