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) 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

=

Cascade

Frenkel pair formation

Cascade formation

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

Embrittlement

Materials with no voids

Materials with voids

Voids

Stacking Fault Tetrahedra

Stacking Fault Tetrahedra

High energy Particle Cascade Vacancy rich area

Subcascades Nucleation of defect Interstitial rich area clusters

Cascade Damage

14MeV neutrons at 300K. Neutron PKA

Comparison of Subcascade Structuresby Thin Foil Irradiation

42 ,2

sin4

ZEM

mT

T

nPKA

Au, KENS irradiation and 14 MeV irradiation at room temperature

14MeV neutrons

13

KENS

neutrons

14MeV neutron irradiated Cu

14MeV neutron irradiated Cu

14MeV neutron irradiated Cu

14MeV neutron irradiated Cu

Temperature Effects of Cascade Damage

Subcascades Subcascades fuse into a large cluster

Lowertemperature

Highertemperature

Thin foil Irradiated Au by Fusion Neutrons

A group of SFTs A large SFT Subcascade Cascade fuses structures into one SFT

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

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

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

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.

Size

(m)

Vacancy

High energy particle

　 10-20 　 10-15 　 10-10 　 10-5 　 100 　 105 　 1010

PHITS

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

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

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)

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

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

0.006ps 0.025ps 1.132ps

7.395ps 96.38ps18.40ps

Marble : interstitial atoms ， Violet ： Vacancy cites

Typical Distribution of Point Defects

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

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.

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

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

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

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 ～ )

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

Interaction between Dislocation and void

Detrapping angle

[ 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)

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

Dislocation Motion by DDD Simulation(no void)

400MPa 600MPa 700MPa

0MPa

200MPa

300MPa

400MPa

500MPa

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650MPa

700MPa

750MPa

800MPa

820MPa

840MPa

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935MPa

Normal stress

Dislocation motion in the crystal with randomly-distributed voids

0MPa

200MPa

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0MPa

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935MPa

0MPa

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930MPa

935MPa

0MPa

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650MPa

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880MPa

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930MPa

935MPa

0MPa

200MPa

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0MPa

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0MPa

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930MPa

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0MPa

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880MPa

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920MPa

930MPa

935MPa

0MPa

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650MPa

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820MPa

840MPa

860MPa

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930MPa

935MPa

0MPa

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860MPa

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935MPa

0MPa

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800MPa

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930MPa

935MPa

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)

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

High energy particle energy spectrum

Primary knock on atom energy spectrum

Formation rate of atoms by nuclear reactions