CF-11 Optimization of Coercivity and Price of a Permanent Magnet considering the Microstructure
Creators: Clemens Wager
Claas Fillies
Thomas Schrefl
Alexander Kovacs
Harald Oezelt
David Böhm
Qais Ali
Hayate Yamano
Masao Yano
Noritsugu Sakuma
Akihito Kinoshita
Tetsuya Shoji
Akira Kato
Publisher: name: IEEE
Year: 2025

Coercivity is the most important extrinsic property in permanent magnet applications. Microstructural parameters such as grain size and surface defects are important considerations in the production of permanent magnets. Yet the relationship between coercivity and microstructure remains in need of further exploration. [1] In this work we optimize the chemical composition of a (Nd,Ce,La,Pr,Tb,Dy)2(Fe,Co,Ni)14(B,C) permanent magnet aiming for high coercivity and low price. To account for the microstructure, we compute the coercive field from the anisotropy field and the magnetization using the microstructural parameters α and Neff [2]. Starting point for the optimization is a set of measured intrinsic material properties for different chemical compositions and temperatures. The design space is explored using a genetic algorithm, NSGA-II [3], which considers many different material designs per generation. The objective functions are evaluated by two surrogate models based on Gaussian Process Regression [4] which also estimate model uncertainty. The regressors were trained on measurement data and are used to predict the intrinsic magnetic properties (magnetization and anisotropy field) and the price for the chemical composition. Our results indicate that the optimal chemical composition for reaching a certain coercivity at lowest price depends on the microstructure. To reach the same coercive field with increasing Neff the Neodymium content or the heavy rare earth content must be increased for room temperature and for 453 K, respectively. Figure 1 shows an example of the pareto front obtained from the multi-objective optimization for 453 K, α=0.45 and Neff=0.91. Along the pareto front we identify three different regions: 1) Neodymium free, 2) Neodymium based but heavy rare earth free and 3) heavy rare earth containing magnet designs. Table 1 gives the chemical composition for pareto optimal designs with a coercivity of at least 1.5 Tesla for different temperatures and microstructural parameters.References: [1] J. Li, H. Sepehri-Amin, T. Sasaki, et al., Science and Technology of Advanced Materials., Vol. 22, p. 386 (2021) [2] S. Bance, B. Seebacher, T. Schrefl, et al., Journal of Applied Physics., Vol. 116 (2014) [3] K. Deb, A. Pratap, S. Agarwal, et al., IEEE Transactions on Evolutionary Computation, Vol. 6, p. 182 (2002) [4] F. Pedregosa, G. Varoquaux, A.Gramfort, et al., Journal of Machine Learning Research., Vol. 12, p. 2825 (2011)
Coercivity is the most important extrinsic property in permanent magnet applications. Microstructural parameters such as grain size and surface defects are important considerations in the production of permanent magnets. Yet the relationship between coercivity and microstructure remains in need of further exploration. [1] In this work we optimize the chemical composition of a (Nd,Ce,La,Pr,Tb,Dy)2(Fe,Co,Ni)14(B,C) permanent magnet aiming for high coercivity and low price. To account for the microstructure, we compute the coercive field from the anisotropy field and the magnetization using the microstructural parameters α and Neff [2]. Starting point for the optimization is a set of measured intrinsic material properties for different chemical compositions and temperatures. The design space is explored using a genetic algorithm, NSGA-II [3], which considers many different material designs per generation. The objective functions are evaluated by two surrogate models based on Gaussian Process Regression [4] which also estimate model uncertainty. The regressors were trained on measurement data and are used to predict the intrinsic magnetic properties (magnetization and anisotropy field) and the price for the chemical composition. Our results indicate that the optimal chemical composition for reaching a certain coercivity at lowest price depends on the microstructure. To reach the same coercive field with increasing Neff the Neodymium content or the heavy rare earth content must be increased for room temperature and for 453 K, respectively. Figure 1 shows an example of the pareto front obtained from the multi-objective optimization for 453 K, α=0.45 and Neff=0.91. Along the pareto front we identify three different regions: 1) Neodymium free, 2) Neodymium based but heavy rare earth free and 3) heavy rare earth containing magnet designs. Table 1 gives the chemical composition for pareto optimal designs with a coercivity of at least 1.5 Tesla for different temperatures and microstructural parameters.References: [1] J. Li, H. Sepehri-Amin, T. Sasaki, et al., Science and Technology of Advanced Materials., Vol. 22, p. 386 (2021) [2] S. Bance, B. Seebacher, T. Schrefl, et al., Journal of Applied Physics., Vol. 116 (2014) [3] K. Deb, A. Pratap, S. Agarwal, et al., IEEE Transactions on Evolutionary Computation, Vol. 6, p. 182 (2002) [4] F. Pedregosa, G. Varoquaux, A.Gramfort, et al., Journal of Machine Learning Research., Vol. 12, p. 2825 (2011)