Introduction to the charge flipping for powder diffraction

Transcription

1 Introduction to the charge flipping for powder diffraction Jan Rohlíček Institute of Physics, Department of Structure Analysis, Academy of Science of the Czech Republic

2 We are here Approx. 800 km from here

3 We are here The main building of the institute is on the other side of Prague

4 We are here

5 We are here Tennis-court Voleyball court

6 We are here Canteen! Tennis-court Voleyball court

7

8 Canteen

9 Department of structure analysis

10 Powder diffractometers in our lab Empyrean (PANalytical) SmartLab (Rigaku)

11 Powder sample powder = polycrystalline material 11

12 Diffraction of the powder sample Single crysta ld iffraction Powder diffraction pattern is a combination of a large number of the single crystal diffraction patterns

13 Diffracted pattern Powder diffraction pattern of alaptide powder on the area detector 13

14 Diffracted pattern 14

15 Problems and limitations Information loss data are projection of a 3D diffraction pattern to 1D 15

16 Problems and limitations intensity Peak overlap extraction of intensities Theta

17 Problems and limitations intensity Peak overlap extraction of intensities. What is the intensity of these reflections? Positions of reflections 17 2 Theta

18 Problems and limitations intensity Peak overlap extraction of intensities. What is the intensity of these reflections? Positions of reflections 18 2 Theta

19 Peak overlap

20 Peak overlap 2.5 Å 2.0 Å 1.7 Å 1.4 Å 1.3 Å

21 El. density Fcalc Fourier sin Θ / λ = 0.2 λ = Å max = 36 2Θ dmax = 2.5 Å

22 Rozlišení ELD sin Θ / λ = 0.25 λ = Å max = 45 2Θ dmax = 2.0 Å

23 Rozlišení ELD sin Θ / λ = 0.3 λ = Å max = 55 2Θ dmax = 1.7 Å

24 Rozlišení ELD sin Θ / λ = 0.35 λ = Å max = 65 2Θ dmax = 1.4 Å

25 Rozlišení ELD sin Θ / λ = 0.4 λ = Å max = 76 2Θ dmax = 1.3 Å

26 Effect of the peak overlap Dual space methods and direct methods need: High resolution data (~ 1.2Å and better) Low peak overlap charge flipping combined with histogram matching may solve the peak overlap issue Direct Space methods Starting model Time consuming process

27 What is charge flipping? Charge flipping is a method for ab initio determination of an approximate scattering density from the set of structure-factor amplitudes Published by Oszlányi & Sütő (2004), Acta Cryst A The output is an approximate scattering density of the structure sampled on a discrete grid Requires only lattice parameters and reflection intensities No use of atomicity, only of the sparseness of the electron density No use of symmetry apart from the input intensities

28 Charge flipping! Fhkl(obs) The direct-space constraint must restrict the scattering densities to a physically meaningful subset. (ed threshold for flipping) assign random phases electron density map Typical requirements are positivity, sparseness and atomicity. flip sign of ed < combine perturbed electron density map back transform R-value Fhkl(calc) hkl(calc) Fhkl(obs) with hkl(calc)

29 Constraints and projections 0 0 Positivity projection

30 Constraints and projections 0 0 Significance + positivity projection (dynamic support with positivity)

31 Constraints and projections 0 0 Significance projection (dynamic support without positivity)

32 Constraints and projections 0 Reflector of the significance + positivity projection the charge flipping operation

33 Constraints and projections 0 0 Constraint on the number of maxima in the density

34 Charge flipping - applet

35 Charge flipping for powders

36 Charge flipping Fhkl(obs) (ed threshold for flipping) assign random phases electron density map flip sign of ed < combine perturbed electron density map back transform R-value Fhkl(calc) hkl(calc) Fhkl(obs) with hkl(calc)

37 Charge flipping for powders Fhkl(obs) with overlap groups (ed threshold for flipping) repartitioning after n cycles electron density histogram assign random phases new Fhkl(obs) new hkl(calc) repartition overlapping reflections electron density map flip sign of ed < combine perturbed electron density map Fhkl(calc) hkl(calc) back transform back transform Fhkl(calc) hkl(calc) R-value perturbed electron density map yes histogram matching n cycles? no Fhkl(obs) with hkl(calc)

38 Electron density histograms Original idea: Zhang & Main, Acta Cryst A46, 1990 used to improve phases, not intensities

39 Electron density histograms Original idea: Zhang & Main, Acta Cryst A46, 1990 used to improve phases, not intensities

40 Charge flipping for powders Zeolite ZSM-5, Si96O192 without histogram matching with histogram matching

41 Charge flipping for powders How to set up the algorithm? Κ = 0.3 Biso = 0 1 HM= 20 5 δ = δauto 500 cycles 100 runs Sisak et al. (2012): Optimizing the input parameters for powder charge flipping

42 Charge flipping for powders

43 Charge flipping for powders

44 Charge flipping for powders C y l l a re e w n a re p r inte? p a m s i t th

45 Charge flipping for powders

46 Rozlišení ELD sin Θ / λ = 0.25 λ = Å max = 45 2Θ dmax = 2.0 Å

47 Advantages and disadvantages + Minimum assumptions and approximations involved + No explicit use of chemical composition and form factors + No explicit use of space group symmetry + Obtaining symmetry with solution + Applicable to x-ray, neutron, electron diffraction - Requires atomic resolution (d<1.3a for light atoms, much more relaxed for heavier atoms - Peak overlap should not be so high

48 End Thank you!