XPCS: X-Ray Photon Correlation Spectroscopy

Transcription

The European X-Ray Free-Electron Laser
1
XPCS: X-Ray Photon Correlation
Spectroscopy
Anders Madsen,
European X-ray Free Electron Laser Facility, Hamburg
anders.madsen@xfel.eu
HSC17: Dynamical properties investigated by neutrons and
synchrotron X-rays
ESRF, 16 September 2014
Anders Madsen, European XFEL,
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
2
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
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
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
L
Transverse
lt=λL/2d
coherence length
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
Growth of X-ray brilliance
7
XFEL.EU
Brilliance
CPU speed
Courtesy: O. Shpyrko, UCSD
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
8
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
λ=0.9Å, d=11µm
Visibility ~ 30%
∆y=λL/d
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)
First X-ray speckle and first XPCS
Nature 352, 608 - 610 (15 August 1991);
(001) reflection
Cu3Au
Kodak
Film
X25, NSLS
PSD gas
Detector
ID10, ESRF
Signal ~ 0.6%
11
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
I/<I>
M ≈ Vscat/Vcoh
speckle contrast = 1/M
J. Goodman, Speckle Phenomena in Optics
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
Data from XPP @ LCLS
Si(111), E=9 keV
M~1, <β> ~ 0.94
C. Gutt et al,
Phys. Rev. Lett. 108, 024801 (2012)
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
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
First XPCS attempts at LCLS
16
Weak speckle patterns: The Poisson-Gamma
distribution
17
J. Goodman, Speckle Phenomena in Optics
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
Detector at 2θ
Contrast decreases if
speckles are not resolved
(approximation)
d
h
Outline
• coherence?
•…
20
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
Dynamic speckle
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
Typical XPCS setup
g (Q, t ) =
( 2)
23
I (Q,τ ) I (Q,τ + t )
I (Q)
2
= β f (Q, t ) + 1
2
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)
Photon statistics and XPCS, is it the same
contrast?
25
Static speckle pattern
XPCS
Photon
statistics
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)
2
β = 60%
relaxation time
t0 ~ few ms
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)
2
Damped oscillation
relaxation time
t0 ~ few µs
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
A. Madsen et al.,
New Journal of Physics 12, 055001 (2010)
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
=
< >ensemble
Non-Ergodicity
30
A particle (atom, molecule) does not explore the entire available
phase space (position, velocity,…) during the measurement time
glasses
< >time
gels
pastes
≠
polymer/
composites
< >ensemble
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
t1
Non-equilibrium dynamics
g ( 2 ) (t1 , t 2 )
32
age
Non-stationary, aging dynamics
t2
∆t
t1
∆t
Outline
• coherence?
• Diffusion is solid crystalline materials (Leitner et al.)
33
Dynamics of a cross-linking polymer gel
34
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)
Initial
35
After 8 h
Hydrogel
Aerogel
O. Czakkel et al., Micropor. Mesopor. Mater. 86, 124 (2005)
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
Europhys. Lett. 95, 28001 (2011)
-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)
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)
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…
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
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)
C. Caronna, Y. Chushkin, A. Madsen
PRL 100, 055702 (2008)
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)
104
105
Age [s]
Aging dynamics in Wigner glass:
L. Angelini et al,
Soft Matter 9, 10955 (2013)
Two-step structural relaxation
41
non-ergodicity level
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)
100
Gel point
280 min
1000
10
4
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)
Is there a Hard sphere glass transition?
44
The Glass Transition
45
The Sample
46
PMMA colloids in cis-decalin (HS system)
Dilute sample
Form factor
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
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)
49
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)
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
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)
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)
ta = (t1+t2)/2
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)
Outline
• coherence?
•…
57
4th generation
hard X-ray sources
58
European XFEL
SACLA
SwissFEL
Pohang XFEL
LCLS - SACLA - SwissFEL – European XFEL – PAL XFEL - …
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,….
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)
60
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
61
The European XFEL. Also visible overground…
Schenefeld site
(XFEL.EU HQ)
62
The Experimental Hall
November 2011
63
The Experimental Hall
June 2013
64
65
June 2013 (MID tunnel)
Facility Outline
66
MID @ SASE-2
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
t
λ
MID experimental
hutch
MID optics
hutch
MID photon
beamline
common SASE-2 beamline
(MID/HED)
67
MID beamline overview
Hutches at SASE-2
First light at XFEL.EU, 4Q 2016
First light at MID, 2Q 2017
68
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
XCCA,
Angular
Correlations
Faster dynamics by XPCS?
70
Length Scale [Å]
Raman
Brillouin
IXS
Spin-Echo
NFS
DLS
XPCS
Scattering Vector Q [Å-1]
Energy [eV]
Frequency [Hz]
INS
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
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)
72
4.5 MHz detector
available at XFEL.EU
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
73
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
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)
Speckle contrast (%)
100
80
60
40
20
0
0
10
Delay τ
20
30
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………..
Inclined beams
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
Optical X-ray X-ray
MID Technical Design Report (TDR)
http://www.xfel.eu/documents/technical_documents/
or
https://bib-pubdb1.desy.de/record/154260
78
Recent XPCS review
79
Check the handouts for
reference list and more
details
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)
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XPCS: X-Ray Photon Correlation Spectroscopy

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