Toshimasa Yoshiie Research Reactor Institute, Kyoto University
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Transcript of Toshimasa Yoshiie Research Reactor Institute, Kyoto University
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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
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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
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Estimation of irradiation damage
• Ion irradiation 100MeV He,1018ions/cm2
• Neutron irradiation 1018n/cm2 ( > 1MeV or > 0.1MeV)• Displacement par atom (dpa) α x deposited energy in crystal lattice
2 x threshold energy of atomic displacement Kinchin-Pease model
EP
E
T
DPA is the number of displacement for 1 atom during irradiation
=
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Cascade
Frenkel pair formation
Cascade formation
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Example of MD Simulation
40keV cascade of iron at 100K
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Clustering of Point Defects
Stress field
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Interstitial Type Dislocation Loops in FCC
Interstitial type dislocation loops in Al
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Embrittlement
Materials with no voids
Materials with voids
Voids
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Stacking Fault Tetrahedra
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Stacking Fault Tetrahedra
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High energy Particle Cascade Vacancy rich area
Subcascades Nucleation of defect Interstitial rich area clusters
Cascade Damage
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14MeV neutrons at 300K. Neutron PKA
Comparison of Subcascade Structuresby Thin Foil Irradiation
42 ,2
sin4
ZEM
mT
T
nPKA
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Au, KENS irradiation and 14 MeV irradiation at room temperature
14MeV neutrons
13
KENS
neutrons
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14MeV neutron irradiated Cu
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14MeV neutron irradiated Cu
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14MeV neutron irradiated Cu
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14MeV neutron irradiated Cu
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Temperature Effects of Cascade Damage
Subcascades Subcascades fuse into a large cluster
Lowertemperature
Highertemperature
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Thin foil Irradiated Au by Fusion Neutrons
A group of SFTs A large SFT Subcascade Cascade fuses structures into one SFT
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Fission-fusion Correlation of SFT in Au
Fusion neutrons Fission neutrons
563K 573K
0.017dpaLarge SFTs
High number density of SFTs
0.044dpaSmall SFTs
Low number density of SFTs
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PKA Energy Spectrum Analysis
α= 0.05 ETH = 80keV
TH
)(SFT E
dEdE
EdN
NSFT: the concentration of SFTs observedα: the SFT formation
efficiency : the neutron fluence
: the differential cross-
section for PKAETH :threshold energy for
SFT formation
dE
d
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MULTI-SCALE MODELING OF IRRADIATION EFFECTS IN
SPALLATION NEUTRON SOURCE MATERIALS
Toshimasa Yoshiie1, Takahiro Ito 2, Hiroshi Iwase 3, Yoshihisa Kaneko4, Masayoshi Kawai3, Ippei Kishida4, Satoshi Kunieda5, Koichi Sato1, Satoshi Shimakawa5,
Futoshi Shimizu5, Satoshi Hashimoto4, Naoyuki Hashimoto6, Tokio Fukahori5, Yukinobu Watanabe7, Qiu Xu1, Shiori
Ishino8
1Research Reactor Institute, Kyoto University 2 Department of Mechanical Engineering, Toyohashi University of
TechnologyHigh Energy Accelerator Research Organization
Osaka City University5Japan Atomic Energy Agency
6Hokkaido University7 Kyushu University
8Univerity of Tokyo
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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.
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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)
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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.
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Size
(m)
Vacancy
High energy particle
10-20 10-15 10-10 10-5 100 105 1010
PHITS
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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
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1. Nuclear Reaction
Nucleation rate of neutrons, photons, charged particles and PKA energy spectrum by them
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10-3 10-2 10-1 100 10110-12
10-11
10-10
10-9
10-8
0
1
2
3
4
5
6 [10-10]
PKA energy (MeV)
Num
ber o
f PK
A /
prot
on
Ene
rgy
depo
sitio
n by
PK
A (M
eV)
Number of PKA energy (left) and energy deposition by PKA (right) in 3 GeV proton irradiated Ni of 3 mm in thickness.
Result of PHITS Simulation
Ni
3GeV protons
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Subcascade Analysis
Large cascades are divided into subcascades. In the case of Ni, subcascade formation energy is calculated to be 10 keV.
Cascade
The number of subcascasdes are obtained from the result of PHITS.
10-3 10-2 10-1 100 10110-12
10-11
10-10
10-9
10-8
0
1
2
3
4
5
6 [10-10]
PKA energy (MeV)
Num
ber o
f PK
A /
prot
on
Ene
rgy
depo
sitio
n by
PK
A (M
eV)
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Number of subcascades by deposition of energy T
TSC : Subcascade formation energy
Total number of subcascades
SCSC T
TN
2
dTNT
σt
MAX
SC
T
T SC
d
d
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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 simulation cell
Periodic boundary condition for the three directions
Initial condition : equilibrium for 50 ps at 300 K, 0MPa
PKA energy : 10keV MD runs with different initial
directions of PKA ( none of which were parallel to the lattice vector.)
35a0
a0 : lattice constant at 300 K
xyz
2. Atomic Collision Simulation by MD
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0.006ps 0.025ps 1.132ps
7.395ps 96.38ps18.40ps
Marble : interstitial atoms , Violet : Vacancy cites
Typical Distribution of Point Defects
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Cascades terminated within 10~20psOn average17 vacancies, 17 interstitials were produced.Formation of defect clusters is calculated by k-Monte Carlo.
Clusters of three point defects are formed.
Number of vacancies
10-3 10-2 10-1 100 101 102
10-1
100
101
102
103
104
105
Time (ps)
Num
ber
of v
acan
cies
10-3 10-2 10-1 100 101 102300
400
500
600
700
800
Time (ps)
Tem
pera
ture
(K
)
Results of MD Calculation
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3. Damage Structure Evolutionby 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 di-vacancies.(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, tri-interstitials, interstitial clusters (interstitial type dislocation loops), vacancies, di-vacancies, 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.
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Reaction Kinetic Analysis
damage production I-I recombination mutual annihilation
absorption by loops absorption by voids
.........
)(2
,,
,2
,
SIIVIIVCIIIIICI
VIVIVIIIIIII
CCMSCMZSCMZ
CCMMZCMZPdt
dC
CI : Interstitial concentration (fractional unit).
CV : Vacancy concentration
Z : Cross section of reaction
M: Mobility
annihilation of interstitials at sink
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4. Estimation of Mechanical Property Changes (Plastic Deformation of Metals)
Plastic Deformation of Metals
Work Hardening
↓
Motions of Dislocation Lines
Dislocation Glide along Slip Planes
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Calculation of Dislocation Motions
Motions of Curved DislocationsExternal Stress
Elastic Interaction between
Dislocations
Line Tension
Very Complicated !
Division of a Dislocation Line↓
Discrete Dislocation Dynamics (DDD) Simulation
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3D-Discrete Dislocation Dynamics
Mixed Dislocation Model
Zbib, et al (1998 ~ )Schwarz et al Fivel et al , Cai et al
Connection of Dislocation Segments with Mixed Characters
Connection of Dislocation Segments with Mixed Characters
b
Peach-Koehler Force
Dislocation Velocity
External StressStresses from another segment
Line tension
Edge+Screw Dislocation Model
Devincre (1992 ~ )
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Stress axis = [1 0 0] slip plane = (1 1 1)slip vector = [1 0 1]
Mobile dislocation
Obstacles ( void )
0.593×10-3 void/ atomthe density along the slip plane : 1.10x104 void / μm2
0.14μm0.14μm
0.14μm
Model Crystal and Mobile DislocationNi: shear modulus = 76.9 Gpa Poisson’s ratio = 0.31 Burgers vector = 0.24916 nm
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Interaction between Dislocation and void
Detrapping angle
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[ Ī Ī 2]
[ Ī l 0]
[ l l l ](Ī Ī 2)
(Ī l 0)( l l l)
void
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
(Statistic Energy Calculation Method)
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10 20
-10
0
1010 2010 20 10 20 10 20
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.
65°
10 20-10
0
10
Determination of Detrapping Angle between Edge Dislocations and 4 Vacancies
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Dislocation Motion by DDD Simulation(no void)
400MPa 600MPa 700MPa
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0MPa
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Normal stress
Dislocation motion in the crystal with randomly-distributed voids
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930MPa
935MPa
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Stress-Strain Curves Calculated with DDD Simulation
Plastic shear strain p = A b / V
Plastic strain p = p Sf
A: area swept by a dislocationb: Burgers vectorV: volume of model crystalSf: Schmid factor(x10-6)
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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
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Important data for materials irradiation effects
High energy particles
High energy particle energy spectrum
Primary knock on atom energy spectrum
Formation rate of atoms by nuclear reactions