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2013-12-06
Microwave Dielectric Properties of Ni0.2CuXZn0.8-XFE2O4 for Application in Antenna
By
Progress In Electromagnetics Research B, Vol. 57, 157-175, 2014
Abstract
Structural, vibrational and microwave dielectric properties of Nickel-Copper-Zinc ferrite (Ni0.2CuxZn0.8-xFe2O4) ceramics have been presented in this paper. Samples have been prepared using conventional auto-combustion method. The X-ray diffraction (XRD) results confirmed the ferrite samples to be of cubic spinel structure, which further was validated by Fourier transform infrared (FT-IR) and Raman spectroscopy. The relative permittivity (εr) increased from 7.474 to 8.132 with successive increase in Cu content. The observed and calculated permittivity using Clausius-Mossoitti relation have been in good agreement. The temperature coefficient of resonant frequency (τf) decreased from -75.85 ppm/°C to -32.12 ppm/°C with increase in successive Cu content. The relative permeability (μr) have been calculated by using the Nicholson-Ross-Weir conversion technique. Using Ni0.2Cu0.2Zn0.6Fe2O4 sample the ferrite resonator antennas have been designed in three different shapes. The experimental and theoretical characteristics of the antennas have been compared and a good agreement has been achieved.
Citation
Kumar Mohit, Vibha Rani Gupta, and Sanjeeb Kumar Rout, "Microwave Dielectric Properties of Ni0.2CuXZn0.8-XFE2O4 for Application in Antenna," Progress In Electromagnetics Research B, Vol. 57, 157-175, 2014.
doi:10.2528/PIERB13090705
References

1. Reaney, I. M. and D. Iddles, "Microwave dielectric ceramics for resonators and filters in mobile phone networks," J. Am. Ceram. Soc., Vol. 89, 2063-2072, 2006.

2. Cava, R. J., "Dielectric materials for applications in microwave communications," J. Mater. Chem.,, Vol. 11, 54-62, 2001.
doi:10.1039/b003681l

3. Rajput, S. S., S. Keshri, V. R. Gupta, N. Gupta, V. Bovtun, and J. Petzelt, "Design of microwave dielectric resonator antenna using MZTO-CSTO composite," Ceramics International, Vol. 38, No. 3, 2355-2362, 2012.
doi:10.1016/j.ceramint.2011.10.088

4. Hunter, C., L. Billonet, B. Jarry, and P. Gullion, "Microwave filters-applications and technology," IEEE Trans. on Microw. Theory and Tech., Vol. 50, No. 3, 794-805, 2002.
doi:10.1109/22.989963

5. Rajput, S. S. and S. Keshri, "Structural, vibrational and microwave dielectric properties of (1 ¡ x)Mg0:95Co0:05TiO3 ¡ (x)Ca0:8Sr0:2TiO3 ceramic composites," J. Alloys Compd., Vol. 581, 223-229, 2013.
doi:10.1016/j.jallcom.2013.05.225

6. Luk, K. M. and K. W. Leung, Dielectric Resonator Antennas, Research Studies Press Ltd., 2002.

7. Fechine, P. B. A., R. S. T. Moretzsohn, R. C. S. Costa, J. Derov, J. W. Stewart, A. J. Drehman, C. Junqueira, and A. S. B. Sombra, "Magneto-dielectric properties of the Y3Fe5O12 and Gd3Fe5O12 dielectric ferrite resonator antennas ," Microwave Opt. Technol. Lett., Vol. 50, No. 11, 2852-2857, 2008.
doi:10.1002/mop.23824

8. Parida, S., S. K. Rout, N. Gupta, and V. R. Gupta, "Solubility limits and microwave dielectric properties of Ca(ZrxTi1¡x)O3 solid solution," J. Alloys Compd., Vol. 546, 216-223, 2013.
doi:10.1016/j.jallcom.2012.08.076

9. Parida, S., S. K. Rout, V. Subramanian, P. K. Barhai, N. Gupta, and V. R. Gupta, "Structural, microwave dielectric properties and dielectric resonator antenna studies of Sr(ZrxTi1¡x)O3 ceramics," J. Alloys Compd., Vol. 528, 126-134, 2012.
doi:10.1016/j.jallcom.2012.03.047

10. Louzir, A., P. Minard, and J. F. Pintos, "Parametric study on the use of magneto-dielectric materials for antenna miniaturization," IEEE Antennas and Propagation Society International Symposium (APSURSI), Vol. 978, No. 1, 1-4, 2010.

11. Hansen, R. C. and M. Burke, "Antennas with magneto-dielectrics," Microwave Opt. Technol. Lett., Vol. 26, No. 2, 75-78, 2000.
doi:10.1002/1098-2760(20000720)26:2<75::AID-MOP3>3.0.CO;2-W

12. Albuquerque, A. S., J. D. Ardisson, W. A. A. Macedo, and M. C. M. Alves, "Nanosized powders of NiZn ferrite: Synthesis, structure, and magnetism," J. Appl. Phys., Vol. 87, 4352-4357, 2000.
doi:10.1063/1.373077

13. Goldman, A., "Magnetic ceramics (ferrites). In: Engineered materials handbook --- `Ceramics and glasses'," ASM International, The Materials Information Society, Vol. 4, 1161, 1991.

14. Ebnabbasi, K., M. Mohebbi, and C. Vittoria, "Coaxial line technique to measure constitutive parameters in magnetoelectric ferrite materials," IEEE Micro. Wireless Comp. Letters, Vol. 23, No. 9, 504-506, 2013.
doi:10.1109/LMWC.2013.2273033

15. Ebnabbasi, K., M. Mohebbi, and C. Vittoria, "Strong magnetoelectric coupling in hexaferrites at room temperature," J. Appl. Phys., Vol. 113, 17C707-1-17C707-3, 2013.

16. Souriou, D., J. L. Mattei, A. Chevalier, and P. Queffelec, "Influential parameters on electromagnetic properties of nickel-zinc ferrites for antenna miniaturization," J. Appl. Phys., Vol. 107, 09A518, 2010.

17. Ebnabbasi, K., M. Mohebbi, and C. Vittoria, "Magnetoelectric effects at microwave frequencies on Z-type hexaferrite," App. Phy. Letters, Vol. 101, 062406-1-062406-3, 2012.

18. Ebnabbasi, K., Y. Chen, A. Geiler, V. Harris, and C. Vittoria, "Magneto-electric effects on Sr Z-type hexaferrite at room temperature," J. Appl. Phys., Vol. 111, 07C719-1-07C719-3, 2012.

19. Mohebbi, M., "K. Ebnabbasi, and C. Vittoria, In-situ deposition of C-axis oriented barium ferrite films for microwave applications," IEEE Trans. on Magn., Vol. 49, No. 7, 4207-4209, 2013.
doi:10.1109/TMAG.2013.2250491

20. Adam, J. D., S. V. Krishnaswamy, S. H. Talisa, and K. C. Yoo, "Thin-film ferrites for microwave and millimeter-wave applications," J. Magn. Magn. Mater., Vol. 83, No. 1--3, 419-424, 1990.
doi:10.1016/0304-8853(90)90570-G

21. Yang, G.-M., J. Lou, O. Obi, and N. X. Sun, "Novel compact and low-loss phase shifters with magnetodielectric disturber," IEEE Micro. Wireless Comp. Letters, Vol. 21, No. 5, 240-242, 2011.
doi:10.1109/LMWC.2011.2123085

22. Kong, L. B., Z. W. Li, G. Q. Lin, and Y. B. Gan, "Ni-Zn ferrites composites with almost equal values of permeability and permittivity for low-frequency antenna design," IEEE Trans. on Magn., Vol. 43, No. 1, 6-10, 43.
doi:10.1109/TMAG.2006.886321

23. Yang, G. M., "Tunable miniaturized RF devices on magneto-dielectric substrates with enhanced performance," Northeastern University, Apr. 2010.

24. Mohit, K., V. R. Gupta, N. Gupta, and S. K. Rout, "Structural and microwave characterization of Ni0:2CoxZn0:8¡xFe2O4 for antenna applications," Ceramics International, Vol. 40, 1575-1586, 2014.
doi:10.1016/j.ceramint.2013.07.045

25. Teo, M. L. S., L. B. Kong, Z. W. Li, G. Q. Lin, and Y. B. Gan, "Development of magneto-dielectric materials based on Li-ferrite ceramics: II. DC resistivity and complex relative permittivity," J. Alloy Compd., Vol. 459, 567-575, 2008.
doi:10.1016/j.jallcom.2007.05.082

26. Slick, P. I., "Ferromagnetic Materials,", Vol. 2, 196.

27. Albuquerque, A. S., J. D. Ardisson, W. A. A. Macedo, and M. C. M. Alves, "Nanosized powders of NiZn ferrite: Synthesis, structure, and magnetism," J. Appl. Phys., Vol. 87, 4352-4357, 2000.
doi:10.1063/1.373077

28. Pathan, A. N., K. Sangshetti, and A. A. G. Pangal, "Synthesis, characterisation and magnetic studies of Co0:4Zn0:4¡XCuXFe2O4 nanoparticles," Nanotechnology and Nanoscience, Vol. 1, No. 1, 8-12, 2010.

29. Su, H., X. Tang, H. Zhang, Z. Zhong, and J. Shen, "Sintering dense NiZn ferrite by two-step sintering process," J. Appl. Phys., Vol. 109, 07A501, 2011.

30. Su, H., X. Tang, H. Zhang, Y. Jing, F. Bai, and Z. Zhong, "Low-loss NiCuZn ferrite with matching permeability and permittivity by two-step sintering process," J. Appl. Phys., Vol. 113, 17B301, 2013.

31. Naser, M. G., E. B. Saion, M. Hashim, A. H. Shaari, and H. A. Ahangar, "Synthesis and characterization of zinc ferrite nanoparticles by a thermal treatment method," Solid State Communications, Vol. 151, 1031-1035, 2011.
doi:10.1016/j.ssc.2011.04.018

32. Joseyphus, R. J., C. N. Chinnasamy, B. Jeyadevan, A. Kasuya, K. Shinoda, A. Narayanasamy, and K. Tohji, "Synthesis of ferrite nanoparticles through aqueous process for biomedical applications," Proceedings, 1st International Workshop on Water Dynamics Tohoku University, 51-53, Mar. 2004.

33. Todaka, Y., M. Nakamura, S. Hattori, K. Tsuchiya, and M. Umemoto, "Synthesis of ferrite nanoparticles by mechanochemical processing using a ball mill," Materials Transactions, Vol. 44, 277-284, 2003.
doi:10.2320/matertrans.44.277

34. Li, S., L. Liu, V. T. John, C. J. O'Connor, and V. G. Harris, "Cobalt-ferrite nanoparticles: Correlations between synthesis procedures, structural characteristics and magnetic properties," IEEE Trans. on Magn., Vol. 37, 2350-2352, 2001.

35. Raval, A. M., N. R. Panchal, and R. B. Jotania, "Structural studies of co-spinel ferrite synthesized by an auto combustion method," Journal of Analytical Techniques, Vol. 1, 01-02, 2010.
doi:10.5355/JAST.2010.1

36. Christou, A. and J. F. Crider, "The strengthening of Ti-55 at. % Ni by formation of a Ti2Ni3 intermetallic phaseJournal of materials science," J. Material Sc., Vol. 7, No. 4, 479-480, 1972.
doi:10.1007/BF02403415

37. Munir, Z. A., "Synthesis of high temperature materials by self-propagating combustion method," Fenmo Yejin Jishu/Powder Metallurgy Technology, Vol. 6, No. 1, 1-24, 1988..

38. Sutka, A. and G. Mezinskis, "Sol-gel auto-combustion synthesis of spinel-type ferrite nanomaterials," Front. Mater. Sci., Vol. 6, 128-141, 2012.
doi:10.1007/s11706-012-0167-3

39. Thant, A. A., S. Srimala, P. Kaung, M. Itoh, O. Radzali, and M. N. Ahmad Fauzi, "Low temperature synthesis of MgFe2O4 soft ferrite nanocrystallites," J. Australian Ceram. Soc., Vol. 46, 11-14, 2010.

40. Huang, C.-L., J.-J. Wang, and C.-Y. Huang, "Sintering behavior and microwave dielectric properties of nano alpha-alumina," Materials Letters, Vol. 59, 3746-3749, 2005.
doi:10.1016/j.matlet.2005.06.053

41. Huang, C.-L., J.-J. Wang, and C.-Y. Huang, "Microwave dielectric properties of sintered alumina using nano-scaled powders of a Alumina and TiO2," J. Am. Ceram. Soc., Vol. 90, 1487-1493, 2007.
doi:10.1111/j.1551-2916.2007.01557.x

42. Zahi, S., "Synthesis, permeability and microstructure of the optimal nickel-zinc ferrites by sol-gel route," J. Electromagnetic Analysis & Applications, Vol. 2, 56-62, 2010.
doi:10.4236/jemaa.2010.21009

43. Goldman, A., Modern Ferrite Technology, Van Nostrand Reinhold, 1990.

44. Slemon, G. R., Magnetoelectric Devices, Wiley, 1966.

45. Bae, S. Y., H. J. Jung, C. S. Kim, and Y. J. Oh, "Magnetic properties of sol-gel derived Ni-Zn ferrite thin films," J. de Phys. IV JP, Vol. 8, No. 2, 261-264, 1998.

46. Lee, J. S., B. I. Lee, and S. K. Joo, "Effects of process parameters on structure and magnetic properties of sputtered Ni-Zn ferrite thin films," IEEE Trans. on Magn., Vol. 35, 3415-3417, 1999.

47. Qian, Z., G. Wang, J. M. Sivertsen, and J. H. Judy, "Ni-Zn ferrite thin films prepared by facing target sputtering," IEEE Trans. on Magn., Vol. 33, 3748-3750, 1997.
doi:10.1109/20.619559

48. Kiyomura, T. and M. Gomi, "Room-temperature epitaxial growth of Ni-Zn ferrite thin films by pulsed laser deposition in high vacuum," Jpn. J. Appl. Phys. Part 2: Lett., Vol. 36, L1000-L1002, 1997.
doi:10.1143/JJAP.36.L1000

49. Verma, A. and D. C. Dube, "Processing of nickel-zinc ferrites via the citrate precursor route for high-frequency applications," J. Am. Ceram. Soc., Vol. 88, 519-523, 2005.
doi:10.1111/j.1551-2916.2005.00098.x

50. Nakamura, T., "Low-temperature sintering of Ni-Zn-Cu ferrite and its permeability spectra," J. Magn. Magn. Mater., Vol. 168, 285-291, 1997.
doi:10.1016/S0304-8853(96)00709-3

51. Rahman, I. Z. and T. T. Ahmed, "A study on Cu substituted chemically processed Ni-Zn-Cu ferrites ," J Magn Magn Mater., Vol. 290--291, 1576-1579, 2005.
doi:10.1016/j.jmmm.2004.11.250

52. Aphesteguy, J. C., A. Damiani, D. D. Giovanni, and S. E. Jacobo, "Microwave-absorbing characteristics of epoxy resin composites containing nanoparticles of NiZn- and NiCuZn-ferrites," Physica B, Vol. 404, No. 18, 2713-2716, 2009.
doi:10.1016/j.physb.2009.06.065

53. Mohit, K., S. K. Rout, S. Parida, G. P. Singh, S. K. Sharma, S. K. Pradhan, and I. W. Kim, "Structural, optical and dielectric studies of NixZn1¡xFe2O4 prepared by autocombustion route," Physica B, Vol. 407, 935-942, 2012.
doi:10.1016/j.physb.2011.12.003

54. Cullity, B. D., Element of X-ray Diffraction, 2nd Ed., Wesley Publication Company Inc., 1978.

55. Smit, J. and H. P. J. Wijn, "Ferrites," John Wiley, 1959.

56. Hakki, B. W. and P. D. Coleman, "A dielectric resonator method of measuring inductive capacities in the millimeter range," IRE Trans. on Microw. Theory Tech., Vol. 8, No. 4, 402-410, 1960.
doi:10.1109/TMTT.1960.1124749

57. Courtney, W. E., "Analysis and evaluation of a method of measuring the complex permittivity and permeability microwave insulators," IEEE Trans. on Microw. Theory and Tech., Vol. 18, No. 8, 476-485, 1970.
doi:10.1109/TMTT.1970.1127271

58. Sebastian, M. T., Dielectric Materials for Wireless Communication, Elsevier Publication, 2008.

59. Krupka, J., "Frequency domain complex permittivity measurements at microwave frequencies," Meas. Sci. Technol., Vol. 16, R1-R16, 2005.

60. Krupka, J., K. Derzakowski, B. Riddle, and J. B. Jarvis, "A dielectric resonator for measurements of complex permittivity of low loss materials as a function of temperature," Meas. Sci. Technol., Vol. 9, 1751-1756, 1998.
doi:10.1088/0957-0233/9/10/015

61. Chen, L. F., C. K. Ong, C. P. Neo, V. V. Varadan, and V. K. Varadan, "Microwave Electronics: Measurement and Materials Characterization," John Wiley & Sons Ltd., 2004.

62. Kobayashi, Y. and S. Tanaka, "Resonant modes of a dielectric rod resonator short-circuited at both ends by parallel conducting plates," IEEE Trans. on Microw. Theory and Tech., Vol. 28, No. 10, 1077-1085, 1980.
doi:10.1109/TMTT.1980.1130228

63. Parida, S., S. K. Rout, L. S. Cavalcante, E. Sinha, M. S. Li, V. Subramanian, N. Gupta, V. R. Gupta, J. A. Varela, and E. Longo, "Structural refinement, optical and microwave dielectric properties of BaZrO3," Ceramics International, Vol. 38, No. 3, 2129-2138, 2012.
doi:10.1016/j.ceramint.2011.10.054

64. Moreira, M. L., P. G. C. Buzolin, V. M. Longo, N. H. Nicoleti, J. R. Sambrano, M. S. Li, J. A. Varela, and E. Longo, "Joint experimental and theoretical analysis of order-disorder effects in cubic BaZrO3 assembled nanoparticles under decaoctahedral shape ," J. Phys. Chem. A., Vol. 115, 4482-4490, 2011.
doi:10.1021/jp1119124

65. Kobayashi, Y. and M. Katoh, "Microwave measurement of dielectric properties of low-loss materials by the dielectric rod resonator method," IEEE Trans. on Microw. Theory and Tech., Vol. 33, No. 7, 586-592, 1985.
doi:10.1109/TMTT.1985.1133033

66. Afsar, M. N., J. R. Birch, and R. N. Clarke, "The measurement of the properties of materials," IEEE Trans. on Microw. Theory and Tech., Vol. 25, No. 1, 183-199, 1977.

67. De Paula, A. L., M. C. Rezende, and J. J. Barroso, "Experimental measurements and numerical simulation of permittivity and permeability of teflon in X band," J. Aerosp.Technol. Manag. Sao Jose dos Campos., Vol. 3, No. 1, 59-64, 2011.
doi:10.5028/jatm.2011.03019410

68. Kajfez, D. and P. Guillon, Dielectric Resonators, , The Artech House Microwave Library, 1986.

69. Petosa, A., A. Ittipiboon, Y. M. M. Antar, and D. Roscoe, "Recent advances in dielectric-resonator antenna technology," IEEE Antennas Propag. Mag., Vol. 40, 35-48, 1998.
doi:10.1109/74.706069

70. Junker, G. P., A. W. Glisson, and A. A. Kishk, "Input impedance of dielectric resonator antennas top loaded with high permittivity and conducting disks," Microw. Opt. Technol. Lett., Vol. 9, 204-207, 1995.
doi:10.1002/mop.4650090412

71. Junker, G. P., A. A. Kishk, A. W. Glisson, and D. Kajfez, "Effect of an air gap around the coaxial probe exciting a cylindrical dielectric resonator antenna," Electron. Lett., Vol. 30, 177-178, 1994.
doi:10.1049/el:19940191

72. Mongia, R. K. and A. Ittipiboon, "Theoretical and experimental investigations on rectangular dielectric resonator antennas," IEEE Trans. on Antenna and Propag., Vol. 45, No. 9, 1348-1356, 1997.
doi:10.1109/8.623123

73. Peng, Z., H. Wang, and X. Yao, "Dielectric resonator antennas using high permittivity ceramics," Ceramics International, Vol. 30, 1211-1214, 2004.
doi:10.1016/j.ceramint.2003.12.079

74. Luk, K. M. and K. W. Leung, Dielectric Resonator Antennas, Research Studies Press Ltd., 2002.

75. Kumari, R., K. Parmar, and S. K. Behera, "Conformal patch fed stacked triangular dielectric resonator antenna for wlan applications," IEEE Int. Conf. Emerging Trends in Robotics and Comm.Tech. , 104-107, Dec. 2010.

76. Grabovickic, R., "Accurate calculations of geometrical factors of Hakki-Coleman shielded dielectric resonators," IEEE Trans. on Appl. Supercond, Vol. 9, 4607-4612, 1999.
doi:10.1109/77.791916

77. Hwang, C. C., J. S. Tsai, and T. H. Huang, "Combustion synthesis of Ni-Zn ferrite by using glycine and metal nitrates|Investigations of precursor homogeneity, product reproducibility, and reaction mechanism," Mater. Chem. Phys., Vol. 93, 330-336, 2005.
doi:10.1016/j.matchemphys.2005.03.056

78. Kugimiya, K. and H. Steinfink, "Influence of crystal radii and electronegativities on the crystallization of AB2X4 stoichiometries," J. Inorganic Chem., Vol. 7, 1762-1770, 1968.
doi:10.1021/ic50067a015

79. Modi, K. B., P. V. Tanna, S. S. Laghate, and H. H.Joshi, "The effect of Zn+2 substitution on some structural properties of CuFeCrO4 system," J. Mater. Sci. Lett., Vol. 19, 1111-1113, 2000.
doi:10.1023/A:1006784304415

80. Sathishkumar, G., C. Venkataraju, and K. Sivakumar, "Structural and dielectric studies of nickel substituted cobalt-zinc ferrite," Mat. Sci. App., Vol. 1, 19-24, 2010.

81. Scherrer, P. and G. Nachricht, "Bestimmung der grÄosse und der innerenstruktur von kolloidteilchen mittels rÄontgenstrahlen, nachrichten von der gesellschaft der wissenschaften, gÄottingen," Mathematisch-Physikalische Klasse, Vol. 2, 98-98, 1918.

82. Shebanova, O. N. and P. Lazer, "Raman spectroscopic study of magnetite (FeFe2O4): A new assignment for the vibrational spectrum," J. State Chem., Vol. 174, 424-430, 2003.
doi:10.1016/S0022-4596(03)00294-9

83. Prince, E., Mathematical Technique in Crystallography and Material Science, Springer Verlag, 1982.

84. Wang, Z., D. Schiferl, Y. Zhao, and H. S. C. O'Neill, "High pressure Raman spectroscopy of spinel-type ferrite ZnFe2O4," J. Phys. Chem. Solids, Vol. 64, 2517-2523, 2003.
doi:10.1016/j.jpcs.2003.08.005

85. Waldron, R. D., "Infrared spectra of ferrites," Phys. Rev., Vol. 99, 1727-1735, 1955.
doi:10.1103/PhysRev.99.1727

86. Hafner, S., "Ordnung/unordnung und ultrarotabsorption IV. Die absorption einiger metalloxyde mit spinellstruktur," Z. Krist., Vol. 115, 331-358, 1961.
doi:10.1524/zkri.1961.115.5-6.331

87. Ostos, C., L. Mestres, M. L. Mart¶³nez-Sarrion, J. E. Garca, A. Albareda, and R. Perez, "Synthesis and characterization of A-site de¯cient rare-earth doped BaZrxTi1¡xO3 perovskite-type compounds ," Solid State Sci., Vol. 11, 1016-1022, 2009.
doi:10.1016/j.solidstatesciences.2009.01.006

88. Tsurumi, T., T. Teranishi, S. Wada, H. Kakemoto, M. Nakada, and J. Akedo, "Wide range dielectric spectroscopy of SrTiO3-SrZrO3 solid solution," 15th IEEE International Symposium on the Applications of Ferroelectrics, isaf'06, 1-8, 2006.

89. Lee, C. T., C. T. Chen, C. Y. Huang, and C. J. Wang, "Lee, C. T., C. T. Chen, C. Y. Huang, and C. J. Wang, Microwave dielectric properties of (Ba1¡xMgx)5Nb4O15 ceramics," Jap. J. Appl. Phys., Vol. 47, No. 6, 4634-4637, 2008.
doi:10.1143/JJAP.47.4634

90. Shannon, R. D. , "Dielectric polarizabilities of ions in oxides and fluorides," J. Appl. Phys., Vol. 73, 348-366, 1993.
doi:10.1063/1.353856

91. Grimes, N. W. and R. W. Grimes, "Dielectric polarizability of ions and the corresponding effective number of electrons," J. Phys.: Condens. Matter, Vol. 10, 3029-3034, 1998.
doi:10.1088/0953-8984/10/13/019

92. Yoon, S. H., D. W. Kim, S. Y. Cho, and K. S. Hong, "Investigation of the relations between structure and microwave dielectric properties of divalent metal tungstate compounds," J. European Ceramic Society, Vol. 26, 2051-2054, 2006.
doi:10.1016/j.jeurceramsoc.2005.09.058

93. Schenck, J. F., "General Electric Corporate Research and Development Center," Schenectady, 12309, 1996.

94. Rajput, S. S., S. Keshri, and V. R. Gupta, "Microwave dielectric properties of (1 - x)Mg0:95Zn0:05TiO3{(x)Ca0:6La0:8=3TiO3 ceramic composites," J. Alloys Compd., Vol. 552, 219-226, 2013.
doi:10.1016/j.jallcom.2012.10.019

95. Balanis, C. A., Antenna Theory Analysis and Design, John Wiley & Sons, Inc., 2005.