Fundamentals of X ray Photon Correlation Spectroscopy

Transcription

1 Fundamentals of X ray Photon Correlation Spectroscopy Asst. Prof. Oleg Shpyrko University i of California i San Diego website: oleg.ucsd.edu

2 X-ray Revolution (Future is Bright!) incandescent light sources (incoherent) lasers (coherent)

3 Brightness/Brilliance: Bending magnet B~ I (I=ring current) FLASH >10 8 Wiggler B~ I*N (N=number of magnets) Undulator B~ I*N 2 (N=number of magnets) ~0.01% coherent X-ray free electron laser B~ I 2 *N 2, 100% coherent

4 Free Electron X-ray Lasers for soft & hard X-rays LCLS, XFEL, FLASH, BESSY-FEL # Photons in coherence volume Brightness λ 3 Femtosecond x-ray yp pulses ( fs) Extremely high brilliance and flux (10 13 /pulse) Transverse coherence FLASH >10 8

5 Laser Speckle

6 When was the first visible light speckle observed?

7 Newton, 1730: "For the Air through which we look upon the Stars, is in perpetual Tremor... But, these Stars do not twinkle when viewed through... large apertures. The only Remedy is a most serene and quiet Air, such as may perhaps be found on the tops of the highest Mountains above the Grosser Clouds. Sir Isaacs Newton, Opticks (1730) Star, speckle (twinkle): Planet, motionless: I. Newton: Opticks, 1730 (Reprinted by Dover Press, New York 1952) Book I, Part I, Prop. VIII, Prob. II., 1730).

8 Speckle in astronomy: a nuisance or resolution enhancement? scattering through randomly inhomogeneous media (Earth s atmosphere) distorts the star ss image speckle contains resolution information limited by the telescope in pre Hubble days, 5m Mt. Palomar telescope has a resolution of 0.02 arcsec time averaged image has resolution of ~ 1 arcsec time resolved speckle helps to bring it to diffraction limit of the telescope dynamic speckle of a star image short term exposure of binary star

9 Exner, 1877 In 1877, Exner sketched the radially granular speckle pattern that he observed within the biht bright central Fraunhoffer ring. K. Exner: Sitzungsber. Kaiserl. Akad. Wiss. (Wien) 76, 522 (1877). K. Exner: Wiedemanns. Ann. Physik 9, 239 (1880).

10 von Laue, 1914 Photograph by M. von Laue of the diffraction pattern produced by a glass plate covered with lycopodium powder. Light from a carbon arc lamp was passed through a prism and the region nm was used to illuminate the sample M. von Laue: Sitzungsber. Akad. Wiss. (Berlin) 44, 1144 (1914).

11 Brief Review - X-ray Speckle, the early years: Speckle of (001) Cu3Au peak Speckle of the Fe3Al (1/2,1/2,1/2) M. Sutton et al., The Observation of Speckle by Diffraction with Coherent X- rays Nature 352, (1991). super-lattice reflection showing frozen-in disorder. d b) Zoom of the central region in a) where the speckle structure is obvious. Grubel et al., ESRF News (1995)

12 First X-ray Speckle: M. Sutton et al., Nature 352, (1991) A. L. Schawlow Laser Light" Scientific American, 219 (3), p. 120, (1968)

13 Brightness is coherence: (i (simplified lifid version) Transverse coherence lengths for a source of size σ x, σ y At distance R from source: ξx = λ R 2πσx ξy = λ R 2πσx σ x, σy R coherent ξ x, ξyξ Brightness B is defined as number of photons, per second, per solid angle, per unit area I coh = 2 π Β σ x σ y ξ x ξ y = 2 R 2 λ Β 4

14 12 orders of magnitude In 6 decades Moore s law for CPU chips

15 Brilliance is Coherence XFEL, 12 orders of magnitude In 6 decades 18 orders of magnitude In 5 decades!

16 X-ray Photon Correlation Spectroscopy (XPCS): 10 μm t t + Δt t + 4Δt t+3δt t + 2Δt speckle pattern t t + Δt t + 2Δt t + 3Δt t + 4Δt O. G. Shpyrko et al., Nature 447, 68 (2007)

17 Slide courtesy of Zhang Jiang

18 XPCS and other spatio-temporal probes S(q, ω) map: Freq quency [H Hz] Raman Brillouin laser PCS Length Scale [Å] INS IXS Spin-Echo XPCS Scattering Vector Q [Å -1 ] Energy [e ev] XPCS is the extension of dynamic light scattering probe (laser PCS) Pros: Smaller lengthscales Non-transparent materials Charge, Spin, Chemical and atomic structure sensitivity Cons: Need fully coherent x-ray sources!

19 XPCS and other spatio temporal probes S(q, ω) map: Length Scale [Å] INS Freq quency [H Hz] Raman Brillouin laser PCS IXS Spin-Echo??? XPCS Energy [e ev] Scattering Vector Q [Å -1 ]

20 Measure: intensity autocorrelation function, g 2 (q, t) Intensity autocorrelation function, g 2 (q, t) : g I( q, τ) I( q, τ + t) 2 ( q, t) = = 1+ β f ( q, t) 2 I (q, q τ ) τ τ τ 2 Intermediate Scattering Function (ISF): f S( q, t) ( q, t ) = = g ( t ) = exp[ 0 α S( q,0) τ 1 ( t τ ) ] β: speckle contrast (Siegert factor) β p ( g ) α: stretching exponent; often α 1 τ 0 : relaxation time constant

21 Signal to Noise

22 Selected highlights: Applications of XPCS Diffusion i of colloids: Liquid Crystal membranes S. B. Dierker et al., PRL 75, 449 (1995) A. C. Price et al., PRL 82, 755 (1999) T. Thurn-Albrecht et al., PRL 77, 5437 A. Fera et al., PRL 85, 2316 (2000) (1996) I. Sikharulidze et al. PRL 88, L. B. Lurio et al., PRL 84, 785 (2000) (2002) D. Pontoni et al., PRL 90 (2003) Complex Fluids: polymer blends, clays S. G. J. Mochrie et al., PRL 78, 1275 (1997) D. Lumma et al., PRL 86, 2042 (2001) P. Falus et al., PRL 94, (2005) P. Falus et al., PRL 97, (2006) R. Bandyopadhyay et al., PRL 93, (2004) Capillary fluctuations of liquid surfaces H. Kim et al., PRL 90, (2003) Z. Jiang et al., PRL 98, (2007) A. Madsen et al., PRL 92, (2004) C. Gutt et al., PRL 91, (2003) S. Streit, PRL 98, (2007) Charge-,Spin-, Orbital- ordered domains O. G. Shpyrko et al., Nature 447, 68 (2007) J. Turner et al., New J. Phys. 10, (2008) Non-equilibrium dynamics, Binary alloys: A. Fluerasu et al., PRL 94, (2005) S. Bauer et al., PRL 74, 2010 (1995) M. Sutton et al., Opt. Exp. (2003) Metal/polymer nano-composite S. Streit et al., PRL 98, (2007) S. Narayanan et al., PRL 98, (2007) Phasons in Quasicrystals: S. Francoual, et al., PRL 91, (2003)

23 Most recent XPCS results: Particle diffusion in glassy polymers: H. Guo et al., PRL 102, (2009) Colloidal diffusion near surface: A. Duri et al., PRL 102, (2009) Atomic-scale diffusion in binary alloys: M. Leitner et al., Nature Mat. 8, (2009) Liquid Surface Fluctuations in Polymers, Supercooled liquids Z. Jiang et al., PRL 101, (2008) Y. Chushkin et al EPL (2008) Reviews: M. Sutton, A review of X-ray intensity fluctuation spectroscopy, Comptes Rendus Physique 9, (2008) Gerhard Grübel, X-Ray Photon Correlation Spectroscopy at the European X- Ray Free-Electron Laser (XFEL) facility, Comptes Rendus Physique 9, no. 5-6, (2008) K. A. Nugent, Coherent methods in the X-ray sciences, Advances in Physics 59, 1-99 (2010)

24 Scattering geometry for XPCS Small Angle X-ray Scattering (SAXS) Usually for soft matter: colloids, diblock polymers Surface Scattering (Diffuse, Reflectivity, ty, GISAXS) Polymers, liquid surfaces, thin films, patterned films High angle (Bragg) diffraction Binary Alloys Charge, Orbital, Spin ordered materials Phason dynamics in quasicrystals Lattice defects, strain Others

25 Technical Requirements for XPCS: Coherence (slits/pinhole μm size), 3+ rd generation synchrotrons Resolving the speckle (no need for oversampling). Usually ~10-20 μm detector at 1-2m away from the sample works High efficiency, small pixel size, need many speckles/pixels p direct detect area detector CCD, APD array Detector readout often limits time resolution Beamline stability

26 Binary Alloys: Cu 3 Au 3 Sutton et al., Nature 1991, PRL 2005 Fe 3 Al Brauer et al., PRL 1995 Mocuta et al., Science 2002 CoGa AlLi AlZn AlAg CoGa, AlLi, AlZn, AlAg Stadler et al

27 Equilibrium: Non-equilibrium: A. Fluerasu et al., Phys. Rev. Lett. 94, (2005) M. Sutton et al., Opt. Exp. (2003) Quenched Cu 3 Au

28 Non Equilibrium (aging) XPCS, cont d: CuPd binary alloy: Ludwig et al., PRB 72, (2005)

29 Charge and Spin-ordered systems: Nb 3 Se (classic CDW system) Sutton, Brock, Thorne et al., J. Phys. 2002, PRB 2001 Cr (CDW/SDW Antiferromagnet) Cr (CDW/SDW Antiferromagnet) O. G. Shpyrko et al., Nature 2007

30 Charge, Spin and Lattice order parameters: Real Space: Spin Density Reciprocal Space: Charge density Charge Density Wave satellites Spin Density Wave satellites Bragg peak

31 Microscopic Magnetic Domains in Chromium: Scanning X-ray Microscopy: [0, 0, 2-2δ] Charge-density wave satellite bulk probe (micron-sized penetration depth) spin, charge, lattice and chemical sensitivity 10 μm

32 Magnetic domain wall fluctuations in real and reciprocal space: 2 λ Real Space: elemental l switching block, w/ volume (λ/2) 3, λ=3-4 nm Momentum Space: transfer of intensity i from satellites 1 to 2 due to switch

33 Autocorrelation data: Bragg speckle O. G. Shpyrko et al., Nature 447, 68 (2007)

34 Charge and Spin-ordered systems: Ho films (helical AFM) Koning, Goedkoop, (2007) Pr 05 Ca 05 MnO 3 (Charge- & Orbital-Order) Pr 0.5 Ca 0.5 MnO 3 (Charge & Orbital Order) Turner, Hill, Kevan et al., arxiv (?) 2008 Nelson, Hill, Livet et al., PRB 2002

35 Spin-ordered systems: Ho thin films (helical l Antiferromagnet) Koning, Goedkoop et al. 52K 64K 71 K

36 Liquid Surface XPCS Thin films, free surfaces: C. Gutt et al., PRL 91, (2003) H. Kim et al., PRL 90, (2003) A. Madsen et al., PRL 92, (2004) Z. Jiang et al., PRL 98, (2007) Z. Jiang et al., PRL 101, (2008) Y. Chushkin et. al., EPL (2008) A. Duri et al., PRL 102, (2009) Liquid Crystal Films: A. C. Price et al., PRL 82, 755 (1999) A. Fera et al., PRL 85, 2316 (2000) I. Sikharulidze et al. PRL 88, (2002) Will be discussed in more details tomorrow

37 Capillary Waves on Liquid Surfaces Chicago Sunset Capillary wave model sharp step-like profile decorated d with height variations due to thermal excitations. See, for example: Buff, Lovett, and Stillinger. Phys. Rev. Lett. 15, 621 (1965)

38 XPCS studies of complex fluids: colloidal glasses, diblock copolymers, clays etc. See, for example: S. G. J. Mochrie et al., PRL 78, 1275 (1997) L.B. Lurio et al., PRL 84, (2000) D. Lumma et al., PRL 86, 2042 (2001) D. Pontoni et al., PRL 90 (2003) P. Falus et al., PRL 94, (2005) P. Falus et al., PRL 97, (2006) A. Duri et al., PRL 102, (2009) H. Guo et al., PRL 102, (2009)

39 Amphiphilic complex fluids Amphiphilic molecules possess two (or more) moieties with very different affinities e.g. soaps, lecithin, C 12 E 5, block copolymers..and organize immiscible fluids into various morphologies

40 Block copolymer phase diagrams: theory and experiment Claim: Polymer based materials offer the prospect of first principles understanding of complex fluid structure, phase behavior, and dynamics e.g. calculate the parameters appearing in the sponge phase Landau free energy.

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42 Crossover from stretched to compressed exponentials in sponge L3 phases: using X-ray speckle (XPCS) 22:07 P. Falus, S. Mochrie et. al, Phys. Rev. Lett 97, (2006)

43 Aging of Soft Matter under jamming transition (using Laser speckle PCS) reviewed in L. Cipelletti et al., Faraday Discuss. 123 (2003) f(q,τ) f Colloidal gels q (cm -1 ) τ (sec) g 2 (t) - 1 f(q q,t) Micellar polycrystal deg 45 deg 80 deg t C:\lucacip\Origin\DLS CCD\000709_F108_000329B t (sec) f(q,t) f(q,τ) exp[-(t/τ f ) 1.5 ], τ f q Concentrated Emulsions t (sec)

44 Compressed exponentials with XPCS (gels and clays): B. Chung et al., Microscopic Dynamics of Recovery in Sheared Depletion Gels Phys. Rev. Lett. 96, (2006) R. Bandyopadhyay et al., Evolution of Particle- Scale Dynamics in an Aging Clay Suspension, Phys. Rev. Lett. 93, (2004)

45 De Gennes narrowing Short time diffusion coefficient defined by τ = 1/D s Q 2 I.e. 1/D s = τ Q 2 D 0 = k B T/6πηR is the Stokes Einstein diffusion coeffient Measured and theoretical D 0 /D s (squares and red lines) and S(Q) (circles and blue lines) vs. QR for PS spheres in glycerol. l

46 XPCS for colloidal spheres Autocorrelations, g 2 (Q,t) for volume fractions of 0.28 (left, single exponential) and 052(right 0.52 (right, double exponential). Using glycerol slows the dynamics into the XPCS accessible range.

47 Dynamics of polymer membranes: Fitting results for φ= Relaxation rate: Γ vs. Undulation rate (k B TQ 3 /η) for φ=0.03 Stretching exponent for φ=0.03

48 Coherent X ray Speckle Imaging Real Space (MFM) Fourier Transform Reciprocal (Momentum) Space * work done with Ash Tripathi, Ian McNulty, Eric Fullerton, et al.

49 Magnetic Field induced Domain Dynamics * work done with Ash Tripathi, Ian McNulty, Eric Fullerton, et al.

50 Can we invert the speckle patterns? Lens-less (ptychographic) x-ray imaging of magnetic domains * work done with Ash Tripathi, Ian McNulty, Eric Fullerton, et al.

51 Off-resonance: On-resonance: 10-2 nm -1

52 a work done with Ash Tripathi, Ian McNulty, Eric Fullerton, et al.

53 work done with Ash Tripathi, Ian McNulty, Eric Fullerton, et al.

54 work done with Ash Tripathi, Ian McNulty, Eric Fullerton, et al.