Alessandro CunsoloINFM Operative Group in Grenoble and CRS-Soft, c/o Institut Laue-Langevin, Grenoble, France

Inelastic X Ray Scattering: a Inelastic X Ray Scattering: a valuable tool to investigate valuable tool to investigate the dynamics of disordered the dynamics of disordered

systemssystems

• Layout of the used IXS spectrometers

•How IXS can be employed to investigate relaxation processes?

• Is a transverse dynamics coupled with IXS spectra?

•A single IXS spectrometer probing the whole dynamic crossover from the hydrodynamic to the single-particle regimes.

•The onset of quantum effects in the dynamics of fluids studied by IXS.

•Conclusions and perspectives

SummarySummary

IXS BEAMLINE (ID16 & ID28)IXS BEAMLINE (ID16 & ID28)

sample

Undulators

MonochromatorSi (h,h,h)

E/E ≈ 10-2

Pre-Monochromator

Si (1,1,1)

≈E/E ≈ 10-4

75 m

Detector6.5 m

Analyzer

Si (h,h,h)

hh EEii(KeV)(KeV) E (meV)E (meV) Flux (p/s)Flux (p/s)

88 15.8215.82 5.55.5 9 * 109 * 101010

99 17.7917.79 33 3 * 103 * 101010

1111 21.7521.75 1.51.5 7 * 107 * 1099

5 Analyzers

Si (h,h,h)

5 Detectors

Toroidal mirrorB

E/E ≈ 10 -8

T-scan ≈ mK

What is a relaxation process? What effect it has on the spectral line-shape?

Q

Ki

The scattering event excites propagating density fluctuations…

IXSiout THz

Q=4isin() = ׀Q׀nm-1

Kout 2

•The propagation of a density fluctuation The propagation of a density fluctuation perturbs the local equilibrium of the fluid.perturbs the local equilibrium of the fluid.

•Such equilibrium is then restored through Such equilibrium is then restored through energy rearrangements affecting the energy rearrangements affecting the density density wavewave towards some towards some internal degree of internal degree of freedomfreedom (relaxation processes). (relaxation processes).

•Therefore the propagation of the density Therefore the propagation of the density wave depends on how its wave depends on how its periodperiod (T) (T) compares with the compares with the relaxation time-scalerelaxation time-scale ( ())..

T >> → Viscous regimeViscous regime

Instantaneous energy rearrangements: the acoustic wave propagates over

successive states of local equilibrium

T << → Elastic regime

The internal degrees of freedom of the fluid are

too slow to efficiently dissipate the energy of

the acoustic wave, which therefore

propagates elastically…

C()

C∞

C0= CS

Viscous regime

Elastic regime=1/

Visco-elastic regime

The frequency dependence of sound velocity at constant temperature and density

Q=Q*~1/d*

Visco-elastic crossover

s(Q)

q

cSQviscous regime

c∞Qelastic regime

s(Q*)=1/

The dispersion curve

An IXS study of relaxation phenomena in waterA. Cunsolo et al. Physical Review Letters 82, 775 (1999)

G. Monaco et al. Physical Review E60, 5505-5521 (1999)

The mysterious case of The mysterious case of fast fast soundsound in water: literature results in water: literature results

The apparent sound velocity (slope of the dispersion curve)

is roughly twice the adiabatic one J. Teixeira et al, PRL, 54,2681,

(1985)

?

cSQ

The IXS spectra of water at low Q

Q= 2 nm-1

Q= 4 nm-1

Q= 7 nm-1

0.1 1 10

1E-4

1E-3

0.01 T1 = 453 K

T2 = 333 K

T3 = 278 K

s/c s ( nm

-1 )

Q ( nm-1 )

Resolution limited range

Dispersion curve of water: first evidence of a viscoelastic behavior

-10 -5 0 5 100

1

2

Inte

nsity

(arb

it. u

nits

)

(meV)

T = 278 KQ = 2 nm-1

s-s

EKEE

AEQSSS

M

22222

),(

A typical DHO best fit lineshapeA typical DHO best fit lineshape

An upgraded resolution would

allow to studyviscoelastic effects also in the

overcooled phase

s,1~1/

q1

s,2~1/

q2

s,3~1/

q1

1/increases with increasing T

t

0

2B 'dt't,QC)'tt,Q(Kt,QC

QMSTQKt,QC

t,QC)tiexp(dt21,QS,QI0

IXS

In a IXS experiment the measured variable is the dynamic structure factor S(Q,)

Where the correlation function C (Q,t) = <(Q,t)(Q,0)> obeys to the memory function equation

t,QCLet m (Q, t) be the memory of the variable current

1

2B2B ,QmiQ)Q(MS

TKImM

TK2,QS

The dynamic structure factor can be written as a functionThe dynamic structure factor can be written as a function of of mm (Q,(Q,) = FT[) = FT[m(Q,t)]

Some hints on the more appropriate

choose for the memory function….

Instantaneous loose of memory

t

Viscous limit

t)Q(Kt,Qm

Visco-elastic regime Exponential

interpolation between the two limits…….

t

Qt

s e QcQcQtQm

222,

Infinitely slow loose of memory

t

Elastic limit

)Q('Kt,Qm

t,Qm

tQD

V

P2

B 2Te1

CC

QMSTQK

Thermal contribution

tQK

Instantaneous term

Q

t2s

22 ecQcQ

fit parameters

From EoS

Viscous contribution

The memory function employed to describe water spectra

The The q = 0q = 0 extrapolated relaxation timescales extrapolated relaxation timescales

0.0

0.6

1.2

1.8

2.4

3.0

0.0

0.6

1.2

1.8

2.4

3.0

0.0

0.6

1.2

1.8

2.4

3.0

0.0

0.6

1.2

1.8

2.4

3.0

0.0

0.6

1.2

1.8

2.4

3.0

0 1 2 3 4 5 6 70.0

0.6

1.2

1.8

2.4

3.0

T = 277 K

T = 373 K

T = 393 K

T = 433 K

(ps)

Q (nm-1)

T = 313 K

T = 333 K

The Arrhenius plot of the q = 0 extrapolated The Arrhenius plot of the q = 0 extrapolated relaxation timerelaxation time

2.0 2.4 2.8 3.2 3.6 4.0

0.1

1

IXS (present work) US, see C.M. Davis and J. Jarzynski in

"Water: a Comprehensive Treatise", (1972). best fit to IXS data

0 ( ps

)

1000 / T ( K -1 )

activation energy

≈

3.8 ± 0.6 Kcal/mole

The qThe q=0 extrapolated s=0 extrapolated sound velocityound velocity

250 300 350 400 450 500

1.6

2.0

2.4

2.8

3.2

T(K)

Soun

d ve

loci

ties (

Km

/s )

The strength of the relaxation processtends to disappear on approaching Tc

The viscoelastic behavior of the lineshapePossible effects of an improved instrumental resolution

-3 0 30.0

0.2

0.4

0.6

0.8

1.0

E = 0.1 meV

Nor

mal

ized

reso

lutio

n fu

nctio

n

Energy (meV)

Convolution for an hypothetical .1 meV (lorentzian) resolution function

(meV)

Raw spectraHypothetical higher resolution spectra

Non convoluted (model)line-shapes

(meV)

Q=2 nm-1

S(Q

,)/S

(Q) (

meV

-1)

Elastic regime

Visco-elastic regime

Viscous regime

Is there any evidence of a transverse dynamics in Is there any evidence of a transverse dynamics in the THz response of water?the THz response of water?

E. Pontecorvo, et al.E. Pontecorvo, et al. Physical Review Physical Review E71E71, 011501/1-12 (2005), 011501/1-12 (2005)

Transverse dynamics: intuitive Transverse dynamics: intuitive conceptsconcepts

If <<1/ (viscous limit)

NO

transverse propagation

When > 1/

a transverse propagation

may occur

TheThe spectral contribution spectral contribution of transverse dynamicsof transverse dynamics

10-4

10-3

10-2

10-1

(a)Q = 10 nm-1

T = 263 K

0 20 40 6010-4

10-3

10-2

10-1

(b)

E (meV)

The inclusion of an

additional mode

improves the

agreement with

experimental

results

The intensity of the additional mode increases systematically with increasing qThe intensity of the additional mode increases systematically with decreasing T

Q = 10 nm-1 Q = 13 nm-1

0.0

0.5

1.0

Q=16.0 nm-1

0.0

0.5

Q=13.1 nm-1

0.0

0.5Q=9.8 nm-1

0.0

0.5Q=7.8 nm-1

0 10 20 30 40 500.0

0.5C L,

T(Q, E

) (

arb.

units

)

Energy ( meV )

Q=5.8 nm-1

CT(Q,

CL(Q,)

0 10 20 30 400

5

10

15

20

25

30

35

L

,T ( m

eV )

Q ( nm-1 )

s from IXS spectra

T from IXS spectra

IXS results versus MD simulations

Crossover from viscoelasticity to transversedynamics: the experimental observation of the

gradual L-T mode-splitting would require a much better resolution ……

M. Sampoli et al. Phys. Rev. Lett. 79, 1678 (1997)

tiN

iiL

tiN

iiT

LTLTLT

i

i

ettJ

ettJ

JtJN

tC

rQ

rQ

vQQ

vQQ

QQQ

1

1

*,,,

ˆ,

ˆ,

0,,1),(

The transition from the hydrodynamic to The transition from the hydrodynamic to the single-particle regimesthe single-particle regimes

T. Scopigno et al., T. Scopigno et al., Europhysics LettersEurophysics Letters 5 500, 189-195 (2000)., 189-195 (2000).

The transition from (viscous) hydrodynamic limit to the single particle one: the case of liquid lithium

Q(nm-1)

Quantum effects in the dynamics of Quantum effects in the dynamics of simple fluidssimple fluids

A.Cunsolo, et al. Journal of Low Temperature Physics 129, 117 (2002).

A.Cunsolo, et al. Journal of Chemical Physics 123, 114509/1-7 (2005)

Quantum-to-classic transition in simple fluids

The lengthscale probed by the experiment must be comparable with the coherence length of quantum

effects

&

TMK3hnQ

BB

31

1

both must be comparable with the mean free path

Quantum effects in dynamical and structural properties of isotopes

The Vineyard prediction:When classical fluids are in corresponding thermodynamic states they have the same statical and dynamical responses….

Corresponding states:Thermodynamic states with same reduced temperature T/Tc

and density /c

E,QSER*K)E,Q(I M

E,QS*K M

'dE 'E,QS*KEIE

M0

0

50

100

150

200

250

0.0

0.5

1.0

1.5

-10 0 10 200.00

0.01

0.02

0.03

0.04

0.05

q = 1.55 Å-1

E (meV)

I(Q

,E) (

arbi

t. un

its)

K*S

M(Q

,)

I 0()

For any fluid the first spectral moments is equal to the recoil energy

MqdEEqSE

2,

22

dEE,QS E

dEE,QS

M2QQS

M

M22

5 10 15 20 25 300.0

0.5

1.0

1.5

2.0

Q (nm-1)

S(Q

) 0-order spectral moments of D2

0-order spectral moments of H2

simulated S(q) of D2

simulated S(q) of H2

Different position of the main diffraction peak :

a clear quantum effect!!

Q = 12.8 nm-1

Contrary to expectations the spectra aredifferent: a much sharper

excitation appears in the H2 line-shape!!

ConclusionsConclusions- IXS technique has proven its capability in providing a rich and physically informative insight on relaxation processes in disordered systems.

-The combined use of IXS and MD simulation allowed to get the first experimental evidence of a transverse dynamics in liquid water

-Owing to the absence of kinematic limitations, nowadays a single IXS spectrometer can cover the whole dynamic crossover between hydrodynamic and single particle regimes.

-IXS can be successfully used to probe the onset of quantum deviations in the dynamic behavior of simple fluids.

-The construction of IXS spectrometers with .1 meV resolution would provide a step forward towards a more exhaustive understanding of the THz dynamics of liquids. Moreover it would allow to partially bridge the dynamic gap existing with low q spectroscopies……

No man’s land

I’m deeply indebted toI’m deeply indebted to

Inelastic Scattering team:Inelastic Scattering team: M. Krisch,M. Krisch, A. Mermet, G. A. Mermet, G. Monaco, C. Masciovecchio, F. Sette and R. VerbeniMonaco, C. Masciovecchio, F. Sette and R. Verbeni

Universita’ di Firenze:Universita’ di Firenze: M. Sampoli M. Sampoli

Universita’ di Roma:Universita’ di Roma: G. Ruocco, T. Scopigno and G. Ruocco, T. Scopigno and E. PontecorvoE. Pontecorvo

Possible applications of high pressure techniques

in out

in

out

High pressure-high temperature sample High pressure-high temperature sample environmentenvironment

Large Volume HP Cells• Low pressures ( Kbar)• “Large” samples ( cm3)• Versatility (High-T & Low-T)

Sample

Cell body

Pressureconnector

sample

NutCell body

X-raybeam Scattered

beam

Sealingsystem

X-ray beam

10 mm

Scattered beam

Preliminary test for a novel-concept HP monochromatorPreliminary test for a novel-concept HP monochromator

sampleHP- monochromator

Si (n,n,n)

≈

Analyzer

Si (n,n,n)

B

E/E ≈ 10 -8

B

0 2 4 6 8 10

5

10

15

20

25

30

Q = 5 nm-1

Plasmon excitation in liquid Lithium

Inte

nsity

(arb

it. u

nits

)Energy loss (eV)

Analogy between viscoelasticity and the response of a RC circuit to a square Analogy between viscoelasticity and the response of a RC circuit to a square wavewave

t

T The analogous of the sound wave

t

V(t)

<< T The analogous of an almost viscous responseA(t)

The analogous of an almost elastic response>> T

t

A(t)