1.1 Rare Earth Permanent Magnets: Properties & Applications
Understanding Rare Earth Elements: Their Role in Permanent Magnets
The elements with atomic numbers between 57 to 71 of the third subgroup are called rare earths. in the Element Periodic Table: La (57), Ce (58), Pr (59), Nd (60), Pm (61), Sm (62), Eu (63), Gd (64), Tb (65), Dy (66), Ho (67), Er (68), Tm (69), Yb (70) and Lu (71), additive Sc (21) and Y (39) with close similar chemical characteristics, and electronic structure.
The light rare earths are La, Ce, Pr, Nd, Pm, Sm, Eu, and the heavy rare earths are Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu. The rare earth permanent - magnet alloys are known as rare earth permanent - magnet materials. Their hard magnetic properties have the origin in some particular metallic compound formed from rare earth 3 d transition metals with single and multi - phase structures (Xu, 1995).
Classification and Development of Rare Earth Permanent-Magnet Alloys
Rare earth permanent - magnet alloys can be generally classified into three varieties according to composition including rare earth cobalt permanent - magnet alloys, rare earth iron permanent - magnet alloys, rare earth iron nitride and iron carbide permanent - magnet alloys.
Based on development generation, rare earth permanent - magnet alloys can be classified into three generations:
- The first generation, 1:5 type rare earth cobalt permanent - magnet alloys, is represented by \(\text{SmCo}_{5}\) with excellent magnetic properties. Later, \(\text{PrCo}_{5}\), \((\text{Sm},\text{Pr})\text{Co}_{5}\), \(\text{MMCo}_{5}\) (MM is the mixture of rare earths) have been developed.
- \(\text{SmCo}_{5}\) is divided into three types, based on their magnetic properties: (1) high coercivity (\(H_{c}\)), linear \(B - H\) demagnetizing curve and almost the coercivity and remanence (\(H_{c}\approx B_{r}\)); (2) low coercivity, non - linear \(B - H\) demagnetizing curve and coercivity smaller than remanence (\(H_{c}
- The characteristics of \(\text{SmCo}_{5}\) are high magnetocrystalline anisotropy (\(K_{1}=(15 - 19)\times10^{6}\text{ J}/\text{m}^{3}\)), high anisotropy field (\(H_{A}=31,840\ \text{kA}/\text{m}\)), low temperature coefficient (as compared to rare earth iron permanent - magnet alloys), and high Curie temperature (\(T_{c}=720^{\circ}\text{C}\), where \(T_{c}\) is the Curie temperature); \(T_{c}\) of \(\text{SmCo}_{5}\) is almost doubles, as compared to \(312^{\circ}\text{C}\) of \(\text{Nd}_{2}\text{Fe}_{14}\text{B}\)).
The maximum magnetic energy product of \(\text{SmCo}_{5}\) predicted by theory can reach \((BH)_{max}=24.9\ \text{kJ}/\text{m}^{3}\) (3MGOe). \((BH)_{max}\) of \(\text{SmCo}_{5}\) product is 130 - 160 \(\text{kJ}/\text{m}^{3}\), which is much lower than the predicted value. The theoretical coercivity is \(H_{c}=31,840\text{kA}/\text{m}\) (400 kOe), while the practical coercivity is \(H_{c}=1592 - 2388\ \text{kA}/\text{m}\) (20 - 30 kOe) in product and \(H_{c}=3980 - 4776\ \text{kA}/\text{m}\) (50 - 60 kOe) in laboratory (Kumar, Das, Wettstein, 1978). The remanence of \(\text{SmCo}_{5}\) is \(B_{r}=0.8 - 0.96\ \text{T}\) (8.0 - 9.5 kGs).
For the second generation, 2:17 type rare earth cobalt permanent - magnet alloys \((\text{RE}_{2}\text{Co}_{17})\), the characteristics are high Curie temperature (maximum \(T_{c}\approx850^{\circ}\text{C}\)), higher intrinsic saturation magnetization than that for \(\text{RECo}_{5}\), and high maximum energy product in theory \((BH)_{max}=525.4\ \text{kJ}/\text{m}^{3}\) (66MGOe). The typical alloys is \(\text{Sm}(\text{Co},\text{Cu},\text{Fe},\text{Zr})_{z}(z = 7 - 8)\). The alloys have cellular structure, which comprises the main phase \(\text{Sm}_{2}\text{Co}_{17}\), \(\text{Cu}\), \(\text{Fe}\), \(\text{Mo}\), with size of about 50 nm is surrounded by the boundary phase \(\text{Sm}(\text{Co},\text{Cu},\text{Fe},\text{M})\) with the thickness of about 10 nm. The coercivity is not related to the size of grains, but is determined by the microstructure of the two - phases, namely 2:17 and 1:5 phases. Due to different domain wall energies between 2:17 and 1:5 phases, the wall of 2:17 phase is pinned by 1:5 phase, and thus leading to large coercivity, for the magnetized process or reversely magnetized process (Yu, Zhang, Li, 1997). The key to obtain large coercivity is heating treatment technology, such as solid solution and isothermal aging.
For the third generation, rare earth iron permanent - magnet alloys, the characteristics are: (1) the maximum energy product sets a record, (2) raw materials is sufficient and cheap ( sufficient \(\text{Fe}\) replaces deficient \(\text{Co}\) in resource, and cheap and sufficient \(\text{Nd}\) replace expensive and relatively deficient \(\text{Sm}\) needed in the first and second generations). The magnetic properties and price is much superior to the first and second generation permanent - magnet alloys. In addition, the third generation alloy can replace other permanent alloys in some applications. Therefore, the third generation permanent - magnet alloys develop fast. The drawback is lower Curie temperature as compared to the first and second generations, and poor temperature coefficient and anti - corrugation. Now, the ways to overcome these drawbacks have been found (Pan, Zhang, 1990). There are many types of \(\text{RE - Fe - B}\) series, such as ternary \(\text{Nd - Fe - B}\), \(\text{Pr - Fe - B}\) and \(\text{RE - Fe - B}\) (\(\text{RE}=\text{La}\), \(\text{Ce}\), \(\text{MM}\cdots\)), qudruple \(\text{Nd - Fe - M - B}\), \(\text{Nd - Fe - M}_{2}\text{B}\).
In addition, the permanent - magnet composites comprising rare earth iron nitrides and nanocrystals have been developed.
For rare earth iron nitride (\(\text{RE - Fe - N}\)) permanent - magnet alloys, the characteristic is the existence of \(\text{N}\), which is different from the first, second and third generation rare earth permanent - magnet alloys. \(\text{Sm}_{2}\text{Fe}_{17}\text{N}_{x}(x = 0 - 3)\) is the interstitial metallic compound and is prepared by heating the powders of \(\text{Sm}_{2}\text{Fe}_{17}\) in \(N_{2}\) gas at 450 - \(550^{\circ}\text{C}\). A cell of \(\text{Sm}_{2}\text{Fe}_{17}\text{N}_{x}\) has three 9e positions. After \(\text{N}\) atoms occupy the 9e sites, \(\text{Sm}_{2}\text{Fe}_{17}\text{N}_{x}\) retains the \(\text{Th}_{2}\text{Zn}_{17}\) structure. However, the lattice parameters and cell volumes increase, and thus significantly modifying the magnetic properties. As compared to \(\text{Sm}_{2}\text{Fe}_{17}\), the anisotropy is modified from \(c\) - plane and \(c\) - axis, the magnetocrystalline anisotropy constant \(K_{1}\) increases from 1.2 \(\text{MJ}/\text{m}^{3}\) to 8.4 \(\text{MJ}/\text{m}^{3}\), the anisotropy field reaches 16,800 kA/m, the saturation magnetization increases 1.54 \(\text{T}\), the specific magnetization increases by 78% (from 100 J/(\(\text{K}\cdot\text{g}\)) to 178 J/(\(\text{K}\cdot\text{g}\))), and the Curie temperature is elevated 343 K from 389 K to 732 K.
The maximum energy of \(\text{Sm}_{2}\text{Fe}_{17}\text{N}_{x}\) is \((BH)_{max}=19.8\ \text{kJ}/\text{m}^{3}\) and the remanence is 1.19 T, while the coercivity is rather small, \(H_{c}=640\ \text{kA}/\text{m}\) (Coey J M D, Sun Hong, 1990; Zhou, et al, 1992). The magnetic properties of \(\text{Gd}\) substituted \(\text{Sm}_{2}\text{Fe}_{18 - \delta}\text{Gd}_{\delta}\text{O}_{0.7}\text{N}_{1.7}\) are: \(B_{r}=1.27\ \text{T}\) (12.7 kGs), \(H_{c}=2000\ \text{kA}/\text{m}\) (25 kOe) (Zhou, et al, 1992). The other characteristics of \(\text{Sm}_{2}\text{Fe}_{17}\text{N}_{x}\) are good stability and anti - wear. The drawback is that the alloy is only used as adhesive magnets, since \(\text{Sm}_{2}\text{Fe}_{17}\text{N}_{x}\) is decomposed above \(600^{\circ}\text{C}\).
Two phase nanocrystalline composites comprise soft and hard magnetic phases with the grain size of nanometer (Coehoorn, et al, 1988; Wihanawasam, et al, 1994; Ding, Mccormick, 1993). The main phase can be hard or soft magnetic property. The composites take advantages of large saturation magnetizations for soft magnetic phase and high magnetocrystalline anisotropy for hard magnetic phase. The two phases are compounded in the nanometer size, the boundary is co - lattice in crystallography, and there exists the exchange coupling in the boundary. The composites have the characteristics as same to the single ferromagnetic phase in magnetized and reversely magnetized processes. In an applied magnetic field, the magnet moments of soft magnetic phase rotate synchronously with that of hard magnetic phase. The coercivity is determined by the strength of exchange coupling at the boundary of the two phases. The enhanced effect of remanence is found for isotropic permanent - magnet alloys prepared. The magnetic moments of the soft magnetic phase are located in the direction of averaged moments of the hard magnetic phase. The soft magnetic phase is about 5 - 10 nm in sizes. The magnetic anisotropy of the hard magnetic phase determines the strength of exchange interactions. For example, for a rare earth permanent - magnet alloy, in which the hard magnetic properties has its origin in the exchange coupling at the boundary between \(\text{Nd}_{2}\text{Fe}_{14}\text{B}\) hard magnetic phase and \(\text{Fe}_{3}\text{B}\) soft magnetic phase, the magnetic properties are: \(B_{r}=1.6\ \text{T}\), remanence \(B_{r}=0.75\ \text{M}\), \(H_{c}=238.8\ \text{kA}/\text{m}\) (Wihanawasam, et al, 1994). In addition, other permanent - magnet composites are \(\text{Sm}_{2}\text{Co}_{17}/\alpha\text{-Fe}\), \(\text{SmCo}_{5}/\alpha\text{-Fe}\), \(\text{Sm}_{2}\text{Fe}_{17}\text{N}_{x}/\alpha\text{-Fe}\), \(\text{Nd}_{2}(\text{Fe}, \text{M})_{14}\text{B}/\alpha\text{-Fe}\) and \(\text{Sm}_{2}\text{Fe}_{17}\text{N}_{x}/\text{Fe - Co}\), etc.
Crystal Structure of Rare Earth Permanent-Magnet Alloys: Impact on Magnetic Propertiess
For the first rare earth permanent - magnet alloys, the crystal structure of magnetic phase is \(\text{CaCu}_{5}\) type structure with space group \(\text{P6}/\text{mmm}\), as shown in Fig. 1.1 (Nesbitt, 1973). For the second rare earth permanent - magnet alloys, 2:17 type rare earth permanent - magnet alloys has \(\text{Th}_{2}\text{Zn}_{17}\) type structure at high temperature, and is modified into \(\text{Th}_{2}\text{Ni}_{17}\) type structure at low temperature. \(\text{Th}_{2}\text{Ni}_{17}\) belongs to the rhombohedral system in crystal structure with space group \(\text{P63}/\text{mmc}\), as shown in Fig. 1.2. For the third generation permanent - magnet alloys, the crystal structure belongs to tetragonal system with space group \(\text{P42}/\text{mmc}\), as shown in Fig. 1.3 (Herbst, 1984). The forth rare earth permanent - magnet alloys,
Fig. 1.1 \(\text{CaCu}_{5}\) - type crystal lattice
(a) Crystal lattice; (b) \(\text{CaCu}_{5}\) - type crystal lattice unit; (c) The projection of atoms of \(\text{CaCu}_{5}\) - type crystal lattice on plane (0001)
Fig. 1.2 \(\text{Th}_{2}\text{Zn}_{17}\) - type rhombic crystal lattice
Fig. 1.3 \(\text{Nd}_{2}\text{Fe}_{14}\text{B}\) - compound crystal lattice (a) and B - contained triangular prism in \(\text{Nd}_{2}\text{Fe}_{14}\text{B}\) crystal lattice (b)
the structure of \(\text{RE}_{2}\text{Fe}_{17}\text{N}_{x}\) is the rhombohedral and hexagonal structures, where \(N\) is in the crystal lattice as interstitial atoms.
\(\text{Th}_{2}\text{Zn}_{17}\) type crystal structure is one of the basic structures in rare earth permanent - magnet compounds. Most of \(\text{RE}_{2}\text{Co}_{17}\) and \(\text{RE}_{2}\text{Fe}_{17}\) compounds have the \(\text{Th}_{2}\text{Zn}_{17}\) type structure at low temperature. \(\text{Th}_{2}\text{Ni}_{17}\) is isomeric with \(\text{Th}_{2}\text{Zn}_{17}\); both have the similar structures. The crystal structure of \(\text{Th}_{2}\text{Zn}_{17}\) is shown in Fig. 1.2. \(\text{Th}_{2}\text{Zn}_{17}\) belongs to the rhombohedral system in crystal structure with space group \(R\overline{3}m\). There are three \(\text{Th}_{2}\text{Zn}_{17}\) formulae and fifty - seven atoms in a cell. Six \(\text{Th}\) (or \(\text{RE}\)) atoms occupy the \(c\) sites. Among and fifty - one \(\text{Zn}\) (or \(\text{Co}\) and \(\text{Fe}\)) atoms, nine atoms occupy the \(d\) sites, eighteen the \(f\) sites, eighteen the \(h\) sites and six the \(c\) sites. The coordinates of each atom are as follows:
\(6c:(0,0,\frac{1}{3}),(\frac{1}{3},\frac{2}{3},0),(\frac{2}{3},\frac{1}{3},\frac{2}{3}),(0,0,\frac{2}{3}),(\frac{1}{3},\frac{2}{3},\frac{1}{3}),(\frac{2}{3},\frac{1}{3},0)\)
\(9d:(\frac{1}{2},0,\frac{1}{2}),(0,\frac{1}{2},\frac{1}{2}),(\frac{1}{2},\frac{1}{2},\frac{1}{2}),(\frac{5}{6},\frac{2}{3},\frac{1}{6}),(\frac{1}{3},\frac{1}{6},\frac{1}{6}),(\frac{5}{6},\frac{1}{6},\frac{1}{6}),(\frac{1}{6},\frac{1}{3},\frac{5}{6}),(\frac{2}{3},\frac{5}{6},\frac{5}{6}),(\frac{1}{6},\frac{5}{6},\frac{5}{6})\)
\(18f:(\frac{1}{3},0,0),(0,\frac{1}{3},0),(\frac{2}{3},\frac{2}{3},0),(\frac{2}{3},0,0),(0,\frac{2}{3},0),(\frac{2}{3},\frac{2}{3},\frac{2}{3}),(\frac{1}{3},\frac{1}{3},0),(\frac{1}{3},0,\frac{2}{3}),(0,\frac{1}{3},\frac{2}{3}),(0,\frac{2}{3},\frac{2}{3}),(\frac{1}{3},\frac{1}{3},\frac{2}{3}),(\frac{2}{3},0,\frac{2}{3})\)
\((0,\frac{1}{3},\frac{1}{3}),(\frac{2}{3},\frac{2}{3},\frac{1}{3}),(\frac{1}{3},0,\frac{1}{3}),(\frac{1}{3},\frac{1}{3},\frac{1}{3}),(\frac{2}{3},0,\frac{1}{3}),(0,\frac{2}{3},\frac{1}{3})\)
\(18(h):(\frac{1}{2},\frac{1}{2},\frac{1}{6}),(\frac{1}{2},0,\frac{1}{6}),(0,\frac{1}{2},\frac{1}{6}),(\frac{1}{2},\frac{1}{2},\frac{5}{6}),(\frac{1}{2},0,\frac{5}{6}),(0,\frac{1}{2},\frac{5}{6}),(\frac{5}{6},\frac{1}{2},\frac{5}{6}),(\frac{5}{6},\frac{2}{3},\frac{5}{6}),(\frac{1}{3},\frac{1}{6},\frac{5}{6}),(\frac{5}{6},\frac{1}{2},\frac{1}{6}),(\frac{5}{6},\frac{2}{3},\frac{1}{6}),(\frac{1}{3},\frac{1}{6},\frac{1}{6}),(\frac{1}{6},\frac{1}{2},\frac{1}{6}),(\frac{1}{6},\frac{1}{3},\frac{1}{2}),(\frac{2}{3},\frac{1}{6},\frac{1}{2}),(\frac{1}{6},\frac{1}{6},\frac{1}{6}),(\frac{1}{6},\frac{1}{3},\frac{1}{6}),(\frac{2}{3},\frac{1}{6},\frac{1}{6})\)
\(6(c):\langle0,0,0.097\rangle,\langle0,0, - 0.097\rangle,(\frac{1}{3},\frac{2}{3},\frac{2}{3}+0.097),(\frac{1}{3},\frac{2}{3},\frac{2}{3}-0.097),(\frac{2}{3},\frac{1}{3},\frac{1}{3}+0.097),(\frac{2}{3},\frac{1}{3},\frac{1}{3}-0.097)\)
The crystal structure of rare earth compounds \((\text{RE}_{x}\text{TM}_{y})\) is shown in Table 1.1.
Table 1.1 The crystal structure of rare earth compounds \((\text{RE}_{x}\text{TM}_{y})\)
| Compounds | Structure | Symmetry | Space group | Sites of RE atom | Sites of TM atom | Elements on the TM sites |
|---|---|---|---|---|---|---|
| \(\text{RE}_{3}\text{TM}\) | \(\text{Fe}_{3}\text{C}\) | orh | Pnma | 4c, 8d | 4c | Co, Ni |
| \(\text{RETM}_{2}\) | \(\text{MgCu}_{2}\) | cub | Fd3m | 8a | 16d | Pt, Co, Fe, Mn, Mg, Pb, Al, Ni |
| \(\text{RETM}_{3}\) | \(\text{PuNi}_{3}\) | rh | \(R\overline{3}m\) | 3a, 6c | 3b, 6c, 18h | Co, Ni, Fe |
| \(\text{RE}_{2}\text{TM}_{7}\) | \(\text{Ce}_{2}\text{Ni}_{7}\) | hex | P63/mmc | 4f1, 4f2 | 2a, 4e, 4f, 6h, 12k | Co, Ni |
| \(\text{Gd}_{2}\text{Co}_{7}\) | rh | \(R\overline{3}m\) | 6c1, 6c2 | 3b, 6c1, 6c2, 9e, 12h | Co, Ni | |
| \(\text{RETM}_{5}\) | \(\text{CaCu}_{5}\) | hex | P6/mmm | 1a | 2c, 3g | Co, Ni, Cu, Ag, Au, Zn, Pt |
| \(\text{RE}_{2}\text{TM}_{17}\) | \(\text{Th}_{2}\text{Zn}_{17}\) | rh | \(R\overline{3}m\) | 6c | 6c, 9d, 18f, 18h | Ni, Co, Fe, Zn |
| \(\text{RE}_{2}\text{Fe}_{14}\text{B}\) | \(\text{Th}_{2}\text{Ni}_{17}\) | tetra | P63/mmc | 2b, 2d | 4f, 6g, 12j, 12k | Ni, Co, Fe, Mg |
Note: 1. orh—orthorhombic, cub—cubic, rh—rhombohedral, hex—hexagonal, tetra—tetragonal;
2. TM—Co, Ni, Fe, et al. transition metal elements.
Magnetic Parameters of Rare Earth Permanent-Magnet Alloys: Performance and Optimization
Magnetic parameters of rare earth permanent - magnet alloys include:
- Coercivity. Coercivity is known as the strength of magnetic field at zero magnetic density. Intrinsic coercivity, \(H_{cm}\), \(H_{ci}\) or \(_{m}H_{c}\), is known as the magnetic field required at magnetization \(4\pi M\) to zero in the reversibly magnetized process.
- Remanence. \(B_{r}\) is known as the remnant magnetic density when the applied magnetic fields monotonously decrease from the magnetic saturation state of material to zero magnetic fields.
\(4\pi M_{r}\) or \(B_{r}\) is defined as remnant magnetization after the permanent - magnet alloys are magnetized to saturation followed by removing the magnetic field. \(B_{r}=4\pi M_{r}\) in CGS unit can be obtained from \(4\pi M = B - H\), and \(B_{r}=\mu_{0}M_{r}\) in SI unit can be obtained from \(\mu_{0}M=B - \mu_{0}H\).
3. Magnetic energy product. \((BH)\) represents the product of \(B_{m}\) and \(H_{m}\), and is the energy density at the gap in magnetic field \(H\), as shown in Fig. 1.4. In the figure, a point \(g\) corresponds to maximum product of \(B_{g}\) and \(H_{g}\), which is known as maximum magnetic energy product \((BH)_{max}\).
Fig. 1.4 Demagnetization curve (2) and magnetic energy curve (1)
4. Magnetic field.
5. Magnetization \(M\). The vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material.
6. Curie temperature. Ferromagnetic materials below the temperature and para - magnetic materials above the temperature.
7. Permanent - magnet alloy. Magnetic materials with large coercivity.
8. Initial magnetization curve. Magnetizations with increasing magnetic fields from zero for thermally demagnetized materials.
Criteria for Permanent-Magnet Alloys: Key Factors in Material Selection
The criterion of permanent - magnet alloys in performances is: (1) anisotropy, (2) Curie temperature, and (3) magnetization.
The main factors whether or not permanent - magnet alloys have in great future are: (1) good magnetic properties, (2) plenty of main materials, and (3) cost and price.
