1. Structural information extracted from the diffraction of XFEL femtosecond pulses in a crystal Belarusian State University Aliaksandr Leonau The Actual Problems of Microworld Physics Gomel, Belarus, July 27 - August 7, 2015

2. Contents 1. Basics of X-ray free electron lasers (XFELs) 2. Irradiating a crystal with an XFEL pulse 3. XFEL-specific supplementary information for the phase retrieval procedure

3. Contents 1. Basics of X-ray free electron lasers (XFELs) 2. Irradiating a crystal with an XFEL pulse 3. XFEL-specific supplementary information for the phase retrieval procedure

4. XFEL – new generation of light sources X-ray Free Electron Laser (XFEL) – the revolutionary new tool to study matter Spatial resolution – Angstroms ( 1 A = 10 -10 m) Temporal resolution – femtoseconds ( 1 fs = 10 -15 s) -Femtochemistry (filming chemical reactions) Courtesy of DESY 1 (25)

5. XFEL – new generation of light sources X-ray Free Electron Laser (XFEL) – the revolutionary new tool to study matter Brightness – one of the main attributes of a light source Light source (with area a) Angular divergence (solid angle Ω) Photon flux Φ Brightness of XFEL ~ 10 24 in [B] units HOW MUCH IS IT ? 2 (25)

6. XFEL – new generation of light sources 3 (25)

7. Basics of XFEL operation Courtesy of SLAC / website: http://lcls.slac.stanford.edu/AnimationViewLCLS.aspx 4 (25)

8. XFEL projects FLASH (2005) & FLASH II (2015)LCLS (2009) SACLA (2011) European XFEL (2016-2017) 5 (25)

9. Contents 1. Basics of X-ray free electron lasers (XFELs) 2. Irradiating a crystal with an XFEL pulse 3. XFEL-specific supplementary information for the phase retrieval procedure

10. “Diffraction before destruction” Neutze et al., Nature 406, 752-757 (2000) Recording of the complete diffraction pattern by a single shot is possible ! HOWEVER…There is a problem ! Object under study alternates drastically: linear response approach no longer valid. 6 (25)

11. “Diffraction before destruction” One should use the pulse shorter than the timescale of destruction… Recording of the complete diffraction pattern by a single shot is possible ! …and… … take into account evolution of the sample on the timescale of the pulse duration! HOWEVER…There is NO problem ! LET US HAVE DIFFRACTION BEFORE DESTRUCTION ! 6 (25)

12. Irradiating of a crystal with XFEL pulse One can irradiate different types of samples (single atoms, molecules, clusters,…) Experiments with crystals (nanocrystals) are of great value for biologists Interaction of the XFEL fs-pulses with a crystal should be well understood and needs high-quality treatment ! The time scale we consider We consider the processes that take place during the passing of the XFEL pulse through the crystal ( t < 100 fs ) How about taking a single crystal (nanocrystal)? 7 (25)

13. General dynamics scheme 8 (25)

14. 9 (25) Model to be considered Total system Free electrons EM field Beyond the present consideration Bound electrons

15. Numerical simulation scheme The system of master equations (two coupled subsystems of integro-differential equations) dimension = number of possible atomic (ionic) configurations dimension = size of velocity grid Kernel #1 Kernel #2 10 (25)

16. Routine Electron-impact ionization: Three-body recombination (via detailed equilibrium principle): 11 (25)

17. Effective charge model Hydrogen-like wave functions: Energy of a configuration: ALL CROSS-SECTIONS AND RATES CAN BE CALCULATED ANALYTICALLY 1 12 (25)

18. Atomic population probabilities P λ (t) Pulse parameters: duration: 40 fs; photon energy: a) 8 keV, b) 4 keV; shape: Gaussian; fluence: 10 4 phs/Å 2. Material: Si. NUMERICAL SIMULATION SET-UP 13 (25)

19. 14 (25) Pulse parameters: duration: 40 fs; photon energy: a) 8 keV, b) 4 keV; shape: Gaussian; fluence: 10 4 phs/Å 2. Material: Si. NUMERICAL SIMULATION SET-UP

20. Contribution of different channels 15 (25) Pulse parameters: duration: 40 fs; photon energy: a) 8 keV, b) 4 keV; shape: Gaussian; fluence: 10 4 phs/Å 2. Material: Si. NUMERICAL SIMULATION SET-UP

21. Atomic scattering factor evolution 16 (25) Pulse parameters: duration: 40 fs; photon energy: a) 8 keV, b) 4 keV; shape: Gaussian; fluence: 10 4 phs/Å 2. Material: Si. NUMERICAL SIMULATION SET-UP

22. Contents 1. Basics of X-ray free electron lasers (XFELs) 2. Irradiating a crystal with an XFEL pulse 3. XFEL-specific supplementary information for the phase retrieval procedure

23. Basics of Patterson method 17 (25) Electron density of the sample is the inverse Fourier transform of its structure (scattering) factor : From the X-ray diffraction experiment one can obtain the intensity distribution function (phase information is unknown): Patterson map = inverse Fourier transform of the intensity distribution function:

24. Basics of Patterson method 18 (25) N 2 peaks (N is the number of atoms in the unit cell) N of them overlap at the origin (corresponding to combination of every atom with itself); N(N-1) are distributed within the unit cell (corresponding to all other possible combinations between the atoms – these peaks can also overlap!)

25. Basics of Patterson method 18 (25) General idea of the method: find possible positions of heavy atoms; assume some trial value for the phase angle of each reflection (on the basis of positions of heavy atoms); calculate electron density and give sensible interpretation

26. Basics of Patterson method 19 (25) Interpretation is a tough challenge ! CAN ONE BRING SOME IMPROVEMENTS ?

27. General idea of resolution improvement 20 (25) Total scattering factor of the cell consisting of two types of atoms: Intensity distribution function:

28. General idea of resolution improvement 21 (25) In case of XFEL light source: Set of parameters of the XFEL pulse It is possible to select such a set, so that:,, remain unchanged because the periodical structure of the crystal does not change

29. General idea of resolution improvement 22 (25) 1 low-fluence + 2 high-fluence cases result in:

30. Numerical simulation Pulse parameters: duration: 5 fs (FWHM); photon energy: 7 keV; shape: Gaussian; fluence: (0.5÷1.0) * 10 4 phs/Å 2. Material: KF. NUMERICAL SIMULATION SET-UP 23 (25)

31. Numerical simulation Pulse parameters: duration: 5 fs (FWHM); photon energy: 7 keV; shape: Gaussian; fluence: (0.5÷1.0) * 10 4 phs/Å 2. Material: KF. NUMERICAL SIMULATION SET-UP 24 (25) L-atoms H-atoms

32. Numerical simulation Pulse parameters: duration: 5 fs (FWHM); photon energy: 7 keV; shape: Gaussian; fluence: (0.5÷1.0) * 10 4 phs/Å 2. Material: KF. NUMERICAL SIMULATION SET-UP 25 (25)

33. Discussion and outlook The approach shown above enables one to create a separate Patterson map for the group of heavy atoms, the ASF of which is sensitive towards the radiation of XFEL fs-pulses. This additional information can be implemented in direct methods of finding the phases that are based on the phase retrieval procedure. In the case of centrosymmetric crystals the present approach even allows one to clearly define the relative phase of the structure factors of light and heavy atoms (i.e., both the absolute value and its sign)

34. Acknowledgements Belarusian State University Prof. Dr. Ilya Feranchuk Dr. Andrei Benediktovitch Siegen University Prof. Dr. Ullrich Pietsch Dr. Dmitry Ksenzov Discussions Dr. Oleksandr Yefanov (CFEL, DESY) Dr. Semen Gorfman (Siegen University) Collaborators Oldenburg University Prof. Dr. Jutta Kunz

35. THANK YOU FOR YOUR ATTENTION !