HAL Id: cea-02338620
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Effect of cavities induced by ion implantation on rare
gases diffusion in uranium dioxide
M. Gerardin, E. Gilabert, D. Horlait, P. Desgardin, G. Carlot, M-F. Barthe
To cite this version:
M. Gerardin, E. Gilabert, D. Horlait, P. Desgardin, G. Carlot, et al.. Effect of cavities induced by ion
implantation on rare gases diffusion in uranium dioxide. SHIM-ICACS - 10th International symposium
on swift heavy ions in matter & 28th international conference on Atomic collisions in solids, Jul 2018,
Caen, France. �cea-02338620�
5
6
7
8
9
10
10
-24
10
-23
10
-22
10
-21
10
-20
10
-19
10
-18
10
-17
10
4
/T (K
-1
)
D
(m
2
.s
-1
)
Long [1], Long
Lindner [2], Lindner
Miekeley [3], Miekeley
Davies [4], Davies
0 100 200 300 400
0.0E+00
1.0E-04
2.0E-04
3.0E-04
4.0E-04
5.0E-04
6.0E-04
7.0E-04
8.0E-04
9.0E-04
Xe[Im
p] (
% at
./ at
.UO
2
)
Depth (nm)
Ions, Xe 800 keV
dpa, Xe 800 keV
Ions, Kr 500 keV
dpa, Kr 500 keV
0.00
0.01
0.02
0.03
0.04
0.05
0.06
dpa
10
21
10
22
10
23
10
24
1x10
-20
1x10
-21
1x10
-22
Burnup (fission.m
-3
)
D (m
2
.s
-1
)
Effect of cavities induced by ion implantation on rare
gases diffusion in uranium dioxide
M. Gerardin
1
*, E. Gilabert
2
, D. Horlait
2
, P. Desgardin
3
, G. Carlot
1
, M-F. Barthe
3
1
CEA/DEN/DEC (Saint Paul Lez Durance, France)
2
CENBG, CNRS/IN2P3 (Gradignan, France)
3
CEMHTI, CNRS/UPR3079 (Orléans, France)
* marie.gerardin@cea.fr
● Objectives
Improve the modelling of fission gas thermal diffusion mechanisms
to better predict UO
2
fuel behaviour under irradiation
Study the interaction between gas and defect induced by irradiation
Gas release
Pressure increase
Precipitation
Fuel swelling
Modification of the oxide
physico-chemical properties limiting fuel life time
in reactor
UO
2
: fluorine structure
UO
2
Pellets
Diffusion coefficient dependance
•
Stoichiometry of the sample
•
Burn up (fission.m
-3
)
● Literature
Arrhenius laws of xenon diffusion in UO
2.00
irradiated at a low burn-up
(<2.10
22
fission.m
-3
)
Xenon diffusion coefficient dependance with
the burn-up [1]
Rare gases
diffusion in UO
2
Thermal desorption
measurements
Gas release fraction
Diffusion
coefficient
Xe 800keV
or
Kr 500 keV
Implantation
Gases are trapped in UO
2
for a
burn-up > 2.10
22
f.m
-3
In which defects ?
𝐷
𝑖
𝜕
2
𝐶
𝑖
(𝑥, 𝑡)
𝜕
2
𝑥
=
𝜕𝐶
𝑖
(𝑥, 𝑡)
𝜕𝑡
𝐶
𝑖
0, 𝑡 = 0
𝐶
𝑖
∞, 𝑡 = 0
𝐶
1
𝑥, 0 = 1 − 𝑀 × 𝐶
𝑆𝑅𝐼𝑀 𝑃𝑟𝑜𝑓𝑖𝑙𝑒
𝐶
2
𝑥, 0 = 𝑀 × 𝐶
𝑆𝑅𝐼𝑀 𝑃𝑟𝑜𝑓𝑖𝑙𝑒
● Diffusion model : two populations
Second Fick law
𝑪
𝟏
: Gaz concentration mobile with
𝑫
𝟏
Burst effect
𝑴
: Fraction of 2 populations
𝑪
𝟐
: Gaz concentration mobile with
𝑫
𝟐
Intrinsic diffusion
● Experimental approach
Seperated effect studies
● Conclusions
Same diffusion mechanism between xenon and krypton
Good agreement with literature
Rare gases trapped in cavities induced by irradiation
Ea ̴ 3 eV
[1] Long, Davies and Findlay, AERE-M1251 (1964)
[2] Lindner and Matzke, Z. Naturforschung 14a (1959)
[3] Miekeley and Felix, JNM 42 (1972)
[4] Davies Long, AERE-R 4347 (1963)
Positron annihilation
spectroscopy (PAS)
+
Defects induced by
implantation
● Arrhenius law (D
2
)
Fission : ̴ 200 MeV
0,3 at (Xe + Kr) per fission U
Consistent with literature
Same diffusion mechanisms
between Xe and Kr
For i = 1 or 2 :
0 100 200 300
0.0
2.0x104
4.0x104
6.0x104
[Gas
] (
at
/c
m
3
)(a
t/
cm
2
)
Depth (nm)
C
SRIM(x,0)
C
1(x,0)
C
1(x,t)
C
2(x,0)
C
2(x,t)
M = 0.95
D
1 = 3.10-17 m2.s-1
D
2 = 1.10-20 m2.s-1
T
final = 500 min
● Trapping effect
Xenon 800 keV at 1.4.10
11
Xe.cm
-2
Ea̴ = 3.10 ± 0.33 eV
D0 = 1.62.10
-10
m
2
.s
-1
Krypton 500 keV at 2.1.10
12
Kr.cm
-2
Ea̴ = 2.81 ± 0.45 eV
D0 = 2.13.10
-11
m
2
.s
-1
D
0
̴ 10
-12
to 5.10
-6
m
2
.s
-1
Arrhenius laws of xenon and krypton
implanted in UO
2
10
13
ions.cm
-2
Diffusion coefficient (D
2
) determined on
isotherms obtained at 1300°C for each dose
D
1
remains constant
D
2
decreases from
10
13
ions.cm
-2
in polycrystals
10
12
ions.cm
-2
in monocrystals
Trapping effect in implanted UO
2
1. Thermal desorption
𝐶
1
𝑥, 0 = 1 − 𝑀 × 𝐶
𝑆𝑅𝐼𝑀 𝑃𝑟𝑜𝑓𝑖𝑙𝑒
𝐶
2
𝑥, 0 = 𝑀 × (1 −
𝑭𝒓
𝒊𝒏𝒊𝒕
) × 𝐶
𝑆𝑅𝐼𝑀 𝑃𝑟𝑜𝑓𝑖𝑙𝑒
𝐶
𝑃
𝑥, 0 = 𝑀 ×
𝑭𝒓
𝒊𝒏𝒊𝒕
× 𝐶
𝑆𝑅𝐼𝑀 𝑃𝑟𝑜𝑓𝑖𝑙𝑒
2. Trapping sites
1E11
1E12
1E13
1E14
1E15
4E-22
6E-22
8E-22
2E-21
4E-21
6E-21
8E-21
2E-20
1E-21
1E-20
D
2
(m
2
.s
-1
)
Fluence (ions.cm
-2
)
Xenon (Poly)
Xenon (Mono)
Krypton (Poly)
Krypton (Mono)
TEM images of cavities after ion implantation
Gas retained in cavities induced by irradiation
[7] A. Michel, NIMB 272 (2012)
[8] C. Onofri, non published
1E11
1E12
1E13
1E14
1E15
1E22
1E23
1E24
1E25
Cavity density (m
-3
)
Fluence (ions.cm
-2
)
Xe 390 keV 600°C [7]
Xe 390 keV 600°C [8]
Xe 390 keV -180°C [8]
Xe 390 keV 800°C [8]
[7]
● Context
UO
2
is the most used fuel in nuclear power plants
TEM image of cavities in
irradiated material at
23 GWj/tU
Transmission
Electron Microscopy
(TEM)
0 100 200 300 400 500
0.00
0.01
0.02
0.03
0.04
0.05
Xe 1.4e11 (1s - Poly)
Simulated with D
2
= 0
Simulated with D
2 0
Re
leas
ed fraction ([
Xe]relea
se
d/[Xe]im
p)
Time (min)
5
6
7
8
9
10
10
-24
10
-23
10
-22
10
-21
10
-20
10
-19
10
-18
10
-17
10
4
/T (K
-1
)
D
(m
2
.s
-1
)
Long [1], Long
Lindner [2], Lindner
Miekeley [3], Miekeley
Davies [4], Davies
Xe 1.4e11, This study
Kr 2.1e12, This study
𝑭𝒓
𝒊𝒏𝒊𝒕
: Fraction of trapped gas atom
Increases with the fluence
1E11
1E12
1E13
1E14
1E15
0
20
40
60
80
Fr
in
it
Fluence (ions.cm
-2
)
Xenon (Poly)
Xenon (Mono)
Krypton (Poly)
Krypton (Mono)
