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

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

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.

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.

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

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

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

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

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.

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

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

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

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

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

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

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.

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

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

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

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

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

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

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.

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

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.

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

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

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.

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

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

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

Mrs. Tannu Gupta

Professor Mohammad Jaleel Akhtar

Dr. Animesh Biswas