Distribution of magnetic particles in suspension under static magnetic fields.doc

精品论文推荐Distribution of magnetic particles in suspension under static magnetic fieldsYan Mi*，Peng Xiaoling，Shi WeitangState Key Laboratory of Silicon Materials，Zhejiang University，Hangzhou （310027）E-mail：mse_yanmiAbstractAqueous suspension containing ferromagnetic Ni and nonmagnetic ZrO2 particles was solidifiedunder a series of static magnetic fields ranged up to 320 kA/m. The results showed that Ni particles tend to form chain-like clusters in the suspension under the external field, because of the dipole-field interaction and the dipole-dipole interaction among Ni particles. The mean cluster length increased as a function of applied field, and saturated at 320 kA/m field. The clusters grew with the field loading time, and became unchanged after 160 kA/m field was loaded for 15 s. The results provide a foundation for the fabrication of ferromagnetic-nonmagnetic Ni-ZrO2 FGMs in a magnetic field.Keywords：Magnetic particle；Magnetic field；Cluster；FGM1.IntroductionFabrication of functionally graded materials (FGMs) has attracted much interest because of their continuously changed mechanical, physical and chemical properties 1-5. FGMs have normally been fabricated by means of vapor deposition, powder metallurgy, plasma spraying, self-propagation high temperature synthesis, electro deposition, etc 6-9. Recently, we have developed a new approach to prepare ferromagnetic-nonmagnetic Ni-ZrO2 FGM with a continuously changing composition via slip casting in a magnetic field based on the distinct difference in magnetic susceptibility between Ni and ZrO2 10.In the new approach, the distribution of ferromagnetic particles under a magnetic field is ofimportance. The distributions of ferromagnetic particles with nano-size in ferrofluid under magnetic field were investigated 11. Jozef ernák 12 also investigated the distributions of nonmagnetic ones with micro-size in ferrofluid. It is regarded that the energy of particles in magnetic field is determined directly by particle size and therefore the distribution of particles was affected. However, very few attempts have been carried out on investigating the distribution of ferromagnetic particles in suspension composed of ferromagnetic and nonmagnetic particles with micro-size under magnetic field. To fabricate designable FGMs, it is necessary to investigate the interactions between magnetic particles and the distributing behaviors of magnetic particles in suspension under an external field. In this paper, Ni and ZrO2 were selected as ferromagnetic particles and nonmagnetic ones to prepare suspension. The distributing behaviors of Ni particles under a uniform magnetic field were investigated.2.ExperimentsNi with an average diameter of 1.2 µm and ZrO2 with an average diameter of 0.75 µm were used as ferromagnetic and nonmagnetic particles, respectively. Polyvinylpyrrolidone (PVP) was selected as the deflocculant. ZrO2 and Ni particles were ball milled with PVP for 6 h in distilled water, respectively. The content of PVP was fixed at 0.7 wt.% in the suspension of ZrO2, and 1.2 wt.% in the suspension of Ni, respectively. The two suspensions were then mixed together through mechanical stirring for 4 h to disperse the particles homogeneously, with 5 wt.% Ni and 95 wt.% ZrO2. The solid content of the mixed suspension was 40 vol.%.The mixed suspension was degassed in a vacuum furnace, and poured into a rubber mold with a gypsum base for solidification. The molds for casting were 10×5 mm cylinders. During slip casting, a uniform magnetic field, which is parallel to the horizontal direction, was applied to the suspension. The- 8 -applied field was ranged up to 320 kA/m. After the magnetic field was removed, the castings with molds were dried at 60 for 48 h in a chest. The green compacts were then put in a VSF-120/150 vacuum sintering furnace and heated from room temperature to 300 at 5 ·min-1, then to 500 at 1 ·min-1. The green compacts were kept at 500 for 2 h to burn out the PVP, followed by sintering at 1350 for 5 h in vacuum to obtain the final samples.The sintered samples were cut and polished for further characterizations. The longitudinal (parallel to the field direction) and transverse microstructures were observed by a MeF-3 optical microscopy (Reichert, Austria). The composition distribution of the cross section was identified using an X-ray energy dispersion spectroscopy (EDS, GENENIS 4000, USA). The magnetic properties Ni particles were measured using the vibrating sample magnetometer (VSM).3.ResultsFig. 1 Microstructures of solidified suspension under the 160 kA/m magnetic field for 30 min on (a) transverse section and (b) longitudinal section.Fig. 1 shows the microstructures of the solidified suspension containing Ni and ZrO2 particles after a field of 160 kA/m was applied for 30 min. White phases dispersing in the black matrix were identified to be Ni particles by means of EDS. Ni particles distribute homogenously on transverse section, as shown in Fig. 1a; whereas chain-like Ni clusters can be discerned along the field direction, as shown in Fig. 1b. It indicates that chain-like magnetic clusters have been formed along the field direction when 160 kA/m was applied.Fig. 2 Probability density function on cluster length in magnetic field for 1 min. (a) H = 16 kA/m, 180 dipolar chains are identified; (b) H = 40 kA/m 149 dipolar chains are identified; (c) H = 80 kA/m, 136 dipolar chains are identified; (d) H= 160 kA/m, 129 dipolar chains are identified; (e) H = 320 kA/m, 128 dipolar chains are identified.Fig. 2 shows the probability density function (PDF) on chain-like cluster length in the suspension after different magnetic fields were applied for 1 min. Fig. 3 shows the mean cluster length as afunction of magnetic field. It can be seen that the mean cluster length increases from 4.37 µm at 16 kA/m to 6.25 µm at 320 kA/m, suggesting that the mean cluster length increases as a function ofmagnetic field. The mean cluster length increases drastically in low fields, increases slowly in highfields, and finally remains nearly unchanged. It is noticeable that 160 kA/m is high enough for thegrowth of the chain-like magnetic clusters.Fig. 3 Variation of mean cluster length under different magnetic fields. Inset: Initial magnetization curve of Ni particles.Fig. 4 Microstructures of solidified suspensions (a) without magnetic field and after a 160 kA/m field was applied for (b) 1 s, (c) 5 s and (d) 15 s.The inset in Fig. 3 shows the initial magnetization curve of Ni particles. Comparing two curves in Fig. 3, one can find that the field dependence of mean cluster length approximates that of the magnetization intensity. In other words, the mean cluster length is related to the magnetization of magnetic particles.The time dependency of the mean cluster length under an external field is also investigated. Fig. 4 shows the microstructures of solidified ZrO2-Ni suspensions under a 160 kA/m field with different applying times. Fig. 4a shows the distribution of Ni particles in solidified suspension without magnetic field. Figs. 4b 4d show the microstructures of solidified suspensions after the 160 kA/m field was applied for 1 s, 5 s and 15 s, respectively. Ni particles distribute homogeneously for the sample prepared without magnetic field, as shown in Fig. 4a. When 160 kA/m field is applied, chain-like clusters are formed along the field direction, as shown in Figs. 4b 4d. It can also be found that the clusters grow rapidly with the increase of applying time, and become unchanged after applying the 160 kA/m for 15 s.4.DiscussionIt is instructive to consider the mechanisms responsible for the formation of the magnetic chain-like clusters. In the absence of magnetic field, Ni and ZrO2 particles in the suspension are subjected to thermal energy ET and gravitational energy Eg. With the addition of deflocculant PVP, Eg is conquered, so Ni and ZrO2 particles disperse homogenously in the suspension 10. As an external magnetic field is applied on the suspension, Ni particles are magnetized along the field direction, and extra energy is induced, which consists of dipole-field energy Ed-f and dipole-dipole energy Ed-d amongNi particles. These energies are expressed as follow 11:ET = kT(1)Ed f= µ0 MHV(2)µ0 ( M iVi ) ( M jV j )E=d d 3 (d r )(d r )(3)GGG GGGd d4 r 3 ijijwhere k is Boltzmanns constant, T the absolute temperature in degrees Kelvin, volumeV = d 3 /6 for a spherical particle of diameter d, µ0 the permeability of free space, M the magnetization intensityGof particles, H the magnetic intensity, r the distance between the magnetic particles, dthe unit vectorof the direction of the magnetic dipoles, and r the unit vector pointing from dipole i to dipole j.Considering that the typical values of parameters in our experiments: k = 1.38×10-23 JK-1, T = 298 K, r= d = 1.2 µm, µ0 = 4×10-7 Hm, M = 4.9×105 Am-1 and H = 1.6×105 Am-1, we can get ET = 4.14 ×10-21 J, Ed-f = 8.91×10-14 J, and Ed-d = 2.27×10-14 J. This suggests that thermal energy ET can beignored in the presence of magnetic field.In a uniform magnetic field, the magnetic dipoles are parallel to the field direction and the magnetic force generated by dipole-field interaction is zero. Then the magnetic force on dipole igenerated by dipole j is 133µ ( M V ) ( M V )F m =0i ij j 5 (cos ) (cos ) r cos ( ) r dcos d cos GGGGGij4 r 4ijijijji (4)where i , jGare the angles between the dipole directions and r . The gravity of a Ni particle isFg = Vgwhere g is the acceleration of gravity, the density of magnetic particles. Supposed that two NiGijparticles are contacted with each other along the field direction,F m equals to 5.69×10-8 N. However,Fg equals to 7.89×10-14 N, with g = 9.8 ms-2 and = 8.9×103 kgm-3. Compared with the magneticforce, the gravity of Ni particles can be neglected. This suggests that the magnetic force is the maindriving force for the distribution of Ni particles.Fig. 5 Schematic diagram of the chain-like clusters forming process. (a) Repulsive interaction between magnetic particles perpendicular to the field direction; (b) Attractive interaction between magnetic particles parallel to the field direction; (c) Formation of chain-like clusters controlled by the interactions among magnetic particles.Fig. 5 shows schematically the formation process of chain-like clusters. In the static magnetic field, each Ni particle can be regarded as a magnetic dipole parallel to the field direction. When two dipoles are approaching, they will interact with each other. If they are put side by side, the magnetic force is negative, so the two dipoles just repel and particles move away from each other, as shown in Fig. 5a. Likewise, if they are arranged in line, the magnetic force is positive. The Ni particles will get closer and form a larger dipole, while ZrO2 particles are pushed aside, as shown in Fig. 5b. The same happens with all the particles which get close to each other. The formed dipoles then become larger and larger due to the dipole-dipole interaction, and finally chain-like Ni clusters are formed, as shown in Fig. 5c. The formation of chain-like clusters in suspension under external field reduces the demagnetizing energy of particle system, and longer clusters are apt to be formed in the higher field.The formation of chain-like clusters is attributed mainly to the dipole-dipole interaction among magnetic particles, and the dipole-dipole force on magnetic particles is proportional to the magnetization M, as we can see from equation (4). It suggests that the mean length of the clusters is determined by the magnetization M of magnetic particles.5.Conclusions(1) Chain-like magnetic clusters are formed in suspension under an external magnetic field. The formation of chain-like clusters is mainly attributed to the dipole-dipole interaction among magnetic particles.(2) The mean cluster length of magnetic particles increases as a function of magnetic field and applying time. The clusters keep nearly unchanged when the magnetic field is bigger than 160 kA/m or the applying time is more than 15s at 160 kA/m field.AcknowledgmentsThis work was supported by the National Natural Science Foundation of China (No. 50471041), the Research Fund for the Doctoral Program of Higher Education (2004335046), Program for New Century Excellent Talents in University (05-0526) and Program for Innovative Research Team in University (IRT0651).References1 A. P. F. Turner. Biosensors-Sense and Sensitivity J. Science, 2000, 290: 13151317.2 J. S. Yin, Z. L. Wang. Preparation of self-assembled cobalt nanocrystal arrays J. Nanostruct. Mater., 1999, 11:845852.3 J. N. Chapman. 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