4.8 Nanocrystalline Microstructure and Coercivity Mechanism Model of NdFeB Alloys with Nb and Ga
Addition of Nb and Ga can increase the coercivity of NdFeB alloys. But the coercivity is far less than that of the theoretical value. So up to now, the research on the coercivity mechanism of NdFeB alloys is still the research focus. Previous investigations pointed out that there were mainly three coercivity mechanism of rare earth iron - based permanent magnets: (1) nucleation hardening model, (2) boundary local pinning model and (3) uniform pinning model (Hadjipanayis, et al, 1988; Kronmüller, Durst, Sagawa, 1988; Durst, Kronmüller, 1987; Pan, Pan, Ma, 1994).
Hadjipanayis, et al (Liu, Pan, Luo, et al, 2004) believed that the boundary local pinning model played the main role on the coercivity mechanism. However, Kronmüller, et al (Kronmüller, Durst, Hock, et al, 1988) thought the coercivity was mainly determined by nucleation hardening model. They both had some experiment proofs, but neither of them was flawless. Kronmüller supported the nucleation hardening model that based on the alloys could reach the saturation magnetization in a lower magnetization field. But these phenomena could also be explained by boundary local pinning model. Therefore, these models could not explain comprehensively the behavior of the domain wall in the boundary.
In this section, we will highlight the reason for the addition of Nb and Ga to improve the coercivity of NdFeB alloys. From the angle of nanocrystalline microstructure and magnetic properties, we study the coercivity mechanism of the alloys and put forward some new experiment proofs.
Experimental Procedure for Studying Nanocrystalline NdFeB Alloyse
The NdFeB alloys are prepared by vacuum melting and mold casting (protected by argon) using the high pure rare earth Nd and Dy (99.99%), high pure metal iron, cobalt and niobium (99.9%), ferroboron alloy with 18% (wt.) boron according to the alloy composition proportion. The alloys are cool down to room temperature. The alloy ingot is milled into powder with a particle diameter about 3 - 4μm under the protection of organic solution. The powder is molded in magnetic field (1.5T) under the press (2 t/cm²). The compacts are sintered at 1,090 - 1,100°C for 1.5 - 2 h, then cooled down to 900°C and solutionized for 1 h, aged at 600°C for 50 min and cooled to room temperature. Thus thermal - demagnetized samples are obtained.
In order to study on the effects of Nb and Ga addition amount on the magnetic properties, \(Nd_{13}Dy_{2}(Fe_{1 - x}Nb_{x})_{79}B_{6}\) was prepared with \(x = 0.01\), 0.02, 0.03, 0.04, 0.05, 0.08 and 0.16, respectively.
Samples were magnetized in the magnetizing field (> 4T). The magnetic properties, namely, remanence and coercivity are measured using a magnetic parameter instrument. The energy product is calculated by demagnetization curve. The Curie temperature of the alloys is measured by vibrating sample magnetometer.
For the scrutinization of the alloy microstructure by ultra - high voltage (1000kV) microscope, the samples are cut into 0.25mm slice vertical to \(c\) axis, milled and cleaned using ion beam thinner. The ultra - high voltage microscope model is JEM - 1000kV: operation voltage 1000kV, vacuum degree \(2.5\times10^{-4}Pa\) and \(0.7\times10^{-5}Pa\) with addition of liquid nitrogen.
The Mössbauer spectroscopy of the alloys is measured by model Oxford - ms500 with 57Co/Rh radioactive source and \(\alpha - Fe\) velocity calibration.
Measuring the Magnetic Properties of Nb- and Ga-Modified NdFeB Alloys
The samples are magnetized in pulsed magnetic field (> 4.5T), then measured using magnetic parameter instrument, seeing Fig. 4.34. When \(x = 0.02\), the intrinsic coercivity increased by 48%, which is the maximum value. When \(x\) is above 0.02, the intrinsic coercivity, remanence and energy product monotonically decrease. The magnetic properties of \(Nd_{13}Dy_{2}(Fe_{0.98}Nb_{0.02})_{79}B_{6}\) are: \(B_{r}=1.38T\), \(_{i}H_{c}=1326\ kA/m\), \((BH)_{max}=380\ kJ/m^{3}\).
Mössbauer Effect Study on NdFeB Alloys with Nb and Ga Additions
This section studied the magnetic properties of \(Nd_{15}Fe_{85 - x}B_{x}\) alloys, \(Nd_{15}(Fe_{1 - x}Nb_{x})_{79}B_{7}\) alloys and \(Nd_{2}Fe_{12 - x}Co_{x}Nb_{x}B\) (\(x = 0.05\), 0.10, 0.15 and 0.20) alloys at the atom level by means of Mössbauer spectrum.
Mössbauer analysis of \(Nd_{15}Fe_{85 - x}B_{x}\) alloy at room temperature
It can be seen from the Mössbauer spectrum of \(Nd_{15}Fe_{85}\) alloy (\(x = 0\)) that there are six rays of \(\alpha - Fe\) and new absorption rays of \(b'\) with the velocity of - 1.8mm/s and 1.2mm/s. There were obvious broadening and dissymmetry at the second and fifth rays of \(\alpha - Fe\). So the velocity of the new phase absorption rays will be - 3 - 3mm/s. The hyperfine field is 180kOe. The absorption rays of \(d\) and \(d'\) of \(Nd_{2}Fe_{14}B\) phase (magnetic phase) appear in the Mössbauer spectrum after adding a little boron in the alloy (\(Nd_{15}Fe_{83}B_{2}\)). Comparing with \(Nd_{15}Fe_{85}\) alloy, the Mössbauer absorption rays intensity of the \(Nd_{15}Fe_{83}B_{2}\) alloy declines evidently. When \(x = 4\) (the nominal composition is \(Nd_{15}Fe_{81}B_{4}\)), the rays of \(Nd_{2}Fe_{17}\) nearly disappeared. The content of \(\alpha - Fe\) is far less than that of \(Nd_{15}Fe_{81}B_{4}\). The intensity of \(\alpha - Fe\) rays is very weak. When \(x = 8\) (the nominal composition is \(Nd_{15}Fe_{77}B_{8}\)), there are only rays of \(Nd_{2}Fe_{14}B\) (magnetic phase, tetragonal phase). The rays of \(\alpha - Fe\) disappear. Besides, there are new rays, which are paramagnetic rays of Nd - rich phase. Therefore, the addition of appropriate boron in the alloy can improve the magnetic properties of the alloy because \(Nd_{2}Fe_{14}B\) phase has high anisotropy. With increasing the boron content, the contents of \(\alpha - Fe\) and \(Nd_{2}Fe_{17}\) decrease. It can be seen from the Mössbauer spectrum of \(Nd_{2}Fe_{14}B_{8}\) alloy that Fe grain positions occupy 27%, paramagnetic phases grain positions occupy 6%. Every \(Nd_{2}Fe_{14}B\) crystal cell has 16 \(Fe_{5}\) & \(Fe_{6}\), 82 \(Fe_{3}\) & \(Fe_{4}\), 4 \(Fe_{1}\) & \(Fe_{2}\) (Ping, Pan, 1985; Zhao, Xia, Ma, Pan, 1989). The neutron diffraction effect of the alloy at the Herbst and shown that every \(Nd_{2}Fe_{14}B\) crystal cell had 68 atoms: 56 Fe, 8 Nd and 4 B.
According to the size of the hyperfine field of \(Nd_{2}Fe_{14}B\), the order should be \(B_{8j_{2}}>B_{16k_{1}},B_{16k_{2}}>B_{8j_{1}},B_{4e}>B_{4c}\). According to the size of the intensity, the order should be \(I_{16k_{1}},I_{16k_{2}}>I_{8j_{1}},I_{8j_{2}}>I_{4e},I_{4c}\). The neighbour atom number of \(RE_{2}Fe_{14}B\) was shown in Table 4.15 (RE represents Y, Sc, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy and Ho) (Qi, 1998).
There are many neighbour RE atoms in grain positions \(8j_{1}\) and \(4c\) while there are few neighbour RE atoms in grain positions \(16k_{1}\), \(16k_{2}\), \(8j_{2}\) and \(4e\). So the RE elements have little effect on the hyperfine field of \(RE_{2}Fe_{14}B\). The hyperfine field of RE elements increases gradually from Y to Gd. But the hyperfine field of RE elements decreases according to the order: Gd, Tb, Dy and Ho. The hyperfine field \(B_{hf}\) of \(Nd_{2}Fe_{14}B\) is 29.55T.
Mössbauer analysis of \(Nd_{15}(Fe_{1 - x}Nb_{x})_{78}B_{7}\) alloys at room temperature
The occupying probability of Fe and Nb in tetragonal phases of \(Nd_{15}(Fe_{1 - x}Nb_{x})_{78}B_{7}\) alloys is shown in Table 4.16. It indicated that Nb primarily occupy \(e\) and \(c\) grain positions. There are few neighbour atoms in grain positions \(e\) and \(c\), which can not result in the hyperfine field change. When \(x\leq0.04\), many Nb atoms enter into grain boundary, Nb - rich and Nd - rich phases rather than enter into tetragonal phases. Therefore, Nb has little effect on the saturation magnetization \(M_{s}\) of \(Nd_{2}Fe_{14}B\) phase. When \(x\geq0.08\), \(Nd_{2}Fe_{14}B\) phase is destroyed and is replaced by new phase.
Mössbauer analysis of \(Nd_{2}Fe_{12 - x}Co_{2}Nb_{x}B\) (\(x = 0.05\), 0.10, 0.15 and 0.20)
The Mössbauer spectrum of 57Fe is formed by six rays. It indicates that hyperfine field is digression according to \(8j_{2}\), \(16k_{2}\), \(8j_{1}\), \(16k_{1}\), \(4e\) and \(4c\). Nb primarily occupies \(j_{2}\) grain position. The distance of neighbor Fe atoms is above 0.244nm (Pan, Ma, Li, 1993). The exchange effect of \(j_{2}\) grain position is positive. Nb enters into \(8j_{2}\) grain position and the exchange effect is positive, which decreases \(T_{c}\) of the alloys.
Nanostructure Analysis of NdFeB Alloys with Niobium (Nb)
The \(_{i}H_{c}\) of NdFeB alloys can increase to 1325 kA/m by adding appropriate content of Nb. Nb has little effect on the anisotropic field \(H_{k}\) because there are few Nb in the tetragonal phases of the alloys. \(Fe_{2}Nb\) phases emerge in the microstructure of \(Nd_{2}Fe_{12}B_{6}\) alloys with Nb. \(Fe_{2}Nb\) is \(MgZn_{2}\) - type structure, whose lattice constants \(a\) and \(c\) are 0.482nm and 0.78nm, respectively. The size of \(Fe_{2}Nb\) is only 2 - 4 nm, which mainly disperses in \(Nd_{2}Fe_{14}B\) phase and Nd - rich phase coherent with \(Nd_{2}Fe_{14}B\) phase. The Nb mainly enriches in grain boundary, which changes the triangle microstructure of the grain boundary of \(Nd_{2}Fe_{12}B_{6}\) alloys. The research shows that there are small Nb - rich precipitates in the grain boundary be - sides \(Fe_{2}Nb\) phase. The percentage composition of Nb in the precipitates is 89% - 97%. It indicates that Nb diffuse into Nb - rich phases and form new particle during aging treatment. The diffusion is propitious to form the intact grain boundary. The crystal defects of the alloys increase after aging treatment. According to the nucleation hardening model, every defect is a position that is easy to form inverse nuclear. In general, the defects' nucleation field is low, which will decrease the intrinsic coercivity of the alloys. However, the addition of Nb can increase the intrinsic coercivity of the alloys. So the result contradicts with the nucleation hardening model. Therefore, the nucleation hardening model can not explain the phenomena (Pan, Liu, Luo, 1990; Zhao, Xia, Ma, Pan, 1989).
By measuring the grain sizes of the NdFeB alloys with Nb, we find that the Nb can inhibit the growth of the grain and decrease the sizes of the grains. The total surface area of the grains and the domain walls pinning increase, which improves the intrinsic coercivity of the alloys. Therefore, Nb has cross effect on the alloys, which can be explained by authors using the theory of "dynamic cross - complementary combination". The appropriate addition of Nb can decrease the sizes of the grains and increase the grain boundary and domain walls pinning, which increases the intrinsic coercivity. Above the discussion can be summarized "grain finery local pinning".
Dynamic Cross-Section and Microstructure of NdFeB Alloys with Nb and Dysprosium (Dy)
The magnetic properties of the NdFeB alloys with addition of Nb and Dy are shown in Table 4.17.
The contents of Nb of the samples No.1, No.2 and No.3 are 0%, 2% (at.) and 2% (at.), respectively. It can be seen that the \(_{m}H_{c}\) of samples No.2 and No.3 increases 13% and 19% than that of sample No.1, respectively. The anisotropic field \(H_{A}\) of the alloys has few changes. We have studied the microstructure using TEM in order to explain the effect of Nb on the alloys. There are strip phases in the microstructure of the alloys with Nb (shown in Fig. 4.34). The strip phase is \(Fe_{2}Nb\), which is called “Laves phase”. The average size of the grain of the alloys with Nb is 5.6 nm while that of the alloys without Nb is 9.3 nm. So Nb can inhibit the grain growth and decrease the grain size, which increases the grain surface area and domain walls pinning.
The effect of Nb increasing \(_{j}H_{c}\) is due to its finer grain structure. Hu Jiafa etc. add 1.75% Nb powder to \(Nd_{16}Fe_{77}B_{7}\) powder with inter - grain alloying. \(_{j}H_{c}\) reaches 14.6kOe(1162.16kA/m) compared to 11.7kOe(931.32kA/m) with no addition of Nb powder.
Microstructure and Cross-Section of NdFeB Alloys Containing Nb, Ga, Co, and Dy
Addition of Ga in NdFeB alloys replaces Fe, which can obviously improve the coercivity. There is appropriate ratio of combined addition of Nb and Ga in the alloys. The NdFeB alloys with nominal composition of \(Nd_{13}Dy_{2}Co_{4}Nb_{0.8}Ga_{1.3}B_{7}Fe_{71.9}\) are prepared by reasonable process. The intrinsic coercivity is above 2000kA/m. The sintering temperature was \(T\geq1105^{\circ}C\). Aging treatment is key factor that affects the coercivity of the alloys. The appropriate aging temperature is according to the composition of the alloys. When the aging temperature is \(525 - 630^{\circ}C\), the NdFeB alloys have high coercivity. The existing forms of Ga and Nb in the alloys are difference. Nb elements mainly exist in matrix phases with the forms of precipitates and inclusion morphology. The grain boundaries have a few Nb elements. Besides, there are some strip \(Fe_{2}Nb\) Laves phases (Fig. 4.34). Nb can decrease the grain size when the content is less than 1.5% - 2% (at.). Ga elements exist in the matrix phases and grain boundaries with the form of Ga - rich phases (Fig. 4.35). The content of Ga for replacement of Fe should be 1% - 2% (at.). The existing form of Ga in the grain boundaries is same to that in the matrix phases, which inhibits the formation of soft magnetic phases (Fig. 4.36). The addition of Ga elements can decrease the grain size and increases the grain boundary area, domain walls pinning effect and the coercivity of the alloys.
Curie Temperature Analysis of NdFeB Alloys Containing Niobium (Nb)
The Curie temperature of the NdFeB alloys is decreased by addition of Nb. The research of Mössbauer on the alloys shows that the matrix phases \(Nd_{2}Fe_{14}B\) of the alloys have exchange action: \(J_{Fe - Fe}>J_{Fe - RE}>J_{RE - RE}\). So the Curie temperature is deter
mined by the distance of neighbour Fe. \(J_{Fe - Fe}\), \(J_{Fe - RE}\) and \(J_{RE - RE}\) are the exchange constants of Fe - Fe, and Fe - RE and RE - RE, respectively. The interatomic exchange integral of Fe is negative when the distance is less than 0.244nm. When the distance is above 0.244nm, the exchange integral is positive (Herbst, Croat, Yelon, 1985). The distances of iron atom in the site \(j_{2}\) between in the sites \(k_{1}\), \(k_{2}\) and \(j_{1}\) are 0.2748nm, 0.2640nm and 0.2784nm, respectively. Therefore, the exchange integral of iron atoms in the site \(j_{2}\) is positive. When the niobium atoms occupy the site \(8j_{2}\), the exchange integral is change into zero, which results in the decrease of Curie temperature of the alloys. The hyperfine field parameters of the alloys are shown in Table 4.18.
A New Coercivity Mechanism Model for Multi-Component NdFeB Alloys
The coercivity mechanism of the NdFeB alloys is still research focus in recent decades. Kronmüller, et al had studied systematically the coercivity mechanism from theoretical derivation to experimental verification. They published many papers and pointed out a nucleation hardening model. Hajipanayis, et al. put forward boundary local pinning model, which can explain many questions and brought great influence on the research of the mechanism. The third model is uniform pinning mechanism model, which is similar to the second model in some aspects (Ding, Pan, Luo, 1990; Zhou, 1995; Pan, Li, Li, et al, 1989; Liu, Luo, Pan, et al, 1991; Liu, Pan, Luo, et al, 1991; Ping, Li, Ma, Pan, et al, 1986; Pan, Pan, Ma, 1994; Liu, Pan, Luo, et al, 1990).
Is the coercivity of NdFeB alloys determined by nucleation hardening or uniform pinning? The effect of temperature, magnetization field and anisotropic field on the coercivity should be studied in order to make clear the question.
The intrinsic coercivity \(_{i}H_{c}\) of the alloys increases greatly after aging at 600 - 900°C. \(_{i}H_{c}\) linearly increases with increasing magnetization field. The main cause is that the coercivity is determined by nucleation hardening and pinning hardening at different temperature, respectively. When the magnetization field is not less than the saturation field of the coercivity, the coercivity is determined by the nucleation field of the magnetization reversal. The coercivity is determined by pinning field when the magnetization field reaches pinning field. It seems that the statement is comprehensive. But the coercivity mechanism of the isotropic sintered NdFeB and rapid - quenched NdFeB magnets is not explained by nucleation hardening model. Mishra et al. pointed out that the coercivity of rapid - quenched NdFeB magnets derived from the pinning field of the grain boundary to the Bloch domain wall.
The nucleation field of the matrix phase \(Nd_{2}Fe_{14}B\) of the alloys should be equal to the anisotropic field of the alloys. But \(_{i}H_{c}\) is far less than the anisotropic field of the alloys. The conceivable reason is that the matrix phase \(Nd_{2}Fe_{14}B\) has many surface defects and forms anti - magnetization domain. The surface defects and roughness of the matrix phase is improved after aging treatment, which increases the coercivity.
Both "nucleation hardening model" and "uniform pinning model" can not explain the coercivity mechanism of the NdFeB with above ternary alloy elements (additive elements such as Nb, Al, Ga etc.). Author gives out "grain finery local pinning" model, which can explain the coercivity mechanism of the NdFeB with above ternary alloy elements especially the alloys with Nb. The coercivity mechanism has been tested by experiments (Pan, Li, Li, et al, 1989; Liu, Luo, Pan, et al, 1991; Liu, Pan, Luo, et al, 1991; Liu, Luo, 1989).
Conclusions: Key Findings on Microstructure and Coercivity in Modified NdFeB Alloys
- The Mössbauer analysis of the \(Nd_{2}Fe_{12 - x}Co_{2}Nb_{x}B\) (\(x = 0.05\), 0.10, 0.15, 0.20) alloys indicates that \(H_{hf}\) (anisotropic field) increases while \(M_{s}\) (saturation magnetization) and \(T_{c}\) (Curie temperature) decrease with Nb content increasing. The nano - microstructure of \((Nd_{9}Dy_{1})_{15}Fe_{78}B_{7}\) alloys shows that there are \(Fe_{2}Nb\) phases in the structure. The lattice constants are: \(a = 0.482nm\), \(c = 0.787nm\). The addition of Nb can decrease the grain size and mainly rich in grain boundary, which increases greatly the intrinsic coercivity (\(_{i}H_{c}\)). Nb has little effect on the anisotropic field \(H_{A}\) because the elements mainly exist in the grain boundary and form Laves phases rather than enter into the crystal lattice. From the microstructure of the alloys are dynamic tested by TEM with 1000kV from room temperature to 400°C. It shows that there is no precipitate and change in the microstructure. But some precipitates emerge from \(Nd_{2}Fe_{14}B\) phases of the NdFeB alloys without Nb at 280°C. Therefore, Nb and Ga can improve the thermal stability of the alloys. The nucleation hardening model and pinning model can not comprehensively explain the coercivity mechanism of NdFeB alloys with Nb and Ga. Author gives out a new "grain finery local pinning" model. This model can explain the phenomena of any addition element increases the coercivity and improves thermal stability of NdFeB ternary alloy, which was the result of grain refinement and increment of the boundary local pinning.
- The Mössbauer analysis of \(Nd_{15}(Fe_{1 - x}Nb_{x})_{79}B_{7}\) (\(x\leq0.04\)) indicates that Nb primarily occupy \(e\) and \(c\) grain positions. But there are few neighbor atoms in \(e\) and \(c\) grain positions. Therefore, there are few Nb atoms in \(e\) and \(c\) grain positions, which can not result in the hyperfine field change. Nb atoms mainly occupy \(8j_{2}\) grain position.
- The microstructure of NdFeB ternary alloys and NdFeB alloys with Nb are analyzed by TEM with 1000kV. It indicates that the ternary alloys with
nominal composition \(Nd_{15}Fe_{77}B_{8}\) produce precipitates (\(Nd_{2}O_{3}\)) when the temperature reaches 280°C. But the alloys with Nb begin to produce precipitates when the temperature is above 400°C. Nb can decrease the grain size and improves the magnetic properties of the alloys.
