Dynamical properties of glass formers probed with coherent …Coherent X-rays The ideal photon source would be a one-mode source (stimulated emission), e.g. unimodal lasers X-ray sources

Dynamical properties of glass formersprobed with coherent X-rays

Beatrice Ruta

Grenoble 21/11/2019

Coherent X-rays and X-ray Photon Correlation Spectroscopy

Glassy systems

Atomic motion in metallic glass formers

Dynamics in oxide and silicates glasses

The EBS-ESRF upgrade

New scientific opportunities

Outline

Page 2


Glassy systems





Outline

Page 3

Coherent X-rays

Page 4Courtesy of C. Gutt

Page 5

The intensity fluctuations are related to the constructive and

destructive interference between the two waves

http://micro.magnet.fsu.edu/primer/java/interference/doubleslit/

Coherence is observed when phases stay correlated (constant phase difference between pairs of points) in time and space two types of coherent lengths.

Coherent Radiation

Determined by monochromaticity: distance over which two waves with slightly different λare out of phase (Δφ=π)

Longitudinal coherent length

2ξL=Nλ

(N+1)(λ-Δλ)

ሻ𝑁λ = (N + 1ሻ(λ − ∆λ

λ = N + 1 ∆λ and N~λ

∆λ

ξ𝐿 =𝑁λ

2=1

2

λ2

∆λ

λ ≈1.5ÅΔλ/λ=1.4x10-4Si (1,1,1)ξL≈0.5 μm

Page 6

Transverse coherent lengths

Determined by beam size D and distance R: distance over which two waves slightly tiltedof an angle θ are out of phase (Δφ=π)

λ

2ξ𝑇= sinθ ≈ θ

D

𝑅= tanθ ≈ θ

ξ𝑇ℎ,𝑣 ≈λ

2

𝑅

𝐷ℎ,𝑣

Page 7

Transverse coherent lengths

Determined by beam size D and distance R: distance over which two waves slightly tiltedof an angle θ are out of phase (Δφ=π)

λ

2ξ𝑇= sinθ ≈ θ

D

𝑅= tanθ ≈ θ

ξ𝑇ℎ,𝑣 ≈λ

2

𝑅

𝐷ℎ,𝑣

To use coherence, the scattering volume VS should be smaller than the coherent volume Vc

This condition is difficult to achieve with X-rays

Page 8

Coherent X-rays

The ideal photon source would be a one-mode source(stimulated emission), e.g. unimodal lasers

X-ray sources are chaotic, because photons aregenerated by spontaneous emission like e.g. light bulbs,radioactive sources …

The key parameter quantifying the coherence properties of the photon source is the degeneracy parameter nc, i.e. the number of photons contained in the coherent volume Vc

nc≈107 for a typical optical lasernc≈10-3 for a typical (old) ESRF undulator

Page 9

Coherent X-rays

Page 10

X-Ray Photon Correlation Spectroscopy

O. Shpyrko et al, Nature 2007

Example: with λ=1Å, d=10μm coherent beam in transmission geometry:Speckle size λ/d*L= 10 μm at 1m detector distance L

Page 11

Page 12

Speckle pattern with X-rays

M. Sutton et al. Nature 1991

How do we measure the dynamics?

Page 13

F. van der Veen & F. Pfeiffer, J. Phys. Cond. Mat. 1998

2

)()(),(

n

triQ

nneQftQI

The intensity of the speckles is related tothe exact spatial arrangement of thescatters inside the system

2)(

)(),(

n

triQ

nneQftQI

Averaged quantities


Page 14

Information on the dynamics can be obtained by measuring a series of specklespatterns and quantifying temporal correlations of intensity fluctuations at a givenwave-vector q


tt+Δt

t+2Δtt+3Δt

A. Madsen, A. Fluerasu and B. Ruta, XPCS, Springer, 2015

𝑔2 𝑄, 𝑡 =ሻ𝐼(𝑄, 0ሻ𝐼(𝑄, 𝑡

ሻ𝐼(𝑄 2= 1 + 𝐴(𝑄ሻ ሻ𝐹(𝑄, 𝑡 2

𝐹 𝑄, 𝑡 =1

ሻ𝑆(𝑄

1

𝑁

𝑖=1

𝑁

𝑗=1

𝑁

𝑒𝑥𝑝 𝑖𝑸 𝒓𝒊 0 − 𝒓𝒋 𝑡

Siegert relation

Intermediate scattering function

experimental contrast

Page 15

The intermediate scattering function

The intermediate scattering function monitors the decay of the density fluctuationson a scale 2π/Q

(0) ( )( , )(Q,t)

( ) (0) (0)

Q Q

Q Q

tS Q tF

S Q

0.1 1 10 100 1,0000.0

0.2

0.4

0.6

f(q

,t)

time (s)

2π/Q

τ

Page 16

Intensity auto-correlation functions

Page 17


1 10 1001.00

1.01

1.02

1.03

1.04

g2(t

)

time (seconds)Δt (seconds)

Page 18


1 10 1001.00

1.01

1.02

1.03

1.04

g2(t

)


Page 19


1 10 1001.00

1.01

1.02

1.03

1.04

g2(t

)


Page 20

Scientific activity with XPCS at ID10, ESRF

XPCS: (saxs, waxs, gi-xpcs)

• Supercooled liquids and glasses

• Soft materials (gels, colloids, …)

• Fluctuations at ordering phase transitions

• Driven dynamics by external fields T, E, B

• Interface dynamics in soft matter systems

• Atomic diffusion in alloys

• …

Energy range: 7,8,10 & 21 keV

Time resolution [2D det.]: ≈ ms - 104 s

Probed length scales: 8·10-4 - 3 Å-1

Y. Chushkin F. Zontone

Page 21

Interpretation of a correlation function

𝑔2 𝑞, 𝑡 = 1 + 𝑎exp −2𝑡

𝜏

𝛽

Kohlrausch-Williams-Watts (KWW) function

Page 22

a(q,t)=A*fq2 (t). Experimental contrast*nonergodicity parameter of

glasses info on secondary relaxation processes or elasticity in the material

β(q,t) = shape parameter info on the distribution of microscopic relaxation processes

τ(q,t) = structural relaxation time info on the mechanism of particle motion on a scale 2π/q

0.1 1 10 100 1,0000.0

0.2

0.4

0.6

g2(q

,t)-

1

time (s)

a

Interpretation of a correlation function

Depending on the value and dependence of the different parameters, it is possible to distinguish different particle motions

β=1 and τ=1/Q2 Brownian motion

β<1 and τ=1/Q Hopping of caged particles

β>1 and τ=1/Q Super diffusion, ballistic like motion and stress relaxation

Page 23

hopping of caged particles

Page 24

Two times correlation functions (TTCF)

Direct measurements of temporal evolution of the dynamics: time-resolvedversion of g2(q,t)

1 2

1 2

1 2

( , ) ( , )( , , )=

( , ) ( , )

P

P P

I Q t I Q tG Q t t

I Q t I Q tStationary dynamics

12 1( , ) ( , , )

tg Q t G Q t t

Courtesy of A. Madsen

10 100 1,000 10,0000.00

0.01

0.02

0.03

0.04

0.05

0.06

tw= 3140 s

tw= 7800 s

tw= 10900 s

time (s)

g2(t

)-1

exp. time

0 4500 9000 135000

4

50

0

9

00

0

1

35

00

t1(s)

t 2(s

)

Page 25

Aging


Broadening of two-time correlation function slowing down of the dynamics

12 1( , ) ( , , )

tg Q t G Q t t

TTCF important also to check the reliability of the measurements

Page 26


TTCF are important also for the data interpretation

Courtesy of F. Perakis

Page 27

Dynamical heterogeneities

normalized variance

F. Perakis et al. PNAS 2017

E. Weeks et al. Science 2000

XPCS on Glasses

Page 28

(τ up to 104 s, Q up to 4 Å-1)glasses

XPCS in Glasses

Page 29

Page 30

10 100 1,0000.00

0.01

0.02

0.03

0.04

0.05

0.06

time (s)

g2(t

)-1

q

Coherent X-rays 8.1 keV (1.53Å)

10 mm square slit

70 cm

Sample

Detector plane

tw

1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2

I(Q)

Q [Å-1]

Qmax

ANDOR CCD

0.04 ph/pixel/frameOne q per measurement

WAXS geometry8 keV: peak at 20°- 45° deg.

XPCS in Glasses

Page 31

XPCS in practise

The problem of the contrast

Ideal condition : VS < Vc

Contrast A= Vc/Vs

With X-rays contrast<1

Signal to noise ratio𝑆𝑁𝑅 ∝ 𝑐𝑜𝑛𝑡𝑟𝑎𝑠𝑡

Courtesy of C. Gutt

Page 32

Path length difference and coherence

Contrast decreases at large angles due to increase in path length difference between scattered waves:

PLD≈2hsin2(θ)+dsin(2θ)≤ξL

Detector at 2θFor x-rays typically 1 μm

In glasses: FSDP at 20-45 degreesLow contrast ≈ 2 - 6 %Thin samples ≈ 20 μm

Courtesy of A. Madsen

Page 33

XPCS in practise

Large speckles Small speckles

Contrast decreases if the speckles are not resolved

Courtesy of C. Gutt

Page 34

XPCS in practise

Signal to noise ratio:

𝑆𝑁𝑅 ~ 𝐴 ∙ ҧ𝐼 ∙ 𝑇 ∙ 𝑑𝑡 ∙ 𝑁𝑝

ҧ𝐼 = count rate per pixel

T= total duration of the measurement

dt= exposure time per frame

Np= number of pixel per detector

A= contrast

If the dynamics is stationary, SNR can be

improved averaging different data sets

Other practical rules:

Thickness of the sample (depends on absorption and contrast/q)

Detector optimization (speckles and dynamics)

Check sample-X-ray interaction

Check always TTCF


Glassy systems





Outline

Page 35

The glass transition: a dynamical process

The final structure depends on thecooling rate (Glass 1 & 2) and evolvesspontaneously with time (Glass 3)

L. Berthier & M. Ediger, Phys. Today 2016Page 36

A liquid that has lost its ability to flow, being trapped in a metastable stateC. A. Angell, Science, 1995

Out-of-equilibrium state aging

Temporal evolution: Every observableevolves with time

Memory effects: strong dependence onthe sample preparation and history

1/Tg1

1/Tg2

slow cooling

fast cooling

supercooled

liquid

log

[rela

xati

on

tim

e

; v

isco

sity

]

1/T

glass

aging

Page 37

The glass transition: a dynamical process

Page 38L.M.C. Janssen Front. Phys. 2018

F(q,t) in supercooled liquids

The slow down of the dynamics toward the glassy state corresponds to a continuous shift of the decay time toward longer time scales and the emerging of different relaxation processes.

Page 39

F(q,t) in glasses

Liquid: texp>>τ

Glass: texp>>τ

The intermediate scattering function of a glass should not decorrelate

L.M.C. Janssen Front. Phys. 2018

Page 40

10-10

10-8

10-6

10-4

10-2

100

102

104

0.0

0.2

0.4

0.6

0.8

1.0

F(Q

,t)

time (s)

liquid frozen, non ergodic

? Glassy state (T<Tg):

No information due to limitation inexperiments

F(q,t) in glasses

Page 41

MD simulations in a Lennard-Jones glass

A the microscopic scale there are structural rearrangements that evolve with time

W. Kob and J-L. Barrat Phys. Rev. Lett. 1997

time


Glassy systems





Outline

Page 42

Anomalous dynamics in metallic glasses:1. The dynamical crossover

The dynamical crossover

10 100 1,000 10,0000.0

0.2

0.4

0.6

0.8

1.0

1.2 T=418 K

T=417 K

T=415 K

T=413 K

T=410 K

T=408 K

F(Q

,t)2

t (s)

decreasing TMg65Cu25Y10

liquid

1012

1013

1014

1015

1016

2.4 2.5 2.6 2.7

102

103

104

105

106

visco

sity (p

oise)

Tg

LIQUID

rela

xat

ion t

ime

(s)

1000/T(1/K)

Q=max of S(Q) 2.56 Å-1

XPCS measurements (ID10 - ESRF)

tatqf exp),(

Tg

Page 44Ruta et al. Phys. Rev. Lett. 2012Ruta et al. Topical Review J. Phys. Cond. Matt. 2017

10 100 1,000 10,0000.0

0.2

0.4

0.6

0.8

1.0

1.2 T=418 K

T=417 K

T=415 K

T=413 K

T=410 K

T=408 K

T=393 K

T=388 K

T=383 K

T=373 K

F(Q

,t)2

t (s)

decreasing T

Tg

Mg65Cu25Y10

liquid

glass

1012

1013

1014

1015

1016

2.4 2.5 2.6 2.7

102

103

104

105

106

visco

sity (p

oise)

GLASSTg

LIQUID

rela

xat

ion t

ime

(s)

1000/T(1/K)


Q=max of S(Q)2.56 Å-1

tatqf exp),(


Page 45Ruta et al. Phys. Rev. Lett. 2012Ruta et al. Topical Review J. Phys. Cond. Matt. 2017

10 100 1,000 10,0000.0

0.2

0.4

0.6

0.8

1.0

1.2 T=418 K

T=417 K

T=415 K

T=413 K

T=410 K

T=408 K

T=393 K

T=388 K

T=383 K

T=373 K

F(Q

,t)2

t (s)

decreasing T

Tg

Mg65Cu25Y10

liquid

glass

1012

1013

1014

1015

1016

2.4 2.5 2.6 2.7

102

103

104

105

106

visco

sity (p

oise)

GLASSTg

LIQUID

rela

xat

ion t

ime

(s)

1000/T(1/K)

β>1

β<1

T>Tg: stationary dynamics, β<1, diffusive motion

T<Tg: aging, β>1 , Anomalous stress-driven dynamics

aging


Q=max of S(Q)2.56 Å-1

tatqf exp),(

Ruta et al. Phys. Rev. Lett. 2012Ruta et al. Topical Review J. Phys. Cond. Matt. 2017


Page 46

1E-3 0.01 0.1 1 100.0

0.2

0.4

0.6

0.8

1.0

1.2

10 100 1,000 10,0000.0

0.2

0.4

0.6

0.8

1.0

1.2

liquid

F(Q

,t)2

t/

b

glass

T=418 K

T=417 K

T=415 K

T=413 K

T=410 K

T=408 K

T=393 K

T=388 K

T=383 K

T=373 K

<1

(g2(t

)-1)/

A(T

)

t (s)

>1

adecreasing T

Q=2.56 Å-1

Tg=405 K

Δβglass~40%

The dynamical crossover at Tg

B. Ruta et al. Topical review, J. Phys. Cond. Matt. 2017 Page 47

0.01 0.1 10.0

0.2

0.4

0.6

0.8

1.0

10 100 1,0000.0

0.2

0.4

0.6

0.8

1.0

T=417 K

T=415 K

T=413 K

T=383 K

T=348 K

T=318 K

t/

F(Q

,t)2

t (s)

(g2(t

)-1

)/A

Temperature

Δβglass~70%

by heating


Mg65Cu25Y10

10-3

10-2

10-1

100

101

0.0

0.2

0.4

0.6

0.8

1.0

liquid

= 0.76,= 2900 s

glass

= 1.60, = 200 s

F(Q

,T)2

t/

T= 383 K

Au49Cu26.9Si16.3Ag5.5Pd2.3

liquid

log

[;

vis

cosi

ty]

1/T

glass

B. Ruta et al., AIP Conf. Proc. 2013 S. Hechler et al., Phys. Rev. Mat. 2018

Page 48


strange in hard glasses …

V. Lubchenko & P. G. Wolynes J. Chem. Phys. 2004

theories for aging predict a continuous decreasing of β below Tg

… similar to soft glasses (colloidal gels, clay suspensions, polymeric gels, …)

L. Cipelletti et al. Phys. Rev. Lett. 2000

J.-P. Bouchaud & E. Pitard ,Eur. Phys. J. E, 2001

E. Ferrero et al. Phys. Rev. Lett. 2014

M. Bouzid et al. Nat. Commun. 2017

P. Chaduri & L. Berthier, Phys. Rev. E, 2017

attributed to rearrangement events induced by internal stresses

Page 49

Hard colloids(Laponite)

Soft colloids(PNIPAM Microgels)

Metallic glass(PdNiCuP)

Common dynamical crossover from diffusiveto stress-driven microscopic dynamics andcompressed correlation functions.

Evenson, Ruta et al. PRL (2015) Nigro/ Ruta et al. submitted

Angelini et al. Soft Matt. (2013)

Common to different glassy systems

XPCSXPCS

XPCS

DMA

DLS

DLS

Page 50

Anomalous dynamics in metallic glasses:2. The hierarchical aging

Direct measurements of the temporal evolution of the dynamics

1 2

1 2

1 2

( , ) ( , )( , , )=

( , ) ( , )

P

P P

I Q t I Q tG Q t t

I Q t I Q t

12 1( , ) ( , , )

tg Q t G Q t t

10 100 1,000 10,0000.00

0.01

0.02

0.03

0.04

0.05

0.06

tw= 3140 s

tw= 7800 s

tw= 10900 s

time (s)

g2(t

)-1

exp. time0 4500 9000 135000

4

50

0

9

00

0

1

35

00

t1(s)

t 2(s

)Two times correlation functions

Page 52

10 100 1,000 10,0000.0

0.2

0.4

0.6

0.8

1.0

tw= 3100 s t

w= 7800 s

tw= 3900 s t

w= 8500 s

tw= 4700 s t

w= 9300 s

tw= 5500 s t

w= 10100 s

tw= 6200 s t

w= 10900 s

tw= 7000 s t

w= 11600 s

time (s)

F(Q

,t)2

T=453 K

3,000 6,000 9,000 12,0001000

2000

3000

4000

5000

6000

tw (s)

(s

)

w 0 w(T, t ) (T)exp(t / )

τ*~6000 s

tw

Pd77Si16.5Cu6.5 (Tg=625 K, Q=2.8 Å-1)

V.M. Giordano & B. Ruta, Nat. Commun. 2016

Microscopic Aging in Metallic Glasses

tatqf exp),(

Page 53

Structural origin of the fast aging

Pd77Si16.5Cu6.5 (Tg=625 K, Q=2.8 Å-1)

Fast aging due to density changes (structural defects annihilation)

400 450 500

1.004

1.005

1.006

1.007

1.008

T (K)

V/V

0

0 500 1000 1400

1.004

1.005

1.006

1.007

1.008

t-t0 (min)

V/V

0

0 70 150

433K

Rel

. volu

me

V/V

0=

(Q0/Q

)3

Isothermal volume relaxation

XRD

Page 54

waiting time (s)


Similarities with jammed soft materials

slow aging

rela

xati

on

tim

e (s

)

Hierarchical aging in complex systems

colloidal gel

fast initial aging

Page 55

waiting time (s)

colloidal gel

Similarities with jammed soft materials

fast initial aging

slow aging

rela

xati

on

tim

e (s

)

Hierarchical aging in complex systems

Universal behavior?


Page 56

1 6 7 8 91

10

Pd77

Si16.5

Cu6.5

(T/Tg=0.73)

Mg65

Cu25

Y10

(T/Tg=0.99)

Zr67

Ni33

(T/Tg=0.58)

tw

/*

/ 0

(T)

Anomalous stationary dynamics well below Tg

fast initial agingτ* ~ 6000 s

Hierarchical aging below Tg

Page 57

400 450 500

1.004

1.005

1.006

1.007

1.008

T (K)

V/V

0

0 500 1000 1400

1.004

1.005

1.006

1.007

1.008

t-t0 (min)

V/V

0

0 70 150

433K

XRD

Structural origin of the stationary regime

Continuous FSDP sharpening

Q=max of S(Q)

Rel

. volu

me

V/V

0=

(Q0/Q

)3

No volume relaxation

Page 58

400 450 500

1.004

1.005

1.006

1.007

1.008

T (K)

V/V

0

0 500 1000 1400

1.004

1.005

1.006

1.007

1.008

t-t0 (min)

V/V

0

0 70 150

433K

Two main processes controlling the aging:1) volume shrinking (density changes)

2) medium range ordering (constant density)

fast aging

stationaryregime

XRD

Structural origin of the stationary regime

Continuous FSDP sharpening

V.M. Giordano & B. Ruta, Nat. Commun. 2016

Q=max of S(Q)

Rel

. volu

me

V/V

0=

(Q0/Q

)3

No volume relaxation

Page 59

the evolution between the two could berelated to a ductile to brittle transition

Fast aging: thermal activation of a cascade of jumps from a high-energyminimum irreversible atomicrearrangements changing density

Stationary: Localized dynamics in a more relaxed minimum constant density butincreasing MRO

Fan et al. Phys. Rev. Lett. 2015

From cascade relaxation to localized motion

Page 60

Anomalous dynamics in metallic glasses:4. Secondary relaxation processes

and crystallization

Contrast decreases at the two highest temperatures

0 500 1000 15000.03

0.04

0.05

0.06

0.01 0.1 10.00

0.02

0.04

0.06

cf Q

2

t-t0 (min)

g2(t

)-1

delay time/

temperature

Temperature activation of an additional relaxation process

V.M. Giordano & B. Ruta, Nature Commun. 2016

XPCS

tcftqg QXPCS 2exp)(),( 2

2

Temperature induced secondary processes

Page 62

Contrast decreases at the two highest temperatureshigh temperature activation of a secondary relaxation with <3s (experimental

temporal resolution)

0 500 1000 15000.03

0.04

0.05

0.06

0.01 0.1 10.00

0.02

0.04

0.06

cf Q

2

t-t0 (min)

g2(t

)-1

delay time/

temperature

tcftqg QXPCS 2exp)(),( 2

2Temperature activation of an additional relaxation process


XPCS


Page 63


0 500 1000 15000.03

0.04

0.05

0.06

0.01 0.1 10.00

0.02

0.04

0.06

cf Q

2

t-t0 (min)

g2(t

)-1

delay time/

temperature

0 500 1000 15000,998

1

1,002

0,998

t -t0 (min)

r 4/r

4(2

98

)

0 500 1000 1500

0,92

0,96

r4

/ r 4

(29

8)

t-t0 (min)

c f

FSDP

stronger ordering at the medium range and

3rd shell expansion

XPCS

XRD


Page 64

The fast secondary relaxation starts at 493K and implies a stronger ordering.

Precursor to crystallization?



Page 65

The fast secondary relaxation starts at 493K and implies a stronger ordering

Precursor to crystallization?• 493K: no evidence of crystallization in XRD spectra• However at 513K: 0.8% crystallization after 7h



Strong support to the interpretation of this process as precursor to crystallization

Page 66

Structural & dynamical measurements during crystallization

How can we go further?

What do we need for these studies?Better contrast (now ≈ 4%)

More Flux + Faster detectors!

Page 67

Anomalous dynamics in metallic glasses:3. The intermittent aging

Au49Cu26.9Si16.3Ag5.5Pd2.3

β≈1.6

β≈1.4

≈ 500 s

Aging triggered by “discrete events”

Page 69I. Gallino/ B. Ruta Acta Mat. 2018

Au49Cu26.9Si16.3Ag5.5Pd2.3

Anomalous enthalpy recovery

XPCS

I. Gallino/ B. Ruta Acta Mat. 2018 Page 70

Au49Cu26.9Si16.3Ag5.5Pd2.3

Anomalous enthalpy recovery

XPCS

Cangialosi et al. Phys. Rev. Lett. (2012)

Polymeric glass

I. Gallino/ B. Ruta Acta Mat. 2018 Page 71

10-2

10-1

100

101

102

103

0.0

0.2

0.4

0.6

0.8

1.0

473 K

Zr50

Cu40

Al10

(t

)/

(0)

t (min)

693 K

Multiple relaxations in the elastic response

ε = 0.3%

Fast process: γ1>1 and almost no thermal contributionSlow process: γ2 <1 , strong T dependence

Τ𝜎(𝑡ሻ 𝜎 0 = 𝐴exp −(Γ1𝑡ሻ𝛾1 + (1 − 𝐴ሻ exp −(Γ2𝑡ሻ

𝛾2

Dynamic Mechanical Analyser under constant tensile strain

10-2

10-1

100

101

102

103

0.0

0.2

0.4

0.6

0.8

1.0

439 K

(a)

σ(t

)/σ

(0)

t (min)

629 K

Zr44

Ti11

Cu10

Ni10

Be25

ε = 0.3%

samples pre-annealed at 0.9 Tg for 48 h

P. Luo/ B. Ruta, W.H. Wang. Phys. Rev. Lett. 2017 Page 72

Dynamical crossovers

Angell’s classification of glass-formers

Debenedetti & Stillinger Nature, 2001

Shi, Russo & Tanaka PNAS, 2018

Fragile to strong dynamical crossover

Page 80

Fragile-to-strong-crossover and LLTs

Fragile-to-strong-crossover and Liquid-Liquid transition

C. Way, P. Wadhwa, R. Busch, Acta Mater. 2007

LLT

2-order of magnitude hysteresis in viscosity

change in fragility: D* = 12 D* = 26.5

kineticsDiscontinuities in total structure factor S(Q)

structure

Stolpe/ Busch Phys. Rev. B 2016

thermodynamics

Peak-like anomalies in heat capacity

Courtesy of R. BuschPage 82

Tg

Au49Cu26.9Si16.3Ag5.5Pd2.3

350 360 370 380 390 400 410

0.998

1.000

1.002(b)

strong glass

LL

T r

eg

ion

frag

ile li

quid

fragile

glass(Qm

ax

1(T

ref)/

Qm

ax

1)3

Temperature (K)

350 360 370 380 390 400 410

10-2

10-1

100

101

102

103

104

105

Tg

strong liquid

D*=23.1

D*=8.9

fragile liquid

(s

)

(a)

386 388 390 392

102

103

<>

(s)

T (K)

386 388 390 392

1.000

1.001

1.002

The supercooled liquid phase (XPCS+DMA)

Glass transition?- Expected Tg is 10 K lower- Aging only at expected Tg

- Stretched correl. functions- Steep temperature dependence

Q=2.78 Å-1

S. Hechler, et al. Phys. Rev. Mat. (2018) Page 83

Tg

2 XRD experiments- Same thermal protocol as XPCS- Continuous cooling with 1.5 K/min

The supercooled liquid phase (XRD)

T-step with long isotherms

Continuous cooling


350 360 370 380 390 400 410

0.998

1.000

1.002(b)

strong glass

LL

T r

eg

ion

frag

ile li

quid

fragile

glass(Qm

ax

1(T

ref)/

Qm

ax

1)3

Temperature (K)

350 360 370 380 390 400 410

10-2

10-1

100

101

102

103

104

105

Tg

strong liquid

D*=23.1

D*=8.9

fragile liquid

(s

)

(a)

386 388 390 392

102

103

<>

(s)

T (K)

386 388 390 392

1.000

1.001

1.002

Au49Cu26.9Si16.3Ag5.5Pd2.3

SLOW

FAST

The supercooled liquid phase (XPCS+DMA+XRD)

Occurrence of important structuralrearrangements which cannot beassociated to the glass transition


The liquid-liquid transition

Au49Cu26.9Si16.3Ag5.5Pd2.3

SLOW

FAST

FAST

SLOW

Q= 0.1 K/min: 1/Q3 ≠ V

Q= 1.5 K/min: 1/Q3 ≈ V

J. Bednarcik et al, J. All. Compd. 2010


The liquid-liquid transition

Au49Cu26.9Si16.3Ag5.5Pd2.3

SLOW

FAST

Q= 0.1 K/min: 1/Q3 ≠ V

Q= 1.5 K/min: 1/Q3 ≈ V

S. Wei et al, Nat. Commun. 2013


350 360 370 380 390 400 410

0.998

1.000

1.002(b)

strong glass

LL

T r

eg

ion

frag

ile li

quid

fragile

glass(Qm

ax

1(T

ref)/

Qm

ax

1)3

Temperature (K)

350 360 370 380 390 400 410

10-2

10-1

100

101

102

103

104

105

Tg

strong liquid

D*=23.1

D*=8.9

fragile liquid

(s

)

(a)

386 388 390 392

102

103

<>

(s)

T (K)

386 388 390 392

1.000

1.001

1.002

Au49Cu26.9Si16.3Ag5.5Pd2.3

Fragile-to-strong liquid-liquid transition

The glass transition is the dominantprocess at faster cooling rates

The LLT is accompanied by a fragile-to-strong dynamical crossover and asurprising shifting of the main peak ofthe S(Q) to lower Qs (increasing 1/Q)



Glassy systems





Outline

Page 83

Page 84

1.30 1.35 1.40 1.45 1.50 1.55

1

2

3

4

5

Glass

TNM model

Rc=0.1 K/min

Rc=1 K/min

Tg

log

[ (

s)]

1000/T (K-1

)

Liquid

Ea,glass=70 kJ/mol

Ea,liquid=470 kJ/mol

1 10 100 1,000 10,0000.0

0.2

0.4

0.6

0.8

1.0

T=723 K

T=693 K

T=668 K

T=648 K

t (s)

F(Q

,t)2

Decreasing T

Qmax=1.53 Å-1

0.8SiO2-0.2Na2O (NS4, Tg=783 K)

The correlation functions decay ina stretched exponential way as inthe liquid phase (β=0.67)

B. Ruta et al., Nat. Commun. (2014)

Page 85

0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.010

-24

10-22

10-20

10-18

10-16

10-14

10-12

10-10

10-8

Na tracer

Na tracer

Na tracer

QNS

QNS

from

NS4-G2

Si-O

dif

fusi

on

(m

2s-1

)

1000/T (K-1)

Na Tg

)(/

)/(1D 2

XPCS

QS

Q

XPCSincoh

incoh

Hempelmann et al, Z. Phys. B (1994)

Kargl et al. Phys. Rev. B. (2006)

XPCS data :

~10 orders of magnitudeslower than the Na diffusion

Closer to the low Textrapolation of the Si-Omatrix

Comparison with diffusion data

J. Horbach et al, Phys. Rev. Lett. (2002)

Wave vector dependence

Mezei et al, Physica Scripta (1987)

QNS data of supercooled CKN

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5 2.0 2.50

50

100

150

200

(Q) (s)S

(Q)

Q (Å-1)

A. Meyer et al, Phys. Rev. Lett. (2004)

Dynamics of oxide glasses

Irradiation-driven dynamics in SiO2 at low temperature

The atomic motion at room temperature in SiO2

is completely induced by the incoming X-rays

By varying appropriately the average incoming flux (flux, exposure time, delay time) is possible to

tune “at will” the dynamics

101

102

103

104

0.0

0.2

0.4

0.6

0.8

1.0

1011

1012

1013

1014

0.0

0.2

0.4

0.6

0.8

1.0 b)

(g2(t

)-1

)/c

t [s]

a)

increasing

flux

F0~110

11 ph/s

F1~310

10 ph/s

F2~1.210

10 ph/s

F3~3.610

9 ph/s

(g2(t

)-1

)/c

tF [ph]

SiO2

Page 88

Page 89

Irradiation-driven dynamics in SiO2 at low temperature

B. Ruta et al. Scient. Report (2017)

Page 90

Same induced dynamics in GeO2 at low temperature


Page 91

No radiation damage

SiO2


Reversible process

The effect of the X-rays is almost instantaneous and leads to a reversible and stationary atomic motion, thus independent on the global accumulated dose within the experimental time

B. Ruta et al. Scient. Report (2017)Page 92

X-rays & Hard matter

Three main processes:

Knock-on events require high energy to break bonds

Electronic rearrangements require pre-existing defects

Radiolysis require lifetime of the excitation ~ vibrations ~1ps possible

This effect is absent in metallic systems where electronic excitations aredelocalized much faster on ~fs time scale

Hard X-rays as pump and probe of the dynamics

Similar to what observed with electrontransmission microscopy on bi-dimensional SiO2

Hobbs et al. J. Nuclear Mat. (1994)

Huang et al. Science (2013)

B. Ruta et al. Scient. Report (2017)Page 93

Page 94

Temperature dependence of the induced dynamics

Courtesy of G. Baldi

Page 95

Temperature dependence of the induced dynamics

G. Pintori et al. Phys. Rev. B (2019)Courtesy of G. Baldi


Glassy systems





Outline

Page 96

The Extremely Brilliant Source upgrade

Page 103

Coherence: a key feature of the EBS-ESRF upgrade

30x at 8keV

ESRF Orange Book


Page 104

The real gain at an undulator beamline as ID10

65x at 8keV

100x at 8keV

Courtesy of J. Chavanne, group head “Insertion Device & Magnets”, ESRF

Huge gain for coherence-based techniques!

800x at 12keV


Page 105

Main parameters for XPCS

Page 106

XPCS at ESRF - EBS

EBS-ESRF will break new ground for XPCS

• Up to 10.000 times faster time scales

• Up to 100 times larger signal to noise ratio

• Extension into hard x-rays beyond 10 keV

Page 107

Adapted from O. Shpyrko J. Synch, Rad. 2014

τmin ≈ 100 ns (now only ≈ ms)

Energy: 6.5 - 35 keV(now mainly at 8 keV)

XPCS at ESRF-EBS

XPCS at ESRF - EBS

Page 108

EBS-L1: A new beamline for coherence based structural & dynamical studies

Approved by SAC in June 2017

Page 109


Glassy systems





Outline

Page 104

Dynamics of supercooled liquids

Theoretical models:Discontinuous hopping of caged

particles : β<1 & τ≈ q-1

MD simulations of SiO2:No q-dependence at low Qs :

β<1 & τ constant

Handle et al. Phys. Rev. Lett. 2019

Batthacharryya et al. J. Chem. Phys. 2010

Page 105

P. Gallo et al. Chem. Rev. 2016Mischima et al. Nature 1985

Hierarchical densifications in metallic glasses

Q. Luo et al. Nat. Commun. 2015H. W. Sheng et al. Nat. Materials 2007

Dynamics at Extreme Conditions

Dynamical evolutions duringpolyamorphic transitions

Nucleation in magmas

F. Vetere et al. Earth-Sci. Rev. 2015

Dynamics of the polyamorphous Ce-based MG

XPCS @ 21 keV with a DAC

τ

Page 113

• Dynamical heterogeneity are ubiquitous in nature

– Supercooled liquids and glasses

– Domain fluctuations and avalanches in high-Tc superconductors and magnetic systems

– Polymers and biomaterials

Dynamical (left) and spatial (right) heterogeneity in simulations of 2D glass transitions

J.P. Garrahan, PNAS (2011) H. Tanaka et al. Nat. Mat. 2010

ESRF - EBS:1. Dynamics from (sub-)µs to s

2. Length scales: from single particles to particle clusters

Intermittent correlations

Courtesy of F. Lehmkühler, Desy, Hamburg, Germany Page 114

Coherent X-rays are a perfect tool to investigate the dynamics in supercooled liquids and glasses

Dynamical crossover and anomalous stress-driven microscopic dynamics in metallic and several soft glasses

Larger sensitivity of XPCS than structural techniques

Perfect tool for measurements in operando conditions

Tricky sample-radiation interactions

Take home message

Page 109

Thank you for your attention!

Documents

Dynamical properties of glass formers probed with coherent …Coherent X-rays The ideal photon source would be a one-mode source (stimulated emission), e.g. unimodal lasers X-ray sources