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Limits of Coherent X-ray Diffraction for Imaging Small Crystals. Ian Robinson Ivan Vartanyants Franz Pfeiffer Mark Pfeifer Garth Williams. Department of Physics University of Illinois Second International Workshop on Noncrystallographic Phase Retrieval. Outline. Nanocrystal Shapes

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Limits of coherent x ray diffraction for imaging small crystals
Limits of Coherent X-ray Diffraction for Imaging Small Crystals

  • Ian Robinson

  • Ivan Vartanyants

  • Franz Pfeiffer

  • Mark Pfeifer

  • Garth Williams

Department of Physics

University of Illinois

Second International Workshop on

Noncrystallographic Phase Retrieval

I. K. Robinson, Phasing Workshop, June 2003


Outline
Outline Crystals

  • Nanocrystal Shapes

  • Vortices During Phasing

  • How small can we go?

  • Future Directions of CXD

I. K. Robinson, Phasing Workshop, June 2003


Lensless x ray microscope
Lensless X-ray Microscope Crystals

I. K. Robinson, Phasing Workshop, June 2003



SEMS Crystals

  • Au blanket film

  • Quartz substrate

  • Annealed at 950°C for 70 hrs.

I. K. Robinson, Phasing Workshop, June 2003


Micron sized gold crystal 111 bragg reflection
Micron-sized gold crystal: Crystals(111) Bragg reflection

I. K. Robinson, Phasing Workshop, June 2003


Imaging of Lattice Strains Crystals

I. K. Robinson, Phasing Workshop, June 2003


Symmetrized data and two best fits chisq 0 0005
Symmetrized Data Crystalsand two best fitsChisq=0.0005

I. K. Robinson, Phasing Workshop, June 2003


2d reconstructions chisquare 0 0005
2D Reconstructions Crystalschisquare = 0.0005

I. K. Robinson, Phasing Workshop, June 2003


3d diffraction method
3D Diffraction Method Crystals

kf

Q=kf - ki

ki

I. K. Robinson, Phasing Workshop, June 2003


3d diffraction data 1 micron au crystal
3D Diffraction Data Crystals1 micron Au crystal

* Center is Symmetric *

I. K. Robinson, Phasing Workshop, June 2003


11 Crystals1

111

Slices through plan view SEM:

I. K. Robinson, Phasing Workshop, June 2003


Generic error reduction method
Generic “Error Reduction” method Crystals

J. R. Fienup Appl. Opt. 21 2758 (1982)

R. W. Gerchberg and W. O. Saxton Optik 35 237 (1972)

I. K. Robinson, Phasing Workshop, June 2003


Real space constraints in crystallograhy r p millane j opt soc am a 13 725 1996
Real-space Constraints in Crystallograhy CrystalsR. P. Millane, J. Opt. Soc Am. A 13 725 (1996)

  • ‘Positivity’ constraint (Sayre)

  • Finite support, molecular envelope

  • Solvent flattening

  • Molecular replacement

  • Non-crystallographic symmetry

  • Non-uniqueness is ‘pathologically rare’ (d>1)

I. K. Robinson, Phasing Workshop, June 2003


Phasing using g s algorithm

cut off “support” Crystals

Phasing using G-S Algorithm

I. K. Robinson, Phasing Workshop, June 2003


Convergence trajectory
Convergence Trajectory Crystals

wide support

narrow support

I. K. Robinson, Phasing Workshop, June 2003


Alternation of er and hio helps to avoid stagnation
Alternation of ER and HIO CrystalsHelps to avoid stagnation

I. K. Robinson, Phasing Workshop, June 2003


Incomplete reconstruction can be striped 0 5 micron pb crystal on sio 2 substrate
Incomplete Reconstruction can be Striped Crystals0.5 micron Pb crystal on SiO2 substrate

I. K. Robinson, Phasing Workshop, June 2003


Stripes caused by vortices vortex pairs separated by inverse of stripe spacing
Stripes caused by “Vortices” CrystalsVortex pairs separated by inverse of stripe spacing

I. K. Robinson, Phasing Workshop, June 2003


Result of patching in 2d
Result of “Patching” in 2D Crystals

I. K. Robinson, Phasing Workshop, June 2003


3d vortices form pairs of loops
3D Vortices Form Pairs of Loops Crystals

I. K. Robinson, Phasing Workshop, June 2003


Vortices are a cause of stagnation during error reduction
Vortices are a Cause of Stagnation during Error Reduction Crystals

Lauren Perskie, UIUC Summer student

Number of vortices / 104

Chisquare

I. K. Robinson, Phasing Workshop, June 2003


Cxd beamline at aps sector 34
CXD Beamline at APS Sector 34 Crystals

I. K. Robinson, Phasing Workshop, June 2003



Roller blade slits in uhv
Roller-Blade Slits in UHV Crystals

I. K. Robinson, Phasing Workshop, June 2003


Lensless x ray microscope1
Lensless X-ray Microscope Crystals

I. K. Robinson, Phasing Workshop, June 2003


Cxd from silver nanocubes
CXD from Silver Nanocubes Crystals

Yugang Sun and Younan Xia, Science 298 2177 (2003)

I. K. Robinson, Phasing Workshop, June 2003


170nm silver nanocubes
170nm Silver Nanocubes Crystals

I. K. Robinson, Phasing Workshop, June 2003


Structure in yoneda peak grazing exit diffraction from a 1000a au polycrystalline film
Structure in “Yoneda” Peak CrystalsGrazing-exit diffraction from a 1000A Au polycrystalline film

Specular (αf ~ αi)

αf ~ αc

αf ~ 0


Competitive grain growth c v thompson ann rev mat sci 30 159 2000
Competitive Grain Growth CrystalsC. V. Thompson, Ann. Rev. Mat. Sci. 30 159 (2000)

αf~αc

αf<αc

I. K. Robinson, Phasing Workshop, June 2003


Angle series 0 01 steps
Angle series, 0.01° steps Crystals

I. K. Robinson, Phasing Workshop, June 2003


Low dislocation Crystalsdensity GeSi filmsThickness close to critical thicknessDislocations aggregate at interface and glide to surface along {111}T. Spila, UIUC Thesis

I. K. Robinson, Phasing Workshop, June 2003



Ge x si 1 x film diffraction
Ge CrystalsxSi1-x Film Diffraction

  • 202 Bragg Peak

  • 2800A film

  • 2° incidence angle

  • 8.5 keV

  • 20μm ×40μm beam

  • onto KB mirror

  • 1μm ×1μm focus

  • 0.5μm sample steps

  • APS 34-ID-C

I. K. Robinson, Phasing Workshop, June 2003


Conclusions and outlook
Conclusions and Outlook Crystals

  • Inversion of CXD by ER-HIO methods

  • Internal structure of Au Nanocrystals

  • Preservation of coherence upon focussing

  • Smallest size now down to 170nm

  • New CXD-Yoneda geometry

  • Dislocation strain structure may be possible

I. K. Robinson, Phasing Workshop, June 2003


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