wwceramics. org/ACT Polymer-Ceramic Composites of 0-3 Connectivity 一 Experimental Parallel Serial ewwwM 0.03 Bruggmen “日: Volume Percentage of SCT Fig on of the experimental dielectric loss with the 4 predicted values(afier Subodh et al. 5) 4.5 and vg is the volume fraction of the ith material. The 24.0 value of the constant a determines the mixing rule where a=-1 means serial mixing, a= 1 parallel mix d a=0 gives the logarithmic The Bruggeman model Em)(E+2e/)e Temperature(C) +e-sa)(e+28) (7) polystyrene-Sm i207(b) polyethylene-Sm2i207composites(after Thomas where the e, em,E,e"i, e"m, e" are the real and imag- inary parts of the permittivity of the filler, matrix, and the temperature variation of the relative permittivity the composite, respectively. Figure 6 shows the com- reasonably small and the material is thus useful for parison of the predicted and experimental loss tangent practical applications. Results for other properties im for epoxy/Srg Ce?Ti12O3 composites. The Bruggeman portant for microwave substrates have been reported less model gives a relatively good fit with the experimental frequently. Walpata et al obtained a temperature results for lower filler contents. The dielectric loss de- compensated thermoplastic composite with a high E, by pends on intrinsic and extrinsic factors. The intrinsic using a second filler with contrasting thermal depen are mainly due to the interaction of the ac elec- dence of permittivity(tEr). They prepared a polyp ld with phonons. The extrinsic factors such henylene sulfide/SrTiO3/mica composite. The use of as defects, interfaces, size and shape of the filler, and one ceramic with a positive ter and the other with a micropores also contribute to dielectric loss negative ter allowed to obtain a temperature-compen- is The temperature coefficient of relative permittivity sated compensate figure 8 shows the variation of E, of one of the important properties that control the over- the composite 38/8/54(mica/SrTiO, /PPS)measured at all performance of the substrate materials. Some groups 2 GHz. The same procedure was also followed by Xiang have reported fabrication and calculation methods et al. to modify ter. Table I gives a list of the dielectric perature-compensated composites properties polym Figure 7 shows the temperature dependence of the Among the many reported composites given in Table relative permittivity of polystyrene and polyethylene I, polystyrene-Sr2Ce2TisO1s has a very loss tangent of composites with Sm2Si2O7. In many cases, however, 0.0004 relatively high permittivity of 13.6 atand vfi is the volume fraction of the ith material. The value of the constant a determines the mixing rule where a 5 1 means serial mixing, a 5 1 parallel mix￾ing, and a 5 0 gives the logarithmic mixing rule.55 The Bruggeman model57 e00 ¼ ðe0 i e0 Þðe0 i þ 2e0 mÞe0 ðe0 i e0 mÞðe0 i þ 2e0 Þe0 m e00 m þ 3ðe0 e0 mÞ ðe0 i e0 mÞðe0 i þ 2e0 Þ e00 i ð7Þ where the e0 i, e0 m, e0 , e00 i, e00 m, e00 are the real and imag￾inary parts of the permittivity of the filler, matrix, and the composite, respectively. Figure 6 shows the com￾parison of the predicted and experimental loss tangent for epoxy/Sr9Ce2Ti12O36 composites. The Bruggeman model gives a relatively good fit with the experimental results for lower filler contents. The dielectric loss de￾pends on intrinsic and extrinsic factors. The intrinsic factors are mainly due to the interaction of the ac elec￾tric field with phonons. The extrinsic factors such as defects, interfaces, size and shape of the filler, and micropores also contribute to dielectric loss. The temperature coefficient of relative permittivity is one of the important properties that control the over￾all performance of the substrate materials. Some groups have reported fabrication and calculation methods to enable temperature-compensated composites.38,59 Figure 7 shows the temperature dependence of the relative permittivity of polystyrene and polyethylene composites with Sm2Si2O7. 40 In many cases, however, the temperature variation of the relative permittivity is reasonably small and the material is thus useful for practical applications. Results for other properties im￾portant for microwave substrates have been reported less frequently. Walpata et al. 60 obtained a temperature￾compensated thermoplastic composite with a high er by using a second filler with contrasting thermal depen￾dence of permittivity (ter). They prepared a polyp￾henylene sulfide/SrTiO3/mica composite. The use of one ceramic with a positive ter and the other with a negative ter allowed to obtain a temperature-compen￾sated compensate. Figure 8 shows the variation of er of the composite 38/8/54(mica/SrTiO3/PPS) measured at 2 GHz. The same procedure was also followed by Xiang et al. 59 to modify ter. Table I gives a list of the dielectric properties of several polymer–ceramic composites. Among the many reported composites given in Table I, polystyrene–Sr2Ce2Ti5O15 has a very loss tangent of 0.0004 with a relatively high permittivity of 13.6 at 0 10 20 30 40 0.01 0.02 0.03 0.04 tan δ Volume Percentage of SCT Experimental Parallel Serial Logarithmic Bruggmen Fig. 6. Comparison of the experimental dielectric loss with the predicted values (after Subodh et al.58). Fig. 7. Variation of relative permittivity with temperature (a) polystyrene–Sm2Si2O7 (b) polyethylene–Sm2Si2O7 composites (after Thomas et al.40). www.ceramics.org/ACT Polymer–Ceramic Composites of 0–3 Connectivity 421