- Email: [email protected]
Influence of high magnetic field on peritectic transformation during solidification of Bi–Mn alloy
Computer Coupling of Phase Diagrams and Thermochemistry 30 (2006) 277–285 www.elsevier.com/locate/calphad
Influence of high magnetic field on peritectic transformation during solidification of Bi–Mn alloy Zhongming Ren ∗ , Xi Li, Yanhui Sun, Yun Gao, Kang Deng, Yunbo Zhong Department of Material Science and Engineering, Shanghai University, Shanghai, 200072, PR China Received 6 November 2005; received in revised form 13 March 2006; accepted 18 March 2006 Available online 25 April 2006
Abstract The influence of high magnetic fields up to 10 T on the peritectic temperature of Bi–Mn alloys has been investigated experimentally. A method for measuring the peritectic temperature in a gradient magnetic field has been developed by relating the change of magnetic levitation force to the phase transformation due to the change in magnetic susceptibility while the transformation occurs. By measuring the temperature at which the magnetizing force changes abruptly, the phase transformation can be detected. It is shown that along with the increase of magnetic field, the temperature of the peritectic phase transformation BiMn1.08 + L → BiMn increased significantly, and in a 10 T field the temperature increase was about 20 ◦ C. It is found that with the high magnetic field, a split and separation of the BiMn grains in the direction perpendicular to the magnetic field occurred, and its morphology changed from flakes to small blocks. This is attributed to the repulsive force among the peritectic BiMn grains generated by the magnetization during the phase transformation. It seems that the precipitation of ferromagnetic phase results in stress in the grains. c 2006 Elsevier Ltd. All rights reserved.
Keywords: High magnetic field; Peritectic phase transformation; Bi–Mn alloy; Magnetization; Magnetic force
1. Introduction Solidification in a high magnetic field is an interesting topic and has attracted much attention of researchers ever since. The experimental research works have demonstrated that high magnetic fields presented a significant influence on solidification. Mikelson and Karklin [1] obtained aligned solidification structure in Al–Ni and Cd–Zn alloys in a 1.5 T magnetic field. Savitsky et al. [2] found that during solidification of a Bi–Mn alloy in a magnetic field the BiMn phase in the alloy aligned along the direction of the magnetic field. Rango [3] extended the investigation to solidification of paramagnetic YBa2 Cu3 O7 material and obtained texture crystal structure in a magnetic field. Katsuk [4] reported that diamagnetic benzophenone crystallized from n-hexane and KCl and BaCl2 crystallized from a solution aligned in a 10 T magnetic field. This alignment behavior has been investigated intensively by several researchers [5–7]. Asai [5] ∗ Corresponding author. Tel.: +86 21 56331102; fax: +86 21 56332939.
E-mail address: [email protected] (Z. Ren). c 2006 Elsevier Ltd. All rights reserved. 0364-5916/$ - see front matter doi:10.1016/j.calphad.2006.03.004
found perpendicular alignment in an Al–Si–Fe alloy during solidification in a strong magnetic field. Texture crystal growth of Bi-2201 [8] and Bi(Pb)2212 [9] have been obtained in a high magnetic field. Segregation of primary silicon in an Al–Si hypereutectic alloy solidified in a high magnetic field was also reported [10]. No mention was made on the influence of magnetic field on flow in the melt, because this is a well known topic. Up to now, nearly all work in this field was on the influence of high magnetic field on kinetics of solidification. From the view of the thermodynamics of phase transformation, the application of high magnetic field in the phase transformation of a material will cause a change in Gibbs energy of the material system by magnetization. This change in Gibbs energy in phase transformation can be expressed as 1G = 1G V + 1G M
(1)
where 1G is the change of Gibbs energy in the phase transformation; 1G V is the change of Gibbs energy due to temperature and pressure; 1G M is the change of Gibbs energy due to magnetization. Further, because the phase transformation temperature is determined by the Gibbs energy,
278
Z. Ren et al. / Computer Coupling of Phase Diagrams and Thermochemistry 30 (2006) 277–285
the temperature of the phase transformation will change due to the magnetization. Based on this point of view, up to now, some work has been performed on the influence of magnetic fields on such solid phase transformation that at least one phase is ferromagnetic, such as the martensitic transformation of steel during heat treatment. Martin et al. [11] have reviewed the investigations about this topic. It was demonstrated that the magnetic field caused the increase of the martensite start temperature by a few degrees due to the decrease in magnetic free energy. Recently, the influence of high magnetic fields on solid phase transformations in the Fe–C system has become one of the focused topics of research. The phase diagram of Fe–C has been analysed with consideration of the influence of magnetic fields. It is shown that the phase diagram was shifted upward so that the Ac1 and Ac3 temperatures increased as the magnetic field was applied [12,13]. The austenite–pearlite transformation [14], austenite–ferrite transformation [15,16], austenite–baintente transformation [17], and recrystalization [18] have also been investigated experimentally. All research work indicated that the magnetic field would change the phase transformation temperature in the Fe–C system. However, up to now, it seems that there is less work on the influence of high magnetic fields on solidification temperature. Peritectic crystalization is one of important melt–solid transformations because quite a lot of metallic materials are peritectic alloys. This phase transformation is diffusioncontrolled, much different from the martensite transformation. Obviously, it is important to learn the behavior of the transformation in the presence of high magnetic field, because possibly the phase transformation can be controlled by means of a magnetic field. Up to now, however, less research, if any, was reported about the influence of high magnetic field on this transformation. Bi–Mn alloys with composition within the range 3%–20%wtMn are peritectic with the peritectic reaction BiMn1.08 (HTP) + L → BiMn (LTP) producing a ferromagnetic phase BiMn. According to the analysis of Ladislav Valko and Marian Valko [19], the influence of magnetic field on phase transformation temperature in this case may be relatively significant. On the other hand, previous work showed that the morphology of BiMn grains solidified with high magnetic field was much different from that of the grains without magnetic field [5]. The mechanism for this difference is still unclear. The aim of this paper is to investigate the influence of high magnetic field on phase transformation temperature and evolution of solidification structure during the peritectic reaction in Bi–Mn alloy experimentally. From the result one can learn more about the influence of high magnetic field on the peritectic phase transformation and other phase transformations with ferromagnetic phases. 2. Experiment The experimental apparatus was as shown in Fig. 1. The superconductor magnet generated a vertical-direction static magnetic field with strength up to 14 T in its room bore.
Fig. 1. Schematic diagram of the experimental apparatus for solidification in a magnetic field. 1 stress gauge, 2 frame, 3 water cylinder, 4 furnace, 5 superconductor magnet, 6 specimen, 7 temperature control system, 8 recorder.
The furnace was set in the room bore of the magnet and the temperature in it could reach 1000 ◦ C. The graphite crucible was hung by a copper wire in the furnace at the position where the magnetic force was the maximum, and the copper wire was connected to a stress gauge. The thermo-couple was inserted in the crucible to detect the temperature of the specimen. All the signals from the stress gauge and the thermo-couple were recorded simultaneously by the recorder. Bi–21%Mn and Bi–6%Mn alloys were investigated in this experiment. According to the phase diagram [20], Bi–21%Mn alloy is composed of a single BiMn phase and, as shown later, is very sensitive to the influence of the magnetic field. Bi–6%Mn alloy is composed of a BiMn phase and α(Bi) phase, and is adapted to observe the influence of the magnetic field on the morphology of BiMn during the peritectic transformation of the alloy. In preparing the alloys, 99.9% pure Bi and 99.9% pure Mn were melted in a vacuum induction furnace and the melt was poured into a graphite mold to speed up the solidification and minimize segregation of composition. The phase transformation temperature was measured in the following way: It is well known that the magnetic force Fm of a substance in a gradient magnetic field is, Fm ≈
dBz χ Bz · . µ0 dz
(2)
Fm —magnetic force per kilogram, N/kg; µ0 = 4π × 10−7 H/m; Bz —magnetic flux in vertical direction, T. χ —the susceptibility of the substance. This equation shows that with a certain magnetic field, that is, the parameter Bz (dBz /dz) is certain, the magnetic force is dependent on the magnetic susceptibility χ of the substance. Usually, the phase transformation will lead to an abrupt change in magnetic susceptibility. So, the magnetic force will change abruptly accordingly during the phase transformation.
Z. Ren et al. / Computer Coupling of Phase Diagrams and Thermochemistry 30 (2006) 277–285
Fig. 2. Distribution of magnetic field.
279
then the specimen was heated up to 380 ◦ C at a rate of 0.25 ◦ C/min and maintained for 30 min, then cooled to below 330 ◦ C at a rate 0.5 ◦ C/min. Meanwhile the force and temperature were recorded. In order to investigate the evolution of the BiMn grains during the peritectic phase transformation, quenching experiments during the cooling or holding at the peritectic temperature of the alloy were carried out to keep at room temperature the morphology of the solidification structure. The specimens such obtained were sectioned and their solidification structures were examined by optical microscopy. Because the Bi–Mn alloy is of magnetic materials, and its magnetic properties are sensitive to changes in solidification structure, the magnetic properties of the alloys were also measured to reveal the influence of the high magnetic field on phase transformation. 3. Results and discussion 3.1. Peritectic phase transformation temperature
Fig. 3. Distribution of parameter Bz · dBz /dz.
As described in Ref. [21], the magnetic susceptibility of Bi–Mn alloy changes abruptly at the occurrence of the peritectic phase transformation, because the BiMn1.08 is paramagnetic and BiMn ferromagnetic. Hence, the magnetic force of the specimen will change responding to the change in the susceptibility. By measuring the temperature of the specimen at which the magnetic force changes abruptly, the phase transformation temperature can be determined. In the measuring experiment with this method, the specimen should be placed at the site where the value Bz (dBz /dz) is the maximum, so that high sensitivity can be achieved. Therefore, distribution of the magnetic field was measured before the experiment, with the result as shown in Fig. 2. Further, the value Bz (dBz /dz) was calculated from this figure, as shown in Fig. 3. It is shown that at the site 8 cm above the center plane of the magnet the value Bz (dBz /dz) was at positive maximum and at the site of 8 cm below the center plane of the magnet at negative maximum. The experimental procedure for measuring the phase transformation temperature was as follows: the alumina crucible with the Bi–Mn alloy specimen was hung at the position where the value Bz (dBz /dz) was at positive maximum and a downward magnetizing force was detected because the alloy is ferromagnetic with positive magnetic susceptibility;
Fig. 4 shows the typical force and temperature curves measured during heating and cooling of the Bi–21wt%Mn alloy and Bi–6wt%Mn alloy, respectively. From the figure one can learn that along with an increase of the temperature, the force decreased gradually at first, and at a certain temperature the force dropped abruptly to its minimum. This indicated the occurrence of the reaction BiMn → BiMn1.08 + L at this temperature. Afterwards, further increasing temperature up to 380 ◦ C did not cause any apparent change in the force. During cooling from 380 ◦ C, the force increased abruptly at a certain temperature, indicating the occurrence of the peritectic phase transformation BiMn1.08 + L → BiMn. The results showed that this method was very sensitive and adept for detecting the occurrence of the phase transformation. In the case of Bi–6%Mn alloy, this phenomenon was also apparent, and the phase transformation temperature detected by this method was the same as that of Bi–21%Mn alloy, even though the force value was minimized. For example, as shown in Fig. 4, with 10 T field the measured transformation temperatures for both alloys were 375 ◦ C in heating up, and 362 ◦ C in cooling down. Therefore, Bi–21%Mn alloy was chosen for measuring the transformation temperature in detail, because its change in force during the phase transformation was sharper. Fig. 5 shows the results of measuring the peritectic phase transformation temperature. Two lines are presented in Fig. 5, one is for heating up of the alloy and the other for cooling. As can be seen, the phase transformation temperature increased linearly along with the increase of the magnetic field. From the phase diagram [20], it is shown that in cooling down of the Bi–21wt%Mn alloy the peritectic transformation temperature is 340 ◦ C and in heating up the reaction BiMn → BiMn1.08 + L occurs at 355 ◦ C. Therefore, the phase transformation temperature for heating up is higher than that for cooling down. No matter whether heating or cooling, more than 20 ◦ C increment in the phase transformation temperature was produced in the 10 T magnetic field.
280
Z. Ren et al. / Computer Coupling of Phase Diagrams and Thermochemistry 30 (2006) 277–285
Fig. 4. Typical measuring curves of force and temperature during heating and cooling of Bi–Mn alloy in a magnetic field. B = 10 T. (a) Bi–21%Mn alloy, (b) Bi–6%Mn alloy. (1) force; (2) temperature; T1 —temperature starting transient of the force during cooling, T2 —temperature starting transient of the force during heating.
Besides, both analyses only dealt with the structural-change phase transformation, not the diffusion-controlled transformation, such as peritectic transformation in this experiment. In order to understand the influence of magnetic field on peritectic phase transformation with ferromagnetic transformed phase, the thermodynamics of the phase transformation under magnetic field should be analyzed. As we know, the magnetization energy Um is [22] Hex
Z Um = −
µ0 M dHeff
(4)
0
Fig. 5. The influence of the high magnetic field on the peritectic transformation temperature of Bi–Mn alloy. 1—cooling from 380 ◦ C to below 340 ◦ C, 2— heating from below 340–380 ◦ C.
It is well known that magnetic field will increase the starting point of the martensite reaction, and the increment of the starting point is proportional to the magnetic field [11]. However, Ladislav Valko and Marian Valko [19] gave a different formula in their analysis on the influence of magnetic field on the melt–solid phase transformation of pure iron, T − T0 = 1T =
T0 H2 1Hs0
(3)
where 1HS0 is the enthalpy, and H is the intensity of the magnetic field. Our result showed a roughly linear relationship between magnetic field and increment of phase transformation temperature, in agreement with the analysis of Ref. [11].
where M is the magnetic moment; Hex is the imposed magnetic field. Heff is the magnetic field inside the substance; and µ0 is the vacuum magnetic permeability, 4π × 107 H/m. In the peritectic transformation BiMn1.08 (HTP) + L → BiMn (LTP), BiMn1.08 and L are non-ferromagnetic, and BiMn ferromagnetic. For the non-ferromagnetic substance BiMn1.08 , M = χα Heff
(5)
Heff = Hex − Nα M
(6)
Hex = (1 + Nα χα )Heff
(7)
where χα is the magnetic susceptibility of the BiMn1.08 ; and Nα is the demagnetizing coefficient due to the shape of a BiMn1.08 grain. Combining Eq. (3) through (7) yields Umα = −
µ0 χα H2 . 2(1 + Nα χα )2 ex
(8)
This equation shows that the magnetization energy is 2. proportional to χα and Hex
281
Z. Ren et al. / Computer Coupling of Phase Diagrams and Thermochemistry 30 (2006) 277–285
T2 − T1 =
1 2µ0 Ms Hex − 2 1 − 2(1 + Nβ χβ )2
β
µ0 Ms Hs + β
µ0 χ L µ0 χ α 2 Hex + H2 2 2(1 + Nα χα ) 2(1 + χ L )2 ex
(S A − S αA ) + (S A − S AL ) + R ln
β
(a A )2 a αA a AL
Box I.
Fig. 6. Microstructure of Bi–6%Mn alloy quenched at different temperatures in cooling from 400 ◦ C. (a) Quenching at 380 ◦ C, (b) quenching at 345 ◦ C, (c) quenching at 340 ◦ C, (d) quenching at 335 ◦ C.
For the diamagnetic liquid Bi, a similar equation can be obtained µ0 χ L UmL = − H2 . (9) 2(1 + χ L )2 ex For the ferromagnetic substance BiMn (|χβ | 1) the approximate expression of U f can be obtained with the assumption that M is saturated at magnetic intensity HS Z Hex Umβ = − µ0 M dHeff 0
Hs
Z =− 0
µ0 χβ Heff dHeff −
Z
Hex
µ0 Ms dHeff
Hs
1 = −µ0 Ms Hex + 1 − 2(1 + Nβ χβ )2
µ0 Ms Hs .
β
µ A = µ A0 + RT1 ln α A µ LA
=
µ LA0
+
(11)
RT1 ln α AL .
With magnetic field, the phase transformation temperature changes to T2 and the chemical potentials are, µαA = µαA0 + S αA (T2 − T1 ) + RT2 ln α αA + Umα β
β
β
2µ0 Ms Hex β
β
(S A − S αA ) + (S A − S AL ) + R ln
β
(a A )2 a αA a AL
.
(13)
This equation indicates that the linear relation holds between the change in transformation temperature and magnetic field, as found from the experimental result shown in this experiment and the analysis of Ref. [11]. From this analysis, one can also learn that in the case of no ferromagnetic phase in the phase transformation, the change in the transformation temperature is 2 , the same as Ladislav Valko and Marian proportional to Hex Valko’s analysis [19]. 3.2. Microstructure of BiMn grain
µαA = µαA0 + RT1 ln α αA β
T2 − T1 ≈
(10)
The chemical potentials for these phases in the state of equilibrium at the peritectic temperature T1 without magnetic field are, β
µ0 χ L 2 and 2(1+χ 2 Hex , because the BiMn phase is ferromagnetic. L) Hence the equation is simplified as,
β
µ A = µ A0 + S A (T2 − T1 ) + RT2 ln α A + Umβ
(12)
µ LA = µ LA0 + S AL (T2 − T1 ) + RT2 ln α AL + UmL where µ is the chemical potential; S is the entropy; R is the universal gas constant; subscript A represents component A; and subscripts α, β, and L represent HTP, LTP and liquid phase, respectively. From these equations, considering the equilibrium among HTP, LTP, and liquid phases, the equation in Box I is deduced. In a strong magnetic field with the strength much larger than µ0 χα the saturation point, µ0 Ms Hex µ0 Ms Hs , 2(1+N H2 , χ )2 ex α α
Fig. 6 shows the microstructures of Bi–6%Mn alloy specimens obtained by quenching at various temperatures during cooling from 400 ◦ C without the magnetic field, which reveals the change in morphology of BiMn grains before and after the peritectic transformation. As shown, above 345 ◦ C the BiMn grains were block like, owing to the cubic crystal structure [21] (in fact, this phase is BiMn1.08 , and called HTP). Below 340 ◦ C the grains were flakes, due to its hexagonal crystal structure (called LTP). The change in morphology indicated that the reaction BiMn1.08 + L → BiMn occurred between 345 and 340 ◦ C, in agreement with the phase diagram of this alloy. Fig. 7 shows the results of the quenching experiment with 10 T field and various temperatures. One can learn that at 380 ◦ C, the morphology of the primary BiMn grains was block like, the same as that without a magnetic field (Fig. 6), and no alignment of grains took place. At 360 ◦ C, some “saw teeth” on the edge of the block grain and a small number of flake grains appeared, indicating the starting of the phase transformation. At 345 ◦ C, the grains were all flakes and aligned along the direction of the field, showing the achievement of the phase transformation. Further, the alignment behavior of the grains below 360 ◦ C was the same as that of the ferromagnetic
282
Z. Ren et al. / Computer Coupling of Phase Diagrams and Thermochemistry 30 (2006) 277–285
Fig. 7. Microstructure of Bi–6%Mn alloy quenched at different temperatures in 10 T field in cooling from 400 ◦ C. (a) 380 ◦ C, perpendicular (b) 380 ◦ C, parallel, (c) 360 ◦ C, perpendicular (d) 360 ◦ C, parallel (e) 355 ◦ C, perpendicular (f) 355 ◦ C, parallel (g) 345 ◦ C, perpendicular (h) 345 ◦ C, parallel.
Fig. 8. Microstructures of the specimens quenched with different maintaining time at 340 ◦ C after cooling from temperature 400 ◦ C. B = 0 T. The maintaining time was (a) 30 s; (b) 60 s; (c) 120 s; (d) 10 h.
BiMn grains described in reference [5]. This means that phase transformation BiMn1.08 + L → BiMn took place and the BiMn grains became ferromagnetic at 360 ◦ C, the same as the above experimental result of measuring the phase transformation temperature. 3.3. Evolution of BiMn grains during peritectic transformation In order to deeply understand the mechanism of the peritectic transformation under high magnetic field, the following experiment was carried out: the alloy was heated to 400 ◦ C and held for 30 min for homogenizing, then it was cooled to the phase transformation temperature determined by the previous experiments (i.e., 340 ◦ C in the case of no magnetic field and 360 ◦ C in the case of imposing a 10 T magnetic field). After a certain time of maintaining this temperature, the specimen was quenched, with the results shown in Figs. 8 and 9. Fig. 8 shows that during the phase transformation without magnetic field some “saw teeth” of MnBi appeared firstly on the edge of the Bi Mn1.08 block, and gradually the “saw teeth” grew to flakes and separated each other, further the flakes coarsened and kept this shape even with 10 h holding at this temperature. With 10 T field, as shown in Fig. 9, the MnBi “saw teeth” also appeared on the edge of the Mn1.08 Bi block at first, then grew to flakes and separated each other. However, with holding time over 5 min at this temperature the flakes were gradually split into small blocks in the perpendicular direction of the field, and the distribution of the small blocks got more uniformly with their separation from each other. Besides, the small blocks
aligned along the direction of the field, resulting in rod-like structure. It is well known that BiMn (LTP) is hexagonal in crystal structure with a single easy magnetizing axis ch001i and BiMn1.08 (HTP) is cubic [23]. Elongating the c axis 3% and contracting the a and b axes of cubic BiMn1.08 crystal will produce hexagonal BiMn crystals. In the presence of a magnetic field, the magnetizing force on the grain is [24] 2 F = −µ0 χ Hex .
(14)
This force promotes the phase transformation BiMn1.08 (HTP) + L − BiMn (LTP) by elongating the c axis and contracting the a and b axes. Accompanying the peritectic phase transformation of the alloy, its magnetic characteristics changed from paramagnetic to ferromagnetic. By measuring the change in magnetic properties of the alloy, the phase transformation can be detected and furthermore the effect of the magnetic field can be discovered. Fig. 10 are the hysteresis loops of the same specimens as shown in Fig. 9. One can learn that for the specimens quenched at 360 ◦ C in the field, the magnetization along the direction of the high magnetic field applied during solidification was easier with larger saturation moment than that in the perpendicular direction of the field, suggesting strong anisotropic characteristics. This is due to the orientation and alignment of the BiMn crystals with their easy axes in the direction of the magnetic field. It is interesting to notice that the specimens quenched after briefly cooling to 360 ◦ C possessed
Z. Ren et al. / Computer Coupling of Phase Diagrams and Thermochemistry 30 (2006) 277–285
283
Fig. 9. Microstructures of the specimens quenched with different maintaining time at 360 ◦ C after cooling from temperature 400 ◦ C. B = 10 T. The maintaining time was (a) 30 s; (b) 60 s; (c) 90 s; (d) 120 s; (e) 5 min; (f) 10 min; (g); 20 min; (h) 60 min.
some extent of coercivity, and along with increasing holding time at 360 ◦ C, the coercivity decreased remarkably, with an apparent increase in the magnetic permeability (the slope of the magnetizing curve) of the alloy. This means that the alloy became softer in magnetism. Because the alloy is composed of Bi and BiMn phases, and the Bi phase is diamagnetic, the magnetic properties of the alloy are determined mainly by the BiMn phase. Therefore, from the above results on the evolution of the BiMn structure during holding at this temperature and the change in the magnetic properties, one can learn that along with the splitting and separation of the flakes in the perpendicular direction of the field, the magnetic characteristics of the BiMn phase were transformed to soft magnetism. From the physics of magnetism, during magnetization the magnetic domains in the substance will rotate their easy axis towards the magnetic field and grow by moving their walls. The grain boundary and stress will retard the rotation and movement of the domains and cause large coercivity and small permeability. Therefore, the result of Fig. 9(a) indicates the presence of grain boundary and stress. The decrease in coercivity and increase in permeability with duration of the holding time (Fig. 9(b)–(d)) indicates the disappearance of the grain boundary and stress due to the splitting of the flakes and separating of the small blocks (Fig. 8). As we know, during the peritectic phase transformation ferromagnetic BiMn (LTP) several grains will nucleate on separated sites on the surface of one paramagnetic BiMn1.08 (HTP) block, as schematically shown in Fig. 11. In the high magnetic field, the LTP grains will be magnetized, and their same-name magnetic poles will be in the same direction. This results in repulsive forces among them, and stresses are generated in the grains, which resulted in the coercivity of the
alloy because the stresses retard the moving of the domain walls during magnetizing. The repulsive force is [25] µ0 (χ + 1) Q m1 Q m2 (15) 4π r2 where Q m1 , Q m2 are the magnetic poles. Along with growth of the LTP grains, their volumes increased and the inter-grain distances decreased. Therefore, according to the formula (14), the repulsive forces increased significantly. Even though the forces may break the particle, more likely the force promotes the dissolution of the boundary between the grains in the block and cause splitting and separation of the BiMn grains. The splitting and separation of the grains caused the release of the stresses in the grains, so the coercivity of the alloy decreased and the permeability increased. The repulsive forces among the separated grains repelled each other, and finally a force balance was established among the grains, resulting in uniform distribution of the grains. From this mechanism, one can get the conclusion that imposing a high magnetic field during phase transformation in which a ferromagnetic phase is included may induce stresses in it by the magnetizing force. It was reported that cracks occurred frequently during unidirectional solidification of TbDyFe in a strong magnetic field [26]. This may be attributed to the mechanism presented here because this magnetic alloy endures peritectic transformation during solidification. FM =
4. Conclusion 1. Applying a high magnetic field leads to increasing temperature of the peritectic transformation BiMn1.08 + L − BiMn in Bi–Mn peritectic alloys. With 10 T magnetic field, the temperature can increase more than 20 ◦ C.
284
Z. Ren et al. / Computer Coupling of Phase Diagrams and Thermochemistry 30 (2006) 277–285
Fig. 10. Hysteresis loops for the specimens shown in Fig. 9 with various holding times at 360 ◦ C. (A) About 30 s, (B) 10 min, (C) 20 min, (D) 60 min. “Parallel and perpendicular ” indicate directions of the magnetization measurement with respect to the magnetic field imposed during the solidification.
Z. Ren et al. / Computer Coupling of Phase Diagrams and Thermochemistry 30 (2006) 277–285
285
Fig. 11. Schematic showing of the splitting of BiMn grains during peritectic phase transformation of Bi–6%Mn alloy in 10 T magnetic field. (a) Generation of magnetizing forces among the ferromagnetic BiMn grains (LTP) in the magnetic field, (b) the increase of the magnetizing forces along with growth of the BiMn grains, (c) separation of the grains.
2. It is found that by imposing a high magnetic field during the peritectic transformation of Bi–Mn alloy, splitting and separation of the BiMn flakes may occur, resulting in small blocks instead of flake grains of the BiMn phase. The repulsive force among the peritectic BiMn grains is generated due to the magnetization during the phase transformation. The force will cause splitting and separation of the grains in the direction perpendicular to the magnetic field. Hence, the grains are refined and distributed uniformly. It is suggested that the precipitation of ferromagnetic phase during phase transformation in the magnetic field will result in stress in the grains. 3. By detecting the magnetizing force in a gradient magnetic field, it is possible to measure the phase transformation temperature. Acknowledgments This work is supported by Natural Science Foundation of China (No. 50234020, 50225416 and 59871026) and the Science and Technology Committee of Shanghai (04DZ14002). References [1] A.E Mikelson, Y.K. Karklin, J. Cryst. Growth 52 (1981) 524. [2] E.M. Savitisky, R.S. Torchinova, S.A.J. Turanoy, J. Cryst. Growth. 52 (1981) 519.
[3] P.D. Rango, M. Lee, P. Lejay, A. Sulpice, R. Tournier, M. Ingold, P. Germi, M. Pernet, Nature 349 (1991) 770. [4] A. Katsuki, R. Tokunaga, S.I. Watanabe, Chem. Lett. (8) (1996) 607. [5] H. Wang, Z.M. Ren, K. Deng, Acta Metall. Sin. 38 (2002) 41. [6] H. Yasuda et al., Mater. Trans. JIM 44 (2003) 2550–2554. [7] H. Morikawa, K. Sassa, S. Asai, Mater. Trans. JIM 139 (1998) 814–818. [8] X.Y. Lu et al., Physica C: Supercond. Appl. 382 (2002) 27–32. [9] W.P. Chen et al., J. Cryst. Growth 204 (1999) 69–77. [10] K. Sassa, H. Morikawa, S. Asai, J. Japan Inst. Met. 61 (1997) 1283. [11] J.W. Martin, R.D. Doherty, B. Cantor, Stability of Microstructure in Metallic Systems, 2nd ed., Cambridge University press, 1997, p. 391. [12] H.D. Joo, S.U. Kim, N.S. Shin, Y.M. Koo, Mater. Lett. 43 (2000) 225–229. [13] H.D. Joo, J.K. Choi, S.U. Kim, N.S. Shin, Y.M. Koo, Metall. Mater. Trans. A 35 (2004) 1663–1668. [14] S. Michio, Mater. Trans. JIM 44 (2003) 2524–2528. [15] X.J. Hao, H. Ohtsuka, Mater. Trans. JIM 45 (2004) 2622–2625. [16] H. Ohtsuka, Y. Xu, H. Wada, Mater. Trans. JIM 41 (2000) 907–910. [17] H. Ohtsuka, Curr. Opin. Solid State Mater. Sci. 8 (2004) 279–284. [18] Y. Zhang, N. Gey, C. He, X. Zhao, L. Zuo, Acta Materialia 52 (2004) 3467–3474. [19] L. Valko, M. Valko, IEEE Trans. Magn. 30 (2) (1994) 1122. [20] W.G. Moffatt, The Handbook of Binary Phase Diagrams, Genium, USA, 1984. [21] T. Chen, W.E. Stutius, IEEE Trans. Magn. 10 (1974) 581–586. [22] H. Morikawa, K. Sassa, S. Asai, Mater. Trans. JIM 39 (1998) 814–818. [23] A.U. Seybolt, H. Hansen, B.W. Roberts, P. Yurcisin, Trans. AIME. J. Metal (May) (1956) 606. [24] D.F. Wan, S. Luo, Physics of Magnetism, Electronic Industry Press, Beijing, 1987, p. 8 (in Chinese). [25] E. Hallen, Electromagnetic Theory, Chapman & Hall Ltd., London, 1962, p. 185. [26] H. Minagawa et al., J. Magn. Magn. Mater. 248 (2002) 230–235.
Influence of high magnetic field on peritectic transformation during solidification of Bi–Mn alloy Zhongming Ren ∗ , Xi Li, Yanhui Sun, Yun Gao, Kang Deng, Yunbo Zhong Department of Material Science and Engineering, Shanghai University, Shanghai, 200072, PR China Received 6 November 2005; received in revised form 13 March 2006; accepted 18 March 2006 Available online 25 April 2006
Abstract The influence of high magnetic fields up to 10 T on the peritectic temperature of Bi–Mn alloys has been investigated experimentally. A method for measuring the peritectic temperature in a gradient magnetic field has been developed by relating the change of magnetic levitation force to the phase transformation due to the change in magnetic susceptibility while the transformation occurs. By measuring the temperature at which the magnetizing force changes abruptly, the phase transformation can be detected. It is shown that along with the increase of magnetic field, the temperature of the peritectic phase transformation BiMn1.08 + L → BiMn increased significantly, and in a 10 T field the temperature increase was about 20 ◦ C. It is found that with the high magnetic field, a split and separation of the BiMn grains in the direction perpendicular to the magnetic field occurred, and its morphology changed from flakes to small blocks. This is attributed to the repulsive force among the peritectic BiMn grains generated by the magnetization during the phase transformation. It seems that the precipitation of ferromagnetic phase results in stress in the grains. c 2006 Elsevier Ltd. All rights reserved.
Keywords: High magnetic field; Peritectic phase transformation; Bi–Mn alloy; Magnetization; Magnetic force
1. Introduction Solidification in a high magnetic field is an interesting topic and has attracted much attention of researchers ever since. The experimental research works have demonstrated that high magnetic fields presented a significant influence on solidification. Mikelson and Karklin [1] obtained aligned solidification structure in Al–Ni and Cd–Zn alloys in a 1.5 T magnetic field. Savitsky et al. [2] found that during solidification of a Bi–Mn alloy in a magnetic field the BiMn phase in the alloy aligned along the direction of the magnetic field. Rango [3] extended the investigation to solidification of paramagnetic YBa2 Cu3 O7 material and obtained texture crystal structure in a magnetic field. Katsuk [4] reported that diamagnetic benzophenone crystallized from n-hexane and KCl and BaCl2 crystallized from a solution aligned in a 10 T magnetic field. This alignment behavior has been investigated intensively by several researchers [5–7]. Asai [5] ∗ Corresponding author. Tel.: +86 21 56331102; fax: +86 21 56332939.
E-mail address: [email protected] (Z. Ren). c 2006 Elsevier Ltd. All rights reserved. 0364-5916/$ - see front matter doi:10.1016/j.calphad.2006.03.004
found perpendicular alignment in an Al–Si–Fe alloy during solidification in a strong magnetic field. Texture crystal growth of Bi-2201 [8] and Bi(Pb)2212 [9] have been obtained in a high magnetic field. Segregation of primary silicon in an Al–Si hypereutectic alloy solidified in a high magnetic field was also reported [10]. No mention was made on the influence of magnetic field on flow in the melt, because this is a well known topic. Up to now, nearly all work in this field was on the influence of high magnetic field on kinetics of solidification. From the view of the thermodynamics of phase transformation, the application of high magnetic field in the phase transformation of a material will cause a change in Gibbs energy of the material system by magnetization. This change in Gibbs energy in phase transformation can be expressed as 1G = 1G V + 1G M
(1)
where 1G is the change of Gibbs energy in the phase transformation; 1G V is the change of Gibbs energy due to temperature and pressure; 1G M is the change of Gibbs energy due to magnetization. Further, because the phase transformation temperature is determined by the Gibbs energy,
278
Z. Ren et al. / Computer Coupling of Phase Diagrams and Thermochemistry 30 (2006) 277–285
the temperature of the phase transformation will change due to the magnetization. Based on this point of view, up to now, some work has been performed on the influence of magnetic fields on such solid phase transformation that at least one phase is ferromagnetic, such as the martensitic transformation of steel during heat treatment. Martin et al. [11] have reviewed the investigations about this topic. It was demonstrated that the magnetic field caused the increase of the martensite start temperature by a few degrees due to the decrease in magnetic free energy. Recently, the influence of high magnetic fields on solid phase transformations in the Fe–C system has become one of the focused topics of research. The phase diagram of Fe–C has been analysed with consideration of the influence of magnetic fields. It is shown that the phase diagram was shifted upward so that the Ac1 and Ac3 temperatures increased as the magnetic field was applied [12,13]. The austenite–pearlite transformation [14], austenite–ferrite transformation [15,16], austenite–baintente transformation [17], and recrystalization [18] have also been investigated experimentally. All research work indicated that the magnetic field would change the phase transformation temperature in the Fe–C system. However, up to now, it seems that there is less work on the influence of high magnetic fields on solidification temperature. Peritectic crystalization is one of important melt–solid transformations because quite a lot of metallic materials are peritectic alloys. This phase transformation is diffusioncontrolled, much different from the martensite transformation. Obviously, it is important to learn the behavior of the transformation in the presence of high magnetic field, because possibly the phase transformation can be controlled by means of a magnetic field. Up to now, however, less research, if any, was reported about the influence of high magnetic field on this transformation. Bi–Mn alloys with composition within the range 3%–20%wtMn are peritectic with the peritectic reaction BiMn1.08 (HTP) + L → BiMn (LTP) producing a ferromagnetic phase BiMn. According to the analysis of Ladislav Valko and Marian Valko [19], the influence of magnetic field on phase transformation temperature in this case may be relatively significant. On the other hand, previous work showed that the morphology of BiMn grains solidified with high magnetic field was much different from that of the grains without magnetic field [5]. The mechanism for this difference is still unclear. The aim of this paper is to investigate the influence of high magnetic field on phase transformation temperature and evolution of solidification structure during the peritectic reaction in Bi–Mn alloy experimentally. From the result one can learn more about the influence of high magnetic field on the peritectic phase transformation and other phase transformations with ferromagnetic phases. 2. Experiment The experimental apparatus was as shown in Fig. 1. The superconductor magnet generated a vertical-direction static magnetic field with strength up to 14 T in its room bore.
Fig. 1. Schematic diagram of the experimental apparatus for solidification in a magnetic field. 1 stress gauge, 2 frame, 3 water cylinder, 4 furnace, 5 superconductor magnet, 6 specimen, 7 temperature control system, 8 recorder.
The furnace was set in the room bore of the magnet and the temperature in it could reach 1000 ◦ C. The graphite crucible was hung by a copper wire in the furnace at the position where the magnetic force was the maximum, and the copper wire was connected to a stress gauge. The thermo-couple was inserted in the crucible to detect the temperature of the specimen. All the signals from the stress gauge and the thermo-couple were recorded simultaneously by the recorder. Bi–21%Mn and Bi–6%Mn alloys were investigated in this experiment. According to the phase diagram [20], Bi–21%Mn alloy is composed of a single BiMn phase and, as shown later, is very sensitive to the influence of the magnetic field. Bi–6%Mn alloy is composed of a BiMn phase and α(Bi) phase, and is adapted to observe the influence of the magnetic field on the morphology of BiMn during the peritectic transformation of the alloy. In preparing the alloys, 99.9% pure Bi and 99.9% pure Mn were melted in a vacuum induction furnace and the melt was poured into a graphite mold to speed up the solidification and minimize segregation of composition. The phase transformation temperature was measured in the following way: It is well known that the magnetic force Fm of a substance in a gradient magnetic field is, Fm ≈
dBz χ Bz · . µ0 dz
(2)
Fm —magnetic force per kilogram, N/kg; µ0 = 4π × 10−7 H/m; Bz —magnetic flux in vertical direction, T. χ —the susceptibility of the substance. This equation shows that with a certain magnetic field, that is, the parameter Bz (dBz /dz) is certain, the magnetic force is dependent on the magnetic susceptibility χ of the substance. Usually, the phase transformation will lead to an abrupt change in magnetic susceptibility. So, the magnetic force will change abruptly accordingly during the phase transformation.
Z. Ren et al. / Computer Coupling of Phase Diagrams and Thermochemistry 30 (2006) 277–285
Fig. 2. Distribution of magnetic field.
279
then the specimen was heated up to 380 ◦ C at a rate of 0.25 ◦ C/min and maintained for 30 min, then cooled to below 330 ◦ C at a rate 0.5 ◦ C/min. Meanwhile the force and temperature were recorded. In order to investigate the evolution of the BiMn grains during the peritectic phase transformation, quenching experiments during the cooling or holding at the peritectic temperature of the alloy were carried out to keep at room temperature the morphology of the solidification structure. The specimens such obtained were sectioned and their solidification structures were examined by optical microscopy. Because the Bi–Mn alloy is of magnetic materials, and its magnetic properties are sensitive to changes in solidification structure, the magnetic properties of the alloys were also measured to reveal the influence of the high magnetic field on phase transformation. 3. Results and discussion 3.1. Peritectic phase transformation temperature
Fig. 3. Distribution of parameter Bz · dBz /dz.
As described in Ref. [21], the magnetic susceptibility of Bi–Mn alloy changes abruptly at the occurrence of the peritectic phase transformation, because the BiMn1.08 is paramagnetic and BiMn ferromagnetic. Hence, the magnetic force of the specimen will change responding to the change in the susceptibility. By measuring the temperature of the specimen at which the magnetic force changes abruptly, the phase transformation temperature can be determined. In the measuring experiment with this method, the specimen should be placed at the site where the value Bz (dBz /dz) is the maximum, so that high sensitivity can be achieved. Therefore, distribution of the magnetic field was measured before the experiment, with the result as shown in Fig. 2. Further, the value Bz (dBz /dz) was calculated from this figure, as shown in Fig. 3. It is shown that at the site 8 cm above the center plane of the magnet the value Bz (dBz /dz) was at positive maximum and at the site of 8 cm below the center plane of the magnet at negative maximum. The experimental procedure for measuring the phase transformation temperature was as follows: the alumina crucible with the Bi–Mn alloy specimen was hung at the position where the value Bz (dBz /dz) was at positive maximum and a downward magnetizing force was detected because the alloy is ferromagnetic with positive magnetic susceptibility;
Fig. 4 shows the typical force and temperature curves measured during heating and cooling of the Bi–21wt%Mn alloy and Bi–6wt%Mn alloy, respectively. From the figure one can learn that along with an increase of the temperature, the force decreased gradually at first, and at a certain temperature the force dropped abruptly to its minimum. This indicated the occurrence of the reaction BiMn → BiMn1.08 + L at this temperature. Afterwards, further increasing temperature up to 380 ◦ C did not cause any apparent change in the force. During cooling from 380 ◦ C, the force increased abruptly at a certain temperature, indicating the occurrence of the peritectic phase transformation BiMn1.08 + L → BiMn. The results showed that this method was very sensitive and adept for detecting the occurrence of the phase transformation. In the case of Bi–6%Mn alloy, this phenomenon was also apparent, and the phase transformation temperature detected by this method was the same as that of Bi–21%Mn alloy, even though the force value was minimized. For example, as shown in Fig. 4, with 10 T field the measured transformation temperatures for both alloys were 375 ◦ C in heating up, and 362 ◦ C in cooling down. Therefore, Bi–21%Mn alloy was chosen for measuring the transformation temperature in detail, because its change in force during the phase transformation was sharper. Fig. 5 shows the results of measuring the peritectic phase transformation temperature. Two lines are presented in Fig. 5, one is for heating up of the alloy and the other for cooling. As can be seen, the phase transformation temperature increased linearly along with the increase of the magnetic field. From the phase diagram [20], it is shown that in cooling down of the Bi–21wt%Mn alloy the peritectic transformation temperature is 340 ◦ C and in heating up the reaction BiMn → BiMn1.08 + L occurs at 355 ◦ C. Therefore, the phase transformation temperature for heating up is higher than that for cooling down. No matter whether heating or cooling, more than 20 ◦ C increment in the phase transformation temperature was produced in the 10 T magnetic field.
280
Z. Ren et al. / Computer Coupling of Phase Diagrams and Thermochemistry 30 (2006) 277–285
Fig. 4. Typical measuring curves of force and temperature during heating and cooling of Bi–Mn alloy in a magnetic field. B = 10 T. (a) Bi–21%Mn alloy, (b) Bi–6%Mn alloy. (1) force; (2) temperature; T1 —temperature starting transient of the force during cooling, T2 —temperature starting transient of the force during heating.
Besides, both analyses only dealt with the structural-change phase transformation, not the diffusion-controlled transformation, such as peritectic transformation in this experiment. In order to understand the influence of magnetic field on peritectic phase transformation with ferromagnetic transformed phase, the thermodynamics of the phase transformation under magnetic field should be analyzed. As we know, the magnetization energy Um is [22] Hex
Z Um = −
µ0 M dHeff
(4)
0
Fig. 5. The influence of the high magnetic field on the peritectic transformation temperature of Bi–Mn alloy. 1—cooling from 380 ◦ C to below 340 ◦ C, 2— heating from below 340–380 ◦ C.
It is well known that magnetic field will increase the starting point of the martensite reaction, and the increment of the starting point is proportional to the magnetic field [11]. However, Ladislav Valko and Marian Valko [19] gave a different formula in their analysis on the influence of magnetic field on the melt–solid phase transformation of pure iron, T − T0 = 1T =
T0 H2 1Hs0
(3)
where 1HS0 is the enthalpy, and H is the intensity of the magnetic field. Our result showed a roughly linear relationship between magnetic field and increment of phase transformation temperature, in agreement with the analysis of Ref. [11].
where M is the magnetic moment; Hex is the imposed magnetic field. Heff is the magnetic field inside the substance; and µ0 is the vacuum magnetic permeability, 4π × 107 H/m. In the peritectic transformation BiMn1.08 (HTP) + L → BiMn (LTP), BiMn1.08 and L are non-ferromagnetic, and BiMn ferromagnetic. For the non-ferromagnetic substance BiMn1.08 , M = χα Heff
(5)
Heff = Hex − Nα M
(6)
Hex = (1 + Nα χα )Heff
(7)
where χα is the magnetic susceptibility of the BiMn1.08 ; and Nα is the demagnetizing coefficient due to the shape of a BiMn1.08 grain. Combining Eq. (3) through (7) yields Umα = −
µ0 χα H2 . 2(1 + Nα χα )2 ex
(8)
This equation shows that the magnetization energy is 2. proportional to χα and Hex
281
Z. Ren et al. / Computer Coupling of Phase Diagrams and Thermochemistry 30 (2006) 277–285
T2 − T1 =
1 2µ0 Ms Hex − 2 1 − 2(1 + Nβ χβ )2
β
µ0 Ms Hs + β
µ0 χ L µ0 χ α 2 Hex + H2 2 2(1 + Nα χα ) 2(1 + χ L )2 ex
(S A − S αA ) + (S A − S AL ) + R ln
β
(a A )2 a αA a AL
Box I.
Fig. 6. Microstructure of Bi–6%Mn alloy quenched at different temperatures in cooling from 400 ◦ C. (a) Quenching at 380 ◦ C, (b) quenching at 345 ◦ C, (c) quenching at 340 ◦ C, (d) quenching at 335 ◦ C.
For the diamagnetic liquid Bi, a similar equation can be obtained µ0 χ L UmL = − H2 . (9) 2(1 + χ L )2 ex For the ferromagnetic substance BiMn (|χβ | 1) the approximate expression of U f can be obtained with the assumption that M is saturated at magnetic intensity HS Z Hex Umβ = − µ0 M dHeff 0
Hs
Z =− 0
µ0 χβ Heff dHeff −
Z
Hex
µ0 Ms dHeff
Hs
1 = −µ0 Ms Hex + 1 − 2(1 + Nβ χβ )2
µ0 Ms Hs .
β
µ A = µ A0 + RT1 ln α A µ LA
=
µ LA0
+
(11)
RT1 ln α AL .
With magnetic field, the phase transformation temperature changes to T2 and the chemical potentials are, µαA = µαA0 + S αA (T2 − T1 ) + RT2 ln α αA + Umα β
β
β
2µ0 Ms Hex β
β
(S A − S αA ) + (S A − S AL ) + R ln
β
(a A )2 a αA a AL
.
(13)
This equation indicates that the linear relation holds between the change in transformation temperature and magnetic field, as found from the experimental result shown in this experiment and the analysis of Ref. [11]. From this analysis, one can also learn that in the case of no ferromagnetic phase in the phase transformation, the change in the transformation temperature is 2 , the same as Ladislav Valko and Marian proportional to Hex Valko’s analysis [19]. 3.2. Microstructure of BiMn grain
µαA = µαA0 + RT1 ln α αA β
T2 − T1 ≈
(10)
The chemical potentials for these phases in the state of equilibrium at the peritectic temperature T1 without magnetic field are, β
µ0 χ L 2 and 2(1+χ 2 Hex , because the BiMn phase is ferromagnetic. L) Hence the equation is simplified as,
β
µ A = µ A0 + S A (T2 − T1 ) + RT2 ln α A + Umβ
(12)
µ LA = µ LA0 + S AL (T2 − T1 ) + RT2 ln α AL + UmL where µ is the chemical potential; S is the entropy; R is the universal gas constant; subscript A represents component A; and subscripts α, β, and L represent HTP, LTP and liquid phase, respectively. From these equations, considering the equilibrium among HTP, LTP, and liquid phases, the equation in Box I is deduced. In a strong magnetic field with the strength much larger than µ0 χα the saturation point, µ0 Ms Hex µ0 Ms Hs , 2(1+N H2 , χ )2 ex α α
Fig. 6 shows the microstructures of Bi–6%Mn alloy specimens obtained by quenching at various temperatures during cooling from 400 ◦ C without the magnetic field, which reveals the change in morphology of BiMn grains before and after the peritectic transformation. As shown, above 345 ◦ C the BiMn grains were block like, owing to the cubic crystal structure [21] (in fact, this phase is BiMn1.08 , and called HTP). Below 340 ◦ C the grains were flakes, due to its hexagonal crystal structure (called LTP). The change in morphology indicated that the reaction BiMn1.08 + L → BiMn occurred between 345 and 340 ◦ C, in agreement with the phase diagram of this alloy. Fig. 7 shows the results of the quenching experiment with 10 T field and various temperatures. One can learn that at 380 ◦ C, the morphology of the primary BiMn grains was block like, the same as that without a magnetic field (Fig. 6), and no alignment of grains took place. At 360 ◦ C, some “saw teeth” on the edge of the block grain and a small number of flake grains appeared, indicating the starting of the phase transformation. At 345 ◦ C, the grains were all flakes and aligned along the direction of the field, showing the achievement of the phase transformation. Further, the alignment behavior of the grains below 360 ◦ C was the same as that of the ferromagnetic
282
Z. Ren et al. / Computer Coupling of Phase Diagrams and Thermochemistry 30 (2006) 277–285
Fig. 7. Microstructure of Bi–6%Mn alloy quenched at different temperatures in 10 T field in cooling from 400 ◦ C. (a) 380 ◦ C, perpendicular (b) 380 ◦ C, parallel, (c) 360 ◦ C, perpendicular (d) 360 ◦ C, parallel (e) 355 ◦ C, perpendicular (f) 355 ◦ C, parallel (g) 345 ◦ C, perpendicular (h) 345 ◦ C, parallel.
Fig. 8. Microstructures of the specimens quenched with different maintaining time at 340 ◦ C after cooling from temperature 400 ◦ C. B = 0 T. The maintaining time was (a) 30 s; (b) 60 s; (c) 120 s; (d) 10 h.
BiMn grains described in reference [5]. This means that phase transformation BiMn1.08 + L → BiMn took place and the BiMn grains became ferromagnetic at 360 ◦ C, the same as the above experimental result of measuring the phase transformation temperature. 3.3. Evolution of BiMn grains during peritectic transformation In order to deeply understand the mechanism of the peritectic transformation under high magnetic field, the following experiment was carried out: the alloy was heated to 400 ◦ C and held for 30 min for homogenizing, then it was cooled to the phase transformation temperature determined by the previous experiments (i.e., 340 ◦ C in the case of no magnetic field and 360 ◦ C in the case of imposing a 10 T magnetic field). After a certain time of maintaining this temperature, the specimen was quenched, with the results shown in Figs. 8 and 9. Fig. 8 shows that during the phase transformation without magnetic field some “saw teeth” of MnBi appeared firstly on the edge of the Bi Mn1.08 block, and gradually the “saw teeth” grew to flakes and separated each other, further the flakes coarsened and kept this shape even with 10 h holding at this temperature. With 10 T field, as shown in Fig. 9, the MnBi “saw teeth” also appeared on the edge of the Mn1.08 Bi block at first, then grew to flakes and separated each other. However, with holding time over 5 min at this temperature the flakes were gradually split into small blocks in the perpendicular direction of the field, and the distribution of the small blocks got more uniformly with their separation from each other. Besides, the small blocks
aligned along the direction of the field, resulting in rod-like structure. It is well known that BiMn (LTP) is hexagonal in crystal structure with a single easy magnetizing axis ch001i and BiMn1.08 (HTP) is cubic [23]. Elongating the c axis 3% and contracting the a and b axes of cubic BiMn1.08 crystal will produce hexagonal BiMn crystals. In the presence of a magnetic field, the magnetizing force on the grain is [24] 2 F = −µ0 χ Hex .
(14)
This force promotes the phase transformation BiMn1.08 (HTP) + L − BiMn (LTP) by elongating the c axis and contracting the a and b axes. Accompanying the peritectic phase transformation of the alloy, its magnetic characteristics changed from paramagnetic to ferromagnetic. By measuring the change in magnetic properties of the alloy, the phase transformation can be detected and furthermore the effect of the magnetic field can be discovered. Fig. 10 are the hysteresis loops of the same specimens as shown in Fig. 9. One can learn that for the specimens quenched at 360 ◦ C in the field, the magnetization along the direction of the high magnetic field applied during solidification was easier with larger saturation moment than that in the perpendicular direction of the field, suggesting strong anisotropic characteristics. This is due to the orientation and alignment of the BiMn crystals with their easy axes in the direction of the magnetic field. It is interesting to notice that the specimens quenched after briefly cooling to 360 ◦ C possessed
Z. Ren et al. / Computer Coupling of Phase Diagrams and Thermochemistry 30 (2006) 277–285
283
Fig. 9. Microstructures of the specimens quenched with different maintaining time at 360 ◦ C after cooling from temperature 400 ◦ C. B = 10 T. The maintaining time was (a) 30 s; (b) 60 s; (c) 90 s; (d) 120 s; (e) 5 min; (f) 10 min; (g); 20 min; (h) 60 min.
some extent of coercivity, and along with increasing holding time at 360 ◦ C, the coercivity decreased remarkably, with an apparent increase in the magnetic permeability (the slope of the magnetizing curve) of the alloy. This means that the alloy became softer in magnetism. Because the alloy is composed of Bi and BiMn phases, and the Bi phase is diamagnetic, the magnetic properties of the alloy are determined mainly by the BiMn phase. Therefore, from the above results on the evolution of the BiMn structure during holding at this temperature and the change in the magnetic properties, one can learn that along with the splitting and separation of the flakes in the perpendicular direction of the field, the magnetic characteristics of the BiMn phase were transformed to soft magnetism. From the physics of magnetism, during magnetization the magnetic domains in the substance will rotate their easy axis towards the magnetic field and grow by moving their walls. The grain boundary and stress will retard the rotation and movement of the domains and cause large coercivity and small permeability. Therefore, the result of Fig. 9(a) indicates the presence of grain boundary and stress. The decrease in coercivity and increase in permeability with duration of the holding time (Fig. 9(b)–(d)) indicates the disappearance of the grain boundary and stress due to the splitting of the flakes and separating of the small blocks (Fig. 8). As we know, during the peritectic phase transformation ferromagnetic BiMn (LTP) several grains will nucleate on separated sites on the surface of one paramagnetic BiMn1.08 (HTP) block, as schematically shown in Fig. 11. In the high magnetic field, the LTP grains will be magnetized, and their same-name magnetic poles will be in the same direction. This results in repulsive forces among them, and stresses are generated in the grains, which resulted in the coercivity of the
alloy because the stresses retard the moving of the domain walls during magnetizing. The repulsive force is [25] µ0 (χ + 1) Q m1 Q m2 (15) 4π r2 where Q m1 , Q m2 are the magnetic poles. Along with growth of the LTP grains, their volumes increased and the inter-grain distances decreased. Therefore, according to the formula (14), the repulsive forces increased significantly. Even though the forces may break the particle, more likely the force promotes the dissolution of the boundary between the grains in the block and cause splitting and separation of the BiMn grains. The splitting and separation of the grains caused the release of the stresses in the grains, so the coercivity of the alloy decreased and the permeability increased. The repulsive forces among the separated grains repelled each other, and finally a force balance was established among the grains, resulting in uniform distribution of the grains. From this mechanism, one can get the conclusion that imposing a high magnetic field during phase transformation in which a ferromagnetic phase is included may induce stresses in it by the magnetizing force. It was reported that cracks occurred frequently during unidirectional solidification of TbDyFe in a strong magnetic field [26]. This may be attributed to the mechanism presented here because this magnetic alloy endures peritectic transformation during solidification. FM =
4. Conclusion 1. Applying a high magnetic field leads to increasing temperature of the peritectic transformation BiMn1.08 + L − BiMn in Bi–Mn peritectic alloys. With 10 T magnetic field, the temperature can increase more than 20 ◦ C.
284
Z. Ren et al. / Computer Coupling of Phase Diagrams and Thermochemistry 30 (2006) 277–285
Fig. 10. Hysteresis loops for the specimens shown in Fig. 9 with various holding times at 360 ◦ C. (A) About 30 s, (B) 10 min, (C) 20 min, (D) 60 min. “Parallel and perpendicular ” indicate directions of the magnetization measurement with respect to the magnetic field imposed during the solidification.
Z. Ren et al. / Computer Coupling of Phase Diagrams and Thermochemistry 30 (2006) 277–285
285
Fig. 11. Schematic showing of the splitting of BiMn grains during peritectic phase transformation of Bi–6%Mn alloy in 10 T magnetic field. (a) Generation of magnetizing forces among the ferromagnetic BiMn grains (LTP) in the magnetic field, (b) the increase of the magnetizing forces along with growth of the BiMn grains, (c) separation of the grains.
2. It is found that by imposing a high magnetic field during the peritectic transformation of Bi–Mn alloy, splitting and separation of the BiMn flakes may occur, resulting in small blocks instead of flake grains of the BiMn phase. The repulsive force among the peritectic BiMn grains is generated due to the magnetization during the phase transformation. The force will cause splitting and separation of the grains in the direction perpendicular to the magnetic field. Hence, the grains are refined and distributed uniformly. It is suggested that the precipitation of ferromagnetic phase during phase transformation in the magnetic field will result in stress in the grains. 3. By detecting the magnetizing force in a gradient magnetic field, it is possible to measure the phase transformation temperature. Acknowledgments This work is supported by Natural Science Foundation of China (No. 50234020, 50225416 and 59871026) and the Science and Technology Committee of Shanghai (04DZ14002). References [1] A.E Mikelson, Y.K. Karklin, J. Cryst. Growth 52 (1981) 524. [2] E.M. Savitisky, R.S. Torchinova, S.A.J. Turanoy, J. Cryst. Growth. 52 (1981) 519.
[3] P.D. Rango, M. Lee, P. Lejay, A. Sulpice, R. Tournier, M. Ingold, P. Germi, M. Pernet, Nature 349 (1991) 770. [4] A. Katsuki, R. Tokunaga, S.I. Watanabe, Chem. Lett. (8) (1996) 607. [5] H. Wang, Z.M. Ren, K. Deng, Acta Metall. Sin. 38 (2002) 41. [6] H. Yasuda et al., Mater. Trans. JIM 44 (2003) 2550–2554. [7] H. Morikawa, K. Sassa, S. Asai, Mater. Trans. JIM 139 (1998) 814–818. [8] X.Y. Lu et al., Physica C: Supercond. Appl. 382 (2002) 27–32. [9] W.P. Chen et al., J. Cryst. Growth 204 (1999) 69–77. [10] K. Sassa, H. Morikawa, S. Asai, J. Japan Inst. Met. 61 (1997) 1283. [11] J.W. Martin, R.D. Doherty, B. Cantor, Stability of Microstructure in Metallic Systems, 2nd ed., Cambridge University press, 1997, p. 391. [12] H.D. Joo, S.U. Kim, N.S. Shin, Y.M. Koo, Mater. Lett. 43 (2000) 225–229. [13] H.D. Joo, J.K. Choi, S.U. Kim, N.S. Shin, Y.M. Koo, Metall. Mater. Trans. A 35 (2004) 1663–1668. [14] S. Michio, Mater. Trans. JIM 44 (2003) 2524–2528. [15] X.J. Hao, H. Ohtsuka, Mater. Trans. JIM 45 (2004) 2622–2625. [16] H. Ohtsuka, Y. Xu, H. Wada, Mater. Trans. JIM 41 (2000) 907–910. [17] H. Ohtsuka, Curr. Opin. Solid State Mater. Sci. 8 (2004) 279–284. [18] Y. Zhang, N. Gey, C. He, X. Zhao, L. Zuo, Acta Materialia 52 (2004) 3467–3474. [19] L. Valko, M. Valko, IEEE Trans. Magn. 30 (2) (1994) 1122. [20] W.G. Moffatt, The Handbook of Binary Phase Diagrams, Genium, USA, 1984. [21] T. Chen, W.E. Stutius, IEEE Trans. Magn. 10 (1974) 581–586. [22] H. Morikawa, K. Sassa, S. Asai, Mater. Trans. JIM 39 (1998) 814–818. [23] A.U. Seybolt, H. Hansen, B.W. Roberts, P. Yurcisin, Trans. AIME. J. Metal (May) (1956) 606. [24] D.F. Wan, S. Luo, Physics of Magnetism, Electronic Industry Press, Beijing, 1987, p. 8 (in Chinese). [25] E. Hallen, Electromagnetic Theory, Chapman & Hall Ltd., London, 1962, p. 185. [26] H. Minagawa et al., J. Magn. Magn. Mater. 248 (2002) 230–235.