diff --git a/resources/dataset/quantities/annotations/generated/energies-14-08509.quantifiedObject.tei.xml b/resources/dataset/quantities/annotations/generated/energies-14-08509.quantifiedObject.tei.xml new file mode 100644 index 00000000..9746425c --- /dev/null +++ b/resources/dataset/quantities/annotations/generated/energies-14-08509.quantifiedObject.tei.xml @@ -0,0 +1,3 @@ + +

This paper presents the design of an axial-flux permanent-magnet (AFPM) generator used for hybrid electric propulsion drone applications. The design objectives of the AFPM generator are high power density, which is defined as output power per generator weight, and high efficiency. In order to satisfy the requirements for the target application and consider the practical problems in the manufacturing process, the structure of the AFPM generator comprising a double-rotor single-stator (DR-SS) was studied. In order to determine the rotor topology and stator winding specifications that had the greatest impact on performance in the DR-SS type design process, we selected three rotor models according to the arrangement of the magnetization direction and three stator models according to the coreless winding specifications. These models were first compared and analyzed. Then, a 3-D finite element method was performed to calculate the magnetic, mechanical, and thermal characteristics of the designed models. By consideration of the output power, efficiency, temperature, and mechanical stability, etc., a topology suitable for the design of generators for UAV systems was determined and manufactured. The reliability of the design result was confirmed through the test.

Since axial-flux permanent-magnet (AFPM) generators are known to have a high power density, which is defined as the ratio of output power to weight , the authors of this paper reviewed the development of an AFPM electric machine for 3 kW class drones. Additionally, among the possible multiple rotor and stator combinations, a combination consisting of NS-type double rotors and a yokeless single stator (DR-SS) was selected, as shown in Figure 1. "NS type" refers to north pole and south pole magnets facing each other at either side; thus, the flux can travel straight through this stator without any circumferential flow . This type of DR-SS is more commonly known as a yokeless and segmented armature (YASA) motor or generator and is often described as having a relatively high power density because it does not require a stator yoke. However, to be precise, a structure in the form of a 'stator yoke' is not required as a magnetic flux path, but is necessary to mechanically hold the teeth and coils of the stator . Thus, the design of stator mechanical fixation in an NS-type DR-SS topology with a stator magnetic core (or stator teeth) becomes a critical part of the entire motor design process. Mechanically robust of stator mechanical fixation in an NS-type DR-SS topology with a stator magnetic core (or stator teeth) becomes a critical part of the entire motor design process. Mechanically robust structures are required to overcome the pull forces at both rotors, increasing the volume and weight of the stator . Therefore, in this study, we selected and designed a DR-SS topology without a stator core. For the rotors, in order to increase the output power, the characteristics of the model according to the combination of permanent-magnet (PM) pole arrangement were compared and reviewed, focusing on the so-called Halbach array structure [8,9]. For the stator, a coreless stator topology was used to reduce the weight of the stator itself and at the same time reduce the weight of the structure supporting it, by reducing the axial attraction force between the rotor and the stator.

This paper focuses on the process of selecting the rotor-Halbach array topology and the coil specifications of the coreless stator, which have the most influence on the power density among the various design variables of the rotor and stator in the generator design process. In other words, in the rotor design part of this paper, three types of Halbach arrays are compared and analyzed according to the arrangement of the magnetization direction. Moreover, in the stator design part, the loss generated from the coil due to the coreless topology is analyzed in detail, and three cases of using a general conductor and a Litz wire conductor are compared and analyzed. After determining the topology of the rotor and stator, the mechanical stability against the electromagnetic force was investigated, and the temperature stability due to the electromagnetic heat source was also evaluated. The magnetic, mechanical, and thermal properties of all analysis processes for AFPM generator design are calculated using a three-dimensional (3-D) finite element method (FEM), and the final determined model is experimentally verified.

This paper focuses on the process of selecting the rotor-Halbach array topology and the coil specifications of the coreless stator, which have the most influence on the power density among the various design variables of the rotor and stator in the generator design process. In other words, in the rotor design part of this paper, three types of Halbach arrays are compared and analyzed according to the arrangement of the magnetization direction. Moreover, in the stator design part, the loss generated from the coil due to the coreless topology is analyzed in detail, and three cases of using a general conductor and a Litz wire conductor are compared and analyzed. After determining the topology of the rotor and stator, the mechanical stability against the electromagnetic force was investigated, and the temperature stability due to the electromagnetic heat source was also evaluated. The magnetic, mechanical, and thermal properties of all analysis processes for AFPM generator design are calculated using a three-dimensional (3-D) finite element method (FEM), and the final determined model is experimentally verified.

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AFPM generator design specifications are shown in Table 1. In consideration of the performance of the engine that is to be used with the generator, the speed was limited to a maximum of 7000 rpm. Additionally, the maximum line voltage constant at no-load was limited to 11 mV/rpm or less in consideration of the AC/DC converter performance to be used for 48 V DC battery charging. The voltage and current values in this paper all represent RMS (root mean square) and not peak value. For the efficient operation of the maximum payload 3 kg UAV system, the efficiency and power density requirements of the generator are required as shown in Table 1, and the generator is operated without a separate cooling device.

The initial design of the generator used a quasi-three dimensional analysis model, which is a model from 3D geometry to a corresponding two dimensional model . Table 2 shows the design results of the initial design model that satisfy the given constraints, and the 3D analysis model for a detailed design review of the rotor and stator is shown in Figure 2. Each of the six phases is indicated by the capital letters A to F, where LP is the phase inductance, RP is the phase resistance, and RL is the load resistance. In consideration of the performance of the engine that is to be used with the generator, the speed was limited to a maximum of 7000 rpm. Additionally, the maximum line voltage constant at no-load was limited to 11 mV/rpm or less in consideration of the AC/DC converter performance to be used for 48 V DC battery charging. The voltage and current values in this paper all represent RMS (root mean square) and not peak value. For the efficient operation of the maximum payload 3 kg UAV system, the efficiency and power density requirements of the generator are required as shown in Table 1, and the generator is operated without a separate cooling device.

The initial design of the generator used a quasi-three dimensional analysis model, which is a model from 3D geometry to a corresponding two dimensional model . Table 2 shows the design results of the initial design model that satisfy the given constraints, and the 3D analysis model for a detailed design review of the rotor and stator is shown in Figure 2. Each of the six phases is indicated by the capital letters A to F, where LP is the phase inductance, RP is the phase resistance, and RL is the load resistance.

In the process of designing the rotor to increase the power density of the generator, three rotor topologies were compared, as shown in Figure 3. The volume and dimensions of the three rotors are all the same, and the thickness of the yoke used to increase the mechanical robustness of the rotor is also considered to have the same dimensions. The stator specifications, dimensions, and weight conditions are all the same. The only difference is the combination of the magnetization directions of the rotor's PM.

In the process of designing the rotor to increase the power density of the generator, three rotor topologies were compared, as shown in Figure 3. The volume and dimensions of the three rotors are all the same, and the thickness of the yoke used to increase the mechanical robustness of the rotor is also considered to have the same dimensions. The stator specifications, dimensions, and weight conditions are all the same. The only difference is the combination of the magnetization directions of the rotor's PM. As shown in Figure 3a, the Halbach arrangement in which four different magnetization directions form one magnetic pole is defined as Type-I. As shown in Figure 3b, a Halbach array composed of three different magnetization directions that can be combined relatively easily is defined as Type-II. As shown in Figure 3c, a typical pole arrangement that is magnetized in only one direction to form one pole is defined as a normal arrangement (NA).

The efficiency presented in Table 3 considers only copper loss at the stator coil and iron loss at the back yoke of the rotor PM. All models are designed with Litz wire so only DC copper loss is considered; eddy current loss is ignored. Even though all three models have similar efficiency values, when looking at the generated voltage, the voltages of Type-I and Type-II are 38.5% and 24.8% higher than the NA, respectively. Additionally, for the same current, the output power and output power density are evaluated to be 39.6% higher in Type-I and 25.6% higher in Type-II than the NA.

Despite having the same back yoke and rotor volume for all three types, the rotor core losses in Type-I and Type-II are significantly lower than the NA, demonstrating the advantage of using the Halbach array.

Since the output power of Type-I is excellent under the same conditions, the PM arrangement of the generator rotor was set as Type-I. Figure 4 shows the voltage and current waveforms in the stator coil that were generated when the Type-I model was analyzed. In the case of Type-II and the NA, the generated voltage values are different as shown in Table 3, but the waveforms are the same as shown in Figure 4. The phase difference of the waveforms in Figure 4 is due to the use of two pairs of balanced three-phase winding arrays electrically shifted by 30° to each other; this is shown in Figure 5. This winding arrangement is also referred to as a dual three-phase winding arrangement [10,11]. As shown in Figure 3a, the Halbach arrangement in which four different magnetization directions form one magnetic pole is defined as Type-I. As shown in Figure 3b, a Halbach array composed of three different magnetization directions that can be combined relatively easily is defined as Type-II. As shown in Figure 3c, a typical pole arrangement that is magnetized in only one direction to form one pole is defined as a normal arrangement (NA). The efficiency presented in Table 3 considers only copper loss at the stator coil and iron loss at the back yoke of the rotor PM. All models are designed with Litz wire so only DC copper loss is considered; eddy current loss is ignored. Even though all three models have similar efficiency values, when looking at the generated voltage, the voltages of Type-I and Type-II are 38.5% and 24.8% higher than the NA, respectively. Additionally, for the same current, the output power and output power density are evaluated to be 39.6% higher in Type-I and 25.6% higher in Type-II than the NA. Despite having the same back yoke and rotor volume for all three types, the rotor core losses in Type-I and Type-II are significantly lower than the NA, demonstrating the advantage of using the Halbach array.

Since the output power of Type-I is excellent under the same conditions, the PM arrangement of the generator rotor was set as Type-I. Figure 4 shows the voltage and current waveforms in the stator coil that were generated when the Type-I model was analyzed. In the case of Type-II and the NA, the generated voltage values are different as shown in Table 3, but the waveforms are the same as shown in Figure 4. The phase difference of the waveforms in Figure 4 is due to the use of two pairs of balanced threephase winding arrays electrically shifted by 30 • to each other; this is shown in Figure 5. This winding arrangement is also referred to as a dual three-phase winding arrangement [10,11].

In general, DC resistance loss is the main loss in the stator coil, and in the case of highspeed operation, AC resistance loss is also considered. However, in the case of a slotless or coreless stator that does not form teeth with a magnetic material (with or without a back yoke), the magnetic flux change occurs directly in the coil; thus, even at a low frequency of several hundred Hz, severe eddy current loss can happen in the coil depending on the diameter of the conductor. Although DC resistance and AC resistance losses occur only in the state of load operation with the current flowing, eddy current loss in the coil occurs not only during load operation but also during no-load operation.

The best way to reduce the eddy current loss of a conductor is to use Litz wire that divides the conductor into multiple strands. However, when using Litz wires with each coated strand for winding, the number of turns that can be wound around the same coil cross-sectional area is reduced by half compared to the normal conductor. Therefore, when using Litz wire, an increase in the volume of the motor or generator is inevitable because the coil cross-sectional area must be at least doubled or the rotor PM size and the number of coil turns must be increased to achieve the same output power as a model using a normal conductor.

In addition, the relative comparison with the coil model is important, so it was calculated only as the maximum average magnetic flux density in one straight conductor. The lower middle part of Table 4 shows the results comparing the eddy current loss power of the coil calculated by (1) and the measured loss power for each model during a no-load operation at a rotational speed of 5000 rpm. If the eddy current loss in the segmented permanent magnet is neglected, the measured value can only be evaluated by the mechanical and conductor eddy current losses. However, since the Coil-III model makes the stator coil with Litz wire so that the conductor eddy current loss is also negligible,

In addition, the relative comparison with the coil model is important, so it was calculated only as the maximum average magnetic flux density in one straight conductor. The lower middle part of Table 4 shows the results comparing the eddy current loss power of the coil calculated by (1) and the measured loss power for each model during a no-load operation at a rotational speed of 5000 rpm. If the eddy current loss in the segmented permanent magnet is neglected, the measured value can only be evaluated by the mechanical and conductor eddy current losses. However, since the Coil-III model makes the stator coil with Litz wire so that the conductor eddy current loss is also negligible, In addition, the relative comparison with the coil model is important, so it was calculated only as the maximum average magnetic flux density in one straight conductor.

The lower middle part of Table 4 shows the results comparing the eddy current loss power of the coil calculated by (1) and the measured loss power for each model during a no-load operation at a rotational speed of 5000 rpm. If the eddy current loss in the segmented permanent magnet is neglected, the measured value can only be evaluated by the mechanical and conductor eddy current losses. However, since the Coil-III model makes the stator coil with Litz wire so that the conductor eddy current loss is also negligible, most of the measured losses of the Coil-III model can be considered as mechanical losses. Since all were made under the same conditions except for the stator winding, the mechanical losses of the Coil-I and Coil-II models are evaluated similarly to those of Coil-III. After subtracting the mechanical loss of Coil-III from the measured losses of Coil-I and Coil-II, it can be seen that the eddy current loss values of Coil-I and Coil-II models are similar to the calculated values.

At the bottom of Table 4, the temperatures in the coil measured during the no-load test of each model are compared. The maximum temperature measured at the coil using three thermocouples during the test held for 30 s at each speed point in increments of 500 rpm, from 500 rpm to 6000 rpm. The housing of the manufactured generator is as shown in Figure 1, and the temperature of Coil-I and Coil-II was severely increased while the room temperature was 25 degrees Celsius across the board. From the comparison of Coil-I and Coil-II, it can be seen that the effect of the parallel circuit with the possibility of a circulating current is not large; rather, the loss decreases as the conductor diameter decreases. This can confirm that the loss is significantly reduced in Coil-III, which has the smallest conductor diameter. Therefore, the stator was determined with the Coil-III model that could completely reduce the conductor eddy current loss as a heat source.

First, centrifugal force causes the deviation of PMs arranged in the circumferential direction of the edges of the rotor yoke. The main cause is the occurrence of shear stress by centrifugal force on the plane where the rotor frame and PM are bonded [14]. The upper part of Figure 8 shows the cross-section of the designed generator rotor, which has rim parts with a height that is 75% of PM thickness to prevent the deviations in the radial direction of the PMs caused by centrifugal force. Finally, the rotor dynamics were performed to confirm the dynamic stability of the rotor system. Figure 9 is the Campbell diagram showing the result of the analysis. The critical speed, which is when the natural vibration mode is the bending mode of the rotating shaft, was shown to be 18,302 rpm. This is illustrated in the mode shape shown in the lower right-hand corner of Figure 10. More than 20% of the separation margin was secured for the maximum operating speed of the generator at 7000 rpm, and no whirling vibration of the rotor system was expected to occur. Second, the axial attraction force due to the magnetism of the PMs attached to the two rotors causes a bending moment with the hub part assembled on the rotary axis as a support, resulting in deflection [15,16]. The direction of deflection is the direction of reducing the air gap, which in turn reduces the performance and stability of the generator, and a robust design of the rotor frame is required. To increase the stiffness in the axial direction of the rotor frame, the stiffener was designed as shown in the upper part of Figure 8 and the thickness of the hub acting as the support was designed to be relatively thicker than the outer part.

A stress analysis was performed to check the designed rotor frame's deflection and stress distribution by magnetic force, and the lower part of Figure 8 is the result of this stress analysis. The maximum deflection was shown at the edge of the rotor frame at 0.11 mm, which means there was a maximum reduction of 22% in the designed 0.5 mm air-gap length. The von Mises stress resulted in 196.44 Mpa in the same area where the maximum deflection occurred. The yield strength of S45C, the material of the rotor frame, is 490 Mpa, and the maximum stress that occurred was lower than this, meaning that it was mechanically stable.

Energies 2021, 14, 8509 9 of 14 Finally, the rotor dynamics were performed to confirm the dynamic stability of the rotor system. Figure 9 is the Campbell diagram showing the result of the analysis. The critical speed, which is when the natural vibration mode is the bending mode of the rotating shaft, was shown to be 18,302 rpm. This is illustrated in the mode shape shown in the lower right-hand corner of Figure 10. More than 20% of the separation margin was secured for the maximum operating speed of the generator at 7000 rpm, and no whirling vibration of the rotor system was expected to occur. Finally, the rotor dynamics were performed to confirm the dynamic stability of the rotor system. Figure 9 is the Campbell diagram showing the result of the analysis. The critical speed, which is when the natural vibration mode is the bending mode of the rotating shaft, was shown to be 18,302 rpm. This is illustrated in the mode shape shown in the lower right-hand corner of Figure 10. More than 20% of the separation margin was secured for the maximum operating speed of the generator at 7000 rpm, and no whirling vibration of the rotor system was expected to occur. Finally, the rotor dynamics were performed to confirm the dynamic stability of the rotor system. Figure 9 is the Campbell diagram showing the result of the analysis. The critical speed, which is when the natural vibration mode is the bending mode of the rotating shaft, was shown to be 18,302 rpm. This is illustrated in the mode shape shown in the lower right-hand corner of Figure 10. More than 20% of the separation margin was secured for the maximum operating speed of the generator at 7000 rpm, and no whirling vibration of the rotor system was expected to occur.

A thermal analysis was performed under rated conditions to ensure the normal and safe operation of the designed model. Since Litz wire and segmented PM were used, the eddy current loss in the coil and PM was negligible, and the main heat source was the DC copper loss. The other heat sources were core losses in the rotor yoke and mechanical losses in the bearings. Although copper loss and iron loss can be calculated through parameters obtained through electromagnetic field analyses and empirical formulas [17][18][19][20][21][22], respectively, mechanical loss varies depending on the parts and the manufacturing method of the manufactured model. Therefore, it was assumed that the mechanical loss was about 7% of the 3 kW rated output power with reference to the prototype reviewed, until the final model was decided. Moreover, it was assumed that the generator operated under natural cooling conditions at a room temperature of 28 • C. All input parameters for the analysis are shown in Table 5.

The connection coefficient, defined in the boundaries of the model, used empirical values. In the case of the rotor yoke, the values of 100 and 200 W/m2K were applied to the inner and outer surfaces of the rotor, respectively, considering that rotation resulted in a fan-like cooling effect. On the other hand, the jig was separated into a top plate and a bottom plate, and the jig top plate to which the generator was attached had only a slight flow of air, with a value of 10 W/m2K applied. The lower plate of the jig was defined as Energies 2021, 14, 8509 10 of 14 infinite, assuming a situation in which heat could escape infinitely due to its connection to the dynamo steel base. The final designed model including the test jig was modeled in 3D as shown in Figure 10a, and the thermal analysis was performed using FEM [23][24][25][26]. When the temperature was saturated, the highest temperature was the stator coil with the largest loss, as shown in Figure 10b. Table 6 shows the range of temperature distribution by dividing the generator into coils, rotor yokes, PMs, and bearings. Representatively, when looking at the material used for coils and PMs that are most vulnerable to temperature, Litz wire has a class F thermal index with a maximum operating point of 155 • C, and PM with SH grade has a maximum operating point of 150 • C. It can be seen that the heat generated by the generator during the rated operation is in the stable range.

The prototype of the model was finally decided based on the electromagnetic field design and mechanical thermal analysis that were produced as shown in Figure 11. In order to check whether the PM arrangement of the rotor composed of the Halbach array was properly manufactured, the magnetic flux density of the PM surface was measured, as shown in Figure 11a. As compared in Figure 12, it can be confirmed that the trends of the predicted values and the measured values match well through the electromagnetic field analysis. Higher harmonics appearing in the analysis compared to the measured values can be regarded as calculation errors according to the element mesh state. As shown in Figure 13, a dynamo set was constructed to test the generator. By connecting a 2 ohm resistive load per phase to the generator, a power generation output of 3.1 kW could be obtained at 6500 rpm. A higher output power could be achieved by connecting a resistor of 1 ohm per phase to the generator. Figure 14a shows the no-load test results according to speed. Moreover, Figure 14b,c shows the load test results according to speed for a resistive load of 2 and 1 ohm, respectively. In the no-load operation, it can be seen that the back EMF is linear with speed, whereas the power loss is non-linear. When the resistive load is 2 ohm, the rated power of 3 kW output occurs at around 7000 rpm, and the mechanical loss at this time is about 200 W. On the other hand, when the resistive load is 1 ohm, the rated output power occurs at around 5000 rpm, and it can be seen that the mechanical loss at this time is about 100 W. It was confirmed through the test that the maximum efficiency was 93.2% at 3000 rpm when the resistive load was 2 ohm, and the As shown in Figure 13, a dynamo set was constructed to test the generator. By connecting a 2 ohm resistive load per phase to the generator, a power generation output of 3.1 kW could be obtained at 6500 rpm. A higher output power could be achieved by connecting a resistor of 1 ohm per phase to the generator. Figure 14a shows the no-load test results according to speed. Moreover, Figure 14b,c shows the load test results according to speed for a resistive load of 2 and 1 ohm, respectively. In the no-load operation, it can be seen that the back EMF is linear with speed, whereas the power loss is non-linear. When the resistive load is 2 ohm, the rated power of 3 kW output occurs at around 7000 rpm, and the mechanical loss at this time is about 200 W. On the other hand, when the resistive load is 1 ohm, the rated output power occurs at around 5000 rpm, and it can be seen that the mechanical loss at this time is about 100 W. It was confirmed through the test that the maximum efficiency was 93.2% at 3000 rpm when the resistive load was 2 ohm, and the maximum output power was 5 kW at 6500 rpm when the resistive load was 1 ohm. Accordingly, the ratio of the maximum output power to the generator weight is 2.5 kW/kg, which satisfies all the design conditions required in Table 1.

Energies 2021, 14, x FOR PEER REVIEW 12 of 15 maximum output power was 5 kW at 6500 rpm when the resistive load was 1 ohm. Accordingly, the ratio of the maximum output power to the generator weight is 2.5 kW/kg, which satisfies all the design conditions required in Table 1. Figure 15 shows the test results confirming that it can be operated for more than 30 min while maintaining a constant output power of over 3 kW. It can be seen that the maximum temperature of the measured coil is about 40 °C, which is lower than the predicted temperature in the analysis. Errors may have accumulated in various assumptions during the calculation process, but one main cause is considered to be the value of the convection coefficient. If this is compensated by reflecting the test error, it is expected that more accurate results can be predicted in a similar system. As a temperature lower than the predicted temperature is measured, it can be seen that the designed generator can be operated stably with a greater margin for the temperature. Figure 15 shows the test results confirming that it can be operated for more than 30 min while maintaining a constant output power of over 3 kW. It can be seen that the maximum temperature of the measured coil is about 40 • C, which is lower than the predicted temperature in the analysis. Errors may have accumulated in various assumptions during the calculation process, but one main cause is considered to be the value of the convection coefficient. If this is compensated by reflecting the test error, it is expected that more accurate results can be predicted in a similar system. As a temperature lower than the predicted temperature is measured, it can be seen that the designed generator can be operated stably with a greater margin for the temperature.

Figure 15 shows the test results confirming that it can be operated for more than 30 min while maintaining a constant output power of over 3 kW. It can be seen that the maximum temperature of the measured coil is about 40 °C, which is lower than the predicted temperature in the analysis. Errors may have accumulated in various assumptions during the calculation process, but one main cause is considered to be the value of the convection coefficient. If this is compensated by reflecting the test error, it is expected that more accurate results can be predicted in a similar system. As a temperature lower than the predicted temperature is measured, it can be seen that the designed generator can be operated stably with a greater margin for the temperature. It is judged that the above design process and review results can be used as reference materials for other studies of the design of an unmanned aerial vehicle generator using AFPM. It is judged that the above design process and review results can be used as reference materials for other studies of the design of an unmanned aerial vehicle generator using AFPM.

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The grain boundary diffusion process (GBDP) has become an important technique in improving the coercivity and thermal stability of Dy-free sintered Nd-Fe-B magnets. The influence of Dy 70 Al 10 Ga 20 and (Pr 75 Dy 25 ) 70 Al 10 Ga 20 alloys by the GBDP on sintered Nd-Fe-B magnets are investigated in this paper. After diffusing Dy 70 Al 10 Ga 20 and (Pr 75 Dy 25 ) 70 Al 10 Ga 20 alloys, the coercivity (H cj ) of the magnets increased from 13.58 kOe to 20.10 kOe and 18.11 kOe, respectively. Meanwhile, the remanence of the magnets decreased slightly. The thermal stability of the diffused magnets was improved by the GBDP. The microstructure shows continuous Rare-earth-rich (RE-rich) grain boundary phases and (Dy, Pr/Nd) 2 Fe 14 B core-shell structures which contribute to improving the coercivity. Moreover, the Dy concentration on the surface of the (Pr 75 Dy 25 ) 70 Al 10 Ga 20 diffused magnets decreased with the Pr substitution for the Dy element. The openness of the recoil loops for the (Pr 75 Dy 25 ) 70 Al 10 Ga 20 diffused magnets is smaller than that of the original magnets and Dy 70 Al 10 Ga 20 diffused magnets. The results show that the (Pr 75 Dy 25 ) 70 Al 10 Ga 20 alloys can effectively optimize the microstructure and improve the magnetic properties and thermal stability of the sintered Nd-Fe-B magnets.

Sintered Nd-Fe-B magnets possessing excellent high intrinsic coercivity and energy products are widely used in wind power, hybrid vehicles, maglev trains, and household appliances, etc. [1,2]. In this application, higher magnetism is required. Since the invention of Nd-Fe-B magnets in 1983, the remanence (J r ) and the maximum energy product (BH) max of the Nd-Fe-B magnets reached the theoretical values, while the H cj is only 30% of the theoretical value . However, the higher H cj is urgently proposed in the face of increasingly harsh working environments, especially in high-temperature and high-humidity climates . There are basically two ways to develop high coercivity. One is to improve the inherent temperature dependence of H cj , and the other is to develop higher coercivity at room temperature to resist thermal demagnetization of the magnets when exposed to high temperature. Heavy rare earth elements Dy/Tb can be substituted for Pr/Nd to increase the magneto-crystalline anisotropy field (H A ), causing a substantial enhancement of H cj by a single alloying method. However, due to the antiferromagnetic coupling between Dy and Fe, it is unfavorable to the saturation magnetization [7,8]. In order not to sacrifice the saturation magnetization, the GBDP (grain boundary diffusion process) technique was proposed by Park et al.. Heavy rare earth elements can be selectively diffused into the magnet interior along the grain boundary (GB), forming a hard core-shell structure surrounding the main grains. Later, researchers successively used heavy rare earth metals/compounds/alloys containing Dy or Tb, such as Dy, Dy 2 O 3 , DyF 3 , DyH 2 , and Dy-Cu or Pr-Dy-Cu [10][11][12][13][14] acting as diffusion sources to improve the H cj .

In addition, the non-rare-earth elements Al/Ga/Cu can also increase the H cj of the sintered Nd-Fe-B magnets and reduce the irreversible loss of magnetic flux. These elements mainly enrich in the RE-rich (Rare-earth rich) liquid phase to improve the wettability and increase the coercivity of the magnets [17][18][19]. Therefore, we select the ternary alloy Pr 70 Al 10 Ga 20 and Dy 70 Al 10 Ga 20 and quaternary alloy (Pr 75 Dy 25 ) 70 Al 10 Ga 20 as the diffusion sources in this work. The (Pr 75 Dy 25 ) 70 Al 10 Ga 20 alloys inculcate the best properties with a large substitution of Pr for Dy after the GBDP, as shown in Supplementary Material. The magnetic properties and thermal stability of the diffused magnets are analyzed. The relationship between microstructure and recoil loops and diffusion mechanism of the magnets are also discussed.

The commercial sintered Nd-Fe-B magnet of N52 was selected and wire-cut into small magnets with a size of ϕ10 × 10 × 5 mm 3 , and the chemical composition was (Pr, Nd) 30 Co 1.0 Cu 0.15 Zr 0.12 Ga 0.3 B 0.94 Fe bal. (wt.%). The ingots of Pr 70 Al 10 Ga 20 , Dy 70 Al 10 Ga 20 , and (Pr 75 Dy 25 ) 70 Al 10 Ga 20 (wt.%) were prepared by arc melting under a high-purity argon atmosphere. Then, these ingots were melt-spun into ribbons with 10 mm in width and 0.17 mm in thickness at a speed of 8 m/s. The magnets were polished with 400 mesh, 800 mesh, 1000 mesh, 1500 2000 mesh, and mesh sandpaper and then ultrasonically washed in alcohol and dried. The ribbons were placed on the top and bottom of the magnet and put in a sintering furnace for diffusion heat treatment. The heat treatments were carried out at 850 • C for 6 h, and then annealed at 490 • C for 3 h in a vacuum (10 -4 Pa) tubular furnace. The magnetic properties at different temperatures were measured by a boron hydride tracer (NIM-500C, National Institute of Metrology, Beijing, China). The melting points of the alloys were measured by differential scanning calorimetry (DSC250, TA Instruments, USA). Additionally, the microstructure of the magnets was observed by a field emission scanning electron microscope (FESEM, MLA650F, FLIR Systems, Inc., Wilsonville, OR, USA). The irreversible magnetic flux loss at elevated temperatures was measured by pulling Helmholtz coils. The phase constitution of the magnets was determined by the X-ray diffraction with a Cu-K α radiation (XRD, D8 Advance, Bruker, Billerica, MA, USA). The elemental distribution of Nd-Fe-B magnets was explored by using an electron probe microanalyzer (EPMA, JXA-8530F, JEOL, Tokyo, Japan). The recoil loops of the magnets were measured by the Physical Property Measurement System (PPMS-DynaCOOL1-9, Quantum Design, San Diego, CA, USA) in fields up to 5 T at room temperature. lower melting points. Additionally, the lower melting point may reduce the activatio energy of the diffusion and improve diffusion efficiency. Moreover, compared with th ternary alloy Dy70Al10Ga20, the quaternary alloy (Pr75Dy25)70Al10Ga20 contains less heav rare earth elements; thus, it reduces the costs. Figure 2 shows demagnetization curves at the room temperature of the origina magnets and Pr70Al10Ga20, Dy70Al10Ga20, and (Pr75Dy25)70Al10Ga20 diffused magnets. It ca be clearly seen that the Hcj of the diffused magnets is improved after the GBDP, while th remanence is only slightly decreased. The coercivity increased from 13.58 kOe to 15.3 kOe, 20.10 kOe, and 18.11 kOe, respectively, after diffusing Pr70Al10Ga20, Dy70Al10Ga20, an (Pr75Dy25)70Al10Ga20 alloys. At the same time, the Jr reduced from 14.3 kG to 14.0 kG, 14. kG, and 14.1 kG, respectively. The increase in the Hcj is mainly because of the partia substitution of Pr and Dy for Nd to form the core-shell structure of (Dy, Pr/Nd)2Fe14B. Th antiferromagnetic coupling of Dy and Fe atoms reduces the Jr of Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 diffused magnets. In addition, the Pr content in the Pr70Al10Ga20 dif fused magnet is higher, and the nonmagnetic volume fraction increases after diffusion which leads to the decrease in the Jr. The increase in the volume fraction of th non-magnetic phases in the grain boundary is another reason for the decrease in the Jr. lower melting points. Additionally, the lower melting point may reduce the activation energy of the diffusion and improve diffusion efficiency. Moreover, compared with the ternary alloy Dy70Al10Ga20, the quaternary alloy (Pr75Dy25)70Al10Ga20 contains less heavy rare earth elements; thus, it reduces the costs. Figure 2 shows demagnetization curves at the room temperature of the original magnets and Pr70Al10Ga20, Dy70Al10Ga20, and (Pr75Dy25)70Al10Ga20 diffused magnets. It can be clearly seen that the Hcj of the diffused magnets is improved after the GBDP, while the remanence is only slightly decreased. The coercivity increased from 13.58 kOe to 15.34 kOe, 20.10 kOe, and 18.11 kOe, respectively, after diffusing Pr70Al10Ga20, Dy70Al10Ga20, and (Pr75Dy25)70Al10Ga20 alloys. At the same time, the Jr reduced from 14.3 kG to 14.0 kG, 14.0 kG, and 14.1 kG, respectively. The increase in the Hcj is mainly because of the partial substitution of Pr and Dy for Nd to form the core-shell structure of (Dy, Pr/Nd)2Fe14B. The antiferromagnetic coupling of Dy and Fe atoms reduces the Jr of Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 diffused magnets. In addition, the Pr content in the Pr70Al10Ga20 diffused magnet is higher, and the nonmagnetic volume fraction increases after diffusion, which leads to the decrease in the Jr. The increase in the volume fraction of the non-magnetic phases in the grain boundary is another reason for the decrease in the Jr. Additionally, the temperature coefficient of coercivity (β) of the magnets can be calculated according to the formula [20,21]:

where T 1 is the elevated temperature, and T 0 is the room temperature. The β increased from -0.5341 %/K of the original magnets to -0.4609 %/K and -0. The structure loss occurs at a high temperature, which leads to demagnetization. The irreversible flux loss is not recoverable when back to room temperature. It is related to the irreversible change of the microstructure of the magnets. The GB microstructure of the diffused magnets was optimized after thermal diffusion treatment. The nucleation of the reverse magnetic domain of the magnets is suppressed, and it is difficult to trigger the magnetization reversal of the magnetic domain due to the hardening of the epitaxial layer of the matrix phase grain [22]. This results in an improvement in temperature coefficients and irreversible magnetic flux losses of the diffused magnets. These results indicate that the thermal stability of the diffused magnets was improved after the GBDP. Figure 3a shows the coercivity curves of the original magnet and the Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 diffused magnets at the temperature range of 293 to 453 K. Additionally, the temperature coefficient of coercivity (β) of the magnets can be calculated according to the formula [20,21]:

where T1 is the elevated temperature, and T0 is the room temperature. The β increased from -0.5341 %/K of the original magnets to -0.4609 %/K and -0.4939 %/K, respectively, for the Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 diffused magnets. Figure 3b is the irreversible flux loss curve of the original magnet and the diffused Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 magnets at 293-453 K. The irreversible flux loss rates of the original magnet and the Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 alloy diffused magnets were 75.5%, 48.6%, and 48.7%, respectively. The irreversible flux loss of the magnets was reduced by about 27% after diffusion, which suggests that the diffused magnets have less magnetic irreversible flux losses. The magnetic flux and coercivity are very sensitive to temperature. The structure loss occurs at a high temperature, which leads to demagnetization.

The irreversible flux loss is not recoverable when back to room temperature. It is related to the irreversible change of the microstructure of the magnets. The GB microstructure of the diffused magnets was optimized after thermal diffusion treatment. The nucleation of the reverse magnetic domain of the magnets is suppressed, and it is difficult to trigger the magnetization reversal of the magnetic domain due to the hardening of the epitaxial layer of the matrix phase grain [22]. This results in an improvement in temperature coefficients and irreversible magnetic flux losses of the diffused magnets. These results indicate that the thermal stability of the diffused magnets was improved after the GBDP. Figure 4 shows the XRD of the original magnets and the Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 diffused magnets (vertical to the c-axis plane, with the observation surface near the surface). As can be seen from the diffraction peaks marked in Figure 4, most of the diffraction peaks are the main phases, and small parts are the RE-rich phase, and no new diffraction peaks appear in the diffused magnets. The characteristic diffraction peaks were located at 29.3, 44.6, 60.8, and 78.5 of 2θ, and Bragg diffraction peaks corresponding to (00l) are compared with JCPDS (Joint Committee on Powder Diffraction Standards) card no. 39-0473. This indicates that the magnets are dominated by 2:14:1 phases before and after the GBDP, and the content of other impurity phases is relatively small. The partially enlarged view of the diffraction peaks of the (006) crystal plane As can be seen from the diffraction peaks marked in Figure 4, most of the diffraction peaks are the main phases, and small parts are the RE-rich phase, and no new diffraction peaks appear in the diffused magnets. The characteristic diffraction peaks were located at 29.3, 44.6, 60.8, and 78.5 of 2θ, and Bragg diffraction peaks corresponding to (00l) are compared with JCPDS (Joint Committee on Powder Diffraction Standards) card no. 39-0473. This indicates that the magnets are dominated by 2:14:1 phases before and after the GBDP, and the content of other impurity phases is relatively small. The partially enlarged view of the diffraction peaks of the (006) crystal plane shows that the main phase peak of the magnet shifted to a large angle direction after diffusing Dy 70 Al 10 Ga 20 , while the main phase peak moved slightly to a small angle direction after diffusing (Pr 75 Dy 25 ) 70 Al 10 Ga 20 . This is because the atomic radius of Dy (0.1773 nm) is smaller than Nd (0.1821 nm). According to the Bragg equation, when the Dy atoms diffuse into the main phase to replace Nd to form the (Nd, Dy) 2 Fe 14 B shell layer, the lattice parameters decrease. For the (Pr 75 Dy 25 ) 70 Al 10 Ga 20 diffused magnet, the lattice parameters of the main phase increase, which is because the diffusion amount of Pr is greater than that of Dy. Based on the Lanthanide contraction effect, the atomic radius of the Dy element is smaller than that of Pr and Nd. Dy instead of Pr/Nd makes the diffraction peaks move to the large angle; in contrast, Pr and Nd move the peak to a small angle. Consequently, the combined effect is that the diffraction peak shifts to a small angle. The shift of the peak also means that Pr and Dy have entered into the main phase, forming a stronger H A of (Dy, Pr/Nd) 2 Fe 14 B shells, thus exhibiting the coercivity enhancement effect. shows that the main phase peak of the magnet shifted to a large angle direction after diffusing Dy70Al10Ga20, while the main phase peak moved slightly to a small angle direction after diffusing (Pr75Dy25)70Al10Ga20. This is because the atomic radius of Dy (0.1773 nm) is smaller than Nd (0.1821 nm). According to the Bragg equation, when the Dy atoms diffuse into the main phase to replace Nd to form the (Nd, Dy)2Fe14B shell layer, the lattice parameters decrease. For the (Pr75Dy25)70Al10Ga20 diffused magnet, the lattice parameters of the main phase increase, which is because the diffusion amount of Pr is greater than that of Dy. Based on the Lanthanide contraction effect, the atomic radius of the Dy element is smaller than that of Pr and Nd. Dy instead of Pr/Nd makes the diffraction peaks move to the large angle; in contrast, Pr and Nd move the peak to a small angle. Consequently, the combined effect is that the diffraction peak shifts to a small angle. The shift of the peak also means that Pr and Dy have entered into the main phase, forming a stronger HA of (Dy, Pr/Nd)2Fe14B shells, thus exhibiting the coercivity enhancement effect. In order to explore the reason for the Hcj enhancement, the microstructure of the magnets was observed after the GBDP. Figure 5a,b,c are BSE-SEM (backscattered electron) images of the original magnets, and the Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 alloy diffused magnets, respectively. The dark gray parts in Figure 5 correspond to the 2:14:1 matrix phase grains, and the bright white and gray white areas correspond to the RE-rich phases. The bright white and gray white in SEM are caused by the difference in composition of the RE-rich phases. Figure 5a shows that the triple junction RE-rich phases of the original magnets were distributed discretely in the magnet interior, and some adjacent matrix phase grains were in direct contact, which is unfavorable to the Hcj. Comparably, the smooth and continuous thin grain boundary RE-rich phases were formed in the Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 diffused magnets. If all grains are surrounded by thin grain boundary phases, then the grains are magnetically isolated from each other. If the grains are in direct contact with each other, there will be a localized exchange coupling effect, and, as a result, the grains are connected together to form a larger ferromagnetic domain grain group. A small grain inversion will drive demagnetization of adjacent grains in chains, because there is no thin layer RE-rich phase boundary, which will not hinder the displacement of the domain wall [23]. Demagnetization of one grain will drive demagnetization of other grains, thus reducing coercivity; that is, the demagnetization resistance will be reduced. In order to explore the reason for the H cj enhancement, the microstructure of the magnets was observed after the GBDP. Figure 5a-c 5 correspond to the 2:14:1 matrix phase grains, and the bright white and gray white areas correspond to the RE-rich phases. The bright white and gray white in SEM are caused by the difference in composition of the RE-rich phases. Figure 5a shows that the triple junction RE-rich phases of the original magnets were distributed discretely in the magnet interior, and some adjacent matrix phase grains were in direct contact, which is unfavorable to the H cj . Comparably, the smooth and continuous thin grain boundary RE-rich phases were formed in the Dy 70 Al 10 Ga 20 and (Pr 75 Dy 25 ) 70 Al 10 Ga 20 diffused magnets. If all grains are surrounded by thin grain boundary phases, then the grains are magnetically isolated from each other. If the grains are in direct contact with each other, there will be a localized exchange coupling effect, and, as a result, the grains are connected together to form a larger ferromagnetic domain grain group. A small grain inversion will drive demagnetization of adjacent grains in chains, because there is no thin layer RE-rich phase boundary, which will not hinder the displacement of the domain wall [23]. Demagnetization of one grain will drive demagnetization of other grains, thus reducing coercivity; that is, the demagnetization resistance will be reduced. Figure 6 shows the EPMA images on the surface (perpendicular to c-axis) of the Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 diffused magnets. The distribution of Dy, Nd, Pr, Al, and Ga elements in the Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 magnets are shown in Figure 6 after the GBDP, respectively. Dy elements are mainly distributed in the main phase grain epitaxial layer to form the (Dy, Pr/Nd)2Fe14B core-shell structure, which is beneficial to increase the coercivity. During the GBDP, Dy penetrates into the Nd-Fe-B sintered magnets through liquid grain boundaries. The Dy-rich shells are only selectively formed on the low-index lattice plane of the main phase grains. These planes, generated by the partial melting of the main phase grains, offer the low-energy configurations at the Nd2Fe14B/GB interfaces [24]. During the subsequent cooling process, the Dy-rich liquid phases precipitate on the edge of the main phase grains and solidify to form (Nd, Dy)2Fe14B hard shells. As shown in Figure 6a, a large amount of Dy elements accumulated on the surface of the Dy70Al10Ga20 diffused magnets, while the enrichment on the (Pr75Dy25)70Al10Ga20 diffused magnets is mitigated. Although the Hcj of the (Pr75Dy25)70Al10Ga20 diffused magnet is 2 kOe lower than that of the Dy70Al10Ga20 diffused one, the heavy rare earth content of the quaternary alloy is much lower than the ternary alloy.

The grain boundary channels, and intergranular regions of the sintered Nd-Fe-B magnets, are typically around 100-1000 nm in size, and the high temperature wettability causes enough capillary thrust for these elements to enter the intergranular channels during liquefaction, which in turn causes the uniform distribution of grain boundaries with the matrix grains [25,26]. According to the distribution of Al and Ga in Figure 6b, most of them remain in the grain boundaries and play a role in wetting the grain boundaries [18]. At the same time, a small amount of Al also exists in the matrix grains, which is possible when the surface of the Nd-Fe-B grains is partially decomposed, and Dy replaces Nd atoms. Meanwhile, Al penetrates into the selected grain facets from the grain boundaries with a high concentration at the grain edges. With a cooling effect coming in place, lighter Al atoms get transported inwards due to the low melting point while matrix restructuring happens, known as core-shell morphology [27]. Although the core-shells are not obvious, a higher concentration of Pr at the grain boundaries takes precedence of surface diffusion by the substitution of Nd atoms, resulting in the intergranular region becoming richer with Nd and hard phase grains taking composition (Pr, Nd)2Fe14B. Therefore, under the combined effect of the above elements, the hard core-shell structure and optimized microstructure can explain the reason why the diffused magnets have an increased Hcj after GBDP.

To investigate the diffusion depth of Dy in different diffused magnets, the EPMA was performed to determine the distribution of the Dy element along the diffusion direction. Figure 7(a1,a2,b1,b2) show the corresponding EPMA mappings at 0-400 μm of Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 diffused magnets. As can be seen from Figure 7(a2,b2), a high concentration of the Dy-rich area is formed on the surface of the magnet, and the Dy-rich area is indicated by the red ellipses in Figure 7(a2,b2). It can be seen from the red rectangular box that the concentration of the Dy element in the 6 after the GBDP, respectively. Dy elements are mainly distributed in the main phase grain epitaxial layer to form the (Dy, Pr/Nd) 2 Fe 14 B core-shell structure, which is beneficial to increase the coercivity. During the GBDP, Dy penetrates into the Nd-Fe-B sintered magnets through liquid grain boundaries. The Dy-rich shells are only selectively formed on the low-index lattice plane of the main phase grains. These planes, generated by the partial melting of the main phase grains, offer the low-energy configurations at the Nd 2 Fe 14 B/GB interfaces [24]. During the subsequent cooling process, the Dy-rich liquid phases precipitate on the edge of the main phase grains and solidify to form (Nd, Dy) 2 Fe 14 B hard shells. As shown in Figure 6a The grain boundary channels, and intergranular regions of the sintered Nd-Fe-B magnets, are typically around 100-1000 nm in size, and the high temperature wettability causes enough capillary thrust for these elements to enter the intergranular channels during liquefaction, which in turn causes the uniform distribution of grain boundaries with the matrix grains [25,26]. According to the distribution of Al and Ga in Figure 6b, most of them remain in the grain boundaries and play a role in wetting the grain boundaries [18]. At the same time, a small amount of Al also exists in the matrix grains, which is possible when the surface of the Nd-Fe-B grains is partially decomposed, and Dy replaces Nd atoms. Meanwhile, Al penetrates into the selected grain facets from the grain boundaries with a high concentration at the grain edges. With a cooling effect coming in place, lighter Al atoms get transported inwards due to the low melting point while matrix restructuring happens, known as core-shell morphology [27]. Although the core-shells are not obvious, a higher concentration of Pr at the grain boundaries takes precedence of surface diffusion by the substitution of Nd atoms, resulting in the intergranular region becoming richer with Nd and hard phase grains taking composition (Pr, Nd) 2 Fe 14 B. Therefore, under the combined effect of the above elements, the hard core-shell structure and optimized microstructure can explain the reason why the diffused magnets have an increased H cj after GBDP.

To investigate the diffusion depth of Dy in different diffused magnets, the EPMA was performed to determine the distribution of the Dy element along the diffusion direction. (Pr75Dy25)70Al10Ga20 diffused magnets is higher than that of the Dy70Al10Ga20 diffused magnets. With the diffusion depth increasing, the Dy-rich area gradually decreases. At the depth of 400 μm, the Dy element still exists in the magnet interior. At the same time, it is observed that the concentration of Dy in the (Pr75Dy25)70Al10Ga20 diffused magnets is higher than that of the Dy70Al10Ga20 diffused magnets at the same depth as the dotted lines in Figure 7(a2,b2). Therefore, the quaternary alloy (Pr75Dy25)70Al10Ga20 can save the Dy elements and promote its diffusion depth. For sintered Nd-Fe-B, the GB provides a channel for the diffusion source. The melting point of the RE-rich grain boundary phase is about 655 °C, which is much lower than the melting point of the main phase of 1185 °C [28]. The element diffusion follows the Fick's second law, which states that in the process of unsteady diffusion, we get

where cx, c0, and cs are the volume concentrations of the diffusion material (kg/m 3 ) at the different depths; A is a fixed value (when the surface concentration and time are determined); and x is the distance (m). Figure 8 shows the fitting curve of the Dy element concentration in the range of different depths in the diffused magnets. Additionally, the diffusion coefficients of the Dy element are approximately 4.988 ± 0.673 × 10 -7 cm 2 /s and 3.139 ± 0.101 × 10 -7 cm 2 /s in the (Pr75Dy25)70Al10Ga20 and Dy70Al10Ga20 diffused magnets, respectively. This also shows that the diffusion efficiency of the Dy elements in the quaternary alloys (Pr75Dy25)70Al10Ga20 is improved under the cooperation of the Pr elements. The concentration of the Dy element can be measured by EPMA along the diffusion direction from the 0 μm to 450 μm in a continuous 100 × 100 μm 2 square indicated by the red boxes in Figure 7(a1,b1). As the diffusion depth increases, the concentration of Dy elements decreases, and the diffusion rate slows down. Figure 9 gives a schematic diagram of the change in the amount of diffusion distinguished from the depth of the diffused magnets [29]. Figure 9a,b show the diffusion mechanism of ternary alloys Dy70Al10Ga20 and quaternary alloys (Pr75Dy25)70Al10Ga20, respectively. During the heat treatment, Dy atoms enter the magnet along the grain boundaries. By replacing Nd atoms with Dy atoms, a thin layer with higher Dy concentration is formed on the edge of the main phase grains, which is called the core-shell structure. The quaternary alloys (Pr75Dy25)70Al10Ga20 have the coordinated diffusion of the Pr element, so that the Dy element can penetrate deeper into the magnets and form a more core-shell structure. At the same time, the surface Dy concentration of the magnets can be regulated by diffusing (Pr75Dy25)70Al10Ga20 alloys. Due to the magnetic isolation effect of the grain boundaries and the high magnetocrystalline anisotropy field of the core-shell structure, the coercivities of the diffused magnets show improvement after the GBDP treatment. For sintered Nd-Fe-B, the GB provides a channel for the diffusion source. The melting point of the RE-rich grain boundary phase is about 655 • C, which is much lower than the melting point of the main phase of 1185 • C [28]. The element diffusion follows the Fick's second law, which states that in the process of unsteady diffusion, we get

where c x , c 0 , and c s are the volume concentrations of the diffusion material (kg/m 3 ) at the different depths; A is a fixed value (when the surface concentration and time are determined); and x is the distance (m). The recoil loops can verify the magnitude of the demagnetization capability and the uniformity of the microstructure [17]. Figure 10 shows the recoil loops of the original magnets, and the Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 diffused magnets. It shows that the recoil loops' opening of the original magnet is larger, while that of the Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 diffused magnets are much smaller. This is because the distribution of the RE-rich phase for the original magnet is non-uniform and discontinuous, and the grain boundary of the Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 diffused magnets are optimized to be more uniform and continuous after the GBDP. However, a large amount of The recoil loops can verify the magnitude of the demagnetization capability and the uniformity of the microstructure [17]. Figure 10 shows the recoil loops of the original magnets, and the Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 diffused magnets. It shows that the recoil loops' opening of the original magnet is larger, while that of the Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 diffused magnets are much smaller. This is because the distribution of the RE-rich phase for the original magnet is non-uniform and discontinuous, and the grain boundary of the Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 diffused magnets are optimized to be more uniform and continuous after the GBDP. However, a large amount of The recoil loops can verify the magnitude of the demagnetization capability and the uniformity of the microstructure [17]. Figure 10 the Dy element enrichment on the surface of the Dy70Al10Ga20 diffused magnets leads to the larger opening of the recoil loops than that of the (Pr75Dy25)70Al10Ga20 diffused magnets. The reduced surface Dy enrichment improves the microstructure uniformity by diffusing the (Pr75Dy25)70Al10Ga20 alloy; thus, the recoil loops' opening of the (Pr75Dy25)70Al10Ga20 diffused magnets is smaller than that of the original and Dy70Al10Ga20 diffused magnets. This is also confirmed by the microstructure of the magnets mentioned in Figures 5 and6.

In this paper, the effects of diffusing Dy70Al10Ga20 ternary alloys and (Pr75Dy25)70Al10Ga20 quaternary alloys on the magnetic properties and microstructure of sintered Nd-Fe-B magnets were investigated.

(1) The coercivity of the Pr70Al10Ga20, Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 alloys diffused Nd-Fe-B magnets increased from 13.58 kOe to 15.34 kOe and 20.10 kOe and 18.11 kOe, respectively, while the remanence is only slightly decreased. (2) The thermal stability of the diffused magnets improves by diffusing Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 alloys. The β increased from -0.5341 %/K for the original This indicates that the diffused magnet has a stronger capability for demagnetization.

Materials 2021, 14, 2583. https://doi.org/10.3390/ma14102583 https://www.mdpi.com/journal/materials

Funding: This work was supported by the National Natural Science Foundation of China (51561009), the Natural Science Foundation of Jiangxi Province (20192BAB206004 and 20202BAB214003), the Key Research and Development Program of Jiangxi Province (20202BBE53014), the Open Foundation of Guo Rui Scientific Innovation Rare Earth Functional Materials Co., Ltd. (KFJJ-2019-0004), the Doctoral Start-up Foundation of Jiangxi University of Science and Technology (205200100110), and the Foundation of Jiangxi Educational Department (GJJ200832 and GJJ190478). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable.

The following are available online at https://www.mdpi.com/article/10 .3390/ma14102583/s1, Figure S1: Demagnetization curve of the (Pr 100-x Dy x ) 70 Al 10 Ga 20 (x = 0, 25, 50, 75, 100) diffused magnets.

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thermodynamic parameters of the LaH 10 superconductor were an object of our interest. LaH 10 is characterised by the highest experimentally observed value of the critical temperature: = T 215 C a K (p a = 150 GPa) and = T 260 C b K (p b = 190 GPa). It belongs to the group of superconductors with a strong electron-phonon coupling (λ a ~ 2.2 and λ b ~ 2.8). We calculated the thermodynamic parameters of this superconductor and found that the values of the order parameter, the thermodynamic critical field, and the specific heat differ significantly from the values predicted by the conventional BCS theory. Due to the specific structure of the Eliashberg function for the hydrogenated compounds, the qualitative analysis suggests that the superconductors of the La δ X 1-δ H 10 -type (LaXH-type) structure, where X ∈ {Sc, Y}, would exhibit significantly higher critical temperature than T C obtained for LaH 10 . in the case of LaScH we came to the following assessments: ∈ T 220 267 , C a K and ∈ T 263 294 , C b K, while the results for LaYH were: ∈ T 218 247 , C a K and ∈ T 261 274 , C b K.

The experimental discovery of the high-temperature superconducting state in the compressed hydrogen and sulfur systems H 2 S (T C = 150 K for p = 150 GPa) and H 3 S (T C = 203 K for p = 150 GPa) 1,2 accounts for carrying out investigations, which can potentially lead to the discovery of a material showing the superconducting properties at room temperature. For the first time, the possibility of the existence of the superconducting state in hydrogenated compounds was pointed out by Ashcroft in 2004 3 . It was stated in his second fundamental work concerning the high-temperature superconductivity, following his first work written in 1968, in which he propounded the existence of the high-temperature superconducting state in metallic hydrogen 4 . The superconducting state in hydrogenated compounds is induced by the conventional electron-phonon interaction. This fact made possible the theoretical description of the superconducting phase in H 2 S and H 3 S even prior to carrying out the suitable experiments 5,6 . The detailed discussion with respect to the thermodynamic properties of the superconducting state occurring in H 2 S and H 3 S one can find in references .

In 2018, there were held the groundbreaking experiments, which confirmed the existence of the superconducting state of extremely high values of the critical temperature in the LaH 10 compound: K for p c ~ 170 GPa 18 ). It was proved on the theoretical basis 19 that the results achieved by Drozdov et al. 20 can be related to the induction of the superconducting phase in the R m 3 structure (T C = 206-223 K). The experimental results reported by Somayazulu et al. 21 should be related to the superconducting state induced in the Fm m 3 structure, where the critical temperature can potentially reach even the value of 280 K. From the materials science perspective, the achieved results imply that all possible actions should be taken in order to examine the hydrogen-containing materials with respect to the existence of the high-temperature superconducting state at room temperature. Attention should be paid to the importance of the discovery of the high-temperature superconducting state in LaH 10 because La can form stable hydrogenated compounds with other metals. Such materials can exhibit so large hydrogen concentration, that they are presently taken into account as basic components of the hydrogen cells intended for vehicle drives 22 .

The purpose of this work is, firstly, to present the performed analysis of the thermodynamic properties of the superconducting state in the LaH 10 compound. We took advantage of the phenomenological version of the Eliashberg equations, for which we fitted the value of the electron-phonon coupling constant on the basis of the experimentally found T C value. Our next step consisted in examining the hydrogenated compounds of the La δ X 1-δ H 10 -type (LaXH-type) on the basis of the achieved results in order to find a system with an even higher value of the critical temperature. Taking into account the structure of the Eliashberg function for hydrogenated compounds, with its distinctly separated parts coming from the heavy elements and from hydrogen, we assumed X to be Sc or Y, what would, in our opinion, fill the gap in the Eliashberg function occurring within the range from about 40 meV to 100 meV. A significant increase in the value of critical temperature should take place as a consequence.

. The fitting between the theory and the experimental results is presented in Fig. 1. We obtained λ a = 2.187 for p a = 150 GPa and λ b = 2.818 for p b = 190 GPa. The symbol Ω C represents the characteristic phonon frequency, its value being assumed as Ω C = 100 meV.

, where  μ is the Coulomb pseudopotential (  μ = 0.1). The quantity Ω C denotes the cut-off frequency (Ω C = 1 eV). The Eliashberg equations were solved for the Matsubara frequency equal to 1000. We used numerical methods presented in the previous paper 24 . In the considered case, we obtained stable equation solutions for T ≥ T 0 = 15 K.

BCS , however the BCS theory approximates well the experimental results for λ < 0.5.

where ρ(0) denotes the value of electronic density of states at Fermi surface; Z n S and Z n N are the wave function normalization factors for the superconducting and the normal state, respectively. Note that ΔF is equal to zero exactly for T = T C . This fact results from the overt dependence of free energy on solutions of Eliashberg equations (Δ n and Z n ) that have been adjusted to the experimental value of critical temperature by appropriate selection of electron-phonon coupling constant (see Fig. 1). Thermodynamic critical field should be calculated from the formula:

) coming from sulphur and from hydrogen are separated due to a huge difference between atomic masses of these two elements. To be precise, the electron-phonon interaction derived from sulphur is crucial in the frequency range from 0 meV to Ω max S equal to about 70 meV, while the contribution derived from hydrogen (Ω = 220 max H meV) is significant above ~100 meV. It is noteworthy that we come upon a similar situation in the case of the LaH 10 compound 30 . Therefore the following factorization of the Eliashberg function for the LaXH compound can be assumed: where λ La , λ X , and λ H are the contributions to the electron-phonon coupling constant derived from both metals (La, X) and hydrogen, respectively. Similarly, the symbols Ω max La , Ω max X , and Ω max H represent the respective maximum phonon frequencies. The value of the critical temperature can be assessed from the generalised formula of the BCS theory 7 :

We are going to consider the case Ω < Ω < ~40 meV 100 meV max La max X

. It means that we are interested in such an X element, the contribution of which to the Eliashberg function fills the gap between contributions coming from lanthanum and hydrogen. It can be assumed that 0 < λ X < 1, while keeping in mind that λ La = 0.68 31 . Additionally, the previous calculations discussed in the work allow to write that λ La + λ H is equal to λ a = 2.187 for p a = 150 GPa or to λ b = 2.818 for p b = 190 GPa. The quantity  μ occurring in the Eq. ( 8) serves now as the fitting parameter. One should remember that the formula for the critical temperature given by the Eq. ( 8) was derived with the use of significant simplifying assumptions (the value of the cut-off frequency is neglected, as well as the retardation effects modeled by the Matsubara frequency). Therefore the value of the Coulomb pseudopotential determined from the full Eliashberg equations usually differs from the value of  μ calculated analytically. The experimental data for the LaH 10 superconductor can be reproduced using Eq. ( 8) and assuming that K. Therefore the superconducting state can potentially exist at room temperature for both cases. Now, let us take into account elements with the identical electron configuration at the valence shell as lanthanum, but lighter than lanthanum: scandium and yttrium, both being selected as X. Attention should be paid to the fact that the electron configuration of X, identical as in lanthanum, should minimize such changes in properties of the obtained compound which could result from changes in both the electron dispersion relation and the matrix elements of the electron-phonon interaction. Applying the formula:

To summarize, the experimental results obtained for the LaH 10 compound get us much closer to the purpose of obtaining the superconducting state at room temperature. The huge difference between atomic masses of lanthanum and hydrogen results in the characteristic structure of the Eliashberg function modeling the electron-phonon interaction in the considered compound, with distinctly separated parts proceeded either from lanthanum or from hydrogen. The proper selection of the additional element (X) in the LaXH compound is expected to fill the ' empty' range of the Eliashberg function between the parts coming from La and H. In our opinion, good candidates are scandium and yttrium. These elements have the electron configuration at the valence shell exactly the same as lanthanum, and yet they are considerably lighter. Our numerical calculations suggest the possible growth in the critical temperature of the LaScH compound equal to about 52 K (150 GPa) or to about 79 K (190 GPa) as compared to the T C value for the LaH 10 compound. As far as the LaYH compound is concerned, the pertinent increase in T C value can reach about 32 K for 150 GPa or about 59 K for 190 GPa.

• In the paper, we assume the relatively simple form of Eliashberg function, which is the linear combination of each of the contributions from La, H and X. Does this mean that any contribution related to Sc or Y will be positive? Of course, this doesn't have to be the case. For example, the properly selected concentration of Sc or Y atoms can lead to a decrease in the electron-phonon coupling constant. On the other hand, one should remember the results obtained for YH 10 compound 32,33 . Based on the DFT method, it was found that the critical temperature for ∈ p (250, 300) GPa can exceed the room temperature ( ) roughly correspond to the physical values of this parameters? In particular, are these values too low, which would lead to the significant overestimation of the critical temperature in our paper. In this case, it is worth referring to the recently obtained DFT results for LaH 10 . In the publication 19 , the authors showed that qualitative compliance with experimental data can be obtained assuming  μ = 0. K for the crystal structure Fm3m). In the first case, the experimental critical temperature was underestimated by 18 K (too high value of  μ ), in the second case, T [ ] C exp was revalued by 11 K (too low value of  μ ). Comparing the results obtained in the paper 19 with ours, it is clearly seen that μ a  and μ b  are fairly well-obtained. In the most interesting case for LaH 10 corresponds to the pressure of 190 GPa, taking into account the possible reduction of μ b  suggested in 19 , the increase in the critical temperature value for the LaScH and LaYH compounds can be expected. It is worth noting that our results also correlate well with the data obtained in the paper 30 , where  μ = 0.22 was assumed, which allowed to reproduce the experimental critical temperature for LaH 10 (p = 190 GPa).

Scientific RepoRtS |(2020) 10:1592 | https://doi.org/10.1038/s41598-020-58065-9

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This paper presents the design of an axial-flux permanent-magnet (AFPM) generator used for hybrid electric propulsion drone applications. The design objectives of the AFPM generator are high power density, which is defined as output power per generator weight, and high efficiency. In order to satisfy the requirements for the target application and consider the practical problems in the manufacturing process, the structure of the AFPM generator comprising a double-rotor single-stator (DR-SS) was studied. In order to determine the rotor topology and stator winding specifications that had the greatest impact on performance in the DR-SS type design process, we selected three rotor models according to the arrangement of the magnetization direction and three stator models according to the coreless winding specifications. These models were first compared and analyzed. Then, a 3-D finite element method was performed to calculate the magnetic, mechanical, and thermal characteristics of the designed models. By consideration of the output power, efficiency, temperature, and mechanical stability, etc., a topology suitable for the design of generators for UAV systems was determined and manufactured. The reliability of the design result was confirmed through the test.

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Since axial-flux permanent-magnet (AFPM) generators are known to have a high power density, which is defined as the ratio of output power to weight , the authors of this paper reviewed the development of an AFPM electric machine for 3 kW class drones. Additionally, among the possible multiple rotor and stator combinations, a combination consisting of NS-type double rotors and a yokeless single stator (DR-SS) was selected, as shown in Figure 1. "NS type" refers to north pole and south pole magnets facing each other at either side; thus, the flux can travel straight through this stator without any circumferential flow . This type of DR-SS is more commonly known as a yokeless and segmented armature (YASA) motor or generator and is often described as having a relatively high power density because it does not require a stator yoke. However, to be precise, a structure in the form of a 'stator yoke' is not required as a magnetic flux path, but is necessary to mechanically hold the teeth and coils of the stator. Thus, the design of stator mechanical fixation in an NS-type DR-SS topology with a stator magnetic core (or stator teeth) becomes a critical part of the entire motor design process. Mechanically robust of stator mechanical fixation in an NS-type DR-SS topology with a stator magnetic core (or stator teeth) becomes a critical part of the entire motor design process. Mechanically robust structures are required to overcome the pull forces at both rotors, increasing the volume and weight of the stator. Therefore, in this study, we selected and designed a DR-SS topology without a stator core. For the rotors, in order to increase the output power, the characteristics of the model according to the combination of permanent-magnet (PM) pole arrangement were compared and reviewed, focusing on the so-called Halbach array structure . For the stator, a coreless stator topology was used to reduce the weight of the stator itself and at the same time reduce the weight of the structure supporting it, by reducing the axial attraction force between the rotor and the stator.

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This paper focuses on the process of selecting the rotor-Halbach array topology and the coil specifications of the coreless stator, which have the most influence on the power density among the various design variables of the rotor and stator in the generator design process. In other words, in the rotor design part of this paper, three types of Halbach arrays are compared and analyzed according to the arrangement of the magnetization direction. Moreover, in the stator design part, the loss generated from the coil due to the coreless topology is analyzed in detail, and three cases of using a general conductor and a Litz wire conductor are compared and analyzed. After determining the topology of the rotor and stator, the mechanical stability against the electromagnetic force was investigated, and the temperature stability due to the electromagnetic heat source was also evaluated. The magnetic, mechanical, and thermal properties of all analysis processes for AFPM generator design are calculated using a three-dimensional (3-D) finite element method (FEM), and the final determined model is experimentally verified.

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This paper focuses on the process of selecting the rotor-Halbach array topology and the coil specifications of the coreless stator, which have the most influence on the power density among the various design variables of the rotor and stator in the generator design process. In other words, in the rotor design part of this paper, three types of Halbach arrays are compared and analyzed according to the arrangement of the magnetization direction. Moreover, in the stator design part, the loss generated from the coil due to the coreless topology is analyzed in detail, and three cases of using a general conductor and a Litz wire conductor are compared and analyzed. After determining the topology of the rotor and stator, the mechanical stability against the electromagnetic force was investigated, and the temperature stability due to the electromagnetic heat source was also evaluated. The magnetic, mechanical, and thermal properties of all analysis processes for AFPM generator design are calculated using a three-dimensional (3-D) finite element method (FEM), and the final determined model is experimentally verified.

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AFPM generator design specifications are shown in Table 1. In consideration of the performance of the engine that is to be used with the generator, the speed was limited to a maximum of 7000 rpm. Additionally, the maximum line voltage constant at no-load was limited to 11 mV/rpm or less in consideration of the AC/DC converter performance to be used for 48 V DC battery charging. The voltage and current values in this paper all represent RMS (root mean square) and not peak value. For the efficient operation of the maximum payload 3 kg UAV system, the efficiency and power density requirements of the generator are required as shown in Table 1, and the generator is operated without a separate cooling device.

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The initial design of the generator used a quasi-three dimensional analysis model, which is a model from 3D geometry to a corresponding two dimensional model . Table 2 shows the design results of the initial design model that satisfy the given constraints, and the 3D analysis model for a detailed design review of the rotor and stator is shown in Figure 2. Each of the six phases is indicated by the capital letters A to F, where LP is the phase inductance, RP is the phase resistance, and RL is the load resistance. In consideration of the performance of the engine that is to be used with the generator, the speed was limited to a maximum of 7000 rpm. Additionally, the maximum line voltage constant at no-load was limited to 11 mV/rpm or less in consideration of the AC/DC converter performance to be used for 48 V DC battery charging. The voltage and current values in this paper all represent RMS (root mean square) and not peak value. For the efficient operation of the maximum payload 3 kg UAV system, the efficiency and power density requirements of the generator are required as shown in Table 1, and the generator is operated without a separate cooling device.

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The initial design of the generator used a quasi-three dimensional analysis model, which is a model from 3D geometry to a corresponding two dimensional model . Table 2 shows the design results of the initial design model that satisfy the given constraints, and the 3D analysis model for a detailed design review of the rotor and stator is shown in Figure 2. Each of the six phases is indicated by the capital letters A to F, where LP is the phase inductance, RP is the phase resistance, and RL is the load resistance.

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In the process of designing the rotor to increase the power density of the generator, three rotor topologies were compared, as shown in Figure 3. The volume and dimensions of the three rotors are all the same, and the thickness of the yoke used to increase the mechanical robustness of the rotor is also considered to have the same dimensions. The stator specifications, dimensions, and weight conditions are all the same. The only difference is the combination of the magnetization directions of the rotor's PM.

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In the process of designing the rotor to increase the power density of the generator, three rotor topologies were compared, as shown in Figure 3. The volume and dimensions of the three rotors are all the same, and the thickness of the yoke used to increase the mechanical robustness of the rotor is also considered to have the same dimensions. The stator specifications, dimensions, and weight conditions are all the same. The only difference is the combination of the magnetization directions of the rotor's PM. As shown in Figure 3a, the Halbach arrangement in which four different magnetization directions form one magnetic pole is defined as Type-I. As shown in Figure 3b, a Halbach array composed of three different magnetization directions that can be combined relatively easily is defined as Type-II. As shown in Figure 3c, a typical pole arrangement that is magnetized in only one direction to form one pole is defined as a normal arrangement (NA).

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The efficiency presented in Table 3 considers only copper loss at the stator coil and iron loss at the back yoke of the rotor PM. All models are designed with Litz wire so only DC copper loss is considered; eddy current loss is ignored. Even though all three models have similar efficiency values, when looking at the generated voltage, the voltages of Type-I and Type-II are 38.5% and 24.8% higher than the NA, respectively. Additionally, for the same current, the output power and output power density are evaluated to be 39.6% higher in Type-I and 25.6% higher in Type-II than the NA.

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Despite having the same back yoke and rotor volume for all three types, the rotor core losses in Type-I and Type-II are significantly lower than the NA, demonstrating the advantage of using the Halbach array.

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Since the output power of Type-I is excellent under the same conditions, the PM arrangement of the generator rotor was set as Type-I. Figure 4 shows the voltage and current waveforms in the stator coil that were generated when the Type-I model was analyzed. In the case of Type-II and the NA, the generated voltage values are different as shown in Table 3, but the waveforms are the same as shown in Figure 4. The phase difference of the waveforms in Figure 4 is due to the use of two pairs of balanced three-phase winding arrays electrically shifted by 30° to each other; this is shown in Figure 5. This winding arrangement is also referred to as a dual three-phase winding arrangement [10,11]. As shown in Figure 3a, the Halbach arrangement in which four different magnetization directions form one magnetic pole is defined as Type-I. As shown in Figure 3b, a Halbach array composed of three different magnetization directions that can be combined relatively easily is defined as Type-II. As shown in Figure 3c, a typical pole arrangement that is magnetized in only one direction to form one pole is defined as a normal arrangement (NA). The efficiency presented in Table 3 considers only copper loss at the stator coil and iron loss at the back yoke of the rotor PM. All models are designed with Litz wire so only DC copper loss is considered; eddy current loss is ignored. Even though all three models have similar efficiency values, when looking at the generated voltage, the voltages of Type-I and Type-II are 38.5% and 24.8% higher than the NA, respectively. Additionally, for the same current, the output power and output power density are evaluated to be 39.6% higher in Type-I and 25.6% higher in Type-II than the NA. Despite having the same back yoke and rotor volume for all three types, the rotor core losses in Type-I and Type-II are significantly lower than the NA, demonstrating the advantage of using the Halbach array.

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Since the output power of Type-I is excellent under the same conditions, the PM arrangement of the generator rotor was set as Type-I. Figure 4 shows the voltage and current waveforms in the stator coil that were generated when the Type-I model was analyzed. In the case of Type-II and the NA, the generated voltage values are different as shown in Table 3, but the waveforms are the same as shown in Figure 4. The phase difference of the waveforms in Figure 4 is due to the use of two pairs of balanced threephase winding arrays electrically shifted by 30 • to each other; this is shown in Figure 5. This winding arrangement is also referred to as a dual three-phase winding arrangement.

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In general, DC resistance loss is the main loss in the stator coil, and in the case of highspeed operation, AC resistance loss is also considered. However, in the case of a slotless or coreless stator that does not form teeth with a magnetic material (with or without a back yoke), the magnetic flux change occurs directly in the coil; thus, even at a low frequency of several hundred Hz, severe eddy current loss can happen in the coil depending on the diameter of the conductor. Although DC resistance and AC resistance losses occur only in the state of load operation with the current flowing, eddy current loss in the coil occurs not only during load operation but also during no-load operation.

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The best way to reduce the eddy current loss of a conductor is to use Litz wire that divides the conductor into multiple strands. However, when using Litz wires with each coated strand for winding, the number of turns that can be wound around the same coil cross-sectional area is reduced by half compared to the normal conductor. Therefore, when using Litz wire, an increase in the volume of the motor or generator is inevitable because the coil cross-sectional area must be at least doubled or the rotor PM size and the number of coil turns must be increased to achieve the same output power as a model using a normal conductor.

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In addition, the relative comparison with the coil model is important, so it was calculated only as the maximum average magnetic flux density in one straight conductor. The lower middle part of Table 4 shows the results comparing the eddy current loss power of the coil calculated by (1) and the measured loss power for each model during a no-load operation at a rotational speed of 5000 rpm. If the eddy current loss in the segmented permanent magnet is neglected, the measured value can only be evaluated by the mechanical and conductor eddy current losses. However, since the Coil-III model makes the stator coil with Litz wire so that the conductor eddy current loss is also negligible,

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In addition, the relative comparison with the coil model is important, so it was calculated only as the maximum average magnetic flux density in one straight conductor. The lower middle part of Table 4 shows the results comparing the eddy current loss power of the coil calculated by (1) and the measured loss power for each model during a no-load operation at a rotational speed of 5000 rpm. If the eddy current loss in the segmented permanent magnet is neglected, the measured value can only be evaluated by the mechanical and conductor eddy current losses. However, since the Coil-III model makes the stator coil with Litz wire so that the conductor eddy current loss is also negligible, In addition, the relative comparison with the coil model is important, so it was calculated only as the maximum average magnetic flux density in one straight conductor.

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The lower middle part of Table 4 shows the results comparing the eddy current loss power of the coil calculated by (1) and the measured loss power for each model during a no-load operation at a rotational speed of 5000 rpm. If the eddy current loss in the segmented permanent magnet is neglected, the measured value can only be evaluated by the mechanical and conductor eddy current losses. However, since the Coil-III model makes the stator coil with Litz wire so that the conductor eddy current loss is also negligible, most of the measured losses of the Coil-III model can be considered as mechanical losses. Since all were made under the same conditions except for the stator winding, the mechanical losses of the Coil-I and Coil-II models are evaluated similarly to those of Coil-III. After subtracting the mechanical loss of Coil-III from the measured losses of Coil-I and Coil-II, it can be seen that the eddy current loss values of Coil-I and Coil-II models are similar to the calculated values.

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At the bottom of Table 4, the temperatures in the coil measured during the no-load test of each model are compared. The maximum temperature measured at the coil using three thermocouples during the test held for 30 s at each speed point in increments of 500 rpm, from 500 rpm to 6000 rpm. The housing of the manufactured generator is as shown in Figure 1, and the temperature of Coil-I and Coil-II was severely increased while the room temperature was 25 degrees Celsius across the board. From the comparison of Coil-I and Coil-II, it can be seen that the effect of the parallel circuit with the possibility of a circulating current is not large; rather, the loss decreases as the conductor diameter decreases. This can confirm that the loss is significantly reduced in Coil-III, which has the smallest conductor diameter. Therefore, the stator was determined with the Coil-III model that could completely reduce the conductor eddy current loss as a heat source.

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First, centrifugal force causes the deviation of PMs arranged in the circumferential direction of the edges of the rotor yoke. The main cause is the occurrence of shear stress by centrifugal force on the plane where the rotor frame and PM are bonded. The upper part of Figure 8 shows the cross-section of the designed generator rotor, which has rim parts with a height that is 75% of PM thickness to prevent the deviations in the radial direction of the PMs caused by centrifugal force. Finally, the rotor dynamics were performed to confirm the dynamic stability of the rotor system. Figure 9 is the Campbell diagram showing the result of the analysis. The critical speed, which is when the natural vibration mode is the bending mode of the rotating shaft, was shown to be 18,302 rpm. This is illustrated in the mode shape shown in the lower right-hand corner of Figure 10. More than 20% of the separation margin was secured for the maximum operating speed of the generator at 7000 rpm, and no whirling vibration of the rotor system was expected to occur. Second, the axial attraction force due to the magnetism of the PMs attached to the two rotors causes a bending moment with the hub part assembled on the rotary axis as a support, resulting in deflection . The direction of deflection is the direction of reducing the air gap, which in turn reduces the performance and stability of the generator, and a robust design of the rotor frame is required. To increase the stiffness in the axial direction of the rotor frame, the stiffener was designed as shown in the upper part of Figure 8 and the thickness of the hub acting as the support was designed to be relatively thicker than the outer part.

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A stress analysis was performed to check the designed rotor frame's deflection and stress distribution by magnetic force, and the lower part of Figure 8 is the result of this stress analysis. The maximum deflection was shown at the edge of the rotor frame at 0.11 mm, which means there was a maximum reduction of 22% in the designed 0.5 mm air-gap length. The von Mises stress resulted in 196.44 Mpa in the same area where the maximum deflection occurred. The yield strength of S45C, the material of the rotor frame, is 490 Mpa, and the maximum stress that occurred was lower than this, meaning that it was mechanically stable.

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Energies 2021, 14, 8509 9 of 14 Finally, the rotor dynamics were performed to confirm the dynamic stability of the rotor system. Figure 9 is the Campbell diagram showing the result of the analysis. The critical speed, which is when the natural vibration mode is the bending mode of the rotating shaft, was shown to be 18,302 rpm. This is illustrated in the mode shape shown in the lower right-hand corner of Figure 10. More than 20% of the separation margin was secured for the maximum operating speed of the generator at 7000 rpm, and no whirling vibration of the rotor system was expected to occur. Finally, the rotor dynamics were performed to confirm the dynamic stability of the rotor system. Figure 9 is the Campbell diagram showing the result of the analysis. The critical speed, which is when the natural vibration mode is the bending mode of the rotating shaft, was shown to be 18,302 rpm. This is illustrated in the mode shape shown in the lower right-hand corner of Figure 10. More than 20% of the separation margin was secured for the maximum operating speed of the generator at 7000 rpm, and no whirling vibration of the rotor system was expected to occur. Finally, the rotor dynamics were performed to confirm the dynamic stability of the rotor system. Figure 9 is the Campbell diagram showing the result of the analysis. The critical speed, which is when the natural vibration mode is the bending mode of the rotating shaft, was shown to be 18,302 rpm. This is illustrated in the mode shape shown in the lower right-hand corner of Figure 10. More than 20% of the separation margin was secured for the maximum operating speed of the generator at 7000 rpm, and no whirling vibration of the rotor system was expected to occur.

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A thermal analysis was performed under rated conditions to ensure the normal and safe operation of the designed model. Since Litz wire and segmented PM were used, the eddy current loss in the coil and PM was negligible, and the main heat source was the DC copper loss. The other heat sources were core losses in the rotor yoke and mechanical losses in the bearings. Although copper loss and iron loss can be calculated through parameters obtained through electromagnetic field analyses and empirical formulas , respectively, mechanical loss varies depending on the parts and the manufacturing method of the manufactured model. Therefore, it was assumed that the mechanical loss was about 7% of the 3 kW rated output power with reference to the prototype reviewed, until the final model was decided. Moreover, it was assumed that the generator operated under natural cooling conditions at a room temperature of 28 • C. All input parameters for the analysis are shown in Table 5.

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The connection coefficient, defined in the boundaries of the model, used empirical values. In the case of the rotor yoke, the values of 100 and 200 W/m2K were applied to the inner and outer surfaces of the rotor, respectively, considering that rotation resulted in a fan-like cooling effect. On the other hand, the jig was separated into a top plate and a bottom plate, and the jig top plate to which the generator was attached had only a slight flow of air, with a value of 10 W/m2K applied. The lower plate of the jig was defined as Energies 2021, 14, 8509 10 of 14 infinite, assuming a situation in which heat could escape infinitely due to its connection to the dynamo steel base. The final designed model including the test jig was modeled in 3D as shown in Figure 10a, and the thermal analysis was performed using FEM. When the temperature was saturated, the highest temperature was the stator coil with the largest loss, as shown in Figure 10b. Table 6 shows the range of temperature distribution by dividing the generator into coils, rotor yokes, PMs, and bearings. Representatively, when looking at the material used for coils and PMs that are most vulnerable to temperature, Litz wire has a class F thermal index with a maximum operating point of 155 • C, and PM with SH grade has a maximum operating point of 150 • C. It can be seen that the heat generated by the generator during the rated operation is in the stable range.

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The prototype of the model was finally decided based on the electromagnetic field design and mechanical thermal analysis that were produced as shown in Figure 11. In order to check whether the PM arrangement of the rotor composed of the Halbach array was properly manufactured, the magnetic flux density of the PM surface was measured, as shown in Figure 11a. As compared in Figure 12, it can be confirmed that the trends of the predicted values and the measured values match well through the electromagnetic field analysis. Higher harmonics appearing in the analysis compared to the measured values can be regarded as calculation errors according to the element mesh state. As shown in Figure 13, a dynamo set was constructed to test the generator. By connecting a 2 ohm resistive load per phase to the generator, a power generation output of 3.1 kW could be obtained at 6500 rpm. A higher output power could be achieved by connecting a resistor of 1 ohm per phase to the generator. Figure 14a shows the no-load test results according to speed. Moreover, Figure 14b,c shows the load test results according to speed for a resistive load of 2 and 1 ohm, respectively. In the no-load operation, it can be seen that the back EMF is linear with speed, whereas the power loss is non-linear. When the resistive load is 2 ohm, the rated power of 3 kW output occurs at around 7000 rpm, and the mechanical loss at this time is about 200 W. On the other hand, when the resistive load is 1 ohm, the rated output power occurs at around 5000 rpm, and it can be seen that the mechanical loss at this time is about 100 W. It was confirmed through the test that the maximum efficiency was 93.2% at 3000 rpm when the resistive load was 2 ohm, and the As shown in Figure 13, a dynamo set was constructed to test the generator. By connecting a 2 ohm resistive load per phase to the generator, a power generation output of 3.1 kW could be obtained at 6500 rpm. A higher output power could be achieved by connecting a resistor of 1 ohm per phase to the generator. Figure 14a shows the no-load test results according to speed. Moreover, Figure 14b,c shows the load test results according to speed for a resistive load of 2 and 1 ohm, respectively. In the no-load operation, it can be seen that the back EMF is linear with speed, whereas the power loss is non-linear. When the resistive load is 2 ohm, the rated power of 3 kW output occurs at around 7000 rpm, and the mechanical loss at this time is about 200 W. On the other hand, when the resistive load is 1 ohm, the rated output power occurs at around 5000 rpm, and it can be seen that the mechanical loss at this time is about 100 W. It was confirmed through the test that the maximum efficiency was 93.2% at 3000 rpm when the resistive load was 2 ohm, and the maximum output power was 5 kW at 6500 rpm when the resistive load was 1 ohm. Accordingly, the ratio of the maximum output power to the generator weight is 2.5 kW/kg, which satisfies all the design conditions required in Table 1.

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Energies 2021, 14, x FOR PEER REVIEW 12 of 15 maximum output power was 5 kW at 6500 rpm when the resistive load was 1 ohm. Accordingly, the ratio of the maximum output power to the generator weight is 2.5 kW/kg, which satisfies all the design conditions required in Table 1. Figure 15 shows the test results confirming that it can be operated for more than 30 min while maintaining a constant output power of over 3 kW. It can be seen that the maximum temperature of the measured coil is about 40 °C, which is lower than the predicted temperature in the analysis. Errors may have accumulated in various assumptions during the calculation process, but one main cause is considered to be the value of the convection coefficient. If this is compensated by reflecting the test error, it is expected that more accurate results can be predicted in a similar system. As a temperature lower than the predicted temperature is measured, it can be seen that the designed generator can be operated stably with a greater margin for the temperature. Figure 15 shows the test results confirming that it can be operated for more than 30 min while maintaining a constant output power of over 3 kW. It can be seen that the maximum temperature of the measured coil is about 40 • C, which is lower than the predicted temperature in the analysis. Errors may have accumulated in various assumptions during the calculation process, but one main cause is considered to be the value of the convection coefficient. If this is compensated by reflecting the test error, it is expected that more accurate results can be predicted in a similar system. As a temperature lower than the predicted temperature is measured, it can be seen that the designed generator can be operated stably with a greater margin for the temperature.

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Figure 15 shows the test results confirming that it can be operated for more than 30 min while maintaining a constant output power of over 3 kW. It can be seen that the maximum temperature of the measured coil is about 40 °C, which is lower than the predicted temperature in the analysis. Errors may have accumulated in various assumptions during the calculation process, but one main cause is considered to be the value of the convection coefficient. If this is compensated by reflecting the test error, it is expected that more accurate results can be predicted in a similar system. As a temperature lower than the predicted temperature is measured, it can be seen that the designed generator can be operated stably with a greater margin for the temperature. It is judged that the above design process and review results can be used as reference materials for other studies of the design of an unmanned aerial vehicle generator using AFPM. It is judged that the above design process and review results can be used as reference materials for other studies of the design of an unmanned aerial vehicle generator using AFPM.

+ + \ No newline at end of file diff --git a/resources/dataset/quantities/annotations/staging/materials-14-02583.quantity.tei.xml b/resources/dataset/quantities/annotations/staging/materials-14-02583.quantity.tei.xml new file mode 100644 index 00000000..b249b8c5 --- /dev/null +++ b/resources/dataset/quantities/annotations/staging/materials-14-02583.quantity.tei.xml @@ -0,0 +1,30 @@ + + + + + + A machine learning software for extracting information from scholarly documents + + + + + +

The grain boundary diffusion process (GBDP) has become an important technique in improving the coercivity and thermal stability of Dy-free sintered Nd-Fe-B magnets. The influence of Dy 70 Al 10 Ga 20 and (Pr 75 Dy 25 ) 70 Al 10 Ga 20 alloys by the GBDP on sintered Nd-Fe-B magnets are investigated in this paper. After diffusing Dy 70 Al 10 Ga 20 and (Pr 75 Dy 25 ) 70 Al 10 Ga 20 alloys, the coercivity (H cj ) of the magnets increased from 13.58 kOe to 20.10 kOe and 18.11 kOe, respectively. Meanwhile, the remanence of the magnets decreased slightly. The thermal stability of the diffused magnets was improved by the GBDP. The microstructure shows continuous Rare-earth-rich (RE-rich) grain boundary phases and (Dy, Pr/Nd) 2 Fe 14 B core-shell structures which contribute to improving the coercivity. Moreover, the Dy concentration on the surface of the (Pr 75 Dy 25 ) 70 Al 10 Ga 20 diffused magnets decreased with the Pr substitution for the Dy element. The openness of the recoil loops for the (Pr 75 Dy 25 ) 70 Al 10 Ga 20 diffused magnets is smaller than that of the original magnets and Dy 70 Al 10 Ga 20 diffused magnets. The results show that the (Pr 75 Dy 25 ) 70 Al 10 Ga 20 alloys can effectively optimize the microstructure and improve the magnetic properties and thermal stability of the sintered Nd-Fe-B magnets.

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Sintered Nd-Fe-B magnets possessing excellent high intrinsic coercivity and energy products are widely used in wind power, hybrid vehicles, maglev trains, and household appliances, etc. . In this application, higher magnetism is required. Since the invention of Nd-Fe-B magnets in 1983, the remanence (J r ) and the maximum energy product (BH) max of the Nd-Fe-B magnets reached the theoretical values, while the H cj is only 30% of the theoretical value . However, the higher H cj is urgently proposed in the face of increasingly harsh working environments, especially in high-temperature and high-humidity climates. There are basically two ways to develop high coercivity. One is to improve the inherent temperature dependence of H cj , and the other is to develop higher coercivity at room temperature to resist thermal demagnetization of the magnets when exposed to high temperature. Heavy rare earth elements Dy/Tb can be substituted for Pr/Nd to increase the magneto-crystalline anisotropy field (H A ), causing a substantial enhancement of H cj by a single alloying method. However, due to the antiferromagnetic coupling between Dy and Fe, it is unfavorable to the saturation magnetization . In order not to sacrifice the saturation magnetization, the GBDP (grain boundary diffusion process) technique was proposed by Park et al.. Heavy rare earth elements can be selectively diffused into the magnet interior along the grain boundary (GB), forming a hard core-shell structure surrounding the main grains. Later, researchers successively used heavy rare earth metals/compounds/alloys containing Dy or Tb, such as Dy, Dy 2 O 3 , DyF 3 , DyH 2 , and Dy-Cu or Pr-Dy-Cu acting as diffusion sources to improve the H cj .

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In addition, the non-rare-earth elements Al/Ga/Cu can also increase the H cj of the sintered Nd-Fe-B magnets and reduce the irreversible loss of magnetic flux. These elements mainly enrich in the RE-rich (Rare-earth rich) liquid phase to improve the wettability and increase the coercivity of the magnets . Therefore, we select the ternary alloy Pr 70 Al 10 Ga 20 and Dy 70 Al 10 Ga 20 and quaternary alloy (Pr 75 Dy 25 ) 70 Al 10 Ga 20 as the diffusion sources in this work. The (Pr 75 Dy 25 ) 70 Al 10 Ga 20 alloys inculcate the best properties with a large substitution of Pr for Dy after the GBDP, as shown in Supplementary Material. The magnetic properties and thermal stability of the diffused magnets are analyzed. The relationship between microstructure and recoil loops and diffusion mechanism of the magnets are also discussed.

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The commercial sintered Nd-Fe-B magnet of N52 was selected and wire-cut into small magnets with a size of ϕ10 × 10 × 5 mm 3 , and the chemical composition was (Pr, Nd) 30 Co 1.0 Cu 0.15 Zr 0.12 Ga 0.3 B 0.94 Fe bal. (wt.%). The ingots of Pr 70 Al 10 Ga 20 , Dy 70 Al 10 Ga 20 , and (Pr 75 Dy 25 ) 70 Al 10 Ga 20 (wt.%) were prepared by arc melting under a high-purity argon atmosphere. Then, these ingots were melt-spun into ribbons with 10 mm in width and 0.17 mm in thickness at a speed of 8 m/s. The magnets were polished with 400 mesh, 800 mesh, 1000 mesh, 1500 mesh, and 2000 mesh sandpaper and then ultrasonically washed in alcohol and dried. The ribbons were placed on the top and bottom of the magnet and put in a sintering furnace for diffusion heat treatment. The heat treatments were carried out at 850 • C for 6 h, and then annealed at 490 • C for 3 h in a vacuum (10 -4 Pa) tubular furnace. The magnetic properties at different temperatures were measured by a boron hydride tracer (NIM-500C, National Institute of Metrology, Beijing, China). The melting points of the alloys were measured by differential scanning calorimetry (DSC250, TA Instruments, USA). Additionally, the microstructure of the magnets was observed by a field emission scanning electron microscope (FESEM, MLA650F, FLIR Systems, Inc., Wilsonville, OR, USA). The irreversible magnetic flux loss at elevated temperatures was measured by pulling Helmholtz coils. The phase constitution of the magnets was determined by the X-ray diffraction with a Cu-K α radiation (XRD, D8 Advance, Bruker, Billerica, MA, USA). The elemental distribution of Nd-Fe-B magnets was explored by using an electron probe microanalyzer (EPMA, JXA-8530F, JEOL, Tokyo, Japan). The recoil loops of the magnets were measured by the Physical Property Measurement System (PPMS-DynaCOOL1-9, Quantum Design, San Diego, CA, USA) in fields up to 5 T at room temperature. lower melting points. Additionally, the lower melting point may reduce the activatio energy of the diffusion and improve diffusion efficiency. Moreover, compared with th ternary alloy Dy70Al10Ga20, the quaternary alloy (Pr75Dy25)70Al10Ga20 contains less heav rare earth elements; thus, it reduces the costs. Figure 2 shows demagnetization curves at the room temperature of the origina magnets and Pr70Al10Ga20, Dy70Al10Ga20, and (Pr75Dy25)70Al10Ga20 diffused magnets. It ca be clearly seen that the Hcj of the diffused magnets is improved after the GBDP, while th remanence is only slightly decreased. The coercivity increased from 13.58 kOe to 15.3 kOe, 20.10 kOe, and 18.11 kOe, respectively, after diffusing Pr70Al10Ga20, Dy70Al10Ga20, an (Pr75Dy25)70Al10Ga20 alloys. At the same time, the Jr reduced from 14.3 kG to 14.0 kG, 14. kG, and 14.1 kG, respectively. The increase in the Hcj is mainly because of the partia substitution of Pr and Dy for Nd to form the core-shell structure of (Dy, Pr/Nd)2Fe14B. Th antiferromagnetic coupling of Dy and Fe atoms reduces the Jr of Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 diffused magnets. In addition, the Pr content in the Pr70Al10Ga20 dif fused magnet is higher, and the nonmagnetic volume fraction increases after diffusion which leads to the decrease in the Jr. The increase in the volume fraction of th non-magnetic phases in the grain boundary is another reason for the decrease in the Jr. lower melting points. Additionally, the lower melting point may reduce the activation energy of the diffusion and improve diffusion efficiency. Moreover, compared with the ternary alloy Dy70Al10Ga20, the quaternary alloy (Pr75Dy25)70Al10Ga20 contains less heavy rare earth elements; thus, it reduces the costs. Figure 2 shows demagnetization curves at the room temperature of the original magnets and Pr70Al10Ga20, Dy70Al10Ga20, and (Pr75Dy25)70Al10Ga20 diffused magnets. It can be clearly seen that the Hcj of the diffused magnets is improved after the GBDP, while the remanence is only slightly decreased. The coercivity increased from 13.58 kOe to 15.34 kOe, 20.10 kOe, and 18.11 kOe, respectively, after diffusing Pr70Al10Ga20, Dy70Al10Ga20, and (Pr75Dy25)70Al10Ga20 alloys. At the same time, the Jr reduced from 14.3 kG to 14.0 kG, 14.0 kG, and 14.1 kG, respectively. The increase in the Hcj is mainly because of the partial substitution of Pr and Dy for Nd to form the core-shell structure of (Dy, Pr/Nd)2Fe14B. The antiferromagnetic coupling of Dy and Fe atoms reduces the Jr of Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 diffused magnets. In addition, the Pr content in the Pr70Al10Ga20 diffused magnet is higher, and the nonmagnetic volume fraction increases after diffusion, which leads to the decrease in the Jr. The increase in the volume fraction of the non-magnetic phases in the grain boundary is another reason for the decrease in the Jr. Additionally, the temperature coefficient of coercivity (β) of the magnets can be calculated according to the formula :

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where T 1 is the elevated temperature, and T 0 is the room temperature. The β increased from -0.5341 %/K of the original magnets to -0.4609 %/K . The structure loss occurs at a high temperature, which leads to demagnetization. The irreversible flux loss is not recoverable when back to room temperature. It is related to the irreversible change of the microstructure of the magnets. The GB microstructure of the diffused magnets was optimized after thermal diffusion treatment. The nucleation of the reverse magnetic domain of the magnets is suppressed, and it is difficult to trigger the magnetization reversal of the magnetic domain due to the hardening of the epitaxial layer of the matrix phase grain. This results in an improvement in temperature coefficients and irreversible magnetic flux losses of the diffused magnets. These results indicate that the thermal stability of the diffused magnets was improved after the GBDP. Figure 3a shows the coercivity curves of the original magnet and the Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 diffused magnets at the temperature range of 293 to 453 K. Additionally, the temperature coefficient of coercivity (β) of the magnets can be calculated according to the formula:

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where T1 is the elevated temperature, and T0 is the room temperature. The β increased from -0.5341 %/K of the original magnets to -0.4609 %/K and -0.4939 %/K, respectively, for the Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 diffused magnets. Figure 3b is the irreversible flux loss curve of the original magnet and the diffused Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 magnets at 293-453 K. The irreversible flux loss rates of the original magnet and the Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 alloy diffused magnets were 75.5%, 48.6%, and 48.7%, respectively. The irreversible flux loss of the magnets was reduced by about 27% after diffusion, which suggests that the diffused magnets have less magnetic irreversible flux losses. The magnetic flux and coercivity are very sensitive to temperature. The structure loss occurs at a high temperature, which leads to demagnetization.

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The irreversible flux loss is not recoverable when back to room temperature. It is related to the irreversible change of the microstructure of the magnets. The GB microstructure of the diffused magnets was optimized after thermal diffusion treatment. The nucleation of the reverse magnetic domain of the magnets is suppressed, and it is difficult to trigger the magnetization reversal of the magnetic domain due to the hardening of the epitaxial layer of the matrix phase grain. This results in an improvement in temperature coefficients and irreversible magnetic flux losses of the diffused magnets. These results indicate that the thermal stability of the diffused magnets was improved after the GBDP. Figure 4 shows the XRD of the original magnets and the Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 diffused magnets (vertical to the c-axis plane, with the observation surface near the surface). As can be seen from the diffraction peaks marked in Figure 4, most of the diffraction peaks are the main phases, and small parts are the RE-rich phase, and no new diffraction peaks appear in the diffused magnets. The characteristic diffraction peaks were located at 29.3, 44.6, 60.8, and 78.5 of 2θ, and Bragg diffraction peaks corresponding to (00l) are compared with JCPDS (Joint Committee on Powder Diffraction Standards) card no. 39-0473. This indicates that the magnets are dominated by 2:14:1 phases before and after the GBDP, and the content of other impurity phases is relatively small. The partially enlarged view of the diffraction peaks of the (006) crystal plane As can be seen from the diffraction peaks marked in Figure 4, most of the diffraction peaks are the main phases, and small parts are the RE-rich phase, and no new diffraction peaks appear in the diffused magnets. The characteristic diffraction peaks were located at 29.3, 44.6, 60.8, and 78.5 of 2θ, and Bragg diffraction peaks corresponding to (00l) are compared with JCPDS (Joint Committee on Powder Diffraction Standards) card no. 39-0473. This indicates that the magnets are dominated by 2:14:1 phases before and after the GBDP, and the content of other impurity phases is relatively small. The partially enlarged view of the diffraction peaks of the (006) crystal plane shows that the main phase peak of the magnet shifted to a large angle direction after diffusing Dy 70 Al 10 Ga 20 , while the main phase peak moved slightly to a small angle direction after diffusing (Pr 75 Dy 25 ) 70 Al 10 Ga 20 . This is because the atomic radius of Dy (0.1773 nm) is smaller than Nd (0.1821 nm). According to the Bragg equation, when the Dy atoms diffuse into the main phase to replace Nd to form the (Nd, Dy) 2 Fe 14 B shell layer, the lattice parameters decrease. For the (Pr 75 Dy 25 ) 70 Al 10 Ga 20 diffused magnet, the lattice parameters of the main phase increase, which is because the diffusion amount of Pr is greater than that of Dy. Based on the Lanthanide contraction effect, the atomic radius of the Dy element is smaller than that of Pr and Nd. Dy instead of Pr/Nd makes the diffraction peaks move to the large angle; in contrast, Pr and Nd move the peak to a small angle. Consequently, the combined effect is that the diffraction peak shifts to a small angle. The shift of the peak also means that Pr and Dy have entered into the main phase, forming a stronger H A of (Dy, Pr/Nd) 2 Fe 14 B shells, thus exhibiting the coercivity enhancement effect. shows that the main phase peak of the magnet shifted to a large angle direction after diffusing Dy70Al10Ga20, while the main phase peak moved slightly to a small angle direction after diffusing (Pr75Dy25)70Al10Ga20. This is because the atomic radius of Dy (0.1773 nm) is smaller than Nd (0.1821 nm). According to the Bragg equation, when the Dy atoms diffuse into the main phase to replace Nd to form the (Nd, Dy)2Fe14B shell layer, the lattice parameters decrease. For the (Pr75Dy25)70Al10Ga20 diffused magnet, the lattice parameters of the main phase increase, which is because the diffusion amount of Pr is greater than that of Dy. Based on the Lanthanide contraction effect, the atomic radius of the Dy element is smaller than that of Pr and Nd. Dy instead of Pr/Nd makes the diffraction peaks move to the large angle; in contrast, Pr and Nd move the peak to a small angle. Consequently, the combined effect is that the diffraction peak shifts to a small angle. The shift of the peak also means that Pr and Dy have entered into the main phase, forming a stronger HA of (Dy, Pr/Nd)2Fe14B shells, thus exhibiting the coercivity enhancement effect. In order to explore the reason for the Hcj enhancement, the microstructure of the magnets was observed after the GBDP. Figure 5a,b,c are BSE-SEM (backscattered electron) images of the original magnets, and the Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 alloy diffused magnets, respectively. The dark gray parts in Figure 5 correspond to the 2:14:1 matrix phase grains, and the bright white and gray white areas correspond to the RE-rich phases. The bright white and gray white in SEM are caused by the difference in composition of the RE-rich phases. Figure 5a shows that the triple junction RE-rich phases of the original magnets were distributed discretely in the magnet interior, and some adjacent matrix phase grains were in direct contact, which is unfavorable to the Hcj. Comparably, the smooth and continuous thin grain boundary RE-rich phases were formed in the Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 diffused magnets. If all grains are surrounded by thin grain boundary phases, then the grains are magnetically isolated from each other. If the grains are in direct contact with each other, there will be a localized exchange coupling effect, and, as a result, the grains are connected together to form a larger ferromagnetic domain grain group. A small grain inversion will drive demagnetization of adjacent grains in chains, because there is no thin layer RE-rich phase boundary, which will not hinder the displacement of the domain wall. Demagnetization of one grain will drive demagnetization of other grains, thus reducing coercivity; that is, the demagnetization resistance will be reduced. In order to explore the reason for the H cj enhancement, the microstructure of the magnets was observed after the GBDP. Figure 5a-c 5 correspond to the 2:14:1 matrix phase grains, and the bright white and gray white areas correspond to the RE-rich phases. The bright white and gray white in SEM are caused by the difference in composition of the RE-rich phases. Figure 5a shows that the triple junction RE-rich phases of the original magnets were distributed discretely in the magnet interior, and some adjacent matrix phase grains were in direct contact, which is unfavorable to the H cj . Comparably, the smooth and continuous thin grain boundary RE-rich phases were formed in the Dy 70 Al 10 Ga 20 and (Pr 75 Dy 25 ) 70 Al 10 Ga 20 diffused magnets. If all grains are surrounded by thin grain boundary phases, then the grains are magnetically isolated from each other. If the grains are in direct contact with each other, there will be a localized exchange coupling effect, and, as a result, the grains are connected together to form a larger ferromagnetic domain grain group. A small grain inversion will drive demagnetization of adjacent grains in chains, because there is no thin layer RE-rich phase boundary, which will not hinder the displacement of the domain wall. Demagnetization of one grain will drive demagnetization of other grains, thus reducing coercivity; that is, the demagnetization resistance will be reduced. Figure 6 shows the EPMA images on the surface (perpendicular to c-axis) of the Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 diffused magnets. The distribution of Dy, Nd, Pr, Al, and Ga elements in the Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 magnets are shown in Figure 6 after the GBDP, respectively. Dy elements are mainly distributed in the main phase grain epitaxial layer to form the (Dy, Pr/Nd)2Fe14B core-shell structure, which is beneficial to increase the coercivity. During the GBDP, Dy penetrates into the Nd-Fe-B sintered magnets through liquid grain boundaries. The Dy-rich shells are only selectively formed on the low-index lattice plane of the main phase grains. These planes, generated by the partial melting of the main phase grains, offer the low-energy configurations at the Nd2Fe14B/GB interfaces. During the subsequent cooling process, the Dy-rich liquid phases precipitate on the edge of the main phase grains and solidify to form (Nd, Dy)2Fe14B hard shells. As shown in Figure 6a, a large amount of Dy elements accumulated on the surface of the Dy70Al10Ga20 diffused magnets, while the enrichment on the (Pr75Dy25)70Al10Ga20 diffused magnets is mitigated. Although the Hcj of the (Pr75Dy25)70Al10Ga20 diffused magnet is 2 kOe lower than that of the Dy70Al10Ga20 diffused one, the heavy rare earth content of the quaternary alloy is much lower than the ternary alloy.

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The grain boundary channels, and intergranular regions of the sintered Nd-Fe-B magnets, are typically around 100-1000 nm in size, and the high temperature wettability causes enough capillary thrust for these elements to enter the intergranular channels during liquefaction, which in turn causes the uniform distribution of grain boundaries with the matrix grains. According to the distribution of Al and Ga in Figure 6b, most of them remain in the grain boundaries and play a role in wetting the grain boundaries. At the same time, a small amount of Al also exists in the matrix grains, which is possible when the surface of the Nd-Fe-B grains is partially decomposed, and Dy replaces Nd atoms. Meanwhile, Al penetrates into the selected grain facets from the grain boundaries with a high concentration at the grain edges. With a cooling effect coming in place, lighter Al atoms get transported inwards due to the low melting point while matrix restructuring happens, known as core-shell morphology. Although the core-shells are not obvious, a higher concentration of Pr at the grain boundaries takes precedence of surface diffusion by the substitution of Nd atoms, resulting in the intergranular region becoming richer with Nd and hard phase grains taking composition (Pr, Nd)2Fe14B. Therefore, under the combined effect of the above elements, the hard core-shell structure and optimized microstructure can explain the reason why the diffused magnets have an increased Hcj after GBDP.

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To investigate the diffusion depth of Dy in different diffused magnets, the EPMA was performed to determine the distribution of the Dy element along the diffusion direction. Figure 7(a1,a2,b1,b2) show the corresponding EPMA mappings at 0-400 μm of Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 diffused magnets. As can be seen from Figure 7(a2,b2), a high concentration of the Dy-rich area is formed on the surface of the magnet, and the Dy-rich area is indicated by the red ellipses in Figure 7(a2,b2). It can be seen from the red rectangular box that the concentration of the Dy element in the 6 after the GBDP, respectively. Dy elements are mainly distributed in the main phase grain epitaxial layer to form the (Dy, Pr/Nd) 2 Fe 14 B core-shell structure, which is beneficial to increase the coercivity. During the GBDP, Dy penetrates into the Nd-Fe-B sintered magnets through liquid grain boundaries. The Dy-rich shells are only selectively formed on the low-index lattice plane of the main phase grains. These planes, generated by the partial melting of the main phase grains, offer the low-energy configurations at the Nd 2 Fe 14 B/GB interfaces. During the subsequent cooling process, the Dy-rich liquid phases precipitate on the edge of the main phase grains and solidify to form (Nd, Dy) 2 Fe 14 B hard shells. As shown in Figure 6a The grain boundary channels, and intergranular regions of the sintered Nd-Fe-B magnets, are typically around 100-1000 nm in size, and the high temperature wettability causes enough capillary thrust for these elements to enter the intergranular channels during liquefaction, which in turn causes the uniform distribution of grain boundaries with the matrix grains. According to the distribution of Al and Ga in Figure 6b, most of them remain in the grain boundaries and play a role in wetting the grain boundaries. At the same time, a small amount of Al also exists in the matrix grains, which is possible when the surface of the Nd-Fe-B grains is partially decomposed, and Dy replaces Nd atoms. Meanwhile, Al penetrates into the selected grain facets from the grain boundaries with a high concentration at the grain edges. With a cooling effect coming in place, lighter Al atoms get transported inwards due to the low melting point while matrix restructuring happens, known as core-shell morphology. Although the core-shells are not obvious, a higher concentration of Pr at the grain boundaries takes precedence of surface diffusion by the substitution of Nd atoms, resulting in the intergranular region becoming richer with Nd and hard phase grains taking composition (Pr, Nd) 2 Fe 14 B. Therefore, under the combined effect of the above elements, the hard core-shell structure and optimized microstructure can explain the reason why the diffused magnets have an increased H cj after GBDP.

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To investigate the diffusion depth of Dy in different diffused magnets, the EPMA was performed to determine the distribution of the Dy element along the diffusion direction. (Pr75Dy25)70Al10Ga20 diffused magnets is higher than that of the Dy70Al10Ga20 diffused magnets. With the diffusion depth increasing, the Dy-rich area gradually decreases. At the depth of 400 μm, the Dy element still exists in the magnet interior. At the same time, it is observed that the concentration of Dy in the (Pr75Dy25)70Al10Ga20 diffused magnets is higher than that of the Dy70Al10Ga20 diffused magnets at the same depth as the dotted lines in Figure 7(a2,b2). Therefore, the quaternary alloy (Pr75Dy25)70Al10Ga20 can save the Dy elements and promote its diffusion depth. For sintered Nd-Fe-B, the GB provides a channel for the diffusion source. The melting point of the RE-rich grain boundary phase is about 655 °C, which is much lower than the melting point of the main phase of 1185 °C. The element diffusion follows the Fick's second law, which states that in the process of unsteady diffusion, we get

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where cx, c0, and cs are the volume concentrations of the diffusion material (kg/m 3 ) at the different depths; A is a fixed value (when the surface concentration and time are determined); and x is the distance (m). Figure 8 shows the fitting curve of the Dy element concentration in the range of different depths in the diffused magnets. Additionally, the diffusion coefficients of the Dy element are approximately 4.988 ± 0.673 × 10 -7 cm 2 /s and 3.139 ± 0.101 × 10 -7 cm 2 /s in the (Pr75Dy25)70Al10Ga20 and Dy70Al10Ga20 diffused magnets, respectively. This also shows that the diffusion efficiency of the Dy elements in the quaternary alloys (Pr75Dy25)70Al10Ga20 is improved under the cooperation of the Pr elements. The concentration of the Dy element can be measured by EPMA along the diffusion direction from the 0 μm to 450 μm in a continuous 100 × 100 μm 2 square indicated by the red boxes in Figure 7(a1,b1). As the diffusion depth increases, the concentration of Dy elements decreases, and the diffusion rate slows down. Figure 9 gives a schematic diagram of the change in the amount of diffusion distinguished from the depth of the diffused magnets. Figure 9a,b show the diffusion mechanism of ternary alloys Dy70Al10Ga20 and quaternary alloys (Pr75Dy25)70Al10Ga20, respectively. During the heat treatment, Dy atoms enter the magnet along the grain boundaries. By replacing Nd atoms with Dy atoms, a thin layer with higher Dy concentration is formed on the edge of the main phase grains, which is called the core-shell structure. The quaternary alloys (Pr75Dy25)70Al10Ga20 have the coordinated diffusion of the Pr element, so that the Dy element can penetrate deeper into the magnets and form a more core-shell structure. At the same time, the surface Dy concentration of the magnets can be regulated by diffusing (Pr75Dy25)70Al10Ga20 alloys. Due to the magnetic isolation effect of the grain boundaries and the high magnetocrystalline anisotropy field of the core-shell structure, the coercivities of the diffused magnets show improvement after the GBDP treatment. For sintered Nd-Fe-B, the GB provides a channel for the diffusion source. The melting point of the RE-rich grain boundary phase is about 655 • C, which is much lower than the melting point of the main phase of 1185 • C. The element diffusion follows the Fick's second law, which states that in the process of unsteady diffusion, we get

+

where c x , c 0 , and c s are the volume concentrations of the diffusion material (kg/m 3 ) at the different depths; A is a fixed value (when the surface concentration and time are determined); and x is the distance (m). The recoil loops can verify the magnitude of the demagnetization capability and the uniformity of the microstructure. Figure 10 shows the recoil loops of the original magnets, and the Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 diffused magnets. It shows that the recoil loops' opening of the original magnet is larger, while that of the Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 diffused magnets are much smaller. This is because the distribution of the RE-rich phase for the original magnet is non-uniform and discontinuous, and the grain boundary of the Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 diffused magnets are optimized to be more uniform and continuous after the GBDP. However, a large amount of The recoil loops can verify the magnitude of the demagnetization capability and the uniformity of the microstructure. Figure 10 shows the recoil loops of the original magnets, and the Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 diffused magnets. It shows that the recoil loops' opening of the original magnet is larger, while that of the Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 diffused magnets are much smaller. This is because the distribution of the RE-rich phase for the original magnet is non-uniform and discontinuous, and the grain boundary of the Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 diffused magnets are optimized to be more uniform and continuous after the GBDP. However, a large amount of The recoil loops can verify the magnitude of the demagnetization capability and the uniformity of the microstructure. Figure 10 the Dy element enrichment on the surface of the Dy70Al10Ga20 diffused magnets leads to the larger opening of the recoil loops than that of the (Pr75Dy25)70Al10Ga20 diffused magnets. The reduced surface Dy enrichment improves the microstructure uniformity by diffusing the (Pr75Dy25)70Al10Ga20 alloy; thus, the recoil loops' opening of the (Pr75Dy25)70Al10Ga20 diffused magnets is smaller than that of the original and Dy70Al10Ga20 diffused magnets. This is also confirmed by the microstructure of the magnets mentioned in Figures 5 and6.

+

In this paper, the effects of diffusing Dy70Al10Ga20 ternary alloys and (Pr75Dy25)70Al10Ga20 quaternary alloys on the magnetic properties and microstructure of sintered Nd-Fe-B magnets were investigated.

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(1) The coercivity of the Pr70Al10Ga20, Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 alloys diffused Nd-Fe-B magnets increased from 13.58 kOe to 15.34 kOe and 20.10 kOe and 18.11 kOe, respectively, while the remanence is only slightly decreased. (2) The thermal stability of the diffused magnets improves by diffusing Dy70Al10Ga20 and (Pr75Dy25)70Al10Ga20 alloys. The β increased from -0.5341 %/K for the original This indicates that the diffused magnet has a stronger capability for demagnetization.

+ + +

The following are available online at https://www.mdpi.com/article/10 .3390/ma14102583/s1, Figure S1: Demagnetization curve of the (Pr 100-x Dy x ) 70 Al 10 Ga 20 (x = 0, 25, 50, 75, 100) diffused magnets.

+ + \ No newline at end of file diff --git a/resources/dataset/units/corpus/energies-14-08509.unit.tei.xml b/resources/dataset/units/corpus/energies-14-08509.unit.tei.xml new file mode 100644 index 00000000..ec96492d --- /dev/null +++ b/resources/dataset/units/corpus/energies-14-08509.unit.tei.xml @@ -0,0 +1,95 @@ + + kW + rpm + mV/rpm + kg + rpm + mV/rpm + kg + % + % + % + % + ° + % + % + % + % + •C + Hz + rpm + rpm + rpm + s + rpm + rpm + rpm + degrees + % + rpm + % + rpm + mm + % + mm + Mpa + rpm + % + rpm + rpm + % + rpm + rpm + % + rpm + % + kW + •C + •C + •C + ohm + kW + rpm + ohm + ohm + ohm + kW + rpm + W + ohm + rpm + % + rpm + ohm + ohm + kW + rpm + ohm + ohm + ohm + kW + rpm + W + ohm + rpm + % + rpm + ohm + kW + rpm + ohm + kW/kg + kW + rpm + ohm + kW/kg + min + kW + °C + min + kW + •C + min + kW + °C + \ No newline at end of file diff --git a/resources/dataset/values/corpus/energies-14-08509.value.tei.xml b/resources/dataset/values/corpus/energies-14-08509.value.tei.xml new file mode 100644 index 00000000..33f31233 --- /dev/null +++ b/resources/dataset/values/corpus/energies-14-08509.value.tei.xml @@ -0,0 +1,139 @@ +three + three + 3 + three + three + three + three + three + three + 7000 + 11 + 3 + three + two + six + 7000 + 11 + 3 + three + two + six + three + three + three + three + four + three + one + three + 38.5 + 24.8 + 39.6 + 25.6 + three + two + three + 30 + three + four + three + one + three + 38.5 + 24.8 + 39.6 + 25.6 + three + two + 30 + three + hundred + half + one + 5000 + one + 5000 + one + 5000 + three + 30 + 500 + 500 + 6000 + 25 + 75 + 18,302 + 20 + 7000 + two + 0.11 + 22 + 0.5 + 196.44 + 490 + 14 + 18,302 + 20 + 7000 + 18,302 + 20 + 7000 + 18,302 + 20 + 7000 + 7 + 3 + 28 + 100 + 10 + 3 + 155 + 150 + 2 + 3.1 + 6500 + 1 + 1 + 2 + 3 + 7000 + 200 + 1 + 5000 + 93.2 + 3000 + 2 + 2 + 3.1 + 6500 + 1 + 1 + 2 + 3 + 7000 + 200 + 1 + 5000 + 93.2 + 3000 + 2 + 5 + 6500 + 1 + 2.5 + 15 + 5 + 6500 + 1 + 2.5 + 30 + 3 + 40 + 30 + 3 + 40 + 30 + 3 + 40 + \ No newline at end of file diff --git a/resources/dataset/values/corpus/materials-14-02583.unit.tei.xml b/resources/dataset/values/corpus/materials-14-02583.unit.tei.xml new file mode 100644 index 00000000..991d42f7 --- /dev/null +++ b/resources/dataset/values/corpus/materials-14-02583.unit.tei.xml @@ -0,0 +1,70 @@ + + kOe + kOe + kOe + % + mm 3 + mm + mm + m/s + • C + • C + Pa + Pa + kOe + kOe + kOe + kOe + kG + kG + . kG + kG + kOe + kOe + kOe + kOe + kG + kG + kG + kG + %/K + %/K + K + K + %/K + %/K + %/K + K + % + % + % + % + l + l + nm + nm + nm + nm + kOe + nm + nm + μm + nm + nm + μm + °C + °C + cm 2 /s + cm 2 /s + cm 2 /s + cm 2 /s + μm + μm + square + • C + kOe + kOe + kOe + kOe + %/K + \ No newline at end of file diff --git a/resources/dataset/values/corpus/materials-14-02583.value.tei.xml b/resources/dataset/values/corpus/materials-14-02583.value.tei.xml new file mode 100644 index 00000000..1d21387b --- /dev/null +++ b/resources/dataset/values/corpus/materials-14-02583.value.tei.xml @@ -0,0 +1,115 @@ + + 13.58 + 20.10 + 18.11 + 1983 + 30 + two + + 30 + 1.0 + 0.15 + 0.12 + 0.3 + 0.94 + 10 + 0.17 + 8 + 400 + 800 + 1000 + 1500 + 2000 + 850 + 490 + 10 + 4 + 13.58 + 15.3 + 20.10 + 18.11 + 14.3 + 14.0 + 14 + 14.1 + 13.58 + 15.34 + 20.10 + 18.11 + 14.3 + 14.0 + 14.0 + 14.1 + 0.5341 + 0.4609 + 293 + 453 + 0.5341 + 0.4609 + 0.4939 + 293 + 453 + 70 + 20 + 75.5 + 48.6 + 48.7 + 27 + 29.3 + 44.6 + 60.8 + 78.5 + 00 + 29.3 + 44.6 + 60.8 + 78.5 + 0.1773 + 0.1821 + 0.1773 + 0.1821 + 70 + one + one + 2 + 100 + 1000 + 0 + 400 + 6 + 100 + 1000 + 400 + 655 + 1185 + 4.988 + 0.673 + 10 + 7 + 3.139 + 0.101 + 10 + 7 + 0 + 450 + 2 + 655 + 1185 + 70 + 20 + 13.58 + 15.34 + 20.10 + 18.11 + 0.5341 + 2583 + 20192 + 20202 + 20202 + 2019 + 100 + 0 + 25 + 50 + 75 + \ No newline at end of file