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Colloidal Crystals Structure and Dynamics Colloidal Crystals Structure and Dynamics Ivan Vartaniants DESY, Hamburg, Germany National Research University, ‘MEPhI’, Moscow, Russia Ivan Vartaniants | APS, Argonne, February 3, 2016 | Page 1 DESY Coherent X-ray Scattering and Imaging Group at DESY Present members: Former members: • S. Lazarev • I. Zaluzhnyy • A. Zozulya (now@PETRA III) • I. Besedin • M. Rose • A. Mancuso (now@XFEL) • P. Skopintsev • O. Gorobtsov • O. Yefanov (now@CFEL) • D. Dzhigaev • N. Mukharamova • R. Dronyak • J. Gulden (now@FH-Stralsund) • U. Lorenz (now@University of Potsdam) • A. Singer (now@UCSD) • R. Kurta (now@XFEL) • A. Shabalin (now@CFEL) Ivan Vartaniants | APS, Argonne, February 3, 2016 | Page 3 High resolution microscopy Ivan Vartaniants | APS, Argonne, February 3, 2016 | Page 4 High resolution electron microscopy Atomic structure of the Au68 gold Atomic resolution imaging of nanoparticle determined by electron graphene microscopy. M. Azubel, et al., Science 345, 909 (2014) A. Robertson and J. Warner, Nanoscale, (2013),5, 4079-4093 Simulated HREM images for GaN[0001] From: Wikipedia From: Web Images From: Web Images Can we develop x-ray microscope with atomic resolution? It does not work with conventional approach due to the lack of atomic resolution X-ray optics Can coherent x-ray diffraction imaging be the way to go? What is Coherence? Coherence is an ideal property of waves that enables stationary interference Soap bubble wikipedia.org Whether X-rays are coherent waves? Max von Laue Nobel Prize in Physics, 1914 W. Friedrich, P. Knipping, M. von Laue, Ann. Phys. (1913) 100 years later LCLS FLASH H. Chapman et al., A. Mancuso et al., Nature (2011) New J. Physics (2010) Coherence LCLS 2 λ LL=λ /(2∆ λ) LT=( R/ 2 D) Longitudinal Coherence Length Transverse Coherence Length Als-Nielsen & McMorrow (2001) Coherence properties of 3rd generation synchrotron sources I.A. Vartanyants & A. Singer “Coherence Properties of Third-Generation Synchrotron Sources and Free-Electron Lasers”, Chapter in: Handbook on Synchrotron Radiation and Free-Electron Lasers Coherent volume (PETRA III, E=12 keV) LV LH LL Coh. Flux Raw Undulator 260 µm 40 µm 0.02 µm 6×1012 ph/s Low-β DCWe Si (111) expect 260 aboutµm two40 µm orders 0.5 of µm magnitude 1.8×1011 ph/s Lowmore-β coherent flux at diffraction limited Raw Undulator 280 µm sources10 µm 0.02 µm 7×1011 ph/s High-β DC Si (111) 280 µm 10 µm 0.5 µm 2×1010 ph/s High-β LV LL 13 LH Coherent X-ray Diffraction Imaging Lensless X-ray Microscopy Partially Coherent Coherent beam X-rays sample electrons CCD neutrons Diffraction Phase Optics: Limited Retrieval Microscope Coherent X-ray Diffraction Imaging in forward direction Kinematical approximation: = d −∙ � qz=0 ( ) , = , , d d − + � Mancuso et al. J. Biotechnol. 149 229 (2010) ( , ) = , , d � Small-angle scattering CDI Inverse Fourier transform: Non-crystallographic samples 1 ( , ) = ( , ) ( ) d d Uniform distribution of (2 ) + electron density 2 � Unfortunately, phases of A(qx,qy) are not known!!! Ivan Vartaniants | APS, Argonne, February 3, 2016 | Page 15 Phase retrieval Ivan Vartaniants | APS, Argonne, February 3, 2016 | Page 16 Iterative phase retrieval algorithm FFT sk(x) Ak(q) Real Space Constraints Reciprocal Space Constraints s'k(x) A'k(q) FFT-1 Real space constraints: Reciprocal space constraint: use all a priori knowledge: Ak ( q ) → Iexp( q ) •finite support •positivity R.W.Gerchberg & W.O. Saxton, Optic (1972) 35, 237 •… J.R. Fienup, Appl Opt. (1982) 21, 2758 V. Elser, J. Opt. Soc. Am. A (2003) 20, 40 14 Example of reconstruction (O.Yefanov) FFT-1 replace apply amplitudes support FFT Bragg Coherent X-ray Diffraction Imaging (Bragg CXDI) Ivan Vartaniants | APS, Argonne, February 3, 2016 | Page 19 Coherent X-ray Diffraction Imaging Lensless X-ray Microscopy CCD Partially Coherent 2θB Coherent beam X-rays sample electrons neutrons Diffraction Phase Optics: Limited Retrieval Microscope Coherent Scattering on Au Crystals •4 micron Au nanocrystal •Coherent X-ray Diffraction •Measurement at APS sector 33-ID (UNICAT) 21 I. Robinson, I. Vartanyants, et al., PRL (2001), 87, 195505 Sensitivity to strain = = − ∙ ∙ Courtesy to I. Robinson Bragg CDI Kinematical approximation: = d ρ(r) – periodic electron density in crystal −∙ � Phase, or Scattered amplitude near Bragg peak: Shape function: projected strain field in crystal: ( ) 1, = d = = ( ) 0, ℎ −∙ −∙ ℎ ∈ Ω � � ∙ ∉ Ω Fh – structure factor = q - h Crystallographic samples, uniform distribution of strain I.A. Vartanyants & I.K. Robinson, JPCM 13, 10593 (2001); I.A. Vartanyants & O.M. Yefanov, in the book:Ivan X Vartaniants-ray Diffraction | APS, Argonne, February Modern 3, 2016 | ExperimentalPage 23 Techniques. (2015), pp. 341-384. 3D mapping of a deformation field inside a nanocrystal SEM Diffraction patterns from Pb Strain field shown by color gradient nanocrystal measured around Resolution: 40÷50 nm (111) Bragg peak M. Pfeifer, et al., Nature, 442, 63 (2006), R. Harder, et al., PRB B 76, 115425 (2007). Coherent Diffractive Imaging Mancuso et al. J. Biotechnol. 149 229 (2010) Pfeifer et al. Nature. 442 63 (2006) Bragg CDI Small-angle scattering CDI Crystallographic samples Non-crystallographic samples Uniform strain field Uniform electron density Ivan Vartaniantsdistribution | APS, Argonne, February 3, in2016 | the Page 25 sample of the sample Coherent imaging with atomic resolution J. Gulden, et al., ''Imaging of Nanocrystals with Atomic ResolutionIvan Vartaniants Using | APS, HighArgonne,- FebruaryEnergy 3, 2016 Coherent | Page 26 X- rays'', XRM-2010 Proceedings, AIP Conf. Proc. 1365, 42-45 (2011) Theory If several Bragg peaks are measured simultaneously: = d = ( ) ( ) ( ) −∙ � ∙ ∙ ∞ ⨂ Here: B(q) – envelope function; (2 ) = ( ) F(q) – structure factor of a unit cell; 3 s(q) – FT of the shape function ∞ � − ℎ Inverse Fourier transform of this relationship: = ( ) ( ) ( ) ⨂ ⨂ ∞ ∙ Here: b(r) – FT of the envelope function B(q); = ; ρuc(r) – electron density of a unit cell; ∞ s(r) – shape function = �+ −+ 11 22 33 I.A. Vartanyants & O.M. Yefanov, in the Ivanbook: Vartaniants X- ray | APS, Diffraction Argonne, February 3, 2016Modern | Page 27 Experimental Techniques. (2015), pp. 341-384. Theory This electron density is peaking at the regular positions of the unit cell due to the function ρ∞(r) and has an overall shape of the sample s(r). Most importantly, it contains the position of the atoms in the unit cell due to the reconstruction of the electron density function of a unit cell ρuc(r). This means the following: If the continuous intensity distribution around several Bragg peaks will be measured simultaneously and phase retrieval methods will be applied to get the phase, then, in principle, the electron density with atomic resolution will be obtained. I.A. Vartanyants & O.M. Yefanov, in the Ivanbook: Vartaniants X- ray | APS, Diffraction Argonne, February 3, 2016Modern | Page 28 Experimental Techniques. (2015), pp. 341-384. CXDI using high energy coherent X-rays E=100 keV Reconstruction Model J. Gulden, et al., ''Imaging of Nanocrystals with Atomic Resolution Using High-Energy Coherent X- rays'', XRM-2010 Proceedings, AIP Conf. Proc. 1365, 42-45 (2011) CXDI using high energy coherent X-rays F=1012 photons F=1013 photons F=1014 photons F=1015 photons Pd nanocrystal 10 nm size An excellent scientific goal for diffraction limited storage ring? First realization of these ideas with photonic (colloidal) crystals Photonic crystals Photonic crystals in nature Artificial photonic crystals Photonic band gap materials https://www.theochem.kth.se/research/phot_crys Ivan Vartaniants | APS, Argonne, February 3, 2016 | Page 33 t/Photonic_Crystals.html Colloidal crystals grown by self-organization Ivan Vartaniants | APS, Argonne, February 3, 2016 | Page 34 Growth of the colloidal crystal film Vertical deposition method A B C = RHCP A B Ivan Vartaniants | APS, Argonne, February 3, 2016 | Page 35 J-M. Meijer, et. al. Langmuir (2012), 28, 7631−7638. Coherent x-ray imaging of defects in colloidal crystals J. Gulden, et al., Phys. Rev. B 81, 224105 (2010) European Synchrotron Radiation Facility ESRF Measurements at azimuthal angle φ = 0° 4 m Experimental conditions (ID06, ESRF): • Energy: E=14 keV • Pinhole size 6.9 μm • Sample detector distance: 3.96 m • Detector pixel size: 9 μm • Detector size: 4005×2671 pixels Ivan Vartaniants | APS, Argonne, February 3, 2016 | Page 38 J. Gulden, et al., Phys. Rev. B 81, 224105 (2010) Measurements at azimuthal angle φ = 0° Diffraction pattern with Results of reconstruction from the subtracted pinhole this diffraction pattern Ivan Vartaniants | APS, Argonne, February 3, 2016 | Page 39 Measurements at azimuthal angle φ = 35° Experimental conditions (ID06, ESRF): • Energy: E=14 keV • Pinhole size 6.9 μm • Sample detector distance: 3.96 m • Detector pixel size: 9 μm • Detector size: 4005×2671 pixels Measurements at azimuthal angle φ = 35° Diffraction patternFor with the firstResults time of reconstruction from the subtracted pinhole this diffraction pattern defect coreStacking fault defect imaged was directly imaged using coherent Ivanx Vartaniants-rays | APS, Argonne, February 3, 2016 | Page 41 Extension to 3D Crystallography with coherent X-rays J. Gulden, et al., Optics Express, 20(4) 4039 (2012) A. Shabalin, et al., (2015)Ivan (inVartaniants preparation) | APS, Argonne, February 3, 2016 | Page 42 PETRA III Structural evolution of colloidal crystal films in the vicinity of the melting transition Ivan
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