The Control of Crystal Orientation in Non-magnetic Metals by Imposition of a High Magnetic Field

Transcription

1 ISIJ International, Vol. 43 (3), No. 6, pp The Control of Crystal Orientation in Non-magnetic Metals by Imposition of a High Magnetic Fiel Tsubasa SUGIYAMA, Masahiro TAHASHI, Kensuke SASSA 1) an Shigeo ASAI 1) Grauate Stuent of Nagoya University, Furo-cho, Chikusa-ku, Nagoya Japan. 1) Dept. of Materials Processing Engineering, Grauate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya Japan. (Receive on November 9, ; accepte in final form on January 8, 3 ) High magnetic file can affect not only ferromagnetic materials but also non-magnetic ones. In general, materials have a crystal magnetic anisotropy where a magnetic susceptibility is ifferent in each crystal irection. So that the utilization of this property can control the crystal orientation by imposition of the high magnetic fiel. Up to now, the possibility of magnetic orientation by imposition of the high magnetic fiel has been stuie, it was sai that existence of crystal magnetic anisotropy an a low viscosity are essential. Then, substance which has crystal magnetic anisotropy can control the crystal orientation by heating up to liqui an soli zone which is a low viscosity. It is foun that the high magnetic fiel can control the crystal orientation of Zinc or Bismuth Tin alloy, nonmagnetic material, by reheating in a soliification process. These experimental results can be explaine by taking into account of a magnetic energies ue to the crystal magnetic anisotropy. An, we iscuss a theoretical analysis on the magnetic rotation of non-magnetic metal crystals by taking account of Lorenz force which acts in of molten metals. KEY WORDS: high magnetic fiel; crystal orientation; soliification process; non-magnetic material. 1. Introuction Recently, thanks to the superconucuting technology, it has become possible to get a high magnetic fiel with relatively wie space even in a small-scale laboratory. By using a high magnetic fiel, a lot of new phenomena an functions have been foun, giving us useful hints for creating new materials so that a new science an technical fiel calle Materials Science of a High Magnetic Fiel, 1) can be expecte to emerge. Uner a high magnetic fiel, various magnetic effects become tangible in not only ferromagnetic materials but also non-magnetic ones such as paramagnetic an iamagnetic, on which the effect of a magnetic fiel has been consiere to be negligible hitherto. The magnetization force resulte from a magnetic fiel is classifie into two kins. One is known as the force in which a magnet pulls ferromagnetic an paramagnetic materials an repels iamagnetic ones an the other as the force in which materials are rotate to a magnetic fiel irection, such as a compass rotating to the north irection ue to the earth magnetic fiel. The former force is mainly usable for magnetic separations, ) magnetic levitations 3) an measurements of magnetic susceptibility of materials. ) The latter is applicable for alignment of crystal orientations an texture structures on the basis of susceptibility ifference ue to crystal an shape magnetic anisotropies. It is important that these two functions work in not only magnetic materials but also non-magnetic materials uner a high magnetic fiel. Especially, a large number of materials have the crystal magnetic anisotropy where the magnetic susceptibility is ifferent in each crystal irection so that they may have the possibility to align to a preferre irection. Since the material properties strongly epen on their crystal orientations, controlling of them may provie an improvement of material characteristics. Therefore, the possibility of magnetic transportation an rotation of non-magnetic materials has been examine uner several processes such as soliification, 4) electro-eposition, 5) vapereposition 6) an soli phase reaction. 7) Now the application of a high magnetic fiel has been recognize as one of the useful technologies in materials processing. In the soliification process of metals, Mikelson et al. 8) reporte that the macrostructure of Al Cu an C Zn alloys, which are non-magnetic materials, aligne to the magnetic fiel irection uring soliification. However, etails on the metho for evaluating the orientations of crystals an textures are not clearly written in this report. Yasua et al. 9) reporte that the crystal orientation of a BiMn alloy, which is a ferro-magnetic material, aligne to the magnetic fiel irection by heating the specimen which was prepare by rapi quenching, up to a liqui soli zone in the magnetic fiel. In this research, a metho is propose where the crystal orientation of non-magnetic metals can be aligne in the soliification process without any nee for pre-processing. Such a metho has not been raise up hitherto. Further ISIJ

2 ISIJ International, Vol. 43 (3), No. 6 more, the theoretical analysis on the rotation of polymer fibers which is theoretically one by Yamato et al. 1) is extene to the rotation of non-magnetic metal crystals by taking account of the Lorenz force which acts in molten metals.. Theory.1. Crystal Orientation Control by Magnetic Fiel When a non-magnetic substance is magnetize in a magnetic fiel, the energy for magnetization of the substance is given by Eq. (1). U B / µ MB...(1) in which M is the magnetization, B an B in are the impose magnetic flux ensity an the magnetic flux ensity in the substance, respectively an m is the permeability in vacuum (4p 1 7 [H/m]).The principle of crystal orientation using a magnetic fiel is that a torque rotates a crystal to take a stable crystal orientation so as to ecrease the magnetization energy. Both zinc an bismuth have a hexagonal crystal structure with a magnetic anisotropy where the magnetic susceptibility is ifferent in each crystal irection. The magnetic susceptibilities along a- or b-axis an c-axis of zinc are c a,b [ ], c [ ], 11) an those of bismuth are c a,b [ ], c [ ], 1,13) respectively. The value of the magnetization energy given by Eq. (1) etermines the preferre crystal irection epening on the magnetic susceptibility of each crystal axis. χ U B...() µ ( 1 Nχ) where N is the emagnetization factor. When crystals are set in a magnetic fiel, the crystals ten to align to the preferre crystal irection. Substituting values of the magnetic susceptibility of zinc an bismuth into Eq. (), we get U c U a,b in the case of zinc an U a,b U c in the case of bismuth. These results tell that c-axis of zinc crystal an a- or b-axis of bismuth are the preferre irections in parallel to the magnetic file irction, as shown in Fig Rotation of Crystal..1. Magnetic Torque The rotation of a crystal particle arises from the torque cause by the impose magnetic fiel. When the particle is precipitate in a melt, the magnetization M arises in it ue to the impose magnetic fiel an the torque cause by the crystal magnetic anisotropy works on the particle. The theoretical expression of the magnetic torque T is erive as follows. A non-magnetic particle is place uner a magnetic fiel in x y coorinate, as shown in Fig., where x-axis is efine to be the irection of an easy magnetization axis with the magnetic susceptibility c 1 an y-axis is efine to be the irection of a ifficult magnetization axis with the magnetic susceptibility c, an the angle between x-axis an the impose magnetic fiel irection is q. Then the impose in Fig. 1. The preferable crystal orientation in zinc an bismuth crystal uner a magnetic fiel. Fig.. Fig. 3. Coorinate. Coorinate. magnetic flux ensity is expresse by Eq. (3). B B cos q i x B sin q i y...(3) The magnetization M arise in the particle is escribe by Eq. (4). M c 1 B cos q i x c B sin q i y...(4) Therefore, the magnetic torque T that acts on volume V of the particle is erive as Eq. (5). M B V( χ T 1 χ) B sin θ V i z...(5) µ µ Hence, the z-component of the magnetic torque T is obtaine as Eq. (6) T 1 VDχB sin θ...(6) µ where Dc c 1 c.... Lorenz Force In the coorinate system shown in Fig. 3, let the particle 3 ISIJ 856

3 ISIJ International, Vol. 43 (3), No. 6 that is place in (r, j, q) rotate in the xy-plane, where x-axis is the irection of the impose magnetic fiel. The impose magnetic flux ensity B, the rotation velocity v of the particle an the rotation raius a are expresse as follows: B Bi x...(7) v r sin θ sin φ θ ix r cos θ sin φ θ iy...(8) a r cos q sin f i x r sin q sin f i y...(9) When an electrically conuctive substance rotates in a magnetic fiel, the current which is inuce ue to the interaction of rotational motion an a magnetic fiel, is given as Eq. (1). J σv B σbr cos θ sin φ θ iz...(1) Then, Lorenz force as an electromagnetic force is inuce by the interaction of the current an the given magnetic fiel. The force that acts on the particle to suppress its rotation is given by Eq. (11). F σ J B Br θ φ θ cos sin iy...(11) Then, the torque cause by Lorenz force is erive as Eq. (1). a σ F θ φ θ Br cos sin iz...(1) If the particle shape is assume to be spherical, the torque L that acts on the particle with a raius r is obtaine as Eq. (13) by integrating Eq. (1) over the particle volume. L σ B r θ φ θ cos sin V 4 θ 5 πr σb...(13) Equation of Rotational Motion When a particle rotates in a liqui, the liqui viscosity inuces a rotating torque R that prevents its rotation θ 3 R 8πηr...(14) where h is the viscosity. Consiering the three torques escribe above, the equation of a rotational motion cause by a magnetic fiel is given as Eq. (15). θ 5 ρr R L T...(15) 5 Substituting Eqs. (6), (13) an (14) into Eq. (15), Eq. (16) is erive θ θ 4 θ ρr 8πηr πr σb 5 15 (Inertia force) (Viscous force) (Lorenz force) (Magnetization force) sin θ...(16) The ratio of the inertia force term to the sum of the viscous force an the Lorenz force terms can be approximately expresse as Eq. (17) 8πηr I θ 3ρr...(17) r B θ 4 θ π ( 3η r σb ) t π σ 15 where t shows a characteristic time. By substituting the physical properties of zinc (r [kg/m 3 ], h [N s/m ], s [1/W m]) into Eq. (17), the interval in which the inertia force term preominantly works uner the B 1T is evaluate as 1 4 s when the particle raius is 1 mm, an 1 6 s when the particle raius is 1 mm. Thus, the inertia term can be neglecte an Eq. (16) is more simplifie to Eq. (18). 8πηr 1 µ 3 5 θ 4 θ π 3 πr σb r DχB sin θ 15 3µ 3 5 The solution of Eq. (18) is given as Eq. (19) VDχB...(18) t 3η r σb tan θ tan θ exp τ τ, 5DχB...(19) where q is an angle between the impose magnetic fiel an the easy magnetization axis at t. The imensionless numbers of T*, a an b are efine as followings. t r σb 5ρ χ T *,, r α β D ρ 3η µησ η By using the above imensionless numbers, Eq. (19) is expresse as Eq. (). tan θ β tan θ exp T * 1 α...() If the initial angle at time t is q 9, the particle will not rotate forever so that the initial angle is given as q 89. By using Eq. (), the rotation time is efine as the interval time that it takes for the particle to rotate from q 89 to q 1. The angle of 1 is consiere to be substantially zero. The relations between the interval time an imensionless numbers of a an b are shown in Figs. 4(a) an 4(b). The relations between the magnetic flux ensity an the rotation time are shown in Fig. 5. It is unerstoo that the particle finishes rotating within one secon when a magnetic fiel of more than 1T is impose, an the rotation time ecreases with increasing the magnetic flux ensity. The relations between the particle raius an the rotation time are shown in Fig. 6. It is unerstoo that the rotation time ecreases with ecrease of the particle raius. If µ ISIJ

4 ISIJ International, Vol. 43 (3), No. 6 (a) Fig. 7. Relations between imensionless number A an raius. (b) Fig. 4. Relations between angle an rotation time. Fig. 8. Schematic view of experimental apparatus. Fig. 5. Relations between angle an rotation time. B 1 T, the rotation time oes not epen on the particles with a raius less than 1 5 m. This result can be interprete from Eq. (18) as the following. The Lorenz force term is a function of five powers of the raius an the viscous force an the magnetization force terms are a function of three powers of the raius, respectively. Thus, the Lorenz force term becomes preominant an the rotation time epens on the raius substantially when the particle raius is large, but the Lorenz force is negligible when the particle raius becomes small. This is the reason why the epenence of the rotation time on the particle raius becomes small when the viscous force an the magnetization force terms have the same powers of the particle raius. A efine as the ratio of the viscous force term to the Lorenz force term in Eq. (18) is given by Eq. (1). A 8πηr 3 4 πr σb η r σb...(1) By substituting h [N s/m ] an s [1/W m] which are the physical properties of metals into Eq. (1), the particle raius is evaluate as 5 mm at which the viscous an the Lorenz force terms give the same contribution uner B 1 T. The viscous force term becomes preominant for the particles with raii less than 5 mm as shown in Fig. 7. Fig. 6. Relations between rotation time an raius. 3 ISIJ 858

5 ISIJ International, Vol. 43 (3), No. 6 Fig. 9. X-ray iffraction patterns of zinc film reheate uner the conitions without an with the magnetic fiel set perpenicular to the sample plane. Fig. 11. Schematic view of experimental apparatus. Fig. 1. X-ray iffraction patterns of zinc film reheate uner the conitions without an with the magnetic fiel set parallel to the surface of substrate. 3. Experiment 3.1. Zinc Film Experiment Figure 8 shows the schematic view of the experimental apparatus. A water-coole pipe was inserte in the bore of a superconucting magnet, an an alumina crucible with a heater was set insie the pipe. A zinc film (1 8 mm ) prepare by ipping a steel plate in a molten zinc bath was set on a stainless steel pipe, which was inserte from the upper part of the magnet bore. The sample plane was ajuste at the position with the maximum magnetic flux ensity in the irection parallel or perpenicular to the magnetic fiel. A thermocouple was inserte through the miair part of the stainless steel pipe, an the temperature of the sample was measure by the thermocouple connecte with the plane. The crucible was fille with argon gas to prevent the oxiation of the sample an the temperature was kept in liqui soli zone of zinc for 3 min. The furnace was then coole own by shutting off the heater Results an Discussion The X-ray iffraction patterns of the sample on which the magnetic fiel was impose in perpenicular irection are shown in Fig. 9. The peak of (11) plane was etecte stronger in the sample obtaine uner no magnetic fiel. On the other han, when a magnetic fiel of 1 T was impose, the peak of (11) ecrease, an the peak of () equivalent to c-plane appeare stronger. The X-ray iffraction patterns of the sample on which the magnetic fiel was impose in parallel irection are shown in Fig. 1. The peak of (11) etecte stronger in the sample obtaine uner no magnetic fiel, similar to the previous result shown in Fig. 9. However, when a magnetic fiel of 1 T was impose, the peak of (11) ecrease, an the peak of (1) equivalent to a, b-plane appeare stronger. That is, regarless of the imposing irection of the magnetic fiel, the zinc crystals aligne to the irection estimate from the viewpoint of the magnetization energy. The magnetic orientation works only when the magnetization energy is larger than a thermal energy kt. 14) This conition can be escribe as Eq. () Dχ V B kt µ...() where k is Boltzmann constant. The conition that a particle raius shoul be larger than nm is erive from Eq. () by using physical properties an experimental conitions aopte in this experiment. The other han, if a rotation time is assume to be one secon, the particle raius is evaluate as less than 1 mm from Eq. (19). Therefore, the particle raius of zinc that is expecte from the magnetization energy an the equation of motion is the range from nm to 1 mm. 3.. Bismuth Tin Bulk Alloy Experiment Bismuth 5mass% tin alloy, which is an eutectic alloy, was use as the specimen. Figure 11 shows the schematic view of the experimental apparatus. The specimen was heate up to 3 C in argon atmosphere at the rate of 3 C/h, an kept for 3 min. Then it was coole own to 55 C at the rate of 18 C/h, an stirre at 55 C for 3 min an then coole to the room temperature in the furnace. The specimen was cut in the irection perpenicular to that of the magnetic fiel an its surface was polishe to examine the crystal structure by use of XRD ISIJ

6 ISIJ International, Vol. 43 (3), No. 6 stable in the irection of the magnetic fiel, the tips of enrite arms isperse in the molten metal align to the magnetic fiel irection an grow. However, the preferre crystal orientation for the magnetic fiel irection is perpenicular to that of the heat flow from the mol wall so that all of the crystals can not align to the magnetic fiel irection. By taking the same proceure mentione in Sec. 3.1., the particle raius of bismuth that is expecte from the magnetization energy an the equation of motion is the range from 1 nm to 1 mm. Fig. 1. Fig. 13. X-ray iffraction patterns of bismuth 5mass%Tin alloy. Relations between facial angle an magnetic flux ensity Results an Discussion The X-ray iffraction patterns of bismuth tin alloy are given in Fig. 1. The peak of (n) scarcely appeare in the case of T, but the peaks of a,b-plane (hk) an (1) increase in the case of 1 T. This result agrees with the theoretical estimation mentione in Sec..1. A metho to evaluate the egree of crystalline orientation from the intensity of X-ray iffraction lines obtaine by X-ray iffraction analyzer (XRD) is propose here as given in Eq. (3). θf ( Ihkl θ hkl ) I...(3) where q F is efine as the facial angle measure from c- plane, q hkl is the facial angle between (hkl) an (n) planes, I hkl is the intensity of (hkl) plane obtaine from the X-ray iffraction pattern. The facial angle q F is reuce to when all crystals are oriente to c-plane an to 9 when oriente to a,b-plane. The facial angle of bismuth crystal is shown in Fig. 13. In the case of T, the bismuth crystal tilte only 4 from the c-plane. The reason coul be explaine as follows; as the alloy soliifies inwar from mol wall, a, b-axis, which is the priority growth orientation, grows in the parallel irection to the heat flow. On the other han, in the case of 1 T, the crystal incline to 6. This result agrees with the theoretical preiction. However, it is not 9 corresponing to the case where all crystals aligne to the magnetic fiel irection. This experimental result can be attribute to interruption cause by heat flow as follows; tips of enrite arms that grow from the mol wall break off by agitation an isperse in the molten metal. As the a,b-axis of the crystal corresponing to the priority growth orientation is hkl 4. Conclusion The control of crystal orientation by imposition of a magnetic fiel has been stuie through experimental an theoretical works. The following results have been obtaine. (1) The equation of motion for a particle rotating in a molten metal uner the imposition of a magnetic fiel has been erive. An analytical solution is obtaine uner the conition of neglecting the inertia force term. () It takes less than one secon for a particle to rotate to the irection of an easy magnetization axis uner a magnetic fiel of 1 T. A metho for crystal orientation of non-magnetic materials which oes not nee any preprocessing has been propose an the usefulness of the metho is shown through experiments. The following results were obtaine. (a) When a zinc film which was prepare by ipping a steel plate in zinc bath was heate up to a soli liqui zone uner the magnetic fiel, the orientation of zinc crystals in the film coul align. (b) When a bismuth tin bulk alloy was heate up to a soli liqui zone uner the magnetic fiel, the orientation of bismuth crystals coul align. Acknowlegement This research was partially supporte by the Ministry of Eucation, Culture, Sports, Science an Technology, Grantin-Ai for Scientific Research on Priority Areas (B) (), Nomenclature A : Dimensionless number [ ] a : Rotation raius of a particle [m] B : Impose magnetic flux ensity [T] B in : Magnetic flux ensity in material [T] F : Lorenz force per unit volume [N/m 3 ] i x : Unit vector in the irection of x [ ] i y : Unit vector in the irection of y [ ] i z : Unit vector in the irection of z [ ] J : Current ensity [A/m ] k : Boltzmann constant [J/K] L : Torque ue to Lorenz force [N m] M : Magnetization [A/m] N : Demagnetizating factor [ ] R : Torque ue to viscosity [N m] r : Raius of a particle [m] t : Characteristic time [s] T : Magnetic torque [N m] T : z-component of T [N m] U : Magnetic energy [N m] 3 ISIJ 86

7 ISIJ International, Vol. 43 (3), No. 6 V : Volume of substance [m 3 ] v : Rotation velocity of substance [m/s] h : Viscosity [N s/m ] q : Angle between irections of impose magnetic fiel an easy magnetization axis [ ] q : Value of q in t [ ] m : Permeability in vacuum [H/m] r : Density [kg/m 3 ] s : Electric conuctivity [1/W m] s : Relaxation time [s] j : Angle between r an z-axis [ ] c : Magnetic susceptibility of a substance [ ] c 1 : c : Magnetic susceptibility in the irection of easy magnetization axis Magnetic susceptibility in the irection of ifficult magnetization axis REFERENCES [ ] [ ] 1) S. Asai: JIM, 61 (1997), 171. ) N. Waki, K. Sassa an S. Asai: Tetsu-to-Hagané, 86 (), ) E. Beaugnon an R. Tournire: Nature, 349 (1991), ) H. Morikawa, K. Sassa an S. Asai: Mater. Trans., JIM, 8 (1998), ) T. Taniguchi, K. Sassa an S. Asai: Mater. Trans., JIM, 41 (), ) M. Tahashi, K. Sassa, I. Hirabayashi an S. Asai: Mater. Trans., JIM, 41 (), ) M. Ito, K. Sassa, M. Doyama, S. Yamaa an S. Asai: Tanso, 191 (), 37. 8) A. E. Mikelson an Ya. Kh. Karklin: J. Cryst. Growth, 5 (1981), 54. 9) H. Yasua, K. Tokiea an I. Ohnaka: Mater. Trans., JIM, 41 (), 15. 1) M. Yamato, T. Kimura, W. Koshimizu, M. Koike, T. Kawai an E. Ito: SNMS-98, Japan Science an Technology Corp., Kawaguchi, Saitama, (1999), ) L. Wehrli: Phys. Konens. Materie, 8 (1968), 94. 1) Lanolt-Börnstein: Eigenschaften er Materie in ihren Aggregatzstänen, 9 teil, Magnetic Properties I, Springer, Berlin, Heielberg, Germany, (196), 1. 13) Lanolt-Börnstein: Eigenschaften er Materie in ihren Aggregatzstanen, 1 teil, Magnetic Properties II, Springer, Berlin, Heielberg, Germany, (1967),. 14) T. Kimura: Proc. of Int. Symp. on Innovative Chemical Reaction Fiel (IMP ), The Society of Non-Traitional Technology, Tokyo, (), ISIJ