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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
  • 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

I. K. Robinson, Phasing Workshop, June 2003

slide5
SEMS
  • 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:(111) Bragg reflection

I. K. Robinson, Phasing Workshop, June 2003

slide7

Imaging of Lattice Strains

I. K. Robinson, Phasing Workshop, June 2003

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

I. K. Robinson, Phasing Workshop, June 2003

2d reconstructions chisquare 0 0005
2D Reconstructionschisquare = 0.0005

I. K. Robinson, Phasing Workshop, June 2003

3d diffraction method
3D Diffraction Method

kf

Q=kf - ki

ki

I. K. Robinson, Phasing Workshop, June 2003

3d diffraction data 1 micron au crystal
3D Diffraction Data1 micron Au crystal

* Center is Symmetric *

I. K. Robinson, Phasing Workshop, June 2003

slide12

111

111

Slices through plan view SEM:

I. K. Robinson, Phasing Workshop, June 2003

generic error reduction method
Generic “Error Reduction” method

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 CrystallograhyR. 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”

Phasing using G-S Algorithm

I. K. Robinson, Phasing Workshop, June 2003

convergence trajectory
Convergence Trajectory

wide support

narrow support

I. K. Robinson, Phasing Workshop, June 2003

alternation of er and hio helps to avoid stagnation
Alternation of ER and HIOHelps 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 Striped0.5 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”Vortex pairs separated by inverse of stripe spacing

I. K. Robinson, Phasing Workshop, June 2003

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

I. K. Robinson, Phasing Workshop, June 2003

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

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

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

I. K. Robinson, Phasing Workshop, June 2003

roller blade slits in uhv
Roller-Blade Slits in UHV

I. K. Robinson, Phasing Workshop, June 2003

lensless x ray microscope1
Lensless X-ray Microscope

I. K. Robinson, Phasing Workshop, June 2003

cxd from silver nanocubes
CXD from Silver Nanocubes

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

I. K. Robinson, Phasing Workshop, June 2003

170nm silver nanocubes
170nm Silver Nanocubes

I. K. Robinson, Phasing Workshop, June 2003

structure in yoneda peak grazing exit diffraction from a 1000a au polycrystalline film
Structure in “Yoneda” PeakGrazing-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 GrowthC. 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

I. K. Robinson, Phasing Workshop, June 2003

slide32

Low dislocationdensity 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
GexSi1-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
  • 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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