The European X-Ray Free-Electron Laser
1
XPCS: X-Ray Photon Correlation
Spectroscopy
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
Anders Madsen, European XFEL,
The European X-Ray Free-Electron Laser
Outline
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
Anders Madsen, European XFEL,
2
The European X-Ray Free-Electron Laser
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)]
Plane, monochromatic wave
Laser
beam
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
Anders Madsen, European XFEL,
The European X-Ray Free-Electron Laser
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)
T. Young
(1801)
Difficult in the X-ray range (e.g. 3rd gen SR facilities)
Why use X-ray coherence?
One answer: coherent illumination leads to interference effects providing
enhanced sensitivity to structure and dynamics in scattering experiments
Anders Madsen, European XFEL,
The European X-Ray Free-Electron Laser
Coherence lengths
Nλ
Coherence volume:
VC ∝ λ3
Coherent dflux Ic:
VC × photon density
(N-1)(λ+∆λ)
0
π
Ic = Bλ2/4
…difficult, even if Brilliance
is2πon the right track
Longitudinal
ll=λ/2(∆λ/λ)
coherence length
Anders Madsen, European XFEL,
L
Transverse
lt=λL/2d
coherence length
The European X-Ray Free-Electron Laser
How many coherent photons?
How many photons are in the coherence volume?
Coherent flux: IC = B λ2 / 4
B: Brilliance
ph/s
-3
B=
in
a
bandwidth
of
10
(Δλ/λ )
2
2
mrad × mm
State of the art SR: B > 1020
(beamlines at 3rd generation synchrotrons
e.g. ESRF, APS and SPring8). Ic > 1010 ph/s
Anders Madsen, European XFEL,
The European X-Ray Free-Electron Laser
Growth of X-ray brilliance
7
XFEL.EU
Brilliance
CPU speed
Anders Madsen, European XFEL,
Courtesy: O. Shpyrko, UCSD
The European X-Ray Free-Electron Laser
The Sun as a coherent light source
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
Anders Madsen, European XFEL,
8
The European X-Ray Free-Electron Laser
Young’s double-slit experiment with X-rays
λ=2.1Å, d=11µm
Visibility ~ 80%
Leitenberger et al.
Physica B336, 36 (2003)
Smooth incoherent
background Σj|Φj|2
Anders Madsen, European XFEL,
λ=0.9Å, d=11µm
Visibility ~ 30%
∆y=λL/d
The European X-Ray Free-Electron Laser
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)
Anders Madsen, European XFEL,
The European X-Ray Free-Electron Laser
First X-ray speckle and first XPCS
Nature 352, 608 - 610 (15 August 1991);
(001) reflection
Cu3Au
Kodak
Film
X25, NSLS
Anders Madsen, European XFEL,
PSD gas
Detector
ID10, ESRF
Signal ~ 0.6%
11
The European X-Ray Free-Electron Laser
Speckle pattern. Statistical properties
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:
Histogram of intensity
Partial coherence
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
1
Anders Madsen, European XFEL,
I/<I>
M ≈ Vscat/Vcoh
speckle contrast = 1/M
J. Goodman, Speckle Phenomena in Optics
The European X-Ray Free-Electron Laser
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
Anders Madsen, European XFEL,
The European X-Ray Free-Electron Laser
Speckle statistics at LCLS:
Perfect coherence (almost)
14
Data from XPP @ LCLS
Si(111), E=9 keV
M~1, <β> ~ 0.94
C. Gutt et al,
Phys. Rev. Lett. 108, 024801 (2012)
Anders Madsen, European XFEL,
The European X-Ray Free-Electron Laser
Which one is speckle, which one is just Poisson statistics?
Poisson-Gamma distribution
15
45
40
400
5
35
400
4.5
450
3
30
4
400
2.8
500
450
25
3.5
1
2.6
400
450
0.9
550
500
3
20
2.5
15
2
10
2.4
0.8
2.2
500
450
600
550
0.7
2
1.5
5
0.6
500
550
1.8
650
600
1
0.5
400
550
450
5000.3
650
450
500
550
600
650
0.1
650
400
450
Anders Madsen, European XFEL,
550
600
1.2
0.2
400
500
550
550
1.4
400
600
500
1.6
600
0.5
0.4
650
600
450
600
650
0
1
650
0
650
0
The European X-Ray Free-Electron Laser
First XPCS attempts at LCLS
Anders Madsen, European XFEL,
16
The European X-Ray Free-Electron Laser
Weak speckle patterns: The Poisson-Gamma
distribution
Anders Madsen, European XFEL,
17
J. Goodman, Speckle Phenomena in Optics
The European X-Ray Free-Electron Laser
Analysis of weak speckle patterns
18
Single-shots at LCLS, Poisson-Gamma statistics
Anders Madsen, European XFEL,
S. O. Hruszkewycz et al., PRL109, 185502 (2012)
The European X-Ray Free-Electron Laser
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
Detector at 2θ
Contrast decreases if
speckles are not resolved
(approximation)
d
h
Anders Madsen, European XFEL,
The European X-Ray Free-Electron Laser
Outline
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
Anders Madsen, European XFEL,
20
The European X-Ray Free-Electron Laser
Coherent scattering. Motivation
Isolated object
21
Static speckle
Diffraction microscopy:
Phase retrieval required
but no limiting optics
Ensemble of objects
Correlation spectroscopy:
Temporal:
XPCS
Temporal: XPCS
Spatial: XCCA
Anders Madsen, European XFEL,
Dynamic speckle
The European X-Ray Free-Electron Laser
X-Ray Photon Correlation Spectroscopy
Temporal intensity
auto-correlation function
of speckle intensity
g (Q, t ) =
( 2)
I (Q,τ ) I (Q,τ + t )
I (Q)
2
g (Q,t ) = β f (Q, t ) +1
( 2)
| f (Q, t ) | ~ Re( FT {S (Q, ω )})
2
Coherence factor !!!!
β=1/M
| f (Q, t ) | ∝ ∫ ∫ ρ ne (Q) ρ me (Q) exp(iQ ⋅ [rn (0) − rm (t )])
VV
Intermediate scattering function: information about the
density correlations in the sample and their time dependencies
Anders Madsen, European XFEL,
The European X-Ray Free-Electron Laser
Typical XPCS setup
g (Q, t ) =
( 2)
23
I (Q,τ ) I (Q,τ + t )
I (Q)
Anders Madsen, European XFEL,
2
= β f (Q, t ) + 1
2
The European X-Ray Free-Electron Laser
Example: Brownian motion
Example: Brownian Motion of Colloids
Intermediate scattering function:
f(Q,t) = exp(-Γt) = exp(-D0Q2t)
Stokes-Einstein free
diffusion coefficient
k BT
D0 =
6πηR
geometrical
factor
viscosity
particle radius
(hydrodynamic)
G. Grübel & F. Zontone, J. Alloys and Comp. 362, 3 (2004)
Anders Madsen, European XFEL,
The European X-Ray Free-Electron Laser
Photon statistics and XPCS, is it the same
contrast?
25
Static speckle pattern
XPCS
Photon
statistics
Anders Madsen, European XFEL,
The European X-Ray Free-Electron Laser
XPCS by a point detector (0D XPCS)
Troika, ESRF
26
I(t)
Evanescent wave XPCS
t
Time average
g (∆t ) =
( 2)
I (t ) I (t + ∆t )
I (t )
Overdamped capillary waves (glycerol):
Simple exponential correlation function
f(t) ~exp(-t/t0)  Lorentzian S(q,ω) centered at ω=0
T. Seydel, A. Madsen, M. Tolan, G. Grübel,
& W. Press, Phys. Rev. B 63, 073409 (2001)
Anders Madsen, European XFEL,
2
β = 60%
relaxation time
t0 ~ few ms
The European X-Ray Free-Electron Laser
XPCS by a point detector (0D XPCS)
Troika, ESRF
27
I(t)
Evanescent wave XPCS
t
Time average
g (∆t ) =
( 2)
I (t ) I (t + ∆t )
I (t )
Propagating capillary waves (water):
Simple exponential correlation function
f(t) ~cos(ω0t)exp(-t/t0)  Lorentzian S(q,ω)
centered at ω=ω0
C. Gutt et al., Phys. Rev. Lett. 91, 076104 (2003)
Anders Madsen, European XFEL,
2
Damped oscillation
relaxation time
t0 ~ few µs
The European X-Ray Free-Electron Laser
2D X-ray Photon Correlation Spectroscopy
Two-times correlation function
Multi-speckle XPCS (1kHz, MAXIPIX)
28
t
series of
speckle patterns
g (t1 , t 2 ) =
( 2)
I (t1 ) I (t 2 )
I (t1 ) I (t 2 )
Average over ensemble of pixels
(e.g. constant q region)
Applications:
Non-ergodic, non-stationary
and heterogeneous systems
Anders Madsen, European XFEL,
A. Madsen et al.,
New Journal of Physics 12, 055001 (2010)
The European X-Ray Free-Electron Laser
Ergodicity
29
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
< >time
Anders Madsen, European XFEL,
=
< >ensemble
The European X-Ray Free-Electron Laser
Non-Ergodicity
30
A particle (atom, molecule) does not explore the entire available
phase space (position, velocity,…) during the measurement time
glasses
< >time
Anders Madsen, European XFEL,
gels
pastes
≠
polymer/
composites
< >ensemble
The European X-Ray Free-Electron Laser
Non-equilibrium dynamics
31
g (t1 , t 2 ) =
( 2)
I (t1 ) I (t 2 )
I (t1 ) I (t 2 )
∆t = t1- t2 = constant
waiting time (t1+t2)/2 (age),
changes along line
t2
~ exp(-t/τ)
age constant
∆t changes
Anders Madsen, European XFEL,
t1
The European X-Ray Free-Electron Laser
Non-equilibrium dynamics
g ( 2 ) (t1 , t 2 )
32
age
Non-stationary, aging dynamics
t2
∆t
t1
Anders Madsen, European XFEL,
∆t
The European X-Ray Free-Electron Laser
Outline
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
Anders Madsen, European XFEL,
33
The European X-Ray Free-Electron Laser
Dynamics of a cross-linking polymer gel
34
OH
OH
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RESORCINOL
cluster formation
gelation
particle formation
mass fractal
structure formation
fractal surface
branched polymer
fractal surface
Crosslinked polymer
smooth surface (not fractal)
FORMALDEHYDE
SOLVENT EXCHANGE
HEAT TREATMENT
+ DRYING
RF HYDROGEL
RF AEROGEL
CARBON GEL
Lin et al., Carbon 35, 1271 (1997); Tamon et al., J. Coll. Int. Sci. 206, 577 (1998)
Anders Madsen, European XFEL,
The European X-Ray Free-Electron Laser
Dynamics of a cross-linking polymer gel
Initial
35
After 8 h
Hydrogel
Aerogel
O. Czakkel et al., Micropor. Mesopor. Mater. 86, 124 (2005)
Anders Madsen, European XFEL,
The European X-Ray Free-Electron Laser
Dynamics of a cross-linking polymer gel
g
( 2)
36
Dynamics appears in the window after 160 min
(t1 , t 2 )
1.05
-1
q = 0.00720 Å
160 min
1.04
160 min
-1
q = 0.01000 Å
-1
q = 0.01280 Å
-1
q = 0.01559 Å
-1
q = 0.01769 Å
-1
1.03
g
(2)
t
(q, t)
q = 0.02049 Å
t2
1.02
1.01
1
1
10
100
1000
t (s)
1.07
t1
t2
230 min
1.06
1.04
(2)
(q, t)
1.05
g
230 min
Continuous data acquisition;
time averaging only in timeintervals where the process is
quasi-stationery (10 min).
1.03
-1
q = 0.00720 Å
-1
1.02
q = 0.01000 Å
τ – Q dispersion can be
measured at various
ages of the sample O. Czakkel and A. Madsen,
-1
q = 0.01280 Å
-1
q = 0.01559 Å
1.01
-1
q = 0.01769 Å
-1
q = 0.02049 Å
-1
q = 0.02399 Å
1
1
10
100
1000
t (s)
t1
Anders Madsen, European XFEL,
Europhys. Lett. 95, 28001 (2011)
The European X-Ray Free-Electron Laser
Dynamics of a cross-linking polymer gel
-1
q = 0.01559 Å
(q, t)
1.05
AGE
-1
1.04
445 min
425 min
393 min
345 min
320 min
290 min
270 min
255 min
230 min
190 min
180 min
170 min
160 min
1.04
1.03
g
1.04
1.06
(2)
1.05
445 min
425 min
393 min
345 min
320 min
290 min
270 min
255 min
230 min
190 min
180 min
170 min
160 min
g
(q, t)
1.06
(2)
q = 0.02049 Å
1.05
(q, t)
445 min
425 min
393 min
345 min
320 min
290 min
270 min
255 min
230 min
190 min
180 min
170 min
160 min
1.07
g
-1
1.07
(2)
q = 0.0100 Å
1.08
37
AGE
1.03
1.03
1.02
AGE
1.02
1.02
1.01
1.01
1.01
1
1
10
100
1000
10
1
4
1
t (s)
4
10
I(q)
1000
100
10
1
0.001
100
t (s)
505 min
475 min
445 min
425 min
393 min
345 min
320 min
290 min
255 min
230 min
190 min
180 min
170 min
160 min
140 min
130 min
120 min
100 min
90 min
80 min
70 min
50 min
40 min
30 min
20 min
10 min
0 min
SAXS
0.01
q (Å)
Anders Madsen, European XFEL,
10
0.1
1000
10
4
1
1
10
100
1000
10
4
t (s)
o The dynamics slows down with time (age)
o Faster than exponential decay of g(2)
o The structure also evolves continuously (SAXS)
O. Czakkel and A. Madsen,
Europhys. Lett. 95, 28001 (2011)
The European X-Ray Free-Electron Laser
Dynamics of a cross-linking polymer gel
38
Slow dynamics (α-relaxation)
KWW form: g
0.02
( 2)
(t ) = β exp(−2[t / t0 ]γ ) + 1
3
Randomly distribured
stresses?
2.5
160 min
0.015
2
170 min
-1
1/tΓ0(sec
[s-1) ]
25
v-11/Γ
[s/m]
1/t0 ∝ Γ
30
180 min
γγ
0.01
1.5
10
1
0.005
180 min
230 min
Bouchaud & Pitard,
EPJ E 6, 231 (2001)
0.5
444 min
0
0
0.005
0.01
0.015
-1
q (Å )
0.02
0.025
5
0
0
0
0.005
0.01
0.015
-1
q (Å )
Hyper-diffusive behavior: The relaxation rate Γ is
proportional to Q (ballistic motion), and decreasing
with time. Analogy with glass formers…
Anders Madsen, European XFEL,
15
444 min
170 min
160 min
190 min
Gel point
280 min
20
0.02
0.025
0
5000
4
1 10
4
1.5 10
2 10
4
2.5 10
4
3 10
t (s)
O. Czakkel and A. Madsen,
Europhys. Lett. 95, 28001 (2011)
4
The European X-Ray Free-Electron Laser
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
Metallic glass: Mg65Cu25Y10 (TG=405K)
Propanediol (TG=170K)
γ>1
γ=1.7
γ<1
γ=1
B. Ruta et al., PRL 109, 165701 (2012)
Anders Madsen, European XFEL,
C. Caronna, Y. Chushkin, A. Madsen
PRL 100, 055702 (2008)
The European X-Ray Free-Electron Laser
Glass studies indicating aging dynamics
40
Aging of the dynamics seems to be a general feature near the glass transition
103
Aging dynamics of glassy ferrofluid:
A. Robert et al., Europhys. Lett. 75, 764 (2006)
Anders Madsen, European XFEL,
104
105
Age [s]
Aging dynamics in Wigner glass:
L. Angelini et al,
Soft Matter 9, 10955 (2013)
The European X-Ray Free-Electron Laser
Two-step structural relaxation
41
non-ergodicity level
Anders Madsen, European XFEL,
The European X-Ray Free-Electron Laser
Missing contrast (non-ergodicity level)
q = 0.01559 Å
-1
445 min
425 min
393 min
345 min
320 min
290 min
270 min
255 min
230 min
190 min
180 min
170 min
160 min
1.06
1.05
1.04
-1
1.04
445 min
425 min
393 min
345 min
320 min
290 min
270 min
255 min
230 min
190 min
180 min
170 min
160 min
1.04
1.03
(2)
1.05
min
min
min
min
min
min
min
min
min
min
min
min
min
g (q, t)
1.06
(2)
q = 0.02049 Å
1.05
(2)
445
425
393
345
320
290
270
255
230
190
180
170
160
1.07
g (q, t)
-1
1.07
g (q, t)
q = 0.0100 Å
1.08
42
1.03
1.02
1.03
1.02
1.02
1.01
1.01
1.01
1
1
1
10
100
1000
10
4
1
t (s)
10
100
1000
10
4
1
1
10
t (s)
t (s)
Debye-Waller model:
β/β0=exp(-Q2r2loc/6)….
Analysis of “missing contrast”
yields the localization length of
fast dynamics assuming rattling
dynamics (DW term, harmonic
oscillator analogy)
Anders Madsen, European XFEL,
100
Gel point
280 min
1000
10
4
The European X-Ray Free-Electron Laser
Missing contrast studies. Studying what you
can’t see…
γ<1
43
Aging of
localization length
γ>1
No aging of
localization length
Aging dynamics of a Laponite glass:
R.
Angelini et al., in press (2014)
Anders Madsen, European XFEL,
The European X-Ray Free-Electron Laser
Is there a Hard sphere glass transition?
Anders Madsen, European XFEL,
44
The European X-Ray Free-Electron Laser
The Glass Transition
Anders Madsen, European XFEL,
45
The European X-Ray Free-Electron Laser
The Sample
46
PMMA colloids in cis-decalin (HS system)
Dilute sample
Form factor
SAXS data from ID02, ESRF
Anders Madsen, European XFEL,
The European X-Ray Free-Electron Laser
Monte Carlo SAXS fitting
Anders Madsen, European XFEL,
47
The European X-Ray Free-Electron Laser
SAXS on concentrated samples
48
Fits allow determination of the
volume fraction Φ
Anders Madsen, European XFEL,
The European X-Ray Free-Electron Laser
XPCS correlation functions
Intermediate scattering function:
f(Q,t) = exp(-Γt) = exp(-D0Q2t)
MSD ∝ D0t, ergo -log(f(Q,t))/Q2 is like MSD
P. Kwasniewski, PhD thesis (ESRF & UJF, 2012)
Kwasniewski,
Fluerasu, Madsen, Soft Matter (in press, 2014)
Anders Madsen, European XFEL,
49
The European X-Ray Free-Electron Laser
Width function
Anders Madsen, European XFEL,
50
The European X-Ray Free-Electron Laser
Comparison with Mode-Coupling Theory
Anders Madsen, European XFEL,
51
The European X-Ray Free-Electron Laser
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)
Anders Madsen, European XFEL,
The European X-Ray Free-Electron Laser
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)
Anders Madsen, European XFEL,
The European X-Ray Free-Electron Laser
Higher-order correlation functions
Levy
dist.
54
coherent X-rays
αi < αc
Grazing incidence XPCS
from monolayer of gold
nanoparticles (7nm)
γ=1.5
D. Orsi et al., PRL 108, 105701 (2012)
Anders Madsen, European XFEL,
The European X-Ray Free-Electron Laser
Higher-order correlation functions
Two-time correlation function
ta
55
Sample with quakes,
just before avalanches set in…
G (t1 , t 2 ) =
I (t1 ) I (t 2 )
I (t1 ) I (t 2 )
τ = |t1 - t2|
τ
D. Orsi et al., PRL 108, 105701 (2012)
Anders Madsen, European XFEL,
ta = (t1+t2)/2
The European X-Ray Free-Electron Laser
Higher-order correlation functions
56
g(4) has a peak
characteristic time t*
Connection with fast dynamics (nonergodicity level, missing contrast,…)
D. Orsi et al., PRL 108, 105701 (2012)
Anders Madsen, European XFEL,
The European X-Ray Free-Electron Laser
Outline
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
Anders Madsen, European XFEL,
57
The European X-Ray Free-Electron Laser
4th generation
hard X-ray sources
58
European XFEL
SACLA
SwissFEL
Anders Madsen, European XFEL,
Pohang XFEL
LCLS - SACLA - SwissFEL – European XFEL – PAL XFEL - …
The European X-Ray Free-Electron Laser
Soft/Hard X-ray FELs worldwide
59
FLASH
DESY, Hamburg, GER
European XFEL
Schenefeld, Hamburg, GER
SACLA
SCSS test
Spring-8
Harima, JAP
PAL XFEL
Pohang, KOR
LCLS
SLAC, Stanford, CA
FERMI
Trieste, ITA
SwissFEL
Villigen, CH
Also projects in Sweden, Poland, China,….
Anders Madsen, European XFEL,
The European X-Ray Free-Electron Laser
European X-Ray Free-Electron Laser Facility
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)
Anders Madsen, European XFEL,
60
The European X-Ray Free-Electron Laser
The European XFEL. An underground facility
Accelerator tunnel (> 2 km long, ~ 6m diameter)
Completed Feb. 2012
Last photon tunnel section was completed
summer 2012 (~6 km tunnel in total drilled)
Total length 3400 m
www.xfel.eu
Anders Madsen, European XFEL,
61
The European X-Ray Free-Electron Laser
The European XFEL. Also visible overground…
Schenefeld site
(XFEL.EU HQ)
Anders Madsen, European XFEL,
62
The European X-Ray Free-Electron Laser
The Experimental Hall
November 2011
Anders Madsen, European XFEL,
63
The European X-Ray Free-Electron Laser
The Experimental Hall
June 2013
Anders Madsen, European XFEL,
64
The European X-Ray Free-Electron Laser
65
June 2013 (MID tunnel)
Anders Madsen, European XFEL,
The European X-Ray Free-Electron Laser
Facility Outline
66
MID @ SASE-2
Anders Madsen, European XFEL,
The European X-Ray Free-Electron Laser
diagnostic
endstand
detector
969 m
967 m
959 m
957.5 m
957 m
956 m
955 m
952 m
950 m
949 m
948.5 m
948 m
946.5 m
940 m
936.5 m
933 m
931 m
929 m
920 m
888.5 m
887.5 m
880 m
729 m
727 m
400 m
380.5 m
0m
Not shown:
MCP at 303m (fine tuning of SASE)
Distribution mirror(s) at 390m and 395m (MID on central branch)
Beam loss monitors
sample
nanofocusing CRL
timing diagnostic
diff. pumping
mirror(s)
shutter-3
X-ray splitdelay line
attenuator
imager-6
slit-3
mono-2
Si(220)
shutter-2
imager-5
high energy CRL
CRL-2
mono-1: Si(111)
XBPM & intensity-2
imager-4
slit-2
attenuator
imager-3
slit-1
imager-2
HR-SSS
high-energy mono
imager-1
horizontal
offset mirror
306 m
305 m
301 m
290 m
264 m
244 m
229 m
227.5 m
220 m
210 m
200 m
198 m
171 m
λ
shutter-1
2D-imager
CRL-1
attenuator
time-of-flight PES
XBPM & intensity-1
K-mono
spont. rad. aperture
transmissive imager
undulator
Anders Madsen, European XFEL,
t
λ
MID experimental
hutch
MID optics
hutch
MID photon
beamline
common SASE-2 beamline
(MID/HED)
67
MID beamline overview
The European X-Ray Free-Electron Laser
Hutches at SASE-2
First light at XFEL.EU, 4Q 2016
First light at MID, 2Q 2017
Anders Madsen, European XFEL,
68
The European X-Ray Free-Electron Laser
Materials Imaging and Dynamics Instrument
Structure and dynamics of condensed matter with hard X-rays
Structural and temporal correlations, coherent imaging,..
Techniques: XPCS, CXDI, XCCA, scattering, pump-probe,…
69 69
CXDI
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
XPCS
Anders Madsen, European XFEL,
XCCA,
Angular
Correlations
The European X-Ray Free-Electron Laser
Faster dynamics by XPCS?
70
Length Scale [Å]
Raman
Brillouin
IXS
Spin-Echo
NFS
DLS
XPCS
Scattering Vector Q [Å-1]
Anders Madsen, European XFEL,
Energy [eV]
Frequency [Hz]
INS
The European X-Ray Free-Electron Laser
Time structure of XFEL.EU
SC linac, up to 17.5 GeV
10 pulse trains/sec
2700 pulses/train
Multi-user mode
pulse train
220 ns between pulses
pulse duration ~ 10 fs
1e12 – 1e13 ph/pulse
single pulse
single pulse
220
220nsns
Anders Madsen, European XFEL,
The European X-Ray Free-Electron Laser
Fast Acquisition of Diffraction Patterns
Sequential mode for coherent scattering
XFEL rep rate:
4.5 MHz, 220 ns (default)
1.3 GHz, 770 ps (possible, reduced intensity)
Speckle methods
Coherent diffractive imaging (CXDI)
Time correlation spectroscopy (XPCS)
Spatial auto- and cross-correlations (XCCA)
Sample survives several pulses
(as many as the detector can store)
From Nature News and Views
G.
B. Stephenson et al., Nature Materials 8, 702 (2009)
Anders Madsen, European XFEL,
72
4.5 MHz detector
available at XFEL.EU
The European X-Ray Free-Electron Laser
Adaptive Gain Integrating Pixel Detector (AGIPD)
AGIPD project leader:
H. Graafsma (DESY)
4.5 MHz, 1M pixels, 200 µm pixel size
On-chip memory, readout between trains
4 adjustable quadrants
Central hole
Anders Madsen, European XFEL,
73
The European X-Ray Free-Electron Laser
MID Instrument at European XFEL
Sample – AGIPD detector distance: 0.2 m - ~9 m
Energy: 5 – 25 keV, higher by high-harmonic lasing?
Work
in European
progress
Anders Madsen,
XFEL,
74
The European X-Ray Free-Electron Laser
Ultrafast dynamics (fs-ps) by XSVS
75
X-Ray Speckle Visibility Spectroscopy
(SVS)
Time-resolution
independent of
detector speed
Contrast analysis yields the degree of
correlation C on summed image
C(∆t) can be mapped out
Sample can be renewed for every shot
(injector, new solid target,..)
C. Gutt et al., Optics Express 17, 55 (2009)
Anders Madsen, European XFEL,
Speckle contrast (%)
100
80
60
40
20
0
0
10
Delay τ
20
30
The European X-Ray Free-Electron Laser
Hard X-Ray Split-Delay Line
76
Co-linear beams
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
Path length difference
1µm  3.3 fs
…also for two-color experiments
and four-wave mixing………..
Anders Madsen, European XFEL,
Inclined beams
The European X-Ray Free-Electron Laser
Inclined beams from split-delay line
Optical
laser
77
X-ray
XX
∆t
X-ray
Early beam
2αi
Late beam
sample
XOX
X-ray Optical X-ray
Upwards deflecting mirror
OXX
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:
2nd pattern
1st pattern
Anders Madsen, European XFEL,
Optical X-ray X-ray
The European X-Ray Free-Electron Laser
MID Technical Design Report (TDR)
http://www.xfel.eu/documents/technical_documents/
or
https://bib-pubdb1.desy.de/record/154260
Anders Madsen, European XFEL,
78
The European X-Ray Free-Electron Laser
Recent XPCS review
79
Check the handouts for
reference list and more
details
Anders Madsen, European XFEL,
The European X-Ray Free-Electron Laser
Acknowledgments
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)
Anders Madsen, European XFEL,
80

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