Magnetic Properties,mechanism Of Coercivity,and Machine Learning Approach Of Melt-spun High Abundant Rare-earth Based Magnets

Partial substituting Pr and Nd in R₂Fe₁₄B permanent magnets by the high abundant rare-earth element of La,Ce and Y is not only beneficial to improving the cost performance of magnets,but also helps to save rare-earth resources and alleviate the unbalanced application of rare-earth elements.Because permanent magnet is very sensitive to its microstructure,R₂Fe₁₄B formed by different rare-earth elements have significant differences in atomic occupancy,crystallization kinetics,microstructure characteristics and magnetic parameters,such as saturation magnetization,magnetocrystalline anisotropy and Curie temperature,as well as in preparation and heat treatment.Therefore,systematically studying on phase structure,magnetic properties,variation of microstructure with composition,magnetic hardening of magnets and regulation of coercivity temperature stability are not only important basic scientific problems for the research on rare-earth permanent magnets at present,but also practical problems for the performance improvement and process optimization of high abundant rare-earth permanent magnets.In this work,two methods of experiment and machine learning are respectively used to study the composition dependence of performance in high abundant rare-earth permanent magnets.Secondly,the mechanisms of coercivity and its temperature stability of magnet are analyzed and discussed by micromagnetic simulation method.The results have important guiding value for the composition design of high abundant rare-earth magnets and the microstructure optimization of permanent magnets.The main contents and conclusions are as follows:Magnetic properties of MM_xFe_100-x-yB_y melt-spun magnets are studied using the mixed rare-earth elements?MM:La-Ce-Pr-Nd alloy?.The magnet with the composition of MM_13.5Fe_79.5B₇ exhibits excellent comprehensive magnetic properties:H_cj=660.8 kA/m?8.3 kOe?,B_r=0.72 T?7.2 kGs?,and?BH?_max=82 kJ/m³?10.3 MGOe?.Based on this composition,performance temperature-stability of the magnets are enhanced by replacing Fe with Co.Among them,remanence temperature coefficient of MM_13.5Fe_67.5Co₁₂B₇ melt-spun magnets between 300 K and 400 K is-0.125%/K,which is equivalent to Nd₂Fe₁₄B??=0.124%/K?,and coercivity temperature coefficient??=-0.334%/K?is higher than that of Nd₂Fe₁₄B??=-0.347%/K?.By reconstructing the relationship between the temperature coefficient of coercivity and the intrinsic magnetism and microstructure of magnets,the correlation between the grain size,orientation,magnetocrystalline anisotropy of magnets and the coercivity temperature stability are directly and clearly presented.It provides a simple theoretical analysis and prediction method for the design and manufacture of high coercivity magnets with low temperature coefficient.The nonlinear relationships between coercivity(H_cj)or maximum magnetic energy product[?BH?_max]of La-Ce-containing melt-spun magnets and the composition are deciphered by machine learning method,and the properties prediction models are successfully constructed.In the four modeling methods,such as linear regression?Linear?,decision trees regression?DTR?,support vector regression?SVR?and gradient boosted regression trees?GBRT?,the algorithm of GBRT shows the highest predicted accuracies:the fitting goodness?R²?of H_cj and?BH?_max are0.895 and 0.905,respectively,and mean absolute errors are 82.8 kA/m?1.04 kOe?and9 kJ/m³?1.13 MGOe?,respectively.Based on GBRT model,a virtual material library withhighdimensioncomponentspaceiscreated,andthe composition-performance-price of magnets is preliminarily analyzed.Considering two variables of“the sum of rare-earth?REs?”and“the relative content of Ce?Ce_p?”,avirtualdatasetofH_cjand?BH?_maxareconstructedfor(PrNd_1-CepCe_Cep)_REsFe_93-REsTM₁B₆?TM is Zr,Nb,Ga or Ti elements?magnets.Taking the design of a Ce-containing bonded magnets with H_cj of 875 kA/m?11 kOe?as an example,a series of magnet compositions satisfying the cost performance requirements are given,such as(Nd_0.7Ce_0.3)₁₃Fe₈₀TM₁B₆,(Nd_0.5Ce_0.5)₁₄Fe₇₉TM₁B₆,(Nd_0.3Ce_0.7)₁₅Fe₇₈TM₁B₆.The reversal magnetizations of permanent magnets with different microstructure characteristics are simulated by finite element micromagnetic method.The relationships between H_cj,?of Nd₂Fe₁₄B and grain size,soft magnetic surface defect thickness,orientation and grain boundary are systematically studied.The results show that reducing the grain size,increasing the sizes of surface defect or grain boundary,and removing the non-magnetic defects would enhance coercivity temperature stability of the magnets.The increase of magnetostatic effect caused by the increase of grain size is the main reason for the reduction in H_cj.With the increase of grain size,the reversal magnetization behavior of magnet changes from uniform rotation to non-uniform rotation near 13 nm.Coercivity of the magnet is equal to the magnetocrystalline anisotropy field in uniform rotation,and decreases rapidly in non-uniform rotation.H_cj decreases exponentially with grain size when grain size is less than 100 nm,and tends to decrease logarithmically when it is greater than 100 nm.Meanwhile,coercivity temperature coefficient of the magnet decreases logarithmically with grain size increasing.The thickness of soft magnetic defect layer on grain surface determines the magnetization reversal behavior of magnet.The orientation dependence of H_cj shows that the magnetization reversal behavior of magnet changed from the“nucleation”type of the S-W model to the“pinning”type of the Kondorsky model with the increase of surface defect thickness.Coercivity of the magnet is equal to the nucleation field of the soft magnetic phase when defect thickness is less than 2 nm,whose value is reciprocal with the square of thickness.When defect thickness is larger than 2 nm,H_cj is equal to the de-pinning field of the domain wall at the interface between soft and hard magnetic phase,whose value is independent of the defect thickness.However,the existence of the soft magnetic surface defect layer is beneficial to the improvement of the coercivity temperature stability of magnet.The effect of grain boundary on the reversal magnetization of magnet depends on the magnetic properties and thickness of grain boundary.For weak ferromagnetic grain boundary,when grain boundary thickness is less than one exchange length,the magnetization reversal behavior of magnet has the same characteristics of uniform rotation,and H_cj is independent of the grain boundary thickness.With the increase of grain boundary thickness,the magnet gradually shows the characteristics of non-uniform rotation,and grain boundary would become the nucleation point of reversed magnetic domain.Coercivity of the magnet increases first and then decreases as grain boundary thickness increases.At the same time,coercivity temperature coefficient of the magnet increases with grain boundary thickness increasing.For non-magnetic grain boundary,magnetized grain would accelerate the reduction in H_cjj of the magnet.Also,the local stray field caused by the non-magnetic grain boundary increase the thermal degradation of H_cj.