MD Simulations of Void Stability MD Simulations of Void Stability in a-Si Under Heavy Ion (Xe) in a-Si Under Heavy Ion (Xe)

Bombardment: Influence of HeBombardment: Influence of He

Brent J. HeuserBrent J. Heuser

University of Illinois, Urbana, ILUniversity of Illinois, Urbana, IL

Work supported by DoE NEER Program Work supported by DoE NEER Program Under Grant No. DE-FG07-01ID14121Under Grant No. DE-FG07-01ID14121

AcknowledgementsAcknowledgements

• Maria Okuniewski, Yinon Ashkenazy (Hebrew Maria Okuniewski, Yinon Ashkenazy (Hebrew Univ.), Robert Averback (UIUC-MSE)Univ.), Robert Averback (UIUC-MSE)

• MCC IBM computer cluster, UIUC, Greg BauerMCC IBM computer cluster, UIUC, Greg Bauer

OutlineOutline

• Introduction—Why do we care about voids/bubbles in a-Si? Introduction—Why do we care about voids/bubbles in a-Si?

• Background—Energetic ion damage process; MD basics;Background—Energetic ion damage process; MD basics;

Interatomic potentials; Simulation details.Interatomic potentials; Simulation details.

• Results of void/bubble closure—Dependence on energy (@p=0) and Results of void/bubble closure—Dependence on energy (@p=0) and

He pressure (@E=2 keV).He pressure (@E=2 keV).

• Special case of unidirectional irradiation—Greater stability observed.Special case of unidirectional irradiation—Greater stability observed.

• Model of void/bubble closure—Viscous flow and surface tension.Model of void/bubble closure—Viscous flow and surface tension.

• Conclusions—He bubbles are stable, voids are not.Conclusions—He bubbles are stable, voids are not.

Why do we care?Why do we care?• Inventory statistics (R.C. Ewing, Proc. Natl. Acad. Sci. Inventory statistics (R.C. Ewing, Proc. Natl. Acad. Sci. 9696, 1999, 3432), 1999, 3432)

• Actinides dominate after 500 yrs.: Actinides dominate after 500 yrs.: 238238Pu, Pu, 131131Sm, Sm, 241241AmAm• 239239Pu and Pu and 237237Np after several hundred yrs.Np after several hundred yrs.• 960 MCi HLW from weapons production (>99% non-actinide; T960 MCi HLW from weapons production (>99% non-actinide; T1/21/2<50 yrs)<50 yrs)• 30,200 MCi commercial spent fuel.30,200 MCi commercial spent fuel.• Pu from weapon dismantlement.Pu from weapon dismantlement.

• Waste storage mediaWaste storage media• Glass—modified borosilicate glasses. Glass—modified borosilicate glasses. • Ceramics—ZirconCeramics—Zircon

• RequirementsRequirements• Hold radioisotopes in matrix (in solution).Hold radioisotopes in matrix (in solution).• Structural integrity over thousands of years.Structural integrity over thousands of years.• Barrier between environment and radioisotopes (leaching).Barrier between environment and radioisotopes (leaching).

Potential ProblemsPotential Problems

+ recoil+ recoil

He introduction

He introduction

Energetic recoil

Energetic recoil

e bubblese bubbles

HeHe

Bubble formationBubble formationleads to compressiveleads to compressivestressesstresses

Devitrification leadsDevitrification leadsto compressive stressesto compressive stresses

Rad. damageRad. damage

V/V>0V/V>0

Actinide DecayActinide Decay

CrackingCracking

a-SiOa-SiO22 vs. a-Si vs. a-Si

Property a-SiOProperty a-SiO22 a-Si a-Si

Mass Mass [g/cc] 2.32 [g/cc] 2.322.572.57

Number Number ( (xx10102222 1/cc) 7.0 5.5 1/cc) 7.0 5.5

TTmeltmelt 1713 C 1414 C

Bond TypeBond Type CovalentCovalent CovalentCovalent

2 keV Xe TRIM Range ~50 A ~50 A 2 keV Xe TRIM Range ~50 A ~50 A

Experience with Si potentialExperience with Si potential

OutlineOutline

• Introduction—Why do we care about voids/bubbles in a-Si? Introduction—Why do we care about voids/bubbles in a-Si?

• Background—Energetic ion damage process; MD basics;Background—Energetic ion damage process; MD basics;

Interatomic potentials; Simulation details.Interatomic potentials; Simulation details.

• Results of void/bubble closure—Dependence on energy (p=0) and Results of void/bubble closure—Dependence on energy (p=0) and

He pressure (E=2 keV).He pressure (E=2 keV).

• Special case of unidirectional irradiation—Greater stability observed.Special case of unidirectional irradiation—Greater stability observed.

• Model of void/bubble closure—Viscous flow and surface tension.Model of void/bubble closure—Viscous flow and surface tension.

• Conclusions—He bubbles are stable, voids are not.Conclusions—He bubbles are stable, voids are not.

Energy Loss of Energetic Ion in a SolidEnergy Loss of Energetic Ion in a SolidTwo Components: Electronic (Ionization) and Nuclear (Collision/Displacement)Two Components: Electronic (Ionization) and Nuclear (Collision/Displacement)

Light ion (like He)Light ion (like He)dE/dx|dE/dx|ee>>dE/dx|>>dE/dx|cc

Energy loss viaEnergy loss viaionizationionization

Heavy ion (like Xe)Heavy ion (like Xe)dE/dx|dE/dx|cc>>dE/dx|>>dE/dx|ee

Displacementcascades

Projectile pathProjectile path Projectile pathProjectile path

Displacement Cascade DetailsDisplacement Cascade Details

High density of Frenkel pairsHigh density of Frenkel pairs(vacancies + interstitials) created(vacancies + interstitials) created

in displacement cascadein displacement cascade

ProjectileProjectile

MD Basics--Solve F=ma and F=-dU/drMD Basics--Solve F=ma and F=-dU/dr

Updated vel. dist. @TUpdated vel. dist. @T22

vvii(T(T22)=v)=vi i (T(T22)) ++vvii

Velocity distribution at TVelocity distribution at T11

TT11

Ri=T1vi

FFii==U/U/R )R )kk

vvii==TT11FFii/m/m

TT22RRii

vi

Interatomic Potential in DetailInteratomic Potential in Detail

-5

0

5

10

0.5 1 1.5 2Distance

Pote

ntia

l Ene

rgy,

U(r)

Near-equil., low-energy Near-equil., low-energy processes like diffusion, processes like diffusion, phase transformation.phase transformation.EAM, S-W potentials here.EAM, S-W potentials here.

High-energy processesHigh-energy processeslike displacement cascades.like displacement cascades.ZBL potential here.ZBL potential here.

Atom @ equil.Atom @ equil.wrt nearest wrt nearest neighborsneighbors

, r, r

Examples of MDExamples of MD100 eV C100 eV C6060 incident on incident onC nanotube lying on PtC nanotube lying on PtK. Nordlund/U. HelsinkiK. Nordlund/U. Helsinki

Low energy self-ion impact on graphiteLow energy self-ion impact on graphite K. Nordlund/U. HelsinkiK. Nordlund/U. Helsinki

50 keV Xe incident on50 keV Xe incident on(100) Au surface(100) Au surfaceK. Nordlund/U. HelsinkiK. Nordlund/U. Helsinki

50 keV Xe incident on50 keV Xe incident onliquid Au surfaceliquid Au surfaceK. Nordlund/U. HelsinkiK. Nordlund/U. Helsinki

Local plasticity near crack in CuLocal plasticity near crack in CuF. Abraham/IBMF. Abraham/IBM

Simulations DetailsSimulations Details50,000 Si atom cell (~100 A on a side)50,000 Si atom cell (~100 A on a side)Amorphous structure created by melt-quenching c-SiAmorphous structure created by melt-quenching c-Si

Periodic BCsPeriodic BCs10 K skin 5 A thick10 K skin 5 A thick

20 A Void/Bubble:20 A Void/Bubble:He pressure 0-1 kbarHe pressure 0-1 kbar

Xe ion: 0.2-2 keVXe ion: 0.2-2 keVUni- & multi-directionalUni- & multi-directional

Interatomic PotentialsInteratomic Potentials

He-He: L-JHe-He: L-JSi-He: Pure repulsive (ZBL)Si-He: Pure repulsive (ZBL)Si-Si: Stillinger-WeberSi-Si: Stillinger-WeberXe-He and Xe-Si: ZBLXe-He and Xe-Si: ZBL

MD using PARCAS on a PC clusterMD using PARCAS on a PC cluster30 psec displacement phase (30 psec displacement phase (V/V=0)V/V=0)30 psec relaxation phase (p=0 @ boundary)30 psec relaxation phase (p=0 @ boundary)~1 cpu hour/psec/processor~1 cpu hour/psec/processor

2 keV Xe Displacement with 1 kbar He2 keV Xe Displacement with 1 kbar He

Color: Distance DisplacedColor: Distance DisplacedSize: EnergySize: Energy

1 keV Xe Displacement with 0.1 kbar He1 keV Xe Displacement with 0.1 kbar He

OutlineOutline

• Introduction—Why do we care about voids/bubbles in a-Si? Introduction—Why do we care about voids/bubbles in a-Si?

• Background—Energetic ion damage process; MD basics;Background—Energetic ion damage process; MD basics;

Interatomic potentials; Simulation details.Interatomic potentials; Simulation details.

• Results of void/bubble closure—Dependence on energy (@p=0) and Results of void/bubble closure—Dependence on energy (@p=0) and

He pressure (@E=2 keV).He pressure (@E=2 keV).

• Special case of unidirectional irradiation—Greater stability observed.Special case of unidirectional irradiation—Greater stability observed.

• Model of void/bubble closure—Viscous flow and surface tension.Model of void/bubble closure—Viscous flow and surface tension.

• Conclusions—He bubbles are stable, voids are not.Conclusions—He bubbles are stable, voids are not.

0

500

1000

1500

2000

2500

3000

3500

4000

0 2 4 6 8 10

Vol

ume

[Å3 ]

Displacement Events

0.1 kbar

Zero

0.01 kbar

1 kbar

Void Closure w/ HeVoid Closure w/ He2 keV Xe2 keV Xe

InitialInitial

P=0P=05 events5 events

P=1 kbarP=1 kbar5 events5 events

Effect of He Gas Effect of He Gas Pressure on ClosurePressure on Closure

2 keV Xe2 keV Xe

Effect of He on ClosureEffect of He on Closure

2 keV Xe: 1 kbar He2 keV Xe: 1 kbar He 1 keV Xe: 0.1 kbar He1 keV Xe: 0.1 kbar He

0

500

1000

1500

2000

2500

3000

3500

4000

0 10 20 30 40 50 60 70 80

Vol

ume

[Å3 ]

Displacement Events

0.2 keV

1 keV

0.6 keV

2 keV

Void Closure w/o HeVoid Closure w/o He

Void Closure w/o HeVoid Closure w/o He

0

500

1000

1500

2000

2500

3000

3500

4000

0 5 10 15 20 25 30

Vol

ume

[Å3 ]

Displacement Events

0.2 keV

1 keV

0.6 keV

OutlineOutline

• Introduction—Why do we care about voids/bubbles in a-Si? Introduction—Why do we care about voids/bubbles in a-Si?

• Background—Energetic ion damage process; MD basics;Background—Energetic ion damage process; MD basics;

Interatomic potentials; Simulation details.Interatomic potentials; Simulation details.

• Results of void/bubble closure—Dependence on energy (@p=0) and Results of void/bubble closure—Dependence on energy (@p=0) and

He pressure (@E=2 keV).He pressure (@E=2 keV).

• Special case of unidirectional irradiation—Greater stability observed.Special case of unidirectional irradiation—Greater stability observed.

• Model of void/bubble closure—Viscous flow and surface tension.Model of void/bubble closure—Viscous flow and surface tension.

• Conclusions—He bubbles are stable, voids are not.Conclusions—He bubbles are stable, voids are not.

Evolving Void Morphology—No HeEvolving Void Morphology—No He(Incident 2 keV Xe along z axis)(Incident 2 keV Xe along z axis)

InitialInitial After 1 displ.After 1 displ. After 2After 2

After 3After 3 After 4After 4 After 5After 5

VoidVoid

Evolving Void Morphology—No HeEvolving Void Morphology—No HeInitialInitial After 1 displ.After 1 displ. After 2After 2

After 3After 3 After 4After 4 After 5After 5

Evolving Void Morphology—No He Evolving Void Morphology—No He ContinuedContinued

After 6After 6 After 7After 7

Evolving Void Morphology—0.1 kbar HeEvolving Void Morphology—0.1 kbar He

InitialInitial After 1 displ.After 1 displ. After 2After 2

After 3After 3 After 4After 4 After 5After 5

Evolving Void Morphology—1 kbar HeEvolving Void Morphology—1 kbar He

InitialInitial After 1 displ.After 1 displ. After 2After 2

After 3After 3 After 4After 4 After 5After 5

Comparision of Void Morphologies after DisplacementsComparision of Void Morphologies after Displacements

No He

0.1 kbar

1 kbar

OutlineOutline

• Introduction—Why do we care about voids/bubbles in a-Si? Introduction—Why do we care about voids/bubbles in a-Si?

• Background—Energetic ion damage process; MD basics;Background—Energetic ion damage process; MD basics;

Interatomic potentials; Simulation details.Interatomic potentials; Simulation details.

• Results of void/bubble closure—Dependence on energy (@p=0) and Results of void/bubble closure—Dependence on energy (@p=0) and

He pressure (@E=2 keV).He pressure (@E=2 keV).

• Special case of unidirectional irradiation—Greater stability observed.Special case of unidirectional irradiation—Greater stability observed.

• Model of void/bubble closure—Viscous flow and surface tension.Model of void/bubble closure—Viscous flow and surface tension.

• Conclusions—He bubbles are stable, voids are not.Conclusions—He bubbles are stable, voids are not.

Model of Void Elongation/Stability in SimulationsModel of Void Elongation/Stability in Simulations

TimeTimeScaleScale

Molten Region

Molten Region

Void

Incident IonIncident Ion

t<0.3 pst<0.3 ps ~0.5-5 ps~0.5-5 ps

Mass flow frommolten region to

concave void surfaces.

Liquid Si goes here because surface tension is reduced by concave surface.

>10 ps>10 ps

Elongated void shapebecomes stable wrt

further closure.Reduced curvaturealong walls Inhibitsfurther masstransport during subsequent displace-ments.

Why?Why?

Effect of Changing the Incident Ion DirectionEffect of Changing the Incident Ion Direction

Elongated void less stable wrtfurther closure.

Incident Ion

Effect of He GasEffect of He Gas

He

Expect effect of He gasExpect effect of He gaswhen gas pressure roughlywhen gas pressure roughly

equals surface tension of a:Siequals surface tension of a:Si

This happens at about 0.05 kbarThis happens at about 0.05 kbar

Viscous Flow TheoryViscous Flow Theory

Energy dissipated by viscous flow; dEF/dt =(1/2)|2|dV162R(R/r)3

 

 

Rate of loss of surface energy; dES/dt8(R2/r)

 Equating; r = (/2) Radius decrease prop. to time

ConclusionsConclusions• He filled voids (bubbles) are stable under heavy ion He filled voids (bubbles) are stable under heavy ion

bombardment for gas pressures greater than or equal bombardment for gas pressures greater than or equal to approximately 0.1 kbar.to approximately 0.1 kbar.

• Void closure (no He case) scales with energy at high Void closure (no He case) scales with energy at high E, but not at low E.E, but not at low E.

• A chain of two or more displacement events A chain of two or more displacement events at the at the same locationsame location near a spherical void or low-pressure He near a spherical void or low-pressure He bubble will induce elongation. bubble will induce elongation.