Kinetic Monte Carlo simulations of Helium implantation and desorption from Nickel

L. Gámez1, B. Gámez1, C.J. Ortiz2, M.J. Caturla2,E. Martínez1, J. M. Perlado1

1 Instituto de Fusión Nuclear (DENIM) Universidad Politécnica de Madrid (UPM)

2 Dept. de Física AplicadaUniversidad de Alicante (UA)

T-meeting on Accelerator Simulation and Theoretical Modelling of Radiation Effects(TM-34567) Kharkov, Ukraine, 9-13 June, 2008

Irradiation of structural materials can alter significantly their mechanical properties

In the presence of gases an enhanced production of bubbles and voids may occur

He could induce swelling of these materials due to the interaction withvacant sites in the lattice and the stabilization of voids and formation of bubbles.

The effects on damage evolution is a very complex problem that depends on a large number of parameters: temperature, dose rate, He per dpa ratio, crystal structure, alloy composition,…

It is necessary to connect different length scales, starting from:microscopic production of defectsinteraction of He with vacancies and self-interstitialsinteraction with grain boundaries and dislocationsdiffusion mechanisms for Hekinetics of bubble and void nucleation.

INTRODUCTION

In order to account for all processes a multiscale model is required

MeV KeV eVBinary collision models

TRIM

MARLOWE

Multiple collisionsClassical

Molecular Dynamics

Diffusion ProcessesRate Theory

Kinetic Monte Carlo

Energy

Time10-12 s 10-10 s 10-3 - 103 s

Significant differences in swelling behaviour

depending on the material: f.c.c. vs b.c.c.

Void swelling in FCC and BCC metals irradiated with fission neutrons B. N. Singh, J. H. Evans, JNM 226 (1995) 277-285

Austenitic (f.c.c.) materials are prone to swelling while ferritic (b.c.c.) materials are resistant to swelling

Production bias model: in-cascade clustering and 1D migration responsible for these differences

Hola

Significant differences are already observed in the initial

damage state depending on material

(a) Fe 30keV, 66 defects (b) Cu 30keV, 69 defects.

Similar number of defects but more vacancy clustering in Cu than in Fe

bcc Fe fcc Cu

Voi

d S

wel

ling

(%)

Dose = 0.1 dpa, Dose Rate = 10-8 dpa/s1000 appm He/dpa

0

0.01

0.02

0.03

0.1 0.15 0.2 0.25 0.3 0.35 0.4

FCC Cascades (HeV) BCC Cascades (HeV) BCC Cascades (HeV + V)

T/Tm (K)

Void swelling in FCC and BCC metals irradiated with fission neutrons

B. N. Singh, J. H. Evans, JNM 226 (1995) 277-285

KMC reproduce qualitatively the experimental swelling dependence with temperature for fcc and bcc

Long term evolution of He-V clusters depends on initial

damage state

M. J. Caturla, N. Soneda, T. Diaz de la Rubia, M. Fluss, J. Nucl. Mat. 2006, 351, 78

Calculations of electron an He irradiation of nickel

Ni selected as a surrogate material for austenitic alloys

Defect production in electron irradiated Ni ⇒ Validation for the model

Desorption of helium from nickel to understand nucleation andstability of He-V complexes

Modeling long term evolution of defects in Ni

Values for migration energies of vacancies and Self-interstitials

from EAM calculations [1] V1 0.44

V2 12.1I1 0.15I2 0.12I3 0.04In 0.12/n

Defect t ype

M igrat ion energy

( eV)

Pre -factor

( cm 2/s)

0.85 eV

0.57 eV0.12 eV0.10 eV0.10 eV0.10 eV

Values for binding energies of vacancy [2] and self-interstitial [1] clusters

from EAM calculations

[1] A. Almazouzi et al. Mater. Res. Soc. Symp. Proc. 735 (1999) 685-690[2] J. B. Adams and W. G. Wolfer, J. Nucl. Mater. 166 (1989) 235[3] C. Domain, private communication

Calculations using KMCO of isochronal annealing of electron irradiated Ni with a concentration of 2 appm, from 4.5K to 612K

All self-interstitials considered mobile

Stage Peak-Exp.* Peak-KMCO56K 45K

61KIII (vacancies) 340K 340K

I (self-interst)II (self-int .clust)

Stage I Stage III

Stages I and III corresponding to self-interstitial migration and vacancy migration are resolved for this low dose in agreement with experiments

* from review by Ehrhart on Landolt-Börnstein, New Series III/25

Resistivity recovery stages in electron irradiated Ni

Trapping sites for self-interstitials I-T binding = 0.25 eV

Including trapping sites for self-interstitials changes annealing stagesSimilar behaviour observed in Ni-Si alloys

* from review by Ehrhart on Landolt-Börnstein, New Series III/25

Effect of traps on resistivity recovery stages

on electron irradiated Ni

Modeling long term evolution of defects in Ni

in the presence of He

Species/React ion Reference M odel

He_int e rst it ia l C. Dom ain [3]

EAMHeV2 C. Dom ain [3]

EAM

EAM

EAM

Energy ( eV)Migrat ion energy – 0.12eV ab init io

HeV -> He_i + V Dissociat ion energy – 2.56 eVAdam s and Wolfer

[2]Migrat ion energy – 1.2 eV ab init io

HeV2 -> HeV + VBinding energy – 0.37 eV

Adam s and Wolfer [2]

HenVm -> He (n-1 )Vm + HeAdam s and Wolfer

[2]

HenVm -> HenV(m -1 ) + VAdam s and Wolfer

[2]

Values for migration energies of He and binding energies of HenVmclusters from ab initio when available and from EAM calculations

• Migration mechanisms for He:• He at interstitial position (He) • Dissociative mechanism: He substitutional HeV -> He + V• Mobility of He substitutional aided by a vacancy: HeV2 mobile• Replacement mechanism: HeV + I -> He

0.5

1

1.5

2

2.5

0 5 10 15 20

Dissociation Energy forHe(n)V(m) -> He(n-1)V(m) + He

HeHe2He3He4He5He6He7He8He9He10

Dis

soci

atio

n En

ergi

e (e

V)

Number of Vacancies

0

1

2

3

4

5

6

0 5 10 15 20

Dissociation Energy for He(n)V(m) -> He(n)V(m-1) + V

He1He2He3He4He6He7

He8

He9

He10

0

He5

Dis

soci

atio

n En

ergy

(eV)

Number of Vacancies

J.B. Adams, W.G. Wolfer, J. Nucl. Mater. 166 (1989) 235

Binding Energies for HenVm

• He 400 eV -> Ni• Implantation at 300K• Dose = 5.6x1012 ions/cm2

• Annealing and measurement of desorption of He from 300K until 1200K• Ramp rate 18.4 K/s• Experiments show the presence of two peaks in the rate of evolution of

Helium with temperature – peaks named B1 and B2

Experimental data from D. Edwards and E. V. Kornelsen, Surface Science 44 (1974) 1 – 10

Modeling long term evolution of defects in Ni

in the presence of He

• He 400 eV -> Ni – damage distribution obtained with SRIM • Implantation at 300K – defects followed until steady state is reached• Annealing and measurement of desorption of He from 300K until 1200K• Ramp rate 18.4 K/s

Two peaks are also obtained from the simulations corresponding to the dissociation of He2V and HeV

Results of OKMC simulations under the conditions of

Edwards et. alN

umbe

r of H

e de

sorb

ed

Temperature (K) 300 500 700 900 1100 300 500 700 900 1100

Temperature (K)

Der

ivat

ive

of #

He

Results of OKMC simulations for two different doses

• He 400 eV -> Ni – damage distribution obtained with SRIM • Dose 5,6×1012 ions/cm2 (Edwards et al) and 5,6×1014 ions/cm2

At higher dose a new peak appears at high temperature related to the dissociation of He2V2 cluster

2.8 He2V2→ HeV2 +He1100 KB3

2.1 – 2.4HeV→ He + V835 KB2

1.7 – 1.8 He2V→ He +HeV~ 677 KB1

Binding energy experiments (eV)

ReactionTemperature THDS peak

[1] P. Ehrhart, Landolt-Bornstein New Series III/25, p.242 (1991)

[3] D. Edwards Jr, E.V. Kornelsen, Surface Science 44 1-10 (1974)

Summary of results of OKMC and experiments

Conclusions

OKMC calculations based mostly on EAM data reproduces both electrical resistivity measurements and He desorption experiments (unlike in b.c.c. Fe)

Two desorption peaks are obtained for low dose He implantation in agreement with experiments

Discrepancies still exist regarding the exact position of these peaks particular the B2 peak

Ab initio values of the reaction associated to this peak could help in the understanding of these differences

At higher doses a new peak appears that has also been observed experimentally

Further calculations will include the effect of trapping sites on these desorption peaks as well as the initial damage (such as the presence of cascade damage instead of isolated Frenkel pairs)

Acknowledgements

We thank C. Domain for providing the ab initio data used in this model

Funding agencies:

Spanish Ministerio de Educación y Ciencia

European Project PERFECT

We thank James McDonald from GuriSystems for computer support