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