# Formation of Interstitial Dislocation Loops by Irradiation in Alpha-Iron under Strain: A Molecular Dynamics Study

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## Abstract

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## 1. Introduction

_{d,i}, which is known as the threshold displacement energy for a structure in a specific direction, i, over a sufficient number of displacement directions. The average value is called E

_{d,avg}. For theoretical quantification of the radiation damage, the E

_{d,avg}is commonly used as a primary value for the Norgett–Robinson–Torrens (NRT) model [24]. Theoretically, the number of FPs generated under a cascade event is affected by E

_{d,avg}, thus E

_{d,avg}must be evaluated properly.

_{d,avg}value, and the number of FP’s generated at relatively low PKA energies. We first evaluated the average free and strained TDE (as an indicator for the energy needed to form the FP’s). The four different deposition energies of PKA (namely, 1, 3, 6, and 10 keV) were then examined, and six strain magnitudes (i.e., −1.4, −0.8, −0.2, 0.4, 1.0, and 1.6%) were hydrostatically applied. We further studied the peak number and the number of survived FPs as well as the efficiency of the defect production during collision cascades.

## 2. Methods

#### 2.1. Threshold Displacement Energy Calculation

_{d,i}over a set of i directions, i.e., E

_{d.avg}; likewise, the average strained TDE is defined as ${E}_{d,avg}^{strained}$. To evaluate E

_{d.avg}accurately, we followed the recommended settings, which were reported in our previous work [25].

_{d,i}, i.e., ${E}_{d,i}^{strained}$. A systematic averaging of four ${E}_{d,i}^{strained}$ of different simulation timings (0, 50, 100, and 150 fs) was applied. This averaging was conducted to overcome the deviation of the ${E}_{d,i}^{strained}$ calculation that would be raised from the thermal vibration effect at 30 K [30]. For the evaluation of the directional effect, the (E

_{d,avg}) of the 210 irreducible crystal directions (ICD) were evaluated for free-strained structure. The method for ICD directions preparation was reported previously [25,30]; however, the ${E}_{d,avg}^{strained}$ evaluation is conducted over 300 quasi-uniform directions.

#### 2.2. The Collision Cascades Evaluation under Strain

#### 2.3. Calculation of Point Defects and Dislocation Formation Energies

_{f}) can be calculated as follows:

_{df}and E

_{perf}are the energy of the system with defects, and the energy of the intact structure without defects, respectively. The number of system atoms, including those with defects, is referred to as N

_{df}, and those of intact structures without defects are referred to as Nperf.

## 3. Results and Discussion

_{d}under strain.

#### 3.1. Evaluation and Validation of Free Strained E_{d} as Compared with DFT, MD and Theoretical Model Results

_{d,avg}by DFT calculation is 32 eV [32], while with the current EAM MD potential, the value is 38.6 ± 2 eV. Thus, both results are comparably reasonable considering the MD error of calculation settings for E

_{d,avg}. Although E

_{d<100>,MD}and E

_{d<110>,MD}are comparable with DFT results (Table S1 and Figure S2), the largest discrepancy between DFT and our EAM-MD was found for the close-packed <111> direction. The large discrepancy between DFT and MD of <111> would be related to the “focused collision sequence”. It is worthy to note that the reentry of atoms to the supercell image hardly affects the simulation result for displacement at the 30 K recoil simulation with non-cubic supercell (8 × 8 × 12) in which the E

_{d<111>}= 43 eV. For cubic supercell, the 8 × 8 × 8 shows the low value (E

_{d<111>}= 18.5 eV) even with a small number of system atoms compared with 16 × 16 × 16 that has E

_{d<111>}= 36.25 eV (Table S2 and Figure S3). Nevertheless, the evaluated E

_{d,avg}with non-cubic supercell converged faster, and the atom’s reentrant effect was not noticed for most of the 210 ICD directions (Figure S3). Therefore, the 8 × 8 × 12 system for E

_{d,avg}evaluation was reasonable (E

_{d,avg}= 38.6 eV ± 2 eV) when compared to DFT results (32 eV), even though the 8 × 8 × 8 systems resulted in smaller E

_{d,<111>}value.

_{d,min<100>}of α-Fe ranges from 13 to 29 eV, which is comparable with our calculations [33]. We found that the current MD E

_{d,avg}was around 3 eV lower than the previously reported value (E

_{d,avg}41.8 eV) [34]. This difference is due to the value of ΔE

_{step,}which was used in both cases, where it is 1 eV in our study, while it was 5 eV in another study [34], which induces an error by 2 eV approximately. Although the value of E

_{d,avg}obtained in the present work was slightly different from that of the ASTM standard (40 eV) [35], the used EAM potential model can still probably describe the interatomic interactions of recoils in contrast to other EAM potentials. For consistency, the entire calculations used the same EAM potential model.

_{d,min}is only confirmed for <100> direction as E

_{d,min<100>,MD}= 20 eV, and E

_{d,min<100>,EXP}= 17 eV, but not for other directions due to the technical limitation in setting the <111> and <110> directions precisely [36].

_{d,i}has the most stable and the slowest deviation changes with angles up to 25° (Figure S4).

_{d,avg}is 23 eV [32,37]; however, the re-calculated E

_{d,avg}for 210 ICD directions is 23.7 eV. The disadvantage of See- ger’s equation is the limitation of the evaluated E

_{d,i}, which is dependent on the values of; E

_{d,<100>}= 17 eV, E

_{d,<110>}= 30 eV, and E

_{d,<111>}= 20 eV, which were obtained experimentally [36]. From a technical standpoint, the values of E

_{d,<110>}and E

_{d,<111>}were not as accurate as of that E

_{d,<100>}. Hence, the relation proposed by Jan and Seeger seems to be ineffective for estimating E

_{d,avg}when compared with our MD results (see Figure S5). Thus, we presented an accurate method to evaluate E

_{d,avg}, which is an important value to estimate the number of FPs formation under cascade events.

#### 3.2. Evaluation of the Strain Effect on E_{d,avg} Value

_{d,avg}$({E}_{d,avg}^{strained}$) are shown in Figure 2a. The ${E}_{d,avg}^{strained}$ increases by moving from tension to compression for both uniaxial and hydrostatic strains, which is in harmony with the results reported in our previous work of bcc materials (W,Mo) [38] and in line with the results reported in Beeler’s work for Fe, which was hydrostatically strained by +2% [39]. The hydrostatic strain increases or decreases E

_{d,avg}considerably in comparison with the uniaxial strain. As presented in Figure 2b, the uniaxial strain shows a minimal effect on changes the ${E}_{d,avg}^{strained}$ compared with the hydrostatic strain given that the amplitude of the strain is fixed. The proportional correlation between strain and defects is the correlation between defects and volume changes induced by strain [40], and such confirmation is shown in Figure 2b despite the strain type.

_{d,i}. TCR of 1.6% and −1.4% were obtained. The TCRs results in over 300 directions are shown in Figure S6. However, the general tendency is that TCRs become negative for tensile strain while becoming positive for compressive strain in most directions.

_{11}, C

_{12}, and C

_{44,}for a cubic crystal. Furthermore, the bulk modulus B and tetragonal shear constant C’ are related to C

_{11}and C

_{12}, i.e., B = 1/3(C

_{11}+ 2C

_{12}), C’ = ½(C

_{11}− C

_{12}). The applied EAM interatomic potential shows a correct description of the elastic moduli of Fe. The values are 2.84 Å, 173.1 GPa, 121.9 GPa, and 52.5 GPa for lattice constant, B, C

_{44}, and C’, respectively [27]. The elastic stiffness constants described by the EAM potential are nicely confirmed with the DFT results [41], which in terms agrees well with the experiments values [42].

#### 3.3. Strain Effect on Collision Cascade Event and FP Formation

_{de}is the nuclear deposition energy, which is estimated to be substituted with the deposition collision energy carried by PKA for cascades. Furthermore, E

_{d}was set to be ~39 eV according to our calculations in Section 3.1 and Section 3.2. Under compressed strains, the peak number of FPs occurred earlier, while under tensile strains, the peaks reached a great height and extended for a longer time (Figure 3). The peak time is one of the main ballistic phase specifications, and it is defined as the period between the initiations of the events until the maximum number of FPs formation is reached. However, most of the defects return to their original lattice locations during recombination time. The strain effects lead to different volume changes affecting the size of the displacement cascade that affect the number of created FPs [43].

_{d}value, then the FPs will be recombined, and energy will be dissipated over the entire volume of atoms [16]. In contrast, the FP will be generated if the transferred recoil energy is ≥E

_{d}. Because E

_{d}tended to decrease from compression to tension, as described in Section 3.2, more FPs are generated with the tensile strain (Figure 3). Furthermore, if the tensile-strained structure is subjected to high PKA energy, the collided atoms rapidly move far away from the parent atoms, which reduces the chances of FPs recombination and results in a higher number of FPs. In comparison, once the structure is compressed, E

_{d}increases, and atoms get closer to one another; hence the transferred energy equally distributes over a larger number of atoms, and more collisions occur without defect generation.

#### 3.4. Effects of Strain on the Formation of Interstitial Dislocation Loop

#### 3.5. Additional Analysis: Defect Production Efficiency under Strain

_{FP}/N

_{NRT}, as shown in Figure 6a, while Figure 6b is the deformed NRT dis- placements (i.e., the estimated number of FPs by the NRT theoretical model and the value of the E

_{d,j (∆V)}-substituted form ${E}_{d,avg}^{strained}$ in Figure 2b). Figure 6a shows the defect production efficiency for strained conditions as a function of PKA energy; defect production efficiency showed similar trends for all strain conditions at 1 and 3 keV; this relation was disturbed at larger PKA energies (especially for 10 keV). In general, the defect production efficiency decreases as PKA increases (from 1~6 keV). However, for 10 keV and under larger tensile strains, the efficiency relation starts to increase. This is because the dislocation loop formation generates further defects, as clarified in Section 3.4 thereby, the efficiency increased again. This shows the sensitivity and complexity nature of the collision events and defect formation and confirms the inconsistency between the theoretical linear relation of the NRT model and the experimental results. Accordingly, the need for the NRT model development was recently suggested by Norland [46].

## 4. Conclusions

_{d}when moving from compression to tension. Hence, more interstitials are likely to accumulate from the FPs at peak time. From the accumulated FPs, the formation energy of the interstitial dislocation loop becomes more stable with a 2 eV reduction compared with the mono interstitial formation energy under tensile strain. In addition, the formation energy of the interstitial dislocation loop, and ${E}_{d,avg}^{strained}$ can be directly used for theoretical models, such as evaluating defect formation by use of the NRT model, which can also be useful for multiscale modeling work.

## Supplementary Materials

_{d,i}) of the current MD study with the DFT study, Figure S3: the system size and shape effect on the E

_{d,avg}evaluation by MD, Figure S4: the angle deviation of E

_{d,i}from the <100>, <110>, <111>, and <321> directions, Figure S5: (a) 210 ICD directions applied to generate 210

**E**

_{d,i}by applying the Seeger theoretical model. (b) The Seeger and the MD differences for E

_{d,i}calculation (ΔE

_{d,I}= E

_{d,i}

_{, theory of each value of 210 ICD}− E

_{d,i}

_{, MD}), Figure S6: The threshold displacement energy change rate (TCR) when structure deformed for 300 specific directions at 30 K. (a) is for uniaxial tensile strain and (b) is for uniaxial compression strain, Figure S7: the formation energy of ½<111> dislocation loop with 7 SIAs and as compared with single <110> defects x 7, Table S1: the comparison of the MD and DFT directional threshold displacement energy (E

_{d,i}) ( i = <100>, <110> and <111>) and the average threshold displacement energy (E

_{d,avg}) values referenced to the experiential results, Table S2: E

_{d,i}values for <111> direction with several supercells in the 0 K recoil simulation.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

- Kilic, M.E.; Alaei, S. Structural properties of β-Fe
_{2}O_{3}nanorods under compression and torsion: Molecular dynamics simulations. Curr. Appl. Phys.**2018**, 18, 1352–1358. [Google Scholar] [CrossRef] - Crocombette, J.-P.; Willaime, F. Ab Initio Electronic Structure Calculations for Nuclear Materials; Elsevier: Amsterdam, The Netherlands, 2012. [Google Scholar] [CrossRef]
- Stoller, R.E. Point defect survival and clustering fractions obtained from molecular dynamics simulations of high energy cascades. J. Nucl. Mater.
**1996**, 233-237, 999–1003. [Google Scholar] [CrossRef] [Green Version] - Bacon, D.J.; Calder, A.F.; Harder, J.M.; Wooding, S.J. Computer simulation of low-energy displacement events in pure bcc and hcp metals. J. Nucl. Mater.
**1993**, 205, 52–58. [Google Scholar] [CrossRef] - Gao, F.; Bacon, D.; Calder, A.; Flewitt, P.; Lewis, T. Computer simulation study of cascade overlap effects in α-iron. J. Nucl. Mater.
**1996**, 230, 47–56. [Google Scholar] [CrossRef] - Gao, F.; Bacon, D.; Flewitt, P.; Lewis, T. A molecular dynamics study of temperature effects on defect production by displacement cascades in α-iron. J. Nucl. Mater.
**1997**, 249, 77–86. [Google Scholar] [CrossRef] - Becquart, C.S.; Decker, K.M.; Domain, C.; Ruste, J.; Souffez, Y.; Turbatte, J.C.; Van Duysen, J.C. Massively parallel molecular dynamics simulations with EAM potentials. Radiat. Eff. Defects Solids
**1997**, 142, 9–21. [Google Scholar] [CrossRef] - Stoller, R.E.; Greenwood, L.R. Subcascade formation in displacement cascade simulations: Implications for fusion reactor materials. J. Nucl. Mater.
**1999**, 271-272, 57–62. [Google Scholar] [CrossRef] - Malerba, L. Molecular dynamics simulation of displacement cascades in α-Fe: A critical review. J. Nucl. Mater.
**2006**, 351, 28–38. [Google Scholar] [CrossRef] - Phythian, W.; Stoller, R.; Foreman, A.; Calder, A.; Bacon, D. A comparison of displacement cascades in copper and iron by molecular dynamics and its application to microstructural evolution. J. Nucl. Mater.
**1995**, 223, 245–261. [Google Scholar] [CrossRef] - Vascon, R.; Doan, N.V. Molecular dynamics simulations of displacement cascades in α-iron. Radiat. Eff. Defects Solids
**1997**, 141, 375–394. [Google Scholar] [CrossRef] - Averback, R.; DE LA Rubia, T.D. Displacement Damage in Irradiated Metals and Semiconductors; Academic Press: Cambridge, MA, USA, 1997. [Google Scholar] [CrossRef]
- Soneda, N.; De La Rubia, T.D. Defect production, annealing kinetics and damage evolution in α-Fe: An atomic-scale computer simulation. Philos. Mag. A
**1998**, 78, 995–1019. [Google Scholar] [CrossRef] - Robinson, M.; Marks, N.A.; Lumpkin, G.R. Sensitivity of the threshold displacement energy to temperature and time. Phys. Rev. B
**2012**, 86, 1–8. [Google Scholar] [CrossRef] - Psakhie, S.G.; Zolnikov, K.P.; Kryzhevich, D.S.; Zheleznyakov, A.V.; Chernov, V.M. Evolution of atomic collision cascades in vanadium crystal with internal structure. Crystallogr. Rep.
**2009**, 54, 1002–1010. [Google Scholar] [CrossRef] - Was, G.S. Fundamentals of Radiation Materials Science: Metals and Alloys; Springer: Heidelberg, Germany, 2016. [Google Scholar]
- R. Bullough Atomic Energy Research Establishment Harwell Berkshire England; Eyre, B.L.; Perrin, R.C. The Growth and Stability of Voids in Irradiated Metals. Nucl. Appl. Technol.
**1970**, 9, 346–355. [Google Scholar] [CrossRef] - Masters, B.C. Dislocation loops in irradiated iron. Philos. Mag.
**1965**, 11, 881–893. [Google Scholar] [CrossRef] - Dudarev, S.L.; Bullough, R.; Derlet, P.M. Effect of theα−γPhase Transition on the Stability of Dislocation Loops in bcc Iron. Phys. Rev. Lett.
**2008**, 100, 135503. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Yao, Z.; Jenkins, M.; Hernández-Mayoral, M.; Kirk, M. The temperature dependence of heavy-ion damage in iron: A microstructural transition at elevated temperatures. Philos. Mag.
**2010**, 90, 4623–4634. [Google Scholar] [CrossRef] - Arakawa, K.; Ono, K.; Isshiki, M.; Mimura, K.; Uchikoshi, M.; Mori, H. Observation of the One-Dimensional Diffusion of Nanometer-Sized Dislocation Loops. Science
**2007**, 318, 956–959. [Google Scholar] [CrossRef] [Green Version] - Kaletta, D. The Role of Gases in Radiation Damage Patterns; Kernforschungszentrum Karlsruhe, Kaletta Institut für Material- und Festkörperforschung: Karlsruhe, Germany, 1979. [Google Scholar]
- Barrow, A.; Korinek, A.; Daymond, M. Evaluating zirconium–zirconium hydride interfacial strains by nano-beam electron diffraction. J. Nucl. Mater.
**2013**, 432, 366–370. [Google Scholar] [CrossRef] - Norgett, M.; Robinson, M.; Torrens, I. A proposed method of calculating displacement dose rates. Nucl. Eng. Des.
**1975**, 33, 50–54. [Google Scholar] [CrossRef] - Banisalman, M.J.; Park, S.; Oda, T. Evaluation of the threshold displacement energy in tungsten by molecular dynamics calculations. J. Nucl. Mater.
**2017**, 495, 277–284. [Google Scholar] [CrossRef] - Plimpton, S. Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput. Phys.
**1995**, 117, 1–19. [Google Scholar] [CrossRef] [Green Version] - Dudarev, S.L.; Derlet, P.M. A ‘magnetic’ interatomic potential for molecular dynamics simulations. J. Phys. Condens. Matter
**2005**, 17, 7097–7118. [Google Scholar] [CrossRef] - Björkas, C.; Nordlund, K.; Dudarev, S. Modelling radiation effects using the ab-initio based tungsten and vanadium potentials. Nucl. Instruments Methods Phys. Res. Sect. B Beam Interactions Mater. Atoms.
**2009**, 267, 3204–3208. [Google Scholar] [CrossRef] - Rycroft, C.H. VORO++: A three-dimensional Voronoi cell library in C++. Chaos Interdiscip. J. Nonlinear Sci.
**2009**, 19, 041111. [Google Scholar] [CrossRef] [Green Version] - Robinson, M.; Marks, N.A.; Whittle, K.R.; Lumpkin, G.R. Systematic calculation of threshold displacement energies: Case study in rutile. Phys. Rev. B
**2012**, 85, 104105. [Google Scholar] [CrossRef] - Stukowski, A. Visualization and analysis of atomistic simulation data with OVITO—The Open Visualization Tool. Model. Simul. Mater. Sci. Eng.
**2009**, 18, 15012. [Google Scholar] [CrossRef] - Olsson, P.; Becquart, C.S.; Domain, C. Ab initio threshold displacement energies in iron. Mater. Res. Lett.
**2016**, 4, 219–225. [Google Scholar] [CrossRef] [Green Version] - Park, S.; Banisalman, M.J.; Oda, T. Characterization and quantification of numerical errors in threshold displacement energy calculated by molecular dynamics in bcc-Fe. Comput. Mater. Sci.
**2019**, 170, 109189. [Google Scholar] [CrossRef] - Setyawan, W.; Selby, A.P.; Juslin, N.; Stoller, R.E.; Wirth, B.D.; Kurtz, R.J. Cascade morphology transition in bcc metals. J. Physics: Condens. Matter
**2015**, 27, 225402. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Wechsler, M.S.; Lin, C.; Sommer, W.F.; Daemen, L.U.L.; Feguson, P.D. Standard Practice for Neutron Radiation Damage Simulation by Charged-Particle Irradiation; ASTM Stand E 521-96; ASTM International: West Conshohocken, PA, USA, 1996. [Google Scholar] [CrossRef]
- Maury, F.; Biget, M.; Vajda, P.; Lucasson, A.; Lucasson, P. Anisotropy of defect creation in electron-irradiated iron crystals. Phys. Rev. B
**1976**, 14, 5303–5313. [Google Scholar] [CrossRef] - Jan, R.V.; Seeger, A. Zur Deutung der Tieftemperatur-Elektronenbestrahlung von Metallen. Phys. Status Solidi
**1963**, 3, 465–472. [Google Scholar] [CrossRef] - Banisalman, M.J.; Oda, T. Atomistic simulation for strain effects on threshold displacement energies in refractory metals. Comput. Mater. Sci.
**2019**, 158, 346–352. [Google Scholar] [CrossRef] - Beeler, B.; Asta, M.; Hosemann, P.; Grønbech-Jensen, N. Effect of strain and temperature on the threshold displacement energy in body-centered cubic iron. J. Nucl. Mater.
**2016**, 474, 113–119. [Google Scholar] [CrossRef] [Green Version] - Beeler, B.; Asta, M.; Hosemann, P.; Grønbech-Jensen, N. Effects of applied strain on radiation damage generation in body-centered cubic iron. J. Nucl. Mater.
**2015**, 459, 159–165. [Google Scholar] [CrossRef] [Green Version] - Wang, H.; Guo, G.-Y. Gradient-corrected density functional calculation of structural and magnetic properties of BCC, FCC and HCP Cr. J. Magn. Magn. Mater.
**2000**, 209, 98–99. [Google Scholar] [CrossRef] - Kittel, C. Intro to Solid State Physics, 7th ed.; Wiley: New York, NY, USA, 1996. [Google Scholar]
- Wang, D.; Gao, N.; Wang, Z.; Gao, X.; He, W.; Cui, M.; Pang, L.; Zhu, Y. Effect of strain field on displacement cascade in tungsten studied by molecular dynamics simulation. Nucl. Instrum. Methods Phys. Res. Sect. B Beam Interact. Mater. Atoms.
**2016**, 384, 68–75. [Google Scholar] [CrossRef] - Calder, A.; Bacon, D.; Barashev, A.; Osetsky, Y. On the origin of large interstitial clusters in displacement cascades. Philos. Mag.
**2010**, 90, 863–884. [Google Scholar] [CrossRef] - Granberg, F.; Byggmästar, J.; Nordlund, K. Defect accumulation and evolution during prolonged irradiation of Fe and FeCr alloys. J. Nucl. Mater.
**2020**, 528, 151843. [Google Scholar] [CrossRef] - Nordlund, K.; Zinkle, S.J.; Sand, A.E.; Granberg, F.; Averback, R.S.; Stoller, R.; Suzudo, T.; Malerba, L.; Banhart, F.; Weber, W.J.; et al. Improving atomic displacement and replacement calculations with physically realistic damage models. Nat. Commun.
**2018**, 9, 1–8. [Google Scholar] [CrossRef]

**Figure 1.**Description of uniaxial and hydrostatic strain applications. The integrated table shows the variations in cell constants and volumes of free strained values (x

_{0}, y

_{0}, z

_{0}, V

_{0}) with a Δ of strain for each strain type.

**Figure 2.**(

**a**) Uniaxial and a hydrostatic correlation between ${E}_{d,avg}^{strained}$ and strain changes in α-Fe. (

**b**) Correlation between uniaxial and hydrostatic strain changes for ${E}_{d,avg}^{strained}$ as volume change. Every single point is the average value of over 300 quasi-uniform directions.

**Figure 3.**The evolution of as Frenkel pairs (FPs) created during the displacement cascade of 10 keV as volume change. Each point is the average of overall direction and timing, i.e., 16 different samples. A similar thermal spike trend for all given PKA energies was noticed; hence the typical behavior of damage evolution over time was shown with 10 keV.

**Figure 4.**(

**a**) The peak number of FP under strain conditions for primary knock-on atom (PKA) energies (1, 3, 6, and 10) keV as a function of hydrostatic strain (

**b**) number of survived FP after 20 ps, the black–box shows the ½<111> dislocation formation for <110> displacement collision direction at 10 keV. The error bar denotes the SEM over the selected samples (

**c**) Analysis of the ½<111> dislocation configuration and defect formation.

**Figure 5.**The formation energy of 7 self-interstitial atoms (SIAs) defects as a function of compression and tensile strain is denoted in black. The formation energy of ½<111> dislocation loop with 7 SIAs is denoted in blue. The energy difference between 7 SIAs defects and ½<111> dislocation loop is denoted in green.

**Figure 6.**(

**a**) The defect production efficiency, which is defined as the ratio between the molecular dynamics (MD) and the Norgett–Robinson–Torrens (NRT) result for defect calculations. (

**b**) Number of surviving Frenkel pairs for various PKA energies versus applied and hydrostatic strain from NRT model applications V

_{NRT}= 0.8 × E

_{pka}/2 E

_{dj(∆V)}[36].

**Table 1.**Dislocation occurrence probability (i.e., how many times dislocation appeared among the 16 different simulation sets). The only formed dislocation was ½<111> type.

PKA Energy (keV) | Probability Occurrence of ½<111> Dislocation Loops among the 16 Sets at 4.8% of Volume Change |
---|---|

1 | 0 |

3 | 1/16 |

6 | 7/16 |

10 | 7/16 |

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Bany Salman, M.; Emin Kilic, M.; Jaser Banisalman, M.
Formation of Interstitial Dislocation Loops by Irradiation in Alpha-Iron under Strain: A Molecular Dynamics Study. *Crystals* **2021**, *11*, 317.
https://doi.org/10.3390/cryst11030317

**AMA Style**

Bany Salman M, Emin Kilic M, Jaser Banisalman M.
Formation of Interstitial Dislocation Loops by Irradiation in Alpha-Iron under Strain: A Molecular Dynamics Study. *Crystals*. 2021; 11(3):317.
https://doi.org/10.3390/cryst11030317

**Chicago/Turabian Style**

Bany Salman, Mohammad, Mehmet Emin Kilic, and Mosab Jaser Banisalman.
2021. "Formation of Interstitial Dislocation Loops by Irradiation in Alpha-Iron under Strain: A Molecular Dynamics Study" *Crystals* 11, no. 3: 317.
https://doi.org/10.3390/cryst11030317