Mg2+ and Cu2+ Charging Agents Improving Electrophoretic Deposition Efficiency and Coating Adhesion of Nano-TbF3 on Sintered Nd-Fe-B Magnets

In order to prepare nano-TbF3 coating with high quality on the surface of Nd-Fe-B magnets by electrophoretic deposition (EPD) more efficiently, Mg2+ and Cu2+ charging agents are introduced into the electrophoretic suspension and the influence on the electrophoretic deposition is systematically investigated. The results show that the addition of Mg2+ and Cu2+ charging agents can improve the electrophoretic deposition efficiency and coating adhesion of nano-TbF3 powders on sintered Nd-Fe-B magnets. The EPD efficiency increases by 116% with a relative content of Mg2+ as 3%, while it increases by 109% with a relative content of Cu2+ as 5%. Combining the Hamaker equation and diffusion electric double layer theory, the addition of Mg2+ and Cu2+ can change the zeta potential of charged particles, resulting in the improvement of EPD efficiency. The relative content of Mg2+ below 3% and Cu2+ below 5% can increase the thickness of the diffusion electric double layer, the excessive addition of a charging agent will compress the diffusion electric double layer, and thicker diffusion layer represents higher zeta potential. Furthermore, the addition of Mg2+ and Cu2+ charging agents greatly improves the coating adhesion, and the critical load for the cracking of the coating increases to 146.4 mN and 40.2 mN from 17.9 mN, respectively.


Introduction
With their excellent magnetic performance, Nd-Fe-B magnets have been widely used in consumer electronics, automobile and wind power generation, etc. [1,2]. However, the low Curie temperature of a sintered Nd-Fe-B magnet limits its application in the field of high temperature. To obtain high-coercive Nd-Fe-B magnets, the heavy rare earth element (HRE) of Tb or Dy is added into the magnets because the (Nd, HRE) 2 Fe 14 B phase has a higher anisotropy field H A than that of the Nd 2 Fe 14 B phase [3,4]. Grain boundary diffusion (GBD) is a commonly used technique to infiltrate heavy rare earth along the grain boundary from the surface into the interior, which only consumes a very small amount of HREs [5,6].
To prepare the diffusion source on the magnet surface, we can use different coating methods such as dipping [7], magnetron sputtering [8], Plasma Spraying [9], vapor deposition [10] and electrophoretic deposition (EPD) [11]. Charged particles of a suspension are deposited electrokinetically by an electric field placed between two oppositely charged electrodes; this process is called EPD. EPD has the advantage of having a lower cost than magnetron sputtering. Compared with coating and dipping, EPD offers many advantages, such as good shape freedom, uniform film, controllable thickness of film and relatively good adhesion [12]. In EPD, the suspension properties affect the EPD process and the quality of the final deposited coatings. The water-based suspensions cause problems in electrophoretic forming, such as gas generated by water electrolysis and joule heating of the suspension, which reduces the stability of the suspension [13]. Therefore, at present, HRE compounds diffusion sources such as TbF 3 , TbH 3 , DyF 3 and DyH 3 are mainly electrophoretically deposited in organic suspension [14][15][16][17]. Actually, organic liquids usually have a low dielectric constant, which limits the charges attached to the particles, and leads to the formation of electronically charged particle flocculation [13].
The dissociation or ionization of surface groups on particles and the adsorption of surfactants are the most important mechanisms to obtain stable nonaqueous EPD suspension and a good EPD process [18]. Charging agents including acids (H + ), bases (OH − ), adsorbed metal ions or adsorbed poly-electrolytes are used to obtain particle surfaces' electrosteric stabilization for an effective EPD process [19]. Das et al. [20] prepared the stable suspension of yttria stabilized zirconia (YSZ) nanoparticles by using phosphate ester (PE) as a charging agent and revealed that the most stable suspension of YSZ nano-powder can be obtained when the PE concentration is 0.01 g/100 mL, because of the high zeta potential. Zarbov et al. [21] added Polyethyleneimine (PEI) into the BaTiO 3 EPD suspension as a charging agent and found that PEI maintains its very strong cationic charge by protonation of the amine groups from the surrounding medium. Guan et al. [22] prepared Dy 2 O 3 film on the magnet surface by EPD and used polyethylene imine (PEI) to improve the coating adhesion and EPD efficiency in an isopropanol suspension. Wang et al. [23] added 5 wt.% MgCl 2 into TbF 3 EPD suspension to improve the EPD efficiency and the coating adhesion. Cu 2+ has also acted as a charging agent in the process of co-deposition to form copper-graphene composite films [24]. These studies focused on improving the EPD process or magnet property by using charging agents, but the effect of different relative content of charging agents on deposition has not been studied. Moreover, it is also important to explain the effect of metal ions on EPD efficiency from the perspective of deposition kinetics. In order to improve the efficiency of EPD and the coating adhesion of nano-TbF3 powders so as to prepare for the grain boundary diffusion process of the sintered magnets, the effect of different relative contents of Mg 2+ and Cu 2+ charging agents on EPD efficiency and coating adhesion were systematically studied. In addition, the mechanism of action of Mg 2+ and Cu 2+ charging agents was analyzed with the theory of EPD and diffusion double layer from the perspective of deposition kinetics.

Experimental
A commercial sintered Nd-Fe-B magnet provided by GRIREM Co., Ltd. was selected as the initial magnet. The magnet was wire cut into cuboids with sizes of 8 × 8× 7 mm (c-axis). Then, the magnet was polished with 600 mesh, 1000 mesh and 2000 mesh sandpaper until the surface of the sample was flat and smooth. Subsequently, the surface of the polished magnet sample was cleaned with conduct alkali washing, acid washing and anhydrous ethanol ultrasonic cleaning and dried for later use. Nano TbF 3 (900 nm) powder provided by GRIREM Advanced Materials Co., Ltd. (Beijing, China), was used as the diffusion source. TbF 3 powder and anhydrous ethanol were mixed into 8 g/L suspension, MgCl 2 or CuCl 2 with a mass of 1-10% relative to TbF 3 was added and mechanical stirring was performed until MgCl 2 or CuCl 2 was completely dissolved; then, the ultrasonic was performed for 2 min until the suspension was uniform. Copper plate as anode and sample as cathode which were soaked in suspension, and TbF 3 coating was obtained by EPD at 60 V voltage for 1-5 min. The deposited samples were then diffused under vacuum at 900 • C for 7 h, followed by tempering at 500 • C for 2 h.
The magnetic properties of the samples were measured by a high temperature permanent magnet measuring instrument (NIM-500C, Beijing, China) and the microstructure of the coating was characterized by a scanning electron microscope (SEM, Tescan Vega II, Brno, Czech Republic). The coating elements were analyzed by ICP. The phases of the coating powders stripped from the surface of magnet were measured by XRD. The viscosity of the suspension was measured by a rotary rheometer (Anton paar MCR302, Graz, Austria). The ζ potential of the suspension was tested by a Zeta potential tester (Brookhaven 90plus, New York, NY, USA). The acidity and alkalinity of the suspension were detected by precision pH test paper. Coating adhesion was tested by a micro-nano mechanical testing system (STEP500-NHT3-MCT3, Anton paar, Graz, Austria). Figure 1 shows the EPD rate of nano-TbF 3 with different relative contents of Mg 2+ (a) and Cu 2+ (b). It was found that with the increase in the relative content of Mg 2+ , the EPD efficiency increased first and then decreased, reaching the highest value when the relative content of Mg 2+ was 3%, with the efficiency improving 116% from 3.1 mg/(cm 2 /min) to 6.7 mg/(cm 2 /min). The voltage was used for ion migration when adding too much Mg 2+ , which resulted in EPD basically unable to occur. For Cu 2+ , the EPD efficiency also first increased and then decreased with the increase in the relative content of Cu 2+ . Unlike Mg 2+ , the EPD efficiency reached the highest when the relative content of Cu 2+ was 5%, with the efficiency improving 109% from 3.1 mg/(cm 2 /min) to 6.47 mg/(cm 2 /min). EPD can continue to occur if Cu 2+ is continuously increased, but the efficiency of EPD will decline rapidly. The reasons will be added later.

EPD Efficiency
of the coating was characterized by a scanning electron microscope (SEM, Tescan Vega Brno, Czech Republic). The coating elements were analyzed by ICP. The phases of th coating powders stripped from the surface of magnet were measured by XRD. The visco ity of the suspension was measured by a rotary rheometer (Anton paar MCR302, Gra Austria). The ζ potential of the suspension was tested by a Zeta potential test (Brookhaven 90plus, New York, USA). The acidity and alkalinity of the suspension we detected by precision pH test paper. Coating adhesion was tested by a micro-nano m chanical testing system (STEP500-NHT3-MCT3, Anton paar, Graz, Austria). Figure 1 shows the EPD rate of nano-TbF3 with different relative contents of Mg 2+ ( and Cu 2+ (b). It was found that with the increase in the relative content of Mg 2+ , the EP efficiency increased first and then decreased, reaching the highest value when the relati content of Mg 2+ was 3%, with the efficiency improving 116% from 3.1 mg/(cm 2 /min) to 6 mg/(cm 2 /min). The voltage was used for ion migration when adding too much Mg which resulted in EPD basically unable to occur. For Cu 2+ , the EPD efficiency also fir increased and then decreased with the increase in the relative content of Cu 2+ . Unlike Mg the EPD efficiency reached the highest when the relative content of Cu 2+ was 5%, with th efficiency improving 109% from 3.1 mg/(cm 2 /min) to 6.47 mg/(cm 2 /min). EPD can continu to occur if Cu 2+ is continuously increased, but the efficiency of EPD will decline rapidl The reasons will be added later. The EPD behavior with different time was studied by adding the best relative conte of Mg 2+ and Cu 2+ . Figure 2 shows the EPD TbF3 amount (a) and EPD rate (b) of nano-Tb at different times. It can be seen in Figure 2a that the amounts of EPD all increased linear with time when EPD was measured from the beginning to three minutes, which is co sistent with the fact that the amount of EPD TbF3 amount is proportional to the time in th EPD theory. It is also found in Figure 2b that the EPD rate reduced when the EPD tim reached 4-5 min because the deposited EPD coating increases the resistance. Howeve the EPD rate with Cu 2+ reduced more than that of the others, which indicates that som changes occur to reduce the EPD efficiency when adding Cu 2+ to the EPD suspension. R latedly, adding Mg 2+ will not affect the EPD process. The EPD behavior with different time was studied by adding the best relative content of Mg 2+ and Cu 2+ . Figure 2 shows the EPD TbF 3 amount (a) and EPD rate (b) of nano-TbF 3 at different times. It can be seen in Figure 2a that the amounts of EPD all increased linearly with time when EPD was measured from the beginning to three minutes, which is consistent with the fact that the amount of EPD TbF 3 amount is proportional to the time in the EPD theory. It is also found in Figure 2b that the EPD rate reduced when the EPD time reached 4-5 min because the deposited EPD coating increases the resistance. However, the EPD rate with Cu 2+ reduced more than that of the others, which indicates that some changes occur to reduce the EPD efficiency when adding Cu 2+ to the EPD suspension. Relatedly, adding Mg 2+ will not affect the EPD process. Figure 3 shows the cross-sectional SEM morphologies of the EPD 90s coated magnet. It can be seen in Figure 3a that the thickness of the coating was about 40 µm. However, Figure 3b,c shows that the thickness increased to about 80 µm with 3% Mg 2+ added and increased to 60 µm with 5% Cu 2+ added. This also proves that the addition of Mg 2+ and Cu 2+ improves the EPD efficiency.  Figure 3 shows the cross-sectional SEM morphologies of the EPD 90s coated magn It can be seen in Figure 3a that the thickness of the coating was about 40 μm. Howev Figure 3b,c shows that the thickness increased to about 80 μm with 3% Mg 2+ added a increased to 60 μm with 5% Cu 2+ added. This also proves that the addition of Mg 2+ a Cu 2+ improves the EPD efficiency. In order to further study the effect of Mg 2+ and Cu 2+ on the EPD efficiency from t perspective of kinetics, we first introduce the EPD Hamaker equation [25]:

Cζ t
In the equation, m is the amount of EPD, ε0 is the dielectric constant of vacuum, ε the dielectric constant of solution, η is the viscosity of EPD suspension, C is the parti concentration in EPD suspension, ζ is the zeta potential of charged particles, E is the a plied electric field strength, L is the electrode spacing and t is the EPD time. In this pap both the applied electric field's strength and the distance between the electrodes were co stant. EPD efficiency was calculated by dividing the EPD quantity by the EPD time. The fore, the EPD efficiency at the same EPD time is inversely proportional to the η and Firstly, the effect of Mg 2+ and Cu 2+ on the viscosity of the EPD suspension was tested   Figure 3 shows the cross-sectional SEM morphologies of the EPD 90s coated magnet. It can be seen in Figure 3a that the thickness of the coating was about 40 μm. However, Figure 3b,c shows that the thickness increased to about 80 μm with 3% Mg 2+ added and increased to 60 μm with 5% Cu 2+ added. This also proves that the addition of Mg 2+ and Cu 2+ improves the EPD efficiency. In order to further study the effect of Mg 2+ and Cu 2+ on the EPD efficiency from the perspective of kinetics, we first introduce the EPD Hamaker equation [25]: In the equation, m is the amount of EPD, ε0 is the dielectric constant of vacuum, εr is the dielectric constant of solution, η is the viscosity of EPD suspension, C is the particle concentration in EPD suspension, ζ is the zeta potential of charged particles, E is the applied electric field strength, L is the electrode spacing and t is the EPD time. In this paper, both the applied electric field's strength and the distance between the electrodes were constant. EPD efficiency was calculated by dividing the EPD quantity by the EPD time. Therefore, the EPD efficiency at the same EPD time is inversely proportional to the η and ζ. Firstly, the effect of Mg 2+ and Cu 2+ on the viscosity of the EPD suspension was tested in order to study the kinetic reason of improving the EPD efficiency. The rotating rheometer tested the viscosity of suspension by shearing generated by a rotating motion, so we tested In order to further study the effect of Mg 2+ and Cu 2+ on the EPD efficiency from the perspective of kinetics, we first introduce the EPD Hamaker equation [25]: In the equation, m is the amount of EPD, ε 0 is the dielectric constant of vacuum, ε r is the dielectric constant of solution, η is the viscosity of EPD suspension, C is the particle concentration in EPD suspension, ζ is the zeta potential of charged particles, E is the applied electric field strength, L is the electrode spacing and t is the EPD time. In this paper, both the applied electric field's strength and the distance between the electrodes were constant. EPD efficiency was calculated by dividing the EPD quantity by the EPD time. Therefore, the EPD efficiency at the same EPD time is inversely proportional to the η and ζ. Firstly, the effect of Mg 2+ and Cu 2+ on the viscosity of the EPD suspension was tested in order to study the kinetic reason of improving the EPD efficiency. The rotating rheometer tested the viscosity of suspension by shearing generated by a rotating motion, so we tested the viscosity with a shear rate of 0-1000 to enhance the accuracy of the test. Figure 4 shows the viscosity of the EPD suspension with different Mg 2+ and Cu 2+ relative contents. It can be found that the viscosity of the EPD suspension increased with the increase in the shear rate (γ) because of the viscous resistance of the particles in the suspension, but the viscosity curves of different Mg 2+ and Cu 2+ relative contents were basically coincident. Since the average viscosity of the various concentrations was essentially consistent across the illustrations, it is clear that the addition of Mg 2+ and Cu 2+ had little impact on the EPD suspension's viscosity.
the viscosity with a shear rate of 0-1000 to enhance the accuracy of the test. Figure 4 show the viscosity of the EPD suspension with different Mg 2+ and Cu 2+ relative contents. It ca be found that the viscosity of the EPD suspension increased with the increase in the shea rate (γ) because of the viscous resistance of the particles in the suspension, but the visco ity curves of different Mg 2+ and Cu 2+ relative contents were basically coincident. Since th average viscosity of the various concentrations was essentially consistent across the illu trations, it is clear that the addition of Mg 2+ and Cu 2+ had little impact on the EPD suspen sion's viscosity. Subsequently, the effect of Mg 2+ and Cu 2+ addition on the zeta potential of EPD sus pension was investigated. Figure 5 shows the dependence of the zeta potential of EPD suspension on the relative contents of Mg 2+ (a) and Cu 2+ (b). It can be seen that the zet potential initially increased and then decreased with the change of Mg 2+ and Cu 2+ relativ content, which is consistent with the change trend of EPD efficiency in Figure 1. Similarly zeta potential also reached the peak value when adding about 3% Mg 2+ and 5% Cu 2+ com pared with Figure 1. According to the EPD Hamaker equation, the EPD efficiency is pro portional to the ζ potential. The effect of Mg 2+ and Cu 2+ on ζ potential was highly consisten with that on EPD efficiency. Therefore, we can confirm that the adding of Mg 2+ and Cu affected the efficiency of EPD by changing the zeta potential of the EPD suspension. In order to explain the lower rate of later EPD with the addition of Cu 2+ , or the highe zeta potential with a higher relative content of Cu 2+ (such as 10%) than without Cu 2+ bu with a lower EPD rate than without Cu 2+ , we analyzed the coating elements. Table 1 show Subsequently, the effect of Mg 2+ and Cu 2+ addition on the zeta potential of EPD suspension was investigated. Figure 5 shows the dependence of the zeta potential of EPD suspension on the relative contents of Mg 2+ (a) and Cu 2+ (b). It can be seen that the zeta potential initially increased and then decreased with the change of Mg 2+ and Cu 2+ relative content, which is consistent with the change trend of EPD efficiency in Figure 1. Similarly, zeta potential also reached the peak value when adding about 3% Mg 2+ and 5% Cu 2+ compared with Figure 1. According to the EPD Hamaker equation, the EPD efficiency is proportional to the ζ potential. The effect of Mg 2+ and Cu 2+ on ζ potential was highly consistent with that on EPD efficiency. Therefore, we can confirm that the adding of Mg 2+ and Cu 2+ affected the efficiency of EPD by changing the zeta potential of the EPD suspension.
the viscosity with a shear rate of 0-1000 to enhance the accuracy of the test. Figure 4 show the viscosity of the EPD suspension with different Mg 2+ and Cu 2+ relative contents. It ca be found that the viscosity of the EPD suspension increased with the increase in the she rate (γ) because of the viscous resistance of the particles in the suspension, but the visco ity curves of different Mg 2+ and Cu 2+ relative contents were basically coincident. Since th average viscosity of the various concentrations was essentially consistent across the illu trations, it is clear that the addition of Mg 2+ and Cu 2+ had little impact on the EPD suspe sion's viscosity. Subsequently, the effect of Mg 2+ and Cu 2+ addition on the zeta potential of EPD su pension was investigated. Figure 5 shows the dependence of the zeta potential of EP suspension on the relative contents of Mg 2+ (a) and Cu 2+ (b). It can be seen that the ze potential initially increased and then decreased with the change of Mg 2+ and Cu 2+ relati content, which is consistent with the change trend of EPD efficiency in Figure 1. Similarl zeta potential also reached the peak value when adding about 3% Mg 2+ and 5% Cu 2+ com pared with Figure 1. According to the EPD Hamaker equation, the EPD efficiency is pr portional to the ζ potential. The effect of Mg 2+ and Cu 2+ on ζ potential was highly consiste with that on EPD efficiency. Therefore, we can confirm that the adding of Mg 2+ and Cu affected the efficiency of EPD by changing the zeta potential of the EPD suspension. In order to explain the lower rate of later EPD with the addition of Cu 2+ , or the high zeta potential with a higher relative content of Cu 2+ (such as 10%) than without Cu 2+ b with a lower EPD rate than without Cu 2+ , we analyzed the coating elements. Table 1 show In order to explain the lower rate of later EPD with the addition of Cu 2+ , or the higher zeta potential with a higher relative content of Cu 2+ (such as 10%) than without Cu 2+ but with a lower EPD rate than without Cu 2+ , we analyzed the coating elements. Table 1 shows the ICP element analysis results of coating; it was found that the coating deposited by adding Cu 2+ contained 0.71 wt.% Cu, while adding Mg 2+ contained none. Figure 6 shows the XRD results of EPD coating with Cu 2+ charging agents; it can be seen that the coating had a peak of copper and no peak of CuCl 2 , which indicates that Cu 2+ in EPD suspension will be reduced to Cu under the electric field. In addition, Mg 2+ can hardly be reduced to elemental because the discharge order is after H + , while Cu 2+ is in front of H + .
Anode: Cu − 2e − = Cu 2+ Cathode: Cu 2+ + 2e × = Cu the ICP element analysis results of coating; it was found that the coating deposited by adding Cu 2+ contained 0.71 wt.% Cu, while adding Mg 2+ contained none. Figure 6 shows the XRD results of EPD coating with Cu 2+ charging agents; it can be seen that the coating had a peak of copper and no peak of CuCl2, which indicates that Cu 2+ in EPD suspension will be reduced to Cu under the electric field. In addition, Mg 2+ can hardly be reduced to elemental because the discharge order is after H + , while Cu 2+ is in front of H + . This process reduces the EPD rate because of consuming Cu 2+ and reducing the content of positive charge in the EPD suspension. Additionally, the process of generating Cu is not conducive to the deposition of TbF3 on the surface of the magnet. This is also the reason for the uneven coating surface in Figure 3c.
According to the diffusion double layer theory [26], Mg 2+ and Cu 2+ affect the zeta potential of the EPD suspension by adsorption. Figure 7 shows a schematic of the diffusion electric double layer region of a TbF3 particle. It can be seen in Figure 7a that when no charging agents are added, the particle surface mainly absorbs the positive and negative ions produced by dissociation in suspension. It can be seen in Figure 7b that when the relative content of Mg 2+ and Cu 2+ was low, the surface charge of the ion was gradually saturated. The diffusion double layer gradually became thicker with the increase in This process reduces the EPD rate because of consuming Cu 2+ and reducing the content of positive charge in the EPD suspension. Additionally, the process of generating Cu is not conducive to the deposition of TbF 3 on the surface of the magnet. This is also the reason for the uneven coating surface in Figure 3c.
According to the diffusion double layer theory [26], Mg 2+ and Cu 2+ affect the zeta potential of the EPD suspension by adsorption. Figure 7 shows a schematic of the diffusion electric double layer region of a TbF 3 particle. It can be seen in Figure 7a that when no charging agents are added, the particle surface mainly absorbs the positive and negative ions produced by dissociation in suspension. It can be seen in Figure 7b that when the relative content of Mg 2+ and Cu 2+ was low, the surface charge of the ion was gradually saturated. The diffusion double layer gradually became thicker with the increase in Mg 2+ and Cu 2+ on the surface, and the zeta potential was also higher, so the EPD efficiency gradually increased. When EPD efficiency reached the highest value, the surface charge of the particles was saturated; as Figure 7c shows, the diffusion electric double layer was compressed by adding charging agents, so the ζ potential decreased with the increase in Cl − in the suspension.
Mg 2+ and Cu 2+ on the surface, and the zeta potential was also higher, so the EPD efficiency gradually increased. When EPD efficiency reached the highest value, the surface charge of the particles was saturated; as Figure 7c shows, the diffusion electric double layer was compressed by adding charging agents, so the ζ potential decreased with the increase in Cl − in the suspension.

Coating Adhesion
Good coating adhesion can ensure the GBD result after EPD. To test it, we applied a linear normal load of transverse movement to the coating, and determined the coating adhesion according to the load when the coating cracked. Figure 8 shows the scratch test results of EPD coating. It was found that the critical load for cracking of the coating without a charging agent was 17.9 mN, but it increased to 146.4 mN and 40.2 mN when Mg 2 and Cu 2+ were added, respectively, which indicates that the addition of Mg 2+ and Cu 2+ charging agents greatly improved the coating adhesion. Figure 9 shows the surface SEM morphologies of the EPD 90 s coated magnet. In Figure 9 (a1,a2,b1,b2), the coating surface with Mg 2+ added showed regular gully morphology with distributed micro-cracks compared with the coating without a charging agent, which is profit for the release of stress [24]. As is seen in Figure 9 (c1,c2), the coating surface with Cu 2+ added exists aggregates on the surface, and shows finer gully morphology, which may be the reason that the coating adhesion was between without charging agents and with Mg 2+ charging agents.

Coating Adhesion
Good coating adhesion can ensure the GBD result after EPD. To test it, we applied a linear normal load of transverse movement to the coating, and determined the coating adhesion according to the load when the coating cracked. Figure 8 shows the scratch test results of EPD coating. It was found that the critical load for cracking of the coating without a charging agent was 17.9 mN, but it increased to 146.4 mN and 40.2 mN when Mg 2+ and Cu 2+ were added, respectively, which indicates that the addition of Mg 2+ and Cu 2+ charging agents greatly improved the coating adhesion. Figure 9 shows the surface SEM morphologies of the EPD 90 s coated magnet. In Figure 9 (a1,a2,b1,b2), the coating surface with Mg 2+ added showed regular gully morphology with distributed micro-cracks compared with the coating without a charging agent, which is profit for the release of stress [24]. As is seen in Figure 9 (c1,c2), the coating surface with Cu 2+ added exists aggregates on the surface, and shows finer gully morphology, which may be the reason that the coating adhesion was between without charging agents and with Mg 2+ charging agents.

Magnetic Performance
The addition of Mg 2+ and Cu 2+ can improve the EPD efficiency and the adhesion of the coating, but it cannot be at the expense of deteriorating the magnetic properties after heat treatment. A high-temperature permanent magnet measuring instrument (NIM-500C) was used to measure the magnetic properties of the permanent magnetic materials at room temperature and high temperatures, respectively. An external field of~3 T was initially applied to make the samples magnetized at full saturation. The remanence (B r ), coercivity (H cj ) and maximum magnetic energy product (BH) max of the magnet were obtained by testing the demagnetization curve of the material. Figure 10 shows the demagnetization curves of the magnet, where it can be seen that the coercivity (H cj ) of the original magnet was 19.3 kOe. With the first heat treatment process of 900 • C for 7 h, and the second heat treatment process of 500 • C for 2 h, the coercivity of the undeposited reference sample decreased to 18.1 kOe, while the coercivity of the EPD sample and EPD sample with Mg 2+ and Cu 2+ increased to 22.3 kOe, 22.2 kOe and 22.6 kOe, respectively. The remanence of all samples did not decrease. It indicates that the addition of Mg 2+ and Cu 2+ had no effect on the TbF 3 coating GBD process. As an aside, the preparation of TbF 3 coating containing copper has some development prospects, because Cu can promote GBD by widening the grain boundary [27].

Magnetic Performance
The addition of Mg 2+ and Cu 2+ can improve the EPD efficiency and the adhesion of the coating, but it cannot be at the expense of deteriorating the magnetic properties after heat treatment. A high-temperature permanent magnet measuring instrument (NIM-500C) was used to measure the magnetic properties of the permanent magnetic materials at room temperature and high temperatures, respectively. An external field of ~3 T was initially applied to make the samples magnetized at full saturation. The remanence (Br), coercivity (Hcj) and maximum magnetic energy product (BH)max of the magnet were obtained by testing the demagnetization curve of the material. Figure 10 shows the demagnetization curves of the magnet, where it can be seen that the coercivity (Hcj) of the original magnet was 19.3 kOe. With the first heat treatment process of 900 °C for 7 h, and the second heat treatment process of 500 °C for 2 h, the coercivity of the undeposited reference sample decreased to 18.1 kOe, while the coercivity of the EPD sample and EPD sample with Mg 2+ and Cu 2+ increased to 22.3 kOe, 22.2 kOe and 22.6 kOe, respectively. The remanence of all samples did not decrease. It indicates that the addition of Mg 2+ and Cu 2+ had no effect on the TbF3 coating GBD process. As an aside, the preparation of TbF3 coating containing copper has some development prospects, because Cu can promote GBD by widening the grain boundary [27].

Conclusions
Nano-TbF3 coating on the surface of the magnet was prepared with the addition of Mg 2+ and Cu 2+ in the EPD suspension, and the effects of Mg 2+ and Cu 2+ on EPD efficiency and coating adhesion were studied. The conclusions were as follows: (1) The addition of Mg 2+ and Cu 2+ can improve the EPD efficiency. With 3% relative content of Mg 2+ added, the efficiency improved 116% from 3.1 mg/(cm 2 /min) to 6.7 mg/(cm 2 /min). With 5% relative content of Cu 2+ added, the efficiency improved 109% from 3.1 mg/(cm 2 /min) to 6.47 mg/(cm 2 /min). (2) The effect of Mg 2+ and Cu 2+ on the EPD efficiency from the perspective of kinetics was analyzed with the Hamaker equation and diffusion double layer theory; it was found that Mg 2+ and Cu 2+ influence the EPD efficiency by changing the zeta potential of

Conclusions
Nano-TbF 3 coating on the surface of the magnet was prepared with the addition of Mg 2+ and Cu 2+ in the EPD suspension, and the effects of Mg 2+ and Cu 2+ on EPD efficiency and coating adhesion were studied. The conclusions were as follows: (1) The addition of Mg 2+ and Cu 2+ can improve the EPD efficiency. With 3% relative content of Mg 2+ added, the efficiency improved 116% from 3.1 mg/(cm 2 /min) to 6.7 mg/(cm 2 /min). With 5% relative content of Cu 2+ added, the efficiency improved 109% from 3.1 mg/(cm 2 /min) to 6.47 mg/(cm 2 /min). (2) The effect of Mg 2+ and Cu 2+ on the EPD efficiency from the perspective of kinetics was analyzed with the Hamaker equation and diffusion double layer theory; it was found that Mg 2+ and Cu 2+ influence the EPD efficiency by changing the zeta potential of charged particles, but not the viscosity of suspension. In addition, the diffusion electric double layer absorbs Mg 2+ or Cu 2+ to increase its thickness, which indicates higher zeta potential of TbF 3 particles when the relative content of Mg 2+ and Cu 2+ is low. When the relative content reaches 3% and 5%, respectively, the diffusion electric double layer reaches saturation, and further addition of a charging agent will compress the diffusion electric double layer and reduce zeta potential. Furthermore, the reduction reaction of Cu 2+ is the reason of the lower rate of later EPD when Cu 2+ charging agents were added. (3) It was found that the addition of Mg 2+ and Cu 2+ charging agents greatly improve the coating adhesion; the critical load for the cracking of the coating increased to 146.4 mN and 40.2 mN from 17.9 mN, respectively. Furthermore, the addition of Mg 2+ and Cu 2+ has no bad effect on TbF 3 coating GBD of the magnet.