Micromagnetic investigation by a simplified approach on the demagnetization field of permanent magnets with nonmagnetic phase inside
Wei LI1, Lizhong ZHAO1,2, Zhongwu LIU1()
1. School of Materials Science and Engineering, South China University of Technology, Guangzhou 510640, China 2. Innovative Center for Advanced Materials, Hangzhou Dianzi University, Hangzhou 310012, China
A simplified analysis method based on micromagnetic simulation is proposed to investigate effects of nonmagnetic particles on the demagnetizing field of a permanent magnet. By applying the additivity law of the demagnetizing field, the complicated demagnetizing field of the real magnet could be analyzed by only focusing on the stray field of the reserved magnet. For a magnet with nonmagnetic particles inside, the particle size has no significant effect on the maximum value of the demagnetization field, but the area of the affected region by the particle is proportional to the particle size. A large particle produces a large affected area overlapped with those influenced by other particles, which leads to the large demagnetization field. With increasing the length of the particle along the magnetization direction, the demagnetization field on the pole surface increases. The pole surface with a convex shape will increase the demagnetization field. The demagnetizing field near the nonmagnetic particle will be further increased by the large macroscopic demagnetizing field near the pole surface. This work suggests some practical approaches to optimize the microstructure of permanent magnets.
. [J]. Frontiers of Materials Science, 2019, 13(3): 323-333.
Wei LI, Lizhong ZHAO, Zhongwu LIU. Micromagnetic investigation by a simplified approach on the demagnetization field of permanent magnets with nonmagnetic phase inside. Front. Mater. Sci., 2019, 13(3): 323-333.
T G Woodcock, Y Zhang, G Hrkac, et al.. Understanding the microstructure and coercivity of high performance NdFeB-based magnets. Scripta Materialia, 2012, 67(6): 536–541 https://doi.org/10.1016/j.scriptamat.2012.05.038
2
H Sepehri-Amin, T Ohkubo, T Shima, et al.. Grain boundary and interface chemistry of an Nd–Fe–B-based sintered magnet. Acta Materialia, 2012, 60(3): 819–830 https://doi.org/10.1016/j.actamat.2011.10.043
3
R K Mishra, J K Chen, G Thomas. Effect of annealing on the microstructure of sintered Nd–Fe–B magnets. Journal of Applied Physics, 1986, 59(6): 2244–2246 https://doi.org/10.1063/1.336366
4
H J Engelmann, A S Kim, G Thomas. Microstructure and magnetic effects of small Cu additions to (Nd, Dy)FeB magnets. Scripta Materialia, 1997, 36(1): 55–62 https://doi.org/10.1016/S1359-6462(96)00312-0
5
M Xia, A B Abrahamsen, C R H Bahl, et al.. The influence of carbon and oxygen on the magnetic characteristics of press-less sintered NdFeB magnets. Journal of Magnetism and Magnetic Materials, 2017, 422: 232–236 https://doi.org/10.1016/j.jmmm.2016.09.014
6
Y H Hou, Y L Wang, Y L Huang, et al.. Effects of Nd-rich phase on the improved properties and recoil loops for hot deformed Nd–Fe–B magnets. Acta Materialia, 2016, 115: 385–391 https://doi.org/10.1016/j.actamat.2016.06.015
7
Q Zhou, W Li, Y Hong, et al.. Microstructure improvement related coercivity enhancement for sintered NdFeB magnets after optimized additional heat treatment. Journal of Rare Earths, 2018, 36(4): 379–384 https://doi.org/10.1016/j.jre.2017.11.007
J Fidler, T Schrefl. Micromagnetic modelling –– the current state of the art. Journal of Physics D: Applied Physics, 2000, 33(15): R135–R156 https://doi.org/10.1088/0022-3727/33/15/201
10
R I Joseph. Ballistic demagnetizing factor in uniformly magnetized rectangular prisms. Journal of Applied Physics, 1967, 38(5): 2405–2406 https://doi.org/10.1063/1.1709907
11
W Si, G P Zhao, N Ran, et al.. Deterioration of the coercivity due to the diffusion induced interface layer in hard/soft multilayers. Scientific Reports, 2015, 5(1): 16212 (9 pages) https://doi.org/10.1038/srep16212
pmid: 26586226
12
X J Weng, L C Shen, H Tang, et al.. Change of coercivity mechanism with the soft film thickness in hard-soft trilayers. Journal of Magnetism and Magnetic Materials, 2019, 475: 352–358 https://doi.org/10.1016/j.jmmm.2018.10.118
13
H Kronmüller. General micromagnetic theory. In: Kronmüller H, Parkin S, eds. Handbook of Magnetism and Advanced Magnetic Materials. John Wiley & Sons, Ltd., 2007, doi: 10.1002/9780470022184.hmm201
14
X Tan, J S Baras, P S Krishnaprasad. Fast evaluation of demagnetizing field in three-dimensional micromagnetics using multipole approximation. In: Proceedings of SPIE — The International Society for Optical Engineering, 2001, 3984: 195–201
15
M J Donahue. Parallelizing a micromagnetic program for use on multiprocessor shared memory computers. IEEE Transactions on Magnetics, 2009, 45(10): 3923–3925 https://doi.org/10.1109/TMAG.2009.2023866
16
W F Brown. Magnetoelastic Interactions. New York: Springer, 1966
17
M Donahue, D Porter. Object oriented micro-magnetic framework. Interagency Report No. NISTIR, 2006, 6376: 13
T Schrefl, J Fidler. Finite element modeling of nanocomposite magnets. IEEE Transactions on Magnetics, 1999, 35(5): 3223–3228 https://doi.org/10.1109/20.800483
20
B B Straumal, Y O Kucheev, I L Yatskovskaya, et al.. Grain boundary wetting in the NdFeB-based hard magnetic alloys. Journal of Materials Science, 2012, 47(24): 8352–8359 https://doi.org/10.1007/s10853-012-6618-5
21
Q Zhou, Z W Liu, X C Zhong, et al.. Properties improvement and structural optimization of sintered NdFeB magnets by non-rare earth compound grain boundary diffusion. Materials & Design, 2015, 86: 114–120 https://doi.org/10.1016/j.matdes.2015.07.067
J Fischbacher, A Kovacs, L Exl, et al.. Searching the weakest link: Demagnetizing fields and magnetization reversal in permanent magnets. Scripta Materialia, 2018, 154: 253–258 https://doi.org/10.1016/j.scriptamat.2017.11.020
24
Q Zhou, Z W Liu, X C Zhong, et al.. Properties improvement and structural optimization of sintered NdFeB magnets by non-rare earth compound grain boundary diffusion. Materials & Design, 2015, 86: 114–120 https://doi.org/10.1016/j.matdes.2015.07.067
25
K Hirota, H Nakamura, T Minowa, et al.. Coercivity enhancement by the grain boundary diffusion process to Nd–Fe–B sintered magnets. IEEE Transactions on Magnetics, 2006, 42(10): 2909–2911 https://doi.org/10.1109/TMAG.2006.879906
26
H Sepehri-Amin, T Ohkubo, K Hono. The mechanism of coercivity enhancement by the grain boundary diffusion process of Nd–Fe–B sintered magnets. Acta Materialia, 2013, 61(6): 1982–1990 https://doi.org/10.1016/j.actamat.2012.12.018
27
T Akiya, J Liu, H Sepehri-Amin, et al.. Low temperature diffusion process using rare earth–Cu eutectic alloys for hot-deformed Nd–Fe–B bulk magnets. Journal of Applied Physics, 2014, 115(17): 17A766 https://doi.org/10.1063/1.4869062
28
F Vial, F Joly, E Nevalainen, et al.. Improvement of coercivity of sintered NdFeB permanent magnets by heat treatment. Journal of Magnetism and Magnetic Materials, 2002, 242–245: 1329–1334 https://doi.org/10.1016/S0304-8853(01)00967-2
29
F Chen, T Zhang, J Wang, et al.. Coercivity enhancement of a NdFeB sintered magnet by diffusion of Nd70Cu30 alloy under pressure. Scripta Materialia, 2015, 107: 38–41 https://doi.org/10.1016/j.scriptamat.2015.05.015
30
W Li, Q Zhou, L Z Zhao, et al.. Micromagnetic simulation of anisotropic grain boundary diffusion for sintered Nd–Fe–B magnets. Journal of Magnetism and Magnetic Materials, 2018, 451: 704–709 https://doi.org/10.1016/j.jmmm.2017.12.002
