Modélisation atomistique des effets d`irradiation sur les propriétés

Modélisation atomistique des effets
d’irradiation sur les propriétés
structurales et mécaniques dans les
verres nucléaires simplifiés
Contributors
J.-M. Delaye*, D. Kilymis**, S. Ispas**, L.-H. Kieu*, S. Peuget*
*Service d’Etudes et Comportement des Matériaux de
Conditionnement (SECM), CEA Marcoule, France
**Laboratoire Charles Coulomb (L2C), UMR5221CNRS,
Université de Montpellier
Atelier « Verres Irradiés »
27 NOVEMBRE 2015
CEA | 10 AVRIL 2012 | PAGE 1
Journées Verre – Nice, 18 – 20
Novembre 2015
OUTLINE
!   Context: Analogy between the behaviors of complex and simplified
nuclear glasses under irradiation (ballistic effects)
!   Classical molecular dynamics simulations
! 
Empirical potentials
! 
Series of displacement cascades
! 
Fracture: origin of the fracture toughness increase under irradiation
! 
Hardness: origin of the hardness decrease under irradiation
!   Conclusions
27 NOVEMBRE 2015
PAGE 2
R7T7 glass: the French nuclear glass to confine the
high level radioactive wastes
R7T7 glass composition: more than 30
components
Borosilicate R7T7 glass
!   The nuclear glasses will be
subjected
to
internal
irradiations (α disintegrations
from minor actinides and β/γ
radiations
from
fission
products)
!   It’s important to understand
the radiation effects on the
macrocopic properties to
certify the long term behavior
of the glass
SiO2, B2O3 and Na2O are the major components
PAGE 3
Swelling under irradiation in R7T7 glass
R7T7 glass has been irradiated internally by 244Cm with different doses and
dose rates
Saturation of the swelling after a
critical dose (4 1018 α/g)
Final swelling is around 0.6%
for each dose rate
PAGE 4
S. Peuget et al., J. Nucl. Mater. 444 (2014) 76
Fracture toughness increase – Hardness decrease
R7T7 glass has been irradiated externally by heavy ions (Kr, Au)
Microindentation is used to measure the critical
charge Pc for which the fracture probability is equal
to 50% → the fracture toughness can be deduced
Fracture toughness increases
by around 25% in the R7T7
glass irradiated by Au ions
R7T7 glass has been doped by short lived actinides (244Cm) or irradiated
externally by heavy ions (Kr, Au, Si)
Hardness is measured by Vickers micro indentation
Hardness decreases
by around 30%
S. Peuget et al. J. Nucl. Mater. 444 (2014) 76
PAGE 5
S. Peuget et al. Nucl. Instr. Meth. Phys. Res. B 246 (2006) 379
Anology between R7T7 glass and simplified glasses:
density
Three simplified glasses have been prepared:
%mol
SiO2
B2O3
Na2O
Al2O3
CaO
ZrO2
SBN14 = CJ1
67.73
18.04
14.23
-
-
-
CJ3
61.16
16.29
12.85
3.89
5.81
-
CJ7
63.77
16.98
13.39
4.05
Irradiated by Au
ions
1.81
The swelling is qualitatively the same as in the R7T7 glass
Saturation of the swelling
with the dose
The swelling is larger in
the simplified glasses
J. deBonfils, PhD, Université de Lyon I, 2007
Anology between R7T7 glass and simplified glasses:
fracture toughness and hardness
Fracture toughness and hardness have been measured in the three
simplified glasses (SBN14 = CJ1, CJ3, CJ7) subjected to heavy ion or
neutron irradiations
The fracture toughness and hardness changes are qualitatively the same as
in the R7T7 glass
Irradiation by heavy ions
SBN14: Increase of the
fracture toughness
(+16%) after
irradiation by neutrons
J. deBonfils et al., J. Non-Cryst. Solids, 356 (2010) 388
Decrease of the hardness after
irradiation by heavy ions
Use of classical molecular dynamics to investigate the
consequences of ballistic effects
!   Atomistic modeling of simplified nuclear glasses based on SiO2 – B2O3 –
Na2O
!   Objective: To understand the atomistic origin of the swelling, fracture
toughness increase and hardness decrease under irradiation (ballistic
effects)
!   Empirical interatomic potentials are used
! 
fitted on structural data (Boron coordination, structure factors) and
macroscopic properties (density, elastic moduli):
Buckingham potentials
PAGE 8
Empirical potentials: macroscopic properties
Glasses
Chemical compositions
(mol%)
CB (Y&B)
SiO2
B2O3
Na2O
69.5
30.5
0
3.01 (3.0)
SBN3
48
48.7
3.3
3.09 (3.07)
SBN10
44.4
46.1
9.6
3.23 (3,21)
SBN12
59.66
28.14
12.20
3.41 (3,43)
SBN14
67.73
18.04
14.23
3.72 (3,73)
SBN55
55.30
14.71
29.99
3.58 (3,62)
Simulated Young modulus (GPa)
Experimental bulk modulus
(GPa)
Experimental density (g/cm3)
SB
Experimental Young modulus (GPa)
!   A series of simple glasses are simulated to validate the potentials
Simulated density (g/cm3)
Simulated bulk modulus (GPa)
PAGE 9
L.-H. Kieu et al., J. Non-Cryst. Solids 357 (2011) 3313
Empirical potentials: WAXS and neutron spectra
!   Neutron spectra are recorded at LLB (7C2 spectrometer, λ = 0.723Å)
Glass compositions studied
Glasses
Chemical compositions
(mol%)
SiO2
B2O3
Na2O
SBN12
59,66
28,14
12,20
SBN14
67,73
18,04
14,23
SBN35
43.95
20.63
35.42
SBN55
55,30
14,71
29,99
Glasses with a Na2O concentration
around 10% – 15% (mol%) are
better reproduced
PAGE 10
Series of displacement
cascades simulated by classical
molecular dynamics
27 NOVEMBRE 2015
CEA | 10 AVRIL 2012 | PAGE 11
SIMULATION OF DISPLACEMENT CASCADES
!   Heavy projectiles are accelerated in the
simulation box one after the other
!   The complete volume is progressively
irradiated
!   Only the ballistic effects are taken into
account (no electronic excitations)
DISPLACEMENT CASCADES IN THE SBN14 GLASS
(SIO2-B2O3-NA2O, SIMPLIFIED NUCLEAR GLASS) (1)
Series of 600eV displacement cascades have been simulated to
completely irradiate the volume
!   Swelling under ballistic effects
Equivalence
4.0 1020 keV/cm3
2 1018 α/g
Experimental swelling in SBN14 irradiated
by heavy ions: ~4.0%
Saturation dose: 5 1020keV/cm3
!   Decrease of the bulk modulus
Bulk modulus decreases from
85GPa to 61GPa (-28%)
(the decrease of the elastic moduli in
the real glass is equal to -30%)
DISPLACEMENT CASCADES IN THE SBN14 GLASS
(SIO2-B2O3-NA2O, SIMPLIFIED NUCLEAR GLASS) (2)
Depolymerization
%B[3]
%B[4]
Q4
Q3
Initial
25%
75%
95.8%
4.2%
Final
47%
53%
85.2%
14.6%
Formation of Non-Bridging
Oxygens on the SiO4 entities
J.-M. Delaye et al., J. Non-Cryst. Solids 357 (2011) 2763
DISPLACEMENT CASCADES IN THE SBN14 GLASS
(SIO2-B2O3-NA2O, SIMPLIFIED NUCLEAR GLASS) (3)
Increase of the disorder
Internal energy increases
Widening of the distributions
Radial distribution
functions
Decrease of Si-O-Si (and Si-O-B) angles
Rings
Analogies between ballistic and quench rate effects (1)
!   The SBN14 glass has been prepared with different quench rates (2 1012K/s, 5 1012K/s,
1013K/s, 5 1013K/s, 1014K/s, 1015K/s, instantaneous quench)
! 
Swelling, increase of the internal energy, decrease of the B coordination, …
Quench rate (1012 K/s)
-23.1
Potential energy
(eV/atom)
2.18
2.16
2.14
2.12
2.1
2.08
1
10
100
Quench rate
1000
(1012
K/s)
10000
-23.15
1
10
100
1000
10000
-23.2
-23.25
-23.3
-23.35
-23.4
3.8
B coordination
Density (g/cm3)
2.2
3.75
… but the effects are amplified in the case of
a displacement cascades accumulation
3.7
3.65
3.6
3.55
3.5
1
10
100
1000
12
Quench rate (10
10000
K/s)
PAGE 16
J.-M. Delaye et al., Nucl. Instr. Meth. B 326 (2014)
256
Analogies between ballistic and quench rate effects (2)
!   Experiment: Comparison between the SBN14 glass quenched rapidly and irradiated
experimentally by Kr
!   Modification of the local order
! 
! 
(3)
Partial conversion of BO4 in BO3 (1)
Increase of NBO on silicon atoms (2)
(4)
Temperature
(2)
In the two cases
(1)
!   Modification of the medium range order
! 
! 
! 
Decrease of Si-O-Si angle (3)
Increase of 3 members silica rings (4)
Increase of the glass disorder
Only visible in the irradiated structure
S. Peuget et al., J. Non-Cryst. Solids 378 (2013) 201
PAGE 17
Influence of the initial structure (1)
!   6 SBN14 glasses have been prepared with different initial volumes
3.9
B coordination
3.85
3.8
3.75
3.7
3.65
3.6
0.6
Potential energy vs initial volume
0.8
0.9
Vl
1
1.1
1.2
1.3
B coordination vs initial volume
4.5
6
4
5
3.5
4
3
% [3]O
% NBO
0.7
2.5
2
3
2
1
1.5
0.6
0.7
0.8
0.9
Vl
1
1.1
1.2
% NBO vs initial volume
1.3
0
0.6
0.7
0.8
%
0.9
[3]O
Vl
1
1.1
1.2
1.3
PAGE 18
vs initial volume
Influence of the initial structure (2)
!   The 6 SBN14 glasses have been subjected to series of displacement cascades
(600eV)
! 
! 
Increase of the potential energy (decrease of the initial variations)
Swelling or densification depending on the initial volume
Increase of Potential energy
Swelling or Densification
PAGE 19
D.A. Kilymis et al., J. Non-Cryst. Solids (2015)
in press
Influence of the initial structure (3)
!   The SBN14 glassy structures are closer from one another at the end of the
displacement cascade accumulation
7
3.9
After irradiation
6
Before irradiation
5
3.8
% NBO
B coordination
3.85
3.75
3.7
3
2
After irradiation
1
3.65
Before irradiation
0
3.6
0.6
0.7
0.8
0.9
Vl
1
1.1
1.2
0.6
1.3
0.7
0.8
0.9
Vl
1
1.1
1.2
1.3
% NBO
B coordination
11
Na coordination
4
Before
irradiation
10
Local
density
distributions
9
8
After irradiation
7
Before irradiation
6
0.6
0.7
0.8
0.9
Vl
1
1.1
Na coordination
1.2
1.3
After
irradiation
PAGE 20
Influence of the initial structure (4)
!   When displacement cascades (600eV) are accumulated in different initial
configurations:
There is a partial but not complete loss of the memory of the pristine structure
??? Could the loss of the memory be complete with a higher irradiation
energy ???
PAGE 21
Simulation of fracture behavior
by classical molecular dynamics
27 NOVEMBRE 2015
CEA | 10 AVRIL 2012 | PAGE 22
Fracturation method
!   Simulation box : rectangular parallelepiped box (105 atoms) of 250 x 50 x 100 Å3
!   3D initial notch : 30Å deep (X direction), 20Å high (Z direction), Ly (Y direction)
!   2 layers of frozen atoms (top and bottom)
Displacement
OY
Frozen atoms
OZ
Tensile rate : 40m/s
Temperature fixed at 5K
OX
Initial notch
Frozen atoms
Displacement
PAGE 23
L.-H. Kieu et al., J. Non-Cryst. Solids 358 (2012) 3268
The four steps of fracture mechanisms
!   Nucleation / Growth / Coalescence / Decohesion (SBN14 glass)
Nanocavity
27 NOVEMBRE 2015
22ps
Cavity growth
Cavity coalescence
44ps
54ps
38ps
Decohesion
PAGE 24
Stress – Strain curves
!   Differences between pristine and disordered SBN14 glass
! 
! 
! 
Decrease of the Young modulus from 74.0GPa to 51.6GPa (-30%)
Decrease of the elastic limit
Increase of the plasticity region (the non linear part of the stress – strain
curve): duration from 10ps to 13ps
Elastic limit
Pristine
Plasticity
Elasticity
Coalescence
Decohesion
PAGE 25
RDFs versus time in the pristine glass: Si-O and [4]B-O
!   The cations behave differently depending on their local coordination
! 
Tetracoordinated elements : Si and [4]B → « strong » elements
RDF Si-O
0 to 24ps : Stretching of the Si-O and 4B-O distances
24 to 40ps : Relaxation of the Si-O and 4B-O distances
RDF [4]B-O
PAGE 26
RDFs versus time in the pristine glass: [3]B-O and Na-O
!   The cations behave differently depending on their local coordination
! 
3B
and Na → « Soft » elements
RDF [3]B-O
No stretching of 3B-O or Na-O distances
RDF Na-O
PAGE 27
Origin of the fracture toughness increase in the
disordered glasses
!   In the disordered (i.e. irradiated) glasses:
Increase of the [3]B relative to the [4]B
→ it explains why the pastic phase increases in the disordered glass
because the [3]B atoms enhance the plastic processes
! 
The enhancement of the plastic processes consumes a larger energy
→ it explains the fracture toughness increase under irradiation
! 
PAGE 28
Simulation of nanoindentation
by classical molecular dynamics
27 NOVEMBRE 2015
CEA | 10 AVRIL 2012 | PAGE 29
Simulation of hardness: Method
!   35nm x 35nm x 25nm (<>2 106 atoms)
!   Indentation speed : 10m/s
!   Step of indentation : 0.1Å
!   Temperature : 300K
!   Indentor : Vickers diamond tip (136°
apex angle)
!   At full loading, a 50ps relaxation period
is applied by keeping the indenter still
PAGE 30
D. Kilymis et al., J. Non-Cryst. Solids 382 (2013) 87
Film of indentation simulated by molecular dynamics
Nano indentation
simulated in
pristine silica by
classical
molecular
dynamics (300K)
PAGE 31
Simulation of hardness: indentation profiles
SBN14 glass
SBN14 glass
Indentation profiles
Hardness decreases
(qualitative observation)
Oliver-Pharr method to
determine the contact surface,
then the hardness
PAGE 32
Quantitative hardness measurements
!   Comparison between simulated and experimental values
Hardness Silica SBN12 SBN14 SBN55 Pristine
(difference with
experimental
value) 5.5GPa 4.40GPa
(-43%) 5.45GPa
(-13%) 4.33GPa
(-15%) Disordered Experiment
(pristine glasses) +1.8% -23.4% 7.45GPa 7.7GPa ( ?) -28.1% 6.30GPa -42.5% 5.1GPa !   Hardness in silica doesn’t change much between pristine and disordered structures
!   Experimental hardness is better reproduced when the Na2O concentration
increases
!   Hardness decreases in the disordered (i.e. irradiated) SBN14 glass
(experimental behavior is reproduced)
PAGE 33
D. Kilymis, J.-M. Delaye, J. Non-Cryst. Solids 401 (2014) 147
Origin of the hardness decrease
!   Increase of the hardness with the %SiO2
!   Decrease of the hardness in the
disordered glasses
!   Correlations with the %[3]B and %NBO
! 
! 
Hardness decreases with the %[3]B
Hardness decreases with the %NBO
Pristine glasses
Disordered glasses
Irradiation: increase of [3]B concentration and %NBO + increase of free volume
PAGE 34
→ hardness decrease
Conclusion
!   Experimentally, in the complex and simplified nuclear glasses subjected to
ballistic effects:
density decreases, hardness decreases, fracture toughness increases
!   Classical molecular dynamics has been used …
… to simulate displacement cascades in SBN14 glass
swelling is associated with depolymerization and increase of disorder
analogies exist between ballistic effects and thermal quench rate effects
… to simulate fracture behavior
the increase of the [3]B concentration favors plasticity → origin of the
fracture toughness increase
… to simulate nano indentation
the increase of the [3]B and NBO concentrations facilitates indenterPAGE 35
penetration → origin of the hardness decrease
Thanks
!   B. Beuneu (LLB), A. Kerrache (CEA Marcoule), L. Cormier (IMPMC): Neutron
spectroscopy
!   M. Barlet (CEA Saclay: DSM / IRAMIS), R. Caraballo, M. Gennisson (CEA
Marcoule): Hardness measurements
!   O. Bouty (CEA Marcoule): WAXS spectroscopy
PAGE 36