High-frequency dynamics in liquids and glasses at the mesoscopic scale

Giulio Università di Trento (I)

outline:

• IXS: science case for amorphous systems • IXS applications in liquids • IXS applications in glasses

Slide: 1 1. IXS: science case for disordered systems University of Trento IXS & disordered systems

 Interplay between structure and dynamics  Vibrations & relaxations at the picosecond time scale

G. Monaco – High frequencyG. dynamics Monaco –…IXS – Chicago,with sub -10/09/2016meV resolution – Pohang, 14/02/2013 Slide: 2 1. IXS: science case for disordered systems University of Trento

Long standing puzzle of the high-frequency dynamics

Microscopic regime  not complete understanding relaxation processes invoked to account for the spectral shape and the broadening of the excitations

Macroscopic regime Free particle regime:  hydrodynamics v=ħw/q impulse approximation

University of Trento G. MonacoG. Monaco – High – frequencyHigh-frequency dynamics vibrational … – Chicago, dynamics 10/09/2016 of glasses – Zurich, 26/06/2013 Slide: 3 1. IXS: science case for disordered systems University of Trento

1992-2016 – development of IXS @ ESRF

100 1010 Si(7,7,7) Si(9,9,9) Si(12,12,12)

Flux on the sample ( photons/s ) 109

Si(11,11,11) 108 10

107

6

Energy resolution ( meV ) meV ( resolution Energy 10 1

105 1985 1990 1995 2000 2005 2010 year

- IXS feasible at large third generation -~10.000 cubes of 0.6x0.6x2.3 mm3 synchrotron radiation sources (ESRF, APS, - perfect crystal properties

SPring-8) - collection of sufficient solid angle - steady development of undulators since the 1990s

G. Monaco – HighG. frequency Monaco – dynamics New opportunities … – Chicago, for IXS 10/09/2016 at the XFEL – , 19/07/2012 Slide: 4 2. IXS applications in liquids University of Trento Short range order in liquids

bcc

fcc

cI16

3 GPa, 650 K 59 GPa, 745 K

106 GPa, 500 K Es. sodium: the short range order of the liquid evolves with P and T following similar transformations as in the solid phase

Raty et al., Nature 449, 448 (07)

G. Monaco – HighG. frequencyMonaco – dynamicsHigh-resolution … – Chicago, inelastic 10/09/2016 x-ray scattering – Grado, 27/09/2013 Slide: 5 2. IXS applications in liquids University of Trento

The dynamic structure factor of sodium Inelastic x-ray scattering data @ ID16, E=23.724 keV, DE=1.4 meV

The spectrum of the liquid is a broadened version of that of the (poly)crystal

Giordano & g.m., PNAS 107, 21985 (10)

G. Monaco – High frequency dynamics … – Chicago, 10/09/2016 Slide: 6 2. IXS applications in liquids University of Trento

A simple crystal-like model

Liquid Na 390 K Polycrystalline Na 295 K

L T

Γ S(q,ω) S 0  S (q,ω)Gω el ω2 Γ2 in model: 0 2 2 ΩLΓL ΩTΓT Sin (q,ω) IL 2 2 2 2 2  IT 2 2 2 2 2 (ω  ΩL )  ω ΓL (ω  ΩT )  ω ΓT

G. Monaco – High frequency dynamics … – Chicago, 10/09/2016 Slide: 7 2. IXS applications in liquids University of Trento

The order fingerprint

First Brillouin zone: Long The longitudinal and transverse dispersion Theory curves in the liquid reflect those for the polycrystal: Trasv an orientational L average over the high symmetry branches of P the single crystal

(density scaling of frequencies for the solid) Giordano & g.m., PNAS 107, 21985 (10)

G. Monaco – High frequency dynamics … – Chicago, 10/09/2016 Slide: 8 2. IXS applications in liquids University of Trento

The disorder fingerprint

 Local order  dispersion  Average disorder  broadening

Giordano & g.m., PNAS 107, 21985 (10)

G. Monaco – High frequency dynamics … – Chicago, 10/09/2016 Slide: 9 2. IXS applications in liquids University of Trento

Liquids: reaching the macroscopic limit

At high q (> 1 nm-1) the dynamics is At low q (< 1 nm-1) macroscopic q-dependent hydrodynamics is recovered

5

4

3

2

) ps (  1

0 250 300 350 400 450 500 T ( K )

Pontecorvo et al., PRE 71, 011501 (2005) g.m. et al., PRE 60, 5505 (1999)

G. MonacoG. Monaco – High – High-frequency frequency vibrational dynamics dynamics … – Chicago, in disordered 10/09/2016 systems – , 22/07/2013 Slide: 10 3. IXS applications in glasses University of Trento

The universal anomalies of glasses

Pohl et al., Rev. Mod. Phys. 74, 991 (02) Zeller and Pohl, PRB 4, 2029 (71)

G. Monaco – HighG. frequencyMonaco – dynamicsHigh-resolution … – Chicago, inelastic 10/09/2016 x-ray scattering – Grado, 27/09/2013 Slide: 11 3. IXS applications in glasses University of Trento

Elastic heterogeneities - I

Spatial heterogeneities of the local Non affine displacement field (silica) shear modulus of a model polymer glass

Yoshimoto et al., PRL 93, 175501 (04) Leonforte et al., PRL 97, 055501 (06)

G. MonacoG. Monaco – High – frequencyHigh-frequency dynamics vibrational … – Chicago, dynamics 10/09/2016 of glasses – Zurich, 26/06/2013 Slide: 12 3. IXS applications in glasses University of Trento

Elastic heterogeneities - II Very limited experimental information on the local elasticity of glasses

Atomic force acoustic microscopy:

f: contact resonance frequency local indentation modulus

Wagner et al., Nat. Mat. 10, 439 (11)

G. MonacoG. Monaco – High – frequencyHigh-frequency dynamics vibrational … – Chicago, dynamics 10/09/2016 of glasses – Zurich, 26/06/2013 Slide: 13 3. IXS applications in glasses University of Trento The dynamic structure factor of glycerol

Inelastic x-ray scattering data @ ID16, E=23.724 keV, DE=1.4 meV

g.m. & Giordano, PNAS 106, 3659 (09)

G. Monaco – HighG. frequencyMonaco – dynamicsHigh-resolution … – Chicago, inelastic 10/09/2016 x-ray scattering – Grado, 27/09/2013 Slide: 14 3. IXS applications in glasses University of Trento Breakdown of the continuum approximation in glasses

3.6 10 IR 3.5 q2

3.4 1

( km/s )

l

( meV )

v 2

3.3 4 3.2 0.1 q 0 1 2 3 4 5 6 0 1 2 3 4 5 6 -1 -1 q ( nm ) q ( nm )

Breakdown of the Debye approximation & appearence of a Reyleigh scattering regime on the mesoscopic lengthscale of glasses

g.m. & Giordano, PNAS 106, 3659 (09)

G. Monaco – High frequency dynamics … – Chicago, 10/09/2016 Slide: 15 3. IXS applications in glasses University of Trento The case of SiO - I 2 7000

T=1620 K Below the BP frequency:

) -1 6500

Negative dispersion of the sound velocity

(m s (m

L v 6000

10

·2

1 4 (THz)

Damping  

 /

/2  0.1 ·4 51 K 318 K

) 0.015 523 K -3 873 K 0.010 1104 K

(THz 1673 K

2 c  BP  IR 

)/ 0.005

 g(

0.000 0 1 2 3 4 Baldi et al., PRL 104, 195501 (10)  (THz) G. Monaco – High frequency dynamics … – Chicago, 10/09/2016 Slide: 16 3. IXS applications in glasses University of Trento Elastic heterogeneities - III

Mizuno et al., PNAS 111, 11949 (2014)

G. MonacoG. Monaco – High – frequencyHigh-frequency dynamics vibrational … – Chicago, dynamics 10/09/2016 of glasses – Zurich, 26/06/2013 Slide: 17 3. IXS applications in glasses University of Trento

The case of SiO2 - II

Baldi et al., PRL 110, 185503 (13)

G. MonacoG. Monaco – High – frequencyHigh-frequency dynamics vibrational … – Chicago, dynamics 10/09/2016 of glasses – Zurich, 26/06/2013 Slide: 18 3. IXS applications in glasses University of Trento

The case of SiO2 - III

Chumakov et al., 112, 025502 (2014)

G. MonacoG. Monaco – High – frequencyHigh-frequency dynamics vibrational … – Chicago, dynamics 10/09/2016 of glasses – Zurich, 26/06/2013 Slide: 19 3. IXS applications in glasses University of Trento

The case of SiO2 - IV

Chumakov et al., 112, 025502 (2014)

G. MonacoG. Monaco – High – frequencyHigh-frequency dynamics vibrational … – Chicago, dynamics 10/09/2016 of glasses – Zurich, 26/06/2013 Slide: 20 University of Trento

Conclusions

1. The X-ray echo scheme promises to offer 102-103 times higher signal than at current IXS beamlines. Experiments not feasible at storage rings will be feasible, and those already feasible will be much faster…

2. In liquids it will be possible to study the q-dependence of the relaxation dynamics up to a fraction of a ns. This includes, in particular, the structural relaxation time in the critical temperature region for the dynamical arrest.

3. In both glasses and liquids, the mesoscopic range will be accessible with a single technique! This can be crucial for metastable systems… Thank you !

G. Monaco – HighG. frequency Monaco – dynamics New opportunities … – Chicago, for IXS 10/09/2016 at the XFEL – Hamburg, 19/07/2012 Slide: 21