Diffusion of radiation Diffusion of radiation damage in Fe and Fe–P damage in Fe and Fe–P

systemssystems

Stewart GordonStewart Gordon

Loughborough University, UKLoughborough University, UK

IntroductionIntroduction

Collision cascade – result of radiation Collision cascade – result of radiation damagedamage

Classical MD of limited timescaleClassical MD of limited timescale Problem: to predict what will happen in the Problem: to predict what will happen in the

long runlong run Key: discovering the state transitionsKey: discovering the state transitions

The dimer method – 1The dimer method – 1

Algorithm to find saddle points on a potential Algorithm to find saddle points on a potential surfacesurface

System of System of NN atoms – 3 atoms – 3NN-dimensional -dimensional potential surfacepotential surface

No need to guide – exceeds limitations of No need to guide – exceeds limitations of molecular staticsmolecular statics

Previously applied to surface diffusionPreviously applied to surface diffusion

The dimer method – 2The dimer method – 2

Dimer – two nearby Dimer – two nearby points on the potential points on the potential surfacesurface

Dimer is rotated to line Dimer is rotated to line of lowest curvatureof lowest curvature

Then translated Then translated towards the saddle towards the saddle using an effective forceusing an effective force

Determines minimum Determines minimum energy barriersenergy barriers

Methodology – 1Methodology – 1

Fe bcc lattice size: 14Fe bcc lattice size: 1433 unit cells unit cells Isolated defectsIsolated defects Total number of atoms: 9827Total number of atoms: 9827 Relaxed using damped MDRelaxed using damped MD Cubic region defines range of moving atomsCubic region defines range of moving atoms

Methodology – 2Methodology – 2

Interatomic potentials: Ackland (Fe–Fe) and Interatomic potentials: Ackland (Fe–Fe) and Morse (Fe–P)Morse (Fe–P)

Calculation of transition times:Calculation of transition times:

Assume standard attempt frequency of Assume standard attempt frequency of  = 10 = 101313 Hz Hz

Fe self-interstitial structureFe self-interstitial structure

Fe bcc latticeFe bcc lattice Defect: Defect:

110110 dumbbell dumbbell Most common defect Most common defect

in collision cascadesin collision cascades

Fe atom on lattice site

Fe interstitial atom

Vacancy

Fe transitions – 1Fe transitions – 1

Transition from Transition from 110110 dumbbell to  dumbbell to 111111 crowdion crowdion

Energy barrier: Energy barrier: 0.160 eV0.160 eV

Transition time at Transition time at 300 K: 49 ps300 K: 49 ps

Fe transitions – 2Fe transitions – 2

The The 111111 crowdion  crowdion translates in the translates in the 111111 direction direction

Energy barrier: Energy barrier: 0.0024 eV0.0024 eV

Transition time at Transition time at 300 K: 0.1 ps300 K: 0.1 ps

Barrier convergence –Barrier convergence –Fe Fe 111111 crowdion transitions crowdion transitions

Moving atomsMoving atoms TranslationTranslation To To 110110 dumbbell dumbbell

10251025 0.0026910.002691 0.0350780.035078

20012001 0.0024470.002447 0.0346720.034672

54895489 0.0023870.002387 0.0345620.034562

67516751 0.0023810.002381 0.0345650.034565

Fe diffusion mechanismFe diffusion mechanism

110110 dumbbell  dumbbell changes to changes to 111111 crowdion –  crowdion – controlling transitioncontrolling transition

Crowdion then Crowdion then translatestranslates

Returns to Returns to 110110 dumbbell dumbbell

Can then explore other Can then explore other 111111 directions directions

QuickTime™ and aMPEG-4 Video decompressor

are needed to see this picture.

P atoms in bcc FeP atoms in bcc Fe

P atoms prefer to sit in substitutional sitesP atoms prefer to sit in substitutional sites Can be displaced into interstitial sites by Can be displaced into interstitial sites by

radiation damageradiation damage P atoms in substitutional sites can attract Fe P atoms in substitutional sites can attract Fe

interstitial clustersinterstitial clusters Here the mechanism for the motion of Here the mechanism for the motion of

isolated interstitial P is investigatedisolated interstitial P is investigated

P interstitial defect in FeP interstitial defect in Fe

110110 Fe–P dumbbell Fe–P dumbbell Some very different Some very different

diffusion mechanisms diffusion mechanisms to be seento be seen

Fe atom on lattice site

Fe interstitial atom

Vacancy

P interstitial atom

Fe–P diffusion mechanisms – 1Fe–P diffusion mechanisms – 1

110110 dumbbell changes  dumbbell changes to tetrahedralto tetrahedral Energy barrier: 0.293 eVEnergy barrier: 0.293 eV Transition time: 8.4 nsTransition time: 8.4 ns

Then forms new Then forms new 110110 dumbbell dumbbell Energy barrier: 0.257 eVEnergy barrier: 0.257 eV Transition time: 2.1 nsTransition time: 2.1 ns

Diffusion through lattice Diffusion through lattice possiblepossible

Dumbbell pivots via Dumbbell pivots via 551551 and and 643643 statesstates

Key transition: Key transition: 551551 to to 643643 Energy barrier: Energy barrier:

0.257 eV0.257 eV Transition time: 2.1 nsTransition time: 2.1 ns

Fe–P diffusion mechanisms – 2Fe–P diffusion mechanisms – 2

[110][551][643][634][515][101]

Fe–P transitions – summaryFe–P transitions – summary

643 dumbbell

0.0037

0.0027

0.257 0.066

0.085

0.227

0.041

0.293

0.257

0.289

0.254

0.0988

0.0796

0.111

0.260

551 dumbbell Face diagonal

Offset tetrahedral

110 dumbbell Tetrahedral

ConclusionsConclusions

Dimer method can be applied to bulk Dimer method can be applied to bulk problemsproblems More moving atoms needed than for surfacesMore moving atoms needed than for surfaces

Unusual transitions can be identifiedUnusual transitions can be identified Diffusion mechanisms for P in Fe have been Diffusion mechanisms for P in Fe have been

determineddetermined

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