xpcs: x-ray photon correlation spectroscopy thanks ...€¦ · intermediate scattering function:...
TRANSCRIPT
![Page 1: XPCS: X-Ray Photon Correlation Spectroscopy Thanks ...€¦ · Intermediate scattering function: information about the density correlations in the sample and their time dependencies](https://reader035.vdocuments.mx/reader035/viewer/2022062605/5fdb9121ee800e0e0773553e/html5/thumbnails/1.jpg)
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
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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
![Page 3: XPCS: X-Ray Photon Correlation Spectroscopy Thanks ...€¦ · Intermediate scattering function: information about the density correlations in the sample and their time dependencies](https://reader035.vdocuments.mx/reader035/viewer/2022062605/5fdb9121ee800e0e0773553e/html5/thumbnails/3.jpg)
The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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?
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
Growth of X-ray brilliance 7
Brilliance
CPU speed
XFEL.EU
Courtesy: O. Shpyrko, UCSD
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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)
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
Poisson-Gamma distribution 15
Which one is speckle, which one is just Poisson statistics?
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
First XPCS attempts at LCLS 16
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
Weak speckle patterns: The Poisson-Gamma distribution 17
J. Goodman, Speckle Phenomena in Optics
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
Analysis of weak speckle patterns 18
Single-shots at LCLS, Poisson-Gamma statistics
S. O. Hruszkewycz et al., PRL109, 185502 (2012)
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
Outline 20
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
![Page 21: XPCS: X-Ray Photon Correlation Spectroscopy Thanks ...€¦ · Intermediate scattering function: information about the density correlations in the sample and their time dependencies](https://reader035.vdocuments.mx/reader035/viewer/2022062605/5fdb9121ee800e0e0773553e/html5/thumbnails/21.jpg)
The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
1),(),(
)(
),(),(),(
2)2(
2)2(
+=
+=
tftg
ItII
tg
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
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
Typical XPCS setup 23
1),()(
),(),(),( 2
2)2( +=
+= tf
ItII
tg QQ
QQQ β
ττ
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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)
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
Photon statistics and XPCS, is it the same contrast? 25
Static speckle pattern
XPCS
Photon statistics
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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)
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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 =
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
Non-equilibrium dynamics 32
),( 21)2( ttg
1t
2tNon-stationary, aging dynamics
age
∆t
∆t
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
Outline 33
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.) • Diffusion is solid crystalline materials (Leitner et al.)
Outlook to the European XFEL & the MID station
![Page 34: XPCS: X-Ray Photon Correlation Spectroscopy Thanks ...€¦ · Intermediate scattering function: information about the density correlations in the sample and their time dependencies](https://reader035.vdocuments.mx/reader035/viewer/2022062605/5fdb9121ee800e0e0773553e/html5/thumbnails/34.jpg)
The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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)
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
Dynamics of a cross-linking polymer gel 35
Hydrogel Aerogel
O. Czakkel et al., Micropor. Mesopor. Mater. 86, 124 (2005)
Initial After 8 h
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
Dynamics of a cross-linking polymer gel 36
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
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
Dynamics of a cross-linking polymer gel 37
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)
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
445 min425 min393 min345 min320 min290 min270 min255 min230 min190 min180 min170 min160 min
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
445 min425 min393 min345 min320 min290 min270 min255 min230 min190 min180 min170 min160 min
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
O. Czakkel and A. Madsen, Europhys. Lett. 95, 28001 (2011)
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
Dynamics of a cross-linking polymer gel 38
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)
O. Czakkel and A. Madsen, Europhys. Lett. 95, 28001 (2011)
γ
Bouchaud & Pitard, EPJ E 6, 231 (2001)
1/t0 ∝ Γ
1/t 0
[s-1
]
v-1 [
s/m
]
![Page 39: XPCS: X-Ray Photon Correlation Spectroscopy Thanks ...€¦ · Intermediate scattering function: information about the density correlations in the sample and their time dependencies](https://reader035.vdocuments.mx/reader035/viewer/2022062605/5fdb9121ee800e0e0773553e/html5/thumbnails/39.jpg)
The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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
![Page 40: XPCS: X-Ray Photon Correlation Spectroscopy Thanks ...€¦ · Intermediate scattering function: information about the density correlations in the sample and their time dependencies](https://reader035.vdocuments.mx/reader035/viewer/2022062605/5fdb9121ee800e0e0773553e/html5/thumbnails/40.jpg)
The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
Two-step structural relaxation 41
non-ergodicity level
![Page 42: XPCS: X-Ray Photon Correlation Spectroscopy Thanks ...€¦ · Intermediate scattering function: information about the density correlations in the sample and their time dependencies](https://reader035.vdocuments.mx/reader035/viewer/2022062605/5fdb9121ee800e0e0773553e/html5/thumbnails/42.jpg)
The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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)
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
445 min425 min393 min345 min320 min290 min270 min255 min230 min190 min180 min170 min160 min
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
445 min425 min393 min345 min320 min290 min270 min255 min230 min190 min180 min170 min160 min
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)….
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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)
![Page 44: XPCS: X-Ray Photon Correlation Spectroscopy Thanks ...€¦ · Intermediate scattering function: information about the density correlations in the sample and their time dependencies](https://reader035.vdocuments.mx/reader035/viewer/2022062605/5fdb9121ee800e0e0773553e/html5/thumbnails/44.jpg)
The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
Is there a Hard sphere glass transition? 44
![Page 45: XPCS: X-Ray Photon Correlation Spectroscopy Thanks ...€¦ · Intermediate scattering function: information about the density correlations in the sample and their time dependencies](https://reader035.vdocuments.mx/reader035/viewer/2022062605/5fdb9121ee800e0e0773553e/html5/thumbnails/45.jpg)
The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
The Glass Transition 45
![Page 46: XPCS: X-Ray Photon Correlation Spectroscopy Thanks ...€¦ · Intermediate scattering function: information about the density correlations in the sample and their time dependencies](https://reader035.vdocuments.mx/reader035/viewer/2022062605/5fdb9121ee800e0e0773553e/html5/thumbnails/46.jpg)
The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
The Sample 46
PMMA colloids in cis-decalin (HS system)
Form factor
Dilute sample
SAXS data from ID02, ESRF
![Page 47: XPCS: X-Ray Photon Correlation Spectroscopy Thanks ...€¦ · Intermediate scattering function: information about the density correlations in the sample and their time dependencies](https://reader035.vdocuments.mx/reader035/viewer/2022062605/5fdb9121ee800e0e0773553e/html5/thumbnails/47.jpg)
The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
Monte Carlo SAXS fitting 47
![Page 48: XPCS: X-Ray Photon Correlation Spectroscopy Thanks ...€¦ · Intermediate scattering function: information about the density correlations in the sample and their time dependencies](https://reader035.vdocuments.mx/reader035/viewer/2022062605/5fdb9121ee800e0e0773553e/html5/thumbnails/48.jpg)
The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
SAXS on concentrated samples 48
Fits allow determination of the volume fraction Φ
![Page 49: XPCS: X-Ray Photon Correlation Spectroscopy Thanks ...€¦ · Intermediate scattering function: information about the density correlations in the sample and their time dependencies](https://reader035.vdocuments.mx/reader035/viewer/2022062605/5fdb9121ee800e0e0773553e/html5/thumbnails/49.jpg)
The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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
![Page 50: XPCS: X-Ray Photon Correlation Spectroscopy Thanks ...€¦ · Intermediate scattering function: information about the density correlations in the sample and their time dependencies](https://reader035.vdocuments.mx/reader035/viewer/2022062605/5fdb9121ee800e0e0773553e/html5/thumbnails/50.jpg)
The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
Width function 50
![Page 51: XPCS: X-Ray Photon Correlation Spectroscopy Thanks ...€¦ · Intermediate scattering function: information about the density correlations in the sample and their time dependencies](https://reader035.vdocuments.mx/reader035/viewer/2022062605/5fdb9121ee800e0e0773553e/html5/thumbnails/51.jpg)
The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
Comparison with Mode-Coupling Theory 51
![Page 52: XPCS: X-Ray Photon Correlation Spectroscopy Thanks ...€¦ · Intermediate scattering function: information about the density correlations in the sample and their time dependencies](https://reader035.vdocuments.mx/reader035/viewer/2022062605/5fdb9121ee800e0e0773553e/html5/thumbnails/52.jpg)
The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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)
![Page 53: XPCS: X-Ray Photon Correlation Spectroscopy Thanks ...€¦ · Intermediate scattering function: information about the density correlations in the sample and their time dependencies](https://reader035.vdocuments.mx/reader035/viewer/2022062605/5fdb9121ee800e0e0773553e/html5/thumbnails/53.jpg)
The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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)
![Page 54: XPCS: X-Ray Photon Correlation Spectroscopy Thanks ...€¦ · Intermediate scattering function: information about the density correlations in the sample and their time dependencies](https://reader035.vdocuments.mx/reader035/viewer/2022062605/5fdb9121ee800e0e0773553e/html5/thumbnails/54.jpg)
The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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.
![Page 55: XPCS: X-Ray Photon Correlation Spectroscopy Thanks ...€¦ · Intermediate scattering function: information about the density correlations in the sample and their time dependencies](https://reader035.vdocuments.mx/reader035/viewer/2022062605/5fdb9121ee800e0e0773553e/html5/thumbnails/55.jpg)
The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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)
![Page 56: XPCS: X-Ray Photon Correlation Spectroscopy Thanks ...€¦ · Intermediate scattering function: information about the density correlations in the sample and their time dependencies](https://reader035.vdocuments.mx/reader035/viewer/2022062605/5fdb9121ee800e0e0773553e/html5/thumbnails/56.jpg)
The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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)
![Page 57: XPCS: X-Ray Photon Correlation Spectroscopy Thanks ...€¦ · Intermediate scattering function: information about the density correlations in the sample and their time dependencies](https://reader035.vdocuments.mx/reader035/viewer/2022062605/5fdb9121ee800e0e0773553e/html5/thumbnails/57.jpg)
The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
Outline 57
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
![Page 58: XPCS: X-Ray Photon Correlation Spectroscopy Thanks ...€¦ · Intermediate scattering function: information about the density correlations in the sample and their time dependencies](https://reader035.vdocuments.mx/reader035/viewer/2022062605/5fdb9121ee800e0e0773553e/html5/thumbnails/58.jpg)
The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
4th generation hard X-ray sources 58
LCLS - SACLA - SwissFEL – European XFEL – PAL XFEL - …
SACLA
Pohang XFEL SwissFEL
European XFEL
![Page 59: XPCS: X-Ray Photon Correlation Spectroscopy Thanks ...€¦ · Intermediate scattering function: information about the density correlations in the sample and their time dependencies](https://reader035.vdocuments.mx/reader035/viewer/2022062605/5fdb9121ee800e0e0773553e/html5/thumbnails/59.jpg)
The European X-Ray Free-Electron Laser
Anders Madsen, 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,….
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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)
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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)
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
The European XFEL. Also visible overground… 62
Schenefeld site (XFEL.EU HQ)
![Page 63: XPCS: X-Ray Photon Correlation Spectroscopy Thanks ...€¦ · Intermediate scattering function: information about the density correlations in the sample and their time dependencies](https://reader035.vdocuments.mx/reader035/viewer/2022062605/5fdb9121ee800e0e0773553e/html5/thumbnails/63.jpg)
The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
The Experimental Hall 63
November 2011
![Page 64: XPCS: X-Ray Photon Correlation Spectroscopy Thanks ...€¦ · Intermediate scattering function: information about the density correlations in the sample and their time dependencies](https://reader035.vdocuments.mx/reader035/viewer/2022062605/5fdb9121ee800e0e0773553e/html5/thumbnails/64.jpg)
The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
The Experimental Hall 64
June 2013
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
65
June 2013 (MID tunnel)
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
Facility Outline 66
MID @ SASE-2
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
Hutches at SASE-2 68
First light at XFEL.EU, 4Q 2016 First light at MID, 2Q 2017
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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)
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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)
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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………..
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
78 MID Technical Design Report (TDR)
http://www.xfel.eu/documents/technical_documents/ or https://bib-pubdb1.desy.de/record/154260
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
Recent XPCS review 79
Check the handouts for reference list and more details
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The European X-Ray Free-Electron Laser
Anders Madsen, European XFEL,
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)