Skip to main content
SpringerLink
Log in

The role of anti-core–shell structure caused by over-saturation diffusion of heavy rare earths in Nd-Fe-B magnets: a micromagnetic simulation study

  • Published:
Applied Physics A Aims and scope Submit manuscript

Abstract

Grain boundary diffusion (GBD) process is an effective method to fabricate high-coercive Nd-Fe-B magnets with less consumption of heavy rare earth (HRE). By this approach, HRE-rich shell forms around the Nd2Fe14B grain, which can hinder the magnetic reversal starting at the edge of the grains and enhance the coercivity of whole magnet. Recently, an anti-core–shell structure was observed in the HRE diffused magnets after over-saturated diffusion, where the HRE concentration in the core is even higher than that in the shell. In this work, the effects of the anti-core–shell structure on the magnetization reversal and magnetic properties of diffused magnet have been clarified by micromagnetic simulations. Three-dimension models were established to analyze the demagnetization process. The results indicate that the anti-core–shell structure leads to a large stray field, which will accelerate the magnetization reversal of the whole magnet. As a result, the beneficial effect of HRE GBD on the coercivity has been reduced. Combined with the existing experimental results, the formation of anti-core–shell structure should be avoided during diffusion. Hence, appropriate diffusion time and diffusion source dosage should be selected for GBD process in order to obtain high-performance products and efficiently use the HRE resources.

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

Access this article

Log in via an institution

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
Fig. 6
Fig. 7

Similar content being viewed by others

Data availability

Not applicable.

References

  1. O. Gutfleisch, M.A. Willard, E. Bruck, C.H. Chen, S.G. Sankar, J.P. Liu, Magnetic materials and devices for the 21st century: stronger, lighter, and more energy efficient. Adv. Mater. 23, 821–842 (2011)

    Article  Google Scholar 

  2. J. He, Z. Yu, J. Cao, W. Song, K. Xu, W. Fan, H. Yu, X. Zhong, H. Mao, C. Mao, Z. Liu, Rationally selecting the chemical composition of the Nd–Fe–B magnet for high-efficiency grain boundary diffusion of heavy rare earths. J. Mater. Chem. C 10, 2080–2088 (2022)

    Article  Google Scholar 

  3. N. Oono, M. Sagawa, R. Kasada, H. Matsui, A. Kimura, Production of thick high-performance sintered neodymium magnets by grain boundary diffusion treatment with dysprosium–nickel–aluminum alloy. J. Magn. Magn. Mater. 323, 297–300 (2011)

    Article  ADS  Google Scholar 

  4. R. Grossinger, X.K. Sun, R. Eibler, K.H.J. Buschow, H.R. Kirchmayr, Temperature dependence of anisotropy fields and initial susceptibilities in R2Fe14B compounds. J. Magn. Magn. Mater. 58, 55–60 (1986)

    Article  ADS  Google Scholar 

  5. J.F. Herbst, R2Fe14B materials: intrinsic properties and technological aspects. Rev. Mod. Phys. 63, 819–898 (1991)

    Article  ADS  Google Scholar 

  6. S. Hirosawa, Y. Matsuura, H. Yamamoto, S. Fujimura, M. Sagawa, H. Yamauchi, Magnetization and magnetic anisotropy of R2Fe14B measured on single crystals. J. Appl. Phys. 59, 873–879 (1986)

    Article  ADS  Google Scholar 

  7. Z. Liu, J. He, R.V. Ramanujan, Significant progress of grain boundary diffusion process for cost-effective rare earth permanent magnets: a review. Mater. Des. 209, 110004 (2021)

    Article  Google Scholar 

  8. J. He, J. Cao, Z. Yu, W. Song, H. Yu, M. Hussain, Z. Liu, Grain boundary diffusion sources and their coating methods for Nd-Fe-B permanent magnets. Metals 11, 1434 (2021)

    Article  Google Scholar 

  9. Z. Liu, J. He, Q. Zhou, Y. Huang, Q. Jiang, Development of non-rare earth grain boundary modification techniques for Nd-Fe-B permanent magnets. J. Mater. Sci. Technol. 98, 51–61 (2022)

    Article  Google Scholar 

  10. S. Sugimoto, Current status and recent topics of rare-earth permanent magnets. J. Phys. D: Appl. Phys. 44, 064001 (2011)

    Article  ADS  Google Scholar 

  11. H. Nakamura, K. Hirota, M. Shimao, T. Minowa, M. Honshima, Magnetic properties of extremely small Nd-Fe-B sintered magnets. IEEE Trans. Magn. 41, 3844–3846 (2005)

    Article  ADS  Google Scholar 

  12. T.-H. Kim, S.-R. Lee, H.-J. Kim, M.-W. Lee, T.-S. Jang, Simultaneous application of Dy–X (X = F or H) powder doping and dip-coating processes to Nd-Fe-B sintered magnets. Acta Mater. 93, 95–104 (2015)

    Article  ADS  Google Scholar 

  13. K. Loewe, D. Benke, C. Kübel, T. Lienig, K.P. Skokov, O. Gutfleisch, Grain boundary diffusion of different rare earth elements in Nd-Fe-B sintered magnets by experiment and FEM simulation. Acta Mater. 124, 421–429 (2017)

    Article  ADS  Google Scholar 

  14. K. Lu, X. Bao, M. Tang, G. Chen, X. Mu, J. Li, X. Gao, Boundary optimization and coercivity enhancement of high (BH)max Nd-Fe-B magnet by diffusing Pr-Tb-Cu-Al alloys. Scr. Mater. 138, 83–87 (2017)

    Article  ADS  Google Scholar 

  15. K. Lu, X. Bao, M. Tang, L. Sun, J. Li, X. Gao, Influence of annealing on microstructural and magnetic properties of Nd-Fe-B magnets by grain boundary diffusion with Pr-Cu and Dy-Cu alloys. J. Magn. Magn. Mater. 441, 517–522 (2017)

    Article  ADS  Google Scholar 

  16. Y. Liu, J. He, H. Yu, Z. Liu, G. Zhang, Restoring and enhancing the coercivity of waste sintered (Nd, Ce, Gd)FeB magnets by direct Pr-Tb-Cu grain boundary diffusion. Appl. Phys. A 126, 657 (2020)

    Article  ADS  Google Scholar 

  17. L. Zhao, J. He, W. Li, X. Liu, J. Zhang, L. Wen, Z. Zhang, J. Hu, J. Zhang, X. Liao, K. Xu, W. Fan, W. Song, H. Yu, X. Zhong, Z. Liu, X. Zhang, Understanding the role of element grain boundary diffusion mechanism in Nd–Fe–B magnets. Adv. Funct. Mater. 32, 2109529 (2022)

    Article  Google Scholar 

  18. H. Sepehri-Amin, J. Liu, T. Ohkubo, K. Hioki, A. Hattori, K. Hono, Enhancement of coercivity of hot-deformed Nd-Fe-B anisotropic magnet by low-temperature grain boundary diffusion of Nd60Dy20Cu20 eutectic alloy. Scr. Mater. 69, 647–650 (2013)

    Article  Google Scholar 

  19. K. Löewe, C. Brombacher, M. Katter, O. Gutfleisch, Temperature-dependent Dy diffusion processes in Nd-Fe-B permanent magnets. Acta Mater. 83, 248–255 (2015)

    Article  ADS  Google Scholar 

  20. T.-H. Kim, T.T. Sasaki, T. Koyama, Y. Fujikawa, M. Miwa, Y. Enokido, T. Ohkubo, K. Hono, Formation mechanism of Tb-rich shell in grain boundary diffusion processed Nd-Fe-B sintered magnets. Scr. Mater. 178, 433–437 (2020)

    Article  Google Scholar 

  21. K.Ž Soderžnik, K.Ž Rožman, M. Komelj, A. Kovács, P. Diehle, T. Denneulin, A. Savenko, M. Soderžnik, S. Kobe, R.E. Dunin-Borkowski, J. Mayer, B. Markoli, S. Šturm, Microstructural insights into the coercivity enhancement of grain-boundary-diffusion-processed Tb-treated Nd-Fe-B sintered magnets beyond the core-shell formation mechanism. J. Alloys Compd. 864, 158915 (2021)

    Article  Google Scholar 

  22. W. Li, Q. Zhang, Q. Zhu, S. Xiao, C. Xu, L. Yang, B. Zheng, S. Mao, Z. Song, Formation of anti-shell/core structure of heavy rare earth elements (Tb, Dy) in sintered Nd-Fe-B magnet after grain boundary diffusion process. Scr. Mater. 163, 40–43 (2019)

    Article  Google Scholar 

  23. S. SDVSS Varma, K.R. Mangipudi, P.R. Budarapu, A coupled quantum-molecular mechanics approach for performance analysis of defective Silicon based photovoltaic solar cells. Phys. Scripta 98, 35007 (2023)

    Article  Google Scholar 

  24. S.M. Dsouza, T.M. Varghese, P.R. Budarapu, S. Natarajan, A Non-intrusive stochastic isogeometric analysis of functionally graded plates with material uncertainty. Axioms 9(3), 92 (2020)

    Article  Google Scholar 

  25. W. Li, Q. Zhou, L.Z. Zhao, Q.X. Wang, X.C. Zhong, Z.W. Liu, Micromagnetic simulation of anisotropic grain boundary diffusion for sintered Nd-Fe-B magnets. J. Magn. Magn. Mater. 451, 704–709 (2018)

    Article  ADS  Google Scholar 

  26. A. Vansteenkiste, J. Leliaert, M. Dvornik, M. Helsen, F. Garcia-Sanchez, B. Van Waeyenberge, The design and verification of MuMax3. AIP Adv. (2014). https://doi.org/10.1063/1.4899186

    Article  Google Scholar 

  27. T. Schrefl, J. Fidler, Finite element modeling of nanocomposite magnets. IEEE Trans. Magn. 35, 3223–3228 (1999)

    Article  ADS  Google Scholar 

  28. K. Hono, H. Sepehri-Amin, Strategy for high-coercivity Nd-Fe-B magnets. Scr. Mater. 67, 530–535 (2012)

    Article  Google Scholar 

Download references

Acknowledgements

This work is supported by National Natural Science Foundation of China (No. U21A2052), Guangdong Basic and Applied Basic Research Fund Project (No. 2022A1515240060) and China Postdoctoral Science Foundation (2023M733642).

Author information

Author notes

  1. Xiangyi Liu and Jiayi He contributed equally to this work.

Authors and Affiliations

  1. School of Materials Science and Engineering, South China University of Technology, Guangzhou, 510640, China

    Xiangyi Liu, Jiayi He, Bin Yuan & Zhongwu Liu

Authors
  1. Xiangyi Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jiayi He
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bin Yuan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zhongwu Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhongwu Liu.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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

Liu, X., He, J., Yuan, B. et al. The role of anti-core–shell structure caused by over-saturation diffusion of heavy rare earths in Nd-Fe-B magnets: a micromagnetic simulation study. Appl. Phys. A 129, 619 (2023). https://doi.org/10.1007/s00339-023-06905-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00339-023-06905-6

Keywords

Search

Navigation