Coherent X-ray Scattering and X-ray Ph C l i SPhoton Correlation Spectroscopy

Laurence LurioDepartment of Physics

Northern Illinois University

httpwwwniuedu~lluriocoherence

Outline

bull Theory of X-ray Photon Correlation Spectroscopyp py

bull Some examples of work done using XPCSbull Experimental tricks of the tradebull Experimental tricks of the tradebull The future of XPCS

XPCS and Dynamics in Soft MatteryLiquid Surface Capillary

WavesGutt et al PRL 91 076104 (2003)

RamanS i

Inelastic X-ray Scattering

1012 1015 Gutt et al PRL 91 076104 (2003)

Colloidal DiffusionGruumlbel et al in Slow Dynamics in Complex

SystemsScattering

BrillouinScattering

InelasticNeutron

Scattering

ncy

[Hz]

106 109 10

Neutron Spin Echo (NSE)

LaserPCSFr

eque

n

XPCS100 103 10

Poin

t Det

ecto

r

Protein DiffusionDebartolo et al (unpublished)

Wavevector Q [Aring-1]

(to date)

10-3 10

10-7 10-5 10-3 10-1 101

P

Atomic Diffusion in CuAu Alloy

Leitner et al Nature Materials 8 717 (2009)Wavevector Q [Aring 1] Leitner et al Nature Materials 8 717 (2009)

What is CoherenceWhat is CoherenceIdeal Youngrsquos double slitexperimentexperimentIntensity varies as

i ( ) d 02 1 cos 2 sin( ) I I d

Real Youngrsquos double slit experiment

Intensity varies as

02 1 cos 2 sin( ) I I d

is the contrast determined by the angular size of the source

Coherence Length and ContrastIt is generally convenient to assume the source has a

2 20( ) exp 2II x x x

g yGaussian intensity profile

0( ) exp 22

I x x x

One can then define a coherence length R

2R

This characterizes the distance over which two slits would produce an interference pattern or more generally the length scale over which any sample will produce interference effectsscale over which any sample will produce interference effects

A more rigorous theory can be found in eg Born and Wolf

Longitudinal coherence

( )E E

eg the number of wavelengths that can be added before the uncertainty adds up to a full

( )

before the uncertainty adds up to a full wavelength

Can also be viewed as a coherence time T = cCan also be viewed as a coherence time Tc c

Speckle Size and ContrastThe speckle widths are approximately the size of the diffraction pattern from a slit the size of the sample

L The contrast is given by the ratio of the scattering volume toThe contrast is given by the ratio of the scattering volume to the coherence volume xyMLWsin()

MM

L

W

Exact numbers require integrals over the sample volume and electric field q g pspatial correlation function For small angles the scattering volume is much smaller than the sample volume

How Practical is it to Make X-rays Coherenty

Consider a point 65 meters downstream of an APS Undulator A 4Undulator A 4

x y

02nm 3 10254μm 12μm

Ge 111y

14μm2x

R

2

306μm

x

yR

μ

2066μm

y y

10~ 3 10 PhotonsCoherence Area

Fraunhofer X-ray Diffraction from a SlitFraunhofer X ray Diffraction from a SlitB Lin et al RSI 67 (9) (1996)Narrow slit coherent

scattering

Wide slit incoherent scattering

Setup for XPCS at Sector 8 of the APS

Optics must preserve coherence

I f b fl t d f h l tImage of x-ray beam reflected from channel cut monochromator (left) vs artificial channel cut which allows better polish of interior faces p

S Naryanan A Sandy M Sprung D Shu and J Sullivan

Scattering of Coherent X-raysScattering of Coherent X rays

( ) iQrI Q e r r r drdr ( ) Q

e eI Q e r r r drdr

For incoherent x-rays the measured scattering represents a statistical average over many incoherent regions within the sample and one obtainssample and one obtains

e e e er r r r r r

For coherent x-rays one measures the Fourier transform of the exact density distribution not the average What one observes is a speckle pattern superposed on the average scattering pattern

Speckle from a Silica Aerogel

What to do with coherent x-rays

bull Try to invert the speckle to get information about the exact structure factor (--- phase retrieval x-ray imaging---) Generally to slow to obtain dynamics information

h d il f h f bbull Ignore the details of the exact structure factor but use the time fluctuations of the pattern to study dynamics of the material (XPCS)dynamics of the material (XPCS)

Measuring Dynamics

22)(

)()()(

tqI

ttqItqItqg

)(q

The Intensity-Intensity Correlation FunctionS lSample

R r

Ez

x

2g Q I Q t I Q t I

fEy

2 g Q I Q t I Q t I

44

01 2 3 4 1 2 3 41 2ex p

f iV e e rd r d r d r d r i Q s r r Q s r r

1 2 3 4 1 2 3 41 24

1 2 3 4

1 21 2

1 1 2 2

ex p

0 0

e e e e

i i

d r d r d r d r i Q s r r Q s r rR

r t r t r t r t

Q s r Q s rE x z t E x z t

31

3 3 0 i

Q s rE x z t

42

4 4 0 i

Q s rE x z t

How to calculate g2 (skipping most of the equations)(skipping most of the equations)

bullCalculate electric field intensity correlation function at the observation pointthe observation point

G2(Q)=fexp(iQrprime)ltEf2(rt) Ef

2(r+rprimet+t)gtrtdrprime

bullThe fourth order correlations in E can be reduced to pairs of second order correlation functions

bullAssume correlation lengths are smaller than sample size and the scattering can be factored into independent space and time parts

Final Result 22

2 ( ) 1 G Q I f Q

The contrast factor is related to the degree of

( ) ( ) ( 0)f Q S Q S Q

gcoherence and can be between 0 and 1

( ) ( ) ( )

( ) 00 iQ re e

f Q Q Q

S Q e r dr

Typical ApplicationsThe average structure is constant but the

l l fl

yp pp

local structure fluctuatesbull Diffusion of particles in solutionpbull Concentration fluctuations in binary liquidsbull Fluctuations of order parameter in a crystalFluctuations of order parameter in a crystalbull Thermally driven surface height

fluctuations in a viscous fluidfluctuations in a viscous fluidbull Vibrations of a membranebull Aging evolution of the ldquoequilibriumrdquobull Aging evolution of the equilibrium

dynamics with time

A dilute colloidal suspensionA dilute colloidal suspension (71 nm Latex in Glycerol)

To theoretically calculate the dynamic scattering factor one has to take the gcorrelation functions for a collection of point scatterers diffusing in the liquidpoint scatterers diffusing in the liquid

1

1( ) exp( i ji j

f Q iQ r t r tN

For Brownian motion this can be reduced toFor Brownian motion this can be reduced to an exponential decay proportional to the diffusion coefficientdiffusion coefficient

2

( ) DQf Q e ( )f Q eHere the diffusion coefficient is related to the viscosity and the radius a via the Stoke-Einstein relation

6BD k T a B

Correlation Functions

Wavevector Dependence

221 DQ

Short Time Diffusion Constants in Concentrated Suspensionp

1 Structural correlations lead to a slowing down of dynamicsof dynamics

2 Hydrodynamic interactions further modify the dynamics at high concentrationdynamics at high concentration

3 These effects can be calculated for the initial d f h l i f i b hdecay rate of the correlation function but the f(Qt) will not generally be an exponential at long times

( ) ( ) ( )D Q D H Q S Q

long times

0( ) ( ) ( )D Q D H Q S Q

Deviations for Stokes-Einstein Diffusion

Example 2

Atomic Diffusion in Metal AlloysLeitner et al Nature Materials 2009

Example 3 Concentrated Polymeric Vesicles

Concentrated Block Copolymer VesiclesFalus et al PRL 94 16105 2005

( ) expf q t t ( ) exp

1

f q t t

In Liquid State Near T E ti l DTg Exponential Decays Become Stretched

Example 4Example 4Antiferromagnetic Domain Fluctuations

O G Sh k l N 447 68 (2007)bull O G Shpyrko et al Nature 447 68 (2007)

Note that although the length scale of the fluctuations isNote that although the length scale of the fluctuations is large (gt10 nm) they require x-rays with wavelengths ~01

nm in order to be visible

Example 5 Dynamics of Liquid SurfacesLiquid Surfaces

bullPolystyrene films on Si wafers (Kim PRL 2003) are highly viscous and show exponential decay

bullThin liquid crystal membranes (Sikharulidze PRL 2002) show transition from oscillatory to ) yoverdamped behavior

From Jiang et al PRL 246104 2008

Limitations of XPCS

bull Too much flux (X-ray damage)ndash Radiation can cause cross linking of polymers and charging of colloids

A bl di ti i t t l (PS) i b b d 107ndash A reasonably radiation resistant polymer (PS) in vacuum can absorb around ~107

Gy (10 min in surface reflection geometry)ndash Protein in water can absorb ~105 Gy (10 sec in transmission geometry)

T littl fl (P i l t i )bull Too little flux (Poor signal to noise)

Some tricks of the trade hellipMultispeckle Detectionp

bullFalus Borthwick Mochrie RSI (2004)

bullSNR increases as NSNR increases as

bullLimitations

bullReadout rate presently around 60 Hz

N

p y

bullEfficiency lt 50

bullNew Camera under development at LBL and APS ~500 Hz at 100 efficiency (John Weizeorick and Alec Sandy) Should see first light this cycle

FocusingFocusingKhalid Laaziri and Mark Sutton

bull Focusing the x-ray beam down to a small spot (~1 m) maintains flux but increases the speckle size SNR ~ photonsspeckle so SNR goes up Disadvantage is thatphotonsspeckle so SNR goes up Disadvantage is that radiation damage goes up as well

bull Fluctuations in Fe3Al3

Heterodyne DetectionLivet et al JSR (2006)Livet et al JSR (2006)

bull Mix a static signal with a weaker dynamic signalF diff i ti l ti ti l ( t)bull For diffusive motion relaxation times are longer exp(-t) instead of exp(-2t)

bull Constant flow can be detected which is invisible toConstant flow can be detected which is invisible to homodyne (example aerosil + carbon-black rubber)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

Outline

bull Theory of X-ray Photon Correlation Spectroscopyp py

bull Some examples of work done using XPCSbull Experimental tricks of the tradebull Experimental tricks of the tradebull The future of XPCS

XPCS and Dynamics in Soft MatteryLiquid Surface Capillary

WavesGutt et al PRL 91 076104 (2003)

RamanS i

Inelastic X-ray Scattering

1012 1015 Gutt et al PRL 91 076104 (2003)

Colloidal DiffusionGruumlbel et al in Slow Dynamics in Complex

SystemsScattering

BrillouinScattering

InelasticNeutron

Scattering

ncy

[Hz]

106 109 10

Neutron Spin Echo (NSE)

LaserPCSFr

eque

n

XPCS100 103 10

Poin

t Det

ecto

r

Protein DiffusionDebartolo et al (unpublished)

Wavevector Q [Aring-1]

(to date)

10-3 10

10-7 10-5 10-3 10-1 101

P

Atomic Diffusion in CuAu Alloy

Leitner et al Nature Materials 8 717 (2009)Wavevector Q [Aring 1] Leitner et al Nature Materials 8 717 (2009)

What is CoherenceWhat is CoherenceIdeal Youngrsquos double slitexperimentexperimentIntensity varies as

i ( ) d 02 1 cos 2 sin( ) I I d

Real Youngrsquos double slit experiment

Intensity varies as

02 1 cos 2 sin( ) I I d

is the contrast determined by the angular size of the source

Coherence Length and ContrastIt is generally convenient to assume the source has a

2 20( ) exp 2II x x x

g yGaussian intensity profile

0( ) exp 22

I x x x

One can then define a coherence length R

2R

This characterizes the distance over which two slits would produce an interference pattern or more generally the length scale over which any sample will produce interference effectsscale over which any sample will produce interference effects

A more rigorous theory can be found in eg Born and Wolf

Longitudinal coherence

( )E E

eg the number of wavelengths that can be added before the uncertainty adds up to a full

( )

before the uncertainty adds up to a full wavelength

Can also be viewed as a coherence time T = cCan also be viewed as a coherence time Tc c

Speckle Size and ContrastThe speckle widths are approximately the size of the diffraction pattern from a slit the size of the sample

L The contrast is given by the ratio of the scattering volume toThe contrast is given by the ratio of the scattering volume to the coherence volume xyMLWsin()

MM

L

W

Exact numbers require integrals over the sample volume and electric field q g pspatial correlation function For small angles the scattering volume is much smaller than the sample volume

How Practical is it to Make X-rays Coherenty

Consider a point 65 meters downstream of an APS Undulator A 4Undulator A 4

x y

02nm 3 10254μm 12μm

Ge 111y

14μm2x

R

2

306μm

x

yR

μ

2066μm

y y

10~ 3 10 PhotonsCoherence Area

Fraunhofer X-ray Diffraction from a SlitFraunhofer X ray Diffraction from a SlitB Lin et al RSI 67 (9) (1996)Narrow slit coherent

scattering

Wide slit incoherent scattering

Setup for XPCS at Sector 8 of the APS

Optics must preserve coherence

I f b fl t d f h l tImage of x-ray beam reflected from channel cut monochromator (left) vs artificial channel cut which allows better polish of interior faces p

S Naryanan A Sandy M Sprung D Shu and J Sullivan

Scattering of Coherent X-raysScattering of Coherent X rays

( ) iQrI Q e r r r drdr ( ) Q

e eI Q e r r r drdr

For incoherent x-rays the measured scattering represents a statistical average over many incoherent regions within the sample and one obtainssample and one obtains

e e e er r r r r r

For coherent x-rays one measures the Fourier transform of the exact density distribution not the average What one observes is a speckle pattern superposed on the average scattering pattern

Speckle from a Silica Aerogel

What to do with coherent x-rays

bull Try to invert the speckle to get information about the exact structure factor (--- phase retrieval x-ray imaging---) Generally to slow to obtain dynamics information

h d il f h f bbull Ignore the details of the exact structure factor but use the time fluctuations of the pattern to study dynamics of the material (XPCS)dynamics of the material (XPCS)

Measuring Dynamics

22)(

)()()(

tqI

ttqItqItqg

)(q

The Intensity-Intensity Correlation FunctionS lSample

R r

Ez

x

2g Q I Q t I Q t I

fEy

2 g Q I Q t I Q t I

44

01 2 3 4 1 2 3 41 2ex p

f iV e e rd r d r d r d r i Q s r r Q s r r

1 2 3 4 1 2 3 41 24

1 2 3 4

1 21 2

1 1 2 2

ex p

0 0

e e e e

i i

d r d r d r d r i Q s r r Q s r rR

r t r t r t r t

Q s r Q s rE x z t E x z t

31

3 3 0 i

Q s rE x z t

42

4 4 0 i

Q s rE x z t

How to calculate g2 (skipping most of the equations)(skipping most of the equations)

bullCalculate electric field intensity correlation function at the observation pointthe observation point

G2(Q)=fexp(iQrprime)ltEf2(rt) Ef

2(r+rprimet+t)gtrtdrprime

bullThe fourth order correlations in E can be reduced to pairs of second order correlation functions

bullAssume correlation lengths are smaller than sample size and the scattering can be factored into independent space and time parts

Final Result 22

2 ( ) 1 G Q I f Q

The contrast factor is related to the degree of

( ) ( ) ( 0)f Q S Q S Q

gcoherence and can be between 0 and 1

( ) ( ) ( )

( ) 00 iQ re e

f Q Q Q

S Q e r dr

Typical ApplicationsThe average structure is constant but the

l l fl

yp pp

local structure fluctuatesbull Diffusion of particles in solutionpbull Concentration fluctuations in binary liquidsbull Fluctuations of order parameter in a crystalFluctuations of order parameter in a crystalbull Thermally driven surface height

fluctuations in a viscous fluidfluctuations in a viscous fluidbull Vibrations of a membranebull Aging evolution of the ldquoequilibriumrdquobull Aging evolution of the equilibrium

dynamics with time

A dilute colloidal suspensionA dilute colloidal suspension (71 nm Latex in Glycerol)

To theoretically calculate the dynamic scattering factor one has to take the gcorrelation functions for a collection of point scatterers diffusing in the liquidpoint scatterers diffusing in the liquid

1

1( ) exp( i ji j

f Q iQ r t r tN

For Brownian motion this can be reduced toFor Brownian motion this can be reduced to an exponential decay proportional to the diffusion coefficientdiffusion coefficient

2

( ) DQf Q e ( )f Q eHere the diffusion coefficient is related to the viscosity and the radius a via the Stoke-Einstein relation

6BD k T a B

Correlation Functions

Wavevector Dependence

221 DQ

Short Time Diffusion Constants in Concentrated Suspensionp

1 Structural correlations lead to a slowing down of dynamicsof dynamics

2 Hydrodynamic interactions further modify the dynamics at high concentrationdynamics at high concentration

3 These effects can be calculated for the initial d f h l i f i b hdecay rate of the correlation function but the f(Qt) will not generally be an exponential at long times

( ) ( ) ( )D Q D H Q S Q

long times

0( ) ( ) ( )D Q D H Q S Q

Deviations for Stokes-Einstein Diffusion

Example 2

Atomic Diffusion in Metal AlloysLeitner et al Nature Materials 2009

Example 3 Concentrated Polymeric Vesicles

Concentrated Block Copolymer VesiclesFalus et al PRL 94 16105 2005

( ) expf q t t ( ) exp

1

f q t t

In Liquid State Near T E ti l DTg Exponential Decays Become Stretched

Example 4Example 4Antiferromagnetic Domain Fluctuations

O G Sh k l N 447 68 (2007)bull O G Shpyrko et al Nature 447 68 (2007)

Note that although the length scale of the fluctuations isNote that although the length scale of the fluctuations is large (gt10 nm) they require x-rays with wavelengths ~01

nm in order to be visible

Example 5 Dynamics of Liquid SurfacesLiquid Surfaces

bullPolystyrene films on Si wafers (Kim PRL 2003) are highly viscous and show exponential decay

bullThin liquid crystal membranes (Sikharulidze PRL 2002) show transition from oscillatory to ) yoverdamped behavior

From Jiang et al PRL 246104 2008

Limitations of XPCS

bull Too much flux (X-ray damage)ndash Radiation can cause cross linking of polymers and charging of colloids

A bl di ti i t t l (PS) i b b d 107ndash A reasonably radiation resistant polymer (PS) in vacuum can absorb around ~107

Gy (10 min in surface reflection geometry)ndash Protein in water can absorb ~105 Gy (10 sec in transmission geometry)

T littl fl (P i l t i )bull Too little flux (Poor signal to noise)

Some tricks of the trade hellipMultispeckle Detectionp

bullFalus Borthwick Mochrie RSI (2004)

bullSNR increases as NSNR increases as

bullLimitations

bullReadout rate presently around 60 Hz

N

p y

bullEfficiency lt 50

bullNew Camera under development at LBL and APS ~500 Hz at 100 efficiency (John Weizeorick and Alec Sandy) Should see first light this cycle

FocusingFocusingKhalid Laaziri and Mark Sutton

bull Focusing the x-ray beam down to a small spot (~1 m) maintains flux but increases the speckle size SNR ~ photonsspeckle so SNR goes up Disadvantage is thatphotonsspeckle so SNR goes up Disadvantage is that radiation damage goes up as well

bull Fluctuations in Fe3Al3

Heterodyne DetectionLivet et al JSR (2006)Livet et al JSR (2006)

bull Mix a static signal with a weaker dynamic signalF diff i ti l ti ti l ( t)bull For diffusive motion relaxation times are longer exp(-t) instead of exp(-2t)

bull Constant flow can be detected which is invisible toConstant flow can be detected which is invisible to homodyne (example aerosil + carbon-black rubber)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

XPCS and Dynamics in Soft MatteryLiquid Surface Capillary

WavesGutt et al PRL 91 076104 (2003)

RamanS i

Inelastic X-ray Scattering

1012 1015 Gutt et al PRL 91 076104 (2003)

Colloidal DiffusionGruumlbel et al in Slow Dynamics in Complex

SystemsScattering

BrillouinScattering

InelasticNeutron

Scattering

ncy

[Hz]

106 109 10

Neutron Spin Echo (NSE)

LaserPCSFr

eque

n

XPCS100 103 10

Poin

t Det

ecto

r

Protein DiffusionDebartolo et al (unpublished)

Wavevector Q [Aring-1]

(to date)

10-3 10

10-7 10-5 10-3 10-1 101

P

Atomic Diffusion in CuAu Alloy

Leitner et al Nature Materials 8 717 (2009)Wavevector Q [Aring 1] Leitner et al Nature Materials 8 717 (2009)

What is CoherenceWhat is CoherenceIdeal Youngrsquos double slitexperimentexperimentIntensity varies as

i ( ) d 02 1 cos 2 sin( ) I I d

Real Youngrsquos double slit experiment

Intensity varies as

02 1 cos 2 sin( ) I I d

is the contrast determined by the angular size of the source

Coherence Length and ContrastIt is generally convenient to assume the source has a

2 20( ) exp 2II x x x

g yGaussian intensity profile

0( ) exp 22

I x x x

One can then define a coherence length R

2R

This characterizes the distance over which two slits would produce an interference pattern or more generally the length scale over which any sample will produce interference effectsscale over which any sample will produce interference effects

A more rigorous theory can be found in eg Born and Wolf

Longitudinal coherence

( )E E

eg the number of wavelengths that can be added before the uncertainty adds up to a full

( )

before the uncertainty adds up to a full wavelength

Can also be viewed as a coherence time T = cCan also be viewed as a coherence time Tc c

Speckle Size and ContrastThe speckle widths are approximately the size of the diffraction pattern from a slit the size of the sample

L The contrast is given by the ratio of the scattering volume toThe contrast is given by the ratio of the scattering volume to the coherence volume xyMLWsin()

MM

L

W

Exact numbers require integrals over the sample volume and electric field q g pspatial correlation function For small angles the scattering volume is much smaller than the sample volume

How Practical is it to Make X-rays Coherenty

Consider a point 65 meters downstream of an APS Undulator A 4Undulator A 4

x y

02nm 3 10254μm 12μm

Ge 111y

14μm2x

R

2

306μm

x

yR

μ

2066μm

y y

10~ 3 10 PhotonsCoherence Area

Fraunhofer X-ray Diffraction from a SlitFraunhofer X ray Diffraction from a SlitB Lin et al RSI 67 (9) (1996)Narrow slit coherent

scattering

Wide slit incoherent scattering

Setup for XPCS at Sector 8 of the APS

Optics must preserve coherence

I f b fl t d f h l tImage of x-ray beam reflected from channel cut monochromator (left) vs artificial channel cut which allows better polish of interior faces p

S Naryanan A Sandy M Sprung D Shu and J Sullivan

Scattering of Coherent X-raysScattering of Coherent X rays

( ) iQrI Q e r r r drdr ( ) Q

e eI Q e r r r drdr

For incoherent x-rays the measured scattering represents a statistical average over many incoherent regions within the sample and one obtainssample and one obtains

e e e er r r r r r

For coherent x-rays one measures the Fourier transform of the exact density distribution not the average What one observes is a speckle pattern superposed on the average scattering pattern

Speckle from a Silica Aerogel

What to do with coherent x-rays

bull Try to invert the speckle to get information about the exact structure factor (--- phase retrieval x-ray imaging---) Generally to slow to obtain dynamics information

h d il f h f bbull Ignore the details of the exact structure factor but use the time fluctuations of the pattern to study dynamics of the material (XPCS)dynamics of the material (XPCS)

Measuring Dynamics

22)(

)()()(

tqI

ttqItqItqg

)(q

The Intensity-Intensity Correlation FunctionS lSample

R r

Ez

x

2g Q I Q t I Q t I

fEy

2 g Q I Q t I Q t I

44

01 2 3 4 1 2 3 41 2ex p

f iV e e rd r d r d r d r i Q s r r Q s r r

1 2 3 4 1 2 3 41 24

1 2 3 4

1 21 2

1 1 2 2

ex p

0 0

e e e e

i i

d r d r d r d r i Q s r r Q s r rR

r t r t r t r t

Q s r Q s rE x z t E x z t

31

3 3 0 i

Q s rE x z t

42

4 4 0 i

Q s rE x z t

How to calculate g2 (skipping most of the equations)(skipping most of the equations)

bullCalculate electric field intensity correlation function at the observation pointthe observation point

G2(Q)=fexp(iQrprime)ltEf2(rt) Ef

2(r+rprimet+t)gtrtdrprime

bullThe fourth order correlations in E can be reduced to pairs of second order correlation functions

bullAssume correlation lengths are smaller than sample size and the scattering can be factored into independent space and time parts

Final Result 22

2 ( ) 1 G Q I f Q

The contrast factor is related to the degree of

( ) ( ) ( 0)f Q S Q S Q

gcoherence and can be between 0 and 1

( ) ( ) ( )

( ) 00 iQ re e

f Q Q Q

S Q e r dr

Typical ApplicationsThe average structure is constant but the

l l fl

yp pp

local structure fluctuatesbull Diffusion of particles in solutionpbull Concentration fluctuations in binary liquidsbull Fluctuations of order parameter in a crystalFluctuations of order parameter in a crystalbull Thermally driven surface height

fluctuations in a viscous fluidfluctuations in a viscous fluidbull Vibrations of a membranebull Aging evolution of the ldquoequilibriumrdquobull Aging evolution of the equilibrium

dynamics with time

A dilute colloidal suspensionA dilute colloidal suspension (71 nm Latex in Glycerol)

To theoretically calculate the dynamic scattering factor one has to take the gcorrelation functions for a collection of point scatterers diffusing in the liquidpoint scatterers diffusing in the liquid

1

1( ) exp( i ji j

f Q iQ r t r tN

For Brownian motion this can be reduced toFor Brownian motion this can be reduced to an exponential decay proportional to the diffusion coefficientdiffusion coefficient

2

( ) DQf Q e ( )f Q eHere the diffusion coefficient is related to the viscosity and the radius a via the Stoke-Einstein relation

6BD k T a B

Correlation Functions

Wavevector Dependence

221 DQ

Short Time Diffusion Constants in Concentrated Suspensionp

1 Structural correlations lead to a slowing down of dynamicsof dynamics

2 Hydrodynamic interactions further modify the dynamics at high concentrationdynamics at high concentration

3 These effects can be calculated for the initial d f h l i f i b hdecay rate of the correlation function but the f(Qt) will not generally be an exponential at long times

( ) ( ) ( )D Q D H Q S Q

long times

0( ) ( ) ( )D Q D H Q S Q

Deviations for Stokes-Einstein Diffusion

Example 2

Atomic Diffusion in Metal AlloysLeitner et al Nature Materials 2009

Example 3 Concentrated Polymeric Vesicles

Concentrated Block Copolymer VesiclesFalus et al PRL 94 16105 2005

( ) expf q t t ( ) exp

1

f q t t

In Liquid State Near T E ti l DTg Exponential Decays Become Stretched

Example 4Example 4Antiferromagnetic Domain Fluctuations

O G Sh k l N 447 68 (2007)bull O G Shpyrko et al Nature 447 68 (2007)

Note that although the length scale of the fluctuations isNote that although the length scale of the fluctuations is large (gt10 nm) they require x-rays with wavelengths ~01

nm in order to be visible

Example 5 Dynamics of Liquid SurfacesLiquid Surfaces

bullPolystyrene films on Si wafers (Kim PRL 2003) are highly viscous and show exponential decay

bullThin liquid crystal membranes (Sikharulidze PRL 2002) show transition from oscillatory to ) yoverdamped behavior

From Jiang et al PRL 246104 2008

Limitations of XPCS

bull Too much flux (X-ray damage)ndash Radiation can cause cross linking of polymers and charging of colloids

A bl di ti i t t l (PS) i b b d 107ndash A reasonably radiation resistant polymer (PS) in vacuum can absorb around ~107

Gy (10 min in surface reflection geometry)ndash Protein in water can absorb ~105 Gy (10 sec in transmission geometry)

T littl fl (P i l t i )bull Too little flux (Poor signal to noise)

Some tricks of the trade hellipMultispeckle Detectionp

bullFalus Borthwick Mochrie RSI (2004)

bullSNR increases as NSNR increases as

bullLimitations

bullReadout rate presently around 60 Hz

N

p y

bullEfficiency lt 50

bullNew Camera under development at LBL and APS ~500 Hz at 100 efficiency (John Weizeorick and Alec Sandy) Should see first light this cycle

FocusingFocusingKhalid Laaziri and Mark Sutton

bull Focusing the x-ray beam down to a small spot (~1 m) maintains flux but increases the speckle size SNR ~ photonsspeckle so SNR goes up Disadvantage is thatphotonsspeckle so SNR goes up Disadvantage is that radiation damage goes up as well

bull Fluctuations in Fe3Al3

Heterodyne DetectionLivet et al JSR (2006)Livet et al JSR (2006)

bull Mix a static signal with a weaker dynamic signalF diff i ti l ti ti l ( t)bull For diffusive motion relaxation times are longer exp(-t) instead of exp(-2t)

bull Constant flow can be detected which is invisible toConstant flow can be detected which is invisible to homodyne (example aerosil + carbon-black rubber)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

What is CoherenceWhat is CoherenceIdeal Youngrsquos double slitexperimentexperimentIntensity varies as

i ( ) d 02 1 cos 2 sin( ) I I d

Real Youngrsquos double slit experiment

Intensity varies as

02 1 cos 2 sin( ) I I d

is the contrast determined by the angular size of the source

Coherence Length and ContrastIt is generally convenient to assume the source has a

2 20( ) exp 2II x x x

g yGaussian intensity profile

0( ) exp 22

I x x x

One can then define a coherence length R

2R

This characterizes the distance over which two slits would produce an interference pattern or more generally the length scale over which any sample will produce interference effectsscale over which any sample will produce interference effects

A more rigorous theory can be found in eg Born and Wolf

Longitudinal coherence

( )E E

eg the number of wavelengths that can be added before the uncertainty adds up to a full

( )

before the uncertainty adds up to a full wavelength

Can also be viewed as a coherence time T = cCan also be viewed as a coherence time Tc c

Speckle Size and ContrastThe speckle widths are approximately the size of the diffraction pattern from a slit the size of the sample

L The contrast is given by the ratio of the scattering volume toThe contrast is given by the ratio of the scattering volume to the coherence volume xyMLWsin()

MM

L

W

Exact numbers require integrals over the sample volume and electric field q g pspatial correlation function For small angles the scattering volume is much smaller than the sample volume

How Practical is it to Make X-rays Coherenty

Consider a point 65 meters downstream of an APS Undulator A 4Undulator A 4

x y

02nm 3 10254μm 12μm

Ge 111y

14μm2x

R

2

306μm

x

yR

μ

2066μm

y y

10~ 3 10 PhotonsCoherence Area

Fraunhofer X-ray Diffraction from a SlitFraunhofer X ray Diffraction from a SlitB Lin et al RSI 67 (9) (1996)Narrow slit coherent

scattering

Wide slit incoherent scattering

Setup for XPCS at Sector 8 of the APS

Optics must preserve coherence

I f b fl t d f h l tImage of x-ray beam reflected from channel cut monochromator (left) vs artificial channel cut which allows better polish of interior faces p

S Naryanan A Sandy M Sprung D Shu and J Sullivan

Scattering of Coherent X-raysScattering of Coherent X rays

( ) iQrI Q e r r r drdr ( ) Q

e eI Q e r r r drdr

For incoherent x-rays the measured scattering represents a statistical average over many incoherent regions within the sample and one obtainssample and one obtains

e e e er r r r r r

For coherent x-rays one measures the Fourier transform of the exact density distribution not the average What one observes is a speckle pattern superposed on the average scattering pattern

Speckle from a Silica Aerogel

What to do with coherent x-rays

bull Try to invert the speckle to get information about the exact structure factor (--- phase retrieval x-ray imaging---) Generally to slow to obtain dynamics information

h d il f h f bbull Ignore the details of the exact structure factor but use the time fluctuations of the pattern to study dynamics of the material (XPCS)dynamics of the material (XPCS)

Measuring Dynamics

22)(

)()()(

tqI

ttqItqItqg

)(q

The Intensity-Intensity Correlation FunctionS lSample

R r

Ez

x

2g Q I Q t I Q t I

fEy

2 g Q I Q t I Q t I

44

01 2 3 4 1 2 3 41 2ex p

f iV e e rd r d r d r d r i Q s r r Q s r r

1 2 3 4 1 2 3 41 24

1 2 3 4

1 21 2

1 1 2 2

ex p

0 0

e e e e

i i

d r d r d r d r i Q s r r Q s r rR

r t r t r t r t

Q s r Q s rE x z t E x z t

31

3 3 0 i

Q s rE x z t

42

4 4 0 i

Q s rE x z t

How to calculate g2 (skipping most of the equations)(skipping most of the equations)

bullCalculate electric field intensity correlation function at the observation pointthe observation point

G2(Q)=fexp(iQrprime)ltEf2(rt) Ef

2(r+rprimet+t)gtrtdrprime

bullThe fourth order correlations in E can be reduced to pairs of second order correlation functions

bullAssume correlation lengths are smaller than sample size and the scattering can be factored into independent space and time parts

Final Result 22

2 ( ) 1 G Q I f Q

The contrast factor is related to the degree of

( ) ( ) ( 0)f Q S Q S Q

gcoherence and can be between 0 and 1

( ) ( ) ( )

( ) 00 iQ re e

f Q Q Q

S Q e r dr

Typical ApplicationsThe average structure is constant but the

l l fl

yp pp

local structure fluctuatesbull Diffusion of particles in solutionpbull Concentration fluctuations in binary liquidsbull Fluctuations of order parameter in a crystalFluctuations of order parameter in a crystalbull Thermally driven surface height

fluctuations in a viscous fluidfluctuations in a viscous fluidbull Vibrations of a membranebull Aging evolution of the ldquoequilibriumrdquobull Aging evolution of the equilibrium

dynamics with time

A dilute colloidal suspensionA dilute colloidal suspension (71 nm Latex in Glycerol)

To theoretically calculate the dynamic scattering factor one has to take the gcorrelation functions for a collection of point scatterers diffusing in the liquidpoint scatterers diffusing in the liquid

1

1( ) exp( i ji j

f Q iQ r t r tN

For Brownian motion this can be reduced toFor Brownian motion this can be reduced to an exponential decay proportional to the diffusion coefficientdiffusion coefficient

2

( ) DQf Q e ( )f Q eHere the diffusion coefficient is related to the viscosity and the radius a via the Stoke-Einstein relation

6BD k T a B

Correlation Functions

Wavevector Dependence

221 DQ

Short Time Diffusion Constants in Concentrated Suspensionp

1 Structural correlations lead to a slowing down of dynamicsof dynamics

2 Hydrodynamic interactions further modify the dynamics at high concentrationdynamics at high concentration

3 These effects can be calculated for the initial d f h l i f i b hdecay rate of the correlation function but the f(Qt) will not generally be an exponential at long times

( ) ( ) ( )D Q D H Q S Q

long times

0( ) ( ) ( )D Q D H Q S Q

Deviations for Stokes-Einstein Diffusion

Example 2

Atomic Diffusion in Metal AlloysLeitner et al Nature Materials 2009

Example 3 Concentrated Polymeric Vesicles

Concentrated Block Copolymer VesiclesFalus et al PRL 94 16105 2005

( ) expf q t t ( ) exp

1

f q t t

In Liquid State Near T E ti l DTg Exponential Decays Become Stretched

Example 4Example 4Antiferromagnetic Domain Fluctuations

O G Sh k l N 447 68 (2007)bull O G Shpyrko et al Nature 447 68 (2007)

Note that although the length scale of the fluctuations isNote that although the length scale of the fluctuations is large (gt10 nm) they require x-rays with wavelengths ~01

nm in order to be visible

Example 5 Dynamics of Liquid SurfacesLiquid Surfaces

bullPolystyrene films on Si wafers (Kim PRL 2003) are highly viscous and show exponential decay

bullThin liquid crystal membranes (Sikharulidze PRL 2002) show transition from oscillatory to ) yoverdamped behavior

From Jiang et al PRL 246104 2008

Limitations of XPCS

bull Too much flux (X-ray damage)ndash Radiation can cause cross linking of polymers and charging of colloids

A bl di ti i t t l (PS) i b b d 107ndash A reasonably radiation resistant polymer (PS) in vacuum can absorb around ~107

Gy (10 min in surface reflection geometry)ndash Protein in water can absorb ~105 Gy (10 sec in transmission geometry)

T littl fl (P i l t i )bull Too little flux (Poor signal to noise)

Some tricks of the trade hellipMultispeckle Detectionp

bullFalus Borthwick Mochrie RSI (2004)

bullSNR increases as NSNR increases as

bullLimitations

bullReadout rate presently around 60 Hz

N

p y

bullEfficiency lt 50

bullNew Camera under development at LBL and APS ~500 Hz at 100 efficiency (John Weizeorick and Alec Sandy) Should see first light this cycle

FocusingFocusingKhalid Laaziri and Mark Sutton

bull Focusing the x-ray beam down to a small spot (~1 m) maintains flux but increases the speckle size SNR ~ photonsspeckle so SNR goes up Disadvantage is thatphotonsspeckle so SNR goes up Disadvantage is that radiation damage goes up as well

bull Fluctuations in Fe3Al3

Heterodyne DetectionLivet et al JSR (2006)Livet et al JSR (2006)

bull Mix a static signal with a weaker dynamic signalF diff i ti l ti ti l ( t)bull For diffusive motion relaxation times are longer exp(-t) instead of exp(-2t)

bull Constant flow can be detected which is invisible toConstant flow can be detected which is invisible to homodyne (example aerosil + carbon-black rubber)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

Coherence Length and ContrastIt is generally convenient to assume the source has a

2 20( ) exp 2II x x x

g yGaussian intensity profile

0( ) exp 22

I x x x

One can then define a coherence length R

2R

This characterizes the distance over which two slits would produce an interference pattern or more generally the length scale over which any sample will produce interference effectsscale over which any sample will produce interference effects

A more rigorous theory can be found in eg Born and Wolf

Longitudinal coherence

( )E E

eg the number of wavelengths that can be added before the uncertainty adds up to a full

( )

before the uncertainty adds up to a full wavelength

Can also be viewed as a coherence time T = cCan also be viewed as a coherence time Tc c

Speckle Size and ContrastThe speckle widths are approximately the size of the diffraction pattern from a slit the size of the sample

L The contrast is given by the ratio of the scattering volume toThe contrast is given by the ratio of the scattering volume to the coherence volume xyMLWsin()

MM

L

W

Exact numbers require integrals over the sample volume and electric field q g pspatial correlation function For small angles the scattering volume is much smaller than the sample volume

How Practical is it to Make X-rays Coherenty

Consider a point 65 meters downstream of an APS Undulator A 4Undulator A 4

x y

02nm 3 10254μm 12μm

Ge 111y

14μm2x

R

2

306μm

x

yR

μ

2066μm

y y

10~ 3 10 PhotonsCoherence Area

Fraunhofer X-ray Diffraction from a SlitFraunhofer X ray Diffraction from a SlitB Lin et al RSI 67 (9) (1996)Narrow slit coherent

scattering

Wide slit incoherent scattering

Setup for XPCS at Sector 8 of the APS

Optics must preserve coherence

I f b fl t d f h l tImage of x-ray beam reflected from channel cut monochromator (left) vs artificial channel cut which allows better polish of interior faces p

S Naryanan A Sandy M Sprung D Shu and J Sullivan

Scattering of Coherent X-raysScattering of Coherent X rays

( ) iQrI Q e r r r drdr ( ) Q

e eI Q e r r r drdr

For incoherent x-rays the measured scattering represents a statistical average over many incoherent regions within the sample and one obtainssample and one obtains

e e e er r r r r r

For coherent x-rays one measures the Fourier transform of the exact density distribution not the average What one observes is a speckle pattern superposed on the average scattering pattern

Speckle from a Silica Aerogel

What to do with coherent x-rays

bull Try to invert the speckle to get information about the exact structure factor (--- phase retrieval x-ray imaging---) Generally to slow to obtain dynamics information

h d il f h f bbull Ignore the details of the exact structure factor but use the time fluctuations of the pattern to study dynamics of the material (XPCS)dynamics of the material (XPCS)

Measuring Dynamics

22)(

)()()(

tqI

ttqItqItqg

)(q

The Intensity-Intensity Correlation FunctionS lSample

R r

Ez

x

2g Q I Q t I Q t I

fEy

2 g Q I Q t I Q t I

44

01 2 3 4 1 2 3 41 2ex p

f iV e e rd r d r d r d r i Q s r r Q s r r

1 2 3 4 1 2 3 41 24

1 2 3 4

1 21 2

1 1 2 2

ex p

0 0

e e e e

i i

d r d r d r d r i Q s r r Q s r rR

r t r t r t r t

Q s r Q s rE x z t E x z t

31

3 3 0 i

Q s rE x z t

42

4 4 0 i

Q s rE x z t

How to calculate g2 (skipping most of the equations)(skipping most of the equations)

bullCalculate electric field intensity correlation function at the observation pointthe observation point

G2(Q)=fexp(iQrprime)ltEf2(rt) Ef

2(r+rprimet+t)gtrtdrprime

bullThe fourth order correlations in E can be reduced to pairs of second order correlation functions

bullAssume correlation lengths are smaller than sample size and the scattering can be factored into independent space and time parts

Final Result 22

2 ( ) 1 G Q I f Q

The contrast factor is related to the degree of

( ) ( ) ( 0)f Q S Q S Q

gcoherence and can be between 0 and 1

( ) ( ) ( )

( ) 00 iQ re e

f Q Q Q

S Q e r dr

Typical ApplicationsThe average structure is constant but the

l l fl

yp pp

local structure fluctuatesbull Diffusion of particles in solutionpbull Concentration fluctuations in binary liquidsbull Fluctuations of order parameter in a crystalFluctuations of order parameter in a crystalbull Thermally driven surface height

fluctuations in a viscous fluidfluctuations in a viscous fluidbull Vibrations of a membranebull Aging evolution of the ldquoequilibriumrdquobull Aging evolution of the equilibrium

dynamics with time

A dilute colloidal suspensionA dilute colloidal suspension (71 nm Latex in Glycerol)

To theoretically calculate the dynamic scattering factor one has to take the gcorrelation functions for a collection of point scatterers diffusing in the liquidpoint scatterers diffusing in the liquid

1

1( ) exp( i ji j

f Q iQ r t r tN

For Brownian motion this can be reduced toFor Brownian motion this can be reduced to an exponential decay proportional to the diffusion coefficientdiffusion coefficient

2

( ) DQf Q e ( )f Q eHere the diffusion coefficient is related to the viscosity and the radius a via the Stoke-Einstein relation

6BD k T a B

Correlation Functions

Wavevector Dependence

221 DQ

Short Time Diffusion Constants in Concentrated Suspensionp

1 Structural correlations lead to a slowing down of dynamicsof dynamics

2 Hydrodynamic interactions further modify the dynamics at high concentrationdynamics at high concentration

3 These effects can be calculated for the initial d f h l i f i b hdecay rate of the correlation function but the f(Qt) will not generally be an exponential at long times

( ) ( ) ( )D Q D H Q S Q

long times

0( ) ( ) ( )D Q D H Q S Q

Deviations for Stokes-Einstein Diffusion

Example 2

Atomic Diffusion in Metal AlloysLeitner et al Nature Materials 2009

Example 3 Concentrated Polymeric Vesicles

Concentrated Block Copolymer VesiclesFalus et al PRL 94 16105 2005

( ) expf q t t ( ) exp

1

f q t t

In Liquid State Near T E ti l DTg Exponential Decays Become Stretched

Example 4Example 4Antiferromagnetic Domain Fluctuations

O G Sh k l N 447 68 (2007)bull O G Shpyrko et al Nature 447 68 (2007)

Note that although the length scale of the fluctuations isNote that although the length scale of the fluctuations is large (gt10 nm) they require x-rays with wavelengths ~01

nm in order to be visible

Example 5 Dynamics of Liquid SurfacesLiquid Surfaces

bullPolystyrene films on Si wafers (Kim PRL 2003) are highly viscous and show exponential decay

bullThin liquid crystal membranes (Sikharulidze PRL 2002) show transition from oscillatory to ) yoverdamped behavior

From Jiang et al PRL 246104 2008

Limitations of XPCS

bull Too much flux (X-ray damage)ndash Radiation can cause cross linking of polymers and charging of colloids

A bl di ti i t t l (PS) i b b d 107ndash A reasonably radiation resistant polymer (PS) in vacuum can absorb around ~107

Gy (10 min in surface reflection geometry)ndash Protein in water can absorb ~105 Gy (10 sec in transmission geometry)

T littl fl (P i l t i )bull Too little flux (Poor signal to noise)

Some tricks of the trade hellipMultispeckle Detectionp

bullFalus Borthwick Mochrie RSI (2004)

bullSNR increases as NSNR increases as

bullLimitations

bullReadout rate presently around 60 Hz

N

p y

bullEfficiency lt 50

bullNew Camera under development at LBL and APS ~500 Hz at 100 efficiency (John Weizeorick and Alec Sandy) Should see first light this cycle

FocusingFocusingKhalid Laaziri and Mark Sutton

bull Focusing the x-ray beam down to a small spot (~1 m) maintains flux but increases the speckle size SNR ~ photonsspeckle so SNR goes up Disadvantage is thatphotonsspeckle so SNR goes up Disadvantage is that radiation damage goes up as well

bull Fluctuations in Fe3Al3

Heterodyne DetectionLivet et al JSR (2006)Livet et al JSR (2006)

bull Mix a static signal with a weaker dynamic signalF diff i ti l ti ti l ( t)bull For diffusive motion relaxation times are longer exp(-t) instead of exp(-2t)

bull Constant flow can be detected which is invisible toConstant flow can be detected which is invisible to homodyne (example aerosil + carbon-black rubber)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

Longitudinal coherence

( )E E

eg the number of wavelengths that can be added before the uncertainty adds up to a full

( )

before the uncertainty adds up to a full wavelength

Can also be viewed as a coherence time T = cCan also be viewed as a coherence time Tc c

Speckle Size and ContrastThe speckle widths are approximately the size of the diffraction pattern from a slit the size of the sample

L The contrast is given by the ratio of the scattering volume toThe contrast is given by the ratio of the scattering volume to the coherence volume xyMLWsin()

MM

L

W

Exact numbers require integrals over the sample volume and electric field q g pspatial correlation function For small angles the scattering volume is much smaller than the sample volume

How Practical is it to Make X-rays Coherenty

Consider a point 65 meters downstream of an APS Undulator A 4Undulator A 4

x y

02nm 3 10254μm 12μm

Ge 111y

14μm2x

R

2

306μm

x

yR

μ

2066μm

y y

10~ 3 10 PhotonsCoherence Area

Fraunhofer X-ray Diffraction from a SlitFraunhofer X ray Diffraction from a SlitB Lin et al RSI 67 (9) (1996)Narrow slit coherent

scattering

Wide slit incoherent scattering

Setup for XPCS at Sector 8 of the APS

Optics must preserve coherence

I f b fl t d f h l tImage of x-ray beam reflected from channel cut monochromator (left) vs artificial channel cut which allows better polish of interior faces p

S Naryanan A Sandy M Sprung D Shu and J Sullivan

Scattering of Coherent X-raysScattering of Coherent X rays

( ) iQrI Q e r r r drdr ( ) Q

e eI Q e r r r drdr

For incoherent x-rays the measured scattering represents a statistical average over many incoherent regions within the sample and one obtainssample and one obtains

e e e er r r r r r

For coherent x-rays one measures the Fourier transform of the exact density distribution not the average What one observes is a speckle pattern superposed on the average scattering pattern

Speckle from a Silica Aerogel

What to do with coherent x-rays

bull Try to invert the speckle to get information about the exact structure factor (--- phase retrieval x-ray imaging---) Generally to slow to obtain dynamics information

h d il f h f bbull Ignore the details of the exact structure factor but use the time fluctuations of the pattern to study dynamics of the material (XPCS)dynamics of the material (XPCS)

Measuring Dynamics

22)(

)()()(

tqI

ttqItqItqg

)(q

The Intensity-Intensity Correlation FunctionS lSample

R r

Ez

x

2g Q I Q t I Q t I

fEy

2 g Q I Q t I Q t I

44

01 2 3 4 1 2 3 41 2ex p

f iV e e rd r d r d r d r i Q s r r Q s r r

1 2 3 4 1 2 3 41 24

1 2 3 4

1 21 2

1 1 2 2

ex p

0 0

e e e e

i i

d r d r d r d r i Q s r r Q s r rR

r t r t r t r t

Q s r Q s rE x z t E x z t

31

3 3 0 i

Q s rE x z t

42

4 4 0 i

Q s rE x z t

How to calculate g2 (skipping most of the equations)(skipping most of the equations)

bullCalculate electric field intensity correlation function at the observation pointthe observation point

G2(Q)=fexp(iQrprime)ltEf2(rt) Ef

2(r+rprimet+t)gtrtdrprime

bullThe fourth order correlations in E can be reduced to pairs of second order correlation functions

bullAssume correlation lengths are smaller than sample size and the scattering can be factored into independent space and time parts

Final Result 22

2 ( ) 1 G Q I f Q

The contrast factor is related to the degree of

( ) ( ) ( 0)f Q S Q S Q

gcoherence and can be between 0 and 1

( ) ( ) ( )

( ) 00 iQ re e

f Q Q Q

S Q e r dr

Typical ApplicationsThe average structure is constant but the

l l fl

yp pp

local structure fluctuatesbull Diffusion of particles in solutionpbull Concentration fluctuations in binary liquidsbull Fluctuations of order parameter in a crystalFluctuations of order parameter in a crystalbull Thermally driven surface height

fluctuations in a viscous fluidfluctuations in a viscous fluidbull Vibrations of a membranebull Aging evolution of the ldquoequilibriumrdquobull Aging evolution of the equilibrium

dynamics with time

A dilute colloidal suspensionA dilute colloidal suspension (71 nm Latex in Glycerol)

To theoretically calculate the dynamic scattering factor one has to take the gcorrelation functions for a collection of point scatterers diffusing in the liquidpoint scatterers diffusing in the liquid

1

1( ) exp( i ji j

f Q iQ r t r tN

For Brownian motion this can be reduced toFor Brownian motion this can be reduced to an exponential decay proportional to the diffusion coefficientdiffusion coefficient

2

( ) DQf Q e ( )f Q eHere the diffusion coefficient is related to the viscosity and the radius a via the Stoke-Einstein relation

6BD k T a B

Correlation Functions

Wavevector Dependence

221 DQ

Short Time Diffusion Constants in Concentrated Suspensionp

1 Structural correlations lead to a slowing down of dynamicsof dynamics

2 Hydrodynamic interactions further modify the dynamics at high concentrationdynamics at high concentration

3 These effects can be calculated for the initial d f h l i f i b hdecay rate of the correlation function but the f(Qt) will not generally be an exponential at long times

( ) ( ) ( )D Q D H Q S Q

long times

0( ) ( ) ( )D Q D H Q S Q

Deviations for Stokes-Einstein Diffusion

Example 2

Atomic Diffusion in Metal AlloysLeitner et al Nature Materials 2009

Example 3 Concentrated Polymeric Vesicles

Concentrated Block Copolymer VesiclesFalus et al PRL 94 16105 2005

( ) expf q t t ( ) exp

1

f q t t

In Liquid State Near T E ti l DTg Exponential Decays Become Stretched

Example 4Example 4Antiferromagnetic Domain Fluctuations

O G Sh k l N 447 68 (2007)bull O G Shpyrko et al Nature 447 68 (2007)

Note that although the length scale of the fluctuations isNote that although the length scale of the fluctuations is large (gt10 nm) they require x-rays with wavelengths ~01

nm in order to be visible

Example 5 Dynamics of Liquid SurfacesLiquid Surfaces

bullPolystyrene films on Si wafers (Kim PRL 2003) are highly viscous and show exponential decay

bullThin liquid crystal membranes (Sikharulidze PRL 2002) show transition from oscillatory to ) yoverdamped behavior

From Jiang et al PRL 246104 2008

Limitations of XPCS

bull Too much flux (X-ray damage)ndash Radiation can cause cross linking of polymers and charging of colloids

A bl di ti i t t l (PS) i b b d 107ndash A reasonably radiation resistant polymer (PS) in vacuum can absorb around ~107

Gy (10 min in surface reflection geometry)ndash Protein in water can absorb ~105 Gy (10 sec in transmission geometry)

T littl fl (P i l t i )bull Too little flux (Poor signal to noise)

Some tricks of the trade hellipMultispeckle Detectionp

bullFalus Borthwick Mochrie RSI (2004)

bullSNR increases as NSNR increases as

bullLimitations

bullReadout rate presently around 60 Hz

N

p y

bullEfficiency lt 50

bullNew Camera under development at LBL and APS ~500 Hz at 100 efficiency (John Weizeorick and Alec Sandy) Should see first light this cycle

FocusingFocusingKhalid Laaziri and Mark Sutton

bull Focusing the x-ray beam down to a small spot (~1 m) maintains flux but increases the speckle size SNR ~ photonsspeckle so SNR goes up Disadvantage is thatphotonsspeckle so SNR goes up Disadvantage is that radiation damage goes up as well

bull Fluctuations in Fe3Al3

Heterodyne DetectionLivet et al JSR (2006)Livet et al JSR (2006)

bull Mix a static signal with a weaker dynamic signalF diff i ti l ti ti l ( t)bull For diffusive motion relaxation times are longer exp(-t) instead of exp(-2t)

bull Constant flow can be detected which is invisible toConstant flow can be detected which is invisible to homodyne (example aerosil + carbon-black rubber)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

Speckle Size and ContrastThe speckle widths are approximately the size of the diffraction pattern from a slit the size of the sample

L The contrast is given by the ratio of the scattering volume toThe contrast is given by the ratio of the scattering volume to the coherence volume xyMLWsin()

MM

L

W

Exact numbers require integrals over the sample volume and electric field q g pspatial correlation function For small angles the scattering volume is much smaller than the sample volume

How Practical is it to Make X-rays Coherenty

Consider a point 65 meters downstream of an APS Undulator A 4Undulator A 4

x y

02nm 3 10254μm 12μm

Ge 111y

14μm2x

R

2

306μm

x

yR

μ

2066μm

y y

10~ 3 10 PhotonsCoherence Area

Fraunhofer X-ray Diffraction from a SlitFraunhofer X ray Diffraction from a SlitB Lin et al RSI 67 (9) (1996)Narrow slit coherent

scattering

Wide slit incoherent scattering

Setup for XPCS at Sector 8 of the APS

Optics must preserve coherence

I f b fl t d f h l tImage of x-ray beam reflected from channel cut monochromator (left) vs artificial channel cut which allows better polish of interior faces p

S Naryanan A Sandy M Sprung D Shu and J Sullivan

Scattering of Coherent X-raysScattering of Coherent X rays

( ) iQrI Q e r r r drdr ( ) Q

e eI Q e r r r drdr

For incoherent x-rays the measured scattering represents a statistical average over many incoherent regions within the sample and one obtainssample and one obtains

e e e er r r r r r

For coherent x-rays one measures the Fourier transform of the exact density distribution not the average What one observes is a speckle pattern superposed on the average scattering pattern

Speckle from a Silica Aerogel

What to do with coherent x-rays

bull Try to invert the speckle to get information about the exact structure factor (--- phase retrieval x-ray imaging---) Generally to slow to obtain dynamics information

h d il f h f bbull Ignore the details of the exact structure factor but use the time fluctuations of the pattern to study dynamics of the material (XPCS)dynamics of the material (XPCS)

Measuring Dynamics

22)(

)()()(

tqI

ttqItqItqg

)(q

The Intensity-Intensity Correlation FunctionS lSample

R r

Ez

x

2g Q I Q t I Q t I

fEy

2 g Q I Q t I Q t I

44

01 2 3 4 1 2 3 41 2ex p

f iV e e rd r d r d r d r i Q s r r Q s r r

1 2 3 4 1 2 3 41 24

1 2 3 4

1 21 2

1 1 2 2

ex p

0 0

e e e e

i i

d r d r d r d r i Q s r r Q s r rR

r t r t r t r t

Q s r Q s rE x z t E x z t

31

3 3 0 i

Q s rE x z t

42

4 4 0 i

Q s rE x z t

How to calculate g2 (skipping most of the equations)(skipping most of the equations)

bullCalculate electric field intensity correlation function at the observation pointthe observation point

G2(Q)=fexp(iQrprime)ltEf2(rt) Ef

2(r+rprimet+t)gtrtdrprime

bullThe fourth order correlations in E can be reduced to pairs of second order correlation functions

bullAssume correlation lengths are smaller than sample size and the scattering can be factored into independent space and time parts

Final Result 22

2 ( ) 1 G Q I f Q

The contrast factor is related to the degree of

( ) ( ) ( 0)f Q S Q S Q

gcoherence and can be between 0 and 1

( ) ( ) ( )

( ) 00 iQ re e

f Q Q Q

S Q e r dr

Typical ApplicationsThe average structure is constant but the

l l fl

yp pp

local structure fluctuatesbull Diffusion of particles in solutionpbull Concentration fluctuations in binary liquidsbull Fluctuations of order parameter in a crystalFluctuations of order parameter in a crystalbull Thermally driven surface height

fluctuations in a viscous fluidfluctuations in a viscous fluidbull Vibrations of a membranebull Aging evolution of the ldquoequilibriumrdquobull Aging evolution of the equilibrium

dynamics with time

A dilute colloidal suspensionA dilute colloidal suspension (71 nm Latex in Glycerol)

To theoretically calculate the dynamic scattering factor one has to take the gcorrelation functions for a collection of point scatterers diffusing in the liquidpoint scatterers diffusing in the liquid

1

1( ) exp( i ji j

f Q iQ r t r tN

For Brownian motion this can be reduced toFor Brownian motion this can be reduced to an exponential decay proportional to the diffusion coefficientdiffusion coefficient

2

( ) DQf Q e ( )f Q eHere the diffusion coefficient is related to the viscosity and the radius a via the Stoke-Einstein relation

6BD k T a B

Correlation Functions

Wavevector Dependence

221 DQ

Short Time Diffusion Constants in Concentrated Suspensionp

1 Structural correlations lead to a slowing down of dynamicsof dynamics

2 Hydrodynamic interactions further modify the dynamics at high concentrationdynamics at high concentration

3 These effects can be calculated for the initial d f h l i f i b hdecay rate of the correlation function but the f(Qt) will not generally be an exponential at long times

( ) ( ) ( )D Q D H Q S Q

long times

0( ) ( ) ( )D Q D H Q S Q

Deviations for Stokes-Einstein Diffusion

Example 2

Atomic Diffusion in Metal AlloysLeitner et al Nature Materials 2009

Example 3 Concentrated Polymeric Vesicles

Concentrated Block Copolymer VesiclesFalus et al PRL 94 16105 2005

( ) expf q t t ( ) exp

1

f q t t

In Liquid State Near T E ti l DTg Exponential Decays Become Stretched

Example 4Example 4Antiferromagnetic Domain Fluctuations

O G Sh k l N 447 68 (2007)bull O G Shpyrko et al Nature 447 68 (2007)

Note that although the length scale of the fluctuations isNote that although the length scale of the fluctuations is large (gt10 nm) they require x-rays with wavelengths ~01

nm in order to be visible

Example 5 Dynamics of Liquid SurfacesLiquid Surfaces

bullPolystyrene films on Si wafers (Kim PRL 2003) are highly viscous and show exponential decay

bullThin liquid crystal membranes (Sikharulidze PRL 2002) show transition from oscillatory to ) yoverdamped behavior

From Jiang et al PRL 246104 2008

Limitations of XPCS

bull Too much flux (X-ray damage)ndash Radiation can cause cross linking of polymers and charging of colloids

A bl di ti i t t l (PS) i b b d 107ndash A reasonably radiation resistant polymer (PS) in vacuum can absorb around ~107

Gy (10 min in surface reflection geometry)ndash Protein in water can absorb ~105 Gy (10 sec in transmission geometry)

T littl fl (P i l t i )bull Too little flux (Poor signal to noise)

Some tricks of the trade hellipMultispeckle Detectionp

bullFalus Borthwick Mochrie RSI (2004)

bullSNR increases as NSNR increases as

bullLimitations

bullReadout rate presently around 60 Hz

N

p y

bullEfficiency lt 50

bullNew Camera under development at LBL and APS ~500 Hz at 100 efficiency (John Weizeorick and Alec Sandy) Should see first light this cycle

FocusingFocusingKhalid Laaziri and Mark Sutton

bull Focusing the x-ray beam down to a small spot (~1 m) maintains flux but increases the speckle size SNR ~ photonsspeckle so SNR goes up Disadvantage is thatphotonsspeckle so SNR goes up Disadvantage is that radiation damage goes up as well

bull Fluctuations in Fe3Al3

Heterodyne DetectionLivet et al JSR (2006)Livet et al JSR (2006)

bull Mix a static signal with a weaker dynamic signalF diff i ti l ti ti l ( t)bull For diffusive motion relaxation times are longer exp(-t) instead of exp(-2t)

bull Constant flow can be detected which is invisible toConstant flow can be detected which is invisible to homodyne (example aerosil + carbon-black rubber)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

How Practical is it to Make X-rays Coherenty

Consider a point 65 meters downstream of an APS Undulator A 4Undulator A 4

x y

02nm 3 10254μm 12μm

Ge 111y

14μm2x

R

2

306μm

x

yR

μ

2066μm

y y

10~ 3 10 PhotonsCoherence Area

Fraunhofer X-ray Diffraction from a SlitFraunhofer X ray Diffraction from a SlitB Lin et al RSI 67 (9) (1996)Narrow slit coherent

scattering

Wide slit incoherent scattering

Setup for XPCS at Sector 8 of the APS

Optics must preserve coherence

I f b fl t d f h l tImage of x-ray beam reflected from channel cut monochromator (left) vs artificial channel cut which allows better polish of interior faces p

S Naryanan A Sandy M Sprung D Shu and J Sullivan

Scattering of Coherent X-raysScattering of Coherent X rays

( ) iQrI Q e r r r drdr ( ) Q

e eI Q e r r r drdr

For incoherent x-rays the measured scattering represents a statistical average over many incoherent regions within the sample and one obtainssample and one obtains

e e e er r r r r r

For coherent x-rays one measures the Fourier transform of the exact density distribution not the average What one observes is a speckle pattern superposed on the average scattering pattern

Speckle from a Silica Aerogel

What to do with coherent x-rays

bull Try to invert the speckle to get information about the exact structure factor (--- phase retrieval x-ray imaging---) Generally to slow to obtain dynamics information

h d il f h f bbull Ignore the details of the exact structure factor but use the time fluctuations of the pattern to study dynamics of the material (XPCS)dynamics of the material (XPCS)

Measuring Dynamics

22)(

)()()(

tqI

ttqItqItqg

)(q

The Intensity-Intensity Correlation FunctionS lSample

R r

Ez

x

2g Q I Q t I Q t I

fEy

2 g Q I Q t I Q t I

44

01 2 3 4 1 2 3 41 2ex p

f iV e e rd r d r d r d r i Q s r r Q s r r

1 2 3 4 1 2 3 41 24

1 2 3 4

1 21 2

1 1 2 2

ex p

0 0

e e e e

i i

d r d r d r d r i Q s r r Q s r rR

r t r t r t r t

Q s r Q s rE x z t E x z t

31

3 3 0 i

Q s rE x z t

42

4 4 0 i

Q s rE x z t

How to calculate g2 (skipping most of the equations)(skipping most of the equations)

bullCalculate electric field intensity correlation function at the observation pointthe observation point

G2(Q)=fexp(iQrprime)ltEf2(rt) Ef

2(r+rprimet+t)gtrtdrprime

bullThe fourth order correlations in E can be reduced to pairs of second order correlation functions

bullAssume correlation lengths are smaller than sample size and the scattering can be factored into independent space and time parts

Final Result 22

2 ( ) 1 G Q I f Q

The contrast factor is related to the degree of

( ) ( ) ( 0)f Q S Q S Q

gcoherence and can be between 0 and 1

( ) ( ) ( )

( ) 00 iQ re e

f Q Q Q

S Q e r dr

Typical ApplicationsThe average structure is constant but the

l l fl

yp pp

local structure fluctuatesbull Diffusion of particles in solutionpbull Concentration fluctuations in binary liquidsbull Fluctuations of order parameter in a crystalFluctuations of order parameter in a crystalbull Thermally driven surface height

fluctuations in a viscous fluidfluctuations in a viscous fluidbull Vibrations of a membranebull Aging evolution of the ldquoequilibriumrdquobull Aging evolution of the equilibrium

dynamics with time

A dilute colloidal suspensionA dilute colloidal suspension (71 nm Latex in Glycerol)

To theoretically calculate the dynamic scattering factor one has to take the gcorrelation functions for a collection of point scatterers diffusing in the liquidpoint scatterers diffusing in the liquid

1

1( ) exp( i ji j

f Q iQ r t r tN

For Brownian motion this can be reduced toFor Brownian motion this can be reduced to an exponential decay proportional to the diffusion coefficientdiffusion coefficient

2

( ) DQf Q e ( )f Q eHere the diffusion coefficient is related to the viscosity and the radius a via the Stoke-Einstein relation

6BD k T a B

Correlation Functions

Wavevector Dependence

221 DQ

Short Time Diffusion Constants in Concentrated Suspensionp

1 Structural correlations lead to a slowing down of dynamicsof dynamics

2 Hydrodynamic interactions further modify the dynamics at high concentrationdynamics at high concentration

3 These effects can be calculated for the initial d f h l i f i b hdecay rate of the correlation function but the f(Qt) will not generally be an exponential at long times

( ) ( ) ( )D Q D H Q S Q

long times

0( ) ( ) ( )D Q D H Q S Q

Deviations for Stokes-Einstein Diffusion

Example 2

Atomic Diffusion in Metal AlloysLeitner et al Nature Materials 2009

Example 3 Concentrated Polymeric Vesicles

Concentrated Block Copolymer VesiclesFalus et al PRL 94 16105 2005

( ) expf q t t ( ) exp

1

f q t t

In Liquid State Near T E ti l DTg Exponential Decays Become Stretched

Example 4Example 4Antiferromagnetic Domain Fluctuations

O G Sh k l N 447 68 (2007)bull O G Shpyrko et al Nature 447 68 (2007)

Note that although the length scale of the fluctuations isNote that although the length scale of the fluctuations is large (gt10 nm) they require x-rays with wavelengths ~01

nm in order to be visible

Example 5 Dynamics of Liquid SurfacesLiquid Surfaces

bullPolystyrene films on Si wafers (Kim PRL 2003) are highly viscous and show exponential decay

bullThin liquid crystal membranes (Sikharulidze PRL 2002) show transition from oscillatory to ) yoverdamped behavior

From Jiang et al PRL 246104 2008

Limitations of XPCS

bull Too much flux (X-ray damage)ndash Radiation can cause cross linking of polymers and charging of colloids

A bl di ti i t t l (PS) i b b d 107ndash A reasonably radiation resistant polymer (PS) in vacuum can absorb around ~107

Gy (10 min in surface reflection geometry)ndash Protein in water can absorb ~105 Gy (10 sec in transmission geometry)

T littl fl (P i l t i )bull Too little flux (Poor signal to noise)

Some tricks of the trade hellipMultispeckle Detectionp

bullFalus Borthwick Mochrie RSI (2004)

bullSNR increases as NSNR increases as

bullLimitations

bullReadout rate presently around 60 Hz

N

p y

bullEfficiency lt 50

bullNew Camera under development at LBL and APS ~500 Hz at 100 efficiency (John Weizeorick and Alec Sandy) Should see first light this cycle

FocusingFocusingKhalid Laaziri and Mark Sutton

bull Focusing the x-ray beam down to a small spot (~1 m) maintains flux but increases the speckle size SNR ~ photonsspeckle so SNR goes up Disadvantage is thatphotonsspeckle so SNR goes up Disadvantage is that radiation damage goes up as well

bull Fluctuations in Fe3Al3

Heterodyne DetectionLivet et al JSR (2006)Livet et al JSR (2006)

bull Mix a static signal with a weaker dynamic signalF diff i ti l ti ti l ( t)bull For diffusive motion relaxation times are longer exp(-t) instead of exp(-2t)

bull Constant flow can be detected which is invisible toConstant flow can be detected which is invisible to homodyne (example aerosil + carbon-black rubber)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

Fraunhofer X-ray Diffraction from a SlitFraunhofer X ray Diffraction from a SlitB Lin et al RSI 67 (9) (1996)Narrow slit coherent

scattering

Wide slit incoherent scattering

Setup for XPCS at Sector 8 of the APS

Optics must preserve coherence

I f b fl t d f h l tImage of x-ray beam reflected from channel cut monochromator (left) vs artificial channel cut which allows better polish of interior faces p

S Naryanan A Sandy M Sprung D Shu and J Sullivan

Scattering of Coherent X-raysScattering of Coherent X rays

( ) iQrI Q e r r r drdr ( ) Q

e eI Q e r r r drdr

For incoherent x-rays the measured scattering represents a statistical average over many incoherent regions within the sample and one obtainssample and one obtains

e e e er r r r r r

For coherent x-rays one measures the Fourier transform of the exact density distribution not the average What one observes is a speckle pattern superposed on the average scattering pattern

Speckle from a Silica Aerogel

What to do with coherent x-rays

bull Try to invert the speckle to get information about the exact structure factor (--- phase retrieval x-ray imaging---) Generally to slow to obtain dynamics information

h d il f h f bbull Ignore the details of the exact structure factor but use the time fluctuations of the pattern to study dynamics of the material (XPCS)dynamics of the material (XPCS)

Measuring Dynamics

22)(

)()()(

tqI

ttqItqItqg

)(q

The Intensity-Intensity Correlation FunctionS lSample

R r

Ez

x

2g Q I Q t I Q t I

fEy

2 g Q I Q t I Q t I

44

01 2 3 4 1 2 3 41 2ex p

f iV e e rd r d r d r d r i Q s r r Q s r r

1 2 3 4 1 2 3 41 24

1 2 3 4

1 21 2

1 1 2 2

ex p

0 0

e e e e

i i

d r d r d r d r i Q s r r Q s r rR

r t r t r t r t

Q s r Q s rE x z t E x z t

31

3 3 0 i

Q s rE x z t

42

4 4 0 i

Q s rE x z t

How to calculate g2 (skipping most of the equations)(skipping most of the equations)

bullCalculate electric field intensity correlation function at the observation pointthe observation point

G2(Q)=fexp(iQrprime)ltEf2(rt) Ef

2(r+rprimet+t)gtrtdrprime

bullThe fourth order correlations in E can be reduced to pairs of second order correlation functions

bullAssume correlation lengths are smaller than sample size and the scattering can be factored into independent space and time parts

Final Result 22

2 ( ) 1 G Q I f Q

The contrast factor is related to the degree of

( ) ( ) ( 0)f Q S Q S Q

gcoherence and can be between 0 and 1

( ) ( ) ( )

( ) 00 iQ re e

f Q Q Q

S Q e r dr

Typical ApplicationsThe average structure is constant but the

l l fl

yp pp

local structure fluctuatesbull Diffusion of particles in solutionpbull Concentration fluctuations in binary liquidsbull Fluctuations of order parameter in a crystalFluctuations of order parameter in a crystalbull Thermally driven surface height

fluctuations in a viscous fluidfluctuations in a viscous fluidbull Vibrations of a membranebull Aging evolution of the ldquoequilibriumrdquobull Aging evolution of the equilibrium

dynamics with time

A dilute colloidal suspensionA dilute colloidal suspension (71 nm Latex in Glycerol)

To theoretically calculate the dynamic scattering factor one has to take the gcorrelation functions for a collection of point scatterers diffusing in the liquidpoint scatterers diffusing in the liquid

1

1( ) exp( i ji j

f Q iQ r t r tN

For Brownian motion this can be reduced toFor Brownian motion this can be reduced to an exponential decay proportional to the diffusion coefficientdiffusion coefficient

2

( ) DQf Q e ( )f Q eHere the diffusion coefficient is related to the viscosity and the radius a via the Stoke-Einstein relation

6BD k T a B

Correlation Functions

Wavevector Dependence

221 DQ

Short Time Diffusion Constants in Concentrated Suspensionp

1 Structural correlations lead to a slowing down of dynamicsof dynamics

2 Hydrodynamic interactions further modify the dynamics at high concentrationdynamics at high concentration

3 These effects can be calculated for the initial d f h l i f i b hdecay rate of the correlation function but the f(Qt) will not generally be an exponential at long times

( ) ( ) ( )D Q D H Q S Q

long times

0( ) ( ) ( )D Q D H Q S Q

Deviations for Stokes-Einstein Diffusion

Example 2

Atomic Diffusion in Metal AlloysLeitner et al Nature Materials 2009

Example 3 Concentrated Polymeric Vesicles

Concentrated Block Copolymer VesiclesFalus et al PRL 94 16105 2005

( ) expf q t t ( ) exp

1

f q t t

In Liquid State Near T E ti l DTg Exponential Decays Become Stretched

Example 4Example 4Antiferromagnetic Domain Fluctuations

O G Sh k l N 447 68 (2007)bull O G Shpyrko et al Nature 447 68 (2007)

Note that although the length scale of the fluctuations isNote that although the length scale of the fluctuations is large (gt10 nm) they require x-rays with wavelengths ~01

nm in order to be visible

Example 5 Dynamics of Liquid SurfacesLiquid Surfaces

bullPolystyrene films on Si wafers (Kim PRL 2003) are highly viscous and show exponential decay

bullThin liquid crystal membranes (Sikharulidze PRL 2002) show transition from oscillatory to ) yoverdamped behavior

From Jiang et al PRL 246104 2008

Limitations of XPCS

bull Too much flux (X-ray damage)ndash Radiation can cause cross linking of polymers and charging of colloids

A bl di ti i t t l (PS) i b b d 107ndash A reasonably radiation resistant polymer (PS) in vacuum can absorb around ~107

Gy (10 min in surface reflection geometry)ndash Protein in water can absorb ~105 Gy (10 sec in transmission geometry)

T littl fl (P i l t i )bull Too little flux (Poor signal to noise)

Some tricks of the trade hellipMultispeckle Detectionp

bullFalus Borthwick Mochrie RSI (2004)

bullSNR increases as NSNR increases as

bullLimitations

bullReadout rate presently around 60 Hz

N

p y

bullEfficiency lt 50

bullNew Camera under development at LBL and APS ~500 Hz at 100 efficiency (John Weizeorick and Alec Sandy) Should see first light this cycle

FocusingFocusingKhalid Laaziri and Mark Sutton

bull Focusing the x-ray beam down to a small spot (~1 m) maintains flux but increases the speckle size SNR ~ photonsspeckle so SNR goes up Disadvantage is thatphotonsspeckle so SNR goes up Disadvantage is that radiation damage goes up as well

bull Fluctuations in Fe3Al3

Heterodyne DetectionLivet et al JSR (2006)Livet et al JSR (2006)

bull Mix a static signal with a weaker dynamic signalF diff i ti l ti ti l ( t)bull For diffusive motion relaxation times are longer exp(-t) instead of exp(-2t)

bull Constant flow can be detected which is invisible toConstant flow can be detected which is invisible to homodyne (example aerosil + carbon-black rubber)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

Setup for XPCS at Sector 8 of the APS

Optics must preserve coherence

I f b fl t d f h l tImage of x-ray beam reflected from channel cut monochromator (left) vs artificial channel cut which allows better polish of interior faces p

S Naryanan A Sandy M Sprung D Shu and J Sullivan

Scattering of Coherent X-raysScattering of Coherent X rays

( ) iQrI Q e r r r drdr ( ) Q

e eI Q e r r r drdr

For incoherent x-rays the measured scattering represents a statistical average over many incoherent regions within the sample and one obtainssample and one obtains

e e e er r r r r r

For coherent x-rays one measures the Fourier transform of the exact density distribution not the average What one observes is a speckle pattern superposed on the average scattering pattern

Speckle from a Silica Aerogel

What to do with coherent x-rays

bull Try to invert the speckle to get information about the exact structure factor (--- phase retrieval x-ray imaging---) Generally to slow to obtain dynamics information

h d il f h f bbull Ignore the details of the exact structure factor but use the time fluctuations of the pattern to study dynamics of the material (XPCS)dynamics of the material (XPCS)

Measuring Dynamics

22)(

)()()(

tqI

ttqItqItqg

)(q

The Intensity-Intensity Correlation FunctionS lSample

R r

Ez

x

2g Q I Q t I Q t I

fEy

2 g Q I Q t I Q t I

44

01 2 3 4 1 2 3 41 2ex p

f iV e e rd r d r d r d r i Q s r r Q s r r

1 2 3 4 1 2 3 41 24

1 2 3 4

1 21 2

1 1 2 2

ex p

0 0

e e e e

i i

d r d r d r d r i Q s r r Q s r rR

r t r t r t r t

Q s r Q s rE x z t E x z t

31

3 3 0 i

Q s rE x z t

42

4 4 0 i

Q s rE x z t

How to calculate g2 (skipping most of the equations)(skipping most of the equations)

bullCalculate electric field intensity correlation function at the observation pointthe observation point

G2(Q)=fexp(iQrprime)ltEf2(rt) Ef

2(r+rprimet+t)gtrtdrprime

bullThe fourth order correlations in E can be reduced to pairs of second order correlation functions

bullAssume correlation lengths are smaller than sample size and the scattering can be factored into independent space and time parts

Final Result 22

2 ( ) 1 G Q I f Q

The contrast factor is related to the degree of

( ) ( ) ( 0)f Q S Q S Q

gcoherence and can be between 0 and 1

( ) ( ) ( )

( ) 00 iQ re e

f Q Q Q

S Q e r dr

Typical ApplicationsThe average structure is constant but the

l l fl

yp pp

local structure fluctuatesbull Diffusion of particles in solutionpbull Concentration fluctuations in binary liquidsbull Fluctuations of order parameter in a crystalFluctuations of order parameter in a crystalbull Thermally driven surface height

fluctuations in a viscous fluidfluctuations in a viscous fluidbull Vibrations of a membranebull Aging evolution of the ldquoequilibriumrdquobull Aging evolution of the equilibrium

dynamics with time

A dilute colloidal suspensionA dilute colloidal suspension (71 nm Latex in Glycerol)

To theoretically calculate the dynamic scattering factor one has to take the gcorrelation functions for a collection of point scatterers diffusing in the liquidpoint scatterers diffusing in the liquid

1

1( ) exp( i ji j

f Q iQ r t r tN

For Brownian motion this can be reduced toFor Brownian motion this can be reduced to an exponential decay proportional to the diffusion coefficientdiffusion coefficient

2

( ) DQf Q e ( )f Q eHere the diffusion coefficient is related to the viscosity and the radius a via the Stoke-Einstein relation

6BD k T a B

Correlation Functions

Wavevector Dependence

221 DQ

Short Time Diffusion Constants in Concentrated Suspensionp

1 Structural correlations lead to a slowing down of dynamicsof dynamics

2 Hydrodynamic interactions further modify the dynamics at high concentrationdynamics at high concentration

3 These effects can be calculated for the initial d f h l i f i b hdecay rate of the correlation function but the f(Qt) will not generally be an exponential at long times

( ) ( ) ( )D Q D H Q S Q

long times

0( ) ( ) ( )D Q D H Q S Q

Deviations for Stokes-Einstein Diffusion

Example 2

Atomic Diffusion in Metal AlloysLeitner et al Nature Materials 2009

Example 3 Concentrated Polymeric Vesicles

Concentrated Block Copolymer VesiclesFalus et al PRL 94 16105 2005

( ) expf q t t ( ) exp

1

f q t t

In Liquid State Near T E ti l DTg Exponential Decays Become Stretched

Example 4Example 4Antiferromagnetic Domain Fluctuations

O G Sh k l N 447 68 (2007)bull O G Shpyrko et al Nature 447 68 (2007)

Note that although the length scale of the fluctuations isNote that although the length scale of the fluctuations is large (gt10 nm) they require x-rays with wavelengths ~01

nm in order to be visible

Example 5 Dynamics of Liquid SurfacesLiquid Surfaces

bullPolystyrene films on Si wafers (Kim PRL 2003) are highly viscous and show exponential decay

bullThin liquid crystal membranes (Sikharulidze PRL 2002) show transition from oscillatory to ) yoverdamped behavior

From Jiang et al PRL 246104 2008

Limitations of XPCS

bull Too much flux (X-ray damage)ndash Radiation can cause cross linking of polymers and charging of colloids

A bl di ti i t t l (PS) i b b d 107ndash A reasonably radiation resistant polymer (PS) in vacuum can absorb around ~107

Gy (10 min in surface reflection geometry)ndash Protein in water can absorb ~105 Gy (10 sec in transmission geometry)

T littl fl (P i l t i )bull Too little flux (Poor signal to noise)

Some tricks of the trade hellipMultispeckle Detectionp

bullFalus Borthwick Mochrie RSI (2004)

bullSNR increases as NSNR increases as

bullLimitations

bullReadout rate presently around 60 Hz

N

p y

bullEfficiency lt 50

bullNew Camera under development at LBL and APS ~500 Hz at 100 efficiency (John Weizeorick and Alec Sandy) Should see first light this cycle

FocusingFocusingKhalid Laaziri and Mark Sutton

bull Focusing the x-ray beam down to a small spot (~1 m) maintains flux but increases the speckle size SNR ~ photonsspeckle so SNR goes up Disadvantage is thatphotonsspeckle so SNR goes up Disadvantage is that radiation damage goes up as well

bull Fluctuations in Fe3Al3

Heterodyne DetectionLivet et al JSR (2006)Livet et al JSR (2006)

bull Mix a static signal with a weaker dynamic signalF diff i ti l ti ti l ( t)bull For diffusive motion relaxation times are longer exp(-t) instead of exp(-2t)

bull Constant flow can be detected which is invisible toConstant flow can be detected which is invisible to homodyne (example aerosil + carbon-black rubber)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

Optics must preserve coherence

I f b fl t d f h l tImage of x-ray beam reflected from channel cut monochromator (left) vs artificial channel cut which allows better polish of interior faces p

S Naryanan A Sandy M Sprung D Shu and J Sullivan

Scattering of Coherent X-raysScattering of Coherent X rays

( ) iQrI Q e r r r drdr ( ) Q

e eI Q e r r r drdr

For incoherent x-rays the measured scattering represents a statistical average over many incoherent regions within the sample and one obtainssample and one obtains

e e e er r r r r r

For coherent x-rays one measures the Fourier transform of the exact density distribution not the average What one observes is a speckle pattern superposed on the average scattering pattern

Speckle from a Silica Aerogel

What to do with coherent x-rays

bull Try to invert the speckle to get information about the exact structure factor (--- phase retrieval x-ray imaging---) Generally to slow to obtain dynamics information

h d il f h f bbull Ignore the details of the exact structure factor but use the time fluctuations of the pattern to study dynamics of the material (XPCS)dynamics of the material (XPCS)

Measuring Dynamics

22)(

)()()(

tqI

ttqItqItqg

)(q

The Intensity-Intensity Correlation FunctionS lSample

R r

Ez

x

2g Q I Q t I Q t I

fEy

2 g Q I Q t I Q t I

44

01 2 3 4 1 2 3 41 2ex p

f iV e e rd r d r d r d r i Q s r r Q s r r

1 2 3 4 1 2 3 41 24

1 2 3 4

1 21 2

1 1 2 2

ex p

0 0

e e e e

i i

d r d r d r d r i Q s r r Q s r rR

r t r t r t r t

Q s r Q s rE x z t E x z t

31

3 3 0 i

Q s rE x z t

42

4 4 0 i

Q s rE x z t

How to calculate g2 (skipping most of the equations)(skipping most of the equations)

bullCalculate electric field intensity correlation function at the observation pointthe observation point

G2(Q)=fexp(iQrprime)ltEf2(rt) Ef

2(r+rprimet+t)gtrtdrprime

bullThe fourth order correlations in E can be reduced to pairs of second order correlation functions

bullAssume correlation lengths are smaller than sample size and the scattering can be factored into independent space and time parts

Final Result 22

2 ( ) 1 G Q I f Q

The contrast factor is related to the degree of

( ) ( ) ( 0)f Q S Q S Q

gcoherence and can be between 0 and 1

( ) ( ) ( )

( ) 00 iQ re e

f Q Q Q

S Q e r dr

Typical ApplicationsThe average structure is constant but the

l l fl

yp pp

local structure fluctuatesbull Diffusion of particles in solutionpbull Concentration fluctuations in binary liquidsbull Fluctuations of order parameter in a crystalFluctuations of order parameter in a crystalbull Thermally driven surface height

fluctuations in a viscous fluidfluctuations in a viscous fluidbull Vibrations of a membranebull Aging evolution of the ldquoequilibriumrdquobull Aging evolution of the equilibrium

dynamics with time

A dilute colloidal suspensionA dilute colloidal suspension (71 nm Latex in Glycerol)

To theoretically calculate the dynamic scattering factor one has to take the gcorrelation functions for a collection of point scatterers diffusing in the liquidpoint scatterers diffusing in the liquid

1

1( ) exp( i ji j

f Q iQ r t r tN

For Brownian motion this can be reduced toFor Brownian motion this can be reduced to an exponential decay proportional to the diffusion coefficientdiffusion coefficient

2

( ) DQf Q e ( )f Q eHere the diffusion coefficient is related to the viscosity and the radius a via the Stoke-Einstein relation

6BD k T a B

Correlation Functions

Wavevector Dependence

221 DQ

Short Time Diffusion Constants in Concentrated Suspensionp

1 Structural correlations lead to a slowing down of dynamicsof dynamics

2 Hydrodynamic interactions further modify the dynamics at high concentrationdynamics at high concentration

3 These effects can be calculated for the initial d f h l i f i b hdecay rate of the correlation function but the f(Qt) will not generally be an exponential at long times

( ) ( ) ( )D Q D H Q S Q

long times

0( ) ( ) ( )D Q D H Q S Q

Deviations for Stokes-Einstein Diffusion

Example 2

Atomic Diffusion in Metal AlloysLeitner et al Nature Materials 2009

Example 3 Concentrated Polymeric Vesicles

Concentrated Block Copolymer VesiclesFalus et al PRL 94 16105 2005

( ) expf q t t ( ) exp

1

f q t t

In Liquid State Near T E ti l DTg Exponential Decays Become Stretched

Example 4Example 4Antiferromagnetic Domain Fluctuations

O G Sh k l N 447 68 (2007)bull O G Shpyrko et al Nature 447 68 (2007)

Note that although the length scale of the fluctuations isNote that although the length scale of the fluctuations is large (gt10 nm) they require x-rays with wavelengths ~01

nm in order to be visible

Example 5 Dynamics of Liquid SurfacesLiquid Surfaces

bullPolystyrene films on Si wafers (Kim PRL 2003) are highly viscous and show exponential decay

bullThin liquid crystal membranes (Sikharulidze PRL 2002) show transition from oscillatory to ) yoverdamped behavior

From Jiang et al PRL 246104 2008

Limitations of XPCS

bull Too much flux (X-ray damage)ndash Radiation can cause cross linking of polymers and charging of colloids

A bl di ti i t t l (PS) i b b d 107ndash A reasonably radiation resistant polymer (PS) in vacuum can absorb around ~107

Gy (10 min in surface reflection geometry)ndash Protein in water can absorb ~105 Gy (10 sec in transmission geometry)

T littl fl (P i l t i )bull Too little flux (Poor signal to noise)

Some tricks of the trade hellipMultispeckle Detectionp

bullFalus Borthwick Mochrie RSI (2004)

bullSNR increases as NSNR increases as

bullLimitations

bullReadout rate presently around 60 Hz

N

p y

bullEfficiency lt 50

bullNew Camera under development at LBL and APS ~500 Hz at 100 efficiency (John Weizeorick and Alec Sandy) Should see first light this cycle

FocusingFocusingKhalid Laaziri and Mark Sutton

bull Focusing the x-ray beam down to a small spot (~1 m) maintains flux but increases the speckle size SNR ~ photonsspeckle so SNR goes up Disadvantage is thatphotonsspeckle so SNR goes up Disadvantage is that radiation damage goes up as well

bull Fluctuations in Fe3Al3

Heterodyne DetectionLivet et al JSR (2006)Livet et al JSR (2006)

bull Mix a static signal with a weaker dynamic signalF diff i ti l ti ti l ( t)bull For diffusive motion relaxation times are longer exp(-t) instead of exp(-2t)

bull Constant flow can be detected which is invisible toConstant flow can be detected which is invisible to homodyne (example aerosil + carbon-black rubber)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

Scattering of Coherent X-raysScattering of Coherent X rays

( ) iQrI Q e r r r drdr ( ) Q

e eI Q e r r r drdr

For incoherent x-rays the measured scattering represents a statistical average over many incoherent regions within the sample and one obtainssample and one obtains

e e e er r r r r r

For coherent x-rays one measures the Fourier transform of the exact density distribution not the average What one observes is a speckle pattern superposed on the average scattering pattern

Speckle from a Silica Aerogel

What to do with coherent x-rays

bull Try to invert the speckle to get information about the exact structure factor (--- phase retrieval x-ray imaging---) Generally to slow to obtain dynamics information

h d il f h f bbull Ignore the details of the exact structure factor but use the time fluctuations of the pattern to study dynamics of the material (XPCS)dynamics of the material (XPCS)

Measuring Dynamics

22)(

)()()(

tqI

ttqItqItqg

)(q

The Intensity-Intensity Correlation FunctionS lSample

R r

Ez

x

2g Q I Q t I Q t I

fEy

2 g Q I Q t I Q t I

44

01 2 3 4 1 2 3 41 2ex p

f iV e e rd r d r d r d r i Q s r r Q s r r

1 2 3 4 1 2 3 41 24

1 2 3 4

1 21 2

1 1 2 2

ex p

0 0

e e e e

i i

d r d r d r d r i Q s r r Q s r rR

r t r t r t r t

Q s r Q s rE x z t E x z t

31

3 3 0 i

Q s rE x z t

42

4 4 0 i

Q s rE x z t

How to calculate g2 (skipping most of the equations)(skipping most of the equations)

bullCalculate electric field intensity correlation function at the observation pointthe observation point

G2(Q)=fexp(iQrprime)ltEf2(rt) Ef

2(r+rprimet+t)gtrtdrprime

bullThe fourth order correlations in E can be reduced to pairs of second order correlation functions

bullAssume correlation lengths are smaller than sample size and the scattering can be factored into independent space and time parts

Final Result 22

2 ( ) 1 G Q I f Q

The contrast factor is related to the degree of

( ) ( ) ( 0)f Q S Q S Q

gcoherence and can be between 0 and 1

( ) ( ) ( )

( ) 00 iQ re e

f Q Q Q

S Q e r dr

Typical ApplicationsThe average structure is constant but the

l l fl

yp pp

local structure fluctuatesbull Diffusion of particles in solutionpbull Concentration fluctuations in binary liquidsbull Fluctuations of order parameter in a crystalFluctuations of order parameter in a crystalbull Thermally driven surface height

fluctuations in a viscous fluidfluctuations in a viscous fluidbull Vibrations of a membranebull Aging evolution of the ldquoequilibriumrdquobull Aging evolution of the equilibrium

dynamics with time

A dilute colloidal suspensionA dilute colloidal suspension (71 nm Latex in Glycerol)

To theoretically calculate the dynamic scattering factor one has to take the gcorrelation functions for a collection of point scatterers diffusing in the liquidpoint scatterers diffusing in the liquid

1

1( ) exp( i ji j

f Q iQ r t r tN

For Brownian motion this can be reduced toFor Brownian motion this can be reduced to an exponential decay proportional to the diffusion coefficientdiffusion coefficient

2

( ) DQf Q e ( )f Q eHere the diffusion coefficient is related to the viscosity and the radius a via the Stoke-Einstein relation

6BD k T a B

Correlation Functions

Wavevector Dependence

221 DQ

Short Time Diffusion Constants in Concentrated Suspensionp

1 Structural correlations lead to a slowing down of dynamicsof dynamics

2 Hydrodynamic interactions further modify the dynamics at high concentrationdynamics at high concentration

3 These effects can be calculated for the initial d f h l i f i b hdecay rate of the correlation function but the f(Qt) will not generally be an exponential at long times

( ) ( ) ( )D Q D H Q S Q

long times

0( ) ( ) ( )D Q D H Q S Q

Deviations for Stokes-Einstein Diffusion

Example 2

Atomic Diffusion in Metal AlloysLeitner et al Nature Materials 2009

Example 3 Concentrated Polymeric Vesicles

Concentrated Block Copolymer VesiclesFalus et al PRL 94 16105 2005

( ) expf q t t ( ) exp

1

f q t t

In Liquid State Near T E ti l DTg Exponential Decays Become Stretched

Example 4Example 4Antiferromagnetic Domain Fluctuations

O G Sh k l N 447 68 (2007)bull O G Shpyrko et al Nature 447 68 (2007)

Note that although the length scale of the fluctuations isNote that although the length scale of the fluctuations is large (gt10 nm) they require x-rays with wavelengths ~01

nm in order to be visible

Example 5 Dynamics of Liquid SurfacesLiquid Surfaces

bullPolystyrene films on Si wafers (Kim PRL 2003) are highly viscous and show exponential decay

bullThin liquid crystal membranes (Sikharulidze PRL 2002) show transition from oscillatory to ) yoverdamped behavior

From Jiang et al PRL 246104 2008

Limitations of XPCS

bull Too much flux (X-ray damage)ndash Radiation can cause cross linking of polymers and charging of colloids

A bl di ti i t t l (PS) i b b d 107ndash A reasonably radiation resistant polymer (PS) in vacuum can absorb around ~107

Gy (10 min in surface reflection geometry)ndash Protein in water can absorb ~105 Gy (10 sec in transmission geometry)

T littl fl (P i l t i )bull Too little flux (Poor signal to noise)

Some tricks of the trade hellipMultispeckle Detectionp

bullFalus Borthwick Mochrie RSI (2004)

bullSNR increases as NSNR increases as

bullLimitations

bullReadout rate presently around 60 Hz

N

p y

bullEfficiency lt 50

bullNew Camera under development at LBL and APS ~500 Hz at 100 efficiency (John Weizeorick and Alec Sandy) Should see first light this cycle

FocusingFocusingKhalid Laaziri and Mark Sutton

bull Focusing the x-ray beam down to a small spot (~1 m) maintains flux but increases the speckle size SNR ~ photonsspeckle so SNR goes up Disadvantage is thatphotonsspeckle so SNR goes up Disadvantage is that radiation damage goes up as well

bull Fluctuations in Fe3Al3

Heterodyne DetectionLivet et al JSR (2006)Livet et al JSR (2006)

bull Mix a static signal with a weaker dynamic signalF diff i ti l ti ti l ( t)bull For diffusive motion relaxation times are longer exp(-t) instead of exp(-2t)

bull Constant flow can be detected which is invisible toConstant flow can be detected which is invisible to homodyne (example aerosil + carbon-black rubber)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

Speckle from a Silica Aerogel

What to do with coherent x-rays

bull Try to invert the speckle to get information about the exact structure factor (--- phase retrieval x-ray imaging---) Generally to slow to obtain dynamics information

h d il f h f bbull Ignore the details of the exact structure factor but use the time fluctuations of the pattern to study dynamics of the material (XPCS)dynamics of the material (XPCS)

Measuring Dynamics

22)(

)()()(

tqI

ttqItqItqg

)(q

The Intensity-Intensity Correlation FunctionS lSample

R r

Ez

x

2g Q I Q t I Q t I

fEy

2 g Q I Q t I Q t I

44

01 2 3 4 1 2 3 41 2ex p

f iV e e rd r d r d r d r i Q s r r Q s r r

1 2 3 4 1 2 3 41 24

1 2 3 4

1 21 2

1 1 2 2

ex p

0 0

e e e e

i i

d r d r d r d r i Q s r r Q s r rR

r t r t r t r t

Q s r Q s rE x z t E x z t

31

3 3 0 i

Q s rE x z t

42

4 4 0 i

Q s rE x z t

How to calculate g2 (skipping most of the equations)(skipping most of the equations)

bullCalculate electric field intensity correlation function at the observation pointthe observation point

G2(Q)=fexp(iQrprime)ltEf2(rt) Ef

2(r+rprimet+t)gtrtdrprime

bullThe fourth order correlations in E can be reduced to pairs of second order correlation functions

bullAssume correlation lengths are smaller than sample size and the scattering can be factored into independent space and time parts

Final Result 22

2 ( ) 1 G Q I f Q

The contrast factor is related to the degree of

( ) ( ) ( 0)f Q S Q S Q

gcoherence and can be between 0 and 1

( ) ( ) ( )

( ) 00 iQ re e

f Q Q Q

S Q e r dr

Typical ApplicationsThe average structure is constant but the

l l fl

yp pp

local structure fluctuatesbull Diffusion of particles in solutionpbull Concentration fluctuations in binary liquidsbull Fluctuations of order parameter in a crystalFluctuations of order parameter in a crystalbull Thermally driven surface height

fluctuations in a viscous fluidfluctuations in a viscous fluidbull Vibrations of a membranebull Aging evolution of the ldquoequilibriumrdquobull Aging evolution of the equilibrium

dynamics with time

A dilute colloidal suspensionA dilute colloidal suspension (71 nm Latex in Glycerol)

To theoretically calculate the dynamic scattering factor one has to take the gcorrelation functions for a collection of point scatterers diffusing in the liquidpoint scatterers diffusing in the liquid

1

1( ) exp( i ji j

f Q iQ r t r tN

For Brownian motion this can be reduced toFor Brownian motion this can be reduced to an exponential decay proportional to the diffusion coefficientdiffusion coefficient

2

( ) DQf Q e ( )f Q eHere the diffusion coefficient is related to the viscosity and the radius a via the Stoke-Einstein relation

6BD k T a B

Correlation Functions

Wavevector Dependence

221 DQ

Short Time Diffusion Constants in Concentrated Suspensionp

1 Structural correlations lead to a slowing down of dynamicsof dynamics

2 Hydrodynamic interactions further modify the dynamics at high concentrationdynamics at high concentration

3 These effects can be calculated for the initial d f h l i f i b hdecay rate of the correlation function but the f(Qt) will not generally be an exponential at long times

( ) ( ) ( )D Q D H Q S Q

long times

0( ) ( ) ( )D Q D H Q S Q

Deviations for Stokes-Einstein Diffusion

Example 2

Atomic Diffusion in Metal AlloysLeitner et al Nature Materials 2009

Example 3 Concentrated Polymeric Vesicles

Concentrated Block Copolymer VesiclesFalus et al PRL 94 16105 2005

( ) expf q t t ( ) exp

1

f q t t

In Liquid State Near T E ti l DTg Exponential Decays Become Stretched

Example 4Example 4Antiferromagnetic Domain Fluctuations

O G Sh k l N 447 68 (2007)bull O G Shpyrko et al Nature 447 68 (2007)

Note that although the length scale of the fluctuations isNote that although the length scale of the fluctuations is large (gt10 nm) they require x-rays with wavelengths ~01

nm in order to be visible

Example 5 Dynamics of Liquid SurfacesLiquid Surfaces

bullPolystyrene films on Si wafers (Kim PRL 2003) are highly viscous and show exponential decay

bullThin liquid crystal membranes (Sikharulidze PRL 2002) show transition from oscillatory to ) yoverdamped behavior

From Jiang et al PRL 246104 2008

Limitations of XPCS

bull Too much flux (X-ray damage)ndash Radiation can cause cross linking of polymers and charging of colloids

A bl di ti i t t l (PS) i b b d 107ndash A reasonably radiation resistant polymer (PS) in vacuum can absorb around ~107

Gy (10 min in surface reflection geometry)ndash Protein in water can absorb ~105 Gy (10 sec in transmission geometry)

T littl fl (P i l t i )bull Too little flux (Poor signal to noise)

Some tricks of the trade hellipMultispeckle Detectionp

bullFalus Borthwick Mochrie RSI (2004)

bullSNR increases as NSNR increases as

bullLimitations

bullReadout rate presently around 60 Hz

N

p y

bullEfficiency lt 50

bullNew Camera under development at LBL and APS ~500 Hz at 100 efficiency (John Weizeorick and Alec Sandy) Should see first light this cycle

FocusingFocusingKhalid Laaziri and Mark Sutton

bull Focusing the x-ray beam down to a small spot (~1 m) maintains flux but increases the speckle size SNR ~ photonsspeckle so SNR goes up Disadvantage is thatphotonsspeckle so SNR goes up Disadvantage is that radiation damage goes up as well

bull Fluctuations in Fe3Al3

Heterodyne DetectionLivet et al JSR (2006)Livet et al JSR (2006)

bull Mix a static signal with a weaker dynamic signalF diff i ti l ti ti l ( t)bull For diffusive motion relaxation times are longer exp(-t) instead of exp(-2t)

bull Constant flow can be detected which is invisible toConstant flow can be detected which is invisible to homodyne (example aerosil + carbon-black rubber)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

What to do with coherent x-rays

bull Try to invert the speckle to get information about the exact structure factor (--- phase retrieval x-ray imaging---) Generally to slow to obtain dynamics information

h d il f h f bbull Ignore the details of the exact structure factor but use the time fluctuations of the pattern to study dynamics of the material (XPCS)dynamics of the material (XPCS)

Measuring Dynamics

22)(

)()()(

tqI

ttqItqItqg

)(q

The Intensity-Intensity Correlation FunctionS lSample

R r

Ez

x

2g Q I Q t I Q t I

fEy

2 g Q I Q t I Q t I

44

01 2 3 4 1 2 3 41 2ex p

f iV e e rd r d r d r d r i Q s r r Q s r r

1 2 3 4 1 2 3 41 24

1 2 3 4

1 21 2

1 1 2 2

ex p

0 0

e e e e

i i

d r d r d r d r i Q s r r Q s r rR

r t r t r t r t

Q s r Q s rE x z t E x z t

31

3 3 0 i

Q s rE x z t

42

4 4 0 i

Q s rE x z t

How to calculate g2 (skipping most of the equations)(skipping most of the equations)

bullCalculate electric field intensity correlation function at the observation pointthe observation point

G2(Q)=fexp(iQrprime)ltEf2(rt) Ef

2(r+rprimet+t)gtrtdrprime

bullThe fourth order correlations in E can be reduced to pairs of second order correlation functions

bullAssume correlation lengths are smaller than sample size and the scattering can be factored into independent space and time parts

Final Result 22

2 ( ) 1 G Q I f Q

The contrast factor is related to the degree of

( ) ( ) ( 0)f Q S Q S Q

gcoherence and can be between 0 and 1

( ) ( ) ( )

( ) 00 iQ re e

f Q Q Q

S Q e r dr

Typical ApplicationsThe average structure is constant but the

l l fl

yp pp

local structure fluctuatesbull Diffusion of particles in solutionpbull Concentration fluctuations in binary liquidsbull Fluctuations of order parameter in a crystalFluctuations of order parameter in a crystalbull Thermally driven surface height

fluctuations in a viscous fluidfluctuations in a viscous fluidbull Vibrations of a membranebull Aging evolution of the ldquoequilibriumrdquobull Aging evolution of the equilibrium

dynamics with time

A dilute colloidal suspensionA dilute colloidal suspension (71 nm Latex in Glycerol)

To theoretically calculate the dynamic scattering factor one has to take the gcorrelation functions for a collection of point scatterers diffusing in the liquidpoint scatterers diffusing in the liquid

1

1( ) exp( i ji j

f Q iQ r t r tN

For Brownian motion this can be reduced toFor Brownian motion this can be reduced to an exponential decay proportional to the diffusion coefficientdiffusion coefficient

2

( ) DQf Q e ( )f Q eHere the diffusion coefficient is related to the viscosity and the radius a via the Stoke-Einstein relation

6BD k T a B

Correlation Functions

Wavevector Dependence

221 DQ

Short Time Diffusion Constants in Concentrated Suspensionp

1 Structural correlations lead to a slowing down of dynamicsof dynamics

2 Hydrodynamic interactions further modify the dynamics at high concentrationdynamics at high concentration

3 These effects can be calculated for the initial d f h l i f i b hdecay rate of the correlation function but the f(Qt) will not generally be an exponential at long times

( ) ( ) ( )D Q D H Q S Q

long times

0( ) ( ) ( )D Q D H Q S Q

Deviations for Stokes-Einstein Diffusion

Example 2

Atomic Diffusion in Metal AlloysLeitner et al Nature Materials 2009

Example 3 Concentrated Polymeric Vesicles

Concentrated Block Copolymer VesiclesFalus et al PRL 94 16105 2005

( ) expf q t t ( ) exp

1

f q t t

In Liquid State Near T E ti l DTg Exponential Decays Become Stretched

Example 4Example 4Antiferromagnetic Domain Fluctuations

O G Sh k l N 447 68 (2007)bull O G Shpyrko et al Nature 447 68 (2007)

Note that although the length scale of the fluctuations isNote that although the length scale of the fluctuations is large (gt10 nm) they require x-rays with wavelengths ~01

nm in order to be visible

Example 5 Dynamics of Liquid SurfacesLiquid Surfaces

bullPolystyrene films on Si wafers (Kim PRL 2003) are highly viscous and show exponential decay

bullThin liquid crystal membranes (Sikharulidze PRL 2002) show transition from oscillatory to ) yoverdamped behavior

From Jiang et al PRL 246104 2008

Limitations of XPCS

bull Too much flux (X-ray damage)ndash Radiation can cause cross linking of polymers and charging of colloids

A bl di ti i t t l (PS) i b b d 107ndash A reasonably radiation resistant polymer (PS) in vacuum can absorb around ~107

Gy (10 min in surface reflection geometry)ndash Protein in water can absorb ~105 Gy (10 sec in transmission geometry)

T littl fl (P i l t i )bull Too little flux (Poor signal to noise)

Some tricks of the trade hellipMultispeckle Detectionp

bullFalus Borthwick Mochrie RSI (2004)

bullSNR increases as NSNR increases as

bullLimitations

bullReadout rate presently around 60 Hz

N

p y

bullEfficiency lt 50

bullNew Camera under development at LBL and APS ~500 Hz at 100 efficiency (John Weizeorick and Alec Sandy) Should see first light this cycle

FocusingFocusingKhalid Laaziri and Mark Sutton

bull Focusing the x-ray beam down to a small spot (~1 m) maintains flux but increases the speckle size SNR ~ photonsspeckle so SNR goes up Disadvantage is thatphotonsspeckle so SNR goes up Disadvantage is that radiation damage goes up as well

bull Fluctuations in Fe3Al3

Heterodyne DetectionLivet et al JSR (2006)Livet et al JSR (2006)

bull Mix a static signal with a weaker dynamic signalF diff i ti l ti ti l ( t)bull For diffusive motion relaxation times are longer exp(-t) instead of exp(-2t)

bull Constant flow can be detected which is invisible toConstant flow can be detected which is invisible to homodyne (example aerosil + carbon-black rubber)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

Measuring Dynamics

22)(

)()()(

tqI

ttqItqItqg

)(q

The Intensity-Intensity Correlation FunctionS lSample

R r

Ez

x

2g Q I Q t I Q t I

fEy

2 g Q I Q t I Q t I

44

01 2 3 4 1 2 3 41 2ex p

f iV e e rd r d r d r d r i Q s r r Q s r r

1 2 3 4 1 2 3 41 24

1 2 3 4

1 21 2

1 1 2 2

ex p

0 0

e e e e

i i

d r d r d r d r i Q s r r Q s r rR

r t r t r t r t

Q s r Q s rE x z t E x z t

31

3 3 0 i

Q s rE x z t

42

4 4 0 i

Q s rE x z t

How to calculate g2 (skipping most of the equations)(skipping most of the equations)

bullCalculate electric field intensity correlation function at the observation pointthe observation point

G2(Q)=fexp(iQrprime)ltEf2(rt) Ef

2(r+rprimet+t)gtrtdrprime

bullThe fourth order correlations in E can be reduced to pairs of second order correlation functions

bullAssume correlation lengths are smaller than sample size and the scattering can be factored into independent space and time parts

Final Result 22

2 ( ) 1 G Q I f Q

The contrast factor is related to the degree of

( ) ( ) ( 0)f Q S Q S Q

gcoherence and can be between 0 and 1

( ) ( ) ( )

( ) 00 iQ re e

f Q Q Q

S Q e r dr

Typical ApplicationsThe average structure is constant but the

l l fl

yp pp

local structure fluctuatesbull Diffusion of particles in solutionpbull Concentration fluctuations in binary liquidsbull Fluctuations of order parameter in a crystalFluctuations of order parameter in a crystalbull Thermally driven surface height

fluctuations in a viscous fluidfluctuations in a viscous fluidbull Vibrations of a membranebull Aging evolution of the ldquoequilibriumrdquobull Aging evolution of the equilibrium

dynamics with time

A dilute colloidal suspensionA dilute colloidal suspension (71 nm Latex in Glycerol)

To theoretically calculate the dynamic scattering factor one has to take the gcorrelation functions for a collection of point scatterers diffusing in the liquidpoint scatterers diffusing in the liquid

1

1( ) exp( i ji j

f Q iQ r t r tN

For Brownian motion this can be reduced toFor Brownian motion this can be reduced to an exponential decay proportional to the diffusion coefficientdiffusion coefficient

2

( ) DQf Q e ( )f Q eHere the diffusion coefficient is related to the viscosity and the radius a via the Stoke-Einstein relation

6BD k T a B

Correlation Functions

Wavevector Dependence

221 DQ

Short Time Diffusion Constants in Concentrated Suspensionp

1 Structural correlations lead to a slowing down of dynamicsof dynamics

2 Hydrodynamic interactions further modify the dynamics at high concentrationdynamics at high concentration

3 These effects can be calculated for the initial d f h l i f i b hdecay rate of the correlation function but the f(Qt) will not generally be an exponential at long times

( ) ( ) ( )D Q D H Q S Q

long times

0( ) ( ) ( )D Q D H Q S Q

Deviations for Stokes-Einstein Diffusion

Example 2

Atomic Diffusion in Metal AlloysLeitner et al Nature Materials 2009

Example 3 Concentrated Polymeric Vesicles

Concentrated Block Copolymer VesiclesFalus et al PRL 94 16105 2005

( ) expf q t t ( ) exp

1

f q t t

In Liquid State Near T E ti l DTg Exponential Decays Become Stretched

Example 4Example 4Antiferromagnetic Domain Fluctuations

O G Sh k l N 447 68 (2007)bull O G Shpyrko et al Nature 447 68 (2007)

Note that although the length scale of the fluctuations isNote that although the length scale of the fluctuations is large (gt10 nm) they require x-rays with wavelengths ~01

nm in order to be visible

Example 5 Dynamics of Liquid SurfacesLiquid Surfaces

bullPolystyrene films on Si wafers (Kim PRL 2003) are highly viscous and show exponential decay

bullThin liquid crystal membranes (Sikharulidze PRL 2002) show transition from oscillatory to ) yoverdamped behavior

From Jiang et al PRL 246104 2008

Limitations of XPCS

bull Too much flux (X-ray damage)ndash Radiation can cause cross linking of polymers and charging of colloids

A bl di ti i t t l (PS) i b b d 107ndash A reasonably radiation resistant polymer (PS) in vacuum can absorb around ~107

Gy (10 min in surface reflection geometry)ndash Protein in water can absorb ~105 Gy (10 sec in transmission geometry)

T littl fl (P i l t i )bull Too little flux (Poor signal to noise)

Some tricks of the trade hellipMultispeckle Detectionp

bullFalus Borthwick Mochrie RSI (2004)

bullSNR increases as NSNR increases as

bullLimitations

bullReadout rate presently around 60 Hz

N

p y

bullEfficiency lt 50

bullNew Camera under development at LBL and APS ~500 Hz at 100 efficiency (John Weizeorick and Alec Sandy) Should see first light this cycle

FocusingFocusingKhalid Laaziri and Mark Sutton

bull Focusing the x-ray beam down to a small spot (~1 m) maintains flux but increases the speckle size SNR ~ photonsspeckle so SNR goes up Disadvantage is thatphotonsspeckle so SNR goes up Disadvantage is that radiation damage goes up as well

bull Fluctuations in Fe3Al3

Heterodyne DetectionLivet et al JSR (2006)Livet et al JSR (2006)

bull Mix a static signal with a weaker dynamic signalF diff i ti l ti ti l ( t)bull For diffusive motion relaxation times are longer exp(-t) instead of exp(-2t)

bull Constant flow can be detected which is invisible toConstant flow can be detected which is invisible to homodyne (example aerosil + carbon-black rubber)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

The Intensity-Intensity Correlation FunctionS lSample

R r

Ez

x

2g Q I Q t I Q t I

fEy

2 g Q I Q t I Q t I

44

01 2 3 4 1 2 3 41 2ex p

f iV e e rd r d r d r d r i Q s r r Q s r r

1 2 3 4 1 2 3 41 24

1 2 3 4

1 21 2

1 1 2 2

ex p

0 0

e e e e

i i

d r d r d r d r i Q s r r Q s r rR

r t r t r t r t

Q s r Q s rE x z t E x z t

31

3 3 0 i

Q s rE x z t

42

4 4 0 i

Q s rE x z t

How to calculate g2 (skipping most of the equations)(skipping most of the equations)

bullCalculate electric field intensity correlation function at the observation pointthe observation point

G2(Q)=fexp(iQrprime)ltEf2(rt) Ef

2(r+rprimet+t)gtrtdrprime

bullThe fourth order correlations in E can be reduced to pairs of second order correlation functions

bullAssume correlation lengths are smaller than sample size and the scattering can be factored into independent space and time parts

Final Result 22

2 ( ) 1 G Q I f Q

The contrast factor is related to the degree of

( ) ( ) ( 0)f Q S Q S Q

gcoherence and can be between 0 and 1

( ) ( ) ( )

( ) 00 iQ re e

f Q Q Q

S Q e r dr

Typical ApplicationsThe average structure is constant but the

l l fl

yp pp

local structure fluctuatesbull Diffusion of particles in solutionpbull Concentration fluctuations in binary liquidsbull Fluctuations of order parameter in a crystalFluctuations of order parameter in a crystalbull Thermally driven surface height

fluctuations in a viscous fluidfluctuations in a viscous fluidbull Vibrations of a membranebull Aging evolution of the ldquoequilibriumrdquobull Aging evolution of the equilibrium

dynamics with time

A dilute colloidal suspensionA dilute colloidal suspension (71 nm Latex in Glycerol)

To theoretically calculate the dynamic scattering factor one has to take the gcorrelation functions for a collection of point scatterers diffusing in the liquidpoint scatterers diffusing in the liquid

1

1( ) exp( i ji j

f Q iQ r t r tN

For Brownian motion this can be reduced toFor Brownian motion this can be reduced to an exponential decay proportional to the diffusion coefficientdiffusion coefficient

2

( ) DQf Q e ( )f Q eHere the diffusion coefficient is related to the viscosity and the radius a via the Stoke-Einstein relation

6BD k T a B

Correlation Functions

Wavevector Dependence

221 DQ

Short Time Diffusion Constants in Concentrated Suspensionp

1 Structural correlations lead to a slowing down of dynamicsof dynamics

2 Hydrodynamic interactions further modify the dynamics at high concentrationdynamics at high concentration

3 These effects can be calculated for the initial d f h l i f i b hdecay rate of the correlation function but the f(Qt) will not generally be an exponential at long times

( ) ( ) ( )D Q D H Q S Q

long times

0( ) ( ) ( )D Q D H Q S Q

Deviations for Stokes-Einstein Diffusion

Example 2

Atomic Diffusion in Metal AlloysLeitner et al Nature Materials 2009

Example 3 Concentrated Polymeric Vesicles

Concentrated Block Copolymer VesiclesFalus et al PRL 94 16105 2005

( ) expf q t t ( ) exp

1

f q t t

In Liquid State Near T E ti l DTg Exponential Decays Become Stretched

Example 4Example 4Antiferromagnetic Domain Fluctuations

O G Sh k l N 447 68 (2007)bull O G Shpyrko et al Nature 447 68 (2007)

Note that although the length scale of the fluctuations isNote that although the length scale of the fluctuations is large (gt10 nm) they require x-rays with wavelengths ~01

nm in order to be visible

Example 5 Dynamics of Liquid SurfacesLiquid Surfaces

bullPolystyrene films on Si wafers (Kim PRL 2003) are highly viscous and show exponential decay

bullThin liquid crystal membranes (Sikharulidze PRL 2002) show transition from oscillatory to ) yoverdamped behavior

From Jiang et al PRL 246104 2008

Limitations of XPCS

bull Too much flux (X-ray damage)ndash Radiation can cause cross linking of polymers and charging of colloids

A bl di ti i t t l (PS) i b b d 107ndash A reasonably radiation resistant polymer (PS) in vacuum can absorb around ~107

Gy (10 min in surface reflection geometry)ndash Protein in water can absorb ~105 Gy (10 sec in transmission geometry)

T littl fl (P i l t i )bull Too little flux (Poor signal to noise)

Some tricks of the trade hellipMultispeckle Detectionp

bullFalus Borthwick Mochrie RSI (2004)

bullSNR increases as NSNR increases as

bullLimitations

bullReadout rate presently around 60 Hz

N

p y

bullEfficiency lt 50

bullNew Camera under development at LBL and APS ~500 Hz at 100 efficiency (John Weizeorick and Alec Sandy) Should see first light this cycle

FocusingFocusingKhalid Laaziri and Mark Sutton

bull Focusing the x-ray beam down to a small spot (~1 m) maintains flux but increases the speckle size SNR ~ photonsspeckle so SNR goes up Disadvantage is thatphotonsspeckle so SNR goes up Disadvantage is that radiation damage goes up as well

bull Fluctuations in Fe3Al3

Heterodyne DetectionLivet et al JSR (2006)Livet et al JSR (2006)

bull Mix a static signal with a weaker dynamic signalF diff i ti l ti ti l ( t)bull For diffusive motion relaxation times are longer exp(-t) instead of exp(-2t)

bull Constant flow can be detected which is invisible toConstant flow can be detected which is invisible to homodyne (example aerosil + carbon-black rubber)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

How to calculate g2 (skipping most of the equations)(skipping most of the equations)

bullCalculate electric field intensity correlation function at the observation pointthe observation point

G2(Q)=fexp(iQrprime)ltEf2(rt) Ef

2(r+rprimet+t)gtrtdrprime

bullThe fourth order correlations in E can be reduced to pairs of second order correlation functions

bullAssume correlation lengths are smaller than sample size and the scattering can be factored into independent space and time parts

Final Result 22

2 ( ) 1 G Q I f Q

The contrast factor is related to the degree of

( ) ( ) ( 0)f Q S Q S Q

gcoherence and can be between 0 and 1

( ) ( ) ( )

( ) 00 iQ re e

f Q Q Q

S Q e r dr

Typical ApplicationsThe average structure is constant but the

l l fl

yp pp

local structure fluctuatesbull Diffusion of particles in solutionpbull Concentration fluctuations in binary liquidsbull Fluctuations of order parameter in a crystalFluctuations of order parameter in a crystalbull Thermally driven surface height

fluctuations in a viscous fluidfluctuations in a viscous fluidbull Vibrations of a membranebull Aging evolution of the ldquoequilibriumrdquobull Aging evolution of the equilibrium

dynamics with time

A dilute colloidal suspensionA dilute colloidal suspension (71 nm Latex in Glycerol)

To theoretically calculate the dynamic scattering factor one has to take the gcorrelation functions for a collection of point scatterers diffusing in the liquidpoint scatterers diffusing in the liquid

1

1( ) exp( i ji j

f Q iQ r t r tN

For Brownian motion this can be reduced toFor Brownian motion this can be reduced to an exponential decay proportional to the diffusion coefficientdiffusion coefficient

2

( ) DQf Q e ( )f Q eHere the diffusion coefficient is related to the viscosity and the radius a via the Stoke-Einstein relation

6BD k T a B

Correlation Functions

Wavevector Dependence

221 DQ

Short Time Diffusion Constants in Concentrated Suspensionp

1 Structural correlations lead to a slowing down of dynamicsof dynamics

2 Hydrodynamic interactions further modify the dynamics at high concentrationdynamics at high concentration

3 These effects can be calculated for the initial d f h l i f i b hdecay rate of the correlation function but the f(Qt) will not generally be an exponential at long times

( ) ( ) ( )D Q D H Q S Q

long times

0( ) ( ) ( )D Q D H Q S Q

Deviations for Stokes-Einstein Diffusion

Example 2

Atomic Diffusion in Metal AlloysLeitner et al Nature Materials 2009

Example 3 Concentrated Polymeric Vesicles

Concentrated Block Copolymer VesiclesFalus et al PRL 94 16105 2005

( ) expf q t t ( ) exp

1

f q t t

In Liquid State Near T E ti l DTg Exponential Decays Become Stretched

Example 4Example 4Antiferromagnetic Domain Fluctuations

O G Sh k l N 447 68 (2007)bull O G Shpyrko et al Nature 447 68 (2007)

Note that although the length scale of the fluctuations isNote that although the length scale of the fluctuations is large (gt10 nm) they require x-rays with wavelengths ~01

nm in order to be visible

Example 5 Dynamics of Liquid SurfacesLiquid Surfaces

bullPolystyrene films on Si wafers (Kim PRL 2003) are highly viscous and show exponential decay

bullThin liquid crystal membranes (Sikharulidze PRL 2002) show transition from oscillatory to ) yoverdamped behavior

From Jiang et al PRL 246104 2008

Limitations of XPCS

bull Too much flux (X-ray damage)ndash Radiation can cause cross linking of polymers and charging of colloids

A bl di ti i t t l (PS) i b b d 107ndash A reasonably radiation resistant polymer (PS) in vacuum can absorb around ~107

Gy (10 min in surface reflection geometry)ndash Protein in water can absorb ~105 Gy (10 sec in transmission geometry)

T littl fl (P i l t i )bull Too little flux (Poor signal to noise)

Some tricks of the trade hellipMultispeckle Detectionp

bullFalus Borthwick Mochrie RSI (2004)

bullSNR increases as NSNR increases as

bullLimitations

bullReadout rate presently around 60 Hz

N

p y

bullEfficiency lt 50

bullNew Camera under development at LBL and APS ~500 Hz at 100 efficiency (John Weizeorick and Alec Sandy) Should see first light this cycle

FocusingFocusingKhalid Laaziri and Mark Sutton

bull Focusing the x-ray beam down to a small spot (~1 m) maintains flux but increases the speckle size SNR ~ photonsspeckle so SNR goes up Disadvantage is thatphotonsspeckle so SNR goes up Disadvantage is that radiation damage goes up as well

bull Fluctuations in Fe3Al3

Heterodyne DetectionLivet et al JSR (2006)Livet et al JSR (2006)

bull Mix a static signal with a weaker dynamic signalF diff i ti l ti ti l ( t)bull For diffusive motion relaxation times are longer exp(-t) instead of exp(-2t)

bull Constant flow can be detected which is invisible toConstant flow can be detected which is invisible to homodyne (example aerosil + carbon-black rubber)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

Final Result 22

2 ( ) 1 G Q I f Q

The contrast factor is related to the degree of

( ) ( ) ( 0)f Q S Q S Q

gcoherence and can be between 0 and 1

( ) ( ) ( )

( ) 00 iQ re e

f Q Q Q

S Q e r dr

Typical ApplicationsThe average structure is constant but the

l l fl

yp pp

local structure fluctuatesbull Diffusion of particles in solutionpbull Concentration fluctuations in binary liquidsbull Fluctuations of order parameter in a crystalFluctuations of order parameter in a crystalbull Thermally driven surface height

fluctuations in a viscous fluidfluctuations in a viscous fluidbull Vibrations of a membranebull Aging evolution of the ldquoequilibriumrdquobull Aging evolution of the equilibrium

dynamics with time

A dilute colloidal suspensionA dilute colloidal suspension (71 nm Latex in Glycerol)

To theoretically calculate the dynamic scattering factor one has to take the gcorrelation functions for a collection of point scatterers diffusing in the liquidpoint scatterers diffusing in the liquid

1

1( ) exp( i ji j

f Q iQ r t r tN

For Brownian motion this can be reduced toFor Brownian motion this can be reduced to an exponential decay proportional to the diffusion coefficientdiffusion coefficient

2

( ) DQf Q e ( )f Q eHere the diffusion coefficient is related to the viscosity and the radius a via the Stoke-Einstein relation

6BD k T a B

Correlation Functions

Wavevector Dependence

221 DQ

Short Time Diffusion Constants in Concentrated Suspensionp

1 Structural correlations lead to a slowing down of dynamicsof dynamics

2 Hydrodynamic interactions further modify the dynamics at high concentrationdynamics at high concentration

3 These effects can be calculated for the initial d f h l i f i b hdecay rate of the correlation function but the f(Qt) will not generally be an exponential at long times

( ) ( ) ( )D Q D H Q S Q

long times

0( ) ( ) ( )D Q D H Q S Q

Deviations for Stokes-Einstein Diffusion

Example 2

Atomic Diffusion in Metal AlloysLeitner et al Nature Materials 2009

Example 3 Concentrated Polymeric Vesicles

Concentrated Block Copolymer VesiclesFalus et al PRL 94 16105 2005

( ) expf q t t ( ) exp

1

f q t t

In Liquid State Near T E ti l DTg Exponential Decays Become Stretched

Example 4Example 4Antiferromagnetic Domain Fluctuations

O G Sh k l N 447 68 (2007)bull O G Shpyrko et al Nature 447 68 (2007)

Note that although the length scale of the fluctuations isNote that although the length scale of the fluctuations is large (gt10 nm) they require x-rays with wavelengths ~01

nm in order to be visible

Example 5 Dynamics of Liquid SurfacesLiquid Surfaces

bullPolystyrene films on Si wafers (Kim PRL 2003) are highly viscous and show exponential decay

bullThin liquid crystal membranes (Sikharulidze PRL 2002) show transition from oscillatory to ) yoverdamped behavior

From Jiang et al PRL 246104 2008

Limitations of XPCS

bull Too much flux (X-ray damage)ndash Radiation can cause cross linking of polymers and charging of colloids

A bl di ti i t t l (PS) i b b d 107ndash A reasonably radiation resistant polymer (PS) in vacuum can absorb around ~107

Gy (10 min in surface reflection geometry)ndash Protein in water can absorb ~105 Gy (10 sec in transmission geometry)

T littl fl (P i l t i )bull Too little flux (Poor signal to noise)

Some tricks of the trade hellipMultispeckle Detectionp

bullFalus Borthwick Mochrie RSI (2004)

bullSNR increases as NSNR increases as

bullLimitations

bullReadout rate presently around 60 Hz

N

p y

bullEfficiency lt 50

bullNew Camera under development at LBL and APS ~500 Hz at 100 efficiency (John Weizeorick and Alec Sandy) Should see first light this cycle

FocusingFocusingKhalid Laaziri and Mark Sutton

bull Focusing the x-ray beam down to a small spot (~1 m) maintains flux but increases the speckle size SNR ~ photonsspeckle so SNR goes up Disadvantage is thatphotonsspeckle so SNR goes up Disadvantage is that radiation damage goes up as well

bull Fluctuations in Fe3Al3

Heterodyne DetectionLivet et al JSR (2006)Livet et al JSR (2006)

bull Mix a static signal with a weaker dynamic signalF diff i ti l ti ti l ( t)bull For diffusive motion relaxation times are longer exp(-t) instead of exp(-2t)

bull Constant flow can be detected which is invisible toConstant flow can be detected which is invisible to homodyne (example aerosil + carbon-black rubber)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

Typical ApplicationsThe average structure is constant but the

l l fl

yp pp

local structure fluctuatesbull Diffusion of particles in solutionpbull Concentration fluctuations in binary liquidsbull Fluctuations of order parameter in a crystalFluctuations of order parameter in a crystalbull Thermally driven surface height

fluctuations in a viscous fluidfluctuations in a viscous fluidbull Vibrations of a membranebull Aging evolution of the ldquoequilibriumrdquobull Aging evolution of the equilibrium

dynamics with time

A dilute colloidal suspensionA dilute colloidal suspension (71 nm Latex in Glycerol)

To theoretically calculate the dynamic scattering factor one has to take the gcorrelation functions for a collection of point scatterers diffusing in the liquidpoint scatterers diffusing in the liquid

1

1( ) exp( i ji j

f Q iQ r t r tN

For Brownian motion this can be reduced toFor Brownian motion this can be reduced to an exponential decay proportional to the diffusion coefficientdiffusion coefficient

2

( ) DQf Q e ( )f Q eHere the diffusion coefficient is related to the viscosity and the radius a via the Stoke-Einstein relation

6BD k T a B

Correlation Functions

Wavevector Dependence

221 DQ

Short Time Diffusion Constants in Concentrated Suspensionp

1 Structural correlations lead to a slowing down of dynamicsof dynamics

2 Hydrodynamic interactions further modify the dynamics at high concentrationdynamics at high concentration

3 These effects can be calculated for the initial d f h l i f i b hdecay rate of the correlation function but the f(Qt) will not generally be an exponential at long times

( ) ( ) ( )D Q D H Q S Q

long times

0( ) ( ) ( )D Q D H Q S Q

Deviations for Stokes-Einstein Diffusion

Example 2

Atomic Diffusion in Metal AlloysLeitner et al Nature Materials 2009

Example 3 Concentrated Polymeric Vesicles

Concentrated Block Copolymer VesiclesFalus et al PRL 94 16105 2005

( ) expf q t t ( ) exp

1

f q t t

In Liquid State Near T E ti l DTg Exponential Decays Become Stretched

Example 4Example 4Antiferromagnetic Domain Fluctuations

O G Sh k l N 447 68 (2007)bull O G Shpyrko et al Nature 447 68 (2007)

Note that although the length scale of the fluctuations isNote that although the length scale of the fluctuations is large (gt10 nm) they require x-rays with wavelengths ~01

nm in order to be visible

Example 5 Dynamics of Liquid SurfacesLiquid Surfaces

bullPolystyrene films on Si wafers (Kim PRL 2003) are highly viscous and show exponential decay

bullThin liquid crystal membranes (Sikharulidze PRL 2002) show transition from oscillatory to ) yoverdamped behavior

From Jiang et al PRL 246104 2008

Limitations of XPCS

bull Too much flux (X-ray damage)ndash Radiation can cause cross linking of polymers and charging of colloids

A bl di ti i t t l (PS) i b b d 107ndash A reasonably radiation resistant polymer (PS) in vacuum can absorb around ~107

Gy (10 min in surface reflection geometry)ndash Protein in water can absorb ~105 Gy (10 sec in transmission geometry)

T littl fl (P i l t i )bull Too little flux (Poor signal to noise)

Some tricks of the trade hellipMultispeckle Detectionp

bullFalus Borthwick Mochrie RSI (2004)

bullSNR increases as NSNR increases as

bullLimitations

bullReadout rate presently around 60 Hz

N

p y

bullEfficiency lt 50

bullNew Camera under development at LBL and APS ~500 Hz at 100 efficiency (John Weizeorick and Alec Sandy) Should see first light this cycle

FocusingFocusingKhalid Laaziri and Mark Sutton

bull Focusing the x-ray beam down to a small spot (~1 m) maintains flux but increases the speckle size SNR ~ photonsspeckle so SNR goes up Disadvantage is thatphotonsspeckle so SNR goes up Disadvantage is that radiation damage goes up as well

bull Fluctuations in Fe3Al3

Heterodyne DetectionLivet et al JSR (2006)Livet et al JSR (2006)

bull Mix a static signal with a weaker dynamic signalF diff i ti l ti ti l ( t)bull For diffusive motion relaxation times are longer exp(-t) instead of exp(-2t)

bull Constant flow can be detected which is invisible toConstant flow can be detected which is invisible to homodyne (example aerosil + carbon-black rubber)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

A dilute colloidal suspensionA dilute colloidal suspension (71 nm Latex in Glycerol)

To theoretically calculate the dynamic scattering factor one has to take the gcorrelation functions for a collection of point scatterers diffusing in the liquidpoint scatterers diffusing in the liquid

1

1( ) exp( i ji j

f Q iQ r t r tN

For Brownian motion this can be reduced toFor Brownian motion this can be reduced to an exponential decay proportional to the diffusion coefficientdiffusion coefficient

2

( ) DQf Q e ( )f Q eHere the diffusion coefficient is related to the viscosity and the radius a via the Stoke-Einstein relation

6BD k T a B

Correlation Functions

Wavevector Dependence

221 DQ

Short Time Diffusion Constants in Concentrated Suspensionp

1 Structural correlations lead to a slowing down of dynamicsof dynamics

2 Hydrodynamic interactions further modify the dynamics at high concentrationdynamics at high concentration

3 These effects can be calculated for the initial d f h l i f i b hdecay rate of the correlation function but the f(Qt) will not generally be an exponential at long times

( ) ( ) ( )D Q D H Q S Q

long times

0( ) ( ) ( )D Q D H Q S Q

Deviations for Stokes-Einstein Diffusion

Example 2

Atomic Diffusion in Metal AlloysLeitner et al Nature Materials 2009

Example 3 Concentrated Polymeric Vesicles

Concentrated Block Copolymer VesiclesFalus et al PRL 94 16105 2005

( ) expf q t t ( ) exp

1

f q t t

In Liquid State Near T E ti l DTg Exponential Decays Become Stretched

Example 4Example 4Antiferromagnetic Domain Fluctuations

O G Sh k l N 447 68 (2007)bull O G Shpyrko et al Nature 447 68 (2007)

Note that although the length scale of the fluctuations isNote that although the length scale of the fluctuations is large (gt10 nm) they require x-rays with wavelengths ~01

nm in order to be visible

Example 5 Dynamics of Liquid SurfacesLiquid Surfaces

bullPolystyrene films on Si wafers (Kim PRL 2003) are highly viscous and show exponential decay

bullThin liquid crystal membranes (Sikharulidze PRL 2002) show transition from oscillatory to ) yoverdamped behavior

From Jiang et al PRL 246104 2008

Limitations of XPCS

bull Too much flux (X-ray damage)ndash Radiation can cause cross linking of polymers and charging of colloids

A bl di ti i t t l (PS) i b b d 107ndash A reasonably radiation resistant polymer (PS) in vacuum can absorb around ~107

Gy (10 min in surface reflection geometry)ndash Protein in water can absorb ~105 Gy (10 sec in transmission geometry)

T littl fl (P i l t i )bull Too little flux (Poor signal to noise)

Some tricks of the trade hellipMultispeckle Detectionp

bullFalus Borthwick Mochrie RSI (2004)

bullSNR increases as NSNR increases as

bullLimitations

bullReadout rate presently around 60 Hz

N

p y

bullEfficiency lt 50

bullNew Camera under development at LBL and APS ~500 Hz at 100 efficiency (John Weizeorick and Alec Sandy) Should see first light this cycle

FocusingFocusingKhalid Laaziri and Mark Sutton

bull Focusing the x-ray beam down to a small spot (~1 m) maintains flux but increases the speckle size SNR ~ photonsspeckle so SNR goes up Disadvantage is thatphotonsspeckle so SNR goes up Disadvantage is that radiation damage goes up as well

bull Fluctuations in Fe3Al3

Heterodyne DetectionLivet et al JSR (2006)Livet et al JSR (2006)

bull Mix a static signal with a weaker dynamic signalF diff i ti l ti ti l ( t)bull For diffusive motion relaxation times are longer exp(-t) instead of exp(-2t)

bull Constant flow can be detected which is invisible toConstant flow can be detected which is invisible to homodyne (example aerosil + carbon-black rubber)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

To theoretically calculate the dynamic scattering factor one has to take the gcorrelation functions for a collection of point scatterers diffusing in the liquidpoint scatterers diffusing in the liquid

1

1( ) exp( i ji j

f Q iQ r t r tN

For Brownian motion this can be reduced toFor Brownian motion this can be reduced to an exponential decay proportional to the diffusion coefficientdiffusion coefficient

2

( ) DQf Q e ( )f Q eHere the diffusion coefficient is related to the viscosity and the radius a via the Stoke-Einstein relation

6BD k T a B

Correlation Functions

Wavevector Dependence

221 DQ

Short Time Diffusion Constants in Concentrated Suspensionp

1 Structural correlations lead to a slowing down of dynamicsof dynamics

2 Hydrodynamic interactions further modify the dynamics at high concentrationdynamics at high concentration

3 These effects can be calculated for the initial d f h l i f i b hdecay rate of the correlation function but the f(Qt) will not generally be an exponential at long times

( ) ( ) ( )D Q D H Q S Q

long times

0( ) ( ) ( )D Q D H Q S Q

Deviations for Stokes-Einstein Diffusion

Example 2

Atomic Diffusion in Metal AlloysLeitner et al Nature Materials 2009

Example 3 Concentrated Polymeric Vesicles

Concentrated Block Copolymer VesiclesFalus et al PRL 94 16105 2005

( ) expf q t t ( ) exp

1

f q t t

In Liquid State Near T E ti l DTg Exponential Decays Become Stretched

Example 4Example 4Antiferromagnetic Domain Fluctuations

O G Sh k l N 447 68 (2007)bull O G Shpyrko et al Nature 447 68 (2007)

Note that although the length scale of the fluctuations isNote that although the length scale of the fluctuations is large (gt10 nm) they require x-rays with wavelengths ~01

nm in order to be visible

Example 5 Dynamics of Liquid SurfacesLiquid Surfaces

bullPolystyrene films on Si wafers (Kim PRL 2003) are highly viscous and show exponential decay

bullThin liquid crystal membranes (Sikharulidze PRL 2002) show transition from oscillatory to ) yoverdamped behavior

From Jiang et al PRL 246104 2008

Limitations of XPCS

bull Too much flux (X-ray damage)ndash Radiation can cause cross linking of polymers and charging of colloids

A bl di ti i t t l (PS) i b b d 107ndash A reasonably radiation resistant polymer (PS) in vacuum can absorb around ~107

Gy (10 min in surface reflection geometry)ndash Protein in water can absorb ~105 Gy (10 sec in transmission geometry)

T littl fl (P i l t i )bull Too little flux (Poor signal to noise)

Some tricks of the trade hellipMultispeckle Detectionp

bullFalus Borthwick Mochrie RSI (2004)

bullSNR increases as NSNR increases as

bullLimitations

bullReadout rate presently around 60 Hz

N

p y

bullEfficiency lt 50

bullNew Camera under development at LBL and APS ~500 Hz at 100 efficiency (John Weizeorick and Alec Sandy) Should see first light this cycle

FocusingFocusingKhalid Laaziri and Mark Sutton

bull Focusing the x-ray beam down to a small spot (~1 m) maintains flux but increases the speckle size SNR ~ photonsspeckle so SNR goes up Disadvantage is thatphotonsspeckle so SNR goes up Disadvantage is that radiation damage goes up as well

bull Fluctuations in Fe3Al3

Heterodyne DetectionLivet et al JSR (2006)Livet et al JSR (2006)

bull Mix a static signal with a weaker dynamic signalF diff i ti l ti ti l ( t)bull For diffusive motion relaxation times are longer exp(-t) instead of exp(-2t)

bull Constant flow can be detected which is invisible toConstant flow can be detected which is invisible to homodyne (example aerosil + carbon-black rubber)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

For Brownian motion this can be reduced toFor Brownian motion this can be reduced to an exponential decay proportional to the diffusion coefficientdiffusion coefficient

2

( ) DQf Q e ( )f Q eHere the diffusion coefficient is related to the viscosity and the radius a via the Stoke-Einstein relation

6BD k T a B

Correlation Functions

Wavevector Dependence

221 DQ

Short Time Diffusion Constants in Concentrated Suspensionp

1 Structural correlations lead to a slowing down of dynamicsof dynamics

2 Hydrodynamic interactions further modify the dynamics at high concentrationdynamics at high concentration

3 These effects can be calculated for the initial d f h l i f i b hdecay rate of the correlation function but the f(Qt) will not generally be an exponential at long times

( ) ( ) ( )D Q D H Q S Q

long times

0( ) ( ) ( )D Q D H Q S Q

Deviations for Stokes-Einstein Diffusion

Example 2

Atomic Diffusion in Metal AlloysLeitner et al Nature Materials 2009

Example 3 Concentrated Polymeric Vesicles

Concentrated Block Copolymer VesiclesFalus et al PRL 94 16105 2005

( ) expf q t t ( ) exp

1

f q t t

In Liquid State Near T E ti l DTg Exponential Decays Become Stretched

Example 4Example 4Antiferromagnetic Domain Fluctuations

O G Sh k l N 447 68 (2007)bull O G Shpyrko et al Nature 447 68 (2007)

Note that although the length scale of the fluctuations isNote that although the length scale of the fluctuations is large (gt10 nm) they require x-rays with wavelengths ~01

nm in order to be visible

Example 5 Dynamics of Liquid SurfacesLiquid Surfaces

bullPolystyrene films on Si wafers (Kim PRL 2003) are highly viscous and show exponential decay

bullThin liquid crystal membranes (Sikharulidze PRL 2002) show transition from oscillatory to ) yoverdamped behavior

From Jiang et al PRL 246104 2008

Limitations of XPCS

bull Too much flux (X-ray damage)ndash Radiation can cause cross linking of polymers and charging of colloids

A bl di ti i t t l (PS) i b b d 107ndash A reasonably radiation resistant polymer (PS) in vacuum can absorb around ~107

Gy (10 min in surface reflection geometry)ndash Protein in water can absorb ~105 Gy (10 sec in transmission geometry)

T littl fl (P i l t i )bull Too little flux (Poor signal to noise)

Some tricks of the trade hellipMultispeckle Detectionp

bullFalus Borthwick Mochrie RSI (2004)

bullSNR increases as NSNR increases as

bullLimitations

bullReadout rate presently around 60 Hz

N

p y

bullEfficiency lt 50

bullNew Camera under development at LBL and APS ~500 Hz at 100 efficiency (John Weizeorick and Alec Sandy) Should see first light this cycle

FocusingFocusingKhalid Laaziri and Mark Sutton

bull Focusing the x-ray beam down to a small spot (~1 m) maintains flux but increases the speckle size SNR ~ photonsspeckle so SNR goes up Disadvantage is thatphotonsspeckle so SNR goes up Disadvantage is that radiation damage goes up as well

bull Fluctuations in Fe3Al3

Heterodyne DetectionLivet et al JSR (2006)Livet et al JSR (2006)

bull Mix a static signal with a weaker dynamic signalF diff i ti l ti ti l ( t)bull For diffusive motion relaxation times are longer exp(-t) instead of exp(-2t)

bull Constant flow can be detected which is invisible toConstant flow can be detected which is invisible to homodyne (example aerosil + carbon-black rubber)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

Correlation Functions

Wavevector Dependence

221 DQ

Short Time Diffusion Constants in Concentrated Suspensionp

1 Structural correlations lead to a slowing down of dynamicsof dynamics

2 Hydrodynamic interactions further modify the dynamics at high concentrationdynamics at high concentration

3 These effects can be calculated for the initial d f h l i f i b hdecay rate of the correlation function but the f(Qt) will not generally be an exponential at long times

( ) ( ) ( )D Q D H Q S Q

long times

0( ) ( ) ( )D Q D H Q S Q

Deviations for Stokes-Einstein Diffusion

Example 2

Atomic Diffusion in Metal AlloysLeitner et al Nature Materials 2009

Example 3 Concentrated Polymeric Vesicles

Concentrated Block Copolymer VesiclesFalus et al PRL 94 16105 2005

( ) expf q t t ( ) exp

1

f q t t

In Liquid State Near T E ti l DTg Exponential Decays Become Stretched

Example 4Example 4Antiferromagnetic Domain Fluctuations

O G Sh k l N 447 68 (2007)bull O G Shpyrko et al Nature 447 68 (2007)

Note that although the length scale of the fluctuations isNote that although the length scale of the fluctuations is large (gt10 nm) they require x-rays with wavelengths ~01

nm in order to be visible

Example 5 Dynamics of Liquid SurfacesLiquid Surfaces

bullPolystyrene films on Si wafers (Kim PRL 2003) are highly viscous and show exponential decay

bullThin liquid crystal membranes (Sikharulidze PRL 2002) show transition from oscillatory to ) yoverdamped behavior

From Jiang et al PRL 246104 2008

Limitations of XPCS

bull Too much flux (X-ray damage)ndash Radiation can cause cross linking of polymers and charging of colloids

A bl di ti i t t l (PS) i b b d 107ndash A reasonably radiation resistant polymer (PS) in vacuum can absorb around ~107

Gy (10 min in surface reflection geometry)ndash Protein in water can absorb ~105 Gy (10 sec in transmission geometry)

T littl fl (P i l t i )bull Too little flux (Poor signal to noise)

Some tricks of the trade hellipMultispeckle Detectionp

bullFalus Borthwick Mochrie RSI (2004)

bullSNR increases as NSNR increases as

bullLimitations

bullReadout rate presently around 60 Hz

N

p y

bullEfficiency lt 50

bullNew Camera under development at LBL and APS ~500 Hz at 100 efficiency (John Weizeorick and Alec Sandy) Should see first light this cycle

FocusingFocusingKhalid Laaziri and Mark Sutton

bull Focusing the x-ray beam down to a small spot (~1 m) maintains flux but increases the speckle size SNR ~ photonsspeckle so SNR goes up Disadvantage is thatphotonsspeckle so SNR goes up Disadvantage is that radiation damage goes up as well

bull Fluctuations in Fe3Al3

Heterodyne DetectionLivet et al JSR (2006)Livet et al JSR (2006)

bull Mix a static signal with a weaker dynamic signalF diff i ti l ti ti l ( t)bull For diffusive motion relaxation times are longer exp(-t) instead of exp(-2t)

bull Constant flow can be detected which is invisible toConstant flow can be detected which is invisible to homodyne (example aerosil + carbon-black rubber)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

Wavevector Dependence

221 DQ

Short Time Diffusion Constants in Concentrated Suspensionp

1 Structural correlations lead to a slowing down of dynamicsof dynamics

2 Hydrodynamic interactions further modify the dynamics at high concentrationdynamics at high concentration

3 These effects can be calculated for the initial d f h l i f i b hdecay rate of the correlation function but the f(Qt) will not generally be an exponential at long times

( ) ( ) ( )D Q D H Q S Q

long times

0( ) ( ) ( )D Q D H Q S Q

Deviations for Stokes-Einstein Diffusion

Example 2

Atomic Diffusion in Metal AlloysLeitner et al Nature Materials 2009

Example 3 Concentrated Polymeric Vesicles

Concentrated Block Copolymer VesiclesFalus et al PRL 94 16105 2005

( ) expf q t t ( ) exp

1

f q t t

In Liquid State Near T E ti l DTg Exponential Decays Become Stretched

Example 4Example 4Antiferromagnetic Domain Fluctuations

O G Sh k l N 447 68 (2007)bull O G Shpyrko et al Nature 447 68 (2007)

Note that although the length scale of the fluctuations isNote that although the length scale of the fluctuations is large (gt10 nm) they require x-rays with wavelengths ~01

nm in order to be visible

Example 5 Dynamics of Liquid SurfacesLiquid Surfaces

bullPolystyrene films on Si wafers (Kim PRL 2003) are highly viscous and show exponential decay

bullThin liquid crystal membranes (Sikharulidze PRL 2002) show transition from oscillatory to ) yoverdamped behavior

From Jiang et al PRL 246104 2008

Limitations of XPCS

bull Too much flux (X-ray damage)ndash Radiation can cause cross linking of polymers and charging of colloids

A bl di ti i t t l (PS) i b b d 107ndash A reasonably radiation resistant polymer (PS) in vacuum can absorb around ~107

Gy (10 min in surface reflection geometry)ndash Protein in water can absorb ~105 Gy (10 sec in transmission geometry)

T littl fl (P i l t i )bull Too little flux (Poor signal to noise)

Some tricks of the trade hellipMultispeckle Detectionp

bullFalus Borthwick Mochrie RSI (2004)

bullSNR increases as NSNR increases as

bullLimitations

bullReadout rate presently around 60 Hz

N

p y

bullEfficiency lt 50

bullNew Camera under development at LBL and APS ~500 Hz at 100 efficiency (John Weizeorick and Alec Sandy) Should see first light this cycle

FocusingFocusingKhalid Laaziri and Mark Sutton

bull Focusing the x-ray beam down to a small spot (~1 m) maintains flux but increases the speckle size SNR ~ photonsspeckle so SNR goes up Disadvantage is thatphotonsspeckle so SNR goes up Disadvantage is that radiation damage goes up as well

bull Fluctuations in Fe3Al3

Heterodyne DetectionLivet et al JSR (2006)Livet et al JSR (2006)

bull Mix a static signal with a weaker dynamic signalF diff i ti l ti ti l ( t)bull For diffusive motion relaxation times are longer exp(-t) instead of exp(-2t)

bull Constant flow can be detected which is invisible toConstant flow can be detected which is invisible to homodyne (example aerosil + carbon-black rubber)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

Short Time Diffusion Constants in Concentrated Suspensionp

1 Structural correlations lead to a slowing down of dynamicsof dynamics

2 Hydrodynamic interactions further modify the dynamics at high concentrationdynamics at high concentration

3 These effects can be calculated for the initial d f h l i f i b hdecay rate of the correlation function but the f(Qt) will not generally be an exponential at long times

( ) ( ) ( )D Q D H Q S Q

long times

0( ) ( ) ( )D Q D H Q S Q

Deviations for Stokes-Einstein Diffusion

Example 2

Atomic Diffusion in Metal AlloysLeitner et al Nature Materials 2009

Example 3 Concentrated Polymeric Vesicles

Concentrated Block Copolymer VesiclesFalus et al PRL 94 16105 2005

( ) expf q t t ( ) exp

1

f q t t

In Liquid State Near T E ti l DTg Exponential Decays Become Stretched

Example 4Example 4Antiferromagnetic Domain Fluctuations

O G Sh k l N 447 68 (2007)bull O G Shpyrko et al Nature 447 68 (2007)

Note that although the length scale of the fluctuations isNote that although the length scale of the fluctuations is large (gt10 nm) they require x-rays with wavelengths ~01

nm in order to be visible

Example 5 Dynamics of Liquid SurfacesLiquid Surfaces

bullPolystyrene films on Si wafers (Kim PRL 2003) are highly viscous and show exponential decay

bullThin liquid crystal membranes (Sikharulidze PRL 2002) show transition from oscillatory to ) yoverdamped behavior

From Jiang et al PRL 246104 2008

Limitations of XPCS

bull Too much flux (X-ray damage)ndash Radiation can cause cross linking of polymers and charging of colloids

A bl di ti i t t l (PS) i b b d 107ndash A reasonably radiation resistant polymer (PS) in vacuum can absorb around ~107

Gy (10 min in surface reflection geometry)ndash Protein in water can absorb ~105 Gy (10 sec in transmission geometry)

T littl fl (P i l t i )bull Too little flux (Poor signal to noise)

Some tricks of the trade hellipMultispeckle Detectionp

bullFalus Borthwick Mochrie RSI (2004)

bullSNR increases as NSNR increases as

bullLimitations

bullReadout rate presently around 60 Hz

N

p y

bullEfficiency lt 50

bullNew Camera under development at LBL and APS ~500 Hz at 100 efficiency (John Weizeorick and Alec Sandy) Should see first light this cycle

FocusingFocusingKhalid Laaziri and Mark Sutton

bull Focusing the x-ray beam down to a small spot (~1 m) maintains flux but increases the speckle size SNR ~ photonsspeckle so SNR goes up Disadvantage is thatphotonsspeckle so SNR goes up Disadvantage is that radiation damage goes up as well

bull Fluctuations in Fe3Al3

Heterodyne DetectionLivet et al JSR (2006)Livet et al JSR (2006)

bull Mix a static signal with a weaker dynamic signalF diff i ti l ti ti l ( t)bull For diffusive motion relaxation times are longer exp(-t) instead of exp(-2t)

bull Constant flow can be detected which is invisible toConstant flow can be detected which is invisible to homodyne (example aerosil + carbon-black rubber)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

Deviations for Stokes-Einstein Diffusion

Example 2

Atomic Diffusion in Metal AlloysLeitner et al Nature Materials 2009

Example 3 Concentrated Polymeric Vesicles

Concentrated Block Copolymer VesiclesFalus et al PRL 94 16105 2005

( ) expf q t t ( ) exp

1

f q t t

In Liquid State Near T E ti l DTg Exponential Decays Become Stretched

Example 4Example 4Antiferromagnetic Domain Fluctuations

O G Sh k l N 447 68 (2007)bull O G Shpyrko et al Nature 447 68 (2007)

Note that although the length scale of the fluctuations isNote that although the length scale of the fluctuations is large (gt10 nm) they require x-rays with wavelengths ~01

nm in order to be visible

Example 5 Dynamics of Liquid SurfacesLiquid Surfaces

bullPolystyrene films on Si wafers (Kim PRL 2003) are highly viscous and show exponential decay

bullThin liquid crystal membranes (Sikharulidze PRL 2002) show transition from oscillatory to ) yoverdamped behavior

From Jiang et al PRL 246104 2008

Limitations of XPCS

bull Too much flux (X-ray damage)ndash Radiation can cause cross linking of polymers and charging of colloids

A bl di ti i t t l (PS) i b b d 107ndash A reasonably radiation resistant polymer (PS) in vacuum can absorb around ~107

Gy (10 min in surface reflection geometry)ndash Protein in water can absorb ~105 Gy (10 sec in transmission geometry)

T littl fl (P i l t i )bull Too little flux (Poor signal to noise)

Some tricks of the trade hellipMultispeckle Detectionp

bullFalus Borthwick Mochrie RSI (2004)

bullSNR increases as NSNR increases as

bullLimitations

bullReadout rate presently around 60 Hz

N

p y

bullEfficiency lt 50

bullNew Camera under development at LBL and APS ~500 Hz at 100 efficiency (John Weizeorick and Alec Sandy) Should see first light this cycle

FocusingFocusingKhalid Laaziri and Mark Sutton

bull Focusing the x-ray beam down to a small spot (~1 m) maintains flux but increases the speckle size SNR ~ photonsspeckle so SNR goes up Disadvantage is thatphotonsspeckle so SNR goes up Disadvantage is that radiation damage goes up as well

bull Fluctuations in Fe3Al3

Heterodyne DetectionLivet et al JSR (2006)Livet et al JSR (2006)

bull Mix a static signal with a weaker dynamic signalF diff i ti l ti ti l ( t)bull For diffusive motion relaxation times are longer exp(-t) instead of exp(-2t)

bull Constant flow can be detected which is invisible toConstant flow can be detected which is invisible to homodyne (example aerosil + carbon-black rubber)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

Example 2

Atomic Diffusion in Metal AlloysLeitner et al Nature Materials 2009

Example 3 Concentrated Polymeric Vesicles

Concentrated Block Copolymer VesiclesFalus et al PRL 94 16105 2005

( ) expf q t t ( ) exp

1

f q t t

In Liquid State Near T E ti l DTg Exponential Decays Become Stretched

Example 4Example 4Antiferromagnetic Domain Fluctuations

O G Sh k l N 447 68 (2007)bull O G Shpyrko et al Nature 447 68 (2007)

Note that although the length scale of the fluctuations isNote that although the length scale of the fluctuations is large (gt10 nm) they require x-rays with wavelengths ~01

nm in order to be visible

Example 5 Dynamics of Liquid SurfacesLiquid Surfaces

bullPolystyrene films on Si wafers (Kim PRL 2003) are highly viscous and show exponential decay

bullThin liquid crystal membranes (Sikharulidze PRL 2002) show transition from oscillatory to ) yoverdamped behavior

From Jiang et al PRL 246104 2008

Limitations of XPCS

bull Too much flux (X-ray damage)ndash Radiation can cause cross linking of polymers and charging of colloids

A bl di ti i t t l (PS) i b b d 107ndash A reasonably radiation resistant polymer (PS) in vacuum can absorb around ~107

Gy (10 min in surface reflection geometry)ndash Protein in water can absorb ~105 Gy (10 sec in transmission geometry)

T littl fl (P i l t i )bull Too little flux (Poor signal to noise)

Some tricks of the trade hellipMultispeckle Detectionp

bullFalus Borthwick Mochrie RSI (2004)

bullSNR increases as NSNR increases as

bullLimitations

bullReadout rate presently around 60 Hz

N

p y

bullEfficiency lt 50

bullNew Camera under development at LBL and APS ~500 Hz at 100 efficiency (John Weizeorick and Alec Sandy) Should see first light this cycle

FocusingFocusingKhalid Laaziri and Mark Sutton

bull Focusing the x-ray beam down to a small spot (~1 m) maintains flux but increases the speckle size SNR ~ photonsspeckle so SNR goes up Disadvantage is thatphotonsspeckle so SNR goes up Disadvantage is that radiation damage goes up as well

bull Fluctuations in Fe3Al3

Heterodyne DetectionLivet et al JSR (2006)Livet et al JSR (2006)

bull Mix a static signal with a weaker dynamic signalF diff i ti l ti ti l ( t)bull For diffusive motion relaxation times are longer exp(-t) instead of exp(-2t)

bull Constant flow can be detected which is invisible toConstant flow can be detected which is invisible to homodyne (example aerosil + carbon-black rubber)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

Example 3 Concentrated Polymeric Vesicles

Concentrated Block Copolymer VesiclesFalus et al PRL 94 16105 2005

( ) expf q t t ( ) exp

1

f q t t

In Liquid State Near T E ti l DTg Exponential Decays Become Stretched

Example 4Example 4Antiferromagnetic Domain Fluctuations

O G Sh k l N 447 68 (2007)bull O G Shpyrko et al Nature 447 68 (2007)

Note that although the length scale of the fluctuations isNote that although the length scale of the fluctuations is large (gt10 nm) they require x-rays with wavelengths ~01

nm in order to be visible

Example 5 Dynamics of Liquid SurfacesLiquid Surfaces

bullPolystyrene films on Si wafers (Kim PRL 2003) are highly viscous and show exponential decay

bullThin liquid crystal membranes (Sikharulidze PRL 2002) show transition from oscillatory to ) yoverdamped behavior

From Jiang et al PRL 246104 2008

Limitations of XPCS

bull Too much flux (X-ray damage)ndash Radiation can cause cross linking of polymers and charging of colloids

A bl di ti i t t l (PS) i b b d 107ndash A reasonably radiation resistant polymer (PS) in vacuum can absorb around ~107

Gy (10 min in surface reflection geometry)ndash Protein in water can absorb ~105 Gy (10 sec in transmission geometry)

T littl fl (P i l t i )bull Too little flux (Poor signal to noise)

Some tricks of the trade hellipMultispeckle Detectionp

bullFalus Borthwick Mochrie RSI (2004)

bullSNR increases as NSNR increases as

bullLimitations

bullReadout rate presently around 60 Hz

N

p y

bullEfficiency lt 50

bullNew Camera under development at LBL and APS ~500 Hz at 100 efficiency (John Weizeorick and Alec Sandy) Should see first light this cycle

FocusingFocusingKhalid Laaziri and Mark Sutton

bull Focusing the x-ray beam down to a small spot (~1 m) maintains flux but increases the speckle size SNR ~ photonsspeckle so SNR goes up Disadvantage is thatphotonsspeckle so SNR goes up Disadvantage is that radiation damage goes up as well

bull Fluctuations in Fe3Al3

Heterodyne DetectionLivet et al JSR (2006)Livet et al JSR (2006)

bull Mix a static signal with a weaker dynamic signalF diff i ti l ti ti l ( t)bull For diffusive motion relaxation times are longer exp(-t) instead of exp(-2t)

bull Constant flow can be detected which is invisible toConstant flow can be detected which is invisible to homodyne (example aerosil + carbon-black rubber)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

Example 4Example 4Antiferromagnetic Domain Fluctuations

O G Sh k l N 447 68 (2007)bull O G Shpyrko et al Nature 447 68 (2007)

Note that although the length scale of the fluctuations isNote that although the length scale of the fluctuations is large (gt10 nm) they require x-rays with wavelengths ~01

nm in order to be visible

Example 5 Dynamics of Liquid SurfacesLiquid Surfaces

bullPolystyrene films on Si wafers (Kim PRL 2003) are highly viscous and show exponential decay

bullThin liquid crystal membranes (Sikharulidze PRL 2002) show transition from oscillatory to ) yoverdamped behavior

From Jiang et al PRL 246104 2008

Limitations of XPCS

bull Too much flux (X-ray damage)ndash Radiation can cause cross linking of polymers and charging of colloids

A bl di ti i t t l (PS) i b b d 107ndash A reasonably radiation resistant polymer (PS) in vacuum can absorb around ~107

Gy (10 min in surface reflection geometry)ndash Protein in water can absorb ~105 Gy (10 sec in transmission geometry)

T littl fl (P i l t i )bull Too little flux (Poor signal to noise)

Some tricks of the trade hellipMultispeckle Detectionp

bullFalus Borthwick Mochrie RSI (2004)

bullSNR increases as NSNR increases as

bullLimitations

bullReadout rate presently around 60 Hz

N

p y

bullEfficiency lt 50

bullNew Camera under development at LBL and APS ~500 Hz at 100 efficiency (John Weizeorick and Alec Sandy) Should see first light this cycle

FocusingFocusingKhalid Laaziri and Mark Sutton

bull Focusing the x-ray beam down to a small spot (~1 m) maintains flux but increases the speckle size SNR ~ photonsspeckle so SNR goes up Disadvantage is thatphotonsspeckle so SNR goes up Disadvantage is that radiation damage goes up as well

bull Fluctuations in Fe3Al3

Heterodyne DetectionLivet et al JSR (2006)Livet et al JSR (2006)

bull Mix a static signal with a weaker dynamic signalF diff i ti l ti ti l ( t)bull For diffusive motion relaxation times are longer exp(-t) instead of exp(-2t)

bull Constant flow can be detected which is invisible toConstant flow can be detected which is invisible to homodyne (example aerosil + carbon-black rubber)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

Example 5 Dynamics of Liquid SurfacesLiquid Surfaces

bullPolystyrene films on Si wafers (Kim PRL 2003) are highly viscous and show exponential decay

bullThin liquid crystal membranes (Sikharulidze PRL 2002) show transition from oscillatory to ) yoverdamped behavior

From Jiang et al PRL 246104 2008

Limitations of XPCS

bull Too much flux (X-ray damage)ndash Radiation can cause cross linking of polymers and charging of colloids

A bl di ti i t t l (PS) i b b d 107ndash A reasonably radiation resistant polymer (PS) in vacuum can absorb around ~107

Gy (10 min in surface reflection geometry)ndash Protein in water can absorb ~105 Gy (10 sec in transmission geometry)

T littl fl (P i l t i )bull Too little flux (Poor signal to noise)

Some tricks of the trade hellipMultispeckle Detectionp

bullFalus Borthwick Mochrie RSI (2004)

bullSNR increases as NSNR increases as

bullLimitations

bullReadout rate presently around 60 Hz

N

p y

bullEfficiency lt 50

bullNew Camera under development at LBL and APS ~500 Hz at 100 efficiency (John Weizeorick and Alec Sandy) Should see first light this cycle

FocusingFocusingKhalid Laaziri and Mark Sutton

bull Focusing the x-ray beam down to a small spot (~1 m) maintains flux but increases the speckle size SNR ~ photonsspeckle so SNR goes up Disadvantage is thatphotonsspeckle so SNR goes up Disadvantage is that radiation damage goes up as well

bull Fluctuations in Fe3Al3

Heterodyne DetectionLivet et al JSR (2006)Livet et al JSR (2006)

bull Mix a static signal with a weaker dynamic signalF diff i ti l ti ti l ( t)bull For diffusive motion relaxation times are longer exp(-t) instead of exp(-2t)

bull Constant flow can be detected which is invisible toConstant flow can be detected which is invisible to homodyne (example aerosil + carbon-black rubber)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

From Jiang et al PRL 246104 2008

Limitations of XPCS

bull Too much flux (X-ray damage)ndash Radiation can cause cross linking of polymers and charging of colloids

A bl di ti i t t l (PS) i b b d 107ndash A reasonably radiation resistant polymer (PS) in vacuum can absorb around ~107

Gy (10 min in surface reflection geometry)ndash Protein in water can absorb ~105 Gy (10 sec in transmission geometry)

T littl fl (P i l t i )bull Too little flux (Poor signal to noise)

Some tricks of the trade hellipMultispeckle Detectionp

bullFalus Borthwick Mochrie RSI (2004)

bullSNR increases as NSNR increases as

bullLimitations

bullReadout rate presently around 60 Hz

N

p y

bullEfficiency lt 50

bullNew Camera under development at LBL and APS ~500 Hz at 100 efficiency (John Weizeorick and Alec Sandy) Should see first light this cycle

FocusingFocusingKhalid Laaziri and Mark Sutton

bull Focusing the x-ray beam down to a small spot (~1 m) maintains flux but increases the speckle size SNR ~ photonsspeckle so SNR goes up Disadvantage is thatphotonsspeckle so SNR goes up Disadvantage is that radiation damage goes up as well

bull Fluctuations in Fe3Al3

Heterodyne DetectionLivet et al JSR (2006)Livet et al JSR (2006)

bull Mix a static signal with a weaker dynamic signalF diff i ti l ti ti l ( t)bull For diffusive motion relaxation times are longer exp(-t) instead of exp(-2t)

bull Constant flow can be detected which is invisible toConstant flow can be detected which is invisible to homodyne (example aerosil + carbon-black rubber)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

Limitations of XPCS

bull Too much flux (X-ray damage)ndash Radiation can cause cross linking of polymers and charging of colloids

A bl di ti i t t l (PS) i b b d 107ndash A reasonably radiation resistant polymer (PS) in vacuum can absorb around ~107

Gy (10 min in surface reflection geometry)ndash Protein in water can absorb ~105 Gy (10 sec in transmission geometry)

T littl fl (P i l t i )bull Too little flux (Poor signal to noise)

Some tricks of the trade hellipMultispeckle Detectionp

bullFalus Borthwick Mochrie RSI (2004)

bullSNR increases as NSNR increases as

bullLimitations

bullReadout rate presently around 60 Hz

N

p y

bullEfficiency lt 50

bullNew Camera under development at LBL and APS ~500 Hz at 100 efficiency (John Weizeorick and Alec Sandy) Should see first light this cycle

FocusingFocusingKhalid Laaziri and Mark Sutton

bull Focusing the x-ray beam down to a small spot (~1 m) maintains flux but increases the speckle size SNR ~ photonsspeckle so SNR goes up Disadvantage is thatphotonsspeckle so SNR goes up Disadvantage is that radiation damage goes up as well

bull Fluctuations in Fe3Al3

Heterodyne DetectionLivet et al JSR (2006)Livet et al JSR (2006)

bull Mix a static signal with a weaker dynamic signalF diff i ti l ti ti l ( t)bull For diffusive motion relaxation times are longer exp(-t) instead of exp(-2t)

bull Constant flow can be detected which is invisible toConstant flow can be detected which is invisible to homodyne (example aerosil + carbon-black rubber)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

Some tricks of the trade hellipMultispeckle Detectionp

bullFalus Borthwick Mochrie RSI (2004)

bullSNR increases as NSNR increases as

bullLimitations

bullReadout rate presently around 60 Hz

N

p y

bullEfficiency lt 50

bullNew Camera under development at LBL and APS ~500 Hz at 100 efficiency (John Weizeorick and Alec Sandy) Should see first light this cycle

FocusingFocusingKhalid Laaziri and Mark Sutton

bull Focusing the x-ray beam down to a small spot (~1 m) maintains flux but increases the speckle size SNR ~ photonsspeckle so SNR goes up Disadvantage is thatphotonsspeckle so SNR goes up Disadvantage is that radiation damage goes up as well

bull Fluctuations in Fe3Al3

Heterodyne DetectionLivet et al JSR (2006)Livet et al JSR (2006)

bull Mix a static signal with a weaker dynamic signalF diff i ti l ti ti l ( t)bull For diffusive motion relaxation times are longer exp(-t) instead of exp(-2t)

bull Constant flow can be detected which is invisible toConstant flow can be detected which is invisible to homodyne (example aerosil + carbon-black rubber)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

FocusingFocusingKhalid Laaziri and Mark Sutton

bull Focusing the x-ray beam down to a small spot (~1 m) maintains flux but increases the speckle size SNR ~ photonsspeckle so SNR goes up Disadvantage is thatphotonsspeckle so SNR goes up Disadvantage is that radiation damage goes up as well

bull Fluctuations in Fe3Al3

Heterodyne DetectionLivet et al JSR (2006)Livet et al JSR (2006)

bull Mix a static signal with a weaker dynamic signalF diff i ti l ti ti l ( t)bull For diffusive motion relaxation times are longer exp(-t) instead of exp(-2t)

bull Constant flow can be detected which is invisible toConstant flow can be detected which is invisible to homodyne (example aerosil + carbon-black rubber)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

Heterodyne DetectionLivet et al JSR (2006)Livet et al JSR (2006)

bull Mix a static signal with a weaker dynamic signalF diff i ti l ti ti l ( t)bull For diffusive motion relaxation times are longer exp(-t) instead of exp(-2t)

bull Constant flow can be detected which is invisible toConstant flow can be detected which is invisible to homodyne (example aerosil + carbon-black rubber)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

What is in the Future for XPCS X F El LX-ray Free Electron Lasers

LCLS at Stanford European Free Electron Laser at HamburgEuropean Free Electron Laser at Hamburg

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)

Referencesbull This talk httpwwwniuedu~lluriocoherenceThis talk httpwwwniuedu lluriocoherencebull XPCS

ndash G Gruumlbel et al (2008) X-Ray Photon Correlation Spectroscopy (XPCS) Soft-Matter Characterization R B a R Pecora Heidelberg SpringerMatter Characterization R B a R Pecora Heidelberg Springer

ndash M Sutton (2008) A review of X-ray intensity fluctuation spectroscopy Comptes Rendus Physics 9 657-667

bull Dynamic Light Scatteringy g gndash B Berne and R Pecora ldquoDynamic Light Scatteringrdquo Dover 2000

bull Coherencendash J Goodman ldquoStatistical Opticsrdquo Wiley 1985

M B d E W lf ldquoP i i l f O i rdquo P 1965ndash M Born and E Wolf ldquoPrinciples of Opticsrdquo Pergamon 1965bull X ndashray Free Electron Lasers

ndash Proposed Science for European XFEL G Gruumlbel et al NIM 262 357 (2007)LCLS ldquoThe First Experiments Studies of Nanoscale Dynamics in Condensedndash LCLS The First Experiments Studies of Nanoscale Dynamics in Condensed Matter Physics rdquo Stephenson et al SLAC-R-611 (2003)