Design Kinetic Parameters for Improved Resilience of Materials under Irradiation

Eda Aydogan; Enrique Martinez; Jesper Byggm\"astar; Matheus A. Tunes; Mohammadhossein Nahavandian; Osman El-Atwani

REVIEW 4 major objections 8 minor 1 cited by

Design Kinetic Parameters for Improved Resilience of Materials under Irradiation

T0 review · 4 major / 8 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Alloys resist radiation best when vacancies and interstitials diffuse at the same speed.

desk verdict A plausible screening rule for W-based HEAs—match Dv and Di and keep migration energies low—read off standard rate theory and backed by MD annealing, but the cascade gap leaves the design rule conditional, not demonstrated. read the letter →

arxiv 2412.13343 v1 pith:CUMDB4TF submitted 2024-12-17 cond-mat.mtrl-sci

Mohammadhossein Nahavandian , Eda Aydogan , Jesper Byggmästar , Matheus A. Tunes , Enrique Martinez , Osman El-Atwani This is my paper · ORCID

classification cond-mat.mtrl-sci

keywords highentropyalloysradiationresistancedefectrecombinationratetheorymoleculardynamicstungstenmigrationenergydiffusioncoefficients

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper proposes a concrete design rule for choosing radiation-tolerant high-entropy alloys without testing every possible composition: pick alloys in which single vacancies and self-interstitials have similar diffusion coefficients and the smallest combined migration energy. When those two kinetic parameters are met, rate-theory calculations show that interstitial-vacancy recombination outcompetes clustering, so the steady-state concentration of surviving defects drops. Molecular dynamics annealing of tungsten and W-based alloys supports the trend: V- and Cr-containing alloys, which satisfy the criteria, annihilate Frenkel pairs (vacancy-interstitial pairs) far more completely than pure W. Published irradiation micrographs of those same alloys show little or no loop and cavity damage, suggesting the kinetic screen can narrow the huge composition space before expensive experiments.

What carries the argument

The carrying mechanism is a steady-state mean-field rate theory of coupled vacancy and interstitial concentrations, with diffusivities from harmonic transition state theory, $D = \nu a^2 \exp(-\Delta E/k_B T)$. The recombination term uses Waite's diffusion-limited rate constant $K_{IV} = 4\pi R_{\mathrm{rec}}(D_i+D_v)/\Omega$, while sink elimination enters through $K_d = \sum_s k_{sd}^2 D_d$. Scanning migration barriers from 0.2 to 1.65 eV and temperatures from 300 to 1000 K, the authors compute steady-state concentrations and show their minimum sits at $D_v \approx D_i$ with low $\Delta E_v+\Delta E_i$; extending the rate theory with clustering terms gives a four-dimensional map of recombination-to-clustering ratios across temperature. The MD leg uses tabGAP machine-learned potentials in LAMMPS, with Wigner-Seitz defect identification, to test the same alloy family and confirm that V- and Cr-rich systems recombine rather than cluster.

What would settle it

Run molecular dynamics displacement cascades, not random Frenkel-pair annealing, on two alloys that have similar $D_v$ and $D_i$ but different total migration energies: if the low-barrier alloy does not retain fewer defects, the recombination criterion fails. Alternatively, irradiate an alloy with $D_v/D_i \approx 1$ and low $\Delta E_v+\Delta E_i$ and count loops and voids; if the defect density matches pure W, the design rule is wrong.

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Extended reading notes

Core claim

The central claim is that radiation resilience in compositionally complex alloys is governed by two kinetic parameters: the ratio $D_v/D_i$ between vacancy and interstitial diffusivities and the sum $\Delta E_v + \Delta E_i$ of their migration energies. Recombination is optimal when the diffusivities are similar and the total migration energy is minimal, because then the recombination rate $K_{IV} = 4\pi R_{\mathrm{rec}}(D_i+D_v)/\Omega$ is large relative to the clustering rates $D_v+D_v$ and $D_i+D_i$, and the steady-state concentrations of both defect types stay low. The paper demonstrates the rule with rate-theory maps spanning migration barriers from 0.2 to 1.65 eV and temperatures from 300 to 1000 K, with MD annealing of randomly placed Frenkel pairs at 2000 K, and with experimental micrographs of W, WTa, WTaV, WTaCrV, and WTaCrVHf after heavy-ion and He irradiation. In the tungsten family, V- and Cr-containing alloys have $D_v/D_i \approx 1$ and low total migration energy, and they retain far fewer defects than pure W.

Load-bearing premise

The load-bearing premise is that behavior under real irradiation follows the averaged rate equations using the reported diffusion coefficients; the paper itself notes in Results and Discussion that the model does not consider damage cascades or time-dependent sink evolution, so the matched-diffusivity rule stands or falls with that approximation.

Editorial extensions

If this is right

Composition screening can be reduced to a kinetic test: compute or measure $D_v$, $D_i$, $\Delta E_v$, and $\Delta E_i$, and keep alloys near $D_v/D_i \approx 1$ with small total migration energy.
The same criterion, if general, should rank other BCC refractory alloy families beyond the W-based systems studied here.
V and Cr additions appear beneficial in refractory alloys partly because they raise interstitial migration energies toward the vacancy value, increasing recombination.
Experimental campaigns can be shortened because candidate alloys are downselected by kinetic parameters before irradiation testing.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Inference: because the rate-theory model excludes damage cascades and sink evolution, the decisive test of the rule would be full-cascade MD or a deliberate mismatch experiment: irradiate an alloy with $D_v\approx D_i$ and high total migration energy, or one with matched diffusivities that is predicted to be bad, and compare surviving defect densities.
Inference: the same kinetic matching may govern He management in these alloys; if recombination is enhanced and interstitial diffusion is slow, He transport is suppressed, which would explain the small uniform bubbles reported for WTaCrV.
Inference: the criterion could be condensed into a dimensionless design index, such as $|D_v-D_i|/(D_v+D_i)$ together with $\Delta E_v+\Delta E_i$, which high-throughput composition searches could optimize directly.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Dear colleague,

The useful core of this paper is a simple idea: use defect kinetic parameters, not trial-and-error alloying, to choose radiation-resistant compositions. The rate-theory maps make the argument visually clear: defect concentration drops when vacancy and interstitial diffusivities converge and total migration energy is small. That is a legitimate read-off from a standard mean-field model, and the MD annealing of W-Cr/V alloys adds new data points. Credit where due: the tabGAP potentials are state-of-the-art, the composition set from binaries to quinary is reasonable, and the authors do not oversell—they explicitly note that the model omits cascades and sink evolution.

The soft spots are real and roughly in the order the stress test puts them. First, the bridge to realistic irradiation is unbuilt. Rate theory uses steady-state fixed sink strengths; MD starts from random Frenkel pairs annealed at 2000 K, one realization per alloy, no error bars. Displacement cascades create correlated clusters, and the optimal condition derived for single defects may shift when cluster mobility and dissociation dominate. That does not kill the rule, but it means "improved resilience under irradiation" is an extrapolation, not a demonstrated fact. Second, the reporting is incomplete: G' and sink strengths are not given, so the rate-theory maps cannot be reproduced without emailing the authors. Third, the experimental "verification" is retrospective, drawn from the authors' own prior irradiations under different doses and temperatures; it is consistent but not a prospective test.

The circularity burden is mild. The rule is derived from a scan, not fitted to the experimental micrographs, and the MD potentials are not tuned to produce the result. The bigger issue is that all supporting pieces come from one group, which makes independent validation more important, not less.

Who should read this: anyone working on radiation-tolerant refractory alloys or HEA screening. It deserves a serious referee, but the referee should push for reproducible parameters and ideally cascade simulations before the rule is used for selection. My recommendation: send it out, require the missing rate-theory values and a statement of what cascade effects would change, and see whether a prospective experiment or cascade MD runs can be added.

Best.

Referee Report

4 major / 8 minor

Summary. The paper proposes a design rule for radiation-resistant high-entropy alloys (HEAs): choose compositions in which the vacancy and self-interstitial diffusion coefficients are similar and the total defect migration energy is minimized, so that recombination is promoted and the steady-state defect concentration is reduced. The authors support this rule with (i) steady-state rate theory calculations scanning migration energies, (ii) molecular dynamics annealing simulations of W and W-based alloys with randomly inserted Frenkel pairs, and (iii) experimental micrographs from prior ion-irradiation studies of W, W-Ta, W-Ta-V, W-Ta-Cr-V, and W-Ta-Cr-V-Hf. The rate-theory maps and the MD results are consistent with the proposed criterion, and the experimental data are offered as qualitative validation.

Significance. If the design rule holds, it offers a simple, physically motivated screening criterion for the huge composition space of HEAs: match vacancy and interstitial diffusivities and keep the sum of migration energies low. The paper has the merit of deriving the rule from a standard rate-theory model rather than fitting it to a specific dataset, and of combining analytical modeling with MD using state-of-the-art machine-learned potentials. The rule is falsifiable and could be tested prospectively by selecting a new composition and irradiating it. However, the current evidence is largely retrospective: the experimental micrographs come from alloys already known to have good radiation resistance, and the modeling omits displacement cascades and time-dependent sink evolution, which are central to realistic irradiation. The significance of the paper therefore rests on the plausibility of the single-defect recombination picture, which is not yet fully established for cascade damage.

major comments (4)

[Methods, Eqs. (1)-(2) and Figs. 1-2] The rate-theory calculations do not report the values of the effective production rate G', the sink strengths k_s^2, or the atomic volume Ω. The steady-state concentrations C_v^st and C_i^st depend explicitly on these parameters, so the maps in Figs. 1 and 2 cannot be reproduced or assessed for sensitivity. More importantly, the paper does not discuss whether the proposed design rule (matched D_v and D_i, low total migration energy) holds in both the sink-dominated and recombination-dominated regimes, which could depend on G' and k_s^2. Please report all parameter values and demonstrate that the ranking of alloys by defect concentration is robust to reasonable variations in G' and sink strength.
[Results and Discussion, Fig. 2] The criterion that the recombination-to-coalescence diffusivity ratio must equal 1 for optimal radiation resistance is not derived from the rate-theory equations in Methods. Equations (1)-(2) and their steady-state solutions contain only recombination and sink-absorption terms; they do not include cluster formation or coalescence. The ratio (D_i+D_v)/(2D_i) and its vacancy counterpart appear to be an ad hoc construct. Please either derive this condition from a model that explicitly includes clustering, or clearly state that it is an empirical heuristic, and define the clustering rate coefficients used to construct Fig. 2.
[Methods - Molecular Dynamics and Fig. 3] The MD annealing simulations use a single realization per alloy, randomly placed Frenkel pairs, and an annealing temperature of 2000 K. The paper itself acknowledges that the model 'does not consider damage cascade, or any time-dependent evolution of sinks' (Results and Discussion). Displacement cascades produce spatially correlated defects and clusters, which can change the balance between recombination and clustering. The current MD results therefore do not directly support the claim that the design rule improves resilience under realistic irradiation. Please add multiple realizations with statistical error bars, and either perform displacement-cascade simulations or discuss quantitatively the conditions under which the single-defect recombination mechanism dominates over cascade-induced clustering.
[Results and Discussion, Fig. 4] The experimental validation is compiled from the authors' own prior studies and the literature, and it is retrospective: the alloys (WTaV, WTaCrV, WTaCrVHf) were previously reported to have good radiation resistance, and they are now shown to satisfy the proposed kinetic criterion. This is not a prospective test of the design rule. A stronger claim would require selecting a new, untested composition based on the criteria and comparing its irradiation response to a control. Please either report such a prediction or explicitly state that the current evidence is retrospective and that a prospective test is needed.

minor comments (8)

[Figure 3 caption] The caption uses 'Frankel pairs' instead of 'Frenkel pairs'; this typo appears in the figure caption while the text correctly uses 'Frenkel'.
[Methods, Eqs. (1)-(2)] In the first pair of rate equations, the term ∑ k_sv^2 D_v C_v^s has a superscript 's' on C_v; this appears to be a typo and should be C_v, since the sink index is already on k_sv^2.
[Methods, Rate theory] The atomic volume Ω in the expression for K_IV is not defined numerically; please specify the value used in the calculations.
[Methods, Rate theory] The diffusion coefficient for vacancies D_v is not written explicitly; the text gives D_i = (1/2)νa^2 exp(-ΔE_d/kBT) but only states that D_v follows harmonic transition state theory. Writing both expressions explicitly would remove ambiguity about the factor 1/2.
[Abstract and Conclusions] The phrase 'the effective migration energies of defects is minimum' should be 'the effective migration energies of defects are minimum' for grammatical correctness.
[Figs. 1-2 and Ref. 27] The values of ΔEv and ΔEi for the alloys taken from Ref. 27 are not tabulated; consider adding a table of the migration energies and the corresponding diffusivity ratios used for the superimposed symbols, so the reader can verify the assignments.
[Fig. 2] The description '4D figure' is unclear; a standard caption explaining the axes, the color scale, and the meaning of the iso-surface or contour would improve readability.
[Results and Discussion, Fig. 4] The experimental micrographs correspond to different irradiation temperatures, doses, and ion species across the alloys, which makes quantitative comparison difficult; a table with the irradiation conditions and quantitative defect densities would strengthen the qualitative visual comparison.

Circularity Check

1 steps flagged · score 6.0 of 10

Partial circularity: the 'maximum diffusivity → optimal recombination' leg of the design rule restates the recombination coefficient's definition; the 'similar diffusivities' leg is a nontrivial model consequence, and experimental support is in-sample.

self definitional [Abstract; Methods (Rate theory, recombination coefficient and Arrhenius diffusivity definitions)]
"It is found that when the diffusion coefficients for single vacancies and interstitials become similar and the effective migration energies of defects is minimum (maximum diffusivities), defect recombination becomes optimal, and the concentration of defects is significantly reduced. ... The second term denotes the recombination rate, derived from Waite's theory ... K_IV = 4πR_rec(D_i + D_v)/Ω ... D_v = νa² exp(−ΔE_d/k_BT), D_i = 1/2 νa² exp(−ΔE_d/k_BT)."

The 'minimum migration energy → maximum diffusivities → optimal recombination' component of the headline claim is not an independent prediction: the model defines the recombination rate as K_IV ∝ (D_i + D_v) and defines each diffusivity by an Arrhenius expression in the migration energy. Scanning migration energies and then reporting that low migration energies give optimal recombination is largely a restatement of that definition. The 'similar D_v and D_i' clause is a separate, non-tautological steady-state consequence of the rate equations, so the circularity is partial rather than total; however, the abstract's load-bearing sentence combines both clauses.

full rationale

The central design rule has two legs. The 'minimum total migration energy (maximum diffusivities) improves recombination' leg is self-definitional: Methods defines K_IV = 4πR_rec(D_i + D_v)/Ω and D = νa²exp(−ΔE/kBT), so finding low defect concentrations when D_i + D_v is large is partly a restatement of the model's recombination term. The 'similar D_v and D_i' leg is not circular: it follows from solving the steady-state rate equations with symmetric sink terms, and the MD annealing simulations provide a separate, though limited, check. The experimental 'verification' uses micrographs from the authors' prior studies of the same alloys (WTaV, WTaCrV, WTaCrVHf) that the criteria select, so it is an in-sample consistency check rather than an out-of-sample prediction; this weakens the support but is not a derivation cycle. The paper also explicitly notes that the model omits cascades and time-dependent sink evolution, which is an external-validity limitation rather than circularity. Overall, one component of the headline claim reduces by construction while the rest retains independent model content, giving a partial circularity score of 6.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The central claim depends on a modest set of modeling choices (rate-theory parameters) and domain assumptions (accuracy of literature migration energies and ML potentials), but no new physical entities are postulated.

free parameters (7)

Effective production rate G' = not reported
Appears in the steady-state rate equations (Eqs. 1-2) and sets the absolute defect concentrations in Figures 1-2, but no value is given in the Methods.
Sink strength k_s^2 = not reported
The elimination terms in Eqs. (1)-(2) depend on sink strengths; the paper assumes equal vacancy and interstitial sink strengths but does not report their magnitude, which shifts the low-concentration region.
Recombination distance R_rec = 3 a0 with a0 = 0.3165 nm
Chosen in the recombination coefficient K_IV = 4π R_rec(D_i+D_v)/Ω; a standard but hand-picked value.
Attempt frequency ν = 10^13 s^-1
Assumed for both vacancy and interstitial jumps in the harmonic transition-state-theory diffusivities; affects absolute diffusivities and therefore the design map.
MD annealing temperature = 2000 K
Single temperature used for all annealing simulations; the rate-theory results in Figure 2 show temperature dependence, but only 2000 K is tested in MD.
Frenkel pair concentration = 0.1% and 2%
The 2% supersaturation is far above reactor-relevant conditions; 0.1% is more realistic but both are random, not cascade-generated.
Annealing time = 10 ns
Final defect concentrations are evaluated after 10 ns; longer times could change the outcome, and no time convergence is shown.

assumptions (5)

domain assumption Mean-field rate theory with constant sink strengths describes defect evolution in CCAs under irradiation.
The central design criteria are extracted from the steady-state solutions of Eqs. (1)-(2); the paper acknowledges the model omits cascades and sink evolution (Results and Discussion).
domain assumption The tabGAP machine-learned potentials accurately model defects in all the W-based alloys tested.
MD annealing relies on tabGAP (Ref 42), developed by co-author Byggmästar; no validation of the potential for each equiatomic composition is provided.
domain assumption The migration energies of the W-based alloys from Ref 27 are accurate.
Placement of W, WTa, WV, WTaV, etc. on the rate-theory maps (Figures 1-2) and the conclusion that V/Cr alloys satisfy the criteria depend on these literature values.
standard math Harmonic transition-state theory with a single attempt frequency gives reliable diffusivities.
Used to convert migration energies into D_v and D_i via Arrhenius expressions in the Methods.
standard math The steady-state solutions of the coupled rate equations are the appropriate measure of radiation resistance.
The maps of C_v+C_i in Figures 1-2 use these algebraic solutions.

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Pith. "Pith review of Design Kinetic Parameters for Improved Resilience of Materials under Irradiation." pith.science (2026). https://pith.science/paper/CUMDB4TF

@misc{pith2026241213343,
  author       = {Pith},
  title        = {Pith review of: Design Kinetic Parameters for Improved Resilience of Materials under Irradiation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CUMDB4TF}},
  note         = {Machine review of arXiv:2412.13343}
}

read the original abstract

High entropy alloys (HEAs) have captured much attention in recent years due to their conceivably improved radiation resistance compared to pure metals and traditional alloys. However, among HEAs, there are millions of design possibilities considering all potential compositions. In this study, we develop criteria to design HEAs with improved radiation resilience taking into consideration defect properties to promote interstitial-vacancy recombination. First, we conduct rate theory calculations on defects followed by molecular dynamics (MD) simulations on pure W and W-based multicomponent concentrated alloys. It is found that when the diffusion coefficients for single vacancies and interstitials become similar and the effective migration energies of defects is minimum (maximum diffusivities), defect recombination becomes optimal, and the concentration of defects is significantly reduced. This is supported by MD simulations indicating improved radiation resistance of V- and Cr-based alloys, which satisfy the above-stated criteria. Furthermore, experimental observations also reinforce the proposed approach. This study sheds light on the design criteria for improved radiation resistance and helps material selection without the need of extensive experimental work.

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Reference graph

Works this paper leans on

44 extracted references · 44 canonical work pages · cited by 1 Pith paper

[1]

J., and Was, G

Zinkle, S. J., and Was, G. S., Acta Materialia (2013) 61 (3), 735

work page 2013
[2]

Lu, C., et al., Nature Communications (2016) 7 (1), 13564

work page 2016
[3]

Aydogan, E., et al., Acta Materialia (2017) 134, 116

work page 2017
[4]

Han, W., et al., Advanced Materials (2013) 25 (48), 6975

work page 2013
[5]

Sun, C., et al., Scientific Reports (2015) 5 (1), 7801

work page 2015
[6]

Aydogan, E., et al., Journal of Nuclear Materials (2017) 487, 96

work page 2017
[7]

A., et al., Nanoscale (2021) 13 (48), 20437

Tunes, M. A., et al., Nanoscale (2021) 13 (48), 20437

work page 2021
[8]

Agarwal, S., et al., Journal of Applied Physics (2022) 131 (12), 125903

work page 2022

Show all 44 references

[9]

Agarwal, S., et al., Journal of Applied Physics (2022) 131 (12) 13

2022
[10]

M., et al., Metallurgical Transactions A (1990) 21 (7), 1847

Wang, L. M., et al., Metallurgical Transactions A (1990) 21 (7), 1847

1990
[11]

Zhang, Y ., et al., Nature Communications (2015) 6 (1), 8736

2015
[12]

Cheng, Z., et al., Journal of Alloys and Compounds (2023) 930, 166768

2023
[13]

Kareer, A., et al., Journal of Nuclear Materials (2019) 526, 151744

2019
[14]

El-Atwani, O., et al., Science Advances (2019) 5 (3), eaav2002

2019
[15]

El-Atwani, O., et al., Materials Today Energy (2021) 19, 100599

2021
[16]

El Atwani, O., et al., Nature Communications (2023) 14 (1), 2516

2023
[17]

Qiu, R., et al., Journal of Nuclear Materials (2024) 599, 155259

2024
[18]

K., et al., Materials & Design (2022) 223, 111239

Iroc, L. K., et al., Materials & Design (2022) 223, 111239

2022
[19]

Ozalp, A., et al., Materials Characterization (2024) 209, 113679

2024
[20]

U., et al., Journal of Alloys and Compounds (2023) 930, 167386

Tukac, O. U., et al., Journal of Alloys and Compounds (2023) 930, 167386

2023
[21]

Rao, Z., et al., Science (2022) 378 (6615), 78

2022
[22]

Hsu, W.-L., et al., Nature Reviews Chemistry (2024) 8 (6), 471

2024
[23]

Lin, Y ., et al., Acta Materialia (2020) 196, 133

2020
[24]

N., et al., Current Opinion in Solid State and Materials Science (2018) 22 (3), 65

Osetsky, Y . N., et al., Current Opinion in Solid State and Materials Science (2018) 22 (3), 65

2018
[25]

Zhu, B., et al., Computational Materials Science (2025) 246, 113341

2025
[26]

Granberg, F., et al., Physical Review Letters (2016) 116 (13), 135504

2016
[27]

Wei, G., et al., Acta Materialia (2024) 274, 119991

2024
[28]

Zhao, S., Journal of Materials Science & Technology (2020) 44, 133

2020
[29]

El-Atwani, O., et al., Acta Materialia (2018) 149, 206

2018
[30]

Yi, X., et al., Acta Materialia (2016) 112, 105

2016
[31]

Yi, X., et al., Nuclear Materials and Energy (2019) 18, 93

2019
[32]

Tunes, D

M.A. Tunes, D. P., B. Sun, P. Willenshofer, S. Samberger, B.K. Derby, J.K.S. Baldwin, S.J. Fensin, D. Sobieraj, J.S. Wróbel, J. Byggmästar, S. Pogatscher, E. Martinez, D. Nguyen - Manh, O. El-Atwani, arXiv:2406.15022 (2024)

2024 arXiv
[33]

Cheng, Z., et al., Materials Characterization (2024) 216, 114252

2024
[34]

N., Journal of Nuclear Materials (2003) 323 (2), 229

Trinkaus, H., and Singh, B. N., Journal of Nuclear Materials (2003) 323 (2), 229

2003
[35]

R., et al., Acta Materialia (2021) 213, 116951

Deluigi, O. R., et al., Acta Materialia (2021) 213, 116951

2021
[36]

Zhai, Y .-X., et al., Scripta Materialia (2024) 242, 115930

2024
[37]

Sizmann, R., Journal of Nuclear Materials (1978) 69-70, 386

1978
[38]

R., Physical Review (1957) 107 (2), 463

Waite, T. R., Physical Review (1957) 107 (2), 463

1957
[39]

A., Journal of Nuclear Materials (1978) 75 (1), 32

Nichols, F. A., Journal of Nuclear Materials (1978) 75 (1), 32

1978
[40]

H., Journal of Physics and Chemistry of Solids (1957) 3 (1), 121

Vineyard, G. H., Journal of Physics and Chemistry of Solids (1957) 3 (1), 121

1957
[41]

P., et al., Computer Physics Communications (2022) 271, 108171

Thompson, A. P., et al., Computer Physics Communications (2022) 271, 108171

2022
[42]

Byggmästar, J., et al., Physical Review Materials (2022) 6 (8), 083801

2022
[43]

Nordlund, K., et al., Physical Review B (1998) 57 (13), 7556

1998
[44]

Stukowski, A., Modelling and Simulation in Materials Science and Engineering (2010) 18 (1), 015012

2010

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [1]

J., and Was, G

Zinkle, S. J., and Was, G. S., Acta Materialia (2013) 61 (3), 735

work page 2013

[2] [2]

Lu, C., et al., Nature Communications (2016) 7 (1), 13564

work page 2016

[3] [3]

Aydogan, E., et al., Acta Materialia (2017) 134, 116

work page 2017

[4] [4]

Han, W., et al., Advanced Materials (2013) 25 (48), 6975

work page 2013

[5] [5]

Sun, C., et al., Scientific Reports (2015) 5 (1), 7801

work page 2015

[6] [6]

Aydogan, E., et al., Journal of Nuclear Materials (2017) 487, 96

work page 2017

[7] [7]

A., et al., Nanoscale (2021) 13 (48), 20437

Tunes, M. A., et al., Nanoscale (2021) 13 (48), 20437

work page 2021

[8] [8]

Agarwal, S., et al., Journal of Applied Physics (2022) 131 (12), 125903

work page 2022