Atomistic Insights into the Irradiation Effects in Molybdenum
Call for Paper, 25 January 2025. Please submit your manuscript via online system or email at editor@ijew.io

ISSN E 2409-2770
ISSN P 2521-2419

Atomistic Insights into the Irradiation Effects in Molybdenum


Waqas Akhtar, M. Mustafa Azeem, Muhammad Bilal Khan


Vol. 9, Issue 12, PP. 187-192, December 2022

DOI

Keywords: Molecular dynamics, Molybdenum, Primary defect formation, Defect clusters, atomic scale

Download PDF


 In this study, we examined the impact of energies of 2.54 keV and 5 keV displacement cascades in molybdenum (Mo) using an atomistic simulation at 300 K. The simulation was carried out using machines learning developed spectral neighbor analysis potential (SNAP). We computed displacement threshold energy ( ), vacancy formation energy ( , interstitial formation energy ( ), interstitial cluster formation energy ( ), activation energy barrier of interstitial , activation energy barrier of vacancy ( ), elastic properties, i.e., shear, bulk, young modulus, poison ratio. The simulations for primary displacement cascades were performed over a statistical average of 20 independent molecular dynamics simulations such that peak time and the surviving number of defects are inversely proportional to the incident energy of primary knock-on atoms (EPKA). Additionally, it is established that the number of clusters (Nclusters) during displacement cascades is directly proportional to EPKA. Furthermore, it was revealed that the number of interstitial clusters is higher than the number of vacancy clusters. This research will provide atomic insight into the interactions of defects in Mo for the development of structural materials for high temperature applications.


  1. Waqas Akhtar, waqas666@hrbeu.edu.cn, College of Material Science & Engineering, Harbin Institute of Technology, Harbin, 150001, China.
  2. Mustafa Azeem, ravian20052007@gmail.com, Department of Civil, Architectural, and Environmental Engineering, Missouri University of Science and Technology, Rolla, MO, 65409, USA.
  3. Muhammad Bilal Khan, m.bilalkhan@giki.edu.pk, Department of Mechanical Engineering, Ghulam Ishaq Khan Institute of Engineering and Technology, Topi, Swabi 23640, KP, Pakistan.

Waqas Akhtar M. Mustafa Azeem Muhammad Bilal Khan “Atomistic Insights into the Irradiation Effects in Molybdenum” International Journal of Engineering Works Vol. 9 Issue 12 PP. 187-192 December 2022. https://doi.org/10.34259/ijew.22.912187192.


[1]          G. S. Was and P. L. Andresen, “G. S. Was and P. L. Andresen, Radiation damage to structural alloys in nuclear power plants: Mechanisms and remediation. 2014.,” Mech. Remediat., 2014.

[2]          P. M. Raole and S. P. Deshpande, “Structural materials for fusion reactors,” Trans. Indian Inst. Met., vol. 62, no. 2, pp. 105–111, 2009, doi: 10.1007/s12666-009-0014-0.

[3]          S. J. Zinkle and G. S. Was, ‘Materials challenges in nuclear energy,’ Acta Mater., vol. 61, no. 3, pp. 735– 758, 2013, doi: 10.1016/j.actamat.2012.11.004.”

[4]          H. G. Kim, J. H. Yang, W. J. Kim, and Y. H. Koo, “Development Status of Accident-tolerant Fuel for Light Water Reactors in Korea,” Nucl. Eng. Technol., vol. 48, no. 1, pp. 1–15, 2016, doi: 10.1016/j.net.2015.11.011.

[5]          S. P. Chakraborty, S. Banerjee, I. G. Sharma, and A. K. Suri, ‘Development of silicide coating over Molybdenum based refractory alloy and its characterization,’ J. Nucl. Mater., vol. 403, . 1–3, pp. 152–159, 2010, doi: 10.1016/j.jnucmat.2010.06.014.”

[6]          T.H. Webster, B.L. Eyre, E.A. Terry, Irradiation Embrittlement and Creep in Fuel Cladding and Core Components, The British Nuclear Energy Society, London, 1972.”

[7]          K. Nordlund, A. . Sand, F. Granberg, S. . Zinkle, and R. Stoller, “Primary Radiation Damage in Materials Review: Review of Current Understanding and Proposed New Standard Displacement Damage Model to Incorporate in Cascade Defect Production Efficiency and Mixing Effects,” Oecd/Nea, vol. NEA/NSC/DO, 2015.

[8]          A. M. Mustafa, Z. Li, and L. Shao, “Molecular Dynamics Simulations of Damage Cascades Creation in Oxide-Particle-Embedded Fe.,” in 25th International Conference on Nuclear Engineering,ASME, 2017, vol. 5, pp. 1–5, doi: 10.1115/ICONE25-67356.

[9]          M. M. Azeem, D. Yun, and M. Zubair, “Atomic insights on interaction mechanism of dislocation with void/impurity/ precipitates in bcc iron,” Int. Conf. Nucl. Eng. Proceedings, ICONE, vol. 2, pp. 1–7, 2021, doi: 10.1115/ICONE28-65197.

[10]        M. M. Azeem, Q. Wang, Z. Li, and Y. Zhang, “Dislocation-oxide interaction in Y2O3 embedded Fe: A molecular dynamics simulation study,” Nucl. Eng. Technol., vol. 52, no. 2, pp. 337–343, 2020, doi: 10.1016/j.net.2019.07.011.

[11]        M. M. Azeem, Q. Wang, and M. Zubair, “Atomistic simulations of nanoindentation response of irradiation defects in iron,” Sains Malaysiana, vol. 48, no. 9, pp. 2029–2039, 2019, doi: 10.17576/jsm-2019-4809-24.

[12]        M. M. Azeem, Q. Wang, Y. Zhang, S. Liu, and M. Zubair, “Effect of Grain Boundary on Diffusion of P in Alpha-Fe: A Molecular Dynamics Study,” Front. Phys., vol. 7, no. 97, pp. 1–7, 2019, doi: 10.3389/fphy.2019.00097.

[13]        M. Mustafa Azeem, K. Abd El Gawad, M. Zubair, S. A. Ibrahim, M. Ado, and G. Mehdi, “Radiation damage effects in oxide dispersion strengthened steel alloys,” in International Conference on Nuclear Engineering, Proceedings, ICONE, 2019, doi: 10.1299/jsmeicone.2019.27.2086.

[14]        M. M. Azeem, Z. Li, Q. Wang, and M. Zubair, “Molecular dynamics studies and irradiation effects in ODSS alloys,” Int. J. Nucl. Energy Sci. Technol., vol. 12, no. 4, pp. 381–399, 2018, doi: 10.1504/IJNEST.2018.10018247.

[15]        M. M. Azeem, Z. Li, Q. Wang, Q. M. N. Amjad, M. Zubair, and O. M. H. Ahmed, “Classical molecular dynamics study for defect sink behavior in oxide dispersed strengthened alloys,” in Proceedings of 2018 15th International Bhurban Conference on Applied Sciences and Technology, IBCAST 2018, 2018, pp. 12–15, doi: 10.1109/IBCAST.2018.8312177.

[16]        M. M. Azeem, Z. Li, Q. Wang, and A. Hussian, “Molecular Dynamics Simulation Study on the Possible Factors Affecting Stability of ODS Steel,” in IOP Conference Series: Materials Science and Engineering, Jul. 2018, vol. 389, p. 012003, doi: 10.1088/1757-899X/389/1/012003.

[17]        Plimpton S."Fast parallel algorithms for short-range molecular dynamics", . Journal of computational physics, 1995, 117(1): 1-19.”

[18]        Y. Zuo, C. Chen, X. Li, Z. Deng, Y. Chen, J. Behler, G. Csányi, A.V. Shapeev, A.P. Thompson, M.A. Wood, and S.P. Ong (2020), ‘Performance and Cost Assessment of Machine Learning Interatomic Potentials’, The Journal of Physical Chemistry A, 124(4), 731-745.”

[19]        C. Chen, Z. Deng, R. Tran, H. Tang, I. H. Chu, and S. P. Ong, ‘Accurate force field for molybdenum by machine learning large materials data,’ Phys. Rev. Mater., vol. 1, no. 4, pp. 1–10, 2017, doi: 10.1103/PhysRevMaterials.1.043603.”

[20]        N. V Doan and R. Vascon, “Displacement cascades in metals and ordered alloys. Molecular dynamics simulations,” Nucl. Instruments Methods Phys. Res. Sect. B Beam Interact. with Mater. Atoms, vol. 135, no. 1, pp. 207–213, 1998, doi: 10.1016/S0168-583X(97)00653-8.

[21]        S. Zheng and S. Wang, “First-principles design of refractory high entropy alloy VMoNbTaW,” Entropy, vol. 20, no. 12, 2018, doi: 10.3390/e20120965.

[22]        P. C. De Camargo, F. R. Brotzen, and S. Steinemann, “Thermal expansion and elastic properties of Nb-Mo alloys,” J. Phys. F Met. Phys., vol. 17, no. 5, pp. 1065–1079, 1987, doi: 10.1088/0305-4608/17/5/008.

[23]        A. M. Ougouag, C. A. Wemple, and C. D. Van Siclen, “Displacement Kerma Cross Sections For Neutron Interactions In Molybdenum,” 2004.

[24]        Maury F, Vajda P, Biget M. Anisotropy of the displacement energy in single crystals of molybdenum[J]. Radiation Effects, 1975, 25(3): 175–185.”

[25]        “Pramana J. Phys., Vol. 72, No. 5. Self-interstitial configuration in molybdenum studied by modified analytical embedded atom method.”

[26]        M. J. Norgett, M. T. Robinson, and I. M. Torrens, ‘A proposed method of calculating displacement dose rates,’ Nucl. Eng. Des., vol. 33, no. 1, pp. 50–54, 1975, doi: 10.1016/0029-5493(75)90035-7.”

[27]        Hong J, Hu Z, Probert M. disulphide monolayers[J]. Nature Communications, Nature Publishing Group, 2015, 6: 1–8.”

[28]        S. V Starikov et al., “Radiation-induced damage and evolution of defects in Mo,” Phys. Rev. B - Condens. Matter Mater. Phys., vol. 84, no. 10, pp. 1–8, 2011, doi: 10.1103/PhysRevB.84.104109.

[29]        Azároff L V. Role of Crystal Structure in Diffusion. I. Diffusion Paths in Closest?Packed Crystals[J]. Journal of Applied Physics, 32(9), 1658–1662.1961.”

[30]        Sizmann R. The effect of radiation upon diffusion in metals[J]. Journal of Nuclear Materials, Volumes 69: 386–412.”

[31]        Heald P N K & P T. Point defects in molybdenum[J]. Philosophical Magazine, 1974: 1137–1147.”

[32]        Dehlinger U. Solid State Physics. Physical Review Materials, 1956, 9: 1–139.”

[33]        L. Bukonte, T. Ahlgren and K H. Modelling of monovacancy diffusion in W over wide temperature range. Applied Physics, 2014.”

[34]        Ma, P.-W., & DUDAREV S L. Effect of stress on vacancy formation and migration in body-centered-cubic metals[J]. Physical Review Materials, 2019, 3.”

[35]        Q. U. A. Sahi and Y. S. Kim, “Primary radiation damage characterization of ?-iron under irradiation temperature for various PKA energies,” Mater. Res. Express, vol. 5, no. 4, 2018, doi: 10.1088/2053-1591/aabb6f.

[36]        M. J. Demkowicz, P. Bellon, and B. D. Wirth, “Atomic-scale design of radiation-tolerant nanocomposites,” MRS Bull., vol. 35, no. 12, pp. 992–998, 2010, doi: 10.1557/mrs2010.704.

[37]        D. H. R. R.E. H. Clark, Nuclear Fusion Research understanding plasma-surface. 2005.

[38]        C. S. Becquart and C. Domain, “Modeling microstructure and irradiation effects,” Metall. Mater. Trans. A, vol. 42, no. 4, pp. 852–870, 2011, doi: 10.1007/s11661-010-0460-7.

[39]        G. S. Was et al., “Emulation of reactor irradiation damage using ion beams,” Scr. Mater., vol. 88, 2014, doi: 10.1016/j.scriptamat.2014.06.003.

[40]        J. B. GIBSON, A. N. GOLAND, M. MILGRAM and G H V. Dynamics of Radiation Damage[J]. Physical Review, 1960, 120.”

[41]        C. P. Chui, W. Liu, Y. Xu, and Y. Zhou, “Molecular Dynamics Simulation of Iron - A Review,” Spin, vol. 5, no. 4, pp. 1–36, 2015, doi: 10.1142/S201032471540007X.

[42]        N. P. Lazarev and A. S. Bakai, “Atomistic simulation of primary damages in Fe, Ni and Zr,” J. Supercrit. Fluids, vol. 82, pp. 22–26, 2013, doi: 10.1016/j.supflu.2013.06.002.

[43]        C. S. Becquart et al., “Modeling the long-term evolution of the primary damage in ferritic alloys using coarse-grained methods,” J. Nucl. Mater., vol. 406, no. 1, pp. 39–54, 2010, doi: 10.1016/j.jnucmat.2010.05.019.

[44]        O. El-Atwani, J. E. Nathaniel, A. C. Leff, K. Hattar, and M. L. Taheri, “Direct Observation of Sink-Dependent Defect Evolution in Nanocrystalline Iron under Irradiation,” Sci. Rep., vol. 7, no. 1, pp. 1–12, 2017, doi: 10.1038/s41598-017-01744-x.

[45]        E. G. Hayward, “Atomistic Studies of Defects in Bcc Iron: Dislocations and Gas Bubbles,” no. August, 2012.

[46]        R. E. Stoller, “Role of cascade energy and temperature in primary defect formation in iron,” J. Nucl. Mater., vol. 276, no. 1, pp. 22–32, 2000, doi: 10.1016/S0022-3115(99)00204-4.

[47]        Y.N. Osetsky, D. Bacon, V. Mohles, Atomic modelling of strengthening mechanisms due to voids and copper precipitates in ?-iron, Philosophical magazine, 83 (2003) 3623-3641.”

[48]        K. P. Zolnikov, A. V. Korchuganov, and D. S. Kryzhevich, “Molecular dynamics simulation of primary radiation damage in Fe-Cr alloy,” J. Phys. Conf. Ser., vol. 774, no. 1, 2016, doi: 10.1088/1742-6596/774/1/012130.