Alignment of magnetic particles in anisotropic Nd–Fe–B bonded magnets

Figure 3(a) displays a typical magnetic hysteresis loop of an MQA Nd–Fe–B Nylon bonded magnet with a magnetic powder loading fraction of 75 vol%. After magnetic alignment (at 30 kOe), the magnetic remanence increases from 4.0 to 8.2 kGs, while the intrinsic coercivity H_ci changes from 9.8 to 10.8 kOe. The enhancement in remanence is due to the magnetic alignment of the easy axis of the magnetic powder in bonded magnets. The alignment-induced enhancement of coercivity is ascribed to the coercivity being mainly controlled by the nucleation of reversal magnetic domains in MQA–Nd–Fe–B powders [26]. Further, the inductive coercivity increases from 2.9 to 5.9 kOe (figure 3(b)), resulting from the increase in remanence Br. The maximum energy product increases from 2.9 to 13 MGOe. As shown in figure 3(c), the magnetization has a jump at a temperature of 490–500 K during 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 in a low-viscosity state. The low viscosity of the binder reduces the friction between binder and particle and facilitates the magnetic powder alignment under the magnetic field. This is a necessary condition to achieve alignment of magnetic particles in Nd–Fe–B bonded magnets during the magnetic alignment process (see details on sample and measurement in the section 'Experimental method'). Similar situations are observed with Nd–Fe–B bonded magnets with the PPS binder (see figure S1 in the supplemental materials, available online at stacks.iop.org/JPD/54/315004/mmedia).

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The magnetic remanence depends on the filling fraction of magnetic powder and their alignment in bonded magnets. The relationship can be expressed as

$$\begin{equation}{B_{\text{r}}} = {\text{ }}f \times {\Phi _{\text{p}}} \times {M_{{{\text{r}}_0}}}\end{equation} \tag{ 1 }$$

where B_r, f and Φ_p are the remanence of bonded magnets, volume fraction of magnetic powder, and DOA of the magnetic particle in the bonded magnet, respectively. M_r0 is the remanence of the magnetic powder, which is determined by its intrinsic DOA (Φ_i) and saturation magnetization (M_s0), i.e. M_r0= Φ_i× M_s0. The observed total DOA (Φ_t) of the bonded magnet is contributed by the intrinsic DOA, Φ_i, (i.e. the degree of c-axis crystal texture of the 2:14:1 phase of Nd–Fe–B) and the extrinsic DOA, Φ_p, (i.e. the degree of particle alignment induced by an external magnetic field). Equation (1) can be rewritten as

$$\begin{equation}{\text{Br}} = {\text{ }}f \times {\Phi _{\text{p}}} \times {\Phi _{\text{i}}} \times {M_{{{\text{s}}_{\text{0}}}}}\ \text{or}\ {\text{Br}} = {\text{ }}f \times {\Phi _{\text{t}}} \times {M_{{{\text{s}}_{\text{0}}}}}.\end{equation} \tag{ 2 }$$

We have investigated the loading fraction of Nd–Fe–B on the alignment and magnetic properties of bonded magnets. As shown in figure 4, the magnetic remanence B_r increases almost linearly while the remanence ratio M_r /M_s remains almost unchanged with the increasing loading volume fractions from 40% to 75% in the aligned Nd–Fe–B bonded magnets. The ratio of M_r /M_s or Φ_t is about 0.88 in both the Nylon and PPS bonded magnets, and the derived Φ_p is 0.97 based on formula (2). In other words, the magnetic powders have been aligned by 97% under an external applied magnetic field of 30 kOe (Φ_p= 0.97). As seen from equation (2), the remanence B_r is directly proportional to the filling fraction of the magnetic powder having a fixed value of Φ_t (∼0.88) in the bonded magnets prepared here. The intrinsic coercivity H_ci remains almost unchanged with the increasing loading fraction of Nd–Fe–B powders (figure 4(c)). The inductive coercivity H_cb increases at higher contents of Nd–Fe–B powders, which is ascribed to the higher remanence of the bonded magnet with the larger filling fraction of Nd–Fe–B powders. If the demagnetization curve M–H has ideal squareness, i.e. the value of H_cb is the same as that of B_r, the maximum energy product (BH)_max equals ¼(B_r)². It is expected that the value of (BH)_max increases parabolically with Br or the filling fraction volume. However, the volume fraction dependence of (BH)_max deviates slightly from a parabolic curve since the real magnet lacks the perfect squareness of the M–H curve (figure 4(d)).

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Figure 5 shows the magnetic hysteresis loop of Magfine (HDDR) Nd–Fe–B bonded magnets. The remanence increases with the magnetic alignment and results in a maximum energy product of about 13 MGOe. Different from the MQA bonded magnets (figure 3), the intrinsic coercivity remains unchanged for non-aligned and aligned samples. The result confirms that the domain wall pinning plays an important role in the magnetization reversal process [27]. It should be noted that the magnetic alignment occurs at a temperature range between 475 and 485 K (figure 5(b)), less than that for MQA Nd–Fe–B nylon bonded magnets by about 15 K (figure 3(c)). This is partially ascribed to the different morphology of Magfine and MQA Nd–Fe–B powder (supplementary material, figure S2). The Magfine particle has an irregular sphere-like shape while MQA powder has a plate-like morphology. For the same viscosity of melted binders, the sphere-like particles are easier to move or rotate than plate-like ones. The correlation between the magnetic alignment temperature and types of magnetic powder will be discussed in section 3.2.

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Figure 6 displays the effect of the loading fraction of Magfine powders on the magnetic properties of the bonded magnets. The magnetic remanence B_r increases linearly with the filling fraction of Nd–Fe–B powder for both Nylon and PPS bonded magnets. For all the Magfine bonded magnets, the remanence ratio M_r /M_s is about 0.89 and comparable to that of the MQA bonded magnets (0.88). The magnetic alignment of the particles is very similar for both types of anisotropic Nd–Fe–B powder under processing conditions and achieves a particle DOA Φ_p = 0.97. Similar to MQA bonded magnets, the inductive coercivity and energy product of Magfine bonded magnets increases almost linearly and parabolically with the loading fraction of magnetic powders, respectively.

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In nylon and PPS bonded magnets, the magnetic powder was bonded to achieve a near-net shape and mechanical integrity. To align the magnetic particles with the externally applied magnetic field, the binder should be in a low-viscosity state to facilitate the rotation of magnetic particles. The magnetic alignment must be done at temperatures slightly above the melting point of the binder. To understand the effect of temperature on magnetic alignments, we have measured the melting point of the binder in bonded magnets with different loading fractions of magnetic powders using DSC (see supplementary materials figures S3 and S4 for the DSC curves of nylon and PPS bonded magnets, respectively). The starting temperature and ending temperature for magnetic alignment were derived from thermal magnetization curves in bonded magnets during the post-compaction magnetic alignment process.

Figure 7 displays the binder melting temperature and magnetic alignment temperature in anisotropic Nd–Fe–B nylon and PPS bonded magnets. The binder melting temperature is the same in bonded magnets with MQA and Magfine magnetic powders and remains almost unchanged with different loading fractions of Nd–Fe–B magnetic powders. However, the magnetic alignment temperature is different for the different types of magnetic powders. As shown in figure 7(a), the starting and ending magnetic alignment temperatures of MQA are higher than that of Magfine in nylon bonded magnets by about 10–20 K. This means that the MQA powder is more difficult to align than Magfine powders in nylon bonded magnets, i.e. MQA powder needs a higher temperature to facilitate magnetic alignment. This is contrary to expectation because the MQA magnetic powder has a slightly lower coercivity than Magfine powder (figure 1), indicating that the response to magnetic alignment should be less in MQA at a fixed applied magnetic field and viscous state of the binder. Further, comparing figures 3(c) and 5(b), the magnetization of the MQA powder is higher than that of the Magfine powder by about 15% at around 450–500 K, under the applied alignment magnetic field of 30 kOe. In other words, the driving force for magnetic alignment of MQA powder is slightly higher than that for Magfine powders, which, again, indicates that MQA should be easier to align. One reason for the difficulty in the magnetic alignment of MQA powder is related to the different morphology of Magfine and MQA powders, as discussed in section 3.1. The irregular sphere-like Magfine particles are easier to rotate than the plate-like MQA powder in binders with similar viscosity. This morphological difference is likely a reflection of the methods via which each of the powders was made.

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In contrast, the difference between the starting and ending magnetic alignment temperatures is only about 3–5 K for both the MQA and Magfine powders in PPS bonded magnets (figure 7(b)). A possible reason is that the temperature dependence of viscosity for PPS is different from that of Nylon-12 [28, 29]. As the temperature reaches the critical point, the viscosity of PPS is relatively low, so that both MQA and Magfine powder can be easily rotated in a narrow temperature range (3–5 K). On the other hand, the relatively wider temperature range (10–15 K) needed to complete the magnetic alignment of magnetic powder in Nylon-12 indicates a slower change in viscosity compared to PPS. Further work is needed to clarify the correlation between magnetic alignment and the viscosity of binders.

During the magnetic alignment process, there are three main types of competing interaction [30, 31]. Firstly, the Zeeman energy due to the interaction between the external applied magnetic field and magnetic powder (E_app) is the driving force to align magnetic particles. Secondly, the inter-particle magneto-static energy (E_stat) promotes the random distribution of the magnetization direction of the different magnetic powders and discourages the magnetic alignment. Thirdly, the interaction between the magnetic particle and binder (E_bind) prevents the particles from moving or rotating. However, E_bind depends on the temperature. When the processing temperature is higher than the melting point of the binder, the interaction between the particle and binder is very weak. The spatial distribution of the direction of the magnetic easy axes for the magnetic particles (i.e. DOA) is determined by the balance between the Zeeman energy (E_app) and the inter-particle static energy (E_stat) in bonded magnets, when E_bind is negligible (e.g. near the melting temperature of the binder). We considered these two contributions to simulate the relationship between the DOA and magnetic alignment field H_app during the magnetic alignment process in anisotropic Nd–Fe–B bonded magnets. The achieved DOA results from the minimization of the total magnetic energy (E_tot):

$$\begin{equation}{E_{{\text{tot}}}} = {E_{{\text{stat}}}} + {E_{{\text{app}}{\text{}}}}\end{equation} \tag{ 3 }$$

During the magnetic alignment process, the coercive Nd–Fe–B magnetic powders are magnetized and display net magnetization. E_stat increases while E_app reduces with the increasing net magnetization under a fixed DOA and an external applied field. If the increased part of E_stat is compensated by the reduction in E_app (i.e. ignoring the particle–binder interaction at alignment temperature), the magnetic particle will rotate to reduce the angle between its effective easy magnetization axis (EMA) and the direction of the alignment field and continue until the distribution of magnetic particles reaches a new balance. Further increase in the alignment magnetic field reduces the angle between the EMA of the magnetic powder and the direction of the applied field, i.e. an enhancement of the DOA. The DOA has been calculated as a function of the alignment field. In the numerical implementation, we fix the particle but rotate the direction of its EMA in response to the externally applied alignment magnetic field, which are mathematically equivalent. The room temperature magnetic properties of anisotropic Nd–Fe–B powder are selected as the starting point. The coercivity and remanence are 15 kOe and 12.5 kGs, respectively (see figure 1).

As shown in figure 8, the DOA increases slowly at a low external field (<5 kOe), then increases rapidly and reaches a value of 0.9 at the external field of 15 kOe (the same as the coercivity). When the external applied field reaches twice that of the coercivity (∼30 kOe), perfect alignment is achieved (DOA = 1.0). Further, the coercivity decreases almost linearly with the temperature, which reduces the required magnetic field strength for alignment. For example, the coercivity of Magfine powder is around 4.5 kOe at ∼425 K (figure 9). In other words, an external field of 10 kOe is enough to fully align Magfine or MQA Nd–Fe–B powder in bonded magnets above 425 K. The numerical calculations confirm that the DOA is 0.99 under an alignment field of 10 KOe for magnetic powder with a coercivity of 4.5 kOe and a remanence of 12 kGs. In our previous work [12], an alignment field of 10 kOe achieved a complete alignment of MQA Nd–Fe–B powder in Nylon-12 bonded magnets (30 vol% binder) with an alignment temperature of 550 K, in qualitative agreement with the modeling results.

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This finding is important for integrating alignment magnetic field sources into AM systems in order to print and align at the same time, especially considering that 90% of alignment can be achieved with a <5 kOe external magnetic field at 425 K. The reason is that it is much easier to incorporate an alignment field source if the required magnetic field strength is low. This means that a sufficient magnetic field for alignment during AM could be supplied with sintered magnets, even with the sintered magnet positioned far enough to shield it from thermal demagnetization.