MAGNETIC MATERIAL CHARACTERIZATION BY OPEN SAMPLE MEASUREMENTS VALENTIN IONIŢĂ, LUCIAN PETRESCU Key words: Magnetic material characterization, Open sample measurements, Correction of experimental data. The paper analyzes the significance of the experimental magnetic characteristic obtained by open sample measurement (e.g. by a vibrating sample magnetometer). It is outlined the influence of the open magnetic circuit shape, the sample shape and magnetic properties, and the equipment setup (e.g. the probe position in the air-gap). It is shown how one could obtain the material characteristic from the sample characteristic. 1. INTRODUCTION Numerical design of electromagnetic devices involves mathematical models of the magnetic material relationship. These models could be linear/ non-linear/ hysteretic, scalar/vector or isotropic/anisotropic. The model identification requires experimental data obtained by various measurement techniques [1]. Each experimental method has specific limitations, regarding the magnetic field range, sample shape, measured magnetic parameters etc. A class of versatile magnetic measurements uses open magnetic circuits, with a variable air-gap, which allows measuring magnetic samples of different sizes or shapes. But, such of methods give us only an external magnetic relationship between the applied magnetic field and a magnetic magnitude (magnetic moment, magnetic flux density or magnetization) that characterizes the entire sample. A numerical model of the magnetic material constitutive relationship, which could be used in a numerical solving of the magnetic field problems, involves an internal relationship. The transformation of the measured external dependence into the material intrinsic relationship is a difficult problem. Laboratory of Technical Magnetism, Electrical Engineering Department, University POLITEHNICA of Bucharest, Splaiul Independentei 313, 642 Bucharest; E-mail: vali@mag.pub.ro Rev. Roum. Sci. Techn. Électrotechn. et Énerg., 54, 1, p. 87 94, Bucarest, 29
88 Valentin Ioniţă, Lucian Petrescu 2 A more complicated relationship occurs for magnetic materials with hysteresis [2], where the identification of the hysteresis model parameters involves many experimental data. Any experimental error may have serious consequences on the numerical identification [3]. An alternative is to use the magneto-optical effects [4], because the magnetization process of a material is related to its micromagnetic structure and it can be studied through the visualization of the magnetic domains and walls dynamics. The extraction of Preisach hysteresis model parameters, starting from the real-time visualization of the magnetic microstructure by magneto-optical Kerr effects, using a polarized light microscope, is possible [5]. For the materials with hysteresis, another problems are the anisotropy presence and the vector hysteresis. A widely experimental method, which can give all the necessary data for the material model identification, is based on the Vibrating Sample Magnetometer (VSM), very sensitive equipment, which uses small samples and can generate large magnetic fields (1 6 A/m) in a small air-gap (a few millimeters). The main problem that occurs in this open sample measurement is the dependence of the measured data of the sample shape and size. The demagnetizing factor of the sample must be considered for the correction, especially for soft magnetic materials. An original correction method based on the computation of the magnetometric demagnetizing factor and of the field correction factor, using the finite element method (FEM) for the experimental device simulation, was proposed in [6]. The computed factors are used in real time, during the measurement. A database was built for our VSM standard setup and for classical sample shapes (disk and rectangular prism). 2. NUMERICAL TREATMENT OF THE DEMAGNETIZATION PHENOMENON The main problem that occurs in open sample measurements is the dependence of the measured data of the sample shape and size. The demagnetizing factor of the sample allows the correction, but it depends on the local magnetic permeability and it can be analytically computed only for ellipsoidal samples. Literature proposes solutions for rectangular prisms [7-8], ring cores [9], and cylinders [1-11]. The proposed demagnetizing factors are analytically computed, depending on the sample geometry only, or result from one- or two-dimensional numerical computation for each magnetic susceptibility value of the sample, which has a given geometry and is placed in a uniform magnetic field. A complete correction must consider the entire magnetic circuit configuration and the measurement probe position [6].
3 Magnetic material characterization by open sample measurements 89 This correction is very useful for soft magnetic materials, like Fe-Si sheets. Our tests consider the results obtained for open sample (VSM 734 LakeShore measurement) and for closed magnetic circuit (measurement with a single sheet tester SST C-3 Brockhaus ), using the same magnetic material (non oriented Fe- Si sheet). The magnetisation curve for VSM is obtained point by point, by a quasistatic measurement, while the SST curve is built from the extreme points of the hysteresis cycles measured on at low frequency (1 Hz) and variable amplitude. The non-oriented Fe-Si sheet has 3 3.5 mm for SST measurement and the VSM sample was obtained by electro-erosion, being a disk with 3.8 mm diameter and.5 mm thickness. One observes from Fig. 1 that the original VSM curve cannot be used in CAD computation, but a numerical correction, based on the finite element simulation of the experimental device improves the experimental characteristics. Similar results were obtained for a rectangular prism sample having the dimensions 3.8, 3.8, and.5 mm see Fig. 2. Consequently, the magnetization curves measured for open samples must be corrected taking into account the demagnetizing factor and the field correction factor. 1.8 1.6 Magnetic flux density B[T] 1.4 1.2 1.8.6 VSM demagnetising correction demagnetising & field corrections SST.4.2-2 2 4 6 8 1 12 14 16 18 2 Magnetic field H[kA/m] Fig. 1 Measured and corrected curves for Fe-Si disk sample.
9 Valentin Ioniţă, Lucian Petrescu 4 Fig. 2 Correction effect for a Fe-Si prism sample. 3. INFLUENCE OF THE MAGNETIC ANISOTROPY The magnetocrystalline anisotropy is a magnetic material characteristic, but the shape anisotropy is a magnetic sample characteristic. The open sample measurement must take into account this difference; a simple solution is the use of a symmetrical sample (from geometrical point of view): sphere or disk. Indeed, even for non-oriented (NU) Fe-Si sheet, the measured characteristics for samples having a prism shape and (3.8 3.6.5) mm show a shape anisotropy that influence the numerical modelling see Fig. 3; for a elongated shape, the anisotropy is stronger. Similar results are obtained for semi-hard magnetic materials, like the magnetic recording tape see Fig. 4.
5 Magnetic material characterization by open sample measurements 91 NO Fe-Si prism 3 2 1 B [T] -4-3 -2-1 1 2 3 4-1 longitudinal transversal -2-3 H [A/m] Fig. 3 Shape anisotropy for Fe-Si sheets. Easy axis, magnetic tape disk rectangle square 2 15 1 5 M [A/m] -1-8 -6-4 -2 2 4 6 8 1-5 -1-15 -2 H [A/m] Fig. 4 Shape anisotropy for magnetic tape; the sample has 5 mm diameter for the disk: (6.7 2.2) mm for the rectangle and (5 5) mm for the square.
92 Valentin Ioniţă, Lucian Petrescu 6 4. INFLUENCE OF THE VECTOR HYSTERESIS AND EQUIPMENT SETUP In an electromagnetic device, the complexity of magnetic material behaviour (nonlinear or with hysteresis) imposes a careful modelling in order to obtain an accurate computation. The microscopic behaviour is usually modelled by Landau- Lifshitz-Gilbert equation [12], which is useful in the magnetic recording domain, but it is often prohibitive for engineering applications. However, a macroscopic material model might be correlated with the magnetization dynamics at microscopic level [13]. This correlation between the microscopic and macroscopic levels can be used for the experimental validation of the macroscopic numerical simulation [13]. The hysteresis complexity imposes complicate mathematical models that require many experimental data for the model identification. The magnetic material has a vectorial memory, so the order of the measurements must be carefully chosen. For example, the measurements of the major hysteresis cycles for different directions of the applied magnetic field, for a magnetic tape (subway access card), look as in Fig. 5 if the measurement order is from the easy magnetization axis to the hard direction. The result is very strange: the saturation magnetization is higher for the hard direction. The explanation is that the previous saturation for another direction and the vectorial memory amplify the magnetization effect. A correct experimental cycle could be obtained if the sample is demagnetized first. Another problem is the equipment setup: the calibration is essentially for the measurement accuracy, but the device setup could be changed during the measurement, due to the magnetic sample moving and the time variation of the device parameters. For example, the measurement of the first order reversal curves (FORC), necessary for the identification of vector Preisach hysteresis model, imposes the rotation of the VSM sample holder and a long time (4-5 hours), so the device setup could be changed and the experimental curves are not correlated. Figure 6 shows some experimental curves that are not correct, because the device setup was changed and the calibration cannot be the same for all the curves. The conclusion is that the calibration must be carefully done for each measurement. 5. CONCLUSIONS A complete correction of the experimental data that are obtained in open sample measurements must consider not only the sample geometry and magnetic behavior, but also the entire magnetic circuit configuration and the measurement probe position. The computation of the magnetometric demagnetizing factor and of the field correction factor can be performed using the finite element method for the experimental device simulation.
7 Magnetic material characterization by open sample measurements 93 Magnetic tape anisotropy 3 6 9 degrees 18 M [A/m] 135 9 45 H [A/m] -1-8 -6-4 -2 2 4 6 8 1-45 -9-135 -18 Fig. 5 Hysteresis cycles for a magnetic tape (disk sample, 5 mm diameter), under various directions of the applied magnetic field. Ascendant curves, magnetic tape 3 6 9 degrees 15 1 5 M [A/m] -8-6 -4-2 2 4 6 8-5 -1-15 H [ka/m] Fig. 6 Ascendant curves for a magnetic tape (square sample, 3.8 3.8 mm). The influence of the demagnetization and of the shape anisotropy on the measured magnetic characteristics can be reduced using symmetrical samples (sphere or thin disk). The hysteretic materials can be characterized by open sample
94 Valentin Ioniţă, Lucian Petrescu 8 measurements if one eliminates the vectorial magnetic history of the sample (by thermal or alternating demagnetization) and if the device is carefully recalibrated for each measurement. ACKNOWLEDGEMENTS The study was partially supported by CEEX 215/26 (ANCS-AMCSIT) contract and by AC-16/28 grant (CNCSIS). Received on July14, 28 REFERENCES 1. F. Fiorillo, Measurement and Characterization of Magnetic Materials, Elsevier, Amsterdam, 24. 2. I. D. Mayergoyz, Mathematical Models of Hysteresis and Their Applications, Academic Press, New York, 23. 3. V. Ionita, L. Petrescu, Computational errors in hysteresis Preisach modelling, in: G. Ciuprina, D. Ioan (Edit.), Mathematics in Industry, 11 ( Scientific Computing in Electrical Engineeering ), pp. 317-322, Springer Verlag, Berlin, 27. 4. A. Hubert, R. Schafer, Magnetic Domains, Springer Verlag, Berlin, 1998. 5. V. Ionita, E. Cazacu, Identification of hysteresis Preisach model using magneto-optic microscopy, Physica B Condensed Matter, 43, 2-3, pp. 376-378, 28. 6. V. Ionita, E. Cazacu, Correction of measured magnetization curves using finite element method, Proceedings of 13-th Biennial IEEE Conf. on Electromagnetic Field Computation, Athens, pp. 119, 28. 7. A. Aharoni, Demagnetizing factors for rectangular ferromagnetic prisms, J. Appl. Phys., 83, pp. 3432-3434, 1998. 8. D.-X. Chen, E. Pardo, and A. Sanchez, Demagnetizing factors for rectangular prisms, IEEE Transactions on Magnetics, 41, pp. 277-288, 25. 9. D.B. Clarke, Demagnetization factors of ringcores, IEEE Transactions on Magnetics, 35, pp. 444-4444, 1999. 1. D.-X. Chen, J. Brug, and R. Goldfarb, Demagnetizing factors for cylinders, IEEE Transactions on Magnetics, 27, pp. 361-3619, 1991. 11. D.-X. Chen, E. Pardo, and A. Sanchez, Radial magnetometric demagnetizing factor of thin disks, IEEE Transactions on Magnetics, 37, pp. 3877-388, 21. 12. L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media, Pergamon Press, Oxford, 1989. 13. A. Aharoni, Introduction to the Theory of Ferromagnetism, University Press, Oxford, 2. 14. V. Ionita, B. Cranganu-Cretu, Experimental validation of electromagnetic field computation in magnetic materials, IEEE Transactions on Magnetics, 44, pp. 882-885, 28.