the goal of data reduction
DESCRIPTION
The goal of Data Reduction. From a series of diffraction images (films), obtain a file containing the intensity ( I ) and standard deviation ( s ( I )) for each reflection, hkl. Final intensities. Set of films. H K L I s 0 0 4 3295.4 174.0 0 0 8 482.1 28.7 - PowerPoint PPT PresentationTRANSCRIPT
The goal of Data Reduction• From a series of diffraction images (films), obtain a file containing the
intensity (I) and standard deviation ((I)) for each reflection, hkl.
H K L I 0 0 4 3295.4 174.00 0 8 482.1 28.70 0 12 9691.0 500.70 0 16 1743.9 67.40 0 20 5856.0 221.00 0 24 14066.5 436.20 0 28 9936.3 311.70 0 36 8409.8 273.40 0 40 790.5 32.80 0 44 103.4 18.4. . . . .. . . . .. . . . .37 7 0 28.5 16.237 7 1 110.1 10.937 7 2 337.4 13.337 7 3 98.5 10.637 7 4 25.9 10.7
Set of filmsFinal intensities
1. Index2. Integrate3.Merge
2,0,0
3,0,-1
4,0,-25,0,-3
5,0,-45,0,-5
4,0,-63,0,-7
2,0,-7
1,0,-80,0,-8
-1,0,-8
Indexing
Assign an h,k,l coordinate to each reflection of the first image.
Integration
Within a spot, sum up the intensity of each pixel.Repeat for each spot on each film.
Merge
Average (merge together) symmetry related reflections.
Plane L=0 K
H
?-H,-K, L=-K, H, L= K,-H, L= H, K,-L= H,-K,-L= K, H,-L=-K,-H,-L=-H,-K,-L= K,-H,-L=-K, H,-L=-H, K, L=-K,-H, L= K, H, L
Plane L=0 K
H
K,-H,L
H,K,L
-H,K,L
-K,-H,L
K,H,L
-H,-K,L
H,-K,L
-K,H,L
Three steps• From a series of diffraction images, obtain a file containing the
intensity (I) and standard deviation ((I)) for each reflection, hkl.
2,0,03,0,-14,0,-25,0,-35,0,-45,0,-5
4,0,-63,0,-72,0,-7
1,0,-80,0,-8-1,0,-8
Set of films
1. index
2. integrate
3. merge
K,-H,L
H,K,L
-H,K,L
-K,-H,L
K,H,L
-H,-K,L
H,-K,L
-K,H,L
Final intensities
H K L I 0 0 4 3295.4 174.00 0 8 482.1 28.70 0 12 9691.0 500.70 0 16 1743.9 67.40 0 20 5856.0 221.00 0 24 14066.5 436.20 0 28 9936.3 311.70 0 36 8409.8 273.40 0 40 790.5 32.80 0 44 103.4 18.4. . . . .. . . . .. . . . .37 7 0 28.5 16.237 7 1 110.1 10.937 7 2 337.4 13.337 7 3 98.5 10.637 7 4 25.9 10.7
2,0,0
3,0,-1
4,0,-25,0,-3
5,0,-45,0,-5
4,0,-63,0,-7
2,0,-7
1,0,-80,0,-8
-1,0,-8
Indexing
How do we find the correct h,k,l coordinate of each reflection?
What’s the h,k,l of this spot?
3 lattice p
oin
ts in
a* d
irection
2 lattice points in
b* direction
For a given spot on the film, we simply have to trace the diffracted ray back to the reciprocal latticepoint (h,k,l)
The answer is HKL=3,2,2
What parameters must be defined to complete this construction?
15 parameters must be determined to index a spot.
The wavelength of the incident radiation
Coordinates (X,Y) of the direct beam
Coordinates (X,Y) for the spot position
Unit cell parametersa,b,c,
The orientation of the unit cell axes with respect to the laboratory axes ().
Which of the 15 parameters are set or known? Which are unknown?
The wavelength of the incident radiation
Coordinates (X,Y) of the direct beam
Coordinates (X,Y) for the spot position
Unit cell parametersa,b,c,
The orientation of the unit cell axes with respect to the laboratory axes ().
How is the unit cell and crystal orientation determined?
Acta Cryst. (1999), D55, 1690-1695
Figure 1.
Choose principle axes by inspection
One dimensional Fourier transforms (7300 orientations)
Find all pairs of spots that can be connected by a vector of given orientation, but any length.
e.g.
One dimensional Fourier transforms (7300 orientations)
Find all pairs of spots that can be connected by a vector of given orientation, but any length.
e.g.
Figure 3. You will find some vector lengths are represented in the diffraction pattern much more frequently than others.These vector lengths differ by integral multiples of one particular value…corresponding to the unit cell dimension.
Figure 3.
One dimensional Fourier transforms (7300 orientations)
Figure 4.
A group of 30 possible non-linear vectors are calculated.
3 vectors at a time are combined to give a basis set of direct-space primitive unit cells.
For each combination of 3 vectors, a distortion index is evaluated which describes how the observed fitted reciprocal lattice deviates from the 14 Bravais lattices.
A chi squared statistics describes the deviations of the observed reflections from the theoretical lattice.
Lattice parameters determined
Xdisplay and Peak Search
1) Display first image in your data set with xdisplay.xdispccd images/my.img
2) Press “Peak Search”. Red circles indicate position of prominent peaks (spots).
3) Evaluate whether you need more or fewer peaks.
4) Pres “OK”
5) Spot positions (x,y) are written to a file “peaks.file.”
Peaks.file• 7777 0.0 0.0 1 1 height X Y frame• 13 2695.7 1350.5 1 1• 27 2669.5 1062.4 1 1• 16 2570.6 1143.5 1 1• 26 2569.4 1302.4 1 1• 30 2562.5 1592.5 1 1• 32 2554.5 1902.4 1 1• 32 2524.5 1103.4 1 1• 22 2514.5 1523.8 1 1• 12 2503.4 1316.6 1 1• 21 2494.5 1949.5 1 1• 15 2492.5 1923.4 1 1• 35 2488.5 1721.5 1 1• 17 2483.5 1870.6 1 1• 12 2479.4 1212.5 1 1• 32 2465.5 1452.5 1 1• 15 2456.4 638.4 1 1• 13 2444.7 900.7 1 1• 14 2437.6 1183.4 1 1• 23 2436.4 1969.4 1 1• Etc…………………………………………..
Run autoindexing script
The autoindexing script is simply titled “a.”
Type “denzo: in the terminal window to start the program Denzo. Then type @a
Select a space group with desired Bravais Lattice (e.g. new space group P4)
Predicted pattern should match observed diffraction pattern.
“go” to refine
Necessary to index film 2 from scratch?
film3? etc?
1o
Film 1, exposed over 1 to 2 degrees Film 2, exposed over 2 to 3 degrees
The first film provides all the parameters need to predict the location of every spot on every film.
The wavelength of the incident radiation
Coordinates (X,Y) of the direct beam
Coordinates (X,Y) for the spot position
Unit cell parametersa,b,c,
The orientation of the unit cell axes with respect to the laboratory axes ().
Integration
Adjust integration box size and background box size.spot elliptical 0.6 0.6background elliptical 0.7 0.7
Paste parameters into integration script (integ.dat).
Insert refined unit cell and crystal orientation parameters into
integration script (integ.dat).Type “list” to obtain refined paramers..
Integrated intensities are written to .x files
Film 1, exposed over 1 to 2 degrees
h k l flag I(profit) I(prosum) 2 (I) cos incid. X pix Y pix29 20 -33 1 202.3 200.8 1.36 17.4 0.556 6.4 1353.0 29 21 -31 1 102.1 105.0 1.08 7.7 0.560 16.8 1421.5 30 26 -19 1 1291.2 1323.2 1.19 50.0 0.554 23.9 1808.7 31 28 -11 1 1554.0 1618.7 1.26 95.1 0.536 24.2 2061.629 22 -29 1 24.0 25.2 1.29 1.2 0.564 28.0 1489.1……………………………………………………….
One .x file for each film
Film 1, exposed over 1 to 2 degrees
Film 2, exposed over 2 to 3 degrees
Film 180, exposed over 180 to 181 degrees
h k l flag I(profit) I(prosum) 2 (I) cos incid. X pix Y pix
29 20 -33 1 202.3 200.8 1.36 17.4 0.556 6.4 1353.0 29 21 -31 1 102.1 105.0 1.08 7.7 0.560 16.8 1421.5 30 26 -19 1 1291.2 1323.2 1.19 50.0 0.554 23.9 1808.7 31 28 -11 1 1554.0 1618.7 1.26 95.1 0.536 24.2 2061.629 22 -29 1 24.0 25.2 1.29 1.2 0.564 28.0 1489.129 20 -33 1 202.3 200.8 1.36 17.4 0.556 6.4 1353.0 29 21 -31 1 102.1 105.0 1.08 7.7 0.560 16.8 1421.5 30 26 -19 1 1291.2 1323.2 1.19 50.0 0.554 23.9 1808.7 31 28 -11 1 1554.0 1618.7 1.26 95.1 0.536 24.2 2061.629 20 -33 1 202.3 200.8 1.36 17.4 0.556 6.4 1353.0 29 21 -31 1 102.1 105.0 1.08 7.7 0.560 16.8 1421.5 30 26 -19 1 1291.2 1323.2 1.19 50.0 0.554 23.9 1808.7 31 28 -11 1 1554.0 1618.7 1.26 95.1 0.536 24.2 2061
h k l flag I(profit) I(prosum) 2 (I) cos incid. X pix Y pix
29 20 -33 1 52.3 50.8 1.36 17.4 0.556 6.4 1353.0 29 21 -31 1 102.1 105.0 1.08 7.7 0.560 16.8 1421.5 30 26 -19 1 1291.2 1323.2 1.19 50.0 0.554 23.9 1808.7 31 28 -11 1 1554.0 1618.7 1.26 95.1 0.536 24.2 2061.629 22 -29 1 24.0 25.2 1.29 1.2 0.564 28.0 1489.129 20 -33 1 202.3 200.8 1.36 17.4 0.556 6.4 1353.0 29 21 -31 1 102.1 105.0 1.08 7.7 0.560 16.8 1421.5 30 26 -19 1 1291.2 1323.2 1.19 50.0 0.554 23.9 1808.7 31 28 -11 1 1554.0 1618.7 1.26 95.1 0.536 24.2 2061.629 20 -33 1 202.3 200.8 1.36 17.4 0.556 6.4 1353.0 29 21 -31 1 102.1 105.0 1.08 7.7 0.560 16.8 1421.5 30 26 -19 1 1291.2 1323.2 1.19 50.0 0.554 23.9 1808.7 31 28 -11 1 1554.0 1618.7 1.26 95.1 0.536 24.2 2061
h k l flag I(profit) I(prosum) 2 (I) cos incid. X pix Y pix-
29 -20 33 1 212.3 220.8 1.36 17.4 0.556 6.4 1353.0 29 21 -31 1 102.1 105.0 1.08 7.7 0.560 16.8 1421.5 30 26 -19 1 1291.2 1323.2 1.19 50.0 0.554 23.9 1808.7 31 28 -11 1 1554.0 1618.7 1.26 95.1 0.536 24.2 2061.629 22 -29 1 24.0 25.2 1.29 1.2 0.564 28.0 1489.129 20 -33 1 202.3 200.8 1.36 17.4 0.556 6.4 1353.0 29 21 -31 1 102.1 105.0 1.08 7.7 0.560 16.8 1421.5 30 26 -19 1 1291.2 1323.2 1.19 50.0 0.554 23.9 1808.7 31 28 -11 1 1554.0 1618.7 1.26 95.1 0.536 24.2 2061.629 20 -33 1 202.3 200.8 1.36 17.4 0.556 6.4 1353.0 29 21 -31 1 102.1 105.0 1.08 7.7 0.560 16.8 1421.5 30 26 -19 1 1291.2 1323.2 1.19 50.0 0.554 23.9 1808.7 31 28 -11 1 1554.0 1618.7 1.26 95.1 0.536 24.2 2061
prok_001.img
prok_001.x
prok_002.img prok_180.img
prok_002.x prok_180.x
h k l flag I(profit) I(prosum) 2 (I) cos incid. X pix Y pix
29 20 -33 1 202.3 200.8 1.36 17.4 0.556 6.4 1353.0 29 21 -31 1 102.1 105.0 1.08 7.7 0.560 16.8 1421.5 30 26 -19 1 1291.2 1323.2 1.19 50.0 0.554 23.9 1808.7 31 28 -11 1 1554.0 1618.7 1.26 95.1 0.536 24.2 2061.629 22 -29 1 24.0 25.2 1.29 1.2 0.564 28.0 1489.129 20 -33 1 202.3 200.8 1.36 17.4 0.556 6.4 1353.0 29 21 -31 1 102.1 105.0 1.08 7.7 0.560 16.8 1421.5 30 26 -19 1 1291.2 1323.2 1.19 50.0 0.554 23.9 1808.7 31 28 -11 1 1554.0 1618.7 1.26 95.1 0.536 24.2 2061.629 20 -33 1 202.3 200.8 1.36 17.4 0.556 6.4 1353.0 29 21 -31 1 102.1 105.0 1.08 7.7 0.560 16.8 1421.5 30 26 -19 1 1291.2 1323.2 1.19 50.0 0.554 23.9 1808.7 31 28 -11 1 1554.0 1618.7 1.26 95.1 0.536 24.2 2061
360 frames, 1 degree
rotation each
With .x files, we can map intensities onto a reciprocal
lattice
1) Accuracy will improve if we Merge multiple observations of the same reciprocal lattice point
2) But, we must test if rotational symmetry exists between lattice points.
h k l flag I(profit) I(prosum) 2 (I) cos incid. X pix Y pix
29 20 -33 1 202.3 200.8 1.36 17.4 0.556 6.4 1353.0 29 21 -31 1 102.1 105.0 1.08 7.7 0.560 16.8 1421.5 30 26 -19 1 1291.2 1323.2 1.19 50.0 0.554 23.9 1808.7 31 28 -11 1 1554.0 1618.7 1.26 95.1 0.536 24.2 2061.629 22 -29 1 24.0 25.2 1.29 1.2 0.564 28.0 1489.129 20 -33 1 202.3 200.8 1.36 17.4 0.556 6.4 1353.0 29 21 -31 1 102.1 105.0 1.08 7.7 0.560 16.8 1421.5 30 26 -19 1 1291.2 1323.2 1.19 50.0 0.554 23.9 1808.7 31 28 -11 1 1554.0 1618.7 1.26 95.1 0.536 24.2 2061.629 20 -33 1 202.3 200.8 1.36 17.4 0.556 6.4 1353.0 29 21 -31 1 102.1 105.0 1.08 7.7 0.560 16.8 1421.5 30 26 -19 1 1291.2 1323.2 1.19 50.0 0.554 23.9 1808.7 31 28 -11 1 1554.0 1618.7 1.26 95.1 0.536 24.2 2061
h k l flag I(profit) I(prosum) 2 (I) cos incid. X pix Y pix
29 20 -33 1 202.3 200.8 1.36 17.4 0.556 6.4 1353.0 29 21 -31 1 102.1 105.0 1.08 7.7 0.560 16.8 1421.5 30 26 -19 1 1291.2 1323.2 1.19 50.0 0.554 23.9 1808.7 31 28 -11 1 1554.0 1618.7 1.26 95.1 0.536 24.2 2061.629 22 -29 1 24.0 25.2 1.29 1.2 0.564 28.0 1489.129 20 -33 1 202.3 200.8 1.36 17.4 0.556 6.4 1353.0 29 21 -31 1 102.1 105.0 1.08 7.7 0.560 16.8 1421.5 30 26 -19 1 1291.2 1323.2 1.19 50.0 0.554 23.9 1808.7 31 28 -11 1 1554.0 1618.7 1.26 95.1 0.536 24.2 2061.629 20 -33 1 202.3 200.8 1.36 17.4 0.556 6.4 1353.0 29 21 -31 1 102.1 105.0 1.08 7.7 0.560 16.8 1421.5 30 26 -19 1 1291.2 1323.2 1.19 50.0 0.554 23.9 1808.7 31 28 -11 1 1554.0 1618.7 1.26 95.1 0.536 24.2 2061
h k l flag I(profit) I(prosum) 2 (I) cos incid. X pix Y pix
29 20 -33 1 202.3 200.8 1.36 17.4 0.556 6.4 1353.0 29 21 -31 1 102.1 105.0 1.08 7.7 0.560 16.8 1421.5 30 26 -19 1 1291.2 1323.2 1.19 50.0 0.554 23.9 1808.7 31 28 -11 1 1554.0 1618.7 1.26 95.1 0.536 24.2 2061.629 22 -29 1 24.0 25.2 1.29 1.2 0.564 28.0 1489.129 20 -33 1 202.3 200.8 1.36 17.4 0.556 6.4 1353.0 29 21 -31 1 102.1 105.0 1.08 7.7 0.560 16.8 1421.5 30 26 -19 1 1291.2 1323.2 1.19 50.0 0.554 23.9 1808.7 31 28 -11 1 1554.0 1618.7 1.26 95.1 0.536 24.2 2061.629 20 -33 1 202.3 200.8 1.36 17.4 0.556 6.4 1353.0 29 21 -31 1 102.1 105.0 1.08 7.7 0.560 16.8 1421.5 30 26 -19 1 1291.2 1323.2 1.19 50.0 0.554 23.9 1808.7 31 28 -11 1 1554.0 1618.7 1.26 95.1 0.536 24.2 2061
prok_001 -> 360.x
Is it Laue group 422 Or Laue group 4?
P4 H, K,L-H,-K,L-K, H,L K,-H,L
H, K,-L H,-K,-L K, H,-L-K,-H,-L
P422
Test existenceof 4-fold
symmetry
Test existence of4-fold Symmetry
andPerpendicular
2-fold symmetry
j observations of the reflection 30 22 6
<I>= (100 + 500 + 300) / 3 = 300
j H K L I
1 30 22 6 100
2 -30 -22 6 500
3 22 -30 6 300
Rsym= |Ij-<I>|
Ij
Discrepancy between symmetry related reflections
|Ij-<I>| = |100-300|+|500-300|+|300-300|
= 200 + 200 + 0 = 400Ij = 100 + 500 + 300
= 900
Rsym = 400/900 = 0.44 = 44%
Discrepancy between symmetry related reflections (Rsym) increases with increasing resolution. Why?
Shell Rsym
100-5.0Å 0.04
5.0-3.0Å 0.06
3.0-2.0Å 0.08
2.0-1.7Å 0.15
Statistics are analyzed as a function of resolution (N shells).
Average I/ decreases with increasing resolution
High resolution shells with I/ <2 should be discarded.
Shell I/
100-5.0 Å 20.0
5.0-3.0 Å 10.0
3.0-2.0 Å 7.0
2.0-1.7 Å 3.0
SIGNAL TO NOISE RATIO (I/)
COMPLETENESS?
What percentage of reciprocalLattice was measured for a givenResolution limit?
Better than 90% I hope.
Shell completeness
100-5.0Å 99.9%
5.0-3.0Å 95.5%
3.0-2.0Å 89.0%
2.0-1.7Å 85.3%
Overall 92.5%
Assignment
Effect of mosaicity and wavelength spread
Figure 5.
Figure 6.