Belarusian
State
University
Structural information extracted from the
diffraction of XFEL femtosecond pulses
in a crystal
Aliaksandr Leonau
The Actual Problems of Microworld Physics
Gomel, Belarus, July 27 - August 7, 2015
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
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
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)
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)
HOW MUCH IS IT ?
Angular
divergence
(solid angle Ω)
Photon
flux Φ
Brightness of XFEL ~ 1024 in [B] units
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XFEL – new generation of light sources
3 (25)
Basics of XFEL operation
Courtesy of SLAC / website: http://lcls.slac.stanford.edu/AnimationViewLCLS.aspx
4 (25)
XFEL projects
FLASH (2005) & FLASH II (2015)
LCLS (2009)
European XFEL (2016-2017)
SACLA (2011)
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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
“Diffraction before destruction”
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approach no
longer valid.
Neutze et al.,
Nature 406, 752-757 (2000)
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“Diffraction before destruction”
Recording of the complete diffraction pattern by a single shot is possible !
HOWEVER… There is NO problem !
One should use the pulse shorter
than the timescale of destruction…
…and…
… take into account evolution of the
sample on the timescale of the pulse
duration!
LET US HAVE DIFFRACTION BEFORE DESTRUCTION !
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Irradiating of a crystal with XFEL pulse
One can irradiate different types of samples (single atoms, molecules, clusters,…)
How about taking a single crystal (nanocrystal)?
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 !
We consider the processes that take place
during the passing of the XFEL pulse
through the crystal ( t < 100 fs )
The time scale we consider
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General dynamics scheme
8 (25)
Model to be considered
Total
system
EM
field
Bound
electrons
Free
electrons
Beyond the present
consideration
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Numerical simulation scheme
The system of master equations
(two coupled subsystems of integro-differential equations)
dimension = number of possible
atomic (ionic) configurations
Kernel
#1
dimension = size of velocity
grid
Kernel
#2
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Routine
Electron-impact ionization:
Three-body recombination (via detailed equilibrium principle):
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Effective charge model
Hydrogen-like wave functions:
ALL CROSS-SECTIONS AND RATES CAN BE CALCULATED ANALYTICALLY
Energy of a configuration:
1
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Atomic population probabilities Pλ(t)
NUMERICAL SIMULATION SET-UP
Material: Si. Pulse parameters: duration: 40 fs; photon energy: a) 8 keV, b) 4 keV;
shape: Gaussian; fluence: 104 phs/Å2.
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Free electron density 𝑓 𝑣, 𝑡 ∙ 𝑣 2
NUMERICAL SIMULATION SET-UP
Material: Si. Pulse parameters: duration: 40 fs; photon energy: a) 8 keV, b) 4 keV;
shape: Gaussian; fluence: 104 phs/Å2.
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Contribution of different channels
NUMERICAL SIMULATION SET-UP
Material: Si. Pulse parameters: duration: 40 fs; photon energy: a) 8 keV, b) 4 keV;
shape: Gaussian; fluence: 104 phs/Å2.
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Atomic scattering factor evolution
NUMERICAL SIMULATION SET-UP
Material: Si. Pulse parameters: duration: 40 fs; photon energy: a) 8 keV, b) 4 keV;
shape: Gaussian; fluence: 104 phs/Å2.
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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
Basics of Patterson method
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:
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Basics of Patterson method
N2 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!)
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Basics of Patterson method
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
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Basics of Patterson method
CAN ONE BRING SOME IMPROVEMENTS ?
Interpretation is a tough challenge !
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General idea of resolution improvement
Total scattering factor of the cell consisting of two types of atoms:
Intensity distribution function:
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General idea of resolution improvement
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
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General idea of resolution improvement
1 low-fluence + 2 high-fluence cases result in:
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Numerical simulation
NUMERICAL SIMULATION SET-UP
Material: KF. Pulse parameters: duration: 5 fs (FWHM); photon energy: 7 keV;
shape: Gaussian; fluence: (0.5÷1.0) * 104 phs/Å2.
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Numerical simulation
L-atoms
H-atoms
NUMERICAL SIMULATION SET-UP
Material: KF. Pulse parameters: duration: 5 fs (FWHM); photon energy: 7 keV;
shape: Gaussian; fluence: (0.5÷1.0) * 104 phs/Å2.
24 (25)
Numerical simulation
NUMERICAL SIMULATION SET-UP
Material: KF. Pulse parameters: duration: 5 fs (FWHM); photon energy: 7 keV;
shape: Gaussian; fluence: (0.5÷1.0) * 104 phs/Å2.
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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)
Acknowledgements
Collaborators
Belarusian State University
• Prof. Dr. Ilya Feranchuk
• Dr. Andrei Benediktovitch
Siegen University
• Prof. Dr. Ullrich Pietsch
• Dr. Dmitry Ksenzov
Oldenburg University
• Prof. Dr. Jutta Kunz
Discussions
• Dr. Oleksandr Yefanov (CFEL, DESY)
• Dr. Semen Gorfman (Siegen University)
THANK YOU
FOR YOUR ATTENTION !