Calculation of the effective dielectric function of composites with periodic geometry

A method for calculating the effective dielectric function of a two-compone nt periodic composite is described. Using a simple Fourier expansion techni que, we obtain an explicit power series expression of H(t), which is one of the characteristic geometric functions of the two-component composite prop osed by Bergman. The relation between the series of H(t) and that of anothe r characteristic geometric function of composite F(s) is studied. The diele ctric function of composite F, Of two kinds of model systems is calculated by using both H(t) and F(s) for finite-size reciprocal lattice. The deviati ons of the numerical results of epsilon (e) from the exact ones, which are caused by the limited size of the reciprocal lattice used, are investigated . It is found that the: accuracies of the numerical results of F(s) differ from those of H(t). For simple cubic arrays of nonoverlapping spheres, the results of epsilon (e), obtained from H(t) are closer to the exact ones, es pecially when the volume fraction of the inclusions is larger and the diele ctric contrast of the composite is higher. For 2-D prisms, the averages of the results of epsilon (e) obtained from using F(s) and those from H(t) are closer to the exact ones. (C) 2000 Elsevier Science B.V. All rights reserv ed.