Ultrafast Electron Diffraction from Molecules in the Gas Phase Martin Centurion
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Ultrafast Electron Diffraction from Molecules in the Gas Phase
Martin Centurion
University of Nebraska – Lincoln
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Outline
Recent progress in Gas Phase diffraction:• UED from aligned molecules.
Opportunities and challenges ahead:• Phase retrieval algorithms.• Pulse parameters
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Ultrafast Gas Phase Electron Diffraction
• Determine the 3D structure of molecules without crystallization.
• Investigate photoreactions of isolated molecules. Image intermediate states with femtosecond and sub-Angstrom resolution.
(groundbreaking picosecond experiments were done by the Zewail group at Caltech)
Structure and Dynamics of Isolated Molecules
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( ) ( ) ( ) tot at molI s I s I s
4 sin( / 2)s
sin( )( ) ij
mol ij i jij
s rI s F f f
s r
rij are the interatomic distances
Molecular Scattering
Total Scattering
Gas Electron Diffraction
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( ) mol
at
s IsM sI
Theory
Experiment
Modified scattering intensity
I-I
I-…
F-FC-F
Azimuthally averaged sM(s)
Radial Distribution function
Sine Transform
Gas Electron Diffraction
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Experiment
Theory
C2F4I2
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Gas Electron Diffraction
Advantages• High Scattering Cross Section.• Compact Setup.
Limited by random orientation of molecules:• 1D Information.• Structure is retrieved by iteratively comparing the data
with a theoretical model.• Low contrast diffraction patterns.
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Non-adiabatic (field-free) alignment
Diffraction from Aligned Molecules
Aligned molecules:3D structure accessible
Random orientation:limited to 1D information
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Fourier-Hankel Transform1,2
Perfect alignment — <cos2α> = 1
α
Partial alignment — <cos2α> = 0.50
From diffraction pattern to structure
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z
r
Fourier-Hankel Transform1,2
1P. Ho et. al. J. Chem. Phys. 131, 131101 (2009). 2D. Saldin, et. al. Acta Cryst. A66, 32–37 (2010).
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100 µm diameter interaction regionOverall resolution 850 fs(first gas phase experiment with sub-ps resolution)
Experiment – Target Interaction Region
Supersonic seeded gas jet (helium)
electron pulse
alignment laser
CF3I
Simple molecule with 3D structure
Target:
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Experimental Setup
Imaging Detector
Turbo pump
Diffusion pump
40fs, 1mJ, 800nm
Magnetic Lens Gas NozzleCathodeA
nodeThird Harmonic generation
Electron pulses• 25 keV• 500 fs • 2000 electrons/pulse
Alignment laser pulses• 800 nm• 300 fs• 2.2 x 1013 W/cm2
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Δ 𝑠𝑀 (𝑡 )=𝑠𝑀 (𝑡 ) −𝑠𝑀𝐺𝑟𝑜𝑢𝑛𝑑
5 min integration timeLaser
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Revivals can also be measured
Data collection Revival
Non-zero background after initial alignment
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Experimental Data
Δ 𝑠𝑀
60° projection
𝑠𝑀
No laser
random orientation
Δ 𝑠𝑀
electrons
Laser polarization
90° projection
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Theory – Reconstruction
Diffraction with Perfect Alignment
Molecular StructurePhase retrieval algorithm
Diffraction with Partial Alignment
There is no algorithm for partial alignment
Molecular Structure
New path
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Perfect alignment Perpendicular
Partial alignment Any orientation
Retrieving Perfect Alignment from Multiple Diffraction Patterns
• Transformation requires knowledge of the degree of alignment (angular distribution), but not the structure.
• There is no inverse transformation.
Rotation and averaging
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Combine multiple diffraction patterns to build the pattern corresponding to perfect alignment
Partial alignment 90°
Retrieving Perfect Alignment from Multiple Diffraction Patterns
60° Random orientation
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partial aligned
uniformguess
Difference with data
defines error
error locally minimized?
no
reconstruct object
Genetic Algorithm for Retrieving Perfect Alignment
smallchange
yes
error reduced?no
yes
retain change
discard change
Rotation and averaging
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Retrieval Result from Data
100k iterations2 hours
The algorithm also optimizes for the degree of alignment.
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Reconstruction of CF3I
Structure from experimental data
Experiment Literature
rCI 2.19±0.07Å 2.14 ÅrFI 2.92±0.09Å 2.89 ÅI-C-F Angle 120±90 1110
C. J. Hensley, J. Yang and M. Centurion, Phys. Rev. Lett. 109, 133202(2012)
r (Å)
z (Å)
The image is retrieved form the data without any previous knowledge of the structure
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Outline
Recent progress in Gas Phase diffraction:• 3D structure determination with aligned
molecules.
Opportunities and challenges ahead:• Phase retrieval algorithms.• Pulse parameters
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Work in progress: Modified iterative phase retrieval algorithm for molecules of unknown symmetry
Simulated pattern in cylindrical coordinates
2D object
Inputs: Diffraction PatternConstraints applied on object plane.Algorithm: Fienup Hybrid Input-Output + Flip-Charge
3D objects
1D. Starodub, J. Spence, D. Saldin, Proc. SPIE Conf., 7800, 7800 (2010).2D. Saldin, et. al. Acta Cryst. A66, 32–37 (2010).
Benzotrifluoride (C7H5F3)
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Temporal Resolution
Ideal parameters:Pulse duration: ~ 20 fsCharge: as high as possible
With RF Gun: 100 fs, 1 million e
Group velocity mismatchLaser with a tilted pulse front
System was purchased from AccTec in Eindhoven
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Summary
• 3D imaging of molecules possible with laser-aligned molecules.
• Molecular dynamics can be probed in a field free environment.
• We are working to apply this method to larger molecules.
• RF gun will greatly improve the experimental conditions.
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Acknowledgements
Funding• Department of Energy, Basic Energy Sciences• Air Force Office of Scientific Research
Group Members• Chris Hensley (postdoc)• Jie Yang (grad student)• Ping Zhang (postdoc)• Omid Zandi (grad student)• Walter Bircher (undergrad)
Former members• Cory Baumgarten
(undergrad)• James Ferguson
(undergrad)