XPCS: X-Ray Photon Correlation Spectroscopy Thanks ...€¦ · Intermediate scattering function: information about the density correlations in the sample and their time dependencies

The European X-Ray Free-Electron Laser

Anders Madsen, European XFEL,

1

Anders Madsen,

European X-ray Free Electron Laser Facility, Hamburg [email protected]

HSC17: Dynamical properties investigated by neutrons and synchrotron X-rays

ESRF, 16 September 2014

XPCS: X-Ray Photon Correlation Spectroscopy

Presenter

Presentation Notes

Thanks organizers for inviting



Outline 2

Introduction to coherent X-rays • coherence? • coherent X-ray scattering, SAXS, WAXS • speckle & photon statistics

Introduction to XPCS • Time correlation functions • 2D XPCS, signal to noise ratio • Two-times and higher order correlations

XPCS examples (depending on time): • Polymer gel during gelation (Czakkel et al.) • Concentrated hard-sphere suspensions (Kwasniewski et al.) • Surface dynamics of nanoparticle suspensions (Orsi et al.) • …

Outlook to the European XFEL & the MID station

Presenter

Presentation Notes

Use examples as talking points to talk about the technique and illustrate the breadth of it’s applications but also to illustrate some of the dynamics similarities between these otherwise rather different systems.



Coherence 3

• Quantum mechanics probability amplitudes (waves) • Optics Young’s double slit experiment, interference • X-ray (and neutron) scattering It’s all about probability amplitudes and interference !!!

Example: Young’s double slit experiment (Thomas Young, 1801) [wave-character of quantum mechanical particles (photons)]

P=|ΣjΦj|2

Φ: probability amplitude Φj ~ exp[-i(ωt-klj)] ω=ck, k=2π/λ, lj(L,y) P(y) ~ cos2(πyd/λL) ∆y=λL/d

Plane, mono- chromatic wave

Laser beam



Coherent X-rays 4

Coherence diffraction limited beam or at least with a noticeable coherence length Coherent beam Easy in optical regime (OL, collimation, or point source) Difficult in the X-ray range (e.g. 3rd gen SR facilities)

T. Young (1801)

Why use X-ray coherence? One answer: coherent illumination leads to interference effects providing enhanced sensitivity to structure and dynamics in scattering experiments

Presenter

Presentation Notes

Demonstrated wave nature of light beginning of 19th century Coherence length prop to wavelength (1/5000), coherent flux scales like lambda squared



Nλ

(N-1)(λ+∆λ)

0 π 2π

Longitudinal coherence length

ll=λ/2(∆λ/λ)

d L

Transverse coherence length

lt=λL/2d

Coherence lengths

Coherence volume: VC ∝ λ3

Coherent flux Ic: VC × photon density

Ic = Bλ2/4

…difficult, even if Brilliance is on the right track

Presenter

Presentation Notes

Huygens principle on the source, no phase relationship (chaotic source)



How many photons are in the coherence volume?

Coherent flux: IC = B λ2 / 4

B: Brilliance

)Δλ/λ(10 of bandwidthainmm mrad

ph/sB 3-22 ×

=

State of the art SR: B > 1020

(beamlines at 3rd generation synchrotrons e.g. ESRF, APS and SPring8). Ic > 1010 ph/s

How many coherent photons?

Presenter

Presentation Notes

1014 in the full beam



Growth of X-ray brilliance 7

Brilliance

CPU speed

XFEL.EU

Courtesy: O. Shpyrko, UCSD



The Sun as a coherent light source 8

Peak ~ 1 W/m2 (@500nm, 0.1%bw)

i.e. 2.5x1018 ph/s/m2 at earth. 1m2 in earth’s distance (150Mkm) subtends 4.4x10-17 mrad2

Sun’s projected area ~ 1.5x1024 mm2 Sun’s peak B ~ 4x1010 ph/s/mm2/mrad2/0.1%bw @ 500nm Sun’s transverse coherence length ~ 10 µm @ 500nm



Leitenberger et al. Physica B336, 36 (2003)

λ=2.1Å, d=11µm Visibility ~ 80%

λ=0.9Å, d=11µm Visibility ~ 30%

∆y=λL/d Smooth incoherent background Σj|Φj|2

Young’s double-slit experiment with X-rays



First speckle (1962) 10

A speckle pattern is the random intensity pattern observed when light with sufficient spatial and temporal coherence is scattered by a medium that introduces random fluctuations of the optical path comparable to the wavelength. It encodes the exact spatial arrangement of the scattering volume but the phase must be determined for an inversion to be possible…

Speckle techniques applied in astronomy, metrology, e-, X-ray and light scattering, and radar imaging. First observation of optical speckle by laser (optical maser) light scattering: J. D. Rigden and E. I. Gordon, Proc. IRE 50, 2367 (1962)

Presenter

Presentation Notes

Rigden and Gordon Bell labs



First X-ray speckle and first XPCS 11

Signal ~ 0.6%

PSD gas Detector

ID10, ESRF

Nature 352, 608 - 610 (15 August 1991);

(001) reflection Cu3Au Kodak Film X25, NSLS



For a “perfectly” random sample, i.e. independent and random scattering amplitudes and phase shifts, and fully coherent illumination the speckle pattern obeys negative exponential statistics:

Gamma distribution of intensity coming from M statistically independent superimposed speckle patterns PM(I)=(M/<I>)MIM-1exp(-MI/<I>)/Γ(M)

σ2=<I>2/M, 1/M=β

M ≈ Vscat/Vcoh speckle contrast = 1/M

I/<I> 1

Speckle pattern. Statistical properties

Histogram of intensity Partial coherence

J. Goodman, Speckle Phenomena in Optics

Presenter

Presentation Notes

Only one adjustable parameter M!



Analysis of static speckle patterns (SAXS): Partial coherence 13

ID10A (ESRF). SAXS geometry, Si(111) mono 10x10 µm beam size, PI CCD (20 µm pixel size) 2.3 m sample-detector distance

M=2.85 Contrast = 35%

Fit with Gamma distribution M=2.85



Speckle statistics at LCLS: Perfect coherence (almost) 14

M~1, <β> ~ 0.94

C. Gutt et al, Phys. Rev. Lett. 108, 024801 (2012)

Data from XPP @ LCLS Si(111), E=9 keV



Poisson-Gamma distribution 15

Which one is speckle, which one is just Poisson statistics?

400 450 500 550 600 650

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First XPCS attempts at LCLS 16



Weak speckle patterns: The Poisson-Gamma distribution 17

J. Goodman, Speckle Phenomena in Optics

Presenter

Presentation Notes

Discrete distribution aka negative binomial distribution



Analysis of weak speckle patterns 18

Single-shots at LCLS, Poisson-Gamma statistics

S. O. Hruszkewycz et al., PRL109, 185502 (2012)



Contrast depends on scattering geometry and the detector 19

Contrast decreases at large angles due to increase in path length difference between scattered waves:

h sin2(2θ) + d sinθ ≤ ll

h

d

Detector at 2θ (approximation) Contrast decreases if

speckles are not resolved



Outline 20





Presenter

Presentation Notes




Coherent scattering. Motivation 21

Diffraction microscopy: Phase retrieval required but no limiting optics

Isolated object

Ensemble of objects

Correlation spectroscopy: Temporal: XPCS Spatial: XCCA

Temporal: XPCS

Static speckle

Dynamic speckle

Presenter

Presentation Notes

Diffraction microscopy or lensless imaging, phase retrieval required to inverse fourier transform and get back to real space Correlation spectroscopy on ensemble of objects: local symmetries and dynamics can be revealed as speckle pattern reflects exact spatial arrangement



1),(),(

)(

),(),(),(

2)2(

2)2(

+=

+=

tftg

ItII

tg

QQ

QQQ

QττTemporal intensity

auto-correlation function of speckle intensity

)}),({Re(~|),(| ωQQ SFTtf

∫ ∫ −⋅∝V V

mnem

en titf )])()0([exp()()(|),(| rrQQQQ ρρ

Intermediate scattering function: information about the density correlations in the sample and their time dependencies

X-Ray Photon Correlation Spectroscopy

β

Coherence factor !!!! β=1/M

Presenter

Presentation Notes

One of the few techniques combining reciprocal space and time



Typical XPCS setup 23

1),()(

),(),(),( 2

2)2( +=

+= tf

ItII

tg QQ

QQQ β

ττ



Example: Brownian motion

RTkD B

πη60 =

Stokes-Einstein free diffusion coefficient

viscosity

geometrical factor particle radius

(hydrodynamic)

Example: Brownian Motion of Colloids

G. Grübel & F. Zontone, J. Alloys and Comp. 362, 3 (2004)

Intermediate scattering function: f(Q,t) = exp(-Γt) = exp(-D0Q2t)



Photon statistics and XPCS, is it the same contrast? 25

Static speckle pattern

XPCS

Photon statistics



XPCS by a point detector (0D XPCS) 26

I(t)

t

Troika, ESRF

Time average

β = 60% relaxation time t0 ~ few ms

Overdamped capillary waves (glycerol): Simple exponential correlation function f(t) ~exp(-t/t0) Lorentzian S(q,ω) centered at ω=0

Evanescent wave XPCS

2)2(

)(

)()()(

tIttItI

tg∆+

=∆

T. Seydel, A. Madsen, M. Tolan, G. Grübel, & W. Press, Phys. Rev. B 63, 073409 (2001)



XPCS by a point detector (0D XPCS) 27

I(t)

t

Troika, ESRF

Time average

Propagating capillary waves (water): Simple exponential correlation function f(t) ~cos(ω0t)exp(-t/t0) Lorentzian S(q,ω) centered at ω=ω0

Evanescent wave XPCS

2)2(

)(

)()()(

tIttItI

tg∆+

=∆

C. Gutt et al., Phys. Rev. Lett. 91, 076104 (2003)

Damped oscillation relaxation time t0 ~ few µs



2D X-ray Photon Correlation Spectroscopy 28

Two-times correlation function Multi-speckle XPCS (1kHz, MAXIPIX)

A. Madsen et al., New Journal of Physics 12, 055001 (2010)

t

series of speckle patterns

)()()()(

),(21

2121

)2(

tItItItI

ttg =

Average over ensemble of pixels (e.g. constant q region)

Applications: Non-ergodic, non-stationary and heterogeneous systems

Presenter

Presentation Notes

Speckle movie. Correlate the intensity in one pixel at time t1 by the intensity in the same pixel at later time t2, and normalize. Averaging over ensemble of pixels with same momentum transfer. This is the so called two-times correlation function.



Ergodicity 29

< >time = < >ensemble

Common assumption in thermodynamics and computational physics; Liouvilles theorem; time a system spends in a given phase space volume is proportional to the size of the volume



Non-Ergodicity 30

< >time ≠ < >ensemble

A particle (atom, molecule) does not explore the entire available phase space (position, velocity,…) during the measurement time

glasses gels pastes polymer/ composites



Non-equilibrium dynamics 31

1t

2t

∆t = t1- t2 = constant

waiting time (t1+t2)/2 (age), changes along line

age constant ∆t changes

~ exp(-t/τ)

)()()()(

),(21

2121

)2(

tItItItI

ttg =

Presenter

Presentation Notes

t1-t2 constant. If degree of correlation constant when t1-t2 constant stationary dynamics. All points line are equivalent i.e. TIME AVERAGING POSSIBLE. Along the age (average time) grows. In the perpendicular direction the age of the system is constant but the time difference (lag time) changes. A cut of The two times function in thet direction is equivalent to the usual one time autocorrelation function.



Non-equilibrium dynamics 32

),( 21)2( ttg

1t

2tNon-stationary, aging dynamics

age

∆t

∆t

Presenter

Presentation Notes

Decay fast in the beginning, slower towards the end of the measurements. TIME AVERAGING NOT POSSIBLE. We can study non-equilibrium and non-stationary dynamics, and correlations of correlations, etc…



Outline 33



XPCS examples (depending on time): • Polymer gel during gelation (Czakkel et al.) • Concentrated hard-sphere suspensions (Kwasniewski et al.) • Surface dynamics of nanoparticle suspensions (Orsi et al.) • Diffusion is solid crystalline materials (Leitner et al.)


Presenter

Presentation Notes




Dynamics of a cross-linking polymer gel 34

SOLVENT EXCHANGE+ DRYING HEAT TREATMENT

RF HYDROGEL RF AEROGEL CARBON GEL

H

OH

O

RESORCINOL

O

2

H H

C

FORMALDEHYDE

Na2CO3, Ea

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cluster formationmass fractal

branched polymer

particle formationfractal surface

gelationstructure formation

fractal surface

Crosslinked polymersmooth surface (not fractal)

Lin et al., Carbon 35, 1271 (1997); Tamon et al., J. Coll. Int. Sci. 206, 577 (1998)

Presenter

Presentation Notes

Polycondensation reaction of resorcinol and formaldehyde in aquaus solution, cross linking of polymers. Particle formation, growth of particle size and density, eventually a gel network. is formed.




Hydrogel Aerogel

O. Czakkel et al., Micropor. Mesopor. Mater. 86, 124 (2005)

Initial After 8 h




O. Czakkel and A. Madsen, Europhys. Lett. 95, 28001 (2011)

Dynamics appears in the window after 160 min

Continuous data acquisition; time averaging only in time-intervals where the process is

quasi-stationery (10 min).

τ – Q dispersion can be measured at various ages of the sample

t1

t 2

t1

t 2

230 min

160 min

),( 21)2( ttg

t

1

1.01

1.02

1.03

1.04

1.05

1 10 100 1000t (s)

q = 0.00720 Å-1

q = 0.01000 Å-1

q = 0.01280 Å-1

q = 0.01559 Å-1

q = 0.01769 Å-1

q = 0.02049 Å-1

g(2) (q

, t)

1

1.01

1.02

1.03

1.04

1.05

1.06

1.07

1 10 100 1000

q = 0.00720 Å-1

q = 0.01000 Å-1

q = 0.01280 Å-1

q = 0.01559 Å-1

q = 0.01769 Å-1

q = 0.02049 Å-1

q = 0.02399 Å-1

t (s)

g(2) (q

, t)

160 min

230 min

Presenter

Presentation Notes

Stationary in 10 min time window. Slow down of dynamics For every age this can be done for many annuli where q is constant an the time averaged correlation functions can be determined for the range of q covered by the detector. Next 10 min interval and so on age resolved dynamics




q = 0.0100 Å -1

1

1.01

1.02

1.03

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1.05

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1 10 100 1000 104

t (s)

445 min425 min393 min345 min320 min290 min270 min255 min230 min190 min180 min170 min160 min

g(2) (q

, t)

q = 0.01559 Å-1

1

1.01

1.02

1.03

1.04

1.05

1.06

1.07

1 10 100 1000 104


t (s)

g(2) (q

, t)

q = 0.02049 Å-1

1

1.01

1.02

1.03

1.04

1.05

1 10 100 1000 104


t (s)

g(2) (q

, t)

1

10

100

1000

104

0.001 0.01 0.1

q (Å)

505 min475 min445 min425 min393 min345 min320 min290 min255 min230 min190 min180 min170 min160 min140 min130 min120 min100 min 90 min 80 min 70 min 50 min 40 min 30 min 20 min 10 min 0 min

I(q)

SAXS o The dynamics slows down with time (age) o Faster than exponential decay of g(2)

o The structure also evolves continuously (SAXS)

AGE AGE

AGE


Presenter

Presentation Notes

The missing contrast can be used to check models for the fast dynamics and exclude some models but we cannot directly measure the fast dynamics. We’re constantly hunting for more flux and will eventually have to go to more powerful sources




0

5

10

15

20

25

30

0 5000 1 104 1.5 104 2 104 2.5 104 3 104

t (s)

1/Γ

Gel point 280 min

0

0.5

1

1.5

2

2.5

3

0 0.005 0.01 0.015 0.02 0.025

q (Å-1)

γ

160 min170 min

180 min

444 min

Randomly distribured stresses?

Hyper-diffusive behavior: The relaxation rate Γ is proportional to Q (ballistic motion), and decreasing with time. Analogy with glass formers…

0

0.005

0.01

0.015

0.02

0 0.005 0.01 0.015 0.02 0.025

190 minΓ (s

ec-1

)

q (Å-1)

444 min

160 min

170 min

180 min

230 min

KWW form: 1)]/[2exp()( 0)2( +−= γβ tttg

Slow dynamics (α-relaxation)


γ

Bouchaud & Pitard, EPJ E 6, 231 (2001)

1/t0 ∝ Γ

1/t 0

[s-1

]

v-1 [

s/m

]

Presenter

Presentation Notes

Concentrate on terminal relaxation. Simple exponential behavior and a relaxation rate scaling with Q-square would indicate diffusive behavior but this is not the case here. Relax rate prop to q indicates hyper-diffusive ballistic behavior, slope is velocity and velocity decreases with age of the system. Cfs also show sign of this non-diffusive behavior by not being simple exponentials. Slowing down of dynamics can also be visualized by plotting the relax time vs time showing two regimes: 280 min, growth of primary clusters stop, fractal structure created. Later structure remains constant but dynamics continues to slow down. Dynamical aging independent on average structure (as measured by X-ray scattering) KWW with q dependent beta>1 is a fitting function, it is not coming out of a model for the microscopic dynamics…. beta=1.5 model for stress relaxations Can one really imagine stress relaxations to be present (even before the gel network is formed)? Implies that the fluid is non-newtonian with elastic properties (can support internal shear stress)



Glass studies indicating stress relaxations 39

Stress relaxations seems to drive the slow dynamics of many out-of-equilibrium systems. Approaching the glassy state there is often a transition to γ > 1

B. Ruta et al., PRL 109, 165701 (2012)

Propanediol (TG=170K)

C. Caronna, Y. Chushkin, A. Madsen PRL 100, 055702 (2008)

γ=1

γ=1.7

Metallic glass: Mg65Cu25Y10 (TG=405K)

γ<1

γ>1

Presenter

Presentation Notes

Smooth transition to stress dynamics (fragile glass) Abrupt transition to stress dynamics Again fits with the KWW form but no connection to a model of the microscopic dynamics



Glass studies indicating aging dynamics 40

Aging of the dynamics seems to be a general feature near the glass transition

Aging dynamics of glassy ferrofluid: A. Robert et al., Europhys. Lett. 75, 764 (2006) Aging dynamics in Wigner glass:

L. Angelini et al, Soft Matter 9, 10955 (2013)

Age [s] 103 104 105

Presenter

Presentation Notes

Smooth transition to stress dynamics Abrupt transition to stress dynamics Now I’ll show you a well system where the dynamics is stationary



Two-step structural relaxation 41

non-ergodicity level



Missing contrast (non-ergodicity level) 42

q = 0.0100 Å -1

1

1.01

1.02

1.03

1.04

1.05

1.06

1.07

1.08

1 10 100 1000 104

t (s)


g(2) (q

, t)

q = 0.01559 Å-1

1

1.01

1.02

1.03

1.04

1.05

1.06

1.07

1 10 100 1000 104


t (s)

g(2) (q

, t)

q = 0.02049 Å-1

1

1.01

1.02

1.03

1.04

1.05

1 10 100 1000 104


t (s)

g(2) (q

, t)

Analysis of “missing contrast” yields the localization length of fast dynamics assuming rattling dynamics (DW term, harmonic oscillator analogy)

Gel point 280 min

Debye-Waller model: β/β0=exp(-Q2r2

loc/6)….



Missing contrast studies. Studying what you can’t see… 43

Aging of localization length

No aging of localization length

γ<1

γ>1

Aging dynamics of a Laponite glass: R. Angelini et al., in press (2014)



Is there a Hard sphere glass transition? 44



The Glass Transition 45



The Sample 46

PMMA colloids in cis-decalin (HS system)

Form factor

Dilute sample

SAXS data from ID02, ESRF



Monte Carlo SAXS fitting 47



SAXS on concentrated samples 48

Fits allow determination of the volume fraction Φ



XPCS correlation functions 49

P. Kwasniewski, PhD thesis (ESRF & UJF, 2012) Kwasniewski, Fluerasu, Madsen, Soft Matter (in press, 2014)

Intermediate scattering function: f(Q,t) = exp(-Γt) = exp(-D0Q2t)

MSD ∝ D0t, ergo -log(f(Q,t))/Q2 is like MSD



Width function 50



Comparison with Mode-Coupling Theory 51



Extreme dynamical heterogeneity 52

Final relaxation of concentrated hard-sphere suspension is avalanche like (intermittent, collective, heterogeneous, and ballistic )

Quantitative analysis is challenging (extreme heterogeneity)

P. Kwasniewski, PhD thesis (ESRF & UJF, 2012) Kwasniewski, Fluerasu, Madsen, Soft Matter (in press, 2014)

Presenter

Presentation Notes

The stress relaxation dynamics in viscoelastic media lacks a microscopic theory that connects with the data. And stress relaxations are different, sometimes a slight modification of the disp relation and shape of the correlation functions, sometimes leading to subtle changes in scaling laws, and sometimes the crazy avalanches here. Advanced techniques and analysis is required to study soft matter dynamics. Even if we’re not diverging at phi_G it seems like it is present in the data as where avalanches start



Extreme dynamical heterogeneity 53

Martensitic phase transformation in AuCd

Two-time correlation function Aging dynamics is avalanche like

L. Müller et al., PRL 107, 105701 (2011)



Higher-order correlation functions 54

Grazing incidence XPCS from monolayer of gold nanoparticles (7nm)

coherent X-rays αi < αc

γ=1.5

D. Orsi et al., PRL 108, 105701 (2012)

Levy dist.



55

τ

ta

)()()()(

),(21

2121 tItI

tItIttG =

τ = |t1 - t2|

ta = (t1+t2)/2

Two-time correlation function Sample with quakes, just before avalanches set in…

Higher-order correlation functions

D. Orsi et al., PRL 108, 105701 (2012)

Presenter

Presentation Notes

Quakes: The step before the dynamics becomes dominated by avalanches



Higher-order correlation functions 56

Connection with fast dynamics (non-ergodicity level, missing contrast,…)

g(4) has a peak characteristic time t*

D. Orsi et al., PRL 108, 105701 (2012)

Presenter

Presentation Notes

Connection to fast dynamics (, maybe the quakes start there



Outline 57





Presenter

Presentation Notes




4th generation hard X-ray sources 58

LCLS - SACLA - SwissFEL – European XFEL – PAL XFEL - …

SACLA

Pohang XFEL SwissFEL

European XFEL



59 Soft/Hard X-ray FELs worldwide

LCLS SLAC, Stanford, CA

European XFEL Schenefeld, Hamburg, GER

SACLA SCSS test Spring-8 Harima, JAP

FERMI Trieste, ITA

PAL XFEL Pohang, KOR

FLASH DESY, Hamburg, GER

SwissFEL Villigen, CH

Also projects in Sweden, Poland, China,….



European X-Ray Free-Electron Laser Facility 60

XFEL.EU HQ surface building artist’s view

1 lab floor 2 office floors Built on top of underground exp. hall (90 x 50 m)



The European XFEL. An underground facility 61

www.xfel.eu

Accelerator tunnel (> 2 km long, ~ 6m diameter) Completed Feb. 2012

Total length 3400 m

Last photon tunnel section was completed summer 2012 (~6 km tunnel in total drilled)



The European XFEL. Also visible overground… 62

Schenefeld site (XFEL.EU HQ)



The Experimental Hall 63

November 2011



The Experimental Hall 64

June 2013



65

June 2013 (MID tunnel)



Facility Outline 66

MID @ SASE-2



MID beamline overview 67

CRL-1

CRL-2

undulator

mono-1: Si(111)

mono-2

Si(220)

X-ray split- delay line

sample

detector

931 m

929 m 0 m

290 m

229 m

946.5 m

967 m

950 m

959 m

horizontal offset m

irror

attenuator

attenuator

attenuator

nanofocusing CRL

mirror(s)

301 m

727 m

880 m

949 m

948 m

955 m

887.5 m

slit-1

slit-2

slit-3

210 m

244 m

400 m

729 m

888.5 m

920 m

936.5 m

957.5 m

969 m

227.5 m

948.5 m

2D-imager

imager-2

imager-3

imager-4

imager-5

imager-6

diagnostic endstand

XBPM &

intensity-1

XBPM &

intensity-2

Not shown: MCP at 303m (fine tuning of SASE) Distribution mirror(s) at 390m and 395m (MID on central branch) Beam loss monitors

λ 220 m

time-of-flight PES

common SASE-2 beamline (MID/HED)

MID photon beamline

MID experimental hutch

MID optics hutch

933 m

high energy CRL

high-energy mono

306 m

171 m

198 m

transm

issive imager

spont. rad. aperture

305 m

imager-1

t

956 m

957 m

diff. pumping

timing diagnostic

264 m

shutter-1

shutter-3

shutter-2

952 m

940 m

λ

380.5 m

HR-SSS

200 m

K-mono



Hutches at SASE-2 68

First light at XFEL.EU, 4Q 2016 First light at MID, 2Q 2017



Materials Imaging and Dynamics Instrument 69 69

Structure and dynamics of condensed matter with hard X-rays Structural and temporal correlations, coherent imaging,.. Techniques: XPCS, CXDI, XCCA, scattering, pump-probe,…

Full burst mode (4.5 MHz) for high rep. rate experiments 1 bunch/train (10 Hz) mode for alignment and special experiments

Bunch charge: 1 pC – >1 nC Photon energy: 5 – 25 keV, possibly > 25 keV Bandwidth: 1e-3, 1e-4, 1e-5, split delay line,.. Seeding: YES Spot size on sample: from 0.1 µm to 0.1 mm

CXDI

XCCA, Angular

Correlations XPCS



Faster dynamics by XPCS? 70

Scattering Vector Q [Å-1]

Length Scale [Å] Fr

eque

ncy

[Hz]

Energy [eV]

Raman

Brillouin

XPCS DLS

IXS

Spin-Echo

INS

NFS



Time structure of XFEL.EU SC linac, up to 17.5 GeV 10 pulse trains/sec 2700 pulses/train Multi-user mode 220 ns between pulses pulse duration ~ 10 fs 1e12 – 1e13 ph/pulse

pulse train

single pulse single pulse

220 ns 220 ns

Presenter

Presentation Notes

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Fast Acquisition of Diffraction Patterns 72

Sequential mode for coherent scattering

From Nature News and Views G. B. Stephenson et al., Nature Materials 8, 702 (2009)

4.5 MHz detector available at XFEL.EU

Sample survives several pulses (as many as the detector can store)

Speckle methods Coherent diffractive imaging (CXDI) Time correlation spectroscopy (XPCS) Spatial auto- and cross-correlations (XCCA)

XFEL rep rate: 4.5 MHz, 220 ns (default) 1.3 GHz, 770 ps (possible, reduced intensity)



Adaptive Gain Integrating Pixel Detector (AGIPD) 73

4.5 MHz, 1M pixels, 200 µm pixel size On-chip memory, readout between trains 4 adjustable quadrants Central hole

AGIPD project leader: H. Graafsma (DESY)



MID Instrument at European XFEL 74

Sample – AGIPD detector distance: 0.2 m - ~9 m Energy: 5 – 25 keV, higher by high-harmonic lasing?

Work in progress



Ultrafast dynamics (fs-ps) by XSVS 75

C. Gutt et al., Optics Express 17, 55 (2009)

Sample can be renewed for every shot (injector, new solid target,..)

0 10 20 300

20

40

60

80

100

Delay τ

Spec

kle

cont

rast

(%)

Time-resolution independent of detector speed

X-Ray Speckle Visibility Spectroscopy (SVS)

Contrast analysis yields the degree of correlation C on summed image

C(∆t) can be mapped out



Hard X-Ray Split-Delay Line 76

Co-linear beams

Inclined beams

Path length difference 1µm 3.3 fs

SDL at MID: 5 – 10 keV Few fs to 800 ps delay From 770 ps – 220 ns The accelerator can do it From 220 ns the detector can resolve single images

…also for two-color experiments and four-wave mixing………..



Inclined beams from split-delay line 77

4 m mirror-sample distance, 2αi = 0.4 deg αi even larger with crystal Separation of two beams at detector

Two images on AGIPD detector:

Early beam

Late beam

2αi sample

2nd pattern 1st pattern

Optical laser

X-ray X-ray Optical

X-ray X-ray Optical XOX

OXX

X-ray X-ray XX

∆t

Upwards deflecting mirror



78 MID Technical Design Report (TDR)

http://www.xfel.eu/documents/technical_documents/ or https://bib-pubdb1.desy.de/record/154260



Recent XPCS review 79

Check the handouts for reference list and more details



Acknowledgments 80

J. Hallmann, T. Roth, W. Lu, G. Ansaldi (XFEL, Hamburg)

F. Zontone, Y. Chushkin, O. Czakkel, C. Caronna, P. Kwasniewski B. Ruta, (ESRF, Grenoble)

A. Moussaid (UJF Grenoble)

A. Robert, M. Sikorski (SLAC, LCLS)

B. Leheny (Johns Hopkins University, Baltimore)

A. Fluerasu (BNL, NSLS-II)

R. Angelini, B. Ruzicka, L. Zulian, G. Ruocco (La Sapienza, Rome)

D. Orsi, L. Cristofolini, G. Baldi (University of Parma)

Documents

XPCS: X-Ray Photon Correlation Spectroscopy Thanks ...€¦ · Intermediate scattering function: information about the density correlations in the sample and their time dependencies