1. No category

Elasticity, Vibrations, and Corrosion Mechanisms
at Nanoscale in Oxide Glasses
Bernard Hehlen
Laboratoire charles Coulomb, University Montpellier II and CNRS
The Physics of Glass Group in few keywords
Fracture, stress corrosion mechanisms (AFM)
M. George, A-C.Genix
Elasticity, plasticity, High pressure, vibrations (Brillouin scattering)
B.Rufflé, M. Foret, R. Vacher, C. Weigel
Vibrations and structure (Raman & Hyper-Raman scattering)
B. Hehlen
In close connection with
The numerical simulation group (classical MD & ab-Initio)
S. Ispas, W. Kob
Vibrational Optical
Spectroscopies
from GHz to THz
Brillouin, IR-absorption,
Raman (tunable lasers), hyper-Raman
Elasticity, Vibrations, and Corrosion Mechanisms
at Nanoscale in Oxide Glasses
Bernard Hehlen
Laboratoire charles Coulomb, University Montpellier II and CNRS
The Physics of Glass Group in few keywords
Fracture, stress corrosion mechanisms (AFM)
M. George, A-C.Genix
Elasticity, plasticity, High pressure, vibrations (Brillouin scattering)
B.Rufflé, M. Foret, R. Vacher, C. Weigel
Vibrations and structure (Raman & Hyper-Raman scattering)
B. Hehlen
In close connection with
The numerical simulation group (Classical MD & ab-initio)
S. Ispas, W. Kob
Vibrational Optical
Spectroscopies
from GHz to THz
Brillouin, IR-absorption,
Raman (tunable lasers), hyper-Raman
Fracture and stress corrosion mechanisms :
an Atomic Force Microscopy study
Sample geometry
σ
DCDC
Double Cleavage Drilled Compression
Opening
Mode
2a
σ a
KI =
c
0.375 + 2
a
c
Dimensions :
4x4x40 mm3
Crack
Propagation
σ
Polishing :
Mechanical + CeO2
RMS : 0.25 nm (10x10 µm2 area)
Slow crack propagation in glasses by AFM
In situ observation of liquid condensate
Signal de hauteur
100 nm
Silice Suprasil 311
v = 0.1 nm/s
RH = 45 ± 1 %
AFM NS3 (AM AFM)
Signal de Phase
Glass-water interactions in corrosion
Chemical bond-by-bond
breaking at the crack tip
Damage in volume due
to the water diffusion
Stress
Water diffusion
OH contents increases
Wiederhorn and Bolz, JACS (1970)
Michalske et Bunker, J. Appl. Phys. (1984)
+ Ion exchange leaching
(e.g. Na+)
Changes in mechanical
properties (essentially
weakening of the vitreous
structure)
Tomozawa, Ann Rev Mat Sci (1996)
Profile of the condensate ?
• Hypothesis A:
Slow evaporation → constant volume
Hc
Hc
L
Stress KI
• Hypothesis B:
Fast evaporation → constant critical width Hc
(thermodynamic equilibrium condition)
H2O
Hc
Hc
H2O
L
L
Experimental answer
A
B
Grimaldi et al, PRL(2008)
Influence on crack propagation
Crack velocity increases with humidity
H2O
H2O
but
H2O
H2O
Reduction of the “transport
limited regime”
Crack velocity
∼ 100%
• Kinetic effect
H2O
Wiederhorn, JACS (1967)
RH ∼ 0%
Humidity
Stress KI
∆P~-100 atm (<0 !)
inside the condensate
(Laplace)
Closure effect
Stress
• Mechanical effect
Silice Suprasil 311
RH = 40 ± 3 %
T = 22 ± 0.5 °C
Crack length (mm)
Chemical effect : alkaline diffusion
Sodalime glass, 45% RH, V ≈ 1 nm/s
30 nm
5 µm
1. Tensile stress
2. Sodium diffusion toward
the crack tip
3. Water layer thickens
4. Accelerated corrosion
Célarié et al., JNCS (2007)
Corrosion + Ionic exchange
H2O
Change in ionic concentration
H2O
pH
CO2
Wetting properties
Na+
Perspectives
Determination of stress-strain field around the crack tip.
non-linear behaviour (simulations)
Link between macroscopic and nanoscopic
scales :
• Simulations
• Experiments ??
AFM, FEM, Near field opt. spectroscopies
Non-linear elastic zone <∼10 nm in SiO2
Han et al. submitted to PRL
3D micro-Brillouin mapping of a Vickers
indentation in a soda-lime silicate glass
Mechanical behavior of glasses: brittle… but plastic at micro-scale
and below
• Indentation test, crack tip
• Typical scales: nano to micrometers
shear flow + permanent densification
(a few % for a window glass, up to 20% for SiO2)
Nanoscale hardly accessible by strandard
spectroscopic tools
→µm-indentation
20 µm
Principles of Brillouin Scattering
Light scattering from thermal agitation
Scattered light has a different frequency νs, depends on:
± δν B = ν s − ν 0 = ±
sound velocity v and optical index n
elastic moduli and density
From spectra analysis:
sound attenuation α or internal friction
Q
−1
=
λ>>a ⇒ continuous elastic medium
2nv
λ0
sin
2παv
δν B
Mechanical properties
High resolution µ-Brillouin spectrometer at the L2C-Montpellier
Frequency resolution
∼25 MHz
4-pass PFP interferometer
+
+
SFP interferometer
Optical microscope
Spatial resolution
∼ 1.2x1.2x6 µm3
θ
2
Brillouin spectra of indented soda-lime silicate glasses
pristine
2 kg Vickers indentation
300
Counts
(a)
νB = 34.60 GHz
SGG Planilux®
Float Glass
(b)
200
5 µm beneath
the surface
100
20 µm
0
33
34
35
Frequency shift (GHz)
Brillouin spectra of indented soda-lime silicate glasses
pristine
2 kg Vickers indentation
300
Counts
(a)
SGG Planilux®
Float Glass
νB = 34.60 GHz
(b)
200
5 µm beneath
the surface
100
20 µm
0
33
34
35
Frequency shift (GHz)
Counts
600
νB = 35.25 GHz
400
200
(c)
0
33
34
35
Frequency Shift (GHz)
Brillouin spectra of indented soda-lime silicate glasses
pristine
2 kg Vickers indentation
300
Counts
(a)
SGG Planilux®
Float Glass
νB = 34.60 GHz
(b)
200
5 µm beneath
the surface
100
20 µm
0
33
34
35
Frequency shift (GHz)
600
400
νB = 35.53 GHz
200
0
Counts
Counts
600
(d)
νB = 35.25 GHz
400
200
(c)
0
33
34
35
33
Frequency shift (GHz)
Zone
νB (GHz)
Pristine Center
34.60
35.53
34
35
Frequency Shift (GHz)
•
•
[Tran et al., APL 2012]
νB change: ~0.93 GHz
Maximum at the center
• νs→ρ Calibration : Brillouin scattering in densified samples (from T. Rouxel-Renne)
• Simple approach :
Densification of 6.3% → linear increase of 0.93 GHz (density gauge)
[Tran et al., APL 2012]
Float
Glass
Top view
Measured
indented
area
20 µm
Vickers indentation
2D Isotropic density gradient in agreement with
- luminescence micro-spectroscopy
[Perriot et al., Phil. Mag. 2010]
[Deschamps et al., J. Phys. -Condens. Matter 2011]
- and Raman micro-spectroscopy
Microscopic origin of the densification ???
Raman Scattering in permanently
densified silicas, d-SiO2
• v-SiO2 has an open network structure…
O
ρs= 5.73 g/cm3
f
v − SiO2
V
ρ SiO
= 1−
≅ 0.62
ρS
2
Si
… as compared to v-GeO2
SiO2 is filled
of voids
f
VGeO
≅ 0.54
2
4-fold
• Permanent densification :
O
Si
θ
Si
Reduction of the Si-O-Si angle θ
In the network and in the small rings (?)
3-fold
SiO4 tetrahedra remain unchanged
(Y.Inamura, M. Arai, et al. JNCS 2001)
θ
→ Puckering of the ring network + bond redistribution
→ modification of the Raman spectra
Is it possible to get quantitative structural information on the local structure
through the Raman spectra ?
Normalized Raman intensities
IN (ω ) (rel. units)
ρ=2.63 g/cm3
RS )
I(
ω
N
ρ=2.43 “
n
R
ρ=2.20 “
D1
D2
RS )
(
I
ω
) =
I( ω
) + 1]
ρ ω s3([n ω
RS
N
1 ω
Glass density
Coupling-to-light coefficient
of the mode σ
RS )
)
I(
ω ∝ Cσ ⋅(
gσ ω
N
[Shuker & Gammon 1970]
Density of state of
the mode σ
For bending modes (σ = R, D1, D2) :
Cσ ∝ ω2
[B. Hehlen JPCM2010]
Density of states of O-bending modes
Density of states
ω
2
After normalization by CB(ω
ω) :
ρ = 2.43 g/cm3
Si
O
θ
Si
cos θ ∝ ω
2
D2
2
R
0
200
Angular-frequency relation
ρ = 2.21 g/cm3
4
g R (ω ) ⋅ dω ≅ C te for the 3 glasses
∫
ρ = 2.63 g/cm3
6
gB(ω) (r.u.)
(
) =
gB ω
RS )
I(
ω
N
D1
400
600
-1
Frequency (cm )
For the R-band and also in the small rings !!
Si-O-Si angle θ in d-SiO2
Small rings :
θ
θ
[B. Hehlen, J.Phys.: Cond Matter 2010]
n=3
n=4
Network angle :
θ
n
n ≅ 6 Max. of the distribution
R-band
n > 6 Average angle
Si-O-Si angle θ in d-SiO2
Small rings :
θ
θ
[B. Hehlen, J.Phys.: Cond Matter 2010]
n=3
n=4
Network angle :
θ
n
n ≅ 6 Max. of the distribution
R-band
RMN
(Devine et al. 1987)
n > 6 Average angle
Si-O-Si angle θ in d-SiO2
Small rings :
θ
θ
[B. Hehlen, J.Phys.: Cond Matter 2010]
n=3
n=4
Network angle :
θ
n
n ≅ 6 Max. of the distribution
R-band
RMN
(Devine et al. 1987)
n > 6 Average angle
Simulations (Rahmani, Benoit, PRB,2003)
Si-O-Si angle θ in d-SiO2
Small rings :
θ
θ
[B. Hehlen, J.Phys.: Cond Matter 2010]
n=3
n=4
Network angle :
θ
n
n ≅ 6 Max. of the distribution
R-band
RMN
(Devine et al. 1987)
n > 6 Average angle
Simulations (Matsubara , Ispas, Kob, 2009)
Simulations (Rahmani, Benoit, PRB,2003)
Si-O-Si angle in sodo-silicates
SiO2 4SiO2:Na2O (NS4)
P(θ
)
θSi-O-SiIntensity
P(θ
θ)
0.40
Distribution of Si-O-Si angles
NS4
NS2(computer simulations)
0.20
0
0.06
Frequency → Angle
gB(ω
ω) → P(θ
θ)
NS2
0.04
(Truflandier, Ispas,Charpentier)
NS4
(Ispas et al PRB 2001)
SiO2
0.02
0
100
From Raman spectra
Boson peak
SiO2
120
2SiO2:Na20 (NS2)
140
160
180
Angle (°)
Comparison with the Raman
Spectra :
Frequency → Angle
gB(ω
ω) → P(θ
θ)
Si-O-Si angle in sodo-silicates
SiO2 20Na2O:80SiO2 (NS4)
0.40
NS4
NS2
P(θ
θ) Intensity P(θ
θ)
From Raman spectra
Boson peak
SiO2
0.20
33Na20:67SiO2 (NS2)
Frequency → Angle
gB(ω
ω) → P(θ
θ)
0
0.06
From computer
simulations
0.04
0.02
0
100
120
140
160
180
Angle (°)
Not perfect, but in qualitative agreement
Angle at maximum of the distribution ?
(Truflandier, Ispas,Charpentier)
(Ispas et al PRB 2001)
Si-O-Si angle in sodo-silicates
Most probable angle
(max. of the distribution)
150
experimental
simulation
Angle (°)
145 SiO
2
140
NS4
NS3
135
NS2
NS1.5
130
Same trend !!
125
120
0
10
20
30
% mol. Na2O
40
D1
Relative density of small rings
D2
RS )
)
I(
ω ∝ Cσ ⋅(
gσ ω
N
Rigid structures
weak θ-dependence with ρ
Cσ(ρ
ρ) ≅
incoherent scatterers
And
Cte
ω max
∫ω
min
gσ (ω ) ⋅ dω ∝ Nσ
Number of rings
ωmax RS
Aσ = ∫
ωmin
I (ω)⋅dω ∝ Nσ
N
The Area of IRS
(D1, D2) ∝ Number of ring
N
Raman
Raman + Time-domain Raman scattering (ISRS)
ISRS
Density of small rings in d-SiO2
Comparison Raman / ISRS
(J. Burgin et al. PRB 2008)
Relative ring density
(Pasquarello et al. PRL 2003)
2.20 g/cm3
2.63 g/cm3
D1 : 1 Ring / 555 SiO2
D2 : 1 Ring / 670 SiO2
D1 : 1 Ring / 380 SiO2
D2 : 1 Ring / 150 SiO2
Concentration of rings
is very small
5
RS
4
ISRS
Increase of the threefold rings
(denser structures)
(3-fold) D2
3
D1 (4-fold)
2
Concentration of fourfold
rings ≈ Cte
1
2.2
2.3
2.4
2.5
3
Density ρ (g/cm )
2.6
2.7
Possible scenario upon densification :
large rings (n ≥ 5) → 4-fold rings (D1)
4-fold rings (D1) → 3-fold rings (D2)
Summary
Elasticity, plasticity, and structure of glasses :
Spatial resolution
• Observation of mechanical damages (AFM)
- Crack propagation
- Stress corrosion mechanisms
- Plastic deformations (polymers)
nanometer
• Continous elastic medium properties (Brillouin Scat.)
- Densification
- Elastic constants
- Sound attenuation (or internal friction)
- Shear strain
micrometer
• Atomic structure (Raman, Hyper-Raman)
- Si-O-Si angles
- Density of small rings
-…
Mid-term project : Tip-Enhanced Raman Scattering (TERS)
micrometer
sub µm to nm