Derivation of Lichtenecker's logarithmic mixture formula from Maxwell's equations

IEEE Transactions on Microwave Theory and Techniques

Volumn 58, Issue 3, 2010, Pages 545-550

  Simpkin, Ray ^a  

^a CALLAGHAN INNOVATION   (New Zealand)

Author keywords

Dielectrics; Electromagnetic theory; Mixture formulas

Indexed keywords

CHARGE CONSERVATION; DIELECTRIC MIXTURES; DIELECTRICS; EFFECTIVE PERMITTIVITY; ELECTROMAGNETIC THEORIES; LOGARITHMIC MIXTURE; MAXWELL'S EQUATIONS; MAXWELL-GARNETT; RANDOMLY DISTRIBUTED; SEMI-EMPIRICAL; SPATIAL DISTRIBUTION; SYMMETRIC MIXTURES;

DIELECTRIC MATERIALS; ELECTRIC FIELDS; MIXTURES; SIZE DISTRIBUTION;

MAXWELL EQUATIONS;

EID: 77949541162     PISSN: 00189480     EISSN: None     Source Type: Journal    
DOI: 10.1109/TMTT.2010.2040406     Document Type: Article

References (12)

1. K. Lichtenecker, "Die Dielektrizitätskonstante natürlicher und künstlicher Mischkörper," Phys. Zeitschr., vol.XXVII, pp. 115-158, 1926.
2. K. Lichtenecker and K. Rother, "Die Herleitung des logarithmischen Mischungs-gesetzes aus allegemeinen Prinzipien der stationaren Stromung," Phys. Zeitschr., vol.XXXII, pp. 255-260, 1931.
3. P. S. Neelakantaswamy, K. F. Aspar, A. Rajaratnam, and N. P. Das, "A dielectric model of the human blood," Biomed. Tech., vol.28, no.1-2, pp. 18-22, 1983.
4. Y. Zheng, S. Wang, J. Feng, Z. Ouyang, and X. Li, "Measurement of the complex permittivity of dry rocks and minerals: application of polythene dilution method and Lichtenecker's mixture formulas," Geophys. J. Int., vol.163, pp. 1195-1202, 2005.
5. A. Büchner, , Wissenschaftliche Veröffentlichungen aus den Siemens- Werken. Berlin, Germany: Siemens-Werken, 1939, vol.18, p. 84.
6. J. A. Reynolds and J. M. Hough, "Formulas for dielectric constant mixtures," Proc. Phys. Soc., vol.LXX, pp. 769-775, 1957.
7. P. S. Neelakantaswamy, R. I. Turkman, and T. K. Sarkar, "Complex permittivity of a dielectric mixture corrected version of Lichtenecker's logarithmic law of mixing," Electron. Lett., vol.21, no.7, pp. 270-271, Mar. 1985.
8. T. Zakri, J.-P. Laurent, and M. Vauclin, "Theoretical evidence of Lichtenecker's mixture formulas based on the effective medium theory," J. Appl. Phys., vol.31, pp. 1589-1594, 1998.
9. A. V. Goncharenko, V. Z. Lozovski, and E. F. Venger, "Lichtenecker's equation: Applicability and limitations," Opt. Commun., vol.174, pp. 19-32, Jan. 2000.
10. J. C. Maxwell-Garnett, "Colours in metal glasses and metal films," Trans. Royal Soc., vol.CCIII, pp. 385-420, 1904.
11. D. A. G. Bruggeman, "Calculation of various physical constants of heterogeneous substances, part I: Dielectric constant and conductivity of mixtures of isotropic substances," Annal. Phys., ser. 5, vol.24, pp. 636-679, 1935.
12. A. R. von Hippel, Dielectrics and Waves. New York: Wiley, 1954.