Radiation Stopping Power, Damage Cascades, Displacement and … · 2020-01-04 · • Predict stopping power of radiation as functions of material, type, energy of radiation • Conceptualize

Radiation Stopping Power Damage Cascades

Displacement and the DPA

2214 ndash Nuclear Materials Slide 1

Learning Objectives

bull Predict stopping power of radiation as functions of material type energy of radiation

bull Conceptualize radiation damage cascades stages and evolution in time

bull Estimate the quantitative displacement rates from radiation and define the DPA

bull Track the buildup of radiation point defects as functions of temperature defect concentration

Building Up to Radiation Effects

Short amp Yip Current Opinions in Solid State Material Science (2015)

hellip wersquoll be here next week

We are herehellip

Courtesy of Elsevier Inc httpwwwsciencedirectcom Used with permissionSource Short M and S Yip Materials Aging at the Mesoscale Kinetics of Thermal Stress RadiationActivations Current Opinion in Solid State and Materials Science 19 no 4 (2015) 245-52

Stopping Power

bull More energetic particles do more damage hellip to a point

bull hellip but how much

bull Charge vs no charge

bull What about damage vs mean free path

Stopping power of protons in iron

httpwwwsrimorg

Courtesy of James F Ziegler Used with permission

CoulombicNuclear Stopping Powerbull Stopping Power is defined as differential energy

loss as a function of energy

119873119873 lowast 119878119878 119864119864 = minus120597120597119864119864120597120597120597120597

bull Separable components due to nuclear (screened nucleus Coulombic) electronic and radiative terms

119873119873 lowast 119878119878 119864119864 = minus120597120597119864119864120597120597120597120597 119899119899119899119899119899119899119899119899

minus120597120597119864119864120597120597120597120597 119890119890119899119899119890119890119899119899

minus120597120597119864119864120597120597120597120597 119903119903119903119903119903119903

bull Integrate inverse of stopping

range of the particle 119877119877119877119877119877119877119877119877119877119877

er over the energy

0119864119864119898119898119898119898119898119898 1

119878119878

Source Wikimedia Commons

bull Not all particles have119864119864119889119889119864119864

identical range stragglingdescribes this variation

RangeThis image is in the public domain

Stopping Power Components

bull Nuclear stopping power First assume Coulombicnucleus interactions describe interatomic potential

119881119881 119903119903 = 119885119885111988511988521205761205762

119903119903(1r dependence)

bull Positive nucleus screenedby negative electron cloud

119881119881 119903119903 =119885119885111988511988521205761205762

41205871205871205761205760119903119903119877119877

minus119903119903119903119903

Effective screening radius

H Paul AIP Conf Proc 1525309 (2013)

119881119881 119903119903 = 11988511988511198851198852120576120576119903119903

2(Coulomb)

119881119881 119903119903 = 119885119885111988511988521205761205762

41205871205871205761205760119903119903119877119877

Pretty graphs by Desmos Grapher (wwwdesmosorg)

minus119903119903119898119898 (Screened)

Decreasing screening strengthUnscreened potential

bull Assume 119903119903119864119864119903119903119909119909 119903119903119903119903119903119903

asymp 0

bull Nuclear stopping power formula (Was p 47)

119889119889119864119864119889119889120597120597 119899119899119899119899119899119899119899119899

=119873119873120587120587119885119885111988511988521205761205764

1198641198641198941198941198721198721

1198721198722ln

12057412057411986411986411989411989412057612057621205741205741198641198641199031199032

4119864119864119894119894

119889119889119864119864119889119889120597120597 119899119899119899119899119899119899119899119899

=119873119873120587120587119885119885111988511988521205761205764

1198641198641198941198941198721198721

1198721198722ln

41198641198641198941198942

12057612057621198641198641199031199032

120574120574 =4119898119898119872119872119898119898 + 119872119872 2

bull Now turn to electronic stopping The Bethe-Bloch formula describes this well

minus119889119889119864119864119889119889120597120597

=4120587120587119896119896021198851198852120576120576411987711987711989011989011989811989811989011989011988811988821205731205732

ln211989811989811989011989011988811988821205731205732

119868119868 1 minus 1205731205732minus 1205731205732

120573120573 =119907119907119894119894119894119894119899119899119888119888

119877119877119890119890 = 119877119877119890119890119877119877119888119888119890119890119903119903119890119890119877119877 119889119889119877119877119877119877119889119889119889119889119890119890119889119889

bull I is the mean excitation energy of the medium

Relative Stopping Powers

bull Plotcompare SeSn

119878119878119890119890119878119878119899119899

=21198721198722

1198981198981198901198901198851198852

ln 120574120574119890119890119864119864119894119894119868119868

ln 120574120574119864119864119894119894119864119864119903119903

bull Electronic stopping power takes over by factors of 102-104 for high energy ionshellip

bull hellip what about neutrons

Relative Stopping PowersH Paul AIP Conf Proc 1525309 (2013)

Relative Stopping PowersWas p 84

bull What does this say aboutbull Energy deposition vs energy

at high-Ebull Same at low-E

bull When is the most damage done to a material

bull Explain damage rates vs ranges of heavy ions amp fast neutrons

bull hellip

It All Starts with Frenkel Pairs

bull Frenkel pair ndash perfect vacancyinterstitial combination

bull Produced very well by electron radiation

Vacancy

Interstitial

The Damage Cascade

bull Frenkel pairs donrsquot stay that way

bull Many ideas about how ldquodamage cascaderdquo evolvesbull Called ldquocascaderdquo due to

subsequent continuing damage effects

bull Whatrsquos wrong with this picture

Was p 128

Original conception of damage cascade showing path of Frenkel pair production

Damage Cascades RevisitedWas p 128

bull Many more forms of damage are possiblebull Single vacancies amp

interstitials not always energetically favorable

bull Frenkel pairs donrsquot explain observed damage

Revised damage cascade accounting for crystallinity

Stable energetically favorable fast-moving defects

Primary Knock-on Atom (PKA)

Collisions can knock atoms in close-packed

directionsHow stable would this be in the

Cascade Stages ndash Ballistics

bull Put simply atoms get knocked around

bull No time to relax

bull ~10MeV neutronsmove how fastbull How long to move one

lattice parameter

K O Trachenko M T Dove E K H Salje J Phys Condens Matter 131947 (2001)

Cascade Stages ndash Thermal Spikebull Temperature rises

very locally for avery short time

Cascade Stages ndash Quench

bull Heat is conducted away EXTREMELY quickly

K O Trachenko M T Dove E K H Salje J Phys Cond Matter 131947 (2001)

Cascade Stages ndash Anneal

bull Most damage ldquoannealsrdquo out or recombinesgets sunk awaybull For neutrons amp ions almost all damage anneals

D S Aidhy et al Scripta Mater 60(8)691 (2009)

119890119890 = 0 119877119877119889119889 119890119890 = 245 119877119877119889119889

Courtesy of Elsevier Inc httpwwwsciencedirectcom Used with permissionSource Aidhy D S Kinetically Driven Point-Defect Clustering in Irradiated MgOby Molecular-Dynamics Simulation Scripta Materialia 60 no 8 (2009) 691-4

Simulated annealing of Frenkel pairs in MgO at 1000K2214 ndash Nuclear Materials Slide 24

Types of Radiation

bull Different radiation produces different cascadesDifferent radiation produces different cascades

Increasing mass same

charge

Moderate mass no

charge

Stopping MechanismMass amp Charge

All electronic

Mostly electronic

Mostly nuclear some coulombic

Entirely nuclear

Simulation Methods ndash BCAWas p 134

bull Binary Collision Approximationbull Uses interatomic

potentials (like MD) to allow atoms to move

bull Does not restrict crystallinity

bull Creates collision cascades pretty well

Simulation Methods ndash MD

bull Solve 119865119865 = 119898119898119877119877 for every pair of atoms

bull Interatomic potentials are the key to interactionsbull Right MD simulation of 1keV cascade in

iron at 100K

Was p 139

bull Interatomic potentials are the key to interactions

bull Attractive amp repulsiveterms

bull Lennard-Jones (LJ) potential widely used

Lennard-Jones Potential

httpwwwcmbirunlredockimagesLennardJonespng

Courtesy of Bo Hanssen amp Sander Jans Used with permission

J Yu et al J Mater Chem193923-3930 (2009)

Attractive terms of selected potentials (dots) and LJ-modified version (lines)

Simulation Methods ndash MDhttpwww-personalumichedu~gswmovieshtml

A video is played in class to demonstrate the concept

Simulation Methods ndash MC

bull With pre-determined bull Example TRIMdistributions for some bull Randomly choose features scattering angles new

mean free pathsbull ldquoRoll the dicerdquo to sample from distributions

bull Let random numbers determine where things move and change

Simulation Methods ndash MChttpwww-personalumichedu~gswmovieshtml

Simulation Methods ndash Rate Theory

C J Ortiz M J Caturla J Computer-Aided Materials Design 14171-181 (2007)

bull Assume rate-controlled equations for defect migration clustering

bull Often employs ldquomean field theoryrdquobull Glosses over details to

accelerate time

Simulation Methods ndash Rate Theorybull How good is the approximation Is it worth it

Damage Cascades ndash Summary

bull Spans multiple time scalesbull Sets the stage for defect migration to higher length scales

bull Simulation also requires multiscale methods with much creativity to get right

Was p 140

Displacement Theory

bull Define a rate of atomic displacements using flux

119877119877 = 0

119864119864119898119898119898119898119898119898119873119873 lowast Φ 119864119864119894119894 lowast 120590120590119863119863 119864119864119894119894 119889119889119864119864119894119894

Reaction rate 1199031199031198941198941198891198891198891198891198991198991198981198983minus119889119889119890119890119899119899

Material number density 1199031199031198861198861198941198941198981198981198891198891198981198983 Displacement cross section

Maximum energy available Energy dependent flux distribution

Displacement Theory

119877119877 = 0

119864119864119898119898119898119898119898119898119873119873 lowast Φ 119864119864119894119894 lowast 120590120590119863119863 119864119864119894119894 119889119889119864119864119894119894

119877119877119873119873

=119863119863119863119863119863119863119889119889119877119877119888119888

119864119864119898119898119898119898119898119898Φ 119864119864119894119894 lowast 120590120590119863119863 119864119864119894119894 119889119889119864119864119894119894

Displacement Theory

119863119863119863119863119863119863119889119889119877119877119888119888

119864119864119898119898119898119898119898119898Φ 119864119864119894119894 lowast 120590120590119863119863 119864119864119894119894 119889119889119864119864119894119894

Known or pre-determined Only unknown quantity

bull Develop expression for displacement cross section

Displacement Theory

119863119863119863119863119863119863119889119889119877119877119888119888

119864119864119898119898119898119898119898119898Φ 119864119864119894119894 lowast 120590120590119863119863 119864119864119894119894 119889119889119864119864119894119894

120590120590119863119863 119864119864119894119894 = 119879119879119898119898119898119898119898119898

119879119879119898119898119898119898119898119898120590120590 119864119864119894119894 119879119879 119907119907

Probability that an atom displaced by a particle with

119879119879 119889119889

119879119879

gy Ei leaves with recoil

bull T is the PKA (displaced atom) recoil energy

energy T (differential energy transfer cross section)

119879119879 119907119907 119879119879 119889119889119879119879 119889119889Number of atomic displacements from a PKA with energy T

Displacement Theory

120590120590119863119863 119864119864119894119894 = 119879119879119898119898119898119898119898119898

119879119879119898119898119898119898119898119898120590120590 119864119864119894119894 119879119879 119907119907

bull Assume there i

119907119907

s some threshold ener

119879119879 119889119889

119879119879

d) below which a displacement does not occur

bull Otherwise a displa

119879119879

119907119907ce

nt will

119879119879

119864119864

u119903119903

r119879119879 = 1 119879119879 ge 119864119864119903119903

119879119879 119907119907119879119879 119907119907 119879119879 119889119889119879119879 119889119889

Displacement Theory

120590120590119863119863 119864119864119894119894 = 119879119879119898119898119898119898119898119898

119879119879119898119898119898119898119898119898120590120590 119864119864119894119894 119879119879 119907119907 119879119879 119889119889119879119879

bull Sharp displacementthreshold model

bull What does thismodel neglect

119879119879 119907119907119879119879 119907119907 119879119879 119889119889119879119879 119889119889

Was p 74

Displacement Theory

120590120590119863119863 119864119864119894119894 = 119879119879119898119898119898119898119898119898

119879119879119898119898119898119898119898119898120590120590 119864119864119894119894 119879119879 119907119907 119879119879 119889119889119879119879

bull Add some smoothnessto this function

bull Accounts for atomicvibrations impurities

119879119879 119907119907119879119879 119907119907 119879119879 119889119889119879119879 119889119889

Was p 75

Displacement Theory

bull What is this threshold energybull Letrsquos estimate

1 Energy to break metal surface bonds ~5eV

2 Shift removed atom to the interior x2

3 Stuff atom in an interstitial site assume no time to relax the lattice x2

4 Displacement isnrsquot in the easiest direction x2

Displacement Theory

bull What is thisthreshold energy

bull Notice any patternsin the databull Crystal structure

bull Melting point

bull Something else

Was p 83

Displacement Theory

120590120590119863119863 119864119864119894119894 = 119879119879119898119898119898119898119898119898

119879119879119898119898119898119898119898119898120590120590 119864119864119894119894 119879119879 119907119907

bull Returning to v(T) assume sufficientl

119879119879 119889119889

119879119879

gh energy PKAs can do more damage

bull Enter the Kinchin-Pease (K-P) model

119879119879 119907119907119879119879 119907119907 119879119879 119889119889119879119879 119889119889

Kinchin-Pease Model

119907119907 119879119879 =21198791198790

119879119879119907119907 120576120576 119889119889120576120576

bull Now split into three relevant rangesE lt 119864119864119903119903 119864119864119903119903 le E lt 2119864119864119903119903 E gt 2119864119864119903119903

119907119907 119879119879 =21198791198790

119864119864119889119889119907119907 120576120576 119889119889120576120576 +

119864119864119889119889

2119864119864119889119889119907119907 120576120576 119889119889120576120576 +

2119864119864119889119889

119879119879119907119907 120576120576 119889119889120576120576

Kinchin-Pease Model

119907119907 119879119879 =21198791198790

119864119864119889119889119907119907 120576120576 119889119889120576120576 +

119864119864119889119889

2119864119864119889119889119907119907 120576120576 119889119889120576120576 +

2119864119864119889119889

119879119879119907119907 120576120576 119889119889120576120576

bull First term is 0 (energy too low to displace)

bull Second term is 1 (only one displacement possible)

bull Third term is steadily increasing

119907119907 119879119879 =21198791198790

1198641198641198891198890119889119889120576120576 +

119864119864119889119889

21198641198641198891198891119889119889120576120576 +

2119864119864119889119889

119879119879119907119907 120576120576 119889119889120576120576

Kinchin-Pease Model

bull Final formulation

Was p 77

Modifications to K-P Model

bull Is the cutoff energy really true

Was p 84 H Paul AIP Conf Proc 1525309 (2013)

copy Springer All rights reserved This content is excluded from copy AIP Publishing LLC All rights reserved This content is excluded from our Creativeour Creative Commons license For more information see Commons license For more information see httpocwmiteduhelpfaq-fair-usehttpocwmiteduhelpfaq-fair-use

Modifications to K-P ModelWas p 77

bullAllow nuclear stoppingpower to diminishbut not disappearafter Ec

bull Also allow electronicstopping to starttaking over before Ec

bull Account for crystallinity Channeling

bull Displaced atom can travelthrough empty spacebetween lattice planesbull Nuclear stopping ~ 0

bull Only electronic stopping

Was p 102

bull Lots of paths to channel

Was p 102

bull Close-packed energy transfer Focusingbull Think packed billiard balls on a pool table

bull Assumes hard sphere collisions

bull Where would this happenbull Close-packed

directions

bull Crowdions

The Real σD Is UglyWas p 108

[Was Gary S Fundamentals of Radiation Materials Science pp 92] removed due to copyright restrictions

Damage After the Cascade

bull What happens to damage after the cascadebull Production

bull Recombination

bull Absorption at sinks

bull Migration

Point Defect Balance

Change = Gain ndash Loss

bull What are the possible gain termsbull Displacement production

bull Reaction production

bull What are the possible loss termsbull Recombination

bull Loss to sinks

bull Diffusion

bull What are the possible sinksbull Grain boundaries

bull Dislocations

bull Impurities

bull Free surfaces

bull Incoherent precipitates

Gain Terms

bull Defect Production Rate

1198701198700 =119863119863119863119863119863119863119889119889119877119877119888119888

lowast 120576120576

bull Reaction Production Rate

1198771198770 = 119903119903=1

119899119899

119877119877120597120597119877119877119903119903

From SRIM etc

Damage cascade efficiency

Ignorehellip for now

Loss Terms Recombination

bull Introduce some recombination rate constant 119870119870119894119894119894119894bull Relate to the relevant defect concentrations

119862119862119894119894 = 119868119868119877119877119890119890119877119877119903119903119889119889119890119890119889119889119890119890119889119889119877119877119890119890 119862119862119890119890119877119877119888119888119877119877119877119877119890119890119903119903119877119877119890119890119889119889119890119890119877119877119862119862119894119894 = 119881119881119877119877119888119888119877119877119877119877119888119888119889119889 119862119862119890119890119877119877119888119888119877119877119877119877119890119890119903119903119877119877119890119890119889119889119890119890119877119877

120597120597119862119862 119894119894119894119894

120597120597119890119890 119877119877119890119890119899119899119894119894119898119898119877119877119894119894119899119899119903119903119886119886119894119894119894119894119899119899= 119870119870119894119894119894119894119862119862119894119894119862119862119894119894

Loss Terms Sinks

bull For each sink define a sink strength 119870119870119889119889bull Relate sink rate to concentrations of defects 119862119862 119894119894119894119894

and sinks

120597120597119862119862 119894119894119894119894

120597120597119890119890 119878119878119894119894119899119899119878119878119889119889= minus

119889119889=1

119860119860119899119899119899119899 119878119878119894119894119899119899119878119878119889119889

119870119870119889119889119862119862 119894119894119894119894 119862119862119889119889

Loss Terms Diffusion

bull We already know this equation from Fickrsquos Law

120597120597119862119862 119894119894119894119894

120597120597119890119890 119863119863119894119894119863119863119863119863119899119899119889119889119894119894119894119894119899119899= 120571120571119863119863 119894119894119894119894 120571120571119862119862 119894119894119894119894

Combining Terms

120597120597119862119862 119894119894119894119894

120597120597119890119890=

119863119863119863119863119863119863119889119889119877119877119888119888

lowast 120576120576 minus 119870119870119894119894119894119894119862119862119894119894119862119862119894119894 minus 119889119889=1

119860119860119899119899119899119899 119878119878119894119894119899119899119878119878119889119889

119870119870119889119889119862119862 119894119894119894119894 119862119862119889119889 + 120571120571119863119863 119894119894119894119894 120571120571119862119862 119894119894119894119894

120597120597119862119862119894119894120597120597119890119890

= 1198701198700 minus 119870119870119894119894119894119894119862119862119894119894119862119862119894119894 minus 119889119889=1

119860119860119899119899119899119899 119878119878119894119894119899119899119878119878119889119889

119870119870119889119889119862119862119894119894119862119862119889119889

120597120597119862119862119894119894120597120597119890119890

= 1198701198700 minus 119870119870119894119894119894119894119862119862119894119894119862119862119894119894 minus 119889119889=1

119860119860119899119899119899119899 119878119878119894119894119899119899119878119878119889119889

119870119870119889119889119862119862119894119894119862119862119889119889

Neglect Spatial Variance

Note on Vacancy Conc

bull 119862119862119894119894 must be adjusted to account for thermal vacancies

119862119862119894119894lowast = 119862119862119894119894 minus 1198621198621198941198940

bull Why do we ignore this for interstitialsbull Equilibrium interstitial concentration is so low

Adjusted vacancy concentration Thermal vacancy concentration

Total vacancy concentration

Equilibrium Defect ConcWas p 200

[Was Gary S Fundamentals of Radiation Materials Science p 200ISBN 9783540494713] removed due to copyright restrictions

Limiting Cases of Point Defect Kinetic Equationsbull (1) Assume low temperature low sink densities

120597120597119862119862119894119894120597120597119890119890

= 1198701198700 minus 119870119870119894119894119894119894119862119862119894119894119862119862119894119894 minus 119889119889=1

119860119860119899119899119899119899 119878119878119894119894119899119899119878119878119889119889

119870119870119889119889119862119862119894119894119862119862119889119889 + 120571120571119863119863119894119894120571120571119862119862119894119894

120597120597119862119862119894119894120597120597119890119890

= 1198701198700 minus 119870119870119894119894119894119894119862119862119894119894119862119862119894119894 minus 119889119889=1

119860119860119899119899119899119899 119878119878119894119894119899119899119878119878119889119889

119870119870119889119889119862119862119894119894119862119862119889119889 + 120571120571119863119863119894119894120571120571119862119862119894119894

Case 1 Low T Low CsWas p 194

Whatrsquos In a Sink Term

119870119870119894119894119894119894 = 4120587120587119903119903119894119894119894119894 119863119863119894119894 + 119863119863119894119894

119870119870119894119894119889119889 = 4120587120587119903119903119894119894119889119889 119863119863119894119894119870119870119894119894119889119889 = 4120587120587119903119903119894119894119889119889 119863119863119894119894

Sink Strength Interaction radius Diffusivities

Case 2 Low T Medium CsWas p 197

[Was Gary S Fundamentals of Radiation Materials Science pp 194 197-8200 ISBN 9783540494713] removed due to copyright restrictions

Compare Cases 1 amp 2Was pp 194 197

Case 3 Low T High CsWas p 198

Case 4 High TemperatureWas p 200

Where Does This Model Break Downbull Near sinks

bull Sinks with biases for defectsbull Interaction radii

bull Defect-dependent sinks

bull Time-variant sinks

bull Time-variant anything else

bull Spatial variance

Return Spatial Variance

120597120597119862119862119894119894120597120597119890119890

= 1198701198700 minus 119870119870119894119894119894119894119862119862119894119894119862119862119894119894 minus 119889119889=1

119878119878119894119894119899119899119878119878119889119889

119870119870119889119889119862119862119894119894119862119862119889119889 + 120571120571119863119863119894119894120571120571119862119862119894119894

120597120597119862119862119894119894120597120597119890119890

= 1198701198700 minus 119870119870119894119894119894119894119862119862119894119894119862119862119894119894 minus 119889119889=1

119878119878119894119894119899119899119878119878119889119889

119870119870119889119889119862119862119894119894119862119862119889119889 + 120571120571119863119863119894119894120571120571119862119862119894119894

bull Whatrsquos in a D anyway

Radiation Enhanced Diffusionbull Da (diffusivity of a type of atom) is a sum of all relevant effects

bull Some are turned on by radiation (interstitialcy)bull Some are enhanced by radiation (vacancy)

119863119863119903119903 = 119903119903=1

119863119863119890119890119863119863119890119890119899119899119886119886119889119889

119891119891119903119903119863119863119903119903119903119903119862119862119903119903

119863119863119903119903 = 119891119891119881119881119863119863119903119903119894119894119862119862119894119894 + 119891119891119894119894119863119863119903119903119894119894 119862119862119894119894 + 119891119891211989411989411986311986311990311990321198941198941198621198622119894119894+119891119891119899119899119903119903119894119894119888119888119903119903119894119894119894119894119899119899119863119863119903119903119899119899119903119903119894119894119888119888119903119903119894119894119894119894119899119899119862119862119899119899119903119903119894119894119888119888119903119903119894119894119894119894119899119899 + 119891119891119903119903119899119899119898119898119877119877119877119877119890119890119899119899119899119899 119863119863119903119903119903119903119899119899119898119898119877119877119877119877119890119890119899119899119899119899119862119862119903119903119899119899119898119898119877119877119877119877119890119890119899119899119899119899 hellip

Components of Radiation Enhanced Diffusion

Was p 207

Returning Spatial Dependence Case Studybull 1D ion irradiation includes

bull A free surface

bull Dislocations

bull Thermal vacancies (not interstitials)

bull Differing interaction radii

bull Spatially dependent defect production

bull Injected interstitials

Experimental Evidence

bull 99995 Febull 35MeV Fe+2 self-ions 450C ~1mA beam current

bull 18 middot 10-3 dpas

bull Peak dosesbull 35 75 105dpa

bull CharacterizationF

bull TEMA 1

bull Image analysis8CD

FA 18CD

200 keV 140 keV 10 keV

17 MeV 1 MeV

Courtesy of Lin Shao Used with permission

bull Void swelling is observed below material surfacebull No swelling observed

beyond 1μm depthbull Range of Fe+2 ions is

~15μm

L Shao et al (2014)

1microm

(a) 35 DPA

(b) 75 DPA

(c) 105 DPA

Surface

Beam direction

bull Correlate damage (point defect creation) with injected interstitials

L Shao et al (2014)

bull Image analysis used to estimate void fraction vs distancebull Squares identify voids

L Shao et al (2014)Courtesy of Lin Shao Used with permission

bull Voids not observed near injected interstitials

L Shao et al (2014)

0 400 800 1200 16000

Fe self ions

35 DPA 70 DPA 105 DPA

Fe depth (nm)

More Experimental Evidence

bull Occurs in complex alloys as well

bull This is a highly general phenomenon

F A Garner M B Toloczko A Certain L Shao J Gigax C Wei ldquoImpact of the Injected Interstitial Effect on Ion-Induced Void Swelling

in Austenitic and Ferritic-ODS Alloysrdquo TMS Poster (2014)

Modeling amp Simulation Explains the Mechanismbull Used SRIM

computer code to calculate damage rate (dpas) and implantation rate (Fecm3-s)

Stopping Range of Ions in Matter

Modeling amp Simulation Explains the Mechanismbull Simultaneously plot damage (V + I) and injected

interstitials (I only)

Damage Fe inject

Modeling amp Simulation Explains the Mechanismbull Use SRIM data as forcing function for point defect

balance equationsbull Assumptions

bull EMI = 018eV (lt110gt split dumbbell is dominant interstitial

defect)bull EM

V = 066eV (atomically pure iron) or 11eV (realistic purity)bull Neglect formation of larger vacancy or interstitial defectsbull Defects can annihilate by diffusion network dislocations

incoherent precipitates nucleated voids recombination free surface annihilation

Simulation Framework

bull MOOSE ndash Multiphysics Object Oriented Simulation Environmentbull Greatly simplifies creating simulations quicklybull Seamless ability to fully couple ODEs amp PDEs on a finite

element frameworkbull Recently open sourced wwwmooseframeworkcom

ODE ndash Ordinary differential equationPDE ndash Partial differential equation

Modeling amp Simulation Explains the Mechanismbull Superimpose both point defect plots

InterstitialsVacancies

Defect Concen-trations (nm3)

Depth (nm)

Modeling amp Simulation Explains the Mechanismbull Plot excess interstitial fraction

Depth (nm)

Excess Interstitials (fraction)

Quantifying the Injected Interstitial Effectbull Artificially ldquoturn offrdquo injected interstitials

bull Run side-by-side simulations all other parameters equal

Screenshot showing difference in input files

Results ndash Point Defects35MeV Fe+2 1mA 1mm2 beam 450C E V

M = 066eV

Without injected interstitials With injected interstitials

Point defects follow Point defects do not quite follow SRIM SRIM forcing function forcing function

InterstitialsVacanciesDamage Rate

Depth (nm)Depth (nm)

Results ndash Vacancy Supersa

35MeturaV Fe+2 1mA

tio 1mm

n2 beam 450C E V

M = 066eV

Peaks near maximum damage region Bimodal distribution shifted to the left by 100nm

SupersatDamage Rate

Depth (nm) Depth (nm)

SupersatDamage Rate

Results ndash Void Nucleation Rate

35MeV Fe+2 1mA 1mm2 beam 450C E VM = 066eV

Clearly peaks at maximum damage region Very bimodal distribution shifted to the left by 100nm

Void NuclDamage Rate

Depth (nm)Depth (nm) Depth (nm)Depth (nm)

Compare with Experiments35MeV Fe+2 1mA 1mm2 beam 450C E V

M = 066eV

00 400 800 1200 1600

Simulation vs Experiments With Without Injected Interstitials

Fe self ions

Swelling

Fe depth (nm)

400 800 1200 16000

Depth (nm)

Explanation

bull Small spatial defect imbalance has large change in vacancy supersaturation at peak injected interstitial locations

bull This in turn affects void nucleation rate

MIT OpenCourseWarehttpocwmitedu

2214 Materials in Nuclear EngineeringSpring 2015

For information about citing these materials or our Terms of Use visit httpocwmiteduterms

Learning Objectives

Stopping Power

CoulombicNuclear Stopping Power

Displacement Theory

Kinchin-Pease Model

The Real σD Is Ugly

Gain Terms

Loss Terms Sinks

Combining Terms

Equilibrium Defect Conc

Limiting Cases of Point Defect Kinetic Equations

Case 1 Low T Low Cs

Case 2 Low T Medium Cs

Compare Cases 1 amp 2

Case 3 Low T High Cs

Case 4 High Temperature

Where Does This Model Break Down

Radiation Enhanced Diffusion

Returning Spatial Dependence Case Study

Modeling amp Simulation Explains the Mechanism