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Nuclear Data and
Materials Irradiation Effects
- Analysis of irradiation damage structures
and multiscale modeling -
Toshimasa Yoshiie
Research Reactor Institute,
Kyoto University
Comparison of irradiation effects between
different facilities
• Power reactors  Research reactors
• Neutron irradiation Ion irradiation
Electron irradiation
DPA (Displacement per atom)
The number of displacement of one atom
during irradiation
DPA dose not represent the effect of
cascades
Estimation of irradiation damage
• Ion irradiation 100MeV He,1018ions/cm2
• Neutron irradiation 1018n/cm2 ( ＞1MeV or ＞0.1MeV)
• Displacement par atom (dpa)
=
αｘ deposited energy in crystal lattice
2ｘ threshold energy of atomic displacement
Kinchin-Pease model
EP
E
DPA is the
number of
displacement for
1 atom during
irradiation
Frenkel pair formation
Cascade formation
Cascade
Example of MD Simulation
40keV cascade of iron at 100K
Clustering of Point Defects
Stress
field
Interstitial Type Dislocation Loops in FCC
Interstitial type dislocation
loops in Al
Voids
Embrittlement
Materials with
no voids
Materials
with voids
Stacking Fault Tetrahedra
Stacking Fault Tetrahedra
Cascade Damage
High energy
Particle
Cascade
Vacancy
rich area
Subcascades
Interstitial rich area
Nucleation of defect
clusters
Comparison of Subcascade Structures
by Thin Foil Irradiation
14MeV neutrons at 300K.
Neutron
PKA
TPKA 
4mn

E sin 2 ,
MT
2
  Z4
Au, KENS irradiation and 14 MeV irradiation
at room temperature
KENS
neutrons
14MeV
neutrons
13
14MeV neutron irradiated Cu
14MeV neutron irradiated Cu
14MeV neutron irradiated Cu
14MeV neutron irradiated Cu
Temperature Effects of Cascade Damage
Lower
temperature
Subcascades
Higher
temperature
Subcascades fuse
into a large cluster
Thin foil Irradiated Au by Fusion Neutrons
A group of SFTs
Subcascade
structures
A large SFT
Cascade fuses
into one SFT
Fission-fusion Correlation of SFT in Au
0.017dpa
0.044dpa
Large SFTs
Small SFTs
High number
density of
SFTs
Low number
density of
SFTs
Fusion neutrons Fission neutrons
563K
573K
PKA Energy Spectrum Analysis
N SFT   

E TH
d ( E )
dE
dE
NSFT: the concentration of
SFTs observed
α: the SFT formation
efficiency
 ：the neutron fluence
d
：the
dE
α= 0.05
ETH = 80keV
differential crosssection for PKA
ETH :threshold energy for
SFT formation
MULTI-SCALE MODELING OF
IRRADIATION EFFECTS IN
SPALLATION NEUTRON SOURCE MATERIALS
Toshimasa Yoshiie1, Takahiro Ito 2, Hiroshi Iwase 3,
4, Masayoshi Kawai3, Ippei Kishida4, Satoshi
Yoshihisa
Kaneko
5, Futoshi Shimizu5,
Kunieda5, Koichi Sato41, Satoshi Shimakawa
6, Tokio Fukahori5,
Satoshi Hashimoto , Naoyuki
Hashimoto
Yukinobu Watanabe7, Qiu Xu1, Shiori Ishino8
2
1Research
Reactor Institute, Kyoto University
Department of Mechanical Engineering, Toyohashi University of Technology
High Energy Accelerator Research Organization
Osaka City University
5Japan Atomic Energy Agency
6Hokkaido University
7 Kyushu University
8Univerity of Tokyo
Motivation
• Spallation neutron source and Accelerator Driven
System (ADS) are a coupling of a target and a proton
accelerator. High energy protons of GeV order
irradiated in the target produce a large number of
neutrons.
• The beam window and the target materials thus
subjected to a very high irradiation load by source
protons and spallation neutrons generated inside the
target.
• At present, there are no materials that enable the
window to be operational for the desired period of
time without deterioration of mechanical properties.
Importance of GeV Order
Proton Irradiation Effects in Materials
• Spallation neutron source
J-PARC (Japan) SNS (USA)
• Accelerator driven system (in the planning stage )
800MW ADS (Minor Actinide transmutation,
Japan Atomic Energy Agency)
5MW Accelerator driven subcritical reactor
(Kyoto University, neutron source)
Purpose and outline
• In this paper, mechanical property changes of nickel by 3 GeV protons
were calculated by multi-scale modeling of irradiation effects. Nickel is
considered to be a most simple model material of austenitic stainless
steels used in beam window. The code consists of four parts.
• Nuclear reaction, the interaction between high energy protons and
nuclei in the target is calculated by PHITS code from 10-22 s.
• Atomic collision by particles which do not cause nuclear reactions is
calculated by molecular dynamics and k-Monte Carlo. As the energy of
particles is high, subcascade analysis is employed. In each
subcascade, the direct formation of clusters and the number of mobile
defects are estimated.
• Damage structure evolution is estimated by reaction kinetic analysis.
• Mechanical property change is calculated by using 3D discrete
dislocation dynamics (DDD). Stress-strain curves of high energy
proton irradiated nickel are obtained.
PHITS
High energy
particle
Size (m)
Vacancy
10-20
10-15
10-10
10-5
100
105
1010
Data flow between each code
Nuclear reactions （PHITS code）
Primary knock-on energy spectrum
Atomic collisions （Molecular dynamics)
Point defect distribution
Damage structural evolutions (Reaction kinetic analysis)
Concentration of defect clusters
Mechanical property change (Three-dimensional discrete dislocation
dynamics)
Stress-strain curve
1. Nuclear Reaction
Nucleation rate of neutrons, photons, charged
particles and PKA energy spectrum by them
Ni
6 [10-10]
10-8
5
10-9
4
10-10
10
3
2
-11
10-12
10-3
1
-2
-1
10
10
10
PKA energy (MeV)
0
0
101
Number of PKA energy (left) and energy
deposition by PKA (right) in 3 GeV proton
irradiated Ni of 3 mm in thickness.
Energy deposition
by PKA (MeV)
3GeV
protons
Number of PKA / proton
Result of PHITS Simulation
Subcascade Analysis
Large cascades are divided into subcascades.
In the case of Ni, subcascade formation energy is
calculated to be 10 keV.
6 [10-10]
10-8
5
10-9
4
10-10
3
2
10-11
10-12
10-3
1
10-2
10-1
100
PKA energy (MeV)
0
101
Energy deposition
by PKA (MeV)
Cascade
Number of PKA / proton
The number of
subcascasdes are
obtained from the
result of PHITS.
Number of subcascades by deposition of energy T
N SC 
T
2TSC
TSC : Subcascade formation energy
Total number of subcascades
 t
TMAX
T SC
dσ
N SC dT
dT
2. Atomic Collision Simulation by MD
Calculation Condition
 Potential model by Daw and Baskes
(1984)
 NVE ensemble ( i.e., number of the
atoms, cell volume and energy were
kept constant)
 35x35x35 lattices (171500 atoms) in a
z
simulation cell
y
 Periodic boundary condition for the
x
three directions
35a0
 Initial condition : equilibrium for 50 ps
at 300 K, 0MPa
a0 : lattice
constant at 300 K  PKA energy：10keV
 MD runs with different initial directions
of PKA ( none of which were parallel
to the lattice vector.)
Typical Distribution of Point Defects
Marble : interstitial atoms，Violet ：Vacancy cites
0.006ps
0.025ps
7.395ps
18.40ps
1.132ps
96.38ps
Results of MD Calculation
Number of vacancies
Number of vacancies
105
104
103
102
101
100
10-1
10-3
800
10-2
10-1
100
Time (ps)
101
102
Temperature (K)
Cascades terminated within 10~20ps
700
On average17 vacancies, 17 interstitials were produced.
600
Formation of defect clusters is calculated by k-Monte Carlo.
500
Clusters of three
point defects are formed.
400
3. Damage Structure Evolution
by Reaction Kinetic Analysis
In order to estimate damage structural evolution, the reaction kinetic analysis is used.
Assumptions used in the calculation are as follows:
(1) Mobile defects are interstitials, di-interstitials, tri-interstitials, vacancies and divacancies.
(2) Thermal dissociation is considered for di-interstitials, tri-interstitials di-vacancies
and tri-vacancies, and point defect clusters larger than 4 are set for stable clusters.
(3) Time dependence of 10 variables, concentration of interstitials, di-interstitials, triinterstitials, interstitial clusters (interstitial type dislocation loops), vacancies, divacancies, tri-vacancies, vacancy clusters (voids), total interstitials in interstitial
clusters and total vacancies in vacancy clusters are calculated to 10 dpa.
(4) Interstitial clusters (three interstitials) and vacancy clusters (three vacancies) are
also formed directly in subcascades.
(5) Materials temperature is 423 K during irradiation.
The result is as follows,
Formation of vacancy clusters of four vacancies, concentration: 0.59x10-3,
Dislocation density: 1.1x10-9cm/cm3.
Reaction Kinetic Analysis
CI : Interstitial concentration (fractional unit).
CV : Vacancy concentration
Z : Cross section of reaction
M: Mobility
dC I
2
 PI  2Z I , I M I C I  Z I ,V ( M I  M V )C I CV
dt
damage production I-I recombination mutual annihilation
 Z I , IC M I C I S I  Z I ,VC M I C I SV  M I C I CS .........
absorption by loops absorption by voids
annihilation of interstitials at sink
4. Estimation of Mechanical Property Changes
(Plastic Deformation of Metals)
t
Plastic Deformation of Metals
Dislocation Glide along Slip Planes
t

Work Hardening
↓
Motions of Dislocation Lines
e
Calculation of Dislocation Motions
Motions of Curved Dislocations
External Stress
Elastic Interaction between
Dislocations
Line Tension
Very
Complicated !
Division of a Dislocation Line
↓
Discrete Dislocation Dynamics (DDD)
Simulation
3D-Discrete Dislocation Dynamics
Edge+Screw Dislocation Model
Devincre (1992～)
Stresses from
another segment
External Stress
Mixed Dislocation Model
Zbib, et al (1998～)
Schwarz et al
Fivel et al ，Cai et al
Line tension
Peach-Koehler Force
Dislocation Velocity
b
Connection of Dislocation Segments
with Mixed Characters
Model Crystal and Mobile Dislocation
Ni: shear modulus = 76.9 Gpa
Poisson’s ratio = 0.31
Burgers vector = 0.24916 nm
Stress axis ＝ [1 0 0]
Mobile dislocation
slip plane＝(1 1 1)
slip vector＝[1 0 1]
Obstacles（void）
0.593×10-3 void/ atom
the density along the slip
plane : 1.10x104 void / μm2
0.14μm
0.14μm
0.14μm
Interaction between Dislocation and void
Detrapping
angle
Determination of Detrapping Angle
(Statistic Energy Calculation Method)
( l l l)
(Ī l 0)
void
(Ī Ī 2)
[lll]
[ Ī Ī 2]
[ Ī l 0]
Stress
Size and orientation of model lattice used for Static energy calculation
of dislocation movement. b is the Burgers vector.
Stable atomic position is determined by an effective medium theory
(EMT) potential for Ni fitted by Jacobsen et al. [K. W. Jacobsen, P.
Stoltze, J. K. Norskov, Surf. Sci. 366 (1996) 394].
Determination of Detrapping Angle between
Edge Dislocations and 4 Vacancies
-10
0
10
10
20
10
20
10
20
10
Motion of dislocation near the slip plane under
shear stress. X axis and Y axis are by atomic
distance. In the left figure, a dislocation is
separated into two partials. Four vacancies are
at (16.0, 0.722, -0.408), (15.5, -0.144, -0.408),
(16.0, 0.144, 0.408) and (15.5, 1.01, 0.408).
Other figures indicate only right partial.
20
10
20
10
0
-10
65
°
10
20
Dislocation Motion by DDD Simulation
(no void)
400MPa
600MPa
700MPa
Dislocation motion in the crystal with
randomly-distributed voids
Normal stress
0MPa
200MPa
300MPa
400MPa
500MPa
600MPa
650MPa
700MPa
750MPa
800MPa
Stress-Strain Curves Calculated with
DDD Simulation
Plastic shear strain
gp = A b / V
Plastic strain
ep = gp Sf
A: area swept by
a dislocation
b: Burgers vector
V: volume of
model crystal
(x10-6) Sf: Schmid factor
Summary
Importance of nuclear data for materials irradiation effects
was shown.
DPA is not good measure of irradiation damage. PKA
energy spectrum is more useful to analyze damage structures.
As an example of the analysis, the mechanical property
change in Ni by 3 GeV proton irradiation was calculated and
preliminary results were obtained.
Nuclear reactions : PHITS
PKA energy spectrum
Atomic collision : MD, k-Monte Carlo, Subcascade analysis.
The number of point defects and clusters in the subcascade
Damage structure evolution : Reaction kinetic analysis
Void density, Dislocation density
Mechanical properties : Discrete dislocation dynamics
Statistic energy calculation
Stress strain curve
Important data for
materials irradiation effects
High energy particles
Primary knock on atom
energy spectrum
Formation rate of atoms
by nuclear reactions
High energy particle
energy spectrum