High-Temperature Phase Transition and Magnetic Properties of SmCo₅ Permanent-Magnet Alloys

For magnetic scientists who are engaged in the investigation and development of magnetic materials, it is very interesting to study the relationship between the high - temperature phase transition and coercivity for SmCo₅ permanent - magnet alloys. Therefore, investigation of the project can accelerate the improvement of magnetic properties and the development of coercivity and micromagnetic theories.

The coercivity of SmCo₅ permanent - magnet alloys cannot be explained by the traditional coercivity theory. It is not consistent with the results predicted by impurity or single - domain theories. The coercivity of SmCo₅ alloys regularly exhibits an abrupt minimum at 750 °C as the alloys are annealed from 25 °C to 900 °C. In addition, the coercivity acquired resolved up to now (Pan, Jin, 1990).

A lot of studies about eutectic decomposition, precipitation phase, crystal defect, phase transition and microstructure have been made for SmCo₅ alloy, since it was discovered in 1967 (Pan, Jin, 1990; Zhou, 1990; Xie, et al., 1980; Strnat, Ray, 1974; Wan, 1977; Fidler, Kronmüller, 1980; Li, Dai, et al., 1982). As the coercivity of SmCo₅ is very sensitive to the crystal defect, precipitation phase and aging treatment, these problems have attracted much attention.

Table 2.1 lists experimental opinions of researchers on decline of \(H_{c}\) of SmCo₅ at 750 °C from 1972 to 1995.

mental results and main conclusions reported by some researcher during the recent thirty years.

Table 2.1 showed that some common conclusions had been reached:

1. SmCo₅ is stable for annealing above 800 °C. It is sub - state below 800°C; eutectic decomposition occurs in annealing, from SmCo₅→Sm₂Co₇+Sm₂Co₁₇.
2. The different ratio between Sm and Co leads to different separated phases. Sm₂Co₁₇ is precipitated from Co - rich SmCo₅, but Sm₂Co₇ is precipitated from Sm - rich SmCo₅ after eutectic decomposition.
3. The coercivity of SmCo₅ is determined by the nucleation field of reversal magnetization.
4. The rotation theory that high magnetocrystalline anisotropy leads to high coercivity cannot explain the coercivity of SmCo₅. However, large domain wall energy (about \(\sqrt{AK}\)) and narrow wall width (about \(1 / \sqrt{AK}\)) produced by the large magnetocrystalline anisotropy energy derives the wall displacement theory of large coercivity (Li, Dai, et al, 1982), where \(A\) and \(K\) are exchange and magnetocrystalline anisotropy energies, respectively.
5. The narrow and large anisotropy field is easily influenced by various defects.

6. As Sm is easily oxidized to Sm₂O₃, the coercivity is very sensitive to heating treatment technology.
7. The reversible magnetization process of SmCo₅ is controlled by reversely magnetized nucleation. However, the reversible magnetization of the whole magnet is avoided due to pinning at crystal boundary (Pan, Jin, 1990).
8. Some effects of defects on the nucleation and pinning have been confirmed by TEM.

The new rule, original theory and new explanation obtained from studies of basic theories and applications for the mechanism of SmCo₅ permanent - magnet alloy are introduced as follows:

1. The experiments performed by Zhou, et al in 1983, showed that the coercivity of SmCo₅ significantly decreases after annealing at 700 - 750°C for short time. The coercivity of the sintered SmCo₅ can be regained after it is annealed at 730°C for less than 250 min and followed by heating at 950°C. However, after it is annealed at 730°C for more than 400 min and followed by heating at 950°C, only can the coercivity be partly restored. X - ray diffraction showed that the precipitate phase phase was not observed for SmCo₅ alloys annealed at 730°C for 50 h. As SmCo₅ alloys alternated the heat treatment between 750°C and 950°C, the reversible change of coercivity is related to the formation and disappearance of inhomogeneous solid solution. SmCo₅ is the homogeneous solid solution alloy, as it is heated at 950°C and followed by fast cooling. However, as it is heated at 700 - 750°C, the Sm - rich or Co - rich region (or atomic cluster) has to be formed due to relatively narrow homogeneous regions. The anisotropy of the rich regions is relatively small, and thus forming nucleation centers of reversely magnetized domains, which leads to a decrease in coercivity. The inhomogeneous solid solution of Sm ions and Co or O ions must be formed due to narrow homogeneous regions, as SmCo₅ was heated from 700°C to 750°C. The rich region of Sm or Co ions inside SmCo₅ had low coercivity and formed the center of reversely magnetized nucleation, which leads to low coercivity. As heated at 950°C, the inhomogeneous region disappeared and the coercivity recovered (Zhou, et al, 1990).
2. New viewpoints discovered by the author from experiments are:
   1. The coercivity mechanism and segregated phase in annealing were investigated for SmCo₅ permanent - magnet alloys in 1982 using positron - annihilation, super - high voltage TEM and magnetic measurement. The results showed that the Sm₂Co₁₇ phase itself is not the center of reversibly magnetized nucleation. Some defects in the separated phase have low magnetic anisotropy and, therefore, form the center of reversibly magnetized nucleation, which leads to low intrinsic coercivity. As SmCo₅ is annealed from 25°C to 900°C, the maximum irreversible loss was found at 750°C (Pan, Jin, 1990).
   2. In 1982, new high temperature phase transition, the separation of Sm₂Co₁₇

2. phase from SmCo₅ and the growth of the phase, has been observed using super high voltage TEM with 1,000 kV for SmCo₅ permanent - magnet film with the thickness of 90 nm. At room temperature, no separated phase is observed. As temperature is raised to 300°C, the fine precipitates are separated. At 350°C, growth of the precipitates can be observed. At 400°C, the precipitation and growth continue. After 420°C for 30 min, the precipitates greatly grow. At 550°C, the precipitates continue growing, but the growth rate is slowing and the stripes of Sm₂Co₇ appear on the original Sm₂Co₁₇. The precipitates grow slowly by 600°C and are merged at 680°C. The precipitates are confirmed to be Sm₂Co₁₇ by electronic diffraction analysis (Pan, Zhao, 1989).
3. In 1982, the maximum irreversible loss occurs at 750°C, as SmCo₅ permanent - magnetic alloys are annealed from 25°C to 900°C. The mechanism was discussed (Pan, Jin, 1990).
4. In 1982, it was observed from TEM that separated Sm₂Co₁₇ is not perfect and are stripe and circle in shape. The separated phases at 650°C are random in the direction. At 750°C, the separated phases turn into particles (Pan, Zhao, 1989).
5. In 1983, it was found that no peak of oxygen was observed in photoelectronic spectra for the sintered SmCo₅ permanent - magnet alloys followed by annealing at 750°C. Based on the results measured at room temperature, about the Sm and Co elements segregated at 900°C, the concentration of oxygen does not observably change after annealing at various temperatures (Pan, 1992).
6. In 1992 observation using 1000kV HVEM found that there was transit area (or called as interference of phases) between the matrix phase of SmCo₅ and the precipitated phase (Sm₂Co₁₇ or Sm₂Co₇) at 750°C, such a transit area had low magnetic anisotropy, and in defect areas in the Sm₂Co₁₇ phase the magnetic anisotropy was very low, which lead to degradation of the coercivity. When temperature was raised from 750°C to 900°C the observation discovered that the aforementioned transit area and defect areas in Sm₂Co₁₇ phase disappeared; it was found from photoelectron energy spectrum that the phenomenon of segregation in Sm and Co elements reduced gradually and at last disappeared, and the segregation area was testified as SmCo₅ phase by X - ray diffraction analysis. That was the reason that the coercivity of SmCo₅ alloys declined to the lowest after annealing at 750°C, but it then turned up when temperature was raised from 750°C to 900°C.
7. In 1994 to 2003 the dynamic observation on SmCo₅ film sample by using HVEM at increasing temperature found new phenomenon and new information about phase transformation at high temperature in experiment as follows:
   • Nucleation speed and coarsening of the new phase (such as Sm₂Co₁₇) precipitated from the matrix phase change along with heating and holding times, solid state phase transformation and new phase coarsening process change with the time.
   • Part of Sm₂Co₁₇ was found to be resolved into the matrix phase again and

disappeared when heated to 600 - 750°C in dynamic observation. The difference in structure between precipitated Sm₂Co₁₇ phase and the matrix phase leads to form new interface which increases system free energy. Thus, extremum of free energy variation can be deduced as: \(\Delta G_{s}=\frac{3}{2}\sqrt{3} \alpha^{2} h_{c}\), where \(\alpha\), \(h_{c}\) are critical size of small phase point of Sm₂Co₁₇ corresponding to different temperature; \(\sigma\) is the interface energy between new phase and the matrix phase.

• The growth rate of new phase of Sm₂Co₁₇ precipitated from the matrix phase of SmCo₅ was also found to be different in the in situ and dynamic observation.
• Sm₂Co₁₇ phase can precipitate from the position of Sm₂Co₁₇.
• That SmCo₅ eutectoid dissolved out phases of Sm₂Co₁₇ and Sm₂Co₇ needs a process and such a process is slowly in heat activation, the precipitated Sm₂Co₁₇ and Sm₂Co₇ phases exist synchronously, but correspondingly exist time of Sm₂Co₇ phase is shorter than that of Sm₂Co₁₇ phase. The minimum nucleation field for eutectoid decompounding of Sm₂Co₁₇ phase from SmCo₅ phase is: \(H_{c}\approx(1 / h + 1 / a)\gamma / M_{s}\).

The following orders were found by the in situ and dynamic observation: SmCo₅ samples were different in coercivity and in variation extent of the coercivity at temperature from 25°C to 1000°C, generally the SmCo₅ samples with higher coercivity the degradation of their coercivity would be smaller at 750°C, and their irreversible magnetic loss also be smaller; and the height of coercivity will effect on nucleation rate as well.

Phase transformation is reversible, that is to say, Sm₂Co₁₇ and Sm₂Co₇ phases may dissolve into the matrix phase of SmCo₅ again, once the sample is put on electronic diffraction repeatedly in the in situ and dynamic observation, then its reversible property will become irreversible.

1. Experiment made by Hanmin Jin, et al. in 1983 indicated that SmCo₅ alloy was annealing at low temperature (50 - 400°C) the coercivity and longevity of positive electron highly complicated change obviously along with last of time. When annealing at 710°C its coercivity and nucleation field did degraded obviously, but the oblivion longevity of its positive electron was not changed basically. SmCo₅ and rhombic Sm₂Co₁₇ have the central Sm³⁺ in conditions as more 8 types with magnetisable axis along plane \(c\) or near plane \(c\) among 11 most possibly defect near neighbor Sm³⁺ distributions. Therefore, there are low magnetic anisotropy areas in the defect areas, such areas become reverse magnetization nucleation centers.
2. Experiment carried out by Hongzu Xie, et al. in 1978 showed: when heated at 750°C the electric resistant rate of SmCo₅ alloy increased with last of time.
3. Experiment conducted by Wanji Zhao, Hongzu Zhai, et al. in 1983 showed: there was no magnetic split when adding tin alone into SmCo₅; but adding iron into SmCo₅ could result in magnetic split, that addition of iron was the root cause.

ing tiny state magnetic split. Using the Mössbauer Effect is a near practice and good method to observe and study the function of adding iron and tin into SmCo₅.

6. Experiment by Houda Song in 1978 indicated: addition of iron and tin into SmCo₅ can make for a stable manufacturing process; the SmCo₅ with addition of iron and tin has a high intrinsic coercivity as the same as that before the addition.
7. Experiment by Xianchun Yang, Jinhua Wu, et al. in 1982 indicated: coercivity of (Sm, Gd, Er)Co_5.5 made by adding gadolinium and erbium was related to precipitation of 2:7 phase, and an appropriate heat treatment condition can make the magnet sample with a proper amount of 2:7 phase, symmetrical and integrated granule of crystals, magnetisable, complete domain orientation, hard to be demagnetized and a high coercivity.
8. Experiment by Mingjie Cheng, Hongzu Xie, et al. in 1982 showed: there were only two phase existed in edge precipitation process, besides SmCo₅ phase the 2nd phase for Sm - rich sample was Sm₂Co₇ phase only, and the 2nd phase for Co - rich sample was Sm₂Co₁₇ phase only.
9. Experiment by D. L. Martin, et al. in 1974 - 1975 indicated: SmCo₅ phase could not be formed at temperature below 800°C and CeCo₅ phase could not be formed either. RECo₅ is instable and it will be eutectoid decomposed at certain temperature.
10. Experiment and calculation by J. Fidler, et al. in 1980 indicated: the place of dislocation had big stress field and strain energy (Fidler, Kronmüller, 1980). Nucleation in precipitate phase caused change of system free energy which is expressed by \(\Delta G\), thus:

    \(\Delta G = 1/V_{p}\int_{p}(G_{p}-G_{m}-G_{p}^{\sigma}-G_{p}^{d})dV+\int_{p}w_{p}dn - 1/2\int_{m}\sigma_{y}^{D}\epsilon_{y}^{D}dV\) (2.1)

    where \(G_{m}\), \(G_{p}\) are the chemical energy of a single cell of the matrix phase and precipitated phase, respectively; \(V_{p}\) is the volume of a single cell; \(G_{p}^{\sigma}\) is elastic aberrance energy; \(G_{p}^{d}\) is interactional energy between dislocation and precipitated phase; \(w_{p}\) is the surface energy density of precipitated phase; \(n\) is unit vector of surface normal of the precipitated phase; \(\sigma_{y}^{D}\) is the stress at place of dislocation; \(\epsilon_{y}^{D}\) is the strain of dislocation.

    Symbol minus (-) in the formula is the driving force for precipitation process, plus (+) is resisting force for the precipitation process.

    Assuming that the elastic property of the precipitated phase is the same as that of base body, and they are anisotropy. When the precipitated phase is a flat ellipsoid, thus the elastic aberrance energy can be obtained as:

    \(G_{2:7}^{\sigma}=(0.043 + 0.174\ Y/Z)\)

    \(G_{2:17}^{\sigma}=(-0.908 + 0.1736\ Y/Z)\) (2.2)

    where, \(Z\) and \(Y\) are the short radius and long radius of the ellipsoid precipitated phase, respectively.

Precipitation energy of 2:17 phase is favorable by looking at elastic aberrance energy alone. This is one of the reasons that the 2:17 phase precipitates at first in SmCo₅ alloy, which had been testified by many experiments.

Interaction energy of precipitation and dislocation \(G_{pD}^{\sigma}\) is expressed by formula as follows:

\(G_{pD}^{\sigma}=\sigma_{y}^{D}\epsilon_{y}^{D}V_{p}\) (2.3)

where \(\sigma_{y}^{D}\) is the stress of dislocation; \(\epsilon_{y}^{D}\) is the elastic strain of precipitation; \(V_{p}\) is the volume of the precipitated phase.

According to Eq. 2.3 the interaction energy between an atom of the precipitated phase and the dislocation stress field can be estimated. Then a conclusion is obtained from above calculation: multiples dislocation is like to nucleation center of Sm₂Co₁₇ phase (only a few screw dislocation will be favored to be nucleation center of Sm₂Co₇ phase), thus precipitation of phase Sm₂Co₁₇ is easier than that of Sm₂Co₇ phase. Though rhombic columnar dislocation has a strong effect on domain wall, its contribution to coercivity is not very big. Fidler concluded on study in theory and practice that screw precipitated phase in some dislocation has strong pinning effect on domain wall; but even precipitated phase almost has no effect on domain wall, unevenly distributed precipitated phase on interspersed dislocation has strong pinning effect on the domain wall.

11. Kronmüller derived micro - magnetic theory to calculate in 1976 the reverse magnetization nucleation field \(H_{A}\) being formed by the sheet precipitated phase in SmCo₅, the coercivity formula was obtained as follows:

\(m_{p}H_{p}=2k_{f}/M_{p}-2\pi M_{p}+2A_{p}\pi^{2}/(M_{p}D^{2})\) (2.4)

where subscript p represents the physical amount of the precipitated phase, by substituting parameters of the precipitated phase in to Eq. 2.4 the nucleation power can be estimated as 7,960 kA/m (100 kOe). This value is far higher than the coercivity obtained in practice. The problem was the calculation neglected the interface (transit area) between the matrix and precipitated phase, and the structure and magnetism of the transit area might act important effect on reverse magnetization domain nucleation. When thickness \(D\) of the precipitated phase is very small, \(Z_{0}=0\), \(z_{0}\approx D\) (\(z_{0}\) is the transit area of phase interface, and \(Z\) and \(z_{0}\) refer to the figure), reverse magnetization domain may nucleate on uneven phase interface. In this condition the nucleation field can be calculated as per continuity of magnetic theory as below.

\(H_{n}=H_{n}^{\infty}+2(A\Delta K)^{1/2}/(M_{p}r_{0})\)

Hereby introduce thickness of the domain wall \(\delta_{n}\), assuming \(\Delta K\approx K_{1}\), and making use of the following formula:

\(\delta_{n}=\pi\sqrt{A/K_{p}}\approx\pi\sqrt{A/\Delta K}\)

Thus the formula above can be written as:

\(H_{n}=H_{n}^{\infty}+2K_{p}\delta_{n}/(\pi M_{p}r_{0})\)

When thickness \(D\) of the precipitated phase is very small thus \(D \ll 2r_{0}\) and when phase interface transit area \(r_{0}\) is also small (\(r_{0}\ll\delta_{n}\)), the formula of nucleation field can be expressed as:

\(H_{n}^{\text{max}} = H_{n}^{\infty}+2K_{1}\delta_{n}/(\pi M_{p}r_{0})\)

Actually, nucleus is very small, thus the exchange integral constant of the precipitated phase and magnetization intensity can not be taken as constants any more because \(D\ll2r_{0}\) and \(r_{0}\ll\delta_{n}\). In the condition of a very thin precipitated phase the anisotropy constant of the precipitated phase \(K_{p}\) will be lowered considerably; if \(K_{p}\) is lowered to \(10^{-3}-10^{-2}\), the \(H_{n}^{\infty}\) would become meaningless, thus \(H_{n}=(2K_{1}\delta_{n})/(\pi M_{p}r_{0})\). Assuming \(\delta_{n}=2.6\) nm, \(r_{0}=26\) nm, \(K_{1}=15\times10^{6}\) erg/cm³, \(M_{p}=\) 955 emu/cm³, and \(H_{n}\) can be calculated as \(H_{n}=7960\times10^{3}\) A/m, that is coincident with the experiments and can explain the reason that the coercivity of SmCo₅ is lower than its theoretical value caused by phase interface of the precipitated phase. The coercivity of SmCo_{5 - m} is determined by nucleation field of reverse domain (Kütterer, et al, 1977).

Nucleation of reverse magnetization domain is a rotational process of magnetic torque, and that the expanding process of reverse magnetization domain is a process of displacement of domain wall; the growth process of reverse magnetization domain nucleus needs to overcome energy of demagnetization field and resistance by increased domain wall energy because of increased surface area of magnetization domain. In this instance coercivity of alloy is mainly determined by critical field of reverse magnetization domain expansion. Kronmüller deduced after analyzing and calculation that the critical field of reverse magnetization domain expansion of SmCo₅ was far smaller than nucleation field.