France



&lt;br/&gt;&lt;br/&gt;Cobalt as a substitute for Iron, and combinations of different rare earths in alloy can increase the Curie temperature and coercivity of Nd2Fe14B type ferromagnets[1].&lt;br/&gt;Complex ferromagnets, with atomic scale ordering, require high resolution simulations which are computationally expensive due to individual treatment of atoms. The compromise of the atomistic model[2], allows nanometer scale simulations with reasonable efficiency, but requires input parameters often derived from ab initio calculations, or Density functional theory, creating a multi-scale model. Complex materials often have several input parameters, such as magnetic exchange and magnetocrystalline anisotropy constants, which cannot be easily evaluated using these methods. As a result, often the requirement is to fit the exchange parameter to macroscopic experimental data.&lt;br/&gt;For simple materials this can be evaluated with few test simulations, as the relationship between exchange and macroscopic properties behaves linearly for single element materials, as in the mean field model. Complex materials can have complex relationships between exchange and macroscopic properties, so many test simulations are often required to perform a full sweep of the parameter space. This body of work details the evaluation of exchange and anisotropy constants for 2:14:1, or Nd2Fe14B type rare earth ferromagnets, using the VAMPIRE atomistic software modelling package.&lt;br/&gt;Treating this as an optimisation problem reduces the number of atomistic simulations required for a given numerical precision of constant. Evaluation of exchange constants was performed using the Curie temperature as a figure of merit with several different methods of evaluating the Curie temperature compared for robustness and consistency, with the optimisation of these exchange constants performed with a combination of linear searching and root finding algorithms. These methods have often been compared for various rock magnets[3].&lt;br/&gt;The search uses a locally linear assumption, to prime the low temperature quantum rescaling in VAMPIRE, and to better parallelise the initial stages of the search.&lt;br/&gt;Similar approaches are taken to calculate the anisotropy constants of Nd2Fe14B to reproduce the First Order Magnetic Phase Transition[4] at high external fields and low temperatures.&lt;br/&gt;The exchange constant of various rare-earth ferromagnets is reproduced, yielding the correct macroscopic Curie temperatures without reliance on density functional theory/ab initio calculations.&lt;br/&gt;Lanthanum was used as the prototype for the Fe-Fe exchange, and this was fixed throughout the other ferromagnets. The Curie temperatures calculated are in good agreement with J.F.Herbst, 1991 [5].&lt;br/&gt;The First Order Magnetic Phase Transition was effectively reproduced, but requires additional tuning for a complete analysis of the relationship between second and fourth order anisotropy constants and the subsequent macroscopic magnetic behaviour.

**References:**

[1] Wei, L, et al. J. Less Common Metals 126 (1986); [2] R. F. L. Evans, W. J. Fan, P. Chureemart, T. A. Ostler, M. O. A.Ellis and R. W. Chantrell, Journal of Physics: Condensed Matter,vol. 26, 103202, (2014); [3] K. Fabian,V. P. Shcherbakov, S.A. McEnroe, Geochemistry, Geophysics, Geosystems, 14, 947, (2013); [4] J. M. Cadogan, J. P. Gavigantt, D. Givordt and H. S. Li, J. Phys. F: Met. Phys. 18 779 (1988); [5] J. F. Herbst Rev. Mod. Phys. 63, 819 (1991)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/4b9dd3a6e04c6e1367a35ec04d9cfb05.jpg)
The exchange paramaters calculated using the optimsiation method result in appropriate Curie temperatures when evaluated using the VAMPIRE atomsitic modelling software package. The Curie temperature calculated from this simulation compares well to the values from literature[5] (Herbst, 1991).&lt;br /&gt;
&lt;br /&gt;
Ce2Fe14B has not been calculated, as the rare earth behaves sufficiently differently to Lanthanum as to prevent using Lanthanum as the base of Cerium&#39;s Fe-Fe exchange in this manner. &lt;br /&gt;
&lt;br /&gt;
The magnitude of the exchange is presented, the heavier rare earths are ferrimagnetic in the 2:14:1 phase.



INTERMAG 2021

 Optimisation of atomistic modelling parameters for Nd2Fe14B-type rare earth ferromagnets, using the Curie temperature and first order magnetic phase transitions as figures of merit

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This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

Cobalt as a substitute for Iron, and combinations of different rare earths in alloy can increase the Curie temperature and coercivity of Nd2Fe14B type ferromagnets[1]. Complex ferromagnets, with atomic scale ordering, require high resolution simulations which are computationally expensive due to individual treatment of atoms. The compromise of the atomistic model[2], allows nanometer scale simulations with reasonable efficiency, but requires input parameters often derived from ab initio calculations, or Density functional theory, creating a multi-scale model. Complex materials often have several input parameters, such as magnetic exchange and magnetocrystalline anisotropy constants, which cannot be easily evaluated using these methods. As a result, often the requirement is to fit the exchange parameter to macroscopic experimental data. For simple materials this can be evaluated with few test simulations, as the relationship between exchange and macroscopic properties behaves linearly for single element materials, as in the mean field model. Complex materials can have complex relationships between exchange and macroscopic properties, so many test simulations are often required to perform a full sweep of the parameter space. This body of work details the evaluation of exchange and anisotropy constants for 2:14:1, or Nd2Fe14B type rare earth ferromagnets, using the VAMPIRE atomistic software modelling package. Treating this as an optimisation problem reduces the number of atomistic simulations required for a given numerical precision of constant. Evaluation of exchange constants was performed using the Curie temperature as a figure of merit with several different methods of evaluating the Curie temperature compared for robustness and consistency, with the optimisation of these exchange constants performed with a combination of linear searching and root finding algorithms. These methods have often been compared for various rock magnets[3]. The search uses a locally linear assumption, to prime the low temperature quantum rescaling in VAMPIRE, and to better parallelise the initial stages of the search. Similar approaches are taken to calculate the anisotropy constants of Nd2Fe14B to reproduce the First Order Magnetic Phase Transition[4] at high external fields and low temperatures. The exchange constant of various rare-earth ferromagnets is reproduced, yielding the correct macroscopic Curie temperatures without reliance on density functional theory/ab initio calculations. Lanthanum was used as the prototype for the Fe-Fe exchange, and this was fixed throughout the other ferromagnets. The Curie temperatures calculated are in good agreement with J.F.Herbst, 1991 [5]. The First Order Magnetic Phase Transition was effectively reproduced, but requires additional tuning for a complete analysis of the relationship between second and fourth order anisotropy constants and the subsequent macroscopic magnetic behaviour.

**References:**

[1] Wei, L, et al. J. Less Common Metals 126 (1986); [2] R. F. L. Evans, W. J. Fan, P. Chureemart, T. A. Ostler, M. O. A.Ellis and R. W. Chantrell, Journal of Physics: Condensed Matter,vol. 26, 103202, (2014); [3] K. Fabian,V. P. Shcherbakov, S.A. McEnroe, Geochemistry, Geophysics, Geosystems, 14, 947, (2013); [4] J. M. Cadogan, J. P. Gavigantt, D. Givordt and H. S. Li, J. Phys. F: Met. Phys. 18 779 (1988); [5] J. F. Herbst Rev. Mod. Phys. 63, 819 (1991)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/4b9dd3a6e04c6e1367a35ec04d9cfb05.jpg)
The exchange paramaters calculated using the optimsiation method result in appropriate Curie temperatures when evaluated using the VAMPIRE atomsitic modelling software package. The Curie temperature calculated from this simulation compares well to the values from literature[5] (Herbst, 1991). 
 
Ce2Fe14B has not been calculated, as the rare earth behaves sufficiently differently to Lanthanum as to prevent using Lanthanum as the base of Cerium's Fe-Fe exchange in this manner. 
 
The magnitude of the exchange is presented, the heavier rare earths are ferrimagnetic in the 2:14:1 phase.

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Composite materials, in the form of laminated and polymer matrix composites, are being increasingly used in manned and unmanned vessels and aircraft structures mainly due to their high strength and high stiffness to weight ratios. Composite structures are susceptible to degradation due to prolonged use, exposure to severe service environments, fatigue, sand abrasion as well as operator abuse, and neglect. This degradation increases the risk of operation and the cost of maintenance. Over the last two decades, progress has been made in structural state awareness using various sensing techniques such as acoustic emission, eddy current, and ultrasonic pitch hatch to diagnose damage and predict remaining life of the composite. Despite this progress, reliable detection and quantification of composite damage, particularly in the early stage, has remained a major challenge. Structural damage may be considered as a process that compromises the integrity of a structure. Delamination and cracking, two of the most common safety concerns of airframe structures, propagate rather slowly in the early stage but grow at a much faster rate in the later stage. Since early stage damage is not detectable using current technologies, it may be possible that by the time this damage is detected, the remaining life of a structure or its capacity has been severely degraded. The objective of this study is to show the feasibility of early stage damage detection utilizing embedding magnetic particles (Terfenol-D powder, a magnetostrictive material) into the composite structure, which is affected by the compressive stress surrounding them. Magnetostrictive materials exhibit dimensional changes in response to external magnetic fields. The inverse is also true; magnetization changes due to applied external stresses. When a composite material is cured, the particles are brought into compression due to shrinking of the resin, which provides a localized magnetic response. In this study, Terfenol-D (Tb0.3Dy0.7Fe1.92) was embedded between layers of a composite structure. A laminated panel, 8 inches by 8 inches, was fabricated from thirteen 0.01 inch thick unidirectional plies of a pre-impregnated AS4/3501-6 carbon/epoxy material system. The panel was pressed in an aluminum mold and cured in autoclave at 175 oC under vacuum pressure for about 3.5 hours. The Rectangular panels were cut to a nominal size of 8 inch by 1-inch tensile specimens. A pair of tapered fiber glass tabs was attached at both ends of the rectangular specimens in accordance with the ASTM standard D-3039/D3479. Figure 1(a) shows the test specimen and a disk cut out of the specimen for built-in anisotropy measurement using a VSM (Vibrating Sample Magnetometer). The specimen was then subjected to a quasi-static load up to 70% of the UTS (ultimate tensile strength/ultimate tensile stress to failure). Figure 1(b) shows the magnetization measurement within the VSM system and shows the reference measurement angle for the built-in anisotropy. Figure 2 shows the magnetization results for the different measurement angles, showing the built-in anisotropy before (2a) and after (2b) the load cycle. Following unidirectional loading, the sample clearly shows a change in built-in anisotropy. The slope of the hysteresis loop is now dependent upon angle, demonstrating a possible way to detect early stage damage using magnetostrictive particles embedded in a composite structure. Additionally, it appears to also provide information on the major load direction.

**References:**



**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ec7579761fac7b3092e06a41e62c5e2b.jpg)
Figure 1. (a) Tensile test specimen and a disk cut for magnetic characterization out of the Terfenol-D powder embedded composite panel. (b) Schematic of the magnetization measurement angle with respect to the tensile specimen loading direction.

![](https://assets.underline.io/uploads/markdown_image/1/image/f66edcf048cee46500e581eb85ca91bf.jpg)
Figure 2. Magnetic hysteresis loop measurement of the Terfenol-D embedded composite panel measured (a) before loading, and (b) after loading to 70% of UTS (Ultimate Tensile Strength).

 Measurement of Built-in Magnetic Anisotropy after Load Cycle for Polymer Composite Embedded Magnetostrictive Particles

In recent years, magnetoelectric composite materials have received more attention in the field of energy and power conversion. Many kinds of research have been devoted to improving magnetoelectric composite materials for energy and power conversions, including transformers, energy harvesters, and ME gyrators [1]. However, numerous researches are mainly focused on how to maximize the power conversion efficiency. Studies have shown that the bias magnetic field has an important effect on many types of magnetoelectric composite materials. And the bias magnetic field also affects the energy conversion characteristics [2]. Generally, the power conversion efficiency of piezoelectric materials is defined as the ratio of output electrical power to input mechanical energy. Correspondingly, the energy conversion process of ME composites introduces the influence of magnetoelastic energy [3]. The efficiency of the entire energy conversion is affected by the process of converting magnetic field energy into mechanical energy and mechanical energy into electrical energy. Therefore, we have introduced nanocrystalline FeCuNbSiB as a functional layer in the magnetoelectric composite material to converge the space magnetic field energy with its extremely high magnetic permeability. The introduction of this functional layer reducing the bias magnetic field demand of the composite material and improving the energy conversion efficiency. Fig. 1 shows the effect of different layers of FeCuNbSiB on the magnetoelectric voltage coefficient of the Galfenol-PZT laminate structure. It can be observed that after the introduction of multilayer FeCuNbSiB, the optimal magnetic bias of the magnetoelectric composite material is reduced from 200 Oe to 110 Oe. This optimal bias reduction is due to the introduction of the high magnetic permeability layer has a certain convergence effect on the magnetic field. Fig. 2 shows the influence of the frequency of the alternating magnetic field on the magnetoelectric voltage coefficient after the FeCuNbSiB layer is introduced. The test of energy conversion efficiency shows that the power conversion efficiency of the magnetoelectric composite material is increased by 8.7% under the optimal load resistance and the optimal bias magnetic field. A series of results show that the introduction of high-permeability layers can significantly improve the magnetic deflection characteristics of the magnetoelectric composite material and increase its power conversion efficiency.

**References:**

[1] C. Q. Zhao, M. J. PourhosseiniAsl and S. Dong, Journal of Physics D: Applied Physics., Vol. 51, p.243001(2018). [2] Z. Xin, C.M. Leung and J. Li, IEEE Transactions on Industrial Electronics., Vol. 66, 2499-2505(2018). [3] Z. Xin, M. Gao and X. Tang, IEEE Sensors Journal., Vol. 20, p.752-759(2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/761d4cb67f6d6e7edcfc6f88a66ab72b.jpg)
Fig.1 Variation of magnetoelectric voltage coefficient with bias magnetic field introducing different layers of FeCuNbSiB

![](https://assets.underline.io/uploads/markdown_image/1/image/fb0cd5547f09c9534037de173f5a39e2.jpg)
Fig.2 The influence of alternating magnetic field frequency on magnetoelectric voltage coefficient under different bias magnetic fields after introducing 5 layers of FeCuNbSiB

 Enhanced power and energy conversion of magnetoelectric laminate heterostructures based on high-permeability FeCuNbSiB nanocrystalline

I. INTRODUCTION As the first generation of rare earth transition metal based permanent magnet, SmCo5 has a high anisotropy field of more than 240 kOe, and the coercivity of its nanocrystalline magnet is as high as 50 kOe [1]. Hot deformation technology is an effective way to prepare anisotropic SmCo5 nanocrystalline magnets. A.M.Gabay et al found that the texture in (00l) direction can be obtained for the SmCo5 magnets after upsetting deformation[2]. Yue et al prepared anisotropic nanocrystalline magnets by upsetting deformation. When the deformation reaches 90%, a strong c-axis texture appears in the crystals[3]. However, the upsetting deformation method can not achieve large-scale continuous production. In addition, the magnetic properties of the magnet at different positions are quite different. A.S. Kim et al prepared anisotropic cylindrical NdFeB magnets by hot extrusion, but there is still a large space to improve the magnetic properties[4]. Up to now, there is no detailed report on the preparation of SmCo5 magnets by hot extrusion. In this paper, a new hot deformation method was designed. The anisotropic SmCo5 nanocrystalline magnet was prepared by hot extrusion. The microstructure, texture and magnetic properties of the hot extruded (HE) SmCo5 magnet were systematically studied, and the deformation mechanism is analyzed in detail. II. EXPERIMENTAL SmCo5 ingot was prepared by induction melting method with 99.9% pure elements, excess Sm of 5 wt.% was added to compensate the Sm losses due to evaporation. The as-cast ingot was crushed into blocks that were subjected to high energy ball milling, which was carried out under argon atmosphere for 5 h in a high energy mill. Then the milled powder was put into WC-Co mold, hot pressed (HP) by spark plasma sintering (SPS) at 700 degree Celsius under 500MPa. Then the HP magnet was extruded by extrusion die with extrusion aperture of 10 mm*2.5 mm. The phase composition and texture of the samples were analyzed by X-ray diffraction (XRD). The alignment of the samples was measured by electron backscattered diffraction (EBSD). The microstructure of the samples was observed by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Magnetic measurement of the samples was carried out in a Quantum Design physical properties measurement system magnetometer with a maximum magnetic field of 9 T. III. RESULTS AND DISCUSSION Fig. 1 (a) shows a schematic diagram, which explains the test direction and regions of the HE magnet. Fig. 1(b) shows the XRD results of the HE magnet in different directions. When the test direction is parallel to the X and Z direction, the HE magnet does not show obvious c-axis texture, the relative intensity ratio between the diffraction peaks of (002) and (111) [I(002)/I(111)] is low, and the diffraction pattern is almost the same as that of the HP magnet. But when the test direction is Y direction, the (00l) peaks in the XRD diffraction pattern is significantly enhanced, along with the decrease of other peaks. Meanwhile, the I(002)/I(111) increases significantly. This result shows that the HE magnet forms a strong c-axis texture in the Y direction. The cross-section of the HE magnet (Fig. 1a, pink section) was observed by SEM. It is worth to note that the grains in the region 1 are aligned along the Y direction (Fig. 2a), indicating a strong c-axis texture. The grains in the region 2 tend to be aligned along the X direction (Fig. 2b), which is perpendicular to the direction of grains in the region 1, indicating that the aligned direction of the grains has changed when approaching the region 2. Furthermore, it is not conducive to the formation of the Y-direction texture. A small amount of grains in the region 3 are aligned along the Y direction (Fig. 2c), the most grains have no obvious alignment. Therefore, the results show that the Y direction is the main alignment direction of the HE magnet. Besides, The XRD results of the three regions show that the value of the I(002)/I(111) follows a sequence: region 1＞region 2＞region 3. In addition, the remanence of the three regions also show the same trend. The poor remanence of the region 3 is due to the change of grains alignment, which is related to the deformation mechanism during the HE process. The deformation mechanism of the HE magnet will be further investigated. IV. CONCLUSIONS The anisotropic nanocrystalline SmCo5 permanent magnet with strong c-axis texture can be prepared by hot extrusion, which provides a promising protocol to fabricate high performance nanocrystalline SmCo5 magnets. Meanwhile, it will be a potential method for improving production efficiency of the anisotropic SmCo5 nanocrystalline magnets.

**References:**

[1] J. Ding, P. G. McCormick, and R. Street, J. Alloys Compounds, 191, 197, (1993). [2] A. M. Gabay, et al., Journal of Magnetism and Magnetic Materials, 321, 3318-3323, (2009). [3] M. Yue, J. H. Zuo, W. Q. Liu, Journal of Applied Physics, 109, 07A711, (2011). [4] A.S. Kim, et. al., Materials Engineering, 12, 93-100, (1990).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/98292bdbe140d5da256dedfbeea968ac.jpg)
Fig. 1. (a) Schematic diagram of the HE SmCo5 magnet , (b) XRD patterns of the HP and HE SmCo5 magnets in different directions.

![](https://assets.underline.io/uploads/markdown_image/1/image/ba94dee0ec8e55e3e474f72b17dcab97.jpg)
Fig. 2. BSE images of the HE SmCo5 magnet in different regions, (a) region 1, (b) region 2, (c) region 3. The red and yellow arrows represent the different directions of the HE SmCo5 magnet, The green arrows represent the alignment of the grains.

 Anisotropic Nanocrystalline SmCo5 Permanent Magnet Prepared by Hot Extrusion

There are several Sm-Fe intermetallic compounds such as Sm2Fe17, SmFe2, SmFe3 phases in the Sm-Fe alloys.1 Among them, the Sm2Fe17 intermetallic compound has been studied for permanent magnet application.2-4 The Sm2Fe17N3 compound possesses a large anisotropy field and a high saturation magnetization and has been prepared in Sm2Fe17N3 powder. Sm-Fe-N bulk magnets cannot be produced by the sintering of Sm-Fe-N powder, however, due to the poor thermal properties of the powder.5 Therefore, it would be desirable if the magnetic properties of the Sm2Fe17 phase could be increased without the need for nitrogenation. Although several studies were carried out on the Sm2Fe17 phase at the early stage of such research, relatively little attention has been paid to this material due to their easy-plane anisotropy. We have continued to study the Sm2Fe17-type phase with the additions of both Ti and Zr to Sm2Fe17-type alloys. The structures and magnetic properties of (Sm,Zr)Fe10 and (Sm,Zr)(Fe,Ti)10 melt-spun ribbons are discussed. (Sm1-xZrx)Fe10 (x = 0–0.3) and (Sm1-xZrx)Fe9.5Ti0.5 (x = 0–0.3) alloy ingots were prepared by induction melting in an argon atmosphere. Small amounts of the alloy ingots were induction melted under an argon atmosphere in a quartz crucible and then ejected through an orifice with argon onto a chromium-coated copper wheel rotating at a surface velocity of 50 m/s. The pulverized melt-spun ribbons were annealed at 973-1273 K for 1 h under an argon atmosphere. The phases in the specimens were examined by X-ray diffraction (XRD). The hysteresis loops of the specimens were measured at room temperature using a vibrating sample magnetometer (VSM). The SmFe10 melt-spun ribbon showed a narrow hysteresis loop with a coercivity less than 1 kOe. The substitution of Zr for Sm in the SmFe10 melt-spun ribbon did not change the structure and magnetic properties. Thus, heat treatment of these specimens was carried out to increase the coercivity. Annealing resulted in an increase in coercivity of the (Sm1-xZrx)Fe10 (x = 0–0.3) specimens. Figure 1 shows the hysteresis loops of the (Sm1-xZrx)Fe10 (x = 0–0.3) melt-spun ribbons annealed at 1073 K. The maximum coercivity of 1.8 kOe was obtained in the (Sm0.9Zr0.1)Fe10 melt-spun ribbon when annealed at 1073 K. Next, (Sm1-xZrx)Fe9.5Ti0.5 (x = 0–0.3) melt-spun ribbons were prepared and the effect of the substitution of Ti for Fe in the SmFe10 alloy was investigated. The substitution of Ti for Fe in the (Sm1-xZrx)Fe10 (x = 0–0.3) melt-spun ribbon resulted in the formation of the amorphous phase. The (Sm1-xZrx)Fe9.5Ti0.5 (x = 0–0.3) melt-spun ribbons showed a narrow hysteresis loop with a coercivity less than 0.5 kOe, regardless of the Zr content. However, heat treatment of these specimens resulted in a large increase in coercivity. Figure 2 shows the hysteresis loops of the (Sm1-xZrx)Fe9.5Ti0.5 (x = 0–0.3) melt-spun ribbons annealed at 1173 K. The maximum coercivity of 4.5 kOe was obtained in the (Sm0.7Zr0.3)Fe9.5Ti0.5 melt-spun ribbon when annealed at 1173 K. The XRD study revealed that the annealed specimen mainly consisted of the Th2Zn17-type phase. In conclusion, the specimens with higher Zr and Ti content tended to exhibit a higher coercivity than those with lower Zr and Ti content. The highest coercivity of 4.5 kOe was achieved in the annealed (Sm0.7Zr0.3)Fe9.5Ti0.5 melt-spun ribbon with the h2Zn17-type phase.

**References:**

 [1] K. H. J. Buschow, J. Less-Common Metals 25, 131 (1971). [2] J. M. D. Coey and H. Sun, J. Magn. Magn. Mater. 87, L251 (1990). [3] T. Iriyama, K. Kobayashi, N. Imaoka, T. Fukuda, H. Kato, and Y. Nakagawa, IEEE Trans. Magn. 28, 2835 (1992). [4] M. Katter, J. Wecker, C. Kuhrt, L. Schultz, and R. Grössinger, J. Magn. Magn. Mater. 117, 419 (1992). [5] F. A. O. Cabral, S. Gama, E. de Morais, N. L. Sanjurjo, C. A. Rubeiro, and C. C. Colucci, IEEE Trans. Magn. 32, 4365 (1996).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/fe0eadfffb15e1fac8b6c6cd9fe03d71.jpg)
Fig. 1 Hysteresis loops of the (a) SmFe10, (b) (Sm0.9Zr0.1)Fe10, (c) (Sm0.8Zr0.2)Fe10, and (d) (Sm0.7Zr0.3)Fe10 melt-spun ribbons annealed at 1073 K.

![](https://assets.underline.io/uploads/markdown_image/1/image/b9409b75c3394903cb0a435fb7ac6405.jpg)
Fig. 2 Hysteresis loops of the (a) SmFe9.5Ti0.5, (b) (Sm0.9Zr0.1)Fe9.5Ti0.5, (c) (Sm0.8Zr0.2)Fe9.5Ti0.5, and (d) (Sm0.7Zr0.3)Fe9.5Ti0.5 melt-spun ribbons annealed at 1173 K.

 Magnetic properties of (Sm,Zr)Fe10 melt-spun ribbons

1. Introduction Anisotropic nanocomposite (NC) magnet which utilizes the exchange coupling effect between the hard and soft magnetic phase is attracting a lot of attention as a next-generation permanent magnet [1]. However, the realization of anisotropic NC magnet is still experiencing many difficulties, and its maximum energy product (BHmax) is less than that of a single-phase permanent bulk magnet [2, 3] since its microstructures are not well-controlled in the nanoscale. In order to realize the nanoscale-controlled microstructure with an effective exchange coupling effect, the grain size of the soft magnetic phase needs to be smaller than twice the domain wall width of the hard magnetic phase [4]. In this work, we attempted to prepare the anisotropic bulk NC magnet with the nanoscale-controlled microstructure by using the powder metallurgy process. SmCo5 compound as a hard magnetic phase which has a high anisotropy field [5] and Fe with high saturation magnetization as a soft magnetic phase were chosen as a preliminary work. The precursor needs to satisfy with the following requirements: (1) anisotropic hard magnetic powder, (2) fine soft magnetic powder. In addition to these requirements, the surface oxide of hard and soft magnetic powder should be as thin as possible for effective exchange coupling effect. Therefore, the preparation and handling of the micro-sized SmCo5 and nano-sized Fe powder have been done in low oxygen atmosphere. Using the mixture of these powders, we have synthesized an anisotropic bulk NC magnet and evaluated its microstructure and magnetic properties. 2. Experimental procedure SmCo5 ingot was prepared by the arc-melting process. The ingot was roughly crushed to around 100 μm powder by a blender. SmCo5 powder was more refined by the jet-milling process in a glove box. Fe nanopowder was prepared by the induction thermal plasma process. The detail experimental set up and condition were described elsewhere [6]. The prepared nano-sized Fe powder was handled in a glove box to prevent the oxidation. Then, SmCo5 powder and Fe nanopowder were mixed with as SmCo5-10 wt.% Fe by a homogenizer in heptane. The mixture was magnetically aligned under 2 T at 300 K, then consolidated at 600 °C under 300 MPa by the direct current sintering process. The phase of SmCo5 powder and SmCo5/Fe NC magnet was analyzed by X-ray diffractometer (XRD). Magnetic measurement was carried out by a vibrating sample magnetometer (VSM). The microstructure of the NC magnet was observed by scanning electron microscope (SEM). 3. Results and discussion In the XRD profile, the compound prepared by the arc-melting was single phase of SmCo5. Even after the jet-milling process, the peaks of single phase SmCo5 without oxides were also detected. The peaks of the jet-milled SmCo5 powder were slightly broadened because the particles were damaged by large mechanical energy during the jet-milling. The median particle size (D50) of the jet-milled powder was measured as 2.5 μm. In Fig. 1(a), the black line represents the hysteresis loop measured along an easy direction of magnetically aligned the jet-milled SmCo5 powder. The coercivity of 12.8 kOe was obtained. The magnetizations at 9 T were almost saturated, and its values were measured as 100 emu/g, which is similar with the intrinsic properties of SmCo5 compound [7]. The red line in Fig. 1(a) shows the hysteresis loop measured along an easy direction of magnetically aligned SmCo5-10 wt.% Fe bulk NC magnet. An anisotropic magnetic behavior was clearly confirmed by the magnetic measurement. The magnetization at 9 T was measured about 10 % higher than that of SmCo5 powder because of the addition of 10 wt.% Fe nanopowder, indicating that the SmCo5 and Fe powders were consolidated without a formation of another intermetallic compounds. The XRD profile also showed the peaks of only SmCo5 and Fe. The recoil loop clearly represented a non-linear spring back effect, indicating that the nano-sized Fe powder with negligibly thin oxide film was partially exchange-coupled with anisotropic SmCo5 powder. Another evidence of exchange-coupling is that the remanent magnetization was increased by the exchange-coupled Fe. In consequence, we realized the exchange-coupled anisotropic SmCo5/Fe bulk nanocomposite magnet by the low oxygen powder metallurgy process. This work proposed the strategy to achieve an improved anisotropic bulk NC magnet. Fig. 1(b) shows the cross-sectional image of SmCo5-10 wt.% Fe bulk NC magnet. There are many pores in the magnet, which leads to the reduction of the effective exchange interaction. In order to obtain the more densified magnet, the higher sintering temperature and/or pressure is effective. Moreover, there is a possibility to refine the Fe nanoparticle by controlling the conditions of thermal plasma such as counterflow gas and radial injection of cooling gas [8]. It is expected that the finer Fe nanoparticle could be more effectively exchange-coupled with a hard magnetic phases. 4. Conclusion In this study, SmCo5 powder was prepared by the jet-milling process, and coercivity of 12.8 kOe and magnetization of 100 emu/g were obtained. Fe nanopowder with average particle size of 100 nm, was synthesized by ITP process. The magnetic measurement revealed the anisotropic magnetic behavior of SmCo5/Fe NC magnet.

**References:**

[1] E. F. Kneller and R. Hawig, IEEE Transactions on Magnetics, Vol. 27, p.3588 (1991) [2] M. Ito, K. Majima and H. Nagai, Journal of alloys and compounds, Vol. 329, p.272 (2001). [3] J. Zhang, S. Y. Zhang and B. G. Shen, Journal of Applied Physics, Vol. 89, p.5601 (2001) [4] R. Fischer, T. Leineweber and H. Kronmüller, Physical Review B, Vol. 57, p.10723 (1998). [5] H. Nakamura, Scripta Materialia, Vol. 154, p.273 (2018). [6] Y. Hirayama and K. Takagi, Journal of Alloys and Compounds, Vol. 792, p.594 (2019). [7] S. Liu, Chinese Physics B, Vol. 28, p.017501 (2019) [8] X. Zhang, Z. Liu and T. Watanabe, Chemical Engineering Science, Vol. 230, p.116217 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/19f15556270244607e86f5e12726992e.jpg)
Fig. 1. (a) Hysteresis loops measured along an easy direction of magnetically aligned SmCo5 powder (black line) and SmCo5-10 wt.% Fe bulk NC magnet (red line). (b) Cross sectional image of SmCo5-10 wt.% Fe bulk NC magnet.

 Preparation of SmCo5 and Fe magnetic precursor for realizing anisotropic bulk nanocomposite magnet by low oxygen powder metallurgy process

[Introduction] Among permanent magnets applying to various industries such as automobiles, power plants, electronics, etc., the Sm-Co hard magnetic materials have been attracted much attention recently due to their high magnetocrystalline anisotropy (~107 J/m3) and saturation magnetization (~1.2 T) as well as high curie temperature (~1190 K)[1]. There have been many efforts to increase the high coercivity of permanent magnet materials in order to improve the maximum magnetic energy further. Since the coercivity depends on the microstructure of the magnet materials, the control of their particle size can be an effective strategy to form single-domain or anisotropic oriented grains through the powder metallurgical approach. For example, the high-energy ball milling process has been used to obtain the fine particles from crushing the casted ingots or ribbons produced by a rapid solidification process[2], although it could result in the inflow of the grinding medium or the oxidation of materials including the rare-earth elements by thermal energy. Recent studies have also reported that the nanoscale Sm-Co nanoparticles can be produced through a chemical or physical combination of Sm and Co precursors with CaO before the reduction diffusion process with metallic calcium as a reductant[3, 4]. However, the toxic compounds can be generated under the chemical process, and there are limitations to industrial applications because of difficulties in mass production. Therefore, in this study, we report the improved method for synthesis of high-performance Sm-Co particles by introducing Ca(ac)2 powder and calcination process, and also aim to understand the relation between the magnetic properties and microstructures of Sm-Co nanoparticles. [Experimental procedures] Sm2O3, CoO, and Ca(ac)2 powder were used for the synthesis of Sm-Co hard magnetic materials. The Sm2O3, CoO, and Ca(ac)2 powder were mixed in an atomic ratio of 1: 5~8: 8~48. The mixture was crushed roughly using the zirconia ball with a diameter of 3 mm. The mass ratio of balls to powder was about 10: 1. The calcination process of the crushed mixture was carried out in the temperature range of 700 to 1000 oC in order to improve homogeneity between elements and decompose from Ca(ca)2 to CaO. After that, these calcinated specimens were reduced to Sm2Co17 or SmCo5 particles at 900 oC for 1 hr under Ar atmosphere using metallic calcium. The reduced products were washed using 0.1 M NH4Cl-methanol solution to remove the residual CaO. [Results and discussion] It was found that the calcination before the reduction diffusion process was a significant step to manufacture successfully Sm-Co particles with high coercivity and squareness (Mr/Ms). As shown in Fig. 1, the Sm-Co particles after the reduction process without the ball milling process showed low coercivity of 1.7 kOe while the mixture crushed by the ball milling had an increased coercivity of 6.6 kOe, and the XRD results showed that both Sm2Co17 and SmCo5 phases were observed. In the condition under the calcination process at 800 oC after the ball milling, the reduced Sm-Co particles showed the coercivity of 7.2 kOe and the magnetization of 93 emu/g under the applied field of 2.5 T. In addition, it was fully composed of the typical Sm2Co17 phase. These results confirmed that the proper condition of milling and calcination is required in order to obtain effectively the targeted phase and advantages for inhibition of the grain growth by addition of Ca(ac)2. Fig. 2a shows the magnetic properties of the aligned Sm2Co17 particles with the amount of Ca(ac)2. In the fixed atomic ratio of Sm: Co to be 1: 8, the atomic ratio of Ca was controlled from 8 to 40. It was observed that all the particles, regardless of the amount of Ca(ac)2, were reduced into the Sm2Co17 phase through the optimized calcination and reduction process. Thus the magnetization values remained relatively constant in the range of 91 to 95 emu/g. However, other magnetic properties such as coercivity, squareness gradually improved as the amount of Ca(ac)2 increased, indicating that the particle size reached toward the single domain size(~300 nm) of Sm2Co17(Fig. 2b), and the fraction of isolated single crystal particles increased. Under the optimal condition, the Sm2Co17 hard magnetic particles were found to have a high alignment of 86% and a maximum energy product of 14.5 MGOe. A more detailed analysis of the microstructural characteristics will be discussed.

**References:**

[1] R. Skomski and D. J. Sellmyer, Springer US, pp. 1-57 (2006). [2] Y. Wang, Y. Li, C. Rong, and J. P. Liu, Nanotechnology, vol. 18, p. 465701 (2007). [3] W. Liu and P. G. McCormick, Journal of Magnetism and Magnetic Materials, vol. 195, p. L279 (1999). [4] B. Shen et al., Angew Chem Int Ed Engl, vol. 58, p. 602 (2019).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e5bd8815942e57540c047f9faf513376.jpg)
Fig. 1. The hysteresis loops of the Sm-Co particles reduced at 900 oC for 1 hr with different conditions.

![](https://assets.underline.io/uploads/markdown_image/1/image/77d703ec33051ddf8bcec5dc7ecbf72b.jpg)
Fig. 2. (a) The magnetic properties of Sm2Co17 particles with the amount of Ca(ac)2 and (b) the SEM images of the particles in an atomic ratio of Sm: Co: Ca = 1: 8: 40.

 Development of a modified mechanochemical process for high-performance Sm-Co particles

In recent years, much efforts has been paid to synthesize new compounds having the potential for permanent magnet application. One of the new compounds is the RFe12 (R = rare earth) intermetallic compound.1-3 Although the binary RFe12 intermetallic compounds with the ThMn12-type structure are not thermodynamically stable and do not exist in bulk form, it has been found that the substitution of T (T = Ti, V, Cr, Mo) for Fe in the RFe12 intermetallic compound stabilizes the ThMn12-type structure.4-6 The objective of the present study was to produce anisotropic Sm(Fe,Ti)12 magnets. In the case of Nd-Fe-B magnets, anisotropic Nd-Fe-B magnets have been produced by either the sintering of Nd-Fe-B powder or hot deformation of hot-pressed Nd-Fe-B magnets. In this study, we attempted to produce anisotropic Sm(Fe,Ti)12 magnets by the hot deformation of hot-pressed Sm(Fe,Ti)12 magnets. The magnetic properties of the hot-deformed Sm(Fe,Ti)12 magnets are discussed. Sm(Fe,Ti)12 alloy ingots were prepared by induction melting in an argon atmosphere. The alloy ingots were induction melted and then ejected through an orifice with argon onto a copper wheel. The resultant melt-spun ribbons were comminuted into powders and then hot-pressed by the spark plasma sintering (SPS) method. Hot deformation of the hot-pressed Sm(Fe,Ti)12 magnets was performed in a vacuum at 973–1173 K under a pressure of ~200 MPa by the SPS method. The specimens were examined by X-ray diffraction (XRD), a scanning electron microscope (SEM), a transmission electron microscope (TEM), and a vibrating sample magnetometer (VSM). The hot-pressed Sm(Fe,Ti)12 magnets were successfully hot deformed to an 80% reduction without cracking. The magnetic properties of the resultant hot deformed Sm(Fe,Ti)12 magnets were examined. Figure 1 shows the hysteresis loops of the hot-deformed Sm(Fe,Ti)12 magnets, measured parallel and perpendicularly to the pressing direction. The magnetic anisotropy of the hot-deformed Sm(Fe,Ti)12 magnets was confirmed by the existence of a higher remanence in the parallel direction than in the perpendicular direction. This indicates that anisotropic Sm(Fe,Ti)12 magnets were successfully produced by the hot deformation of hot-pressed Sm(Fe,Ti)12 magnets. In order to examine the crystallographic alignment of the Sm(Fe,Ti)12 phase, the surface of the SmFe11Ti magnets were examined by XRD. The results are shown in Figure 2. The XRD patterns of the hot-deformed Sm(Fe,Ti)12 magnets show clear diffraction peaks of the Sm(Fe,Ti)12 phase, but the XRD pattern of the Sm(Fe,Ti)12 magnet hot-deformed at 1173 K was slightly different from that of the Sm(Fe,Ti)12 magnet hot-deformed at 973 K. It was found that the hot-deformed Sm(Fe,Ti)12 magnets contained a small amount of the α-Fe phase together with the Sm(Fe,Ti)12 phase. Although the magnetic measurements revealed that the hot-deformed Sm(Fe,Ti)12 magnets exhibited slight magnetic anisotropy, they did not show clear crystallographic alignment of its Sm(Fe,Ti)12 phase. In conclusion, Sm(Fe,Ti)12 magnets were successfully produced by the hot deformation. Magnetic measurements revealed that the hot-deformed Sm(Fe,Ti)12 magnets exhibited a relatively low coercivity value but were slightly magnetically anisotropic. However, no clear crystallographic alignment of its Sm(Fe,Ti)12 phase was observed in the XRD studies.

**References:**

[1] F. R. De. Boer, et al. J. Less-Common Met. 135, 199 (1987). [2] L. X. Liao, Z. Altounian, and D. H. Ryan, J. Appl. Phys. 70, 6006 (1991). [3] L. Shultz and J. Wecker, J. Appl. Phys. 64, 5711 (1988). [4] Y. Wang, et al. J. Appl. Phys. 67, 4954 (1990). [5] Y. Otani, H. S. Li, and J. M. D. Coey, IEEE Trans. Magn. 26, 2658 (1990). [5] J. Yang, Ph. Oleinek, K.-H. Müller, J. Appl. Phys. 88, 988 (2000). [6] E. Tomey, et al. J. Alloys Compd. 231, 195 (1995).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/7d88021d8a27ee02aab711e56a845f03.jpg)
Fig. 1 Hysteresis loops of the hot-deformed Sm(Fe,Ti)12 magnets 
produced at (a) 973 K, (b) 1073 K, and (c) 1173 K.

![](https://assets.underline.io/uploads/markdown_image/1/image/b74f592c60860d1bb2f93a16317539c9.jpg)
Fig. 2 XRD patterns of the hot-deformed Sm(Fe,Ti)12 magnets 
produced at (a) 973 K, (b) 1073 K, and (c) 1173 K.

 Magnetic properties of Sm(FeTi)12 hot deformed magnets

At present, rare-earth-based permanent magnet (REPM) R2Fe14B is one of the most widely used permanent magnets with excellent performance. However, improving this material's properties is still the main topic so far in this field [1]. For R2Fe14B alloys, it needs to use heavy rare earth elements to obtain high coercive force, which is not conducive to the balanced application of rare earth resources. In contrast, R2Fe14C system has the same tetragonal structure as R2Fe14B but a larger magnetic anisotropy field, especially when R is a light rare earth element [2]. This means a great potential to obtain high coercive force in this system, which is necessary for developing medium performance and high coercive force magnets based on high abundance light rare earth elements [3]. However, the R2Fe14C system suffers from the low phase stability of the tetragonal phase produced by a sluggish solid-state reaction process. Therefore, in this study, we carried on a thorough investigation in the Pr2Fe14C system considering the effects of element doping and heat treatment on the phase evolution. Fig.1 shows the XRD patterns of the as-spun and annealed samples of Pr15Fe79(C1-xBx)6 (x = 0, 0.05, 0.2, 0.4 and 0.6) series. In the as-spun flakes, only α-Fe and Pr2Fe17 phase are found in the samples with x = 0, 0.05, 0.2 and 0.4, while the Pr2Fe14C phase were not observed until x = 0.6. It suggests that, without enough amount of B doping, α-Fe and Pr2Fe17 can not form 2:14:1 phase via solid-state transformation in Pr-Fe-C system. On the other hand, after the annealing process at 750 °C, the 2:14:1 phase starts to form even in the x = 0.05 sample. As shown in Fig. 1(b), the amount of the 2:14:1 phase is small then, but it becomes dominant when the B content is 0.2. The amount of α-Fe dramatically decreases at the same time. Due to the high rare-earth content in these samples, there is also a pronounced peak at 2θ = 30° of the Pr-rich phase crystallized during the annealing. The oxidation of the rare-earth-rich phase during the annealing process causes the other peak at 2θ = 29°. More importantly, the lower limit of the solid-state reaction temperature of the 2:14:1 phase decreases continuously with the doping of B, from 950 °C to 600 °C. It means that the B doping reduces the forming energy of the 2:14:1 phase. Fig.2 shows the initial magnetization and demagnetization curves for the annealed samples with different B contents. With the increase of B content, both the remanent magnetization (Mr) and the coercivity field (Hc) exhibit an overall enhancement. This is consistent with the XRD results, indicating that the content of the 2:14:1 phase is increased. There is also a waist-like feature on the demagnetization curve of the samples with low B content, which is a sign of the coexistence of soft and hard magnetic phases. Even though the magnetization is not saturated at 3 T, the Mr and Hc are still as high as 70.5 emu/g and 19.1 kOe, respectively, in the sample with x=0.6. This considerable value of coercivity may be related to the fine microstructure of the samples. As can be seen from the inset of Fig.2, the average grain size is about 2 mm and does not change too much with the increase of annealing temperature. This is because the main phase is surrounded by a rare-earth-rich phase, limiting the growth of the main phase grains. This is another advantage of the R2Fe14C system. We systematically investigated the phase evolution of the Pr2Fe14C system and established an effective way to obtain a relatively large percent of 2:14:1 phase. By optimizing the composition and process, we can also control the microstructure of the main phase and obtain promising magnetic properties. The Pr2Fe14C material has great potential to be used for bonded magnets and hot deformed magnets. Acknowledgments This work was supported by the Beijing Natural Science Foundation (No. 2182006), the General Program of Science and Technology Development Project of Beijing Municipal Education Commission of China (No. KM201710005006), the National Natural Science Foundation of China [No.51401002], and Program of Top Disciplines Construction in Beijing (PXM2019_014204_ 500031).

**References:**

[1] Buschow, K. H. J., New developments in hard magnetic materials. Reports on Progress in Physics 1991, 54 (9), 1123. [2] Burzo, E., Permanent magnets based on R-Fe-B and R-Fe-C alloys. Reports on Progress in Physics 1998, 61 (9), 1099. [3] Coey, J. M. D., Permanent magnets: Plugging the gap. Scripta Materialia 2012, 67 (6), 524-529.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/2dd1f0ce47d374061700e3ab8fde8143.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/d6ceed3758db8ef26d6326330b67b88b.jpg)

 Phase and magnetism evolution in Pr2Fe14C system upon B doping and heat treatment

The high performance permanent magnets are indispensable for many commercial and military applications. Rare-earth hard magnetic nanoparticles have drawn great attention due to their potential applications in nanocomposite permanent magnets with high performance. Different methods have been employed to prepare hard magnetic nanoparticles including chemical methods, electrodeposition, spark erosion and ball milling. The ball milling technique, used for the preparation of nanoparticles, is a simple, inexpensive and efficient method for size reduction of nanocrystalline powders. The experimental parameters involved in ball-milling technique, such as milling time, milling energy, and ball size, are determinant in what concerns the magnetic properties of the nanoparticles. The milling temperature and milling medium are also known as critical factors impacting the morphology and performance of the nanoparticles. Here, we report results on the morphology, structure, and magnetic properties of Ce14Fe76Co4B6 nanoparticles prepared by high-energy ball milling at low temperature, in liquid nitrogen, from nanaocristaline ribbons precursors. At regulate intervals of time, in the milling vial was introduced liquid nitrogen, in order to compensate the evaporation. We found that: (i) the optimal interval for introducing liquid nitrogen into the vial is 20 minutes, since for a longer interval, the liquid nitrogen evaporates and the sample becomes contaminated, (ii) the morphology and size of the powders change with the milling time, from large particles with irregular shapes to small dimensions (about 150 nm) and rounded shapes for a milling time of 420 minutes (the microstructure of powders milled 420 h, is shown in Figure 1.) (iii) the structure and magnetic properties of the nanoparticles were kept close to those of the precursor ribbons by milling in liquid nitrogen (a comparison between the hysteresis curves for powders and the precursor ribbons is shown in Figure 2). The Ce14Fe76Co4B6 nanoparticles obtained by ball milling in liquid nitrogen have great potential to be used for the production high performance nanocomposite permanent magnets. Acknowledgement This work was supported by a grant of the Romanian Ministry of Education and Research, CCCDI - UEFISCDI, project number PN-III-P2-2.1-PED-2019-2054, within PNCDI III. &lt;!--![endif]----&gt;&lt;!--![endif]----&gt;&lt;!--![endif]----&gt;

**References:**

[1] Baolu Zhou, Zhongxue Li and Congcong Chen, Global Potential of Rare Earth Resources and Rare Earth Demand from Clean Technologies, Minerals 7 (2017) 203. [2] Thanh Anh Huynh and Min-Fu Hsieh, Performance Analysis of Permanent Magnet Motors for Electric Vehicles (EV) Traction Considering Driving Cycles, Energies 11 (2018) 1385. [3] M. Grigoras, M. Lostun, G. Stoian, D.D. Herea, H. Chiriac, N. Lupu, Microstructure and magnetic properties of Ce10+xFe84−xB6 nanocrystalline ribbons versus preparation conditions, J. Magn. Magn. Mater. 432 (2017) 119–123. [4] J. F. Herbst, M. S. Meyer and F. E. Pinkerton, Magnetic hardening of Ce2Fe14B, J. Appl. Phys. 111, 07A718 (2012).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/eaaa31845ba980e59e6fd93570814151.jpg)
Fig 1. The SEM micrograph of Ce14Fe76Co4B6 
powders milled 420 h in liquid nitrogen.

![](https://assets.underline.io/uploads/markdown_image/1/image/c84ddc682ad13f3ca51fdaac70d5be13.jpg)
Fig 2. The hysteresis curve of Ce14Fe76Co4B6 ribbons (black) and powders (red) milled 420 h in liquid nitrogen.

 Characterization and Magnetic properties of Ce-FeCo-B Nanoparticles Prepared by Cryo-milling

HDDR process can not only refine the coarse R2Fe14B grains (~ 100 μ m) into fine grains (~300 nm), but also induce these fine grains to be oriented along the c-axis. The grain refinement can improve the coercivity of the magnetic materials, and the grain orientation is helpful to obtain high remanence, so the anisotropic R2Fe14B materials with high coercivity, remanence and maximum energy products can be obtained after HDDR process. Recent researches show that the coercivity of HDDR R2Fe14B magnetic materials can be enhanced to ~20 kOe by refining the grain size of the materials or by diffusion of the eutectic alloys with the low melting point, but there is still a big gap between the coercivity and its anisotropic field (70 kOe). This indicates that the coercivity of HDDR magnetic materials still has a lot of room to improve, especially the grain size of HDDR powder is close to that of R2Fe14B single domain particles. In order to further improve the coercivity, it is necessary to study the coercivity mechanism of HDDR magnetic materials. In this study, the initial magnetization curve of thermally demagnetized HDDR anisotropic Pr-Fe-B sample was firstly investigated. The results show that the magnetization increase moderately with external magnetic field, but it is not only different from the rapid rise of magnetization of sintered R-Fe-B magnets but also different from the slow increase of melt-spun R-Fe-B powders at the beginning and then the sudden rapid increase at a certain critical field. Therefore, it is not easy to determine the type of the coercivity mechanism for the powders. In order to study the coercivity mechanism of the above HDDR anisotropic powders in detail, the temperature dependence of coercivity of the sample was measured. The coercivity decrease monotonically with the increase of temperature. According to the micromagnetic model, the coercivity Hc can be generally expressed Hc=αφαk2K1/MS-NeffMs. Due to the preferential nucleation of inhomogeneous regions in the magnetic powder, a correction factor αk should be introduced. In addition, because the grain alignment in the magnetic powder is not completely consistent, the correction factor αφ is also introduced. The dependence of the anisotropy constants K1, and saturation magnetization (Ms) of the main phase Pr2Fe14B on the temperature are all from the literature. The measured data of HDDR Pr-Fe-B and the theoretical formula were compared to analyze that the coercivity mechanism is controlled by the nucleation of the reversed domain or by the uniform rotation of the magnetic moment. （1）Uniform rotation model: Firstly, in order to analyze whether the coercivity mechanism belongs to uniform rotation of the magnetic moments, the dependence of HC/MS on 2K1/Ms2 was investigated. It is found that the experimental data only fall on a straight line in a part of the temperature region. Even in the section of the line, the slope of the line is not 1, which does not meet the theoretical requirements of uniform rotation. So we can exclude the possibility that the magnetization process is uniform rotation of the magnetic moments. （2）Strongly correlated reverse domain nucleation model When the grains in the magnetic powder are strongly magnetically coupled, a reversion of a misaligned grain would drive the reversion of the neighboring grains. Therefore, the coercivity of the material depends on the grains with the smallest nucleation field. In this case, αφ= αφmin, The coefficient can be calculated for a given temperature. The value of this angle is about 40 ~ 60 degrees on the basis of the calculation results of the external field angle corresponding to the minimum nucleation field αφmin at 50K ~ 350K. Fig.1 shows the HC/MS vs 2αφminK1/Ms2 curve of the powder. The purpose of this curve is to analyze whether the coercivity mechanism of the above powder is the nucleation mechanism of strongly magnetically coupled grains. It can be seen from the figure that the experimental data points basically fall on a straight line, which means that under the framework of micromagnetism, the nucleation mechanism with the magnetically coupled grains can describe the magnetization reversal process of the HDDR powder. Fig.2 shows magnetic domain patterns of the HDDR treated Pr-Fe-B alloys. In the case of the HDDR treated alloys, very fine maze-like magnetic domains were observed and these domains extend over more than 1 μm in the original large single particles with the mean size of 10 μm (Fig.2 (b) and (c)). This domain pattern shows a characteristic of interaction domains, and each domain consists of several fine grains, which are magnetically coupled to form large interaction domains. The evolution of the magnetic domain of HDDR anisotropic Pr-Fe-B magnetic powder under the external applied magnetic field (0 T → 2 T → 0 T → -2 T → 0 T → 2 T) was also investigated. Only the disappearance of the labyrinth domain composed of multiple grains and the appearance of the magnetic domain under the condition of positive magnetization field and negative reverse magnetization field were observed, while the domain wall movement was not observed, which further implies that the nucleation of demagnetization is the main mechanism controlling the coercivity of anisotropic HDDR Pr-Fe-B powder.

**References:**

[1] T. Takeshita, R. Nakayama, in 11th Workshop on Rare Earth Magnets and their Applications, Pittsburg, USA, 49 (1990). [2] K. D. Durst and H. Kronmüller, J. Magn. Magn. Mater. 68, 63 (1987). [3] H. Kronmüller, K. D. Durst, and M. Sagawa, J. Magn. Magn.Mater. 74, 291（1988）. [3] W. L. Chen, W. Liu, and Z. D. Zhang, Phy. Rev. B, 72，224419 (2005)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/573cdeaf9631d4c74e5e89dbcdd1548c.jpg)
Fig.1 The dependence of Hc/Ms on 2𝛼𝜑minK1/MS2 of HDDR powders

![](https://assets.underline.io/uploads/markdown_image/1/image/6c2d8f8fab2a230db89ba7a5b00ecf97.jpg)
Fig. 2 Magnetic domain Kerr images of Pr-Fe-B alloys (a) before and (b) after the HDDR treatment. (c) zoom in of red rectangle region in the figure (b)

Optimisation of atomistic modelling parameters for Nd2Fe14B-type rare earth ferromagnets, using the Curie temperature and first order magnetic phase transitions as figures of merit

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