**3. Results and Discussion**

Table 1 shows the chemical composition of the magnet which is the well-controlled type of oxygen content at 800 ppm. The minor components are Cu, Al, Co, Nb, etc.

Considering the magnet composition, a 100% extracted ratio of REE into Mg can be calculated to be 1.730% in Nd and 0.233% in Dy, respectively. Table 2 shows the characterization of the extracted concentration of Nd and Dy with increasing reaction time by XRF measurement. Figure 1 reveals converted values with the extraction efficiency by using Equations (1) and (2). While all of Nd is completely reacted at 6 h, the extraction of Dy is 72% at the same reaction time.

$$\text{Percentage of extraction Nd } (\%) = \left(\frac{\text{C}\_{\text{Nd in Mg}}}{1.730} \times 100\right) \tag{1}$$

$$\text{Percentage of extraction of Dy } (\%) = \left(\frac{\text{C}\_{\text{Dy in Mg}}}{0.233} \times 100\right) \tag{2}$$


**Table 2.** The concentration of elements in the Mg region by XRF.

**Figure 1.** Variation of Nd and Dy extraction efficiency with increasing time.

To understand the extraction behavior of Dy in detail, the microstructures are observed with increasing reaction time on the magnet side. Figure 2 shows that liquid Mg diffused inside the magnet along the grain boundaries and formed ligaments (dark regions) around the magnet (grey region), forming a reaction zone inside the magnet. In morphology, the pattern of Mg infiltration is developed as the changing size and the number of Mg zone with increasing reaction time. Because the Mg can be infiltrated in the entire magnet area in just 30 min, the REEs in the magnet can be totally extracted by the strengthened Mg ligament networking. The liquid Mg diffuses into a magnet to form a diffusion layer on the surface which, in turn, alters the chemical composition of the surface layer. This change in the composition of the surface layer decreases the surface energy and melting point of the solid, allowing it to transform into a liquid state by melting.

The liquid Mg first reacts with RE-rich and RE-oxide phases through the grain boundary in magnets as the diffusion path. Due to the low melting point in the RE-rich phase, which is only 600 ◦C, the initial extraction curves of Nd and Dy are rapidly increased in Figure 1 [21]. The high reaction temperature of 900 ◦C promotes the liquid-liquid reaction between RE-rich and Mg. On the other hand, the liquid–solid reaction arises from the high melting points, which are 2230 ◦C in Nd2O3 and 2408 ◦C in Dy2O3. Thus, the oxides remained with small particles in the microstructures due to the relatively slow reactivity. Approximately 1 μm-sized white particles, which are identified as the RE oxide phase, were observed, as shown in Figure 2a–g.

With increasing reaction time, it is observed that the Mg infiltration is gradually increased and the distribution of oxides is decreased. This means that the oxides can be decomposed despite the slow reactivity with Mg. Considering the total extraction time of Nd at 6 h, the remained oxides indicate Dy2O3 after 6 h. It was thermodynamically demonstrated that the Nd2O3 reacts faster with Mg when comparing Gibbs free energy of Nd2O3 and Dy2O3 [16].

Figure 3 shows the change in the matrix (RE2Fe14B) with increasing reaction time. At 30 min, the co-existence between needle-shaped particles and the oxide phase is observed in the matrix. The reaction with the particles in the matrix complies with the tendency of oxides in the grain boundary. To identify the phase of needle-shaped particles, the XRD and the STEM-EDS experiments are conducted. The XRD analysis is conducted on the reacted specimen for 3 h. The phases are defined with Fe, Fe2B, Mg, RE2O3, Mg12RE, and RE2Fe17 in Figure 4. Because of the gathering of all of the phase information about both grain boundary and the matrix, the Dy oxide phases and RE2O3 are discovered in the grain boundary, while the remaining phases in the matrix are defined to be Fe, Fe2B, Mg, and Mg12RE. Interestingly, the needle-shaped particles are characterized with the

RE-Fe intermetallic phases using phase elimination. Because of the chemical similarity, the RE2Fe17 phase cannot be clearly determined to be Nd2Fe17 or Dy2Fe17, even though the Nd is known to generate only the Nd-Mg-based intermetallic phase, and the formation of Nd2Fe17 is not reported [14].

**Figure 2.** The microstructure of the reaction region in the magnet with Mg for different reaction times: (**a**) 30 min, (**b**) 1 h, (**c**) 3 h, (**d**) 6 h, (**e**) 12 h, (**f**) 24 h, and (**g**) 48 h.

**Figure 3.** Microstructure of the matrix in reaction region with respect to the reaction Table (**a**) 30 min, (**b**) 1 h, (**c**) 3 h, (**d**) 6 h, (**e**) 12 h, (**f**) 24 h, and (**g**) 48 h.

**Figure 4.** XRD pattern of the matrix at a reaction time at 3 h.

To precisely define the intermetallic phase, Figure 5 shows the results of characterized phases in the matrix by STEM-EDS. To observe the morphologies, the areas in the reacted specimen at 3 h are divided into three zones, marked as 1, 2, and 3. The chemical compositions for each zone are collected in Table 3 by EDS in STEM. While there is little Nd and Dy inside zone 3, as most of the REEs were swept to the Mg side, it is observed that REE-Fe intermetallic compounds in zones 1 and 2 are indeed Dy2Fe17. These results match well with the XRD results.

**Figure 5.** TEM image of the matrix at a reaction time at 3 h.


The formation of Dy2Fe17 can be inferred by the heat of the mixing values between Dy-Mg and Nd-Mg. Even though the values of heat of the mixing between Mg and REEs (Nd and Dy) are the same with −6 cal/mol during the reaction, the values between Dy-Fe and Nd-Fe is different to be ΔHmix DyFe <sup>=</sup> <sup>−</sup>3 cal/mol, and <sup>Δ</sup>Hmix NdFe = +1 cal/mol, respectively [22]. Thus, the diffusion of Dy to Mg can be interfered with due to its reaction with Fe as Fe exhibits a higher affinity towards Dy as compared to Nd. Similar to the results of the analysis, the Dy-Fe intermetallic compounds, Dy2Fe17, are observed in the results of the phase analysis on the matrix.

To investigate the reactivity between Mg and Dy2Fe17, the thermodynamic calculations were carried out using Equation (3):

$$2\text{Mg}\_{\text{(l)}} + \text{Dy}\_{2}\text{Fe}\_{17(s)} \to 2\text{MgDy}\_{\text{(s)}} + 17\text{Fe}\_{(s)}\tag{3}$$

The standard Gibbs free energy change, Δ*G*◦, of the reaction between Mg and Dy2Fe17, shown in (3), is 85,778.2 J/mol (at 900 °C) [23], and the Gibbs free energy change for reaction (3), Δ*G*, is expressed as follows:

$$
\Delta G = \Delta G^{\circ} + RT \ln \mathsf{K} \left( \frac{\alpha\_{\mathrm{Fe}}^{17} \alpha\_{\mathrm{MgDy}}^{2}}{\alpha\_{\mathrm{Mg}}^{2} \alpha\_{\mathrm{Dy2Fe17}}} \right) \tag{4}
$$

The activity of the chemical species *i* at temperature T/K is α<sup>i</sup> and the condition for reaction (3) and (4) to proceed are:

$$
\Delta G = 85,778.2 + 2RT \ln a \\
\text{MgDy} < 0 \tag{5}
$$

The activity of *α*Mg, αDy2Fe17, *α*Dy2O3, and *α*Fe are defined as 1. The condition for reaction (5) to progress is as follows at 900 °C:

#### αMgDy < 0.01218

It is indicated that the reaction priority can be derived, considering the grain boundary as well as the matrix, during Mg infiltration. According to the Ellingham diagram, the reaction of REEs with Mg is inevitably hindered because of the high-affinity properties with oxygen in REEs give rise to RE2O3 formation around the grain boundary in advance. Despite the same group, there is a large difference in reactivity of Nd2O3 and Dy2O3 with Mg which is *α* < 0.0433 and *α* < 0.00535, respectively [16]. Moreover, the Dy-Fe reactivity is considered with α < 0.01218 in the matrix, which is five times higher than Dy2O3 reactivity. It is suggested that the decomposition of Dy2Fe17 in the matrix leads to the Dy extraction process after Dy in the RE-rich phase on the grain boundary can be initially swept to Mg.

To check the tendency of reaction priority, based on the thermodynamics, the reaction time dependence of volume fractions in Dy2O3 and Dy2Fe17 is experimentally revealed in Figure 6a,b, respectively. The phase fractions are estimated by the SEM image analysis. It is observed that the decomposition rate of Dy2Fe17 is gradually decreasing with increasing reaction time while Dy2O3 is relatively stable except for 48 h. Considering the curves of extraction efficiency in Figure 1, the slope of extraction efficiency is drastically increased before 3 h because the RE-rich reaction with initial infiltrated Mg into the grain boundary is almost complete. Steadily expanding Mg reaction zone into the matrix, while the Nd and Nd2O3 are totally reacted, the slope of Dy extraction is simultaneously found to be gradual. The decomposition of Dy2Fe17 is mainly contributed to improving Dy extraction because the volume of Dy2Fe17 is started to be dramatically decreased from 3 h to 6 h in Figure 6b. Nevertheless, the reason for the gradual slope is that the relatively small amount of Dy compared to in the RE-rich phase. Finally, Dy2O3 phases, which are the most stable phase, started to decompose with increasing time once the decomposition of Dy2Fe17 was almost complete. Infiltrating Mg into the magnet with increasing time, the oxide and intermetallic phases are generated depending on the reaction zones, which are the grain boundary and the matrix. Before decomposing Dy2O3, the Dy2Fe17 phases are induced by a reaction between magnets and liquid Mg in the matrix via RE-rich reaction. It is suggested that the Dy2Fe17 phases are attributed to the first main hurdles, considering thermodynamic activity and the analysis of extraction behavior, prior to the decomposing Dy2O3 phases.

**Figure 6.** The volume fraction of remained phase with reaction time (**a**) Dy2O3 (**b**) Dy2Fe17.

#### **4. Conclusions**

The phase transformation in the microstructures of magnets during the LME process is systematically investigated with increasing reaction time. The liquid Mg is diffused into the magnet area and it gradually expanded its reaction zones inside the grain boundary and matrix. The REEs in the RE-rich phases rapidly swept to the Mg side. Since then, in spite of the magnet with well-controlled oxygen contents, the RE-oxide phases with a foam of RE2O3 are distributed in the grain boundary and the RE-Fe intermetallic compounds are simultaneously discovered with needle-shaped particles in the matrix. The RE-Fe phases are precisely defined with Dy2Fe17 by quantitative analysis and comparing thermodynamic reactivity. While the extraction of Nd is complete in the RE-rich reaction without the formation of intermetallic compounds, the extraction curves of Dy behave quite differently due to Mg reactivity. In terms of thermodynamics, the formation of Dy-Fe intermetallic compounds is inferred, and their reactivity is compared with oxides. The extraction behavior of Dy shows that the de-oxidized Dy in the RE-rich phase of the grain boundary is quickly reacted with Mg in 3 h. Even though there is a Dy2O3 phase in the same area, the Mg reaction preferentially arises with Dy2Fe17 in the matrix due to differences in stability and reactivity. Afterwards, the Dy extraction is finalized to the reaction of Dy2O3 with Mg. It is suggested that the appearance of Dy2Fe17 phases is intrinsic in the decomposing behavior of magnet, unlike Nd, and is attributed to the first hurdles prior to the decomposing Dy2O3 phases.

**Author Contributions:** Conceptualization, T.-S.K. and S.-W.N.; methodology, S.-W.N., S.-M.P. and M.Z.R.; validation, T.-S.K. and S.-W.N.; analysis, S.-W.N. and S.-M.P.; writing—original draft preparation, S.-W.N.; writing—review and editing T.-S.K. and M.-S.S. supervision T.-S.K. and D.-H.K.; project administration, T.-S.K.; All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by a grant from project of development of environment friendly pyrometallurgy process for high purity HREE and materialization (Project number: 20000970) by Korea evaluation Institute of Industrial Technology (KEIT) in Republic of Korea.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no confliction of interest.

#### **References**


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