Growth of Helium Bubbles in Tungsten under Realistic Rates

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA

U N C L A S S I F I E DLA-UR-14-27989

Growth of Helium Bubbles in Tungsten underRealistic Rates

November 6, 2014

Luis Sandoval, Danny Perez, Blas P. Uberuagaand Arthur F. Voter

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Motivation: Helium induced morphology in tungsten

300 s 2000 s 4300 s 9000 s 22000 s

Cross-sectional SEM images of W targets exposed to He plasma. T = 1120 K,ΓHe+ ∼ 5× 1022m2s−1, 〈Eions〉 ∼ 60 eV. 1

1Baldwin, M. J. and Doerner, R. P. Nucl. Fusion 48, 035001 (2008).

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Motivation: time limitations of direct MD simulations

t = 5 ns t = 10 ns

t = 15 ns

t = 25 ns t = 30 ns

t = 20 ns

• Impact of He atoms on W at a rate of0.2 He ps−1. The kinetic energy per He atomis 60 eV. The interactions are determined bya short-range-modified Ackland-Thetfordpotential (Juslin and Wirth, 2013).

• For the simulation box used, this impact ratecorresponds to a flux of 5× 1027 He m s−1

(∼ 4 orders of magnitude higher than theone expected in the ITER divertor).

• Only ∼ 2.5 % of the incoming ionscontribute to the growth process of the deepbubble, that is, its growth rate is∼ 5 He ns−1.

• A study at slower impact (and growth)rates, comparable to experiments, is needed.

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Single He Bubble Growth in a perfect W lattice

Langevin thermostatat 1000 K

Initial configuration:1 tungsten vacancywith 8 helium atoms

d = 1.9 nm

NVT

NVE

At a given rate anew helium atomis inserted insidethe buble

Simulation setup. Pressure in the helium bubble. a

aSefta, F. et al. Nuclear Fusion 53, 073015 (2013).

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Parallel Replica Dynamics2 (ParRep)

True infrequent events have an exponential first-passage time distribution:

p(t) = k exp(−kt) . (1)

We can exploit properties of exponential to parallelize time, by having manyprocessors seek the first escape event:

dephasing correlated events

parallel time

Arbitrary accurate dynamics if implemented carefully.2Voter, A. F. Phys. Rev. B 57, 13985 (1998).

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Standard Parallel Replica Dynamics

• Standard Parallel Replica Dynamics relies on the separation of timescalebetween vibrations and transitions between basins.

• A state is taken to be the ensemble of points of configuration space thatconverge to the same fixed point under a local minimization of the energyof the system.

• This definition limits the range of possible applications to systems wherethe basins are deep enough and well separated from each other.

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Superstate Parallel Replica Dynamics

• A superstate is defined as all the points of configuration space that sharethe same values/range of suitably-defined slow variables of the system, sothat equilibration within the state is much faster then escape from thestate.

The definition of states can be optimized by lumping individual shallowstates into superstates.

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Superstate Parallel Replica Dynamics

• In our study, ParRep transitions are defined as changes in atomicpositions where at least one tungsten atom has moved a distance greaterthan 0.25 nm, slightly lower than 〈111〉/2, the Burgers vector ofprismatic 〈111〉 dislocation loops. Concerning these transitions, themotion of He atoms is ignored.

Frenkel pairnucleation

Interstitial diffusion Vacancy diffusion Adatom diffusion

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Growth rate effects

Point obtained by using 10.000 replicas(160.000 cores ~ 53% of Titan)

ParRep MD

Average He content in the bubble at thetime of the first detected event.

10 15 20 25 30 35He atoms

45

50

55

60

Pre

ssure

(G

Pa)

1012 He s−1

1011 He s−1

1010 He s−1

109 He s−1

108 He s−1

b)

Average pressure in the He bubble vs Hecontent and growth rate.

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Growth rate effects

0 20 40 60 80 100 120He atoms

20.019.519.018.518.017.517.016.516.0

Avera

ge p

osi

tion

of

cente

r of

mass

()

1012 He s−1

1011 He s−1

1010 He s−1

109 He s−1

108 He s−1c)

Average position of the center of mass ofthe He bubble.

0 20 40 60 80 100 120He atoms

22.5

22.0

21.5

21.0

20.5

20.0

19.5

Avera

ge p

osi

tion o

f t

he low

est

He a

tom

()

1012 He s−1

1011 He s−1

1010 He s−1

109 He s−1

108 He s−1

d)

Average position of the lowest/deepest Heatom.

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Growth rate effects

108 109 1010 1011 1012

Growth rate (He s−1 )

200

220

240

260

280

300

Bubble

conte

nt

(He a

tom

s)

at

the b

urs

ting p

oin

tParRep ParRep

ParRep

ParRep

MDMD

MD

e)

Mean value of the He content in the bubble at thebursting point as a function of growth rate.

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Interstitial diffusion and adatom formation

a)

Diffusion hopping time as a function ofthe number of He atoms per W vacancyfor two cases: one W interstitial on thesurface of a 2-vacancy bubble, and one Winterstitial on a 15-vacancy bubble.

b)

Snapshots showing the diffusion of a W in-terstitial to the top of the bubble, the sub-sequent nucleation of additional Frenkelpairs, and the tearing off process ofadatom nucleation. Blue: W vacancies;red: W interstitials; green: adatoms.

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Interstitial diffusion and bubble growth

Initial

Final vacancy configuration c)

1 2,3 4 5 6 7 8

Final vacancy configuration for the 15-vacancy bubble (when adatoms are formed)from 8 independent ParRep simulations. The orange spheres denote the vacanciesnucleated in the tearing off process.

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107 108 109 1010 1011 1012


0.00.51.01.52.02.53.03.54.0

Next

Frenke

l pair

a)

rc =3.2

rc =4.8

Average number of interstitial clustersaround the He bubble after a new Frenkelpair is nucleated, when at least one inter-stitial is already present, as a function ofthe growth rate.

107 108 109 1010 1011 1012


0.00.51.01.52.02.53.03.54.0

Frenke

l pair

per

event

b)

Average number of Frenkel pairs per eventas detected by ParRep as a function of thegrowth rate.

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108 109 1010 1011 1012


0

20

40

60

80

100

Loca

tion o

f v

aca

nci

es

(%) top

side

bottom

c)

Spatial probability for the nucleation ofnew vacancies with respect to the centerof the current vacancy cluster (see d)), asa function of the growth rate.

Norm

aliz

ed

his

tog

ram

dy

new vacancy

top

side

bottom

current vacancycluster (bubble)

d)

Histogram of the location of new vacan-cies in the direction perpendicular to thesurface for all the simulations.

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Conclusions

• For the slowest growth rates we considered, the system is able toefficiently explore the accessible state space, facilitating the occurrence oftransitions involving fewer W atoms.

• Significant differences across time scales are observed, which include thepressure experienced by the He bubble, the number of W vacancies andHe atoms in the bubble at bursting point, and the dynamics of Frenkelpair nucleation.

• Our main finding is the existence of two growth regimes, depending onwhether the growth of the bubbles occur slower or faster than thediffusion of interstitials around it.

• These findings highlight the importance of simulating materials underrealistic conditions and the potential pitfalls of extrapolating from shorttimescale simulations alone.

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Acknowledgements

The authors would like to thank Brian Wirth and Chun-Yaung (Albert) Lu forthe useful discussion. L.S., D.P., and B.P.U. ackowledge support by theU.S.DOE, Office of Science, Office of Fusion Energy Sciences and Office ofAdvanced Scientific Computing Research through the Scientific Discoverythrough Advanced Computing (SciDAC) project on Plasma-SurfaceInteractions. A.F.V. was supported by the U.S. U.S.DOE, Office of BasicEnergy Sciences, Materials Sciences and Engineering Division. This researchused resources of the National Energy Research Scientific Computing Center,which is supported by the Office of Science of the U.S.DOE under ContractNo. DE-AC02-05CH11231, and resources of the Oak Ridge LeadershipComputing Facility at Oak Ridge National Laboratory, which is supported bythe Office of Science of the U.S.DOE under Contract DE-AC05-00OR22725.Los Alamos National Laboratory is operated by Los Alamos National Security,LLC, for the National Nuclear Security Administration of the U.S. DOE, undercontract DE-AC52-O6NA25396.

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