Table 1 Summary of cascade simulations using molecular dynamics across different materials relevant to the TPBAR and some other nuclear materials of interest

 Di et al.¹⁵⁶

α-Zr under -1 to +1% tensile strain

10 KeV PKA

250,800 atoms/ 18 nm \(\times\) 18 nm \(\times\) 18 nm

40 ps

Mendelev’s EAM¹⁵⁷ with Ziegler-Biersack-Littmark (ZBL)

Defect cluster analysis, Strain effects

 Zhou et al.²¹

HCP - Zr

1 to 80 keV

69.8 nm \(\times\) 70.5 nm \(\times\) 68.5 nm (1.43 million atoms)

35 ps

Mendelev’s EAM¹⁵⁷ with ZBL

Defect evolution and cluster analysis

 Wooding et al.¹⁶³

α-Zr

Up to 20 keV

72 \({a}_{0}\) \(\times\) 41\(\sqrt{3}\) \({a}_{0}\) \(\times\) 35 \({c}_{0}\) 532, 360 atoms

20 ps

many-body functions of the Finnis–Sinclair type by Ackland et al.¹⁶⁴

Defect evolution and cluster analysis, power-law dependence of Frenkel pairs

 Wang et al.¹⁶⁵

Hcp - Zr

Up to 30 keV

256 × 255 × 408 (Å)

25 ps

Mendelev’s EAM¹⁵⁷ with ZBL

Dislocation analysis, nanocrack healing due to cascades

 Khiara et al.¹⁶⁶

α-Zr

20 keV

112 \({a}_{0}\) \(\times\) 48\(\sqrt{3}\) \({a}_{0}\) \(\times\) 64 \({c}_{0}\), 1,376,400 atoms

100 ps

Mendelev’s EAM¹⁵⁷ with ZBL

Dislocation unpinning due to cascades, cascades radius calculations

 Kim et al.¹⁶⁷

α-Zr

20 keV

348,192 atoms

20 ps

Mendelev’s EAM¹⁵⁷ with ZBL

Effect of hydrostatic strain states on defect evolution and clusters

 Jin et al.¹⁶⁸

α-Zr

6 keV

84.5 × 195.2 × 92.6 (Å)

30 ps

Mendelev’s EAM¹⁵⁷ with ZBL

Effect of [0001] symmetric tilt grain boundaries on annihilation of defects

 Tian-Yu et al.¹⁶⁹

α-Zr

1 keV

50 × 40 × 20 cells, 160,000 atoms

-

Mendelev’s EAM¹⁵⁷ with ZBL

Analysis of sputtered atoms, surface vacancies and adatoms due to near-surface cascades

 Wang et al.¹⁷⁰

HCP Zr and ZrCu interface

40 keV

20 × 20 × 30 nm

200 ps

EAM by Mendelev¹⁷¹

Effect of Zr₂Cu precipitate in Zr matrix, defect distribution around precipitate boundary

 Tikhonchev et al.¹⁷²

BCC Nb-5-25%Zr in HCP Zr matrix

20 keV

200 × 200 × 200 (Å), 323,000

20 ps

Semiempirical n-body potential by Lin et al.¹⁷³

Distribution of defects in Zr matrix versus in the Nb-Zr precipitate, role of interphase boundary

 Wang et al.¹⁷⁴

HCP Zr

10 keV

339.5 × 326.9 × 398.7 (Å), 1,905,120 atoms

60 ps

EAM by Mendelev¹⁷¹ with ZBL

Role of \(\left\{10\bar{1}1\right\}\) and \(\left\{10\bar{1}2\right\}\) twin boundaries in interstitial absorption and localized deformation

 March-Rico et al.¹⁷⁵

α-Zr

Up to 15 keV

35.4 × 35.7 × 27.8 nm, 1,515,874 atoms

100 ps

BIMD 19 EAM by Wimmer et al.¹⁷⁶

Interaction of cascades with δ-hydrides

 Tian et al.¹⁷⁷

HCP Zr

50 keV

144 \({a}_{0}\) \(\times\) 84 \({b}_{0}\) \(\times\) 88 \({c}_{0}\)

27 ps

EAM by Mendelev¹⁷¹ with ZBL

mechanism of basal vacancy cluster formation due to local strain during irradiation

 Voskoboinikov et al.²³

Pure Ni

5–20 keV

2 million atoms

20 ps

EAM potential¹⁷⁸ with ZBL

Defect analysis, variable timestep analysis and temperature effects

 Fullarton et al.¹⁷⁹

Pure Ni

1–10 keV

40 a × 40 a × 40 a, a = 3.52 Å

30 ps

EAM potential by Mishin¹⁸⁰ re-parameterized by Stoller¹⁸¹

Defect formation and clustering near-surface and in bulk

 Voskoboinikov et al.¹⁸²

Pure Ni

20 keV

2,002,536 atoms

100 ps

EAM potential by Mishin et al.¹⁷⁸

Comparison of defect evolution due to surface cascades versus bulk

 Zarkadoula et al.²⁷

Pure Ni

150 keV

600 × 600 × 600 (Å), 20 million atoms

70 ps

embedded-atom (EAM) potential by Bonny et al.¹⁴¹ for Ni-Fe-Cr alloys

effects of the e-ph coupling strength and the electronic thermal conductivity on Ni cascades

 Chen et al.¹⁸³

Pure Ni

Up to 30 keV

445.6 × 299 × 293.5 (Å), 3,573,000 atoms

25 ps

EAM by Mishin et al.¹⁷⁸ with ZBL

Effect of cascades on closure of nano-cracks

 Huang et al.¹⁸⁴

Ni-graphene nanocomposite

Up to 10 keV

124.6 × 129.5 × 174.5 (Å), 285,000 atoms

23 ps

EAM potential by Bonny et al.¹⁴¹ for Ni-Ni, AIREBO by Stuart for C-C¹⁸⁵ and Lennard-Jones for C-Ni¹⁸⁶

High sink efficiency of Ni-graphene interface for irradiation defects annealing

 Do et al.²²

CoCrFeMnNi HEA, Pure Ni, Pure Fe

10 keV

50 a\(\times\) 50 a \(\times\) 50 a, 500,000 atoms

5000 ps

modified embedded atom method (MEAM) potential¹⁸⁷

Defect evolution and distribution, dislocation extraction analysis

 Beland et al.¹⁹

Ni, NiFe and NiCo alloys

Upto 40 keV

2 million

35 ps

EAM potential by Bonny¹⁴¹ and Mishin¹⁸⁰ with ZBL

Defect analysis and potential comparison

 Crocombette et al.¹⁸⁸

Ni₃Al and UO₂

580 keV

–

100 ps

Buckingham for UO₂¹³⁴, EAM for Ni₃Al¹⁸⁹ with ZBL

Cell molecular dynamics for cascades

 Deluigi et al.²⁰

FeNiCrCoCu HEA, pure Ni and pure W.

40 keV

1 million atoms

100 ps

EAM potentials¹⁹⁰ with ZBL

Defect analysis and effect of PKA type

 Roy et al.¹³

LiAlO₂ and LiAl₅O₈

5–15 keV

21 a × 21 a × 21 a, 225,000 atoms

20 ps

Buckingham core-shell^150,152 model with ZBL

Defect analysis, cation exchange analysis, core-shell model analysis

 Collette et al.¹⁴²

Fe-10Ni-20Cr

(SS 316 L)

5–15 keV

100a\(\times\) 80\(a\times\) 160a, a = 3.59 Å, 7,680,000 atoms

100 ps

Finnis-Sinclair embedded atom model

(EAM) developed

by Bonny et al.¹⁴¹

Effect of dislocations on defect evolution during cascades, defect cluster analysis

 Tikhonchev et al.¹⁹¹

Fe–9 at.%Cr binary alloy

20 keV

19 nm \(\times\) 19 nm \(\times\) 19 nm

25 ps

concentration dependent N-body potential¹⁹²

Defect analysis, characteristic of Cr rich clusters

 Kedharnath et al.¹⁹³

\(\alpha\)-Fe

3 keV

30 nm \(\times\) 30 nm \(\times\) 14 nm (2 million atoms)

150 ps

EAM potential by Mendelev et al.¹⁹⁴

Grain boundary interaction with cascades, effect of radiation on tensile properties

 Peng et al.¹⁹⁵

Bcc iron

Up to 200 keV

480 a\(\times\) 480 a \(\times\) 480 a, 137.8 nm side length cube, 221 million atoms

40 ps

EAM potential by Bonny et al.¹⁹⁶ with ZBL

Punch out mechanism and formation of both

interstitial and vacancy dislocation loops

 Lin et al.¹⁹⁷

F321 austenitic steel represented by Fe-Ni-Cr

Up to 100 keV

25 nm \(\times\) 25 nm \(\times\) 25 nm

150 ps

EAM potential by ref. ²⁰ with ZBL

Defect evolution with dislocation loops analysis

 Juslin and Nordlund¹⁹⁸

He in Ferritic/ martensitic steel represented by Fe₉₀Cr₁₀

5 keV

42 a\(\times\) 42 a \(\times\) 42 a, 148,176 atoms

25 ps

Fe-Cr by Olsson et al.¹⁹⁹, Fe-He by Juslin²⁰⁰, Cr-He by Terentyev²⁰¹

Impact of He atoms in reducing the recombination in FeCr

 Henriksson et al.²⁰²

Fe₃C and Cr₂₃C₆ in Ferritic steel (Fe-Cr-C)

1 keV

158,000 atoms

50 ps

Many body potential for Fe-Cr-C system by Henriksson et al.²⁰³

Increase in damage when recoil is initiated inside Fe₃C or Cr₂₃C₆ particles in ferrite

 Gang et al.²⁰⁴

Ferritic/ martensitic steel Fe90%-Cr10%

15 keV

500,000 atoms

20 ps

Fe-Cr by Olsson et al.¹⁹⁹

Defect evolution and clustering, Fe-Cr dumbbell formation

 Jay et al.³¹

Si in diamond-like crystals

Upto 100 KeV PKA

1 million atoms

1000 ps

Stillinger Weber²⁰⁵

Two temperature model for electronic stopping, Defect clustering

 Borodin et al.³⁰

Si

Upto 5 keV

20 nm \(\times\) 20 nm \(\times\) 20 nm

5500 ps

Tersoff²⁰⁶ with ZBL

Defect analysis

 Delaye et al.²⁰⁷

SiO₂–B₂O₃–Na₂O glass

0.6 KeV

8000 atoms

–

Born–Mayer–Huggins potentials^205,208 with ZBL

Evolution of bond angle, densification

 Samolyuk et al.³²

Cubic phase of SiC(3C-SiC)

Up to 50 keV

150 a\(\times\) 150 a \(\times\) 150 a, 22 million atoms

20 ps

Tersoff potential²⁰⁶ and Gao-Weber²⁰⁹ potential with ZBL

comparison of radiation damage using the two potentials

 Balboa et al.²¹⁰

(U_1-yPu_y)O₂

5–75 keV PKA

38 nm \(\times\) 38 nm \(\times\) 38 nm

50 ps

Potashnikov pair potentials²¹¹ and Cooper many body potential²¹²

Cooper and Potashnikov potentials were compared for defect clustering and dislocation density

 Martin et al.²¹³

UO₂

10 keV

187,500 atoms

30 ps

Empirical potential (Buckingham) by Morelon et al.¹³⁴

Temperature dependence of radiation damage, cascade overlap study

 Martin et al.²¹⁴

UO₂

1–80 keV

68 a\(\times\) 68 a \(\times\) 68 a, 3.8 \(\times\) 10⁶ atoms

20 ps

Empirical potential (Buckingham) by Morelon et al.¹³⁴

Defect and recombination analysis, damage volume analysis

 Buchan et al.³⁷

Diamond

2.5 keV

10 nm \(\times\) 10 nm \(\times\) 10 nm

1 ps

Environment dependent interaction potential²¹⁵ with ZBL

Defect analysis

 McKenna et al.²¹⁶

Graphite

2 keV

24 a\(\times\) 39 a \(\times\) 15 a, 112,320 atoms

5 ps

Environment dependent interatomic potential developed by Marks et al.²¹⁵ combined with ZBL

Defect analysis considering PKA energy scaled by threshold energy

 Christie et al.³⁸

Graphite

0.1–2 keV

15.77 \(\times\) 15.77 \(\times\) 15.77 nm³, 440,448 atoms

5 ps

Environment dependent interatomic potential developed by Marks et al.²¹⁵ combined with ZBL

Cascade structure study, atoms kinetics, PKA length

 Fu et al.²¹⁷

W and W-Re

1-300 keV

63 nm \(\times\) 63 nm \(\times\) 63 nm

100 ps

Finnis-Sinclair type potential²¹⁸ with ZBL

Defect analysis, cluster size analysis, dislocation loop analysis

 Zhang et al.²¹⁹

BCC W

10–50 keV

31.652 nm \(\times\) 31.652 nm \(\times\) 31.652 nm, 2 million atoms

90 ps

Finnis-Sinclair⁴⁹ type with Derlet–Nguyen–Manh–Dudarev (DNMD)⁵² W

Potential with ZBL

Defect analysis and role of grain boundaries

 Setyawan et al.²²⁰

W

0.1-100 keV

38 nm \(\times\) 38 nm \(\times\) 38 nm (120 times a₀)

50 ps

W potential⁵⁴ modified from Ackland et al. N-body semi-empirical potential⁵⁰

Defect clusters, self-interstitial atom loops

 Liu et al.¹¹²

W

1–200 keV

150 a\(\times\) 150 a \(\times\) 150 a, a = 3.185 Å,

8.1 million atoms

150 ps

neuroevolution potential (NEP) combined with ZBL using the Gaussian approximation potential (GAP) data from¹¹³

Potential development, defect analysis and cluster analysis

 Ullah et al.²²¹

Ni_0.8Fe_0.2 and Ni_0.8Cr_0.2

5 keV

11.5 nm\(\times\) 11.5 nm \(\times\) 11.5 nm, 132,000 atoms

30 ps

EAM potential by Bonny et al.¹⁴¹

Defect analysis as a function of dose (dpa), cluster analysis

 Zhou et al.²²²

Monocrystalline S

Up to 5 keV

19.1 nm\(\times\) 19.1 nm \(\times\) 16.3 nm, 448,000 atoms

50 ps

Tersoff potential²⁰⁶ with ZBL

Temperature and strain effects on defect production

 Boev et al.¹²

V-Ti alloys

5–20 keV

12 nm\(\times\) 12 nm \(\times\) 12 nm, 432,000 atoms

12 ps

EAM potential by Lipnitskii et al.²²³ combined with ZBL

Defect and cluster analysis

 Voskoboinikov et al.²²⁴

Al

5–20 keV

4 million atoms

~15 ps

EAM potential by Zope et al.²²⁵ with ZBL

Defect and cluster analysis, near surface cascades

 Roy et al.⁵

Ti alloys

10-40 keV

20 nm \(\times\) 20 nm \(\times\) 20 nm

20 ps

EAM potentials by Zhou et al.²²⁶ with ZBL

Defect and cluster analysis

 Sahoo et al.³⁴

β-Li₂TiO₃

2 keV

8 a × 8 a × 8 a

100 ps

long-range Coulombic potential, and medium range Buckingham potential with ZBL

Defect and cluster analysis, amorphization analysis

 Parashar et al.²²⁷

Single crystal Nb

0.25–2 keV

128,000 atoms

6 ps

Force matched EAM potential by Fellinger et al.²²⁸

Radiation effect on tensile strength, temperature effect on radiation damage

 Zarkadoula et al.²⁷

Ni_xFe_yCr_(100-x-y) alloys

30–50 keV

2.5–3.6 million atoms

100 ps

embedded-atom (EAM) potential by Bonny et al.¹⁴¹ for Ni-Fe-Cr alloys

Effect of inclusion of electronic effects and 2 temperature model in cascade simulations

 Nordlund et al.²²⁹

Cu and W

Up to 100 keV

-

50 ps

W^50,54, Cu²³⁰

Addressing limitations of Norgett−Robinson−Torrens displacements per atom (NRT-dpa) model, two new complementary displacement production estimators (athermal

recombination corrected dpa, arc-dpa) and atomic mixing (replacements per atom, rpa)

functions

 Granberg et al.²³¹

Ni-Fe and Ni

-Co-Cr

simulations up to the dose ∼ 0.57 dpa by running

1500 consecutive 5 keV recoils

110,000 atoms

30 ps

Zhou et al.²²⁶, EAM potentials for Ni-Co and Lin et al.²³² EAM for Cr

point defect damage level saturation with a dose at about 0.3 dpa, defect and cluster analusis in NiFe and NiCoCr

 Lin et al.²⁶

NiCoCrFe HEA

10–50 keV

100 a\(\times\) 100 a \(\times\) 100 a, a = 3.52 Å,

4 million atoms

140 ps

Lee and Baskes¹⁸⁷ MEAM potential modified by Choi et al.²³³

Defect evolution and cluster analysis, Cascade temperature analysis, dislocation analysis