International ournal of Applied Ceramic Technolog-Sebastian and Jantunen Vol.7,No.4,2010 Licht 0-S2 △-S3 EMt 7S4 Modified Lichteneck -o- S5 10203040506070 BaTiO3 powder(vol%) Variation of relative Permittivity with BaTiO3 poud loading and their particle size (S1=0.151um, S2=0.254um S3=0319μm,S=08321um,S5=0916μum, after Cho et al.3 shape of the filler used in the polymer-ceramic com- posites. A small value of n indicates a near-spherical shape for the filler, while a high value of n shows a largely nonspherically shaped particle. However, the particle size should be small for a better fitting with the theoretical prediction. The EMT model fits well for the polymer-Sm2Si2O7 composites as shown in Fig. 4 However, Teirikangas et al. reported that in som cases, the morphology factor n used in EMT is not in- Volume fraction of Sm2 Si207 dependent of the selection of the polymer. Several quan titative rules of mixture models had been proposed for permitivity(a) polystyrene- Si 07(6) polyethylene-Sm25i207 each componen. s of the dielectric properties of Fig. 4. Comparison of theoretical and experimental relative redictions of the However, the theoretical composites at 8 GHz(after Thomas et al) models do not completely agree with the experimental somewhat sensitive to both the polymer and the ce- that it is difficult to obtain the correct Er of the powders ramic, thus reducing the feasibility of the Lichtnecker Instead, E, of the bulk ceramic is used. The er of the equation for different materials. The relative permit- powder may be different from that of the bulk. In fer- tivity of composites also depends on the distribution of roelectric BaTiO3 powders, Er varies with particle of the filler, shape, and size of the fillers and the interfac between ceramics and polymers. Recently, Rao et al. ace grain sizes. Figure 5 shows the variation of Er with proposed a model(Effective Medium Theory, EMT)to The number of theoretical models available for pre predict the relative permittivity of the composite in listing loss tangent is relatively less, as it is more com which the dielectric property of the composite is treated plicated. 4 The following relations are used to model the as an effective medium whose relative permittivity is dielectric loss tangent of the composites btained by averaging the permittivity values of the constituents. The emt model is a self-consistent model that assumes a random unit cell consisting of each filler an8)2=∑m(tan)2 surrounded by a concentric matrix layer. The model includes a morphology factor"n, "which is determined where tan 8 and tan 8; are the loss tangent of the com- empirically. This correction factor compensates for th osite, the loss tangent of ith material, a is a constant,somewhat sensitive to both the polymer and the ce￾ramic, thus reducing the feasibility of the Lichtnecker equation for different materials.41 The relative permit￾tivity of composites also depends on the distribution of the filler, shape, and size of the fillers and the interface between ceramics and polymers. Recently, Rao et al. 51 proposed a model (Effective Medium Theory, EMT) to predict the relative permittivity of the composite in which the dielectric property of the composite is treated as an effective medium whose relative permittivity is obtained by averaging the permittivity values of the constituents. The EMT model is a self-consistent model that assumes a random unit cell consisting of each filler surrounded by a concentric matrix layer. The model includes a morphology factor ‘‘n,’’ which is determined empirically. This correction factor compensates for the shape of the filler used in the polymer–ceramic com￾posites. A small value of n indicates a near-spherical shape for the filler, while a high value of n shows a largely nonspherically shaped particle. However, the particle size should be small for a better fitting with the theoretical prediction. The EMT model fits well for the polymer–Sm2Si2O7 composites as shown in Fig. 4. However, Teirikangas et al. 41 reported that in some cases, the morphology factor n used in EMT is not in￾dependent of the selection of the polymer. Several quan￾titative rules of mixture models had been proposed for predictions of the basis of the dielectric properties of each component.6,50,52,53 However, the theoretical models do not completely agree with the experimental observations. One of the reasons for the poor fitting is that it is difficult to obtain the correct er of the powders. Instead, er of the bulk ceramic is used. The er of the powder may be different from that of the bulk. In fer￾roelectric BaTiO3 powders, er varies with particle or grain sizes.53 Figure 5 shows the variation of er with vol% of BaTiO3 powder having different grain sizes. The number of theoretical models available for pre￾dicting loss tangent is relatively less, as it is more com￾plicated.54 The following relations are used to model the dielectric loss tangent of the composites. General mixing model55,56 ðtan dcÞ a ¼ Xvfiðtan diÞ a ð6Þ where tan dc and tan di are the loss tangent of the com￾posite, the loss tangent of ith material, a is a constant, Fig. 4. Comparison of theoretical and experimental relative permittivity (a) polystyrene–Sm2Si2O7 (b) polyethylene–Sm2Si2O7 composites at 8 GHz (after Thomas et al.40). Fig. 5. Variation of relative permittivity with BaTiO3 powder loading and their particle size (S1 5 0.151 mm, S2 5 0.254 mm, S3 5 0.319 mm, S4 5 0.832 mm, S5 5 0.916 mm, after Cho et al.53). 420 International Journal of Applied Ceramic Technology—Sebastian and Jantunen Vol. 7, No. 4, 2010