Simulation of displacement cascades in -Fe and Fe-10% Cr

04/22/23

Simulation of displacement cascades in -Fe and Fe-10% Cr

Terentiev Dmitryand Malerba Lorenzo

04/22/23

Main Goals

Simulation of displacement cascades and their analysis: Fe-Cr vs Fe

Study of collisional stage: cascade core, peak time, volume and density vs PKA energy

Control of cascade growth via direct visualization

Study of final atomic configuration: distribution of defects, clustering, visualization

04/22/23

Simulation technique

Molecular Dynamics Microcanonical statistical ensemblePeriodic boundary conditionsSimulation cell size up to 1 000 000 atoms Simulation time up to 30 psEither pure Fe or 10% Cr atoms in Fe matrix

The interatomic potentialEAM for ferromagnetic Fe-10%Cr

04/22/23

Criteria for defect analysis

Distributions & Visualization

Defects (Wigner-Seitz cell combined with linked cells method) vacancy - no atoms in the cell replacement - one atom, but number doesn’t correspond to

initial interstitial - 2 atoms in one cell displacement = interstitials + replacements

Clustering formation Vacancy cluster - distance is <= than 2nd nn Interstitial cluster - distance is <= than 3rd nn

Cascade core – at maximum number of defects Cascade volume and density peak time

Visualization of mobile defects, finding right criteria for SIA clustering

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Simulation of collision cascades:Initial parameters

Recoil energies from 1 keV up to 40 keV (also < 1 keV)

Maximum size of simulation box: 80 l. u. side

Simulation scheme:

Collisional stage: 50000.01 fs 20

Post collisional :10000.1 fs 90

Cooling 10001 fs 10

Total simulation time 30ps

Table with cascade parameters

Recoil energy

Sim.Time

Num.Cascade

Boxsize

1keV 10ps 20 303 l.u.

2keV 10ps 20 403 l.u.

5keV 20ps 20 403 l.u.

8keV 20ps 20 503 l.u.

10keV 30ps 20 653 l.u.

15keV 30ps 15 653 l.u.

20 keV 30ps 15 653 l.u.

30 keV 30ps 8 803 l.u.

40 keV 30ps 8 803 l.u.

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Predicted threshold displacement energies and other results

Direction Our Potential

Experiment (Maury et al 76)

Simonelli 93 (C. Becquart & C. Domain

2000)

Finnis-Sinclair

(Calder & Bacon 93)

Ackland (Ackland & Bacon 97 )

<100> 22 17 17 18 21 <110> 37 >30 47 31 30 <111> 29 20 21 >70 >100

Threshold displacement energies of Fe atom in pure Fe matrix at 300 K (all values are ±1eV)

Pure Fe FeCr(10%) Direction Fe atom Cr atom Fe atom Cr atom

<100> 22 21 22 21 <110> 37 32 37 32 <111> 29 29 28 29

Average threshold displacement energies for Cr and Fe atoms in pure Fe and Fe-Cr (10% ) alloy.

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Angle dependence of ED

ComparisonP. Vajda: "Anisotropy of electron radiation damage", Rev. Mod. Phys., (1977) (origin work: Erginsoy et al (1964))

D.J. Bacon, A. F. Calder, J.M. Harder, S.J. Wooding “Computer simulation of low-energy displacement events in pure bcc and hcp metals”, Journal of nuclear materials,1993

0 10 20 30 4010

20

30

40

50

60

Born-Mayer our calculation Finnis-Sinclair10

0 di

rect

ion

110

dire

ctio

n

knoc

k - o

n ki

netic

ene

rgy

(eV

)

knock -on direction, 0

100 plane

0 10 20 30 40 50 60 70 80 9010

20

30

40

50

60

[110

]

[100

]

[111

]

110 plane

knoc

k -o

n ki

netic

ene

rgy

(eV

)

knock-on direction , 0

Born-Mayer our calculation Finnis-Sinclair

[210], [221],[211] predicted correctly

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Peak time distributions

no essential influence of Cr atoms on characteristics pronounced increase of core density, cascade volume and peak time at 10keV – 20(30) keV and then slope changes after 30 keV looks like cascade volume and density become saturated these effects can be explained because above 10-20 keV gradual subcascade splitting occurs and each of these is a replica of lower energy cascades

0 5 10 15 20 25 30 35 40

2000

4000

6000

8000

10000

12000

Num

ber o

f def

ects

at p

eak

time

Energy, KeV

Max Number of defects NdFeCr NdFe

0 5 10 15 20 25 30 35 40

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

2400

Pea

k tim

e, fs

Energy, KeV

Peak time TpFeCr TpFe

0 5 10 15 20 25 30 35 400

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

Cas

cade

vol

ume,

A3

Inintial energy, KeV

Cascade volume CvolFeCr CvolFe

0 5 10 15 20 25 30 35 401

2

3

4

5

6

7

8

Cor

e de

nsity

, 1/A

3

Initial energy, KeV

Core Density DenFeCR DenFe

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Evolution of collision cascades

102 103 104

102

103

104

Num

ber o

f dis

plac

ed a

tom

s

time, fs

0.5 keV 2 keV 5 keV 10 keV 20 keV

Evolution of no. of displacements

Evolution of no. of Frenkel pairs

shift of maximum with rise of recoil energy increase of Ndisp during post-collisional stage, while Nvac decreases

102 103 104100

101

102

103

Num

ber o

f Fre

nkel

pai

rs

time, fs

0.5 keV 2 keV 5 keV 10 keV 20 keV

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Evolution of dumbbells NFe-Fe > NFe-Cr but! only during collision stage

Nmix increases at the expense of Fe-Fe dumbbells

Fe-Fe/Fe-Cr replacement processes take place during cooling stage as well

rearrangement of dumbells distribution

Evolution of collision cascades

1x103 2x103 3x103 4x103 5x103 6x103 7x103 8x103

100

101

102

103

104

num

ber o

f dum

bells

time, fs

10 kev_cascade FeFe FeCr CrCr

5,0x103 1,0x104 1,5x104 2,0x104 2,5x104 3,0x104100

101

102

103

104

num

ber o

f dum

bells

time, fs

20 kev_cascade FeFe FeCr CrCr

~ 4.5 ps ~ 8 ps

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Visualization of cascades

20 keV energy

1st snap shot after 50fs

Film up to 3ps

initial PKA position

135 direction

60 l.u.

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Visualization of cascades

10-3

10-2

10-1

100

101

102

103

K

eV

101

102

103

104

105

106

107

20 keV energy

Particles energy – Evolution

Film from 1ps up to 10 ps

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Visualization of cascadesThe distribution of dumbells – red – Cr atoms, blue – Fe atoms, 60 l.u. – box size

Configurations at the final stage of simulation 30ps. Simulation temperature - 300K

20 keV cascade

Sim. Time from 5ps up to 30 ps

04/22/23

Final distributions of defects

NRT efficiency becomes stable at ~ 0.3

Fraction of Cr ~ 0.65 in surviving dumbbells, whereas concentration is 10%, very small amount of Cr-Cr dumbbells, although Cr-Cr has MAX Ebind

Approximation of Fr; pairs gives 0.87 exponential factor, which is slightly higher than for pure Fe

1 10

0.2

0.3

0.4

0.5

0.6

0.7

0.8

NR

T ef

ficie

ncy

Energy, keV

NRT efficiency Fe-12% Cr Fe

0 10 20 30 400

10

20

30

40

50

60

70

Num

ber o

f dum

bbel

ls

PKA energy, keV

Dumbbell distribution Fe-Fe Fe-Cr Cr-Cr

1 101

10

100Number of Frenkel pairs

in FeCr exp = 0.87 in Fe exp = 0.89

N F

r. pa

irs

PKA energy, keV

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Clustered fraction for vacancies and interstitials

• significant influence of criteria for vacancy and interstitial clustering detection

• considerable increase of clustering from 10 keV PKA energy for SIA clustering, but not regular

• at the moment no essential influence of Cr component

• despite that 65% of dumbbells contain Cr, only 20% of Cr atoms belong to big clusters (with size more than 5 atoms)

• discrepancy between our results and other simulation results for pure Fe

3rd nn for SIA 2nd nn for vacancy

0 5 10 15 20 25 30 35 40 45 50

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

Clu

ster

frac

tion

of S

IA

Energy, keV

SIA clustering, 3rd nn criteria FeCr Fe

0 5 10 15 20 25 30 35 40 45 500.080.100.120.140.160.180.200.220.240.260.280.300.320.340.360.380.40

Clu

ster

frac

tion

Vac

anci

es

Energy, keV

Vacancy clustering, 2rd nn criteria FeCr Fe

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VisualizationSubcascade formation evidence

Final assesmentFinal assesment

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VisualizationDense cascade (affected by PBC)

Final assesmentFinal assesment

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Conclusions

The TDE predicted by the potential are in the correct range of values, considering the existing uncertainties.

The evolution in time of the cascades is physically acceptable. Long lived cascades (Epka>10keV) may be connected with formation of dense cascades. With rising energy, this effect disappears, which could be connected with formation of subcascades (in some cases)

The total number of Frenkel pairs obtained in displacement cascades is less than NRT (efficiency < 0.3 - asymptote). Quite stable after 10 kev PKA energy.

During the post-cascade stage a tendency to increasing number of Fe-Cr dumbbells at the expense of Fe-Fe dumbbells was observed.

In all considered cases the number of mixed dumbbells exceeds Fe-Fe dumbbells. Clustering in high energy cascades needs more detailed study and longer simulations, nevertheless there is evidence of big SIA cluster formation in the case of cascade splitting, while the formation of big vacancy clusters could be a product of dense cascades.

After the cooling stage of the cascade, small vacancy clusters and sizeable interstitial were detected, this qualitatevly agrees with other calculations. But statistic is too poor to give a certain conclusion.