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Some rare-earth intermetallic compounds are superior in magnetic properties such as saturation magnetization and magnetocrystalline anisotropy, and are suitable for permanent magnetic materials. This is due, at least in part, to the orbital magnetic moment of the 4f shell, and also to its interaction with the crystal field. Thus it is important to know the 4f orbital magnetic moment of rare-earth ions in those compounds in order to theoretically search for novel permanent magnets. However, first-principles calculations based on density functional theory (DFT) still have a problem with the treatment of 4f orbital magnetic moments: even for 3d transition metals, they are often underestimated in DFT calculations. Therefore some additional corrections such as the so-called DFT+U method [1] [2] or the self-interaction correction (SIC) are necessary to describe the strongly correlated 4f electronic states adequately. Of course, comparison with experimental inputs is inevitable to validate these corrections.&lt;br/&gt;A suitable material to study the 4f orbital magnetic moment with reference to experimental information is SmFe&lt;sub&gt;12&lt;/sub&gt; with ThMn&lt;sub&gt;12&lt;/sub&gt; structure [3] [4]. This is due to its relatively simple crystal structure, and also the abundance of recent detailed experimental results, as it has received renewed attention as a promising candidate for new permanent magnet materials in the last few years. Of course it is well known that this system is thermodynamically unstable, but also that Ti substitution for Fe can stabilize the crystal structure. In the resulting crystal structure, the volume of the so-called interstitial region is larger than in other well-known rare-earth intermetallics such as Nd&lt;sub&gt;2&lt;/sub&gt;Fe&lt;sub&gt;14&lt;/sub&gt;B or SmCo&lt;sub&gt;5&lt;/sub&gt;. Thus we can expect that the 4f electrons of Sm ions are well localized enough to form the well-defined 4f orbital magnetic moment.&lt;br/&gt;We calculate the electronic structure of SmFe&lt;sub&gt;12&lt;/sub&gt; and orbital moment of the Sm ions with the DFT+U method (GGA+U). In the frame work of the first-principles method, we have to investigate ground state properties, however, the DFT+U method sometimes might converge to metastable states [5]. Therefore, we examine several initial conditions and investigate the properties of a possible ground state.&lt;br/&gt;In present study, we use three initial conditions to approach the true ground state. The initial conditions are reflected in the orbital potential for 4f states of the Sm ions, the matrix elements of which are specified by the magnetic quantum number m. First one is set so that m=3,2,1,0,-1 states are occupied (Condition 1). Second one is set so that m=3,2,1,0,-2 states are occupied (Condition 2). The final one is set so that mainly m=3,2,1,0,-2 states are occupied, however, these states include the hybridization between different m reflecting four-fold symmetry (Condition3). We tested these conditions and search the true ground states.&lt;br/&gt;According to the calculated U dependence of the orbital moment and total energy shown in Figure 1, the third one (Condition 3) yields the lowest energy regardless of the U value. The calculated orbital moment of the Sm ions is about 3.0μ&lt;sub&gt;B&lt;/sub&gt; which is smaller than the maximum value expected from 4f&lt;sup&gt;5&lt;/sup&gt; configuration regardless of the U value. This implies that the orbital moment of the Sm ions is partially quenched due to the crystal field. The calculated 4f charge density has the four-fold symmetry which reflects the symmetry of the crystal.&lt;br/&gt;The calculated total, f-partial, and m-resolved f-partial density of states (DOS) are shown in Figure 2 (a) and (b). In Figure 2 (a), DOS is mainly composed by the Fe states and the down spin Sm f-states are well localized below the fermi level. Increasing U value, the gap between upper and lower Hubbard part of Sm f states becomes larger. In our calculation, we have confirmed that the anti-parallel spin configuration between Fe and Sm becomes stable.&lt;br/&gt;From the calculated f-partial density of states in Figure 2 (b), m=3,2,1,0,-2 states are mainly occupied. It yields the orbital moment roughly 4.0μ&lt;sub&gt;B&lt;/sub&gt;. In addition, hybridized states between m=3 and m=-1, m=2 and m=-2, and m=1 and m=-3 are also realized according to the initial condition. These states cause the reduction of the orbital moment from 4.0μ&lt;sub&gt;B&lt;/sub&gt; to 3.0μ&lt;sub&gt;B&lt;/sub&gt; due to the partial quenching of the orbital moment.&lt;br/&gt;In our DFT+U calculation, the quenching of the orbital moment is predicted, the comparison with the experimental data such as XMCD is expected. For future work, we are going to investigate the effect of the quenching of the orbital moment to magnetocystalline anisotropy energy.

**References:**

[1] V. I. Anisimov, J. Zaanen, and O. K. Andersen, Phys. Rev. B., Vol. 44, p. 943 (1991).&lt;br/&gt;[2] A. I. Liechtenstein, V. I. Anisimov, and J. Zaanen, Phys. Rev. B., Vol. 52, p. 5467 (1995).&lt;br/&gt;[3] Y. Hirayama &lt;i&gt;et al&lt;/i&gt;., Scripta Mater., Vol. 138 p.62-65 (2017).&lt;br/&gt;[4] Y. Harashima &lt;i&gt;et al&lt;/i&gt;., JPS Conf., Proc. 5 011021 (2015).&lt;br/&gt;[5] P. Larson, I. I. Mazin, D. A. Papaconstantopoulos, Phys. Rev. B., Vol. 67, p. 214405 (2003).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/b5996e56e128ba38c565fd1cb782b50a.jpg)
The U dependence of the calculated (a) orbital moment and (b) total energy including spin-orbit coupling. Bule, red and black plots correspond to the initial conditions Condition1, Conditon2 and Condition3 (see text). The magnetization axis is set (001) direction.

![](https://assets.underline.io/uploads/markdown_image/1/image/90fadae7780a3329e44ab8a1e7d70d88.jpg)
The calculated density of states (DOS) of SmFe&lt;sub&gt;12&lt;/sub&gt; with U=0.8 Ryd and J=0.0615 Ryd. (a) Black line corresponds to total DOS and red line corresponds to Sm f-partial DOS. (b)Sm f-partial DOS and m-resolved Sm f-partial DOS. The magnetization axis is set the (001) direction with spin-orbit coupling.

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 Theoretical investigation of the orbital moment of the Sm ions in SmFe12 with the GGA+U method.

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Some rare-earth intermetallic compounds are superior in magnetic properties such as saturation magnetization and magnetocrystalline anisotropy, and are suitable for permanent magnetic materials. This is due, at least in part, to the orbital magnetic moment of the 4f shell, and also to its interaction with the crystal field. Thus it is important to know the 4f orbital magnetic moment of rare-earth ions in those compounds in order to theoretically search for novel permanent magnets. However, first-principles calculations based on density functional theory (DFT) still have a problem with the treatment of 4f orbital magnetic moments: even for 3d transition metals, they are often underestimated in DFT calculations. Therefore some additional corrections such as the so-called DFT+U method [1] [2] or the self-interaction correction (SIC) are necessary to describe the strongly correlated 4f electronic states adequately. Of course, comparison with experimental inputs is inevitable to validate these corrections. A suitable material to study the 4f orbital magnetic moment with reference to experimental information is SmFe12 with ThMn12 structure [3] [4]. This is due to its relatively simple crystal structure, and also the abundance of recent detailed experimental results, as it has received renewed attention as a promising candidate for new permanent magnet materials in the last few years. Of course it is well known that this system is thermodynamically unstable, but also that Ti substitution for Fe can stabilize the crystal structure. In the resulting crystal structure, the volume of the so-called interstitial region is larger than in other well-known rare-earth intermetallics such as Nd2Fe14B or SmCo5. Thus we can expect that the 4f electrons of Sm ions are well localized enough to form the well-defined 4f orbital magnetic moment. We calculate the electronic structure of SmFe12 and orbital moment of the Sm ions with the DFT+U method (GGA+U). In the frame work of the first-principles method, we have to investigate ground state properties, however, the DFT+U method sometimes might converge to metastable states [5]. Therefore, we examine several initial conditions and investigate the properties of a possible ground state. In present study, we use three initial conditions to approach the true ground state. The initial conditions are reflected in the orbital potential for 4f states of the Sm ions, the matrix elements of which are specified by the magnetic quantum number m. First one is set so that m=3,2,1,0,-1 states are occupied (Condition 1). Second one is set so that m=3,2,1,0,-2 states are occupied (Condition 2). The final one is set so that mainly m=3,2,1,0,-2 states are occupied, however, these states include the hybridization between different m reflecting four-fold symmetry (Condition3). We tested these conditions and search the true ground states. According to the calculated U dependence of the orbital moment and total energy shown in Figure 1, the third one (Condition 3) yields the lowest energy regardless of the U value. The calculated orbital moment of the Sm ions is about 3.0μB which is smaller than the maximum value expected from 4f5 configuration regardless of the U value. This implies that the orbital moment of the Sm ions is partially quenched due to the crystal field. The calculated 4f charge density has the four-fold symmetry which reflects the symmetry of the crystal. The calculated total, f-partial, and m-resolved f-partial density of states (DOS) are shown in Figure 2 (a) and (b). In Figure 2 (a), DOS is mainly composed by the Fe states and the down spin Sm f-states are well localized below the fermi level. Increasing U value, the gap between upper and lower Hubbard part of Sm f states becomes larger. In our calculation, we have confirmed that the anti-parallel spin configuration between Fe and Sm becomes stable. From the calculated f-partial density of states in Figure 2 (b), m=3,2,1,0,-2 states are mainly occupied. It yields the orbital moment roughly 4.0μB. In addition, hybridized states between m=3 and m=-1, m=2 and m=-2, and m=1 and m=-3 are also realized according to the initial condition. These states cause the reduction of the orbital moment from 4.0μB to 3.0μB due to the partial quenching of the orbital moment. In our DFT+U calculation, the quenching of the orbital moment is predicted, the comparison with the experimental data such as XMCD is expected. For future work, we are going to investigate the effect of the quenching of the orbital moment to magnetocystalline anisotropy energy.

**References:**

[1] V. I. Anisimov, J. Zaanen, and O. K. Andersen, Phys. Rev. B., Vol. 44, p. 943 (1991). [2] A. I. Liechtenstein, V. I. Anisimov, and J. Zaanen, Phys. Rev. B., Vol. 52, p. 5467 (1995). [3] Y. Hirayama et al., Scripta Mater., Vol. 138 p.62-65 (2017). [4] Y. Harashima et al., JPS Conf., Proc. 5 011021 (2015). [5] P. Larson, I. I. Mazin, D. A. Papaconstantopoulos, Phys. Rev. B., Vol. 67, p. 214405 (2003).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/b5996e56e128ba38c565fd1cb782b50a.jpg)
The U dependence of the calculated (a) orbital moment and (b) total energy including spin-orbit coupling. Bule, red and black plots correspond to the initial conditions Condition1, Conditon2 and Condition3 (see text). The magnetization axis is set (001) direction.

![](https://assets.underline.io/uploads/markdown_image/1/image/90fadae7780a3329e44ab8a1e7d70d88.jpg)
The calculated density of states (DOS) of SmFe12 with U=0.8 Ryd and J=0.0615 Ryd. (a) Black line corresponds to total DOS and red line corresponds to Sm f-partial DOS. (b)Sm f-partial DOS and m-resolved Sm f-partial DOS. The magnetization axis is set the (001) direction with spin-orbit coupling.

technical paper

Additive manufacturing (AM) via 3-D printing technologies have become a frontier in materials research, including its application in the development and recycling of permanent magnets1,2. The increasing criticality in availability of the rare earth minerals in magnets present a demanding challenge to the losses from conventional or subtractive manufacturing. AM allows for a minimal waste production and re-utilization of recovered rare earths in the magnet processing. In-situ alignment during 3D printing of magnetic materials has opened new horizons for manufacturing of complex permanent magnets3,4. The introduction of functionalized magnetic 3D printing (Fig. 1a) as an AM process yields several unique advantages including rapid prototyping of multi-directionally aligned magnetic systems, and reduced energy requirement due to the elimination of post-production alignment3. In this work, we have developed a mechanism to align magnetic materials using fused filament 3D printer with a novel magnetic field source architecture (Fig. 1b). The work addresses opportunities to integrate magnetic field into 3D printing process to enable printing, and alignment of anisotropic permanent magnets, without requiring further processing. The principle behind the analysis is rotation of magnetic particles in a molten matrix under low magnetic field. The alignment architecture was designed and optimized for weight and applied field. An in-depth finite element modeling and CAD was performed followed by prototyping of the magnetic field source (Fig. 1c-d). Several electromagnetic core models were developed using finite element modeling to obtain a field strength of &gt; 1 T with a magnetic material in the nozzle. The electromagnetic simulations were coupled with thermal analysis to obtain realistic transient thermal profiles. Design modifications were incorporated to improve the thermal performance of the models without compromising the electromagnetic output. The results predict models that could be operated over prolonged durations (&gt; 10 hours) at less than the rated temperature (80 oC) and at the rated current (5 A), while producing field strength of &gt; 1 T. As a future prospective, the model would be implemented as a prototype to be incorporated with the 3D printer. Magnetization vs. field measurements of extruded and printed Sm-Co (15 vol.%) in PLA and Nd-Fe-B/Sm-Fe-N composite (65 vol.%) in Nylon-12, prepared with and without magnetic field, confirmed alignment of magnetic particles (Fig. 2a-b). Field vs. alignment and printer temperature vs. alignment analyses were performed to understand the effects of process variables on the degree of alignment of the samples. Finally, a multiphysics model was developed, that couples fluid dynamics and electromagnetic interactions, to predict the degree of alignment (DoA) of a polymer bonded magnet printed under applied field. The model predicts the flow of magnetic particles in a viscous fluid through a nozzle under applied magnetic field. A particle-fluid interactive flow simulation was performed to model the flow regime of molten bonded magnet. The interactions between the drag, inertial, and magnetophoretic forces were analyzed to predict the particle trajectory. A torque balance was performed between the drag torque, magnetic torque on particles from the applied field, and torque from particle-particle interactions. The analysis was used to predict the degree of rotation of magnetic particles during printing. The simulated DoA of 0.68 compares well with the experimentally obtained for 65 vol.% NdFeB+SmFeN in Nylon-12. For 15 vol.% Sm-Co in PLA, the simulated DoA of 0.86 also compared well with 0.83 obtained experimentally (Fig.2c-d). This process can be used for any permanent magnet composition or hybrid magnets and presents a benchmark for application of this technology in industrial and commercial applications. This work is supported by the Critical Materials Institute (CMI), an Energy Innovation Hub funded by the U.S. Department of Energy (DOE), Office of Energy Efficiency and Renewable Energy, Advanced Manufacturing Office. Ames Laboratory is operated for the U.S. Department of Energy by Iowa State University of Science and Technology under Contract No. DE-AC02-07CH11358.

**References:**

1. C. Huber et al., Appl. Phys. Lett., 109, 162401 (2016) http://arxiv.org/abs/1605.07309. 2. L. Li, B. Post, V. Kunc, A. M. Elliott, and M. P. Paranthaman, Scr. Mater. (2017). 3. A. Sarkar et al., Addit. Manuf., 34, 101289 (2020) https://linkinghub.elsevier.com/retrieve/pii/S2214860420306618. 4. Y. Kim, H. Yuk, R. Zhao, S. A. Chester, and X. Zhao, Nature, 558, 274–279 (2018) http://www.nature.com/articles/s41586-018-0185-0.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/0f1fa7ee3edeb633b194223095ca2154.jpg)
Figure 1. a) Schematic of in-situ alignment mechanism for magnetic 3D printing, b) Representation of the prototyped 3D printer, c) Novel EM-core design with advanced cooling technology, and d) FEM simulation of c-core @ 5A current.

![](https://assets.underline.io/uploads/markdown_image/1/image/a0cec09893008e380b67cbc258cb5916.jpg)
Figure 2. a-b) MH loop for aligned magnetic samples, and c-d) Simulation validation.

 Advancing Additive Manufacturing of Bonded Permanent Magnets via in-situ Magnetic Field Alignment During 3D Printing

Today, the 3D-printing technology faces a new challenge - the Additive Manufacturing (AM) of functional magnetic materials, especially permanent magnets. AM should provide very good functional properties of the printed magnets, namely locally tailored remanent magnetization Mr and coercivity Hc. The highest magnetic performance is reached for Nd-Fe-B magnets based on the hard magnetic Nd2Fe14B phase, and on extrinsic properties (micro and nanostructure) mastered during the production. Ideal microstructure consists of magnetically decoupled grains of the hard magnetic RE2Fe14B (RE = Rare earth element) phase. The main challenge for Nd-Fe-B magnets, which arises during direct AM techniques, consists of an unsuitable microstructure appearing after re-melting of Nd-Fe-B precursor by the laser, followed by a fast solidification of the alloy. This usually leads to a very low coercivity in magnets made from commonly used commercial Nd-Fe-B alloy powders. Thus, one of the main obstacles in successful 3D printing of full-dense hard magnetic materials, is the engineering of a desired phase composition and the mastering of an appropriate microstructure. In the contrast to conventional Nd-Fe-B-based bulk alloys, a large HC has been found in annealed Pr-Fe-Cu-B compounds. The Pr2Fe14B phase is isostructural to Nd2Fe14B and the Pr-Fe-B and Nd-Fe-B ternary phase diagrams exhibit the same phases. By doping the system with Cu, additional phases can be formed in the sample and some of them affecting drastically the hard-magnetic properties of the magnet. Kajitani et al. [4] found a new grain-boundary phase with tetragonal structure (space group I4/mcm) and Pr6Fe13Cu stoichiometry in hot-pressed Pr17Fe76B5.5Cu1.5 alloys. Annealing at 500 °C leads to an increase in HC of 50 % compared to the hot-pressed state, which was associated to the formation of the antiferromagnetic grain-boundary phase. Further investigations by Marcondes et al. [5] proved the occurrence of the antiferromagnetic Pr3Fe13Cu phase and it was found that annealing at 500 °C improves the HC drastically due to the formation of the Pr3Fe13Cu phase at the expense of the Pr,Cu-rich grain-boundary phase. Recently, the occurrence of the RE6(Fe,Ga)14 within the grain boundary [6]–[8] of Nd-Fe-B permanent magnets was reported. The magnets show good hard- magnetic properties, but the role of the RE6Fe13(Cu,Ga) phase is not clear yet. Our studies explore the applicability of Pr-Fe-Cu-B based alloys for the use in Additive Manufacturing (AM) techniques to produce fully dense permanent magnets. Induction molten Pr17Fe76B5.5Cu1.5 alloys were annealed at high temperature (1000 °C for 5 hours), followed by a low temperature annealing (500 °C for 3 hours). The samples show the formation of soft magnetic Pr2Fe17 phase at high temperature accompanied by low coercivity. After a low temperature annealing, the mentioned Pr6Fe13Cu is forming (see Fig. 1) and an increase of coercivity can be observed. Based on these experiments, the composition has been optimized regarding the coercivity. For this, three pre-alloys (Pr6Fe13Cu, Pr2Fe14B, FeB) were prepared by induction melting and two compositional series by mixing the Pr6Fe13Cu with FeB or Pr2Fe14B were prepared by arc melting. The heat treatments were the same for all samples and the development of coercivity was characterized. The shape of the hysteresis is drastically changing within the sample series. High amount of the Pr6Fe13Cu phase leads to a shoulder and decreasing saturation magnetization, which indicates the non-ferromagnetic properties of the phase. The combination of Pr6Fe13Cu + FeB shows the largest coercvity of ~1250 kA/m which is comparable to a sintered magnet (without heavy Rare Earth elements). In both sample series, the formation of the reported Pr6Fe13Cu phase could be observed by SEM-EDX. The large coercivity in the bulk state makes this material interesting to use as stable precursors for AM of fully dense magnets. The material needs to be in powder form for techniques like SLM. Therefore, the hydrogen decrepitation (HD) process was successfully applied on high coercive samples. Afterwards, the material was suction casted which simulates the remelting and rapid solidification during the SLM process. After the aforementioned annealing, the coercivity is equal to the as-cast condition which demonstrates that the magnetic hardening mechanism is stable throughout the different preparation steps and the material will exhibit large coercivity after SLM. We thank the German Research Foundation (DFG) and the Collaborative Research Center/Transregio 270 HoMMage, Project ID No. 405553726, TRR 270, for making this work possible.

**References:**

[1] O. Gutfleisch, “Controlling the properties of high energy density permanent magnetic materials by different processing routes,” J. Phys. D. Appl. Phys., vol. 33, no. 17, pp. R157–R172, Sep. 2000. [2] T. G. Woodcock et al., “Understanding the microstructure and coercivity of high performance NdFeB-based magnets,” Scripta Materialia, vol. 67, no. 6. pp. 536–541, 2012. [3] G. Hrkac et al., “Impact of different Nd-rich crystal-phases on the coercivity of Nd-Fe-B grain ensembles,” Scr. Mater., vol. 70, no. 1, pp. 35–38, 2014. [4] T. Kajitani, K. Nagayama, and T. Umeda, “Microstructure of Cu-added Pr-Fe-B magnets: Crystallization of antiferromagnetic Pr6Fe13Cu in the boundary region,” J. Magn. Magn. Mater., vol. 117, no. 3, pp. 379–386, Dec. 1992. [5] P. V. P. Marcondes and R. N. Faria, “Microstructural studies on Pr-Fe-B-Cu magnets produced by upset forging of cast ingot,” Mater. Sci. Eng. A, vol. 272, no. 2, pp. 245–249, 1999. [6] K. Niitsu et al., “Magnetization measurements for grain boundary phases in Ga-doped Nd-Fe-B sintered magnet,” J. Alloys Compd., vol. 752, pp. 220–230, 2018. [7] G. Ding et al., “Coercivity enhancement in Dy-free sintered Nd-Fe-B magnets by effective structure optimization of grain boundaries,” J. Alloys Compd., vol. 735, pp. 795–801, 2018. [8] T. T. Sasaki et al., “Formation of non-ferromagnetic grain boundary phase in a Ga-doped Nd-rich Nd-Fe-B sintered magnet,” Scr. Mater., vol. 113, pp. 218–221, 2016.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/254a76c7d50f328f1a476ac33e1bda97.jpg)
Fig. 1: Microstructural evolution during the annealing treatment of Pr-Fe-Cu-B alloys. The sample is shown in as-cast condition (top) and annealing (bottom).

 High coercivity in bulk Pr-Fe-Cu-B alloys as a stable precursor for permanent magnets by Additive Manufacturing

Current production of dense Nd-Fe-B permanent magnets is restricted to the powder metallurgical way consisting of powder production, pressing and magnet field alignment, sintering and post processing. This method allows the production of simple shaped magnets with superior magnetic performance. Bonded magnets show a higher geometrical flexibility on the expense of magnetic performance due the mixing with non-magnetic polymer with a volume content of up to 50%. Additive Manufacturing by means of laser powder bed fusion (LPBF) offers the opportunity to overcome design restrictions of conventional production techniques and allows new strategies for the application-oriented product development. LPBF is characterized by a layer-by-layer local melting of powder on a built platform by a focused laser beam, which is scanned across the powder. New powder is applied on top of melted material afterwards and the melting process is continued. Local melting, rapid solidification, directional heat transfer and several re-melting and re-heating cycles control the microstructural development of metals during LPBF. For this reason, achievable microstructures and properties differ in general significantly from such ones, which can be obtained from conventional fabrication processes. We applied laser powder bed fusion to commercial Nd-lean MQPTM-S powder from Magnequench for the additive manufacturing of Nd-Fe-B bulk permanent magnets. Samples were manufactured on a “M2 cusing” machine from Concept Laser GmbH under protective Argon atmosphere and an Oxygen content below 0.2%. Nd-Fe-B behaves very different compared to established materials during LPBF and the resulting magnetic performance is mainly controlled by the energy input from the laser beam and depends on the processing parameter laser power PL, laser scan velocity vL and hatch distance hy. The latter one represents the offset of neighbouring laser scan lines [1]. The impact of processing parameter laser power and scan velocity on coercivity is shown in Figure 1 (a). It is obvious, that Hc is enhanced, when laser power increases or scan velocity decreases – in other words, if the energy input raises. A similar behaviour was observed for remanence Br and maximum energy product (BH)max. However, the enhancement of magnetic performance is limited by a material specific maximum allowed limit of processibility, at which the samples will be increasingly destroyed. For optimized processing parameter a coercivity of 920 kA/m (1.16 T), a remanence of 0.63 T and a maximum energy product of 63 kJ/m3 is obtained. Thereby, Br and (BH)max represent the highest reported values for additively manufactured permanent magnets so far. The demagnetization branch of the hysteresis curve for a magnet with optimized magnetic properties is shown in Figure 1 (b) and compared to the initial MQPTM-S powder and a polymer bonded magnet from the powder, which is produced by injection molding with a loading factor of 60 vol.%. The coercivity of the powder is 700 kA/m and is slightly reduced by injection molding. However, LPBF leads to an unexpected enhancement of coercivity and the value of the powder is exceeded by 30% without the addition of any rare earth containing eutectics or other post processes. The composition of the used material exhibits 20 wt.% of rare earth, which is equivalent to 8 at.% and is in the range of α-Fe/Nd2Fe14B nanocomposites [2]. These are typically prepared by melt spinning and show coercivities of 400 – 600 kA/m for comparable compositions [2,3], e.g rare earth content between 8 and 9 at.%. These values are clearly exceeded by our LPBF-processed Nd-Fe-B magnets. The link between LPBF-processing and enhanced magnetic performance is the microstructure of the magnets and the microstructural development is controlled – as described above – by several factors. In the case of LPBF-processed Nd-Fe-B magnets we obtained a unique fine-grained microstructure with a grain size between 60 and 600 nm. Our results demonstrate, that improved magnetic performance can be achieved by LPBF of Nd-Fe-B bulk permanent magnets with an optimized coercivity, which is unexpected high for the given Nd-lean composition. This offers new perspectives for the development of new manufacturing processes for the production of improved Nd-Fe-B permanent magnets.

**References:**

[1] F. Bittner, J. Thielsch and W.-G. Drossel: Progress in Additive Manufacturing, Vol. 5, p. 3-9 (2020) [2] G.C. Hadjipanayis: Journal of Magnetism and Magnetic Materials, Vol. 200, p. 379-391 (1999) [3] C. Wang, M. Yan and Q. Li: Materials Science and Engineering B, Vol. 150, p. 77-82 (2008)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/0747ee065f8f32f43ee73c42c10486b5.jpg)
Figure 1: Magnetic performance of additively manufactured Nd-Fe-B permanent magnets produced by laser powder bed fusion: (a) dependence of Hc on laser power and scan velocity and (b) demagnetization curve of additively manufactured magnet (“AM Magnet”, solid line), initial MQPTM-S powder (“powder”, dashed line) and injection molded magnet from MQPTM-S with loading of 60 vol.% (“injection molding”, dotted line).

 Unexpected coercivity enhancement > 1 T for Nd-Fe-B permanent magnets with 20 wt.% Nd produced by laser powder bed fusion

Excellent hard magnetic properties have been achieved in rare earth transition metal films (Nd-Fe-B, Sm-Co) produced by sputtering, pulsed laser deposition and molecular beam epitaxy. Such films can serve as model systems to probe intrinsic magnetic properties or to study the link between microstructure and extrinsic magnetic properties. They can also be used to produce miniaturized magnetic field sources for applications. In the latter case, the films must be patterned at a length scale comparable to the film thickness, because of the demagnetising field effect. The choice of film thickness will depend on the targeted application, nm-sized field sources require nm-thick films while µm-sized sources require µm-thick films. The film deposition rate becomes very relevant as the film thickness is increased, especially if the ultimate aim is for commercial production. What is more, deposition on large surface areas is needed to allow batch fabrication and integration of micro-magnets. We have previously reported on triode sputtering of 5 µm thick Nd-Fe-B films at deposition rates of up to 18 µm/h [1]. We then demonstrated how such films could be physically patterned at the micro-scale using a topographic approach based on pre-patterning of the substrate or post-deposition etching of the magnetic layer [2]. We also showed that localised heating by laser irradiation through a mask can be exploited to produce magnetisation reversal at the µm-scale in the so-called thermo-magnetic patterning approach [3]. Small arrays of micro-magnets produced using these approaches have already been used in a range of bio-medical experiments [4]. In this work we will demonstrate the potential that triode sputtering holds for batch fabrication of even thicker micro-magnets, for future integration into micro-scaled devices. Deep Reactive Ion Etching (DRIE) was used to anisotropically etch 55 µm deep trenches into Si substrates of diameter 100 mm and thickness 525 µm. Patterns consisting of squares with lateral size varying from 20 to 400 μm, and 4 mm long stripes with width varying from 20 to 400 μm, were used as test structures (Fig 1). Ta (100 nm) / Nd-Fe-B (50 µm) / Ta (100 nm) trilayers were deposited onto these topographically patterned substrates heated to a temperature of 500°C or 700°C. The NdFeB layer deposited at 500°C was amorphous, while that deposited at 700°C was crystallised. Post-deposition crystallisation of the former was achieved by annealing the full wafer in a Rapid Thermal Annealing (RTA) furnace, under secondary vacuum (10-6 mbar) at 600 °C, with a heating rate of 20°C/s and a dwell time of 10 minutes. Hereafter the samples will be referred to as 1-step processed (Tdep = 700°C) or 2-step processed (Tdep = 500°C + Tanneal = 600°C). Despite the relatively large thickness of the NdFeB layers, film peel-off does not occur. It should be noted that NdFeB films deposited onto non-patterned Si substrates start to peel off the substrate at a film thickness greater than 10 µm. The stress relief afforded by topographic patterning of the substrate depends on the dimensions of the pattern features and the film thickness, and some peel off was observed in 50 µm thick NdFeB layers deposited on square structures of width 500 µm prepared in another study. For the samples detailed here, some cracking of the deposit was observed in expansive regions far from etched features. SEM images of fractured cross-sections of stripes of two different width (200 µm and 30 µm) of each sample type are compared in Fig 2. Deposition on the sidewalls of the etched trenches leads to the deposition on the “hills” being wider than the underlying Si pillars. A shadowing effect results in the profiles of the deposit in the “valleys” being different to that on the neighbouring “hills”, and the effect becomes stronger as the feature size is reduced. The shadowing effect can be enhanced by increasing the depth of the trenches, as will be shown elsewhere. SEM imaging at higher resolution reveals that the NdFeB grains of the 1-step processed sample are columnar and have widths as large as 1 µm while those of the 2-step processed film are almost equiaxed with diameters in the range of 200 – 500 nm (not shown). Hysteresis loops measured on pieces taken from each sample are shown as insets to Fig 2. The 1-step sample has a coercivity of 1.2 T and an M0T/M7.5T of 0.79 while the corresponding values for the 2-step sample are 2.2 T and 0.85. The higher coercivity of the latter is due to its much finer microstructure and the 2-stage initial magnetization curve may be explained by easy domain wall motion in grains coarser than 300 nm, the single domain particle size of Nd2Fe14B, and domain wall pinning in finer grains. An in-house developed Scanning Hall Probe Microscope (SHPM) equipped with a Hall cross of active area size 4 x 4 µm2 [5], was used to measure the stray magnetic field produced at different heights above out-of-plane magnetized pieces of each sample. In this presentation we will provide full details of structural and magnetic characterization and will compare measured field profiles with simulated profiles. We will finish by discussing future prospects for the fabrication, integration and use of high-performance NdFeB micro-magnets.

**References:**

[1] N.M. Dempsey et al., “High performance hard magnetic NdFeB thick films for integration into Micro-Electro-Mechanical-Systems”, Appl. Phys. Lett. 90 092509 (2007) [2] A. Walther et al., “Micro-patterning of NdFeB and SmCo magnet films for integration into Micro-Electro-Mechanical-Systems”, J. Magn. Mag. Mat. 321 (2009) 590–594 [3] F. Dumas-Bouchiat et al., “Thermo-magnetically patterned micro-magnets”, Appl. Phys. Lett. 96, 102511 (2010). [4] N.M. Dempsey, “Magnetism and Biology” in " Handbook of Magnetic Materials", J.M.D. Coey et al. (eds), Springer, in-press [5] Gorky Shaw et al., “A Scanning Hall Probe Microscope for high resolution, large area, variable height Magnetic Field Imaging”, Rev Sci Inst 87 (2016) 113702

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/71d2432dd00b4772234c43bc8e6f423d.jpg)
Fig 1: Schematic of the pre-patterned substrates.

![](https://assets.underline.io/uploads/markdown_image/1/image/d17c28d143c41c74d8f313da1a848cdf.jpg)
Fig 2: SEM images of fractured cross-sections of stripes of width 200 µm (top) and 30 µm (bottom) prepared using 1-step (left) and 2-step processing. Insets: M(H) loops of pieces taken from 1-step (left) and 2-step processed samples.

 Batch fabrication of 50 µm thick anisotropic NdFeB micro-magnets

I. INTRODUCTION A phase with extraordinarily high room-temperature coercivity in the Sm-Fe-Ti system was first observed in thin films crystallized from an amorphous precursor where μ0Hc reached 3.85 T for a Sm2Fe7Ti1 composition [1]. Giant room-temperature coercivities up to 5.03 T were reported later [2] in a ‘new and possibly metastable phase’ with Sm2Fe7Ti1 composition prepared by mechanical alloying. The reason for the maximum in coercivity at the Sm2Fe7Ti1 composition has been a subject of debate. The observed unit cell expansion is smaller than expected when replacing the respective Fe atoms with Ti, which led to the conclusion that the amount of Ti in the Sm5Fe17 phase has to be smaller than weighted and thus the remaining Ti must form a secondary phase [3]. The interesting question arises then, whether the high coercivity is caused solely by the intrinsic magnetic properties of the Sm5Fe17 phase or is a result of a multi-phase microstructure. To answer this, in this work we have performed a detailed microstructural investigation of samples with varying Ti contents and correlated our findings with the observed magnetic properties. II. EXPERIMENTAL Mechanical alloying of Sm-Fe-Ti samples was carried out by high energy ball milling (SPEX 8000D) under argon atmosphere from elemental Fe (74 -149 μm, 99.9%, Alfa Aesar), Ti (-74 μm, 99%, Alfa Aesar) powders and Sm pieces (3-4 mm, 99.9%, ChemPUR). The resultant powders were subsequently compacted, and heat treated in a horizontal tube furnace at different temperatures. The samples were handled in an Ar filled glovebox (p(O2) &lt; 0.1 ppm, MBraun) to avoid oxidation. Magnetic measurements were performed using a Quantum Design Physical Property Measurement System (PPMS) vibrating sample magnetometer (VSM). The magnetization measurements were extended up to 43 T using a non-destructive pulsed-field coil at the Dresden High Magnetic Field Laboratory. A single 1.44 MJ capacitor bank was used. When fully charged, it could produce a maximum magnetic field of 60 T with a rise time of about 7 ms and a total pulse duration of 25 ms. In our experiments, the capacitor module was charged to about two thirds. The magnetization was detected by the induction method using a coaxial pick-up coil system surrounding the sample. All pulsed-field data were calibrated against the magnetization recorded in steady fields. III. RESULTS AND DISCUSSION As shown in Fig. 1a, ultrahigh coercivities, 7.18 T at room temperature (8.86 T at 10 K), were achieved for the Sm20Fe70Ti10 alloy. The coercivity as high as 2.18 T is maintained even at 500 K. Anisotropy field μ0Ha of 20.7±0.8 T determined from high-field pulse measurements demonstrates that Hc reaches 35% of the Ha at room temperature. Large switching field of around 7 T is visible in the initial magnetization curve. This behavior is similar to fine-grained (below the critical single-domain grain size) Nd-Fe-B alloys. The Curie temperature TC of Sm20Fe70Ti10 is 577 K and calculated exchange stiffness parameter A is 7.72 pJ/m. Because of high rare earth content as well as presence of a nonmagnetic secondary phase, the magnetization was only 60 A m2 kg-1, which is roughly 0.58 T. Detailed transmission electron microscopy investigations presented in Fig. 1b show two-phase microstructure consisting of the Sm5Fe17-based hard magnetic matrix phase with size below 200 nm and fine, &lt;100 nm, Fe2Ti grains. Majority of the Fe2Ti secondary phase grains are located at the grain boundaries as well as inside of the 5:17 grains. No distinct segregation of any element at the grain boundaries can be seen. Despite high areal fraction of the Fe2Ti grains, near single-phase demagnetization loops are observed. Aiming at enhancing Ms by realizing Sm5Fe17/α-Fe composite magnets, the effect of Ti content on the phase constitution, magnetic properties and microstructure was investigated in detail for Sm20Fe70Tix with 4≤x≤10. The fraction of Fe2Ti phase decreases with x and for x=4 Sm2Fe17 phase appears. Ms increases and Hc decreases for the Ti-lean compositions. Based on the microstructural investigations, it is concluded that the reduced coercivities are the consequence of both intrinsic and extrinsic factors, such as the lower anisotropy field, larger grain size and smaller volume fraction of the Fe2Ti precipitates. ACKNOWLEDGEMENTS We acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), Project ID No. 405553726-TRR 270, and Elements Strategy Initiative Center for Magnetic Materials (ESICMM), Grant Number JPMXP0112101004, through the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. We also acknowledge the support of the HLD at HZDR, member of the European Magnetic Field Laboratory (EMFL).

**References:**

1. N. Kamprath, N.C. Liu, H. Hegde, F.J. Cadieu, J. Appl. Phys. 64 (1988) 5720–5722. 2. L. Schultz, K. Schnitzke, J. Wecker, J. Magn. Magn. Mater. 83 (1990) 254–256. 3. H. Stadelmaier, G. Schneider, E.T. Henig, M. Ellner, Mater. Lett. 10 (1991) 303–309.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/8e90a5cf8fd14c1e53d388b8def552ce.jpg)
Fig. 1 (a) Room temperature hysteresis loop and (b) the corresponding microstructure of the Sm20Fe70Ti10 sample. Two-phase microstructure consisting of the Sm5Fe17-based hard magnetic matrix phase with fine Fe2Ti grains is visible.

 Magnetic properties and microstructure of Sm5Fe17-based two-phase magnets

Revived interest on SmFe12-based compounds of the ThMn12 type as the permanent magnet materials has brought into focus the Sm1-xZrx(Fe,Co)11+δTi1-δ alloys remarkable by their high Curie temperature, large magnetization and strong magnetic anisotropy. However, attempts to develop practically useful coercivity in these alloys has encountered considerable difficulties. As most of the ongoing efforts rely on pulverization or on creation of a nanostructure in powders or melt-spun ribbons, relatively unexplored remain the massive cast alloys and "thick" ribbons melt-spun at a low solidification rate, even though they can be utilized as magnets without the need for costly compaction. In this study, alloys of Sm1.1-xZrx(Fe0.8Co0.2)11.3-yTi0.7By with 0 ≤ x ≤ 0.6 and 0 ≤ y ≤ 0.9 were subjected to structural, microscopic, thermomagnetic and isothermal magnetic characterization in samples immediately after arc-melting and after melt-spinning at a low wheel speed of 0.75–6.0 m/s. Slower solidification rates and Zr were found to generally promote the ThMn12-type crystal structure, whereas higher solidification rates and B tend to suppress the 1:12 structure in favor of the TbCu7-type one. When added simultaneously, B and Zr can alter the morphology of the 1:12 phase thus noticeably affecting the coercivity (Fig. 1). In particular, this alloying was found to generate in the arc-melted ingots a microstructure of isolated 1:12 crystallites 1–3 μm in size (Fig. 2); a better control of the minority phases, at least some of which are ferromagnetic, would be needed, however, to obtain in the alloy with such microstructure a Hc greater than 0.5–0.7 kOe. A moderately accelerated solidification can refine the 1:12 crystallites and increase the Hc; a Sm0.7Zr0.4(Fe,Co)10.8Ti0.7B0.5 alloy exhibited a Hc of 1.5 kOe and a maximum energy product (BH)max of 2.5 MGOe when it was melt-spun at 1.5 m/s into a 0.26-mm-thick ribbon. However, a more rapid solidification was found to suppress the 1:12 phase in favor of the magnetically softer 1:7 phase. After annealing at 800–900 °C, the alloys with the large B and Zr substitutions develop reasonably high Hc and (BH)max values even if melt-spun at the moderate wheel speed of 6 m/s. The respective values for the Sm0.7Zr0.4(Fe,Co)10.8Ti0.7B0.5 alloy were 4.1 kOe and 7.8 MGOe, whereas for a very Sm-lean Sm0.5Zr0.6(Fe,Co)10.6Ti0.7B0.7 alloy they were 3.6 kOe and 7.4 MGOe. In comparison, the parent Sm1.1(Fe,Co)11.3Ti0.7 alloy subjected to the same processing developed a Hc of only 0.4 kOe. The work was supported by the U.S. Department of Energy under Grant DE-FG02-90ER45413.

**References:**



**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c2bc2978a39790ea8a94a07f85548392.jpg)
Fig. 1. Coercivity of bulk arc-melted alloys controlled through B and Zr substitutions.

![](https://assets.underline.io/uploads/markdown_image/1/image/3204a80ef4adcec70392f0d44b5abc93.jpg)
Fig. 2. Microstructure of arc-melted Sm0.5Zr0.6(Fe0.8Co0.2)10.8Ti0.7B0.5 alloy features fine well-separated crystallites of the 1:12 phase.

 Microstructure and Hard Magnetic Properties of Sm1-xZrx(Fe,Co)11.3-yTi0.7By Ingots and Thick Melt-Spun Ribbons

Demand for rare earths or cobalt is set to soar the next decade boosted especially by demand for valuable NdPr or SmCo magnets used in electric motors (electric vehicles, wind turbines, consumer electronics, military & aerospace applications). The global permanent magnet market size is expected to reach €30 billion by 2030 from the current €20 billion. It is predicted that by 2030 a) Market for rare-earth oxides will increase 5-fold, b) annual NdFeB shortages of 48,000 tonnes expected by 2030, c) annual Dy oxide Shortages of 1850 tonnes is expected by 2030. Extending the forecasting Dr. M.Sagawa had predicted that by 2050 every one on earth will be served by at least 2 robots each one having at least 10 magnets, a market that has to be served by novel groundbreaking approaches [1]. In Fig. 1. the opportunities that exist for novel permanent magnets are shown. For centuries the design concepts of alloys has been based on only one or two principle elements, while minor fraction of other elements are added for property enhancement. This classical approach was broken in 2004 by Yeh et.al, [2] who suggested of a new alloy design concept, which he called high entropy alloys. The original definition was “multiprincipal elements alloys composed of five or more elements in equal or near-atomic percentages” .. Most of the current dominant (PMs) are intermetallic compounds containing rare earth elements e.g. NdPr or Sm and Co, both expensive and originating mainly from either China or Congo. These natural elements from the periodic table have a fixed atomic radii, fixed valence electron configuration and specific electronegativity, parameters that are crucial for the formation of intermetallic compounds. By creating artificial elements of the type of HEAs based on multicomponent rare-earth elements (RE-HEAs) and HEAs based on multicomponent transition metal elements (TM-HEAs), we have created a library of elements with tunable atomic radii, valence electron configuration and electronegativity. This approach enhances the opportunities for discovering novel permanent magnets [3]. The concept of using artificial elements based on either rare-earths or transition metals is depicted in Fig. 2. for the case of SmCo5-type alloys, an approach that we followed for the stabilization of the SmFe3CoNi magnetic phase [4,5]. We have extended this substitutional approach to the class of RFe12-xTx a and R2Fe14B alloys and the results so far are very promising. For example: Sample Ms (emu/g) HA (T) Tc (K) (BH)maxTheory (MGOe) (RE-HEAs)-Co5 75-90 &gt;10 &gt;800 8-18 Sm(TM-HEAs)5 65-80 &gt;8 &gt;800 8-15 (RE-HEAs)-Fe11T 120-135 &gt;5 570-600 8-18 (RE-HEAs)2-Fe14B 125-145 4-6 550-600 10-25 We will present a general approach by unlocking the new possibilities of using artificial elements to create new magnetic alloys that can be processed towards (PMs) to address the opportunities that are shown in Figure 1. This approach also works not only with metallic alloying but with oxides, pnictides, nitrides etc. We can also use the configurational entropy to stabilize metastable phases, since entropy is increased and competes with enthalpy towards negative Gibbs energy.

**References:**

1. J.M.D.Coey, Engineering 6 (2020) 119–131. 2. Yeh, J. W et al, Adv. Eng. Mater. 6, 299-303 (2004) 3. PCT/EP2019/074449 , approved June 2020, Rare Earth Based High Entropy Alloys (RE_HEAs) as building blocks for novel materials:Rare-Earth-HEAS permanent Magnets 4. P. Soderlind, et al. Phys. Rev. B 96, 100404(R) – Published 14 September 2017 5. Landa et al. Journal of Alloys and Compounds 765 (2018) 659-663.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ecf9f0013e053c9c7c2683178359ac0f.jpg)
Figure 1. Opportunities for novel magnet alloys, suitable for permanent magnets, as a function of (BH)max vs cost (Arnold Engineering)

![](https://assets.underline.io/uploads/markdown_image/1/image/81de3429a852f73a7faab3f1e4932d1b.jpg)
Figure 2. Three steps towards HEA-Magnetic Alloys. Step1 is the fabrication of the artificial elements RE-HEAs and TM-HEAs with variable atomic radii and valence electron concentration, Step2 use these artificial elements to synthesize model structures as counter-alloys of existing structures e.g. SmCo5 and in Step3 with proper heat treatment stabilize through entropy optimization a phase e.g. SmFe3CoNi, that otherwise is not possible because the formation energy is just slightly positive.

 “Αrtificial Elements” Based on High Entropy Alloys as “Building Blocks” for Novel Magnetic Alloys Suitable for Permanent Magnets: Special Case SmFe3CoNi

Nd-Fe-B bonded magnets have been widely applied in data storage and consumer electronic devices [1-3]. Theoretically, the maximum energy product of anisotropic magnets is four times as that of isotropic magnets, hence making anisotropic bonded magnets attractive. To produce bonded magnets, magnetic powders are mixed with thermoset- or thermoplastic- polymers for compression or injection molding methods, respectively. In addition to the specific performance of the magnetic powder used, a higher remanent magnetization, hence high energy product, can be achieved with a higher loading fraction of magnetic powder. For anisotropic bonded magnets, a high degree of magnetic alignment (DOA) of the powders in polymer matrix is important. However, the desire for higher loading fraction needs to be balanced with the requirement for good mechanical properties which decreases with loading fraction. As part of our endeavor to develop high-performance Nd-Fe-B bonded magnets, we studied different processing parameters that contribute to the resultant magnetic alignment and hence magnetic properties of anisotropic Nd-Fe-B bonded magnets. We select Nylon12 as binder and Magfine Nd-Fe-B powder to fabricate bonded magnets. Magfine powder is a commercial Nd-Fe-B anisotropic magnetic powder produced by hydrogenation, disproportionation, desorption, and recombination (HDDR). Different loading fractions of Nd-Fe-B powder were mixed with binder and warm-compacted (450 K) into bonded magnets with a diameter of 8mm and a length of 5mm. To magnetically align Nd-Fe-B powder in the as-prepared bonded magnets, a post-compaction magnetic field alignment was performed with an applied external magnetic field of up to 30 kOe. Samples were heated in magnetic fields from 300 to 530 K (Nylon-12) with a dwell time of 15 min at 530 K, and then cooled down to 300 K. After each alignment process, the magnetic hysteresis loops were measured again at 300 K using a Quantum Design Versalab VSM magnetometer. For Nd-Fe-B bonded magnet with 70% loading fraction of magnetic powder, the magnetic remanence increases from 4.8 kGs to 7.2 kGs, while the intrinsic coercivity remains almost unchanged (12 kOe) upon magnetic alignment (Fig. 1). The enhancement of remanence is due to the magnetic alignment of magnetic powder in bonded magnets. Thermomagnetic measurement data shown in Fig. 2 reveal a jump of magnetization at 480-490 K during post-compaction annealing under external applied fields. This temperature is slightly higher than the melting point of Nylon-12 (450 K), which means the binder (Nylon-12) is melted and at a low viscous state. The low viscosity of binder reduces friction between binder and particle and facilitates the magnetic powder alignment under magnetic field. This is a necessary condition for achieving alignment of magnetic particles in Nd-Fe-B bonded magnets during post-compaction magnetic alignment process. We performed magneto-static calculations which show that the DOA are determined mainly by the interplay between the Zeeman energy (Eapp.) and the inter-particle magnetic-static energy (Estat.) at the chosen alignment temperature and the applied magnetic fields. The good alignment can be achieved by an alignment magnetic field which is twice as its coercivity in anisotropic Nd-Fe-B bonded magnet.

**References:**

1. J. M. D. Coey and K. O’Donnell, J. Appl. Phys., vol. 81, no. 8 PART 2B, pp. 4810–4815, 1997. 2. J. Ormerod and S. Constantinides, J. Appl. Phys., vol. 81, no. 8 PART 2B, pp. 4818–4820, 1997. 3. M. P. Paranthaman et al., Jom, vol. 68, no. 7, pp. 1978–1982, 2016.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/aa6cc50624b84ea940e8b8226900b19a.jpg)
Fig. 1. Magnetic hysteresis of J-H of nonaligned- and aligned samples for 75 vol% Magfine Nd-Fe-B Nylon bonded magnets.

![](https://assets.underline.io/uploads/markdown_image/1/image/a31262fd5b839b2fb205f3d5100df188.jpg)
Fig. 2. Thermomagnetic curve of J-T for 75 vol% Magfine Nd-Fe-B Nylon bonded magnets

 Magnetic alignment in anisotropic Nd-Fe-B bonded magnets

In this work, SEM image analysis and fractal dimension calculations are carried out on the fractures obtained under the same conditions for N50-type with high remanence, 30EH-type with high coercivity, and isotropic commercial Nd-Fe-B permanent magnets. It is further proved that the fractal dimensions of the fractures parallel and perpendicular to the c-axis for Nd-Fe-B permanent magnets are different. In other words, there is anisotropy in fractal dimension. In addition, it was discovered for the first time that the difference between the fractal dimensions D⊥ and D∥ of N50-type magnet with high remanence is large, and the difference between the fractal dimensions D⊥ and D∥ of the 30EH-type magnet with high coercivity is small, indicating that both remanence and coercivity are sensitive parameters with the microstructure. The difference in the fractal dimension of the fracture will provide new insights for studying the relationship between the magnetic properties and the microstructure of permanent magnetic materials. The anisotropic fractal dimension of the fracture will serve as a new performance parameter in the research of Nd-Fe-B permanent magnets. Keywords: Nd-Fe-B, Fractal dimension, Anisotropy, Performance parameter Introduction The magnetic properties of permanent magnets are closely related to the microstructure. However, researchers have seldom focused on the fractal characteristics of fractures in Nd-Fe-B permanent magnets. In fact, it is significant to study the fractal dimension of the fractured microstructure of permanent magnets with statistical self-similarity. Zhu et al. [1] reported the line-measuring dimension of fracture cracks of N50-type permanent magnets, and pointed out that the fractal dimension perpendicular to the c-axis and parallel to the c-axis has some anisotropic trends, but the difference in anisotropy is not obvious. In this work, N50-type, 30EH-type, and isotropic magnets are selected as the research objects. The anisotropic characteristics in fractal dimension of permanent magnets fractures parallel and perpendicular to the c-axis are explored. Experimental N50-type, 30EH-type, and isotropic commercial Nd-Fe-B permanent magnets were selected as the research specimens. A Zeiss field emission scanning electron microscope (FE-SEM) was used to observe the fracture morphology of all samples. The fractal dimensions of the fractures were calculated by the method of box counting dimension based on the image processing function of MATLAB. Results and Discussion The fractal dimensions of different types of magnet fractures parallel and perpendicular to the c-axis are summarized in Fig. 1. The difference ΔD between the fractal dimension D⊥ and D∥ of N50-type and 30EH-type magnets are 0.0856 and 0.0311, respectively. However, there is almost no difference in the fractal dimension of the isotropic magnet. In a word, the fractal dimension of the magnet oriented by the magnetic field has obvious anisotropy. The fractal dimension can be used as a research method to prove the anisotropy of magnets. The internal microstructure of magnet has a great influence on the magnetic parameters such as remanence, coercivity, and maximum energy product. Comparing the difference in fractal dimensions between N50-type and 30EH-type magnets, it can be found that N50-type magnet with higher remanence has larger anisotropic fractal dimensions, while 30EH-type magnet with higher coercivity has smaller anisotropic fractals dimension. The difference in ΔD of different magnets is inherently related to remanence and coercivity, which indirectly indicates that remanence and coercivity are sensitive parameters of microstructure. Conclusions The calculation on fractal dimensions of the fractures for the N50-type and 30EH-type commercial Nd-Fe-B permanent magnets along different crystalline axes demonstrates that the fractal dimensions of the fracture of the permanent magnet are anisotropic. So that the fractal dimension of the fracture can be used as a method to characterize the anisotropy of Nd-Fe-B magnet, which specifically characterizes whether the magnet has anisotropy, the magnitude of remanence and coercivity, and even the level of magnetic properties.

**References:**

[1] M.G. Zhu, W. Li, Y.K. Fang, et al. Fractal study for the fractured surface of Nd-Fe-B permanent magnets. J. Appl. Phys. 2011, 109, 07A706.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/18fb790553f6c2980aa53ad0431aab56.jpg)
Figure 1 Fractal dimensions of fractures parallel and perpendicular c-axis for different types of magnets

 Anisotropic Fractal Dimension of Nd-Fe-B Permanent Magnets Fracture Surface

I. INTRODUCTION With the increasing risk of global rare earth supply and the growing environmental cost of recycling Nd2Fe14B waste by conventional hydrometallurgical technology, development of green and efficient recycling technology has become particularly important [1]. Recently, the reduction diffusion (RD) technology has been developed as an eco-friendly method for recycling Nd2Fe14B sludge waste [2]. At present, researchers mainly use granular calcium or CaH2 as reducing agent, and the amount of reducing agent will affect the phase, morphology, and magnetic properties of recycled powders [3]. Owing to the differences in physical and chemical properties of different reducing agents, the phase, morphology, and magnetic properties of the powders are substantially different in the recovery process. However, the influence of different reducing agents to the recovery of Nd2Fe14B sludge waste by RD method is rarely reported. In this paper, we respectively used granular calcium and CaH2 as reducing agents to recycled Nd2Fe14B sludge waste by RD method. The effect of different reducing agents on the phase, microstructure, and magnetic properties of the recycled powder were investigated. II. EXPERIMENTAL The multi-wire cutting sludge waste was collected from Anhui Earth-Panda Advance Magnetic Material Co. Ltd. The sludge was purified and then mixed with appropriate amount of Ca or CaH2. The mixtures compacted and heated to 1073 K, 1123 K, 1173 K, and 1323 K under high purity argon atmosphere for 2 h. Finally, deionized water was used to wash the powder for removing CaO and then vacuum dried at room temperature to obtain the recycled powders. The phase and orientation were characterized by X-ray diffraction meter (XRD). Microscopic morphology was observed by scanning electron microscopy (SEM). The magnetic properties of the samples at room temperature were measured by a vibrating sample magnetometer (VSM) with a maximum magnetic field of 3T. III. RESULTS AND DISCUSSIONS The XRD patterns of the recycled powders at different reaction temperatures are shown in Fig. 1. The results show that single phase Nd2Fe14B powder can be obtained with granular calcium as the reducing agent at 1323 K. However, when CaH2 is used as the reducing agent, single phase Nd2Fe14B powder can be obtained at 1123 K. This indicates that the latter can carry out the RD reaction at lower reaction temperature. In addition, Fig.1(a) shows that the diffraction peak of Nd2O3 is detected at 1073 K, which indicates that the Ca has not completely reacted with Nd2O3, but the diffraction peak of Nd2O3 is not detected at 1073 K with CaH2 as reducing agents. This proves that CaH2 is more prone to reduction reactions since the melting point of CaH2 (948 K) is lower than that of Ca (1115 K), so the former can be liquefied at lower temperature and thus liquid-solid RD reactions can occur more easily. In addition, since the size of CaH2 powder is smaller than that of granular calcium, it can be better mixed with sludge waste, which is beneficial to promote the RD reaction. On the other hand, the magnetic properties of the recovered powder of the latter (M3T=141.55 emu/g) are higher than that of the former (M3T=137.00 emu/g). And the M3T is increased by 12.9% compared with the purified sludge raw material (M3T=125.38 emu/g). To explore the reason, we observed the morphology of the cross section and powder of the products, and the results are shown in Fig. 2. Since CaH2 releases hydrogen during the RD process, there are many pores in the cross section as shown in Fig.2(c), instead of the dense and smooth cross section shown in Fig. 2(a). From Fig.2(b), it can be seen that the powder has severe sintering and agglomeration, but the dispersion of the powder is better and the powder particle size is more uniform in Fig. 2(d). Owing to the better dispersibility, it is easier to remove CaO during the washing process, so the non-magnetic phase and oxygen content in the corresponding washed magnetic powder are lower, which is also the reason for the better magnetic performance. IV. CONCLUSIONS In summary, using CaH2 as a reducing agent can obtain a single-phase Nd2Fe14B powder at 1123 K by RD method, which is lower than the 1323 K with Ca as the reducing agent. Besides, the dispersion of the powder is better and the powder particle size is more uniform. The magnetic properties of the recovered powder of the former (M3T=141.55 emu/g) are higher than that of the latter (M3T=137.00 emu/g). And the M3T is increased by 12.9% compared with the purified sludge. ACKNOWLEDGEMENT This work was supported by the National key R & D project (2018YFC1903405, No. 2016YFB0700902), and by State Key Laboratory of Rare Earth Permanent Magnetic Materials Opening Foundation (No. SKLREPM17OF02).

**References:**

[1] O. Takeda, T.H. Okabe. Metall. Mater. Trans. E. 1 (2014) 160-173. [2] S.K. Haider, J.Y. Lee, D. Kim, Y.S. Kang. ACS Sustainable Chem. Eng. 8 (2020) 8156-8163. [3] C.Q. Chen, D. Kim, C. Choi. J. Magn. Magn. Mater. 355 (2014) 180-183.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/cfe0e3b8c51ae6e7f90d40fc0c30d0d5.jpg)
Fig. 1 XRD patterns of recycled powder obtained at different temperatures with Ca (a) or CaH2(b) as reducing agent, and recycled powder after washing (c) and the hysteresis loop of recycled powder (d)

![](https://assets.underline.io/uploads/markdown_image/1/image/173ce736e80abaa2509bfd3607afee06.jpg)
Fig.2. SEM micrograph of the cross section and recycled powder of the reaction products with Ca (a and b) or CaH2 (c and d) as reducing agent

Theoretical investigation of the orbital moment of the Sm ions in SmFe12 with the GGA+U method.

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Theoretical investigation of the orbital moment of the Sm ions in SmFe12 with the GGA+U method.

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Next from INTERMAG 2021

Advancing Additive Manufacturing of Bonded Permanent Magnets via in-situ Magnetic Field Alignment During 3D Printing

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Photonic Crystal Nanostructures with the Magnetic Layer of Gradient Thickness for Optical Magnetic Switching

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