Inelastic X Ray Scattering: a valuable tool to investigate the dynamics of  disordered systems
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Inelastic X Ray Scattering: a valuable tool to investigate the dynamics of disordered systems. Alessandro Cunsolo INFM Operative Group in Grenoble and CRS-Soft, c/o Institut Laue-Langevin, Grenoble, France. Summary. Layout of the used IXS spectrometers

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

Alessandro Cunsolo

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


Summary

  • 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


DE/E ≈ 10-8

Monochromator

Si (h,h,h)

6.5 m

DE/E ≈ 10-4

Undulators

Pre-Monochromator

Si (1,1,1)

qB

Toroidal mirror

75 m

IXS BEAMLINE (ID16 & ID28)

5 Analyzers

Si (h,h,h)

Analyzer

Si (h,h,h)

2q

5 Detectors

Detector

T-scan ≈ mK

sample

DE/E ≈ 10-2


What is a relaxation process?

What effect it has on the spectral line-shape?


The scattering event excites propagating density fluctuations…

Q

Kout

2q

Ki

IXS

hw = Ei-Eout  THz

׀Q׀ = Q=4p/lisin(q)  nm-1


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

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

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


Instantaneous energy rearrangements: the acoustic wave propagates over successive states of local equilibrium

T >>t→Viscous regime


T << 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…


The dispersion curve

c∞Q

Visco-elastic regime

Visco-elastic crossover

elastic regime

Elastic regime

w=1/t

Q=Q*~1/d*

C∞

ws(Q)

ws(Q*)=1/t

C(w)

cSQ

Viscous regime

viscous regime

C0= CS

q

w

The frequency dependence of sound velocity at constant temperature and density


  • An IXS study of relaxation phenomena in water

  • Cunsolo et al. Physical Review Letters82, 775 (1999)

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


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 mysterious case of fast sound in water: literature results


Q= 2 nm-1

Q= 4 nm-1

Q= 7 nm-1

The IXS spectra of water at low Q


A typical DHO best fit lineshape

Ws,1~1/t1

Ws,2~1/t2

hws

-hws

Ws,3~1/t3

Resolution limited range

q1

q2

q1

An upgraded resolution would

allow to study

viscoelastic effects also in the overcooled phase

Dispersion curve of water: first evidence of a viscoelastic behavior

1/t increases with increasing T


The dynamic structure factor can be written as a functionof

m(Q,w) = FT[m(Q,t)]

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

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

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

Some hints on the more appropriate

choose for the memory function….


Instantaneous loose of memory

Viscous limit

Visco-elastic regime

Exponential

interpolation between the two limits…….

t

t

t

Infinitely slow loose of memory

Elastic limit

t


The memory function employed to describe water spectra

fitparameters

Instantaneous term

Thermal contribution

Viscous contribution

From EoS


t0(433 K)

t0(393 K)

t0(373 K)

t0(333 K)

t0(313 K)

t0(277 K)

The q = 0 extrapolated relaxation timescales


activation energy

3.8 ± 0.6 Kcal/mole

The Arrhenius plot of the q = 0 extrapolated relaxation time


The strength of the relaxation process

tends to disappear on approaching Tc

The q=0 extrapolated sound velocity


Non convoluted (model)

line-shapes

Raw spectra

Q=2 nm-1

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

Elastic regime

Hypothetical higher resolution spectra

S(Q,w)/S(Q) (meV-1)

Visco-elastic regime

Viscous regime

hw (meV)

hw (meV)

The viscoelastic behavior of the lineshape

Possible effects of an improved instrumental resolution


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

E. Pontecorvo, et al. Physical Review E71, 011501/1-12 (2005)


Transverse dynamics: intuitive concepts

If w<<1/t (viscous limit) 

NO

transverse propagation

When w> 1/t

a transverse propagation

may occur


The inclusion of an

additional mode

improves the

agreement with

experimental

results

Thespectral contribution of transverse dynamics


The intensity of the additional mode increases systematically with decreasing T

The intensity of the additional mode increases systematically with increasing q

Q = 10 nm-1

Q = 13 nm-1


IXS results versus MD simulations

CT(Q,E)

CL(Q,E)

Crossover from viscoelasticity to transverse

dynamics: 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)


The transition from the hydrodynamic to the single-particle regimesT. Scopigno et al., Europhysics Letters 50, 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 simple fluidsA.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

&

both must be comparable with the mean free path


Quantum effects in dynamical and structural properties of isotopes

Different position of the main diffraction peak :

a clear quantum effect!!

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

Q = 12.8 nm-1

Contrary to expectations the spectra are

different: a much sharper

excitation appears in the H2 line-shape!!

Corresponding states:

Thermodynamic states with same reduced temperature T/Tcand densityr/rc

The Vineyard prediction:

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


Conclusions

  • - 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.


No man’s

land

-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……


I’m deeply indebted to

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

  • Universita’ di Firenze: M. Sampoli

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


Possible applications of high pressure techniques


Pressure

connector

Cell

body

out

sample

Sealing

system

in

out

X-ray

beam

in

X-ray

beam

Scattered

beam

Scattered

beam

10 mm

High pressure-high temperature sample environment

  • Large Volume HP Cells

  • Low pressures ( Kbar)

  • “Large” samples ( cm3)

  • Versatility (High-T & Low-T)

Cell

body

Nut

Sample


Preliminary test for a novel-concept HP monochromator

Analyzer

Si (n,n,n)

DE/E ≈ 10-8

HP- monochromator

Si (n,n,n)

qB

sample

qB


T

V(t)

The analogous of the sound wave

t

t << T

The analogous of an almost viscous response

A(t)

A(t)

t >> T

The analogous of an almost elastic response

t

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

t


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