X-ray Photon Correlation Spectroscopy (XPCS) at Synchrotron and FEL sources

Transcription

1 X-ray Photon Correlation Spectroscopy (XPCS) at Synchrotron and FEL sources Christian Gutt Department of Physics, University ofsiegen, Germany

2 Outline How to measure dynamics in condensed matter systems Coherence X-ray speckle patterns Howto exploitx-ray intensityfluctuations Examples for slow dynamics XPCS at FEL sources

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4 How to measure dynamics in condensed matter systems

5 How to measure dynamics in condensed matter systems F Q, τ = % & exp (iq(r / (t) r 3 (t + τ)) S Q, ω = 8 F Q, τ exp iωτ dτ Time domain intermediate scattering function Frequency domain dynamic structure factor

6 Elastic processes waves, phonons... Restoring force the system goes back to its previous configuration

7 Relaxational processes diffusion, viscosity... No restoring force the system evolves with time and does not comeback

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9 An example molecular dynamics simulation of liquid water Intermediate scattering function is complex (many correlation processes) and spans many ordersofmagntiude -> experiments in the time domain

10 Laser Speckle

11 Optical Speckles Incoherent light Coherent light Close up

12 VLC movie

13 Coherent scattering from disorder: Speckle sample with disorder (e.g. domains) Incoherent Beam: Diffuse Scattering Measures averages Coherent Beam: Speckle Speckle depends on exact arrangement Speckel statistics encodes coherence properties

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15 XPCS Theory I(t)I(t +τ ) = E(t)E * (t)e(t +τ )E * (t +τ ) Gaussian momentum theorem = E(t)E * (t) E(t +τ )E * (t +τ ) + E(t)E * (t +τ ) 2 I(t) I(t) g 1 (τ ) I(t)I(t +τ ) I(t) 2 =1+ g 1 (τ ) 2

16 XPCS Theory E(t) = A N j=1 b j exp(iqr j (t)) N j,k=1 g 1 (q,τ ) = A 2 b k b j exp(iq(r j (t) r k (t +τ )) Time dependent density correlation function

17 Experiment I(t)I(t +τ ) I(t) 2 =1+ β g 1 (τ ) 2 Speckle contrast < 1 Speckle blurring leads to small contrast Partial coherenceof the x-ray source Detector pixels P larger than speckle size S S λ D L

18 High contrast Signal to noise ratio SNR β Low contrast I(t)I(t +τ ) I(t) 2 =1+ β g 1 (τ ) 2

19 High coherence Low coherence

20 intensity intensity Contrast = β Imax Imin = Imax + Imin = β = pixel Imax Imin Imax + Imin = pixel

21 Coherence Spatial coherence Temporal coherence

22 Young s Double Slit Experiment Thomas Young, Light is a wave Visibility (coherence) v = I I max max + I I min min

23 Spatial coherence in Young s Double-Slit experiment Born and Wolf, Optics

24 v = I I max max + I I min min

25 v = I I max max + I I min min

26 v = I I max max + I I min min

27 Fringe visibility as a function of distance between the pinholes Γ( r1, r2,τ ) =< V * ( r1, t )V (r2, t + τ ) > No fringes visibility: coherence length exceeded

28 Young s experiment with X-rays v = I I max max + I I min min Leitenberger et al. J. Synchrotron Rad. 11, 190 (2004)

29 Vartaniants et al. PRL 2012 Young s experiment at an XFEL (here LCLS)

30 v = I I max max + I I min min Vartaniants et al. PRL 2012

31 Vartaniants et al. PRL 2012

32 A. Robert, SLAC

33 Contrast (Visibility) β(q) of a speckle pattern is determined by the coherence properties of the X-ray beam Γ r, τ mutual coherence function (MCF) SAXS Q small probing transverse coherence Γ(r, 0) Δτ = Q r H r % ck L τ N WAXS Q large probing transverse AND temporal coherence Γ r, Δτ Δτ = Q r H r % /ck L ~τ N

34 High contrast Signal to noise ratio SNR β Low contrast

35 Speckle size needs to match pixel size of detector Large speckles Small speckles Good detector No good detector

36 Brilliance of X-rays Sources Coherent Flux: F 0 = B λ 2 (Δλ/λ) (ESRF: ID10A F 0 ~10 10 ph/s)

37 Examples

38 Antiferromagnetic domain fluctuations in Chromium Spin density waves Domain wall Rotation of spin volumes O.G. Shpyrko et al. Nature 447, 68 (2007)

39 Time

40 Correlation functions F Q, t = exp ( t /τ P Q )

41 Quantum rotation of spin blocks Blue line: Thermally activated jumps over an energy barrier Red line: Quantum tunneling through an energy barrier 1 2

42 How Solid are Glasses? PABLO G. DEBENEDETTI AND FRANK H. STILLINGER, Nature 410, 259 (2001)

43 Atomic dynamics in metallic glasses F Q, t = exp ( t /τ P Q ) B. Ruta et al. Phys. Rev. Lett. 109, (2012) B. Ruta et al. Nature Comm. 5, 3939 (2014)

44 Reality check for glasses Fast relaxation dynamics exists below the glass transition temperature Tg. Glasses are not completely frozen in Stress dominates dynamics below Tg B. Ruta et al. Phys. Rev. Lett. 109, (2012) B. Ruta et al. Nature Comm. 5, 3939 (2014)

45 XPCS at diffraction limited strorage rings (DLSR) ESRF upgrade MBA lattice Coherent Flux: F 0 = B λ 2 (Δλ/λ) Increase of B by factor up to times faster time scale accessible in XPCS τ ~1/B H unusual scaling because XPCS correlates pairs of photons

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47 Problems that can be adressed at DLSR Dynamics in the supercooled state Dynamics in confinement Domain fluctuations in hard condensed matter Protein diffusion in cells Kinetics of biomineralization processes Liquids under extreme conditions (e.g. pressure) Driven dynamics under external (B,E,T) fields Local structures and their relaxations...

48 XPCS at XFELs

49 Serial mode Temporal resolution depends on rep rate of the machine

50 Ultrafast XPCS using a split and delay line Delay times between 100 fs and 1 ns

51 Measure speckle contrast as a function of pulse separation

52 Ultrafast XPCS at XFEL dynamics in extreme conditions Calculated correlation function supercooled liquid water Dynamics on time-scales ranging from 100 fs to 1000 ps 206 K 284 K Cooling

53 J.A. Sellberg et al. Nature 510, 381 (2014)

54 Water at T=1500 K, p = 12 Gpa at least for a few ps

55 Pump-probe XPCS in Plasma Physics Kluge, Gutt et al. Plasma Physics 2014

56 The end