The technique to retrieve the microwave permeability of metals from the measured constitutive parameters of composites with fine powder of these metals is developed. The technique is based on the modified Sihvola mixing rule and describes a wide range of contrasts in the component susceptibility, accounts for both the inclusion shape and the percolation threshold. These parameters are related to the Bergman-Milton shape-distribution width and to composite structure. The technique is applied to retrieve the microwave permeability of nickel. The metal permeability is calculated from the measured permittivity and permeability of paraffin-bound composites filled with nickel flakes or spheres with account for skinning in conducting inclusions. The measurements are performed using the transmission coaxial-cell in the frequency range up to 15 GHz. The effects of filling factor, inclusion shape and size on the retrieved permeability spectra are analyzed. The permeability retrieval procedure is based on parameter fitting of the selected mixing model for the measured permittivity and permeability data. The retrieved permeability is close to the data available from archived literature sources that are obtained with thick nickel wires and foils.
Sergey Nickolaevich Starostenko,
Artem Olegovich Shiryaev,
"A Technique to Retrieve High-Frequency Permeability of Metals from Constitutive Parameters of Composites with Metal Inclusions of Arbitrary Shape, Estimate of the Microwave Permeability of Nickel," Progress In Electromagnetics Research M,
Vol. 76, 143-155, 2018. doi:10.2528/PIERM18071707
1. Olmedo, L., G. Chateau, C. Deleuze, and J. L. Forveille, "Microwave characterization and modelization of magnetic granular materials," J. Appl. Phys., Vol. 73, 6992, 1993. doi:10.1063/1.352408
2. Lederer, P. and C. Brewitt-Taylor, "Measurement of microwave properties of magnetic particulate composites," IEEE Proc. SCI. Meas. Techn., Vol. 147, No. 4, 209, 2000. doi:10.1049/ip-smt:20000528
3. Odelevskiy, V. I., "Generalized conductivity of heterogeneous systems,", Ph.D. Thesis, Leningrad, 1947 (in Russian).
4. Pal, R., Electromagnetic, Mechanical and Transport Properties of Composite Materials, CRC Press, Taylor & Frances, London, New-York, 2015.
5. Starostenko, S. N., K. N. Rozanov, A. O. Shiryaev, A. N. Shalygin, and A. N. Lagarkov, "Determination of sendust intrinsic permeability from microwave constitutive parameters of composites with sendust spheres and flakes," J. Appl. Phys., Vol. 121, 245107-245123, 2017. doi:10.1063/1.4989848
6. Starostenko, S. N., K. N. Rozanov, A. O. Shiryaev, A. N. Lagarkov, and A. N. Shalygin, "Selection of a mixing model and determination of inclusion microwave permeability for a composite filled with metal powder," J. Magn. Magn, Mater., Vol. 459, 305-310, 2018. doi:10.1016/j.jmmm.2017.10.021
7. Starostenko, S. N., et al. "Estimation of the superhigh-frequency magnetic permeability of alsifer from the measured permeability of composites," Physics of the Solid State, Vol. 59, No. 11, 2203-2210, 2017. doi:10.1134/S1063783417110282
8. Landau, L. D., L. P. Pitaevskii, and E. M. Lifshitz, Electrodynamics of Continuous Media, Butterworth-Heinemann, Oct. 1984.
9. Tuncer, E., "The Landau-Lifshitz/Looyenga dielectric mixture expression and its self-similar fractal nature,", arXiv:cond-mat/0503750, 2005.
10. Wiener, O., , Der Abhandlungen derMathematisch-Physischen Klasse der Königl. Sachsischen Gesellschaft der Wissenschaften, 32, 509, 1912.
11. Lagarkov, A. N., V. N. Semenenko, V. A. Chistyaev, and I. T. Iakubov, "High-frequency modes in magnetic spectra of carbonyl iron," J. Magn. Magn. Mater., Vol. 324, 3402-3405, 2012. doi:10.1016/j.jmmm.2012.02.052
12. Shlepnev, Yu. and S. McMorrow, "Nickel characterization for interconnect analysis," IEEE International Symposium on Electromagnetic Compatibility, 524-529, Aug. 2011.
13. Zivkovic, I. and A. Murk, "Characterization of magnetically loaded microwave absorbers," Progress In Electromagnetics Research B, Vol. 33, 277-289, 2011. doi:10.2528/PIERB11071108
14. Starostenko, S. N., K. N. Rozanov, A. O. Shiryaev, V. A. Garanov, and A. N. Lagarkov, "Permeability of nickel determined from microwave constitutive parameters of composites filled with nickel powders,", submitted to IEEE Trans. Magn., doi 10.1109/TMAG.2018.2852366.
15. Bozorth, R. M. and N. Y. Ferromagnetism, , D. Van Nostrand Co. Inc., 1951.
16. Galek, T., K. Porath, E. Burkel, and U. van Rienen, "Extraction of effective permittivity and permeability of metallic powders in the microwave range," Model. Simul. Mater. Sci. Eng., Vol. 18, 025015-025028, 2010. doi:10.1088/0965-0393/18/2/025015
17. Lomayeva, S. F., A. V. Syugaev, A. N. Maratkanova, and A. A. Shakov, "Structure and microwave properties of Fe powders prepared by surfactant-assisted ball milling in organic media," J. Alloys Compd., Vol. 721, 18-27, 2017. doi:10.1016/j.jallcom.2017.05.311
18. Ignatenko, M., M. Tanaka, and M. Sato, "Absorption of microwave energy by a spherical nonmagnetic metal particle," Jap. J. Appl. Phys., Vol. 48, No. 6R, 67001-67006, 2009. doi:10.1143/JJAP.48.067001
19. Sihvola, A. H., "Mixing rules," Artificial Materials Handbook, Vol. I: ed. F. Capolino, 9.1–9.12, CRC press, Taylor & Francis, 2009.
20. Sihvola, A. H. and J. Au. Kong, "Effective permittivity of dielectric mixtures," IEEE Trans. on Geoscience and Remote Sensing, Vol. 26, No. 4, Jul. 1988.
21. Bergman, D. J., "Bounds for the complex dielectric constant of a two component material," Phys. Rev. B, Vol. 23, 3058-65, 1981. doi:10.1103/PhysRevB.23.3058
22. Zhang, D. and E. Cherkaev, "Reconstruction of spectral function from effective permittivity of a composite material using rational function approximations," Journal of Computational Physics, Vol. 228, 5390-5409, 2009. doi:10.1016/j.jcp.2009.04.014
23. Ghosh, K. and R. Fuchs, "Spectral theory for two-component porous media," Phys Rev. B, Vol. 38, No. 8, 5222-5236, 1988. doi:10.1103/PhysRevB.38.5222
24. Rozanov, K. N., M. Y. Koledintseva, and J. Drewniak, "A mixing rule for predicting frequency dependence of material parameters in magnetic composites," J. Magn. Magn. Mater., Vol. 324, 1063-1066, 2012. doi:10.1016/j.jmmm.2011.10.028
25. Osipov, A. V., K. N. Rozanov, N. A. Simonov, and S. N. Starostenko, "Reconstruction of intrinsic parameters of a composite from the measured frequency dependence of permeability," J. Phys. Condens. Matter., Vol. 14, 9507-9523, 2002. doi:10.1088/0953-8984/14/41/308
26. Rozanov, K. N., A. V. Osipov, D. A. Petrov, S. N. Starostenko, and E. P. Yelsukov, "The effect of shape distribution of inclusions on the frequency dependence of permeability in composites," J. Magn. Magn. Mater., Vol. 321, 738-741, 2009. doi:10.1016/j.jmmm.2008.11.039
27. Petrov, D. A., K. N. Rozanov, and M. Y. Koledintaeva, "Influence of higher-order modes in coaxial waveguide on measurements of material parameters," IEEE Trans. EMC, Vol. 3, 66-70, 2018.
28. Arkadiev, W., "Absorption of electromagnetic waves in two parallel wires," Ann. Physik, Vol. 58, No. 4, 105-138, 1919. doi:10.1002/andp.19193630202
29. Simon, I., "Magnetic permeability of nickel in the region of centimeter waves," Nature, No. 3996, 735, 1946. doi:10.1038/157735a0