X-ray Photon Correlation Spectroscopy (XPCS) at Synchrotron and FEL - - PowerPoint PPT Presentation

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X-ray Photon Correlation Spectroscopy (XPCS) at Synchrotron and FEL - - PowerPoint PPT Presentation

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X-ray Photon Correlation Spectroscopy (XPCS) at Synchrotron and FEL sources Christian Gutt Department of Physics, University ofSiegen, Germany gutt@physik.uni-siegen.de Outline How to measure dynamics in condensedmatter systems

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

Christian Gutt Department of Physics, University ofSiegen, Germany gutt@physik.uni-siegen.de

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Outline

  • How to measure dynamics in condensedmatter systems
  • Coherence
  • X-ray speckle patterns
  • How to exploitX-ray intensityfluctuations
  • Examples for slow dynamics
  • XPCS at FEL sources
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How to measure dynamics in condensed matter systems

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How to measure dynamics in condensed matter systems 𝐺 𝑅, 𝜐 =

% & βˆ‘βˆ‘ exp

(𝑗𝑅(𝑠

/ (𝑒) βˆ’ 𝑠 3(𝑒 + 𝜐))

Time domain intermediate scattering function 𝑇 𝑅, πœ• = 8 𝐺 𝑅, 𝜐 exp π‘—πœ•πœ π‘’πœ Frequency domain dynamic structure factor

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

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Relaxationalprocesses – diffusion, viscosity... No restoring force – the system evolves with time and does not come back

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An example – molecular dynamics simulation of liquid water

Intermediate scattering function is complex (many correlation processes) and spans many orders of magntiude

  • > experiments in the time domain
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Laser Speckle

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Incoherent light Coherent light Close up

Optical Speckles

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VLC movie

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Coherent scattering from disorder: Speckle

  • Incoherent Beam:

Diffuse Scattering

  • Measures averages

sample with disorder (e.g. domains)

  • Coherent Beam: Speckle
  • Speckle depends on

exact arrangement

  • Speckel statistics

encodes coherence properties

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XPCS – Theory

I(t)I(t +Ο„ ) = E(t)E*(t)E(t +Ο„ )E*(t +Ο„ )

= E(t)E*(t) E(t +Ο„ )E*(t +Ο„ ) + E(t)E*(t +Ο„ )

2

Gaussian momentum theorem

I(t)

I(t) g1(Ο„ )

I(t)I(t +Ο„ ) I(t)

2

=1+ g1(Ο„ )

2

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XPCS Theory

E(t) = A bj exp(iqrj(t))

j=1 N

βˆ‘

g1(q,Ο„ ) = A2 bkbj exp(iq(rj(t)βˆ’r

k(t +Ο„ )) j,k=1 N

βˆ‘

Time dependent density correlation function

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Experiment

I(t)I(t +Ο„ ) I(t)

2

=1+ Ξ² g1(Ο„ )

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 β‰ˆ Ξ» D Γ— L

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High contrast Low contrast

Signal to noise ratio

SNR∝ β

I(t)I(t +Ο„ ) I(t)

2

=1+ Ξ² g1(Ο„ )

2

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High coherence Low coherence

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50 100 150 200 5 10 15 20 25 30

intensity pixel

π·π‘π‘œπ‘’π‘ π‘π‘‘π‘’ = 𝛾 = 𝐽𝑛𝑏𝑦 βˆ’ π½π‘›π‘—π‘œ 𝐽𝑛𝑏𝑦 + π½π‘›π‘—π‘œ = 0

50 100 150 200 5 10 15 20 25 30

intensity pixel

𝛾 = 𝐽𝑛𝑏𝑦 βˆ’ π½π‘›π‘—π‘œ 𝐽𝑛𝑏𝑦 + π½π‘›π‘—π‘œ = 1

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Coherence

Spatial coherence Temporal coherence

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Thomas Young, 1773-1829

Young’s Double Slit Experiment

  • Light is a wave
  • Visibility (coherence)

min max min max

I I I I v + βˆ’ =

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

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min max min max

I I I I v + βˆ’ =

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min max min max

I I I I v + βˆ’ =

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min max min max

I I I I v + βˆ’ =

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Fringe visibilityas a function of distance between the pinholes > + =< Ξ“ ) , ( ) , ( ) , , (

2 1 * 2 1

Ο„ Ο„ t r V t r V r r No fringes visibility: β€žcoherence length exceededβ€œ

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Leitenberger et al. J. Synchrotron Rad. 11, 190 (2004)

Young’s experiment with X-rays

min max min max

I I I I v + βˆ’ =

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

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Vartaniants et al. PRL 2012

min max min max

I I I I v + βˆ’ =

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Vartaniants et al. PRL 2012

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  • A. Robert, SLAC
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Ξ“ r,𝜐 mutual coherence function (MCF) Ξ”πœ = 𝑅 𝑠

H βˆ’ 𝑠 % /𝑑𝑙L~𝜐N

WAXS Q large probing transverse AND temporal coherence Ξ“ 𝑠, Ξ”πœ SAXS Q small probing transverse coherence Ξ“(𝑠, 0) Ξ”πœ = 𝑅 𝑠

H βˆ’ 𝑠 %

𝑑𝑙L β‰ͺ 𝜐N

Contrast (Visibility) Ξ²(Q) of a speckle pattern is determined by the coherence properties of the X-ray beam

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High contrast Low contrast

Signal to noise ratio

SNR∝ β

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Large speckles Small speckles

Good detector No good detector

Speckle size needs to match pixel size of detector

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Coherent Flux: F0= B Ξ»2

2 (Δλ

Δλ/Ξ») (ESRF: ID10A F0~1010 ph/s)

Brilliance of X-rays Sources

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Examples

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Antiferromagnetic domain fluctuations in Chromium

Spin density waves Domain wall O.G. Shpyrko et al. Nature 447, 68 (2007)

Rotation of spin volumes

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Time

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Correlation functions

𝐺 𝑅, 𝑒 = exp (βˆ’ 𝑒 /𝜐P

Q)

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Quantum rotation of spin blocks

Blue line: Thermally activated jumps over an energy barrier Red line: Quantum tunneling through an energy barrier

1 2

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How Solid are Glasses ?

PABLO G. DEBENEDETTI AND FRANK H. STILLINGER, Nature 410, 259 (2001)

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Atomic dynamics in metallic glasses

  • B. Ruta et al. Phys. Rev. Lett. 109, 165701 (2012)
  • B. Ruta et al. Nature Comm. 5, 3939 (2014)

𝐺 𝑅, 𝑒 = exp (βˆ’ 𝑒 /𝜐P

Q)

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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, 165701 (2012)
  • B. Ruta et al. Nature Comm. 5, 3939 (2014)
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XPCS at diffraction limited strorage rings (DLSR)

Coherent Flux: F0= B Ξ»2

2 (Δλ

Δλ/Ξ») ESRF upgrade MBA lattice Increase of B by factor 50 - 100

up to 10.000 times faster time scale accessible in XPCS

𝜐 ~1/𝐢H

unusual scaling because XPCS correlates pairs of photons

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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
  • ...
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XPCS at XFELs

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Serial mode

Temporal resolution depends on rep rate of the machine

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Ultrafast XPCS using a split and delay line

Delay times between 100 fs and 1 ns

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Measure speckle contrast as a function of pulse separation

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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 Cooling 284 K 206 K

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

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

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Pump-probe XPCS in Plasma Physics

1.255 1.26 1.265 1.27 1.275

0.05 0.5

Kluge, Gutt et al. Plasma Physics 2014

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The end