Toward understanding the microstructure characteristics, phase selection and magnetic properties of laser additive manufactured Nd-Fe-B permanent magnets

Nd-Fe-B permanent magnets play a crucial role in energy conversion and electronic devices. The essential magnetic properties of Nd-Fe-B magnets, particularly coercivity and remanent magnetization, are significantly influenced by the phase characteristics and microstructure. In this work, Nd-Fe-B magnets were manufactured using vacuum induction melting (VIM), laser directed energy deposition (LDED) and laser powder bed fusion (LPBF) technologies. The microstructure evolution and phase selection of Nd-Fe-B magnets were then clarified in detail. The results indicated that the solidification velocity (V) and cooling rate (R) are key factors in the phase selection. In terms of the VIM-casting Nd-Fe-B magnet, a large volume fraction of the α-Fe soft magnetic phase (39.7 vol.%) and Nd2Fe17B x metastable phase (34.7 vol.%) are formed due to the low R (2.3 × 10−1 °C s−1), whereas only a minor fraction of the Nd2Fe14B hard magnetic phase (5.15 vol.%) is presented. For the LDED-processed Nd-Fe-B deposit, although the Nd2Fe14B hard magnetic phase also had a low value (3.4 vol.%) as the values of V (<10−2 m s−1) and R (5.06 × 103 °C s−1) increased, part of the α-Fe soft magnetic phase (31.7 vol.%) is suppressed, and a higher volume of Nd2Fe17B x metastable phases (47.5 vol.%) are formed. As a result, both the VIM-casting and LDED-processed Nd-Fe-B deposits exhibited poor magnetic properties. In contrast, employing the high values of V (>10−2 m s−1) and R (1.45 × 106 °C s−1) in the LPBF process resulted in the substantial formation of the Nd2Fe14B hard magnetic phase (55.8 vol.%) directly from the liquid, while the α-Fe soft magnetic phase and Nd2Fe17B x metastable phase precipitation are suppressed in the LPBF-processed Nd-Fe-B magnet. Additionally, crystallographic texture analysis reveals that the LPBF-processed Nd-Fe-B magnets exhibit isotropic magnetic characteristics. Consequently, the LPBF-processed Nd-Fe-B deposit, exhibiting a coercivity of 656 kA m−1, remanence of 0.79 T and maximum energy product of 71.5 kJ m−3, achieved an acceptable magnetic performance, comparable to other additive manufacturing processed Nd-Fe-B magnets from MQP (Nd-lean) Nd-Fe-B powder.

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Introduction
Nd-Fe-B permanent magnets, renowned for their impressive coercivity and magnetic energy product, are garnering growing attention owing to the demand for enhanced efficiency and reduced weight in electronic devices, clean energy vehicles, and aerospace applications [1][2][3][4][5].Nd-Fe-B magnets belong to the ternary complex peritectic system [6], where its magnetic properties, particularly coercivity, predominantly stem from the Nd 2 Fe 14 B peritectic hard magnetic phase.
Conventionally, Nd-Fe-B magnets have been fabricated through methods such as sintering [7], bonding a [8] Nd hotdeformed processes [9].Among these methods, sintered Nd-Fe-B magnets usually require the post-machining to obtain the end-use component, consequently resulting in raw material wastage and magnetic performance loss because of their limited shape flexibility and complexity [10].Although bonded Nd-Fe-B magnets allow much higher geometrical flexibility due to the moldability of the polymer binder, the magnetic properties and thermal stability are significantly reduced when the nonmagnetic polymer reaches a volume fraction of 50%.Similarly, the complex manufacturing procedure and low shape freedom of hot-deformed Nd-Fe-B components also limit their application.Therefore, traditional manufacturing methods are inadequate for fulfilling contemporary application requirements due to their drawbacks, such as low shape freedom, complex processing, high cost and raw material waste.
In recent years, laser additive manufacturing (LAM) has attracted tremendous attention from academia and industrial communities for its capabilities to fabricate components with very slight dimensional or geometric limitations, which can minimize or even eliminate the need for postprocess machining [11][12][13].To date, LAM has been widely used to reliably fabricate dense components for various materials, including superalloys, titanium alloys, aluminum alloys and steel [14][15][16].More importantly, the increased material utilization and resource efficiency have contributed to a growing market advantage within the processing of functional materials [17], especially in the manufacturing of Nd-Fe-B magnet deposits, which are frequently composed of rare earth elements [18][19][20][21].
Recently, Sridharan et al [22] employed the laser directed energy deposition (LDED) technique to successfully produce Nd-Fe-B deposits using MQA-38-14 powder (Magnequench Corp.).They found that the absence of the Nd 2 Fe 14 B hard magnetic phase led to a reduction in coercivity (80 kA m −1 ), while a considerable fraction of the unfavorable soft magnetic phase was formed in the Nd-Fe-B components.Jacimovic et al [23] first employed laser powder bed fusion (LPBF) to fabricate Nd-Fe-B samples from MQP-S-11-9 powder.In their work, parameters such as scanning velocity and layer thickness were adjusted to fabricate Nd-Fe-B samples with an intrinsic coercivity (H c ) of 695 kA m −1 and a maximum magnetic energy product (BH) max of 45 kJ m −3 .In comparison, the LPBF process is more conducive to obtaining the substantially desired Nd 2 Fe 14 B microstructure than the LDED process.In addition, Bittner et al [24,25] explored the influences of different energy input densities on magnetic properties and showed that the magnetic properties of Nd-Fe-B deposits also varied with the different hatch distances while keeping the same line energy input.From the abovementioned results, it can be concluded that the solidification conditions have a notable influence on the formation of the Nd 2 Fe 14 B peritectic phase [26].However, the relationship between phase formation and solidification conditions has not yet been clear.
As mentioned above, clarifying the favorable formation conditions of the Nd 2 Fe 14 B hard magnetic phase is a prerequisite for developing Nd-Fe-B magnets with exceptional performance produced by LAM processes.However, rapid solidification of the melt pool and repeated rapid reheating cycles leads to complex microstructural evolution during the LAM process [27,28].Therefore, it is of great scientific significance to deeply understand the microstructure evolution and phase components of Nd-Fe-B deposits during the LAM process to obtain extraordinary magnetic properties.
Given the significant difference in the solidification and cooling conditions between the LDED and LPBF processes, i.e. the LDED process involves a large melt pool reaching sizes of up to several millimeters and cooling rates of approximately 10 2 -10 3 K s −1 [29], and the LPBF process encompasses a melt pool ranging in size from dozens to hundreds of microns and experiences rapid cooling rates of 10 4 -10 6 K s −1 [30], both LDED and LPBF technologies were employed in this work to prepare Nd-Fe-B deposits.The differences in the phase composition, microstructures and magnetic properties between the LDED-and LPBF-processed Nd-Fe-B deposits were then investigated.The inherent solidification characteristics and phase selection mechanism were also discussed in detail.Furthermore, to understand the phase formation under non-equilibrium solidification conditions, an Nd-Fe-B alloy ingot was also manufactured for comparative analysis.In general, the powder particle sizes used in the LDED typically range from 53 to 150 µm, and from 15 to 53 µm for the LPBF process.Therefore, the initial MQP-S powder was further sieved, resulting in particle size distribution of D 10 = 10.1 µm, D 50 = 28.2µm, and D 90 = 50.2µm, which were used for the LPBF process; while the remaining coarse powder was used for the LDED process, as displayed in figures 1(a) and (b), respectively.The energy dispersive spectroscopy (EDS) maps (figure 1(c)) in the cross-section of the particles exhibit an even distribution of the chemical elements within the particle.The elemental composition of the MQP-S powder was measured with an inductive coupled plasma atomic emission spectrometer and is listed in table 1.

Processes
Figure 2(a) illustrates the schematic diagram during the LPBF process.As shown in figure 2(b), a series of bulk deposits with dimensions of 8 mm × 8 mm × 5 mm were manufactured using a BLT-S210 system (BLT, Xi'an, China), which is fitted with a single mode, continuous wave infrared fiber laser (wavelength 1070 nm) operating at a maximum laser power of 400 W. The LPBF process was conducted within an argon gas-filled chamber, and the oxygen concentration was maintained at below 100 ppm to prevent oxidation.Samples were built on a 316l steel substrate with dimensions of 100 mm × 100 mm × 10 mm and preheated to 200 • C to reduce the thermal gradient in the deposits during the LPBF process, ultimately reducing residual stresses and warping of the deposits.A layer thickness (T) of 30 µm and hatch distance (H) of 100 µm were used in LPBF process.In addition, the scanning strategy was selected with a reciprocating pattern between hatches and a rotation angle of 90 • for the adjacent layers, as illustrated schematically in figure 2(c).The laser power, scan velocity, hatch distance and layer thickness are critical process parameters for controlling the heat input during the LPBF process, which directly impact the solidification behavior of the melt pool.Therefore, the cooperative influence of four parameters can be summarized by the volume energy density E v , which is defined as follows: where P is the laser power, V is the scanning speed, H is the hatch distance, and T is the layer thickness.
According to the experimental results, LPBF-processed Nd-Fe-B deposits with high quality can be obtained when E v is varied within the range of 33.3 J mm −3 and 83.3 J mm −3 .Considering the cost-effectiveness required for industrial production, we opted for the lowest energy consumption from the set of successfully printed samples as representatives for further investigation in the LPBF process.Note that concerning the LPBF Nd-Fe-B deposit (P = 120 W, V = 1400 mm s −1 ), the sample was damaged during removal from the substrate due to the lower volume energy density (E v = 28.6 J mm −3 ) and the large number of unmelted defects inside the sample.Therefore, the LPBF Nd-Fe-B deposit (P = 120 W, V = 1200 mm s −1 ) with the lowest energy density (E v = 33.3J mm −3 ) was selected for in-depth investigation in this work.
The LDED experiment was performed using the LSF-VI LSF system [31].A schematic diagram of the LDED process is shown in figure 2(d).This system comprises a 6 kW semiconductor laser, a three-axis computer numerical control (CNC) working table, and an enclosed chamber with an insert atmosphere.Furthermore, a set of process parameters with a laser power of 1500 W, scanning speed of 700 mm min −1 and beam diameter of 3 mm were utilized to prepare a Nd-Fe-B block deposit with dimensions of 15 mm × 15 mm × 8 mm on a 316l steel substrate with dimensions of 140 mm × 50 mm ×6 mm.Notably, the suitable E v for the LDED-processed Nd-Fe-B sample (figure 2(e)) was 214.3 J mm −3 .Note that the LDED process utilized the same scanning strategy as the LPBF process.The detailed LAM process parameters are listed in table 2.
In addition, the Nd-Fe-B magnet constitutes a complex multi-phase alloy.To accurately clarify the phase components and microstructure evolution under non-equilibrium solidification conditions, a Nd-Fe-B magnet ingot (near-equilibrium solidification) with a diameter of 14 mm and height of 60 mm was prepared in a vacuum induction melting (VIM) furnace ( [32] referred to as casting Nd-Fe-B ingot hereafter) for comparison.For preparation of the Nd-Fe-B ingot, the high-purity alumina crucibles filled with the MQP-S powder were slowly heated to 2000 K over 80 min, held at that temperature for 40 min, and then slowly cooled to room temperature (125 min) under an argon atmosphere (<10 −3 Pa).The average cooling rate (R) of the entire solidification process was 2.3 × 10 −1 • C s −1 .Subsequently, the cylindrical samples were cut from the Nd-Fe-B ingot for further analysis.
The element compositions of the above three Nd-Fe-B samples are listed in table 3. Note that there are differences in element content between the initial powder and three samples, especially for rare earth elements (Nd and Pr), which indicates  slight evaporation of alloying elements during the manufacturing process due to high heat input.

Characterizations
After the LAM process, the processed Nd-Fe-B samples were removed from the substrate using wire electrical discharge machining, and then mounted in epoxy resin by cold embedding and ground with #600 ∼ #3000 sandpaper.Next, the cross-section of the specimens was polished with 2.5 µm diamond grinding paste and finally etched by immersion in a 1% Nital aqueous solution for a duration of 5 s.The microstructural characterization and elemental analysis were revealed using scanning electron microscopy (Sigma 300, ZEISS) with backscattered electron contrast (BSE) and EDS.Electron backscatter diffraction (EBSD) analysis was conducted for LDED and casting Nd-Fe-B samples using step sizes of 0.3 µm and 2.5 µm in a scanning electron microscope (Sigma 300, ZEISS) equipped with an EBSD detector (Oxford Instruments Nordlys NANO).In particular, EBSD analysis of the LPBF Nd-Fe-B component was performed using a step size of 0.01 µm in a scanning electron microscope (AMBER, TESCAN) equipped with a transmission Kikuchi diffraction (TKD) detector (Oxford Symmetry S2).Transmission electron microscopy (TEM) analysis was examined using a Double Cs Corrector Transmission Electron Microscope (Themis Z, FEI).X-ray diffraction patterns from the as-received powder and as-built samples were collected using a PANalytical X'Pert PRO diffractometer with Cu Kα radiation (λ = 0.15406 nm), where the angle 2θ was varied in the range of 20 • and 90 • in steps of 0.03 • , and the voltage and current used for the experiment were 40 kV and 40 mA, respectively.The thermal behaviors of the samples were investigated using a differential scanning calorimeter (DSC, NETZSCH STA 449C) under a heating rate of 10 K min −1 from 40    a current of 240 µA.The results were acquired with a voxel size of 5.08 µm and analyzed using Dragonfly ® software.The magnetic properties of Nd-Fe-B samples were measured by a superconducting quantum interference device magnetometer (Quantum Design MPMS, USA) with a maximum applied magnetic field of µ 0 H = (±7) T at room temperature.The Vickers microhardness was tested using a TH701 hardness tester with a load of 200 g and a dwell time of 15 s.

Phase components and microstructure characteristics
The x-ray diffraction (XRD) results, including the MQP-S powder, casting Nd-Fe-B ingot, LPBF-processed and LDED-processed Nd-Fe-B deposits, are shown in figure 3.
The main phases identified from the XRD spectra include the Nd 2 Fe 14 B hard magnetic phase, Nd 2 Fe 17 B x metastable phase [33], α-Fe soft magnetic phase and Nd-oxide phase.Most of the samples presented a strong α-Fe peak at a 2θ angle of 44.5 • , except for the LPBF-processed magnets.Especially for the powder, the enrichment of Fe was also detected in the interior microstructure [34], which was consistent with the XRD results of the MQP-S powder.It could be reasonably inferred that the precipitation of the α-Fe soft magnetic phase might be inhibited during the LPBF-processed Nd-Fe-B magnet.In addition, it is worth mentioning that the Nd 2 Fe 17 B x metastable phase was identified in all bulk magnets.Moreover, the presence of the (Nd, Pr) 2 O 3 phase should be attributed to the interaction of oxygen in the powder screening process and the printing chamber with the high activity of the rare earth elements Nd and Pr [35].
To further investigate the microstructure and elemental distribution, BSE imaging and EDS analysis were performed on the Nd-Fe-B samples.Figure 4 shows BSE microstructure images, EDS elemental maps and phase composition of casting Nd-Fe-B ingot.It can be clearly observed that the Nd 2 Fe 17 B x metastable phase (#S1) and hard magnetic Nd 2 Fe 14 B (#S2) phase are attached to the primary α-Fe phase (#S3) with the peritectic reaction growth mode.Moreover, the EDS mapping results shown in figure 4(c) indicate that there exists a Zr/Ti/B-rich phase (#S4) inside the α-Fe phase.From the atomic ratio of elements, this phase can be preliminarily determined as (Zr 0.5 Ti 0.5 )B 2 (P6/mmm, a = 0.309, c = 0.339) [36,37], which is distributed as irregular strips in the interior of the α-Fe phase.Furthermore, as shown in figure 4(c), the Nd-rich phase can be observed inside the α-Fe phase.In fact, the content of rare earth element (Nd, Pr) in MQP-S powder was only approximately 8.2 at.% (figure 1(b)), lower than the minimum required by the peritectic reaction (11.7 at.%) [23].Combined with the phase diagram [38], it can be seen that this composition falls within the hypo-peritectic reaction region, and the α-Fe soft magnetic phase is dominant in the casting Nd-Fe-B ingot.Therefore, the significant presence of the α-Fe soft magnetic phase (approximately 52.9 vol.%), measured by Image-Pro Plus ® software from three scanning electron microscopy (SEM) images (figure 4(a)) throughout the sample, aligns with the prominent Fe peak observed in the XRD spectrum.
Figures 5(a) and (b) show the microstructure from the sections perpendicular and parallel to the building direction in the middle of the Nd-Fe-B magnet processed by the LDED process.It can be observed that there is no significant distinction between the microstructure of the melt pool interior (MPI) and the heat-affected zone.In figure 5(c), it can be clearly seen that there are the Nd 2 Fe 17 B x metastable phase (#S1), Nd 2 Fe 14 B hard magnetic phase (#S2), α-Fe soft magnetic phase (#S3), (Zr 0.5 Ti 0.5 )B 2 phase (#S4) and Nd-rich phase (#S5) in the LDED processed deposit according to the EDS element analysis.Furthermore, it should be noted that the morphology of the (Zr 0.5 Ti 0.5 )B 2 phase (#S4) in the Nd 2 Fe 17 B x phase transforms into short rod-like clusters, which is different from the casting Nd-Fe-B ingot.Compared with the casting Nd-Fe-B ingot, all the phase exhibit finer sizes, and the precipitation of Fe is partially suppressed in the LDED processed sample, resulting in a greatly reduced volume fraction of the α-Fe soft magnetic phase (approximately 35.3 vol.%), as shown in figure 5(a).
According to figures 4 and 5, no cracks and pores are observed within the casting Nd-Fe-B ingot and LDED Nd-Fe-B deposit.In contrast, Nd-Fe-B deposits with intrinsically hard and brittle characteristics cannot accommodate extremely rapid cooling rates (up to 10 6 • C s −1 ) and steep temperature gradients (up to 10 7 K m −1 ) during the LPBF process [39] and eventually exhibit undesirable cracking phenomena within the samples under thermal stress [25,40].Figure 6(a) presents the defects of the LPBF sample using the X-CT technique.Apparently, two main types of defects are observed in the samples: cracks (highlighted by the black arrows) and lack of fusion (highlighted by the green circles).In detail, most of the cracks with lengths greater than 200 µm propagate through several deposited layers, forming a network of cracks.In addition, the cracks with straight features present transgranular cracking behavior, as shown in figure 6(b).In fact, the brittleness and limited thermal conductivity of the Nd-Fe-B magnet, when combined with large residual stresses developed during LPBF processing, result in the samples vulnerable to crack formation.
Figure 7 shows the microstructure of the Nd-Fe-B deposit processed by LPBF on the scale of the melt pool.The SEM images of the cross sections perpendicular and parallel to the building direction are shown in figures 7(a) and (b).The microstructure consists of short columnar grains with a length of approximately 2 µm at the melt pool boundaries and globular nanosized grains in the MPIs.It is worth noting that the size of the globular nanosized grains varies across the melt pool.As shown in figure 7(c), there exists a heterogonous globular fine grain distribution in the melt pool, exhibiting a finer grain zone with a grain size of approximately 90 nm and an adjacent coarser grain zone with a size of approximately 300 nm.The grain size gradually increases from the bottom to the top region of the melt pool.Consequently, coarse grains with a size of approximately 1 µm and the shape of the grains resembled polygons with no defined orientation (figure 7(d)) are observed in the vicinity of the heat-affected regions, particularly in proximity to the boundary of the melt pool.This primarily occurs due to the repeatedly rapid reheating annealing/tempering treatment on the already-deposited track from the deposition of adjacent subsequent tracks, initiating grain coarsening of the heat-affected zone in the already-deposited track [41].As suggested by Sepehri-Amin et al [42], the sharp edge of the polygonal grain may reduce the coercivity of the magnet via easier reversal of the magnetic domains.In addition, the EDS Figure 9 shows a high-angle annular dark field-scanning transmission electron microscopy image and its EDS mapping between the nanosized Nd 2 Fe 14 B grains.As observed in figure 9   intergranular phase is formed.In addition, the width of the Zr/Ti/Fe-rich intergranular phase is approximately 15 nm, and it may play a role in isolating the Nd 2 Fe 14 B grains [44].Furthermore, Sepehri-Amin et al [45] demonstrated that the Fe-rich intergranular phase exhibits ferromagnetic when the Fe + Co content exceeds 65 at.%.Therefore, the intergranular Zr/Ti/Fe-rich phase (Fe + Co content up to 70 at.%)can be speculated to be ferromagnetic, suggesting that the Nd 2 Fe 14 B grains are magnetically coupled in the LPBF-processed Nd-Fe-B deposit.In addition, the morphology and size of the Zr/Ti/Fe-rich intergranular phase produced by the LPBF process are completely different from those in the LDED and casting processed samples.This is mainly due to the high cooling rate (1.45 × 10 6 • C s −1 ), which suppresses the precipitation of the (Zr 0.5 Ti 0.5 )B 2 phase.Consequently, the excess Zr, Ti and Fe are expelled from the solidified front of the Nd 2 Fe 14 B grains into residual liquid, resulting in a higher concentration of the Zr/Ti/Fe-rich phase distributed along the grain boundaries of the Nd 2 Fe 14 B grains.Additionally, granular Nd-rich precipitates with a diameter of approximately 20 nm are detected within the Nd 2 Fe 14 B phase grain, as shown in figure 9(a).
Figure 10 shows the EBSD analysis results of the microstructure in the casting Nd-Fe-B ingot, LDED-processed Nd-Fe-B deposit with E v = 214.3J mm −3 , and LPBF-processed Nd-Fe-B deposit with E v = 33.3J mm −3 , respectively.Note that the analysis regions were selected from the middle of the samples along the X-Z direction (building direction).The MPI zone and the melt pool boundary (MPB) zone of the LPBF Nd-Fe-B deposit are shown in figures 10(c) and (d).According to the band contrast map and phase color maps in figures 10(a) and (d), the microstructure of the Nd-Fe-B deposit mainly consists of the Nd 2 Fe 14 B hard magnetic phase, Nd 2 Fe 17 B x metastable phase, α-Fe soft magnetic phase, hcp-Nd 2 O 3 phase, (Zr 0.5 Ti 0.5 )B 2 phase and Nd 1.1 Fe 4 B 4 (B-rich) phase.Among them, the Nd 2 Fe 17 B x metastable phase (R 3m, a = 0.859 nm, c = 1.246 nm) [33] has crystallographic parameters close to those of the hard magnetic Nd 2 Fe 14 B phase (P42/mnm, a = 0.879 nm, c = 1.217 nm), as shown in figure 10(e).In particular, no α-Fe soft magnetic phase is observed.The grain size distributions of Nd 2 Fe 14 B phase in the three Nd-Fe-B samples are also shown in figure 10(g).Based on the cooling rate among the casting, LDED and LPBF processes, it can be found that the grain size decreases as the cooling rate increases.More specifically, the average grain sizes of Nd 2 Fe 14 B in the casting, LDED-processed and MPI zones of LPBF-processed Nd-Fe-B deposits are 6.7 µm, 0.95 µm and 0.067 µm, respectively.In summary, the high cooling rate in the LPBF-processed Nd-Fe-B deposit should be essential for the formation of the Nd 2 Fe 14 B hard magnetic phase with a large volume fraction and small grain size.
To further shed light on the crystallographic texture of the Nd 2 Fe 14 B hard magnetic phase in the LPBF Nd-Fe-B deposit, the corresponding inverse pole figure maps and the pole figure maps were identified by TKD-EBSD on the MPI and MPB zones, as displayed in figure 11.As shown in figure 11(a) and (c), no strong crystallographic texture of the Nd 2 Fe 14 B hard magnetic phase was observed in both MPI and MPB zones, showing random crystallographic orientation.Although the hard magnetic Nd 2 Fe 14 B phase exhibits a strong crystallographic texture on the {001} crystal plane with maximum multiples of uniform distributed (MUD) values of 18.49 for the MPI zone (figure 11(b)) and 16.66 for the MPB zone (figure 11(d)), the crystallographic texture is influenced by the orientation of larger grain size in the selected EBSD region, resulting in an overestimation of the MUD values, especially in the micron-scale TKD-EBSD region.Furthermore, the microstructure of the LPBF-processed Nd-Fe-B magnets primarily consists of short columnar grains (approximately 2 µm in length) along the melt pool boundaries and nanosized equiaxed grains (100-600 nm) within the melt pool (see figure 7).This observation further confirms the lack of a strong crystallographic orientation in the Nd 2 Fe 14 B grains, as also reported by Bittner et al [25].Therefore, it can be inferred that the LPBFproceessed Nd-Fe-B magnets exhibit isotropic magnetic characteristics.

Microhardness
Figure 13 shows the microhardness of the Nd-Fe-B samples manufactured by casting, LDED, and LPBF processes.Obviously, from the casting Nd-Fe-B ingot (444 HV) to the LDED Nd-Fe-B deposit (741 HV) and then to the LPBF Nd-Fe-B deposit (893 HV), the average microhardness shows an increasing trend.This phenomenon can be attributed to the presence of distinct matrix phases within the three Nd-Fe-B samples, corresponding to the α-Fe soft magnetic phase, Nd 2 Fe 17 B x metastable phase and Nd 2 Fe 14 B hard magnetic phase (hard and brittle characteristics), as shown in figure 10.Furthermore, the decrease in grain size resulting from the increase in cooling rate is another contributing factor to the increase in microhardness.

Discussion
In this section, a detailed discussion is conducted regarding the reasons for differences in phase selection under different solidification conditions based on the results presented above.During the solidification process, phases and microstructures   are influenced by solidification conditions such as the temperature gradient (G), solidification velocity (V), cooling rate (R), and alloy composition (C 0 ).Hence, the solidification behaviors of the LDED-processed Nd-Fe-B deposit with E v of 214.3 J mm −3 and the LPBF-processed Nd-Fe-B deposit with E v of 33.3 J mm −3 were investigated, and the G, V and R at the MPB during the solidification process were calculated via finite element thermal transfer analysis employing the commercial ABAQUS software.The modeling process parameters and the temperature-dependent material properties are presented in the supplementary information.More detailed descriptions of the model can be found in a previous study [51,52].Corresponding simulated results for both the LDED and LPBF processes are displayed in figure S1 (supplementary information).
The DSC curves of the Nd-Fe-B alloy prepared by casting, LDED and LPBF processes are shown in figures 14(a) and (b).Figures 14(c) and (d) also present the phase diagram of Nd-Fe-B permanent magnets under equilibrium solidification and nonequilibrium Scheil-Gulliver solidification modes, which were calculated using the Thermocalc ® software, respectively.
As shown in figure 14(c), in the course of equilibrium solidification, the initial solidification process involves the formation of the (Zr 0.5 Ti 0.5 )B 2 phase from the liquid phase.Subsequently, as the temperature decreases to 1 280 • C, the γ-Fe phase initiates precipitation and growth, followed by the formation of the Nd 2 Fe 14 B phase through the L +γ−Fe → Nd 2 Fe 14 B peritectic reaction at 1180 • C.Meanwhile, the volume fraction of the Nd 2 Fe 14 B hard magnetic phase increases at the expense of the γ-Fe phase.Finally, the Nd 1.1 Fe 4 B 4 phase begins to form at approximately 1020 • C.However, it can be found that a Nd 2 Fe 17 B x metastable phase is observed in the casting Nd-Fe-B ingot.In fact, this presence can be attributed to the overheating of the Nd-Fe-B alloy melt (150−200 • C above the melting point, T m ) during the casting process, resulting in a metastable crystallization process [53].The main reason is that the short-range atomic clusters with similar crystal structures to the Nd 2 Fe 14 B phase will be subjected to destruction by thermal motion in the overheating alloy melt.Consequently, in the subsequent cooling process of the alloy melt, the Nd 2 Fe 17 B x metastable phase forms first, followed by the formation of the Nd 2 Fe 14 B phase due to the absence of Nd 2 Fe 14 B crystalline nuclei.As a result, two peritectic reactions will occur, for instance, L +γ-Fe → Nd 2 Fe 17 B x + L ′ and Nd 2 Fe 17 B x + L ′ → Nd 2 Fe 14 B +L ′ ′ .Therefore, it can be clearly observed that the Nd 2 Fe 17 B x metastable phase (#S1) and Nd 2 Fe 14 B hard magnetic phase (#S2) are attached to the primary α-Fe soft magnetic phase (#S3) with the peritectic reaction growth mode, as shown in figures 4(b) and 10(a).In addition, the initial powder contained a relatively low rare earth element (Nd, Pr) concentration of approximately 8.2 at.%, along with an excess of Fe.Therefore, a substantial quantity of the α-Fe soft magnetic phase is expected to be presented in the Nd-Fe-B samples.Based on the above analysis, the corresponding phase of each endothermic peak in the DSC curve can be determined, as shown in figures 14(a) and (b).
The solidification path during the nonequilibrium Scheil-Gulliver solidification process is shown in figure 14(d), which also indicates the preferential precipitation of the (Zr 0.5 Ti 0.5 )B 2 phase.In general, the rapid cooling rates (∼10 3 -10 6 • C s −1 ) experienced during the LAM process offer significant advantages by directly facilitating the formation of the Nd 2 Fe 14 B peritectic phase and suppressing the precipitation of the primary γ-Fe phase.This leads to a shift in the solidification mode.Nonetheless, the LDED-and LPBFprocessed Nd-Fe-B deposits exhibit distinct phase composition characteristics.Specifically, a considerable quantity of Nd 2 Fe 17 B x metastable phases are observed in the LDEDprocessed Nd-Fe-B deposit (figure 10(b)), which was not predicted in the Scheil-Gulliver solidification simulation.Note that the Scheil-Gulliver solidification model was solely calculated based on the assumption that the liquid phase was fully diffused, while the solid phase was not diffused.This model did not consider the actual influence of the moving velocity of the solid−liquid interfaces during the solidification process.However, the solid−liquid interface moving velocity plays a crucial role in phase selection during rapid solidification [54].Based on interface response functions, Umeda et al [55] established the relationship between the critical solid−liquid interface moving velocity and Nd concentration (at%) for the phase transition from the γ-Fe phase to the Nd 2 Fe 14 B peritectic phase, and the results demonstrated that a shift in the solidification mode occurs from the primary γ-Fe phase to the primary Nd 2 Fe 14 B phase solidification when the velocity of solid−liquid interface exceeds 10 −2 m s −1 (for MQP-S powder containing 7.5 at% Nd).Based on the simulation results of the solidification velocity of the melt pool in the LDED and LPBF processes shown in figures S1(b) and (e), it can be demonstrated that transformation from the primary γ-Fe phase to the primary Nd 2 Fe 14 B phase solidification does not occur in the LDED process, which is attributed to its V being below 10 −2 m s −1 .Furthermore, Gao et al [56][57][58] found that the nucleation of the Nd 2 Fe 17 B x phase becomes more favorable compared to that of the γ-Fe phase or Nd 2 Fe 14 B phase when the melt undercooling is larger than 60 K. Hence, a shift in the solidification sequence to the primary Nd 2 Fe 17 B x metastable phase from the primary γ-Fe phase can occur in the LDED Nd-Fe-B deposit.In addition, the distribution of the (Zr 0.5 Ti 0.5 )B 2 phase in the Nd 2 Fe 17 B x metastable phase matrix in figure 10(d) serves as additional evidence supporting this theory.Therefore, an increase in the cooling rate (5.06 × 10 3 • C s −1 ) in the LDED process can facilitate the formation of the Nd 2 Fe 17 B x metastable phase and inhibit the prepicitation of the γ-Fe soft magnetic phase.Furthermore, the partial presence of the α-Fe soft magnetic phase and Nd 2 Fe 14 B phase in the LDED Nd-Fe-B deposit should also be attributed to the reheating annealing/tempering effect from the repeated deposition of adjacent new tracks and layers.As a result, the Nd 2 Fe 17 B x phase decomposes into the α-Fe phase and Nd 2 Fe 14 B phase [59,60].Thus, the solidification sequence for the LDED-processed Nd-Fe-B alloy can be summarized as follows: In the case of the LPBF-processed Nd-Fe-B deposit, significant undercooling of the melt was generated due to the high solidification velocity (>10 −2 m s −1 ) and rapid cooling rate (1.45 × 10 6 • C s −1 ), which can be very favorable to the direct formation of the Nd 2 Fe 14 B hard magnetic phase while inhibit the precipitation of both the (Zr 0.5 Ti 0.5 )B 2 phase and the soft magnetic γ-Fe phase, as shown in figures 10(c) and (d).Therefore, a large volume fraction of Nd 2 Fe 14 B hard magnetic phase precipitated contributes to the superior magnetic properties of the LPBF-processed Nd-Fe-B deposit.
A schematic diagram of the phase selection mechanisms under the casting, LDED and LPBF processes is illustrated in figure 15.The (Zr 0.5 Ti 0.5 )B 2 phase initially precipitates from the liquid melt in both the casting-and LDED-processed Nd-Fe-B alloys; however, it exhibits distinct morphologies and sizes because of the different solidification conditions in the melt (figures 15(a) and (b)).In contrast, the (Zr 0.5 Ti 0.5 )B 2 phase and soft magnetic phase are absent in the LPBFprocessed Nd-Fe-B magnets due to the high cooling rate.Note that the presence of Zr, Ti and Fe surrounding the Nd 2 Fe 14 B phase results in the formation of an intergranular Zr/Ti/Fe-rich phase (figure 15(c)).Furthermore, as the solidification velocity and cooling rate increase, the matrix phase in the casting, LDED and LPBF-processed Nd-Fe-B deposits undergoes a transition from the α-Fe soft magnetic phase, the Nd 2 Fe 17 B x metastable phase, to the Nd 2 Fe 14 B hard magnetic phase.
Based on the discussion above, the cooling rate was selected as the key solidification parameter to establish the relationship with the magnetic properties of Nd-Fe-B samples prepared by the casting, LDED and LPBF processes.As seen from figure 16, when the cooling rate increases from 2.3 × 10 −1 • C s −1 (casting) to 5.06 × 10 3 • C s −1 (LDED), the magnetic properties show minimal variation, which can be attributed to the precipitation of a small amount of the Nd 2 Fe 14 B phase at a relatively low cooling rate (∼10 3 • C s −1 ).Only when the cooling rate increases to 1.45 × 10 6 • C s −1 in the LPBF process that the peritectic reaction is hindered, resulting in the primary Nd 2 Fe 14 B phase precipitated directly from the liquid phase, and the precipitation of the α-Fe soft magnetic phase and Nd 2 Fe 17 B x metastable phase is suppressed.As a result, the magnetic properties are significantly enhanced.Similarly, Pei et al [61] reported that the strip casting technique, similar to melt spinning, can effectively suppress the formation of α-Fe dendrite phase and enhance the magnetic properties due to the high cooling rate (10 3 -10 4 • C s −1 ).For instance, when the concentration of rare earth (Nd/Pr) is approximately 8 at.%, the coercivity of Nd-Fe-B samples prepared by melt spinning can be achieved within the range of 400-600 kA m −1 [62][63][64].
Another crucial factor contributing to the enhancement in coercivity is the grain refinement resulting from a high cooling rates.Sepehri-Amin et al [42,65] found that the increase in coercivity as the grain size decreases can be attributed to the reduction in the stray field generated by the neighboring grains, as demonstrated by micromagnetic simulations.
In summary, the H c , B r and (BH) max exhibit simultaneous increases from 95 kA m −1 , 0.57 T and 10.4 kJ m −3 for the LDED Nd-Fe-B deposit to 656 kA m −1 , 0.79 T and 71.3 kJ m −3 for the LPBF Nd-Fe-B magnet, representing substantial enhancements by 5.9 times, 0.39 times and 5.88 times, respectively.Notably, the LPBF process allows an innovative production process with mold-free fabrication of near netshaped permanent magnets with superior magnetic properties.

Conclusions
In this work, Nd-Fe-B alloys were prepared under distinct solidification conditions employing three different technologies: VIM for near-equilibrium solidification, LDED for nearrapid solidification, and LPBF for rapid solidification.The intrinsic relationship among the microstructure, phase selection and magnetic properties of the Nd-Fe-B alloys was investigated, resulting in the achievement of Nd-Fe-B permanent magnet with superior magnetic properties.
The main conclusions are as follows the LDED Nd-Fe-B magnet to 656 kA m −1 , 0.79 T and 71.5 kJ m −3 for the LPBF Nd-Fe-B magnet, representing significant enhancements by 5.9 times, 0.39 times and 5.88 times, respectively.(5) The LPBF process with a small melt pool and rapid laser scanning promotes high solidification rates, which refines the grains and opens up new avenues and opportunities for developing innovative materials with far-from-equilibrium phases and improved properties.In addition, from the perspective of the energy consumption of the fabrication process, the LPBF process appears to be more applicable since it precisely directs energy source to the designated locations, aligning with the objectives of sustainable energy conservation and emissions reduction.

Figure 1 .
Figure 1.SEM image of MQP-S powder.(a) Morphology of the LPBF MQP-S powder; (b) morphology of the LDED MQP-S powder; (c) the distribution of chemical elements in the cross-sectioned MQP-S powder.

Figure 4 .
Figure 4. Microstructure of the Nd-Fe-B ingot produced by casting.(a) EDS mapping; (b) phase identification under different color contrasts; (c) microstructure and element distribution of the interior α-Fe phase.
(b), the Zr and Ti elements are enriched in the Nd 2 Fe 14 B grain boundary, and the composition line scan profile of elements marked in figure 9(a) indicates the presence of Fe with approximately 65 at.% in the grain boundary except for Zr and Ti segregation, suggesting that the Zr/Ti/Fe-rich

Figure 5 .
Figure 5. Microstructure of the Nd-Fe-B samples processed by the LDED process with a volume energy density Ev = 214.3J mm −3 .(a) Perpendicular to the building direction; (b) parallel to the building direction; (c) EDS mapping and phase identification under different color contrasts.

Figure 6 .
Figure 6.Defects in the LPBF-processed Nd-Fe-B deposit.(a) X-CT image of defects; (b) SEM morphology of crack.

Figure 10 (
f) shows that there is a large volume fraction of the α-Fe soft magnetic phase (39.7 vol.%) and Nd 2 Fe 17 B x phase (34.7 vol.%) in the casting Nd-Fe-B ingot, while the volume fraction of the Nd 2 Fe 14 B phase is only 5.15 vol.%.In general, the magnetic performance of Nd-Fe-B depends on the formation of the Nd 2 Fe 14 B hard magnetic phase, and the absence of the Nd 2 Fe 14 B hard magnetic phase or the presence of other soft magnetic phases might lead to poor magnetic properties.Compared with the casting Nd-Fe-B ingot, the volume fraction of the Nd 2 Fe 14 B hard magnetic phase also has a low value (3.4 vol.%) in the LDED Nd-Fe-B deposit, and the volume fraction of the α-Fe phase and Nd 2 Fe 17 B x phase are 31.7 vol.% and 47.5 vol.%, respectively.For the LPBF-processed Nd-Fe-B deposit, the volume fraction of the Nd 2 Fe 14 B hard

Figure 7 .
Figure 7. Microstructure of the Nd-Fe-B deposit after LPBF with volume energy density Ev = 33.3J mm −3 .(a) Perpendicular to the building direction; and (b) parallel to the building direction; (c) the grain feature at the bottom of the melt pool; (d) the grain feature at the top of the melt pool; (e) EDS mapping of Nd-rich phase.

Figure 8 .
Figure 8. TEM analysis of the LPBF-processed Nd-Fe-B alloy with Ev = 33.3J mm −3 .(a) STEM image of the sample; (b) the element mapping in the areas framed in (a); (c) SAED pattern image for region c (shown in (a)); (d) HRTEM image for the selected region d in panel (a); and (e) corresponding FFT image for region I in panel (d).

Figure 9 .
Figure 9. TEM analysis of the LPBF-processed Nd-Fe-B alloy with Ev = 33.3J mm −3 .(a) HAADF-STEM image of the precipitated Nd 2 Fe 14 B phase and the line scan results of the element distribution between grains (indicated by the yellow arrow); (b) EDS map analysis.

Figure 12
Figure12presents the demagnetization curves of the Nd-Fe-B samples prepared by casting, LDED with E v = 214.3J mm −3 , and LPBF with E v = 33.3J mm −3 , respectively.The demagnetization curve of the MQP-S powder is also compared.A theoretical density of 7.43 g cm −3 was assumed for the Nd-Fe-B magnets.As shown in figure12(a), the MQP-S powder possesses a coercivity (H c ) of 485 kA m −1 and a remanence (B r ) of 0.81 T. The LPBF-processed Nd-Fe-B deposit presented superior magnetic properties with H c of 656 kA m −1 and B r of 0.79 T, which benefited from the presence of a considerable volume fraction of the Nd 2 Fe 14 B hard magnetic phase.In contrast, in the LDED-processed Nd-Fe-B deposit, a large number of α-Fe soft magnetic phase and Nd 2 Fe 17 B x metastable phase are precipitated in the absence of the Nd 2 Fe 14 B hard magnetic phase.This led to a low H c of 95 kA m −1 and low B r of 0.57 T, which are comparable to the values observed in the casting Nd-Fe-B ingot with H c of 108 kA m−1

Figure 10 .
Figure 10.EBSD analysis of three processed Nd-Fe-B samples.(a) EBSD results of the casting Nd-Fe-B ingot: (i) and (ii) show the BC map and phase map; (b) EBSD results of the LDED-processed Nd-Fe-B deposit: (i) and (ii) show the BC map and phase map; (c) EBSD results of melt pool interior (MPI) in the LPBF-processed Nd-Fe-B deposit: (c-i) and (c-ii) show the BC map and phase map; (d) EBSD results of melt pool interior (MPI) in the LPBF-processed Nd-Fe-B deposit: (i) and (ii) show the BC map and phase map of melt pool boundary (MPB) in LPBF-processed Nd-Fe-B deposit; (e) schematic of the Nd 2 Fe 14 B and Nd 2 Fe 17 Bx crystal structures; (f) the volume fractions of different phases of the three Nd-Fe-B samples; (g) the Nd 2 Fe 14 B grain size of the three Nd-Fe-B samples.

12 .
Magnetic properties.(a) Demagnetization curves of MQP-S powder and Nd-Fe-B samples with different solidification conditions; (b) comparison of maximum energy product (BH)max under different processes; (c) comparison of coercivity-remanence and (d) (BH)max of Nd-Fe-B magnets fabricated from Nd-lean powder in this work and literature thus far.

Figure
Figure Thermodynamic characteristics of Nd-Fe-B magnets under different solidification conditions.(a) DSC curves of the Nd-Fe-B samples and (b) enlarged DSC curves; the phase diagram of the Nd-Fe-B alloy calculated based on (c) equilibrium solidification and (d) nonequilibrium Scheil-Gulliver solidification.

Figure 16 .
Figure 16.Relationship between cooling rates and magnetic properties based on different solidification processes.

( 1 )
In the casting Nd-Fe-B ingot, the microstructure is mainly composed of dendrites α-Fe with attached Nd 2 Fe 17 B x phases.For the LDED processed sample, the grain size of α-Fe and Nd 2 Fe 17 B x phases becomes finer due to the high cooling rate (5.06 × 10 3 • C s −1 ).The microstructure of the LPBF processed Nd-Fe-B deposit differs from that of the casting and LDED Nd-Fe-B samples due to the rapid solidification of the melt pool, resulting in a nanocrystalline microstructure structure.For instance, Nd 2 Fe 14 B columnar grains appear at the of the melt pool/track with a length of approximately 2 µm, while globular Nd 2 Fe 14 B grains ranging in size from 50 nm to 1 µm are located inside the melt pool.(2) For the casting and LDED-processed Nd-Fe-B samples, a large volume fraction of the α-Fe phase (39.7 vol.% and 31.7 vol.%) and Nd 2 Fe 17 B x phase (34.7 vol.% and 47.5 vol.%) are formed, respectively.In contrast, the high solidification velocity (>10 −2 m s −1 ) and high cooling rate (1.45 × 10 6 • C s −1 ) play a crucial role in the formation of the Nd 2 Fe 14 B peritectic phase (55.8 vol.%) and the suppression of the α-Fe phase and Nd 2 Fe 17 B x phase precipitation in the LPBF-processed Nd-Fe-B deposit.(3) The morphology and size of the (Zr 0.5 Ti 0.5 )B 2 phase vary between the casting-and LDED-processed magnets due to the different solidification conditions.In terms of the casting Nd-Fe-B ingot, the (Zr 0.5 Ti 0.5 )B 2 phase, with a width of approximately 5 µm, is distributed in the interior of the α-Fe phase as irregular strips.In the LDED-processed Nd-Fe-B deposit, the (Zr 0.5 Ti 0.5 )B 2 phase inside the Nd 2 Fe 17 B x phase transforms into short rod-like clusters with a width of approximately 2 µm.For the LPBF-processed Nd-Fe-B deposit, the precipitation of the (Zr 0.5 Ti 0.5 )B 2 phase is suppressed, and the excess Zr/Ti/Fe is enriched surrounding the Nd 2 Fe 14 B grains, thus forming an intergranular phase with a width of approximately 15 nm.(4) A coercivity (H c ) of 656 kA m −1 and a remanence (B r ) of 0.79 T are achieved in the LPBF processed Nd-Fe-B deposit.However, the LDED-processed deposit exhibits lower values of 95 kA m −1 for H c and 0.57 T for B r , respectively, which are basically the same as the values of the casting Nd-Fe-B ingot with H c of 108 kA m −1 and B r of 0.57 T. As the cooling rate increases, the H c , B r and maximum magnetic energy product (BH) max increase simultaneously from 95 kA m −1 , 0.57 T and 10.4 kJ m −3 for Pr 0.7 Zr 2.6 Ti 2.5 Co 2.5 Fe 75 B 8.8 (at.%) with a particle diameter D 50 of 43.3 µm and D 90 of 68.5 µm.Most particles are spherical, and only a minor proportion of particles are rod-like.

Table 1 .
ICP analysis of the MQP-S powder.

Table 2 .
The LAM process parameters.

Table 3 .
ICP analysis of the above three Nd-Fe-B magnets.