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The goal of Data Reduction

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

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The goal of Data Reduction

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  1. 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 0 0 12 9691.0 500.7 0 0 16 1743.9 67.4 0 0 20 5856.0 221.0 0 0 24 14066.5 436.2 0 0 28 9936.3 311.7 0 0 36 8409.8 273.4 0 0 40 790.5 32.8 0 0 44 103.4 18.4 . . . . . . . . . . . . . . . 37 7 0 28.5 16.2 37 7 1 110.1 10.9 37 7 2 337.4 13.3 37 7 3 98.5 10.6 37 7 4 25.9 10.7 • Index • Integrate • Merge

  2. 2,0,0 3,0,-1 4,0,-2 5,0,-3 5,0,-4 5,0,-5 4,0,-6 3,0,-7 2,0,-7 1,0,-8 0,0,-8 -1,0,-8 Indexing Assign an h,k,l coordinate to each reflection of the first image.

  3. Integration Within a spot, sum up the intensity of each pixel. Repeat for each spot on each film.

  4. K Plane L=0 H Merge K Plane L=0 ? -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 K,H,L K,-H,L H,K,L H,-K,L H -H,K,L -H,-K,L -K,-H,L -K,H,L Average (merge together) symmetry related reflections.

  5. K,-H,L K,H,L 2,0,0 3,0,-1 H,K,L H,-K,L 4,0,-2 5,0,-3 -H,K,L -H,-K,L 5,0,-4 5,0,-5 4,0,-6 -K,-H,L -K,H,L 3,0,-7 2,0,-7 1,0,-8 0,0,-8 -1,0,-8 Three steps • From a series of diffraction images, obtain a file containing the intensity (I) and standard deviation (s(I)) for each reflection, hkl. H K L I s 0 0 4 3295.4 174.0 0 0 8 482.1 28.7 0 0 12 9691.0 500.7 0 0 16 1743.9 67.4 0 0 20 5856.0 221.0 0 0 24 14066.5 436.2 0 0 28 9936.3 311.7 0 0 36 8409.8 273.4 0 0 40 790.5 32.8 0 0 44 103.4 18.4 . . . . . . . . . . . . . . . 37 7 0 28.5 16.2 37 7 1 110.1 10.9 37 7 2 337.4 13.3 37 7 3 98.5 10.6 37 7 4 25.9 10.7 2. integrate Set of films Final intensities 3. merge 1. index

  6. 2,0,0 3,0,-1 4,0,-2 5,0,-3 5,0,-4 5,0,-5 4,0,-6 3,0,-7 2,0,-7 1,0,-8 0,0,-8 -1,0,-8 Indexing How do we find the correct h,k,l coordinate of each reflection?

  7. What’s the h,k,l of this spot? 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 3 lattice points in a* direction What parameters must be defined to complete this construction?

  8. Coordinates (X,Y) for the spot position Coordinates (X,Y) of the direct beam The orientation of the unit cell axes with respect to the laboratory axes (fyk). 15 parameters must be determined to index a spot. The wavelength of the incident radiation Unit cell parameters a,b,c, a,b,g

  9. Coordinates (X,Y) for the spot position Coordinates (X,Y) of the direct beam The orientation of the unit cell axes with respect to the laboratory axes (fyk). Which of the 15 parameters are set or known? Which are unknown? The wavelength of the incident radiation Unit cell parameters a,b,c, a,b,g

  10. How is the unit cell and crystal orientation determined? Acta Cryst. (1999), D55, 1690-1695

  11. Figure 1.

  12. Choose principle axes by inspection

  13. 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.

  14. 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.

  15. 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.

  16. Figure 3.

  17. One dimensional Fourier transforms (7300 orientations)

  18. Figure 4.

  19. Lattice parameters determined 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.

  20. 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.”

  21. 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…………………………………………..

  22. Run autoindexing script The autoindexing script is simply titled “a.” Type “denzo: in the terminal window to start the program Denzo. Then type @a

  23. Select a space group with desired Bravais Lattice (e.g. new space group P4)Predicted pattern should match observed diffraction pattern.“go” to refine

  24. Necessary to index film 2 from scratch? film3? etc? 1o Film 2, exposed over 2 to 3 degrees Film 1, exposed over 1 to 2 degrees

  25. Coordinates (X,Y) for the spot position Coordinates (X,Y) of the direct beam The orientation of the unit cell axes with respect to the laboratory axes (fyk). The first film provides all the parameters need to predict the location of every spot on every film. The wavelength of the incident radiation Unit cell parameters a,b,c, a,b,g

  26. Integration Adjust integration box size and background box size. spot elliptical 0.6 0.6 background elliptical 0.7 0.7

  27. Insert refined unit cell and crystal orientation parameters into integration script (integ.dat).Type “list” to obtain refined paramers.. Paste parameters into integration script (integ.dat).

  28. Integrated intensities are written to .x files Film 1, exposed over 1 to 2 degrees h k l flag I(profit) I(prosum) c2 s(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 2061.6 29 22 -29 1 24.0 25.2 1.29 1.2 0.564 28.0 1489.1 ……………………………………………………….

  29. One .x file for each film prok_001.img prok_180.img prok_002.img 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) c2 s(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 2061.6 29 22 -29 1 24.0 25.2 1.29 1.2 0.564 28.0 1489.1 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 2061.6 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 h k l flag I(profit) I(prosum) c2 s(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 2061.6 29 22 -29 1 24.0 25.2 1.29 1.2 0.564 28.0 1489.1 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 2061.6 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 h k l flag I(profit) I(prosum) c2 s(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 2061.6 29 22 -29 1 24.0 25.2 1.29 1.2 0.564 28.0 1489.1 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 2061.6 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 prok_180.x prok_002.x prok_001.x

  30. h k l flag I(profit) I(prosum) c2 s(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 2061.6 29 22 -29 1 24.0 25.2 1.29 1.2 0.564 28.0 1489.1 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 2061.6 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 h k l flag I(profit) I(prosum) c2 s(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 2061.6 29 22 -29 1 24.0 25.2 1.29 1.2 0.564 28.0 1489.1 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 2061.6 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 360 frames, 1 degree rotation each h k l flag I(profit) I(prosum) c2 s(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 2061.6 29 22 -29 1 24.0 25.2 1.29 1.2 0.564 28.0 1489.1 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 2061.6 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 h k l flag I(profit) I(prosum) c2 s(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 2061.6 29 22 -29 1 24.0 25.2 1.29 1.2 0.564 28.0 1489.1 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 2061.6 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 prok_001 -> 360.x With .x files, we can map intensities onto a reciprocal lattice • Accuracy will improve if we Merge multiple observations of the same reciprocal lattice point • But, we must test if rotational symmetry exists between lattice points.

  31. Is it Laue group 422Or Laue group 4? P422 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 Test existence of 4-fold Symmetry and Perpendicular 2-fold symmetry Test existence of 4-fold symmetry

  32. Discrepancy between symmetry related reflections Rsym= S|Ij-<I>| SIj j observations of the reflection 30 22 6 <I>= (100 + 500 + 300) / 3 = 300 S|Ij-<I>| = |100-300|+|500-300|+|300-300| = 200 + 200 + 0 = 400 SIj = 100 + 500 + 300 = 900 Rsym = 400/900 = 0.44 = 44%

  33. Statistics are analyzed as a function of resolution (N shells). Discrepancy between symmetry related reflections (Rsym) increases with increasing resolution. Why?

  34. SIGNAL TO NOISE RATIO (I/s) Average I/s decreases with increasing resolution High resolution shells with I/s <2 should be discarded.

  35. COMPLETENESS? What percentage of reciprocal Lattice was measured for a given Resolution limit? Better than 90% I hope. Overall 92.5%

  36. Assignment

  37. Effect of mosaicity and wavelength spread Dl

  38. Figure 5.

  39. Figure 6.

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