SpringerLink
Log in

The influence of lead on mechanical properties of BCC and FCC iron from a constructed bond-order potential

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

To design and apply liquid Pb as coolant in nuclear reactors, it is important to understand its atomic behaviors with the steel container through molecular dynamics (MD) simulations. A reliable and capable Fe–Pb potential is the key to the MD simulations. In this work, an analytical bond-order potential (BOP) of Fe–Pb has been constructed through the data-fitting of various phases from experiments and first-principles calculations. The newly constructed potential has a better performance in predicting different Fe–Pb phases than the Fe–Pb potentials already published in the literature. Molecular dynamics simulations based on this BOP have been conducted to study the effect of Pb on bulk and grain boundary of BCC and FCC iron. For bulk iron, it is found that of the addition of Pb decreases the elastic constants, elastic moduli, and ductility of BCC Fe more significant than that of FCC Fe. The calculations of two typical tilt symmetrical grain boundaries of Fe and Fe96Pb4 indicate that the appearance of Pb would cause a more considerable brittleness for BCC Fe than that for FCC Fe. The obtained results are in good agreement with similar experimental observations in the literature, which not only provides a strong support to the reliability of newly constructed Fe–Pb potential, but sheds lights on the understanding of mechanical properties of Fe–Pb system.

Graphical abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: This work is purely theoretical, having no associated experimental or observational data].

References

  1. V. Sobolev, Thermophysical properties of lead and lead–bismuth eutectic. J. Nucl. Mater. 362(2–3), 235–247 (2007). https://doi.org/10.1016/j.jnucmat.2007.01.144

    Article  ADS  Google Scholar 

  2. E.P. Loewen, A.T. Tokuhiro, Status of research and development of the lead-alloy-cooled fast reactor. J. Nucl. Sci. Technol. 40(8), 614–627 (2003). https://doi.org/10.1080/18811248.2003.9715398

    Article  Google Scholar 

  3. L.K. Mansur, A.F. Rowcliffe, R.K. Nanstad, S.J. Zinkle, W.R. Corwin, R.E. Stoller, Materials needs for fusion, generation IV fission reactors and spallation neutron sources—similarities and differences. J. Nucl. Mater. (2004). https://doi.org/10.1016/j.jnucmat.2004.04.016

    Article  Google Scholar 

  4. N. Baluc, Materials for fusion power reactors. Plasma Phys. Controlled Fusion 48(12B), B165–B177 (2006). https://doi.org/10.1088/0741-3335/48/12b/s16

    Article  Google Scholar 

  5. E. Ricci, C. Tomasi, R. Novakovic, S. Amore, D. Giuranno, Wetting property of liquid Pb on different steel candidates as structural materials for the Generation IV nuclear reactors. High Temp. High Pressures 50(1), 49–61 (2021). https://doi.org/10.32908/hthp.v50.871

    Article  Google Scholar 

  6. H.A. Abderrahim, P. Kupschus, E. Malambu, P. Benoit, D. Vandeplassche, MYRRHA: a multipurpose accelerator driven system for research & development. Nucl. Instrum. Methods A 463, 487–494 (2001). https://doi.org/10.1016/S0168-9002(01)00164-4

    Article  ADS  Google Scholar 

  7. B. Xu, P. Li, C. Chan, Application of phase change materials for thermal energy storage in concentrated solar thermal power plants: a review to recent developments. Appl. Energy 160, 286–307 (2015). https://doi.org/10.1016/j.apenergy.2015.09.016

    Article  Google Scholar 

  8. T. Auger, G. Lorang, Liquid metal embrittlement susceptibility of T91 steel by lead? Bismuth. Scr. Mater. 52(12), 1323–1328 (2005). https://doi.org/10.1016/j.scriptamat.2005.02.027

    Article  Google Scholar 

  9. R.L. Klueh, A.T. Nelson, Ferritic/martensitic steels for next-generation reactors. J. Nucl. Mater. 371(1–3), 37–52 (2007). https://doi.org/10.1016/j.jnucmat.2007.05.005

    Article  ADS  Google Scholar 

  10. C. Keller, M.M. Margulies, Z. Hadjem-Hamouche, I. Guillot, Influence of the temperature on the tensile behaviour of a modified 9Cr–1Mo T91 martensitic steel. Mater. Sci. Eng. A 527(24–25), 6758–6764 (2010). https://doi.org/10.1016/j.msea.2010.07.021

    Article  Google Scholar 

  11. G. Kalinin, V. Barabash, A. Cardella, J. Dietz, K. Ioki, R. Matera, R.T. Santoro, R. Tivey, Assessment and selection of materials for ITER in-vessel components. J. Nucl. Mater. 283–287, 10–19 (2000). https://doi.org/10.1016/S0022-3115(00)00305-6

    Article  ADS  Google Scholar 

  12. O. Yeliseyeva, V. Tsisar, G. Benamati, Influence of temperature on the interaction mode of T91 and AISI 316L steels with Pb–Bi melt saturated by oxygen. Corros. Sci. 50(6), 1672–1683 (2008). https://doi.org/10.1016/j.corsci.2008.02.006

    Article  Google Scholar 

  13. J. Zhang, F. Guyot, Experimental study of the bcc-fcc phase transformations in the Fe-rich system Fe-Si at high pressures. Phys Chem Minerals 26, 419–424 (1999). https://doi.org/10.1007/s002690050203

    Article  ADS  Google Scholar 

  14. C. Engin, H.M. Urbassek, Molecular-dynamics investigation of the fcc→bcc phase transformation in Fe. Comput. Mater. Sci. 41(3), 297–304 (2008). https://doi.org/10.1016/j.commatsci.2007.04.019

    Article  Google Scholar 

  15. L.T. Belkacemi, E. Meslin, B. Décamps, B. Radiguet, J. Henry, Radiation-induced bcc-fcc phase transformation in a Fe 3%Ni alloy. Acta Mater. 161, 61–72 (2018). https://doi.org/10.1016/j.actamat.2018.08.031

    Article  ADS  Google Scholar 

  16. Z. Shi, Y. Shen, D. Peng, Y. Chuan Jiang, H. Gong, Fundamental effect of lead on mechanical properties of iron from a constructed iron-lead potential. Comput. Mater. Sci. (2022). https://doi.org/10.1016/j.commatsci.2022.111587

    Article  Google Scholar 

  17. Y.C. Jiang, J. Zhao, L. Sun, H.R. Gong, X. Gong, Effects of alloying elements on cohesion and brittleness of grain boundary of iron. Mater. Chem. Phys. (2022). https://doi.org/10.1016/j.matchemphys.2021.125291

    Article  Google Scholar 

  18. X. Gong, H. Chen, F. Zhang, W. Zhu, H. Ma, B. Pang, Y. Yin, Degradation of tensile mechanical properties of two AlxCoCrFeNi (x=0.3 and 0.4) high-entropy alloys exposed to liquid lead-bismuth eutectic at 350 and 500°C. J. Nucl. Mater. (2022). https://doi.org/10.1016/j.jnucmat.2021.153364

    Article  Google Scholar 

  19. T. Liu, J. Hui, B. Zhang, X. He, M. Liu, J. Qiu, W. Liu, Corrosion mechanism of lead-bismuth eutectic at grain boundary in ferritic steels and the effect of alloying elements: a first-principles study. J. Nucl. Mater. (2022). https://doi.org/10.1016/j.jnucmat.2022.153915

    Article  Google Scholar 

  20. X.W. Zhou, R.A. Johnson, H.N.G. Wadley, Misfit-energy-increasing dislocations in vapor-deposited CoFe/NiFe multilayers. Phys. Rev. B (2004). https://doi.org/10.1103/PhysRevB.69.144113

    Article  Google Scholar 

  21. A.R. Alian, S.A. Meguid, S.I. Kundalwal, Unraveling the influence of grain boundaries on the mechanical properties of polycrystalline carbon nanotubes. Carbon 125, 180–188 (2017). https://doi.org/10.1016/j.carbon.2017.09.056

    Article  Google Scholar 

  22. S. Mishra, N. Luhadiya, S.I. Kundalwal, Atomistic insights into the H2 adsorption and desorption behavior of novel Li-functionalized polycrystalline CNTs. Carbon 207, 23–35 (2023). https://doi.org/10.1016/j.carbon.2023.03.002

    Article  Google Scholar 

  23. S. Mishra, P.P. Maware, V. Choyal, S.I. Kundalwal, Atomistic insights into the fracture mechanisms of Stone–Wales-defected CNTs under transversely isotropic loading. Eur. Phys. J. Plus (2023). https://doi.org/10.1140/epjp/s13360-023-04104-z

    Article  Google Scholar 

  24. A. Maulana, Z. Su’ud, K.D. Hermawan, Khairurrijal, Simulation study of steels corrosion phenomenon in liquid lead–bismuth cooled reactors using molecular dynamics methods. Prog. Nucl. Energy 50(2–6), 616–620 (2008). https://doi.org/10.1016/j.pnucene.2007.11.087

    Article  Google Scholar 

  25. D.G. Pettifor, New many-body potential for the bond order. Phys. Rev. Lett. 63(22), 2480–2483 (1989). https://doi.org/10.1103/PhysRevLett.63.2480

    Article  ADS  Google Scholar 

  26. D.G. Pettifor, I.I. Oleinik, Analytic bond-order potentials beyond Tersoff–Brenner. I. Theory. Phys. Rev. B 59(13), 8487–8499 (1999). https://doi.org/10.1103/PhysRevB.59.8487

    Article  ADS  Google Scholar 

  27. D.G. Pettifor, I.I. Oleinik, Bounded analytic bond-order potentials for s and p bonds. Phys. Rev. Lett. 84(18), 4127–4127 (2000). https://doi.org/10.1016/j.msea.2003.09.001

    Article  ADS  Google Scholar 

  28. D.G. Pettifor, I.I. Oleinik, Analytic bond-order potential for open and close-packed phases. Phys. Rev. B (2002). https://doi.org/10.1103/PhysRevB.65.172103

    Article  Google Scholar 

  29. Z.B. Liang, Y.C. Jiang, X. Gong, H.R. Gong, Atomistic modelling of the immiscible Fe-Bi system from a constructed bond order potential. J. Phys. Condens. Matter (2022). https://doi.org/10.1088/1361-648X/ac2e8e

    Article  Google Scholar 

  30. X.W. Zhou, D.K. Ward, M.E. Foster, An analytical bond-order potential for the aluminum copper binary system. J. Alloys Compd. 680, 752–767 (2016). https://doi.org/10.1016/j.jallcom.2016.04.055

    Article  Google Scholar 

  31. D.K. Ward, X.W. Zhou, B.M. Wong, F.P. Doty, J.A. Zimmerman, Analytical bond-order potential for the Cd–Zn–Te ternary system. Phys. Rev. B (2012). https://doi.org/10.1103/PhysRevB.86.245203

    Article  Google Scholar 

  32. D. Pettifor, M. Finnis, D. Nguyen-Manh, D. Murdick, X. Zhou, H. Wadley, Analytic bond-order potentials for multicomponent systems. Mater. Sci. Eng. A 365(1–2), 2–13 (2004)

    Article  Google Scholar 

  33. L. Goodwin, A.J. Skinner, D.G. Pettifor, Generating transferable tight-binding parameters: application to silicon. Europhys. Lett. 9(7), 701 (1989)

    Article  ADS  Google Scholar 

  34. D.K. Ward, X.W. Zhou, B.M. Wong, F.P. Doty, J.A. Zimmerman, Analytical bond-order potential for the cadmium telluride binary system. Phys. Rev. B (2012). https://doi.org/10.1103/PhysRevB.85.115206

    Article  Google Scholar 

  35. G. Kresse, J. Hafner, Ab initio molecular dynamics for open-shell transition metals. Phys. Rev. B Condens. Matter 48(17), 13115–13118 (1993). https://doi.org/10.1103/physrevb.48.13115

    Article  ADS  Google Scholar 

  36. G. Kresse, D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59(3), 1758–1775 (1999). https://doi.org/10.1103/PhysRevB.59.1758

    Article  ADS  Google Scholar 

  37. L.C. Liu, H.R. Gong, S.F. Zhou, X. Gong, Adsorption, diffusion, and permeation of hydrogen at PdCu surfaces. J. Membr. Sci. 588, 117206 (2019). https://doi.org/10.1016/j.memsci.2019.117206

    Article  Google Scholar 

  38. J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple. Phys. Rev. Lett. 77(18), 3865–3868 (1996). https://doi.org/10.1103/PhysRevLett.77.3865

    Article  ADS  Google Scholar 

  39. L. Sun, C.Y. Wu, J.C. Han, H.R. Gong, M.L. Chang, D.C. Chen, Band structure and thermoelectric performances of antimony under trigonal transformation. J. Appl. Phys. 125(14), 145102.1-145102.10 (2019). https://doi.org/10.1063/1.5088868

    Article  Google Scholar 

  40. J.C. Han, C.Y. Wu, L. Sun, H.R. Gong, X. Gong, Influence of trigonal deformation on band structure and Seebeck coefficient of tellurium. J. Phys. Chem. Solids 135, 109114 (2019). https://doi.org/10.1016/j.jpcs.2019.109114

    Article  Google Scholar 

  41. M. Methfessel, A.T. Paxton, High-precision sampling for Brillouin-zone integration in metals. Phys. Rev. B Condens. Matter 40(6), 3616–3621 (1989). https://doi.org/10.1103/physrevb.40.3616

    Article  ADS  Google Scholar 

  42. P.E. Blochl, Projector augmented-wave method. Phys. Rev. B Condens. Matter 50(24), 17953–17979 (1994). https://doi.org/10.1103/physrevb.50.17953

    Article  ADS  Google Scholar 

  43. D.E. Gray, H. Wise, American Institute of Physics Handbook (McGraw-Hill, New York, 1972)

    Google Scholar 

  44. Y.K. Vohra, A.L. Ruoff, Static compression of metals Mo, Pb, and Pt to 272 GPa: comparison with shock data. Phys. Rev. B Condens. Matter 42(13), 8651–8654 (1990). https://doi.org/10.1103/physrevb.42.8651

    Article  ADS  Google Scholar 

  45. S. Plimpton, Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117(1), 1–19 (1995). https://doi.org/10.1006/jcph.1995.1039

    Article  ADS  MATH  Google Scholar 

  46. T. Gao, H. Song, B. Wang, Y. Gao, Y. Liu, Q. **e, Q. Chen, Q. **ao, Y. Liang, Molecular dynamics simulations of tensile response for FeNiCrCoCu high-entropy alloy with voids. Int. J. Mech. Sci. (2023). https://doi.org/10.1016/j.ijmecsci.2022.107800

    Article  Google Scholar 

  47. W. Liu, Y. Wei, F. Zhang, J. Zhou, Tensile behavior of ferritic/austenitic iron with a bimodal structure: an atomistic study. Mater. Today Commun. (2022). https://doi.org/10.1016/j.mtcomm.2022.103883

    Article  Google Scholar 

  48. J. Xu, Y. Jiang, L. Yang, J. Li, Assessment of the CSL and SU models for bcc-Fe grain boundaries from first principles. Comput. Mater. Sci. 122, 22–29 (2016). https://doi.org/10.1016/j.commatsci.2016.05.009

    Article  Google Scholar 

  49. J.A.C. Lilly, J.R. McDowell, High-field conduction in films of mylar and teflon. J. Appl. Phys. 39, 141–147 (1968). https://doi.org/10.1063/1.1655720

    Article  ADS  Google Scholar 

  50. J. Zarestky, C. Stassis, Lattice dynamics of γ-Fe. Phys. Rev. B 35, 4500 (1987). https://doi.org/10.1103/PhysRevB.35.4500

    Article  ADS  Google Scholar 

  51. R.E. Newnham, Properties of Materials: Anisotropy, Symmetry, Structure (Oxford University Press, 2005)

    Google Scholar 

  52. W.R. Warke, K.L. Johnson, N.N. Breyer, Corrosion by Liquid Metals (Springer, Boston, 1970)

    Google Scholar 

  53. E. Nunes, E.C. Passamani, C. Larica, J.C.C. Freitas, A.Y. Takeuchi, E. Baggio-Saitovitch, A.C. Doriguetto, A.A.R. Fernandes, Extended solubility in non-equilibrium Pb/Fe system. Mater. Sci. Eng. A 390(1–2), 13–18 (2005). https://doi.org/10.1016/j.msea.2004.05.032

    Article  Google Scholar 

  54. E. Nunes, E. Passamani, C. Larica, J. Freitas, A. Takeuchi, Solubility study of Fe0.95Pb0.05 alloy prepared by high energy ball milling. J. Alloys Compd. 345, 116–122 (2002). https://doi.org/10.1016/S0925-8388(02)00410-3

    Article  Google Scholar 

  55. G.A. Dorofeev, E.P. Elsukov, Mechanical alloying of the Fe–Pb system immiscible in the equilibrium state. Phys. Met. Metallogr. 103(6), 593–599 (2007). https://doi.org/10.1134/s0031918x07060087

    Article  ADS  Google Scholar 

  56. D. Gorse, T. Auger, J.-B. Vogt, I. Serre, A. Weisenburger, A. Gessi, P. Agostini, C. Fazio, A. Hojna, F.D. Gabriele, J.V.D. Bosch, G. Coen, A. Almazouzi, M. Serrano, Influence of liquid lead and lead–bismuth eutectic on tensile, fatigue and creep properties of ferritic/martensitic and austenitic steels for transmutation systems. J. Nucl. Mater. 415(3), 284–292 (2011). https://doi.org/10.1016/j.jnucmat.2011.04.047

    Article  ADS  Google Scholar 

  57. F. Mouhat, F.-X. Coudert, Necessary and sufficient elastic stability conditions in various crystal systems. Phys. Rev. B (2014). https://doi.org/10.1103/PhysRevB.90.224104

    Article  Google Scholar 

  58. G. Coen, J.V.D. Bosch, A. Almazouzi, J. Degrieck, Investigation of the effect of lead–bismuth eutectic on the fracture properties of T91 and 316L. J. Nucl. Mater. 398(1–3), 122–128 (2010). https://doi.org/10.1016/j.jnucmat.2009.10.021

    Article  ADS  Google Scholar 

  59. O. Milton, The Materials Science of Thin Films: Deposition and Structure, World Scientific (2006)

  60. K. Chen, M. Bielawski, Interfacial fracture toughness of transition metal nitrides. Surf. Coat. Technol. 203(3), 598–601 (2008). https://doi.org/10.1016/j.surfcoat.2008.05.040

    Article  Google Scholar 

  61. J.F. Nye, Physical Properties of Crystals. Clarencon (1985)

  62. C. He, M. Cheng, M. Zhang, W.X. Zhang, Interfacial Stability and Electronic Properties of Ag/M (M = Ni, Cu, W, and Pd) and Cu/Cr Interfaces. J. Phys. Chem. C 122(31), 17928–17935 (2018). https://doi.org/10.1021/acs.jpcc.8b05920

    Article  Google Scholar 

  63. H. Zheng, X.-G. Li, R. Tran, C. Chen, M. Horton, D. Winston, K.A. Persson, S.P. Ong, Grain boundary properties of elemental metals. Acta Mater. 186, 40–49 (2020). https://doi.org/10.1016/j.actamat.2019.12.030

    Article  ADS  Google Scholar 

  64. R.J. Kurtz, H.L. Heinisch, The effects of grain boundary structure on binding of He in Fe. J. Nucl. Mater. 329–333, 1199–1203 (2004). https://doi.org/10.1016/j.jnucmat.2004.04.262

    Article  ADS  Google Scholar 

  65. Y.A. Du, L. Ismer, J. Rogal, T. Hickel, J. Neugebauer, R. Drautz, First-principles study on the interaction of H interstitials with grain boundaries inα- andγ-Fe. Phys. Rev. B (2011). https://doi.org/10.1103/PhysRevB.84.144121

    Article  Google Scholar 

  66. H. Beladi, G.S. Rohrer, The relative grain boundary area and energy distributions in a ferritic steel determined from three-dimensional electron backscatter diffraction maps. Acta Mater. 61(4), 1404–1412 (2013). https://doi.org/10.1016/j.actamat.2012.11.017

    Article  ADS  Google Scholar 

  67. D. Scheiber, R. Pippan, P. Puschnig, L. Romaner, Ab initiocalculations of grain boundaries in bcc metals. Modell. Simul. Mater. Sci. Eng. (2016). https://doi.org/10.1088/0965-0393/24/3/035013

    Article  Google Scholar 

  68. T. Hickel, A. Dick, B. Grabowski, F. Körmann, J. Neugebauer, Steel design from fully parameter-free Ab initio computer simulations. Mater. Technol. 1, 4–8 (2009). https://doi.org/10.2374/SRI08SP109

    Article  Google Scholar 

  69. A. Legris, G. Nicaise, J.-B. Vogt, J. Foct, D. Gorse, D. Vancon, Embrittlement of a martensitic steel by liquid lead. Scr. Mater. 43, 997–1001 (2000). https://doi.org/10.1016/s1359-6462(00)00523-6

    Article  Google Scholar 

  70. I.P. Serre, J.-B. Vogt, Mechanical behavior in liquid lead of Al2O3 coated 15–15Ti steel and an alumina-forming austenitic steel designed to mitigate their corrosion. Eng. Fail. Anal. (2022). https://doi.org/10.1016/j.engfailanal.2022.106443

    Article  Google Scholar 

  71. Z. Hamouche-Hadjem, T. Auger, I. Guillot, D. Gorse, Susceptibility to LME of 316L and T91 steels by LBE: effect of strain rate. J. Nucl. Mater. 376(3), 317–321 (2008). https://doi.org/10.1016/j.jnucmat.2008.02.031

    Article  ADS  Google Scholar 

  72. E. Stergar, S.G. Eremin, S. Gavrilov, M. Lambrecht, O. Makarov, V. Iakovlev, Influence of LBE long term exposure and simultaneous fast neutron irradiation on the mechanical properties of T91 and 316L. J. Nucl. Mater. 473, 28–34 (2016). https://doi.org/10.1016/j.jnucmat.2016.02.008

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work is financially supported by Natural Science Foundation of Hunan Province (Grant No. 2022JJ30719). We are grateful for resources from the High Performance Computing Center of Central South University.

Author information

Author notes

  1. Dikang Peng and **glun Hu have contributed equally.

Authors and Affiliations

  1. State Key Laboratory of Powder Metallurgy, Central South University, Changsha, 410083, Hunan, China

    Dikang Peng, **glun Hu, Yuchuan Jiang, Lei Sun, Haoran Gong, Lingyun Yang & Chao** Liang

  2. National Key Laboratory of Science and Technology for High-Strength Structural Materials, Central South University, Changsha, 410083, China

    Chao** Liang

Authors
  1. Dikang Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. **glun Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yuchuan Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Lei Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Haoran Gong
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Lingyun Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Chao** Liang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Lingyun Yang or Chao** Liang.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Peng, D., Hu, J., Jiang, Y. et al. The influence of lead on mechanical properties of BCC and FCC iron from a constructed bond-order potential. Eur. Phys. J. Plus 138, 1082 (2023). https://doi.org/10.1140/epjp/s13360-023-04668-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-023-04668-w

Search

Navigation