Phase Formation of a Solid-Liquid Mn–Ga Diffusion Couple under a Magnetic Field
2019 Volume 60 Issue 10 Pages 2195-2198
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2019 Volume 60 Issue 10 Pages 2195-2198
In-field heat treatments of an Mn–Ga diffusion couple were performed at 773 K for 12, 24 and 48 h to investigate the phase formation under magnetic fields. Formation of the MnGa3, Mn2Ga5, MnGa, Mn3Ga2 and β-Mn phases was confirmed for magnetic fields of 0 T and 5 T. For a diffusion-controlled process, there is a parabolic relationship between the thickness of the phase layers and annealing time for the MnGa and Mn2Ga5 phases. The parabolic coefficients of MnGa and Mn2Ga5 for a zero magnetic field were determined as 8.7 × 10−3 µm2s−1 and 4.6 × 10−1 µm2s−1 respectively. For a magnetic field of 5 T, the parabolic coefficients were evaluated as 11 × 10−3 µm2s−1 for the MnGa phase and 4.5 × 10−1 µm2s−1 for the Mn2Ga5 phase.
Fig. 4 Average thickness of the MnGa and Mn2Ga5 phase layers as a function of the square root of annealing time with and without μ0H = 5 T. The solid and broken lines represent the least-squares fits to the data of μ0H = 0 T and 5 T, respectively.
Physical and metallurgical phenomena such as phase transformations,1) transformation kinetics,2) recrystallization,3) grain boundary migration or phase growth,4,5) texture formation6,7) and atomic diffusion8–10) are all affected by magnetic fields H. Experimental results for Mg–Al8) and Ni–Al9) diffusion couples have showed that atomic diffusion is suppressed by a magnetic field. Fujii et al. reported that the diffusivity of carbon to ferromagnetic (FM) α-Fe was suppressed by a magnetic field.10) Recently, we found that the solid-liquid reaction of Fe–Ga was influenced by a magnetic field.11) These effects of a magnetic field on the atomic diffusion in metals can be explained by the reduction in the frequency factor k0 of the atomic diffusion.8–11)
Reports on FM Fe-based amorphous alloys12,13) and Mn–Bi alloys14,15) suggest that the activation energy Q of the diffusion process is also suppressed by a magnetic field. Mitsui et al. noted that the solid-solid and solid-liquid reactions from non-FM Bi and α-Mn into the FM MnBi phase were enhanced by a magnetic field.14,15) FM MnBi has a large saturation magnetization MS (= 3.9 μB/f.u.) and a high Curie temperature TC (> 630 K).16) It is thus assumed that the effect of the magnetic field on the Mn–Bi reaction occurs due to the large gain in Zeeman energy for forming the MnBi ferromagnet.14,15)
Gallium is a nonmagnetic element that has a low melting point of approximately 303 K. Additionally, the Mn–Ga system has some FM phases with a large MS and high TC.17–24) For example, Ms = 2.51 μB/f.u.19) and TC = 610–700 K20) for MnGa and Ms = 1.7 μB/f.u. and TC = 770 K21) for Mn3Ga are reported. For Mn2Ga5, MS and TC are 2.71 μB/f.u. and TC = 450 K, respectively.22) Therefore, an Mn–Ga combination may be an interesting system for investigating the effect of a magnetic field on atomic diffusion in a metal. However, to the best of our knowledge, there have been no detailed reports on the effects of a magnetic field on the Mn–Ga reaction or atomic diffusion.
In this paper, we report on the experimental results for in-field heat treatment (IFHT) of an Mn–Ga diffusion couple at 773 K for 12, 24 and 48 h in a zero field with μ0H = 5 T.
Mn–Ga diffusion couples were prepared as follows. First, an Mn ingot (99.9%) was prepared by the arc-melting method in an argon atmosphere. The obtained button ingot was turned over and remelted several times and then annealed at 873 K for 24 h in a quartz tube with argon gas and slowly cooled to room temperature. X-ray diffraction measurements confirmed that the button ingot was a single phase of α-Mn. Next, the Mn button ingot was shaped into a disk-like sample by shaving and polishing its surface. The diameter and length of the Mn disk were approximately 11 mm and 5 mm respectively.
As shown in Fig. 1, the Mn disk was then inserted into an IFHT quartz cell with an inner diameter of 12 mm and fixed by quartz wool to prevent the sample moving in the magnetic field. To prepare the Mn–Ga diffusion couple, Ga (99.99%) flakes were put on the flat surface of the Mn disk and fixed by quartz wool. The Mn–Ga diffusion couple was made into an Mn:Ga = 5:1 (in mass%) sample.
Mn–Ga diffusion couple sealed in the in-field heat treatment quartz-cell.
IFHT of the Mn–Ga diffusion couples was carried out using a 5-T cryocooled superconducting magnet (5T-CSM) with a 50.8-mm experimental bore (Tamakawa Co., Ltd.). Figure 2 shows a schematic illustration of the IFHT furnace in the 5T-CSM. The interface of the Mn–Ga diffusion couple was placed at the center of and perpendicular to the direction of the magnetic field. The Mn–Ga diffusion couple in the IFHT quartz cell (Fig. 1) was annealed with argon gas at 773 K for an annealing times of t = 12, 24 and 48 h with and without μ0H = 5 T. The Ga flake became liquid on the Mn disk in temperatures up to 773 K. The homogeneity of the magnetic field at the sample position was 0.1% for a 10-mm in diameter spherical volume. Two thermocouples were placed at the sample position: one was inserted into the IFHT quartz cell and the other was positioned outside of the quartz cell.
Schematic illustration of the in-field heat treatment furnace with a 5-T cryocooled superconducting magnet. 1, quartz wool; 2, non-inductive winding water-cooling jacket; 3, Pt–PtRh type thermocouple; 4, quartz cell; 5, heater; 6, cryocooled superconducting magnet.
After IFHT, the Mn–Ga diffusion-couple sample was cut perpendicular to the Mn–Ga interface (parallel to the magnetic field). Microstructural observation and elemental analysis were performed using an electron probe micro analyzer (EPMA). The thickness of the observed reactant phases was measured perpendicular to the interface of the Mn–Ga diffusion couple. The average value of the thickness W was evaluated by measuring 16 sections on one Mn–Ga diffusion couple.
From the phase diagram for the binary Ga–Mn system,18,24,25) we expected that four intermetallic compounds with some composition range and β-Mn phases would be observed between the Ga and α-Mn phases for our sample at an annealing temperature of 773 K. Figure 3 shows the typical results of EPMA elemental mapping for the Mn–Ga diffusion couples after various IFHT conditions with and without the application of μ0H = 5 T. As the figure shows, α-Mn (i) and three other phases (ii–iv) were clearly observed in all samples. From the EPMA analysis, the composition of these phases was detected as (ii) 41, (iii) 33 and (iv) 24 at% Mn. The phase diagram shows that the MnGa phase existed for the composition range from 40–50 at% Mn.18,24,25) We used the Ga–Mn phase diagram to evaluate the (ii) MnGa, (iii) Mn2Ga5 and (iv) MnGa3 phases in order from the left side of each of the panels in Fig. 3. Additionally, tiny β-Mn and Mn3Ga2 phases (blue-green area in Fig. 3) were also detected between the α-Mn and MnGa phases. The effect of the magnetic field on these phases is discussed elsewhere. As can be seen in Fig. 3, there was a large resin area in the MnGa3 phase layer, and for this reason only W of the MnGa and Mn2Ga5 phase layers were evaluated in this study.
EPMA elemental mapping in the Mn–Ga diffusion couples after in-field heat treatment at 773 K for 12 h in a zero field (a), 12 h in 5 T (b), 24 h in a zero field (c), and 24 h in 5 T (d).
A parabolic relationship between W and t has been reported for a diffusion-controlled process for the reactant phases.8,26) This relationship can be expressed as
| \begin{equation} W^{2} = kt, \end{equation} | (1) |
Average thickness of the MnGa and Mn2Ga5 phase layers as a function of the square root of annealing time with and without μ0H = 5 T. The solid and broken lines represent the least-squares fits to the data of μ0H = 0 T and 5 T, respectively.
Magnetic field dependence of the parabolic coefficient of Mn2Ga5 (a) and MnGa (b) phases.
This result is inconsistent with the previous results for an Mn–Bi system. The solid-solid and solid-liquid reactions from non-FM Bi and Mn into the FM MnBi phase were enhanced by H, which is due to the large gain in Zeeman energy for forming the MnBi ferromagnet.14,15) In the present study, no effect of the magnetic field on the solid-liquid reaction into the FM MnGa and Mn2Ga5 phases was detected. The reason for this is probably the existence of competition between the effects of H on the reductions in k0 and Q in the diffusion process.
In the simple model, k can be expressed by the following Arrhenius equation:
| \begin{equation} k = k_{0}\exp\left(- \frac{Q}{RT}\right), \end{equation} | (2) |
Li et al. reported that the k0 of the Ni–Al diffusion couple decreased on applying a magnetic field.27) This reduction in k0 with solid-solid diffusion was due to the Lorentz force.27) It has also been reported that the viscosity of liquid Ga is enhanced by a magnetic field.28) This field-induced viscosity leads to a reduction in k0 in the present Mn–Ga reaction.
From eq. (2), the reductions in both k0 and Q by the application of a magnetic field lead to enhancement and suppression of k in the MnGa phase, resulting in there being no significant effect from the magnetic field. To the best of our knowledge, the magnetic properties of the FM Mn–Ga phases are still unclear, so that further detailed discussion is difficult at the present stage. Further investigations of the effect of a magnetic field on Mn–Ga diffusion are now in progress.
The effect of the magnetic field on the phase formation of a Mn–Ga diffusion couple was investigated. The EPMA analysis confirmed the existence of the MnGa3, Mn2Ga5, MnGa, Mn3Ga2 and β-Mn phases. The present results suggest that the reaction in the Mn–Ga diffusion couple for the MnGa and Mn2Ga5 phases was diffusion controlled. The parabolic coefficient k of the MnGa phase was estimated to be 8.7 × 10−3 µm2s−1 for a zero field and 11 × 10−3 µm2s−1 for μ0H = 5 T. For the MnGa3 phase, the values calculated were k = 4.6 × 10−1 µm2s−1 for a zero field and k = 4.5 × 10−1 µm2s−1 for μ0H = 5 T.
This work was supported by KAKENHI (16K14374). EPMA analysis was performed at the Division of Instrumental Analysis, Research Support Center, Kagoshima University.
