volume | PIER Journals

Abstract

A unit cell based numerical approach to model the metal powders and metal-dielectric composites at microwave frequencies is proposed. The unit cell based numerical modeling helps to compute the equivalent reflection and transmission coefficients of these materials, which are commonly used measured parameters at RF and microwave frequencies. The computation of the reflection and transmission coefficients of these artificial dielectric samples also facilitates the determination of their effective constitutive properties, defined in terms of the effective permittivity and permeability, using the reflection transmission approach. The applicability of the proposed unit cell method is first verified for some mixed dielectrics using the classical mixing formulas, and the standard waveguide approach. Once the validity of the proposed approach is ascertained, the effective constitutive properties of copper powder is determined. A detailed parametric analysis is also carried out in order to study the effect of various parameters such as the packing fraction, the grain size and the gap between adjacent spherical shaped metal particles, on the effective constitutive properties of the copper powder compact. This detailed analysis is quite helpful in order to optimize various parameters of the microwave sintering of metal powders and metal-dielectric composites before the actual start of the sintering process using microwaves.

1. Meredith, R. J., Engineers Handbook of Industrial Microwave Heating, IET Power & Energy Series, London, UK, 1998.
doi:10.1049/PBPO025E

2. Ku, , H. S.-L., "Productivity improvement of composites processing through the use of industrial microwave technologies," Progress In Electromagnetics Research, Vol. 66, 267-285, 2006.
doi:10.2528/PIER06111901 Google Scholar

3. Metaxas, A. C. and R. J. Meredith, Industrial Microwave Heating, IEE Power & Engineering Series 4, London, UK, 1988.
doi:10.1049/PBPO004E

4. Link, G., L. Feher, M. Thumm, H.-J. Ritzhaupt-Kleissl, R. Boehme, and A. Weisenburger, "Sintering of advanced ceramics using a 30 GHz, 10-kW, CW industrial gyrotron," IEEE Transactions on Plasma Science, Vol. 27, No. 2, 547-554, 1999.
doi:10.1109/27.772284 Google Scholar

5. Varadan, V. K., Y. Ma, A. Lakhtakia, and V. V. Varadan, "Modeling of porous ceramics during microwave sintering," Progress In Electromagnetics Research, Vol. 6, 303-313, 1992. Google Scholar

6. Roy, R., D. Agrawal, J. Cheng, and S. Gedevanishvili, "Full sintering of powdered-metal bodies in a microwave field," Nature, Vol. 399, 668-670, Jun. 1999. Google Scholar

7. Ma, J., J. F. Diehl, E. J. Johnson, K. R. Martin, N. M. Miskovsky, C. T. Smith, G. J. Weisel, B. L. Weiss, and D. T. Zimmerman, "Systematic study of microwave absorption, heating and microstructure evolution of porous copper powder metal compacts," J. Appl. Phys., Vol. 101, 074906, 2007.
doi:10.1063/1.2713087 Google Scholar

8. Rybakov, K. I., V. E. Semenov, S. V. Egorov, A. G. Eremmev, I. V. Plotnikov, and Y. V. Bykov, "Microwave heating of conductive powder materials," J. Appl. Phys, Vol. 99, 023506, 200.
doi:10.1063/1.2159078 Google Scholar

9. Anklekar, R. M., K. Bauer, D. Agrawal, and R. Roy, "Improved mechanical properties and microstructural development of microwave sintered copper and nickel steel PM parts," Powder Metallurgy, Vol. 48, 39-46, 2005.
doi:10.1179/003258905X37657 Google Scholar

10. Buchelnikov, V. D., D. V. Louzguine-Luzgin, A. P. Anzulevich, I. V. Bychkov, N. Yoshikawa, M. Sato, and A. Inoue, "Modeling of microwave heating of metallic powders," Physica B, Vol. 403, 4053-4058, 2008.
doi:10.1016/j.physb.2008.08.004 Google Scholar

11. Anzulevich, A. P., V. D. Buchelnikov, I. V. Bychkov, and D. V. Louzguine-Luzgin, "Microwave penetrating and heating of metallic powders," PIERS Proceedings, 844-847, Moscow, Russia, Aug. 2009. Google Scholar

12. Garnett, J. C. M., "Colours in metal glasses and metal films," Philosophical Trans. of the Royal Society, Vol. CCIII, 385-42, London, 1904. Google Scholar

13. Goncharenko, A., V. Lozovski, and E. Venger, "Lichteneckers equation: Applicability and limitations," Optics Communications, Vol. 174, No. 1-4, 1932, 2000.
doi:10.1016/S0030-4018(99)00695-1 Google Scholar

14. Simpkin, R., "Derivation of Litchenker's logarithmic mixture formula from Maxwell's equations," IEEE Trans. on Microw. Theory and Tech., Vol. 58, No. 3, 545-550, Mar. 2010.
doi:10.1109/TMTT.2010.2040406 Google Scholar

15. Bruggeman, D., "Calculation of various physical constants of heterogeneous substances," Ann. Phys., Vol. 32, No. 12, 636-664, 1935.
doi:10.1002/andp.19354160705 Google Scholar

16. Tinga, W. R., W. A. G. Vos, and D. F. Blossey, "Generalized approach to multiphase dielectric mixture theory," J. of Applied Physics, Vol. 44, No. 9, 3897-3902, 1973.
doi:10.1063/1.1662868 Google Scholar

17. Tao, R. B., Z. Chen, and P. Sheng, "First-principles Fourier approach for the calculation of effective dielectric constant of periodic composites," Physical Review B, Vol. 41, No. 4, 2417-2420, 1990.
doi:10.1103/PhysRevB.41.2417 Google Scholar

18. Kiley, E. M., V. V. Yakovlev, K. Ishizaki, and S. Vaucher, "Applicability study of classical and contemporary models for effective complea permittivity of metal powders," Journal of Microwave Power and Electromagnetic Energy, Vol. 46, No. 1, 26-38, 2012. Google Scholar

19. Parkash, A., J. K. Vaid, and A. Mansingh, "Measurement of dielectric parameters at microwave frequencies by cavity-perturbation technique," IEEE Trans. on Microw. Theory and Tech., Vol. 27, No. 9, 791-795, Sep. 1979.
doi:10.1109/TMTT.1979.1129731 Google Scholar

20. Baker-Jarvis, J., E. Vanzura, and W. Kissick, "Improved technique for determining complex permittivity with the transmission/reflection method," IEEE Trans. on Microw. Theory and Tech., Vol. 38, No. 8, 1096-1103, Aug. 1990.
doi:10.1109/22.57336 Google Scholar

21. Hasar, U. C., "A new microwave method based on transmission scattering parameter measurements for simultaneous broadband and stable permittivity and permeability determination," Progress In Electromagnetics Research, Vol. 93, 161-176, 2009.
doi:10.2528/PIER09041405 Google Scholar

22. Akhtar, M. J., L. E. Feher, and M. Thumm, "A waveguide-based two-step approach for measuring complex permittivity tensor of uniaxial composite materials," IEEE Trans. on Microw. Theory and Tech., Vol. 54, No. 5, May 2006.
doi:10.1109/TMTT.2006.873623 Google Scholar

23. Smith, D. R., D. C. Vier, T. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Physical Review E, Vol. 71, 036617, 2005.
doi:10.1103/PhysRevE.71.036617 Google Scholar

24. Chen, X., T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Physical Review E, Vol. 70, 016608, 2004.
doi:10.1103/PhysRevE.70.016608 Google Scholar

25. Hasar, U. C., J. J. Barroso, C. Sabah, I. Y. Ozbek, Y. Kaya, D. Dal, and T. Aydin, "Retrieval of effective electromagnetic parameters of isotropic metamaterials using reference-plane invariant expressions," Progress In Electromagnetics Research, Vol. 132, 425-441, 2012. Google Scholar

26. Engheta, N. and R. W. Ziolkowski, "Metamaterials: Physics and Engineering Explorations," IEEE Press, 2006. Google Scholar

27. Zimmerman, D. T., J. D. Cardellino, K. T. Cravener, K. R. Feather, N. M. Miskovsky, G. J. Weisel, and , "Microwave absorption in percolating metal-insulator composites," Appl. Phys. Letters, Vol. 93, No. 214103, 1-3, 2008. Google Scholar

28. "Computer Simulation Technology,", CST, Darmstadt, Germany, 1998-2013, [Online] Available: www.cst.com. Google Scholar

29. "Ansys HFSS,", ANSYS, Inc., PA, USA, 2011. [Online]. Available: www.ansys.com. Google Scholar

30. Galek, T., K. Porath, E. Burkel, and U. van Rienen, "Extraction of effective permittivity and permeability of metallic powders in the microwave range," Modelling and Simulations in Materials Science and Engineering, Vol. 18, 025014-1-025014-13, 2010. Google Scholar

31. Takayama, S., G. Link, S. Miksch, M. Sato, J. Ichikawa, and M. Thumm, "Millimetre wave effects on sintering behaviour of metal powder compacts," Powder Metallurgy, Vol. 49, 274-280, 2006.
doi:10.1179/174329006X110835 Google Scholar

32. Doyle, W. T., "The Clausius-Mossotti problem for cubic array of spheres," J. Appl. Phys., Vol. 49, No. 2, 795-797, 1978.
doi:10.1063/1.324659 Google Scholar

33. Pozar, D. M., Microwave Engineering, John Willey & Sons, Inc., New York, 1999.

Mrs. Tannu Gupta

Professor Mohammad Jaleel Akhtar

Dr. Animesh Biswas