Continuing with our previous work  in this paper, we present an effective method that minimizes the uncertainty in the measurement of the real dielectricpermittivity of a material. As we indicated previously, the method is valid only for low loss materials in view of the nature of the exact relations between permittivity, sample and cavity dimensions, measured resonant frequency and the unloaded Q- factor for the resonant structures. Resonant methods are the preferred technique in dielectricpermittivity measurements over non-resonant measurements , in view to their higher accuracy and sensitivity. Although, recent papers have discussed the problems associated to the estimation of uncertainty in the measurement of dielectricpermittivity of materials, but only a few have proposed a systematic methodology for the reduction of the uncertainty associated to the measurement of the dielectricpermittivity using resonant cavities .
In this work, barium iron niobate, Ba (Fe1/2Nb1/2) O3 powder has been successfully synthesized by the sol-gel method. The formation of the perovskite structure of BFN was followed with the help of X-ray diffraction (XRD), and has shown a crystallite size at a nanometric scale. The pure perovskite phase was obtained at relatively low temperature (900°C /8 h) compared to the conventional solid-state reaction. Moreover, dielectric measurements showed strong relaxation and diffuse phenomena, and a maximum of the dielectricpermittivity at a temperature lower than those reported in the literature, together with resonance phenomenon at high frequenc
particles form clusters, the surface of which is less than the sum of the surface of their constituent particles. In- creasing the number of clusters with increasing bulk filler content is accompanied by decrease in the dielectric layer between the particles. It leads to increase in electric capacity and accordingly ε ''. In the composites ob- tained with the addition of aluminum nano-particles with size of 50 nm, the character of the dielectric permittiv- ity variation does not change. However, with increasing of Al content in the composite the value of ε '' decreases throughout the temperature range studied. This is probably due to the fact that the aluminum nano-particles oc- cupy vacancies-defects on the surface of the composites. This promotes the change in the electric resistance and the imaginary part of the dielectricpermittivity. Using aluminum nano-particles allows obtaining composites having the desired dielectricpermittivity and dielectric loss. Analysis of the frequency dependence of the dielec- tric permittivity and dielectric loss of PE+xvol.%TlInSe 2 composites and the same composite with aluminum
The dielectric parameters and have been meas- ured for a nematic liquid crystal BKS/B07 in the fre- quency range of 1 kHz to 10MHz for the temperature range of 70˚C to 135˚C. Figure 3 and Figure 4 represent typical frequency dependence spectra of the real and imaginary part of the dielectricpermittivity measured for nematic sample BKS/B07 and dye doped mixtures 1 and 2. The dielectricpermittivity is found to be either con- stant or to decrease as the frequency increases [17-22] for pure sample. Lower values of at higher frequency suggest that the molecules rotate about their long mo- lecular axis . The behaviour of for the dye based mixtures 1 and 2 is similar to that of pure sample but the values of dielectric constants are higher in comparison to the corresponding values of pure sample.
Natural rubber (NR) based composites containing different carbon nanofillers (fullerenes, carbon nanotubes and graphene nanoplatelets) at concentrations from 2 to 10 phr have been prepared. Their dielectric properties (di- electric permittivity, dielectric loss) have been studied in the 1 - 12 GHz frequency range. It was found that the dielectric constant and dielectric loss of filled composites depend on amount and type of filler loading. It has been established that with increasing the frequency of the electromagnetic field the dielectricpermittivity values increase, while those of the dielectric losses get lower. The higher the concentration of the fillers is (keeping identical all other conditions), the higher the values of dielectricpermittivity and dielectric losses are. The ob- served effects are related first of all to the impact that the chemical nature and crystallographic structure of the fillers and elastomer matrix studied have upon the polarization time and mechanism as well as upon the relaxa- tion time and mechanism. The latter processes determine the dielectric properties of the materials. The dielectric properties of the developed natural rubber composites containing conductive fillers (fullerenes, CNTs, GNPs) indicate that these composites can be used as broadband microwave absorbing materials.
The results of these measurements explain the observed microwave properties of the composites. It is obvious that the dielectricpermittivity and the dielectric loss of the composite medium depends on the intrinsic permittivity of the phases, their volume fraction, their shape and size, their geometrical arrangement associated with the material mixture and their textural characteristics. The textural characteristics of the activated carbons used as functional fillers are different (Table 2). This is the reason for their different effect on the real part of dielectricpermittivity and dielectric loss angle tangent as well as on the microwave properties of the composites. It was found that the highest value of the total shielding effectiveness possess the composites containing the activated carbon Norit. It has the lowest values of specific surface area, area and volume of micropores and the highest values of external surface area, volume of mesopores and average pore diameter. With gradually increasing the values of the indices in the first group and gradually decreasing the values of the indices in the second group, the value of total shielding effectiveness in the row Norit, AG-K and ART decreases. It is obvious that these indices have influence on the rubber matrix-filler particle interactions, such as multicontact chain adsorption to the surface of the filler. The spatial inhomogeneities formed give rise to polarization phenomena and to a frequency dependence of the dielectricpermittivity 37. It may be considered as a prove for the effect of activated carbons textural
In order to avoid the above drawbacks, it is reasonable to use electrodeless measurements which allow characterization of the ﬁlm itself, before the following technological process of subsequent layers deposition. To provide the electrodeless measurements of the dielectricpermittivity ( ε ) and dielectric loss tangent (tan δ ) of materials at microwave frequencies the metal cavity resonators are widely used [1– 4]. However, for the millimeter and especially sub-millimeter wavelengths, the above method is faced with considerable diﬃculties: (i) the microwave surface resistance of cavity metal walls increases at higher frequencies that leads to the decrease of the quality ( Q ) factor of the resonator, i.e., the accuracy of measurements decreases, (ii) the installation of the tested sample into the cavity usually involves disassembling and reassembling which if done frequently inevitably results in a variation of resonator
Walsh’s approach yields closed form solutions for rough surface backscatter when plane wave incidence is assumed, but the scattered ﬁelds for any realizable source can be found numerically. In Section 2 it is shown that Walsh’s method can be used to develop the scattering equations for a horizontal dipole over a rough surface. The x component of the electric ﬁeld has been derived, unlike in the original work where the y and z components alone were presented. The equations have been modiﬁed to include the case where the dielectricpermittivity of the surface is arbitrary, thus removing the assumption of a good conducting surface and allowing Walsh’s method to be applied to more general rough surfaces. The equations for stratiﬁed media backscatter are outlined in Section 3. The ﬁeld above the layers has a direct wave and a reﬂected component, similar to the rough surface case. One of the terms in the scattering is negligible, which makes it possible to express the scattering from stratiﬁed media using a reﬂection coeﬃcient. A justiﬁcation for modeling ice ridges as a rough surface over layers is provided in Section 4.
Figure 3. As seen in the concentration interval studied dielectricpermittivity values for the non-filled and filled composites are relatively close at lower frequencies (up to 7 GHz). At frequencies higher than 7 GHz the dielec- tric permittivity increases with the increasing filler con- centration. Moreover, there is a tendency of a more pro- nounced difference in the values for the non-filled and filled composites. The values we obtained for the non- filled composites are close to the ones for natural rubber at 1000 Hz reported in literature which are 2.40 - 2.70 . As the figure shows our investigations also confirm the fact that the dielectricpermittivity increases at higher frequencies. Of particular interest is the 9 - 12 GHz range wherein there is a relatively fast increase in the dielectricpermittivity and its dependence on the GNP is the most prominent. Having in mind that the dielectricpermittivity is related to the composites polarity , probably at frequencies higher than 9 GHz the polarization of the natural rubber matrix is hampered. Hence, the dielectric
2003; Lu et al., 2004; Wei et al., 2007) It is known that the cubic- tetragonal phase transition displays a continuous crossover with increase in the content of Sn from a sharp ferroelectric phase transition to a diffused phase transition and towards a relaxor-type behavior. On the other hand, the Zr addition in BZT lowers the dielectric loss due to its larger ionic size which expands the perovskite lattice whereas increase in its concentration induces a reduction in the average grain size, decreases the dielectricpermittivity (𝜀 𝑟 ) enabling it to maintain a low and stable leakage current (Rehrig et al., 1999; Zhi et al., 2000 and 2001). The Curie temperature of barium titanate system can be altered by the substitution of dopants into either A- or B-site. Partial replacement of titanium by tin, zirconium, or hafnium generally leads to a reduction in Tc and an increase in the permittivity maximum (𝜀 𝑚𝑎𝑥 ) with dopant content (Hennings et al., 1982). Therefore, co-
Table II lists the real and imaginary parts of the dielectricpermittivity at 3GHz and the refractive index values at 589nm for the tested nematic liquid crystals. The studied materials exhibit a dielectric anisotropy varying between 0.25 and 0.83 with low associated losses (typically tan δ ⊥ ~0.05 and tan δ || ~ tan δ ⊥ /2). Figure 4 shows dielectric anisotropy ∆ε (in microwave regime) vs birefringence ∆n (589nm) for two sets of data. One set of data was measured by us at 3GHz for the 9 nematic LCs, as listed in Table II. The other set of data was obtained from the work done by Lim K.C. et al at 30GHz .
+ (23) Equations (21) and (23) give the relation between the electromagnetic parameters of the unknown medium and the resonant frequency. The cut off wave number can be determined if the dielectricpermittivity constant is known or viceversa. This system is solved numerically using the Matlab function fsolve. The solution given in Equation (21) reduces to the simple form given in  and  when n = 0 . The possible sources of uncertainty present in this configuration are the exact dimensions of the cavity, losses in the wall’s finite conductivity and resolution of the measurement equipment -. Equations (21) and (23) reduce to the limit case of a simple cavity resonator filled with a single material when a = b or when the electromagnetic parameters of both mediums are equal. Because the frequency variable was canceled in Equations (21) and (23), some solutions could be added or eliminated. The solution obtained should be checked by using ω 1 = ω 2 .
were successfully obtained from mixed oxide method by two different synthesis techniques such as solid state and HBM. XRD studies revealed cubic structure without showing any secondary phase. FE-SEM images show sample is dense and have different microstructures with certain amount of porosity. The frequency dependent dielectric study reveals a normal ferroelectric behavior in the material. It is found that HBM and Tin/Zirconium concentration has significant influence on structural and dielectric properties of Ba(Ti 0.96 Sn 0.01 Zr 0.03) O 3 . The temperature
From the graphs in Figs. 5 and 6 for two-layered and multilayered dielectrics, one can see that increase of the number of layers gives rise to that the properties of these dielectric become closer to the properties of a homogeneous layer with eﬀective value of dielectricpermittivity. For multilayered structures with number of layers more than 20, the model of such a homogeneous layer produces quite satisfactory results. However, it is typical only for the eﬀective permittivity, determined by transmission coeﬃcient and only for TE polarization, but for TM polarization, at the values of angle of incidence more than 20 ◦ , one observes noticeable discrepancies from the Braggeman’s values. The matter is that formula (9) is applicable to the cases, when the electric ﬁeld is parallel to the boundaries of layers of a multilayered structure, as it occurs for TE polarization, but in the cases of ﬁeld orthogonal to the layers, the mixing formula (9) must be written with the index of a power − 1 for all dielectric permittivities [2, 3]. That is why for TM polarization, whose electric vector lies in the plane of incidence, its normal component increases with increase of the angle of incidence, and formula (9) becomes inapplicable. Besides, noticeable disagreements from Braggeman’s values arise for eﬀective permittivities, determined by reﬂection coeﬃcients, for both polarizations. Calculations show that the presence of great number of periodical layers by itself is not an essential feature. The relation between the wavelength of transmitting radiation and total thickness of a homogeneous layer is of importance to a far greater extent. The greater the wavelength is in comparison with the given thickness, the more accurate description one obtains using the Braggeman’s formula as for transmission, as for reﬂection from a layer. This formula provides suﬃciently complete description of dielectric properties of a plane layered heterogeneous medium only in the limiting case of negligibly small thickness of a medium in comparison with the wavelength of transmitting radiation. It is clear, because the Braggeman’s formula (9) was established for electrostatic ﬁelds.
Most soil moisture sensors are designed to estimate soil volumetric water content based on the dielectric constant (soil bulk permittivity) of the soil. The dielectric constant can be thought of as the soil's ability to transmit electricity. The dielectric constant of soil increases as the water content of the soil increases. This response is due to the fact that the dielectric constant of water is much larger than the other soil components, including air. Thus, measurement of the dielectric constant gives a predictable estimation of water content.
size variance. The variance provides a measure of local struc- ture and so it is clear that local structure plays a significant role in the dielectric response. Such information is not avail- able via conventional Rietveld analysis of di ﬀ raction data and probes of local structure are required. Nevertheless, it appears that variance may be a useful metric to guide the tuning of properties in TTBs and could be extended to other structure types which contain perovskite units such as Ruddlesen- Popper and Dion-Jacobsen phases.
Dielectric resonator antennas (DRAs) were first discovered in 1983 by Long et. al., and since then they have been widely studied . There have been several works reported in literature to improve various parameters (impedance bandwidth, axial ratio bandwidth, gain etc.) of DRAs [2-20]. Their inherent features of high radiation efficiency & ease of excitation, compactness, and ability to obtain radiation patterns using different excitation modes offer much to an antenna application . Furthermore, the shape of a DRA can be custom, resulting in favorable operating modes or polarizations. Also, the DRAs supporting circular polarizations have been studied and can be found in the literature. Traditionally, circular polarization is achieved using quadrature couplers and elaborate feed systems which can also be done with DRAs as well [3, 4].
We use a green diode laser of wavelength 532 nm incident on a dense flint glass. The laser radiation passes through a beam splitter which splits the light into two parts: One part is sent to a monitoring branch for moni- toring the stability of the probe laser and another part is sent through collimating slits incident on the dielectric surface. The light reflected by the dielectric is further detected along the detector branch using a high sensitivity light sensor. The incident light is attenuated to the desired intensity and next, polarized at 45 ˚ with respect to the plane of incidence so that it has equal intensities in the parallel and perpendicular components defined with re- spect to the plane of incidence (shown in Figure 1).
The frequency dependence of real (ε’) and imaginary (ε”) part of dielectric constant on a log-log plot at differ- ent temperatures are shown in Figure 4. Up to 200˚C, real part of dielectric constant is higher than its imagi- nary part, and both values decreases with frequency. With further increase in temperature, there is a sudden rise in ε” and it starts with higher value than ε’, inter- secting at 3 kHz at 250˚C; intersecting frequency shift towards higher frequency as temperature increased (4 kHz at 300˚C). Higher values of both the components of dielectric constant, as temperature rises, reveal the effect of space charge polarization and/or conducting ion mo- tion. The relatively higher values of ε” at low frequency, especially at higher temperature, suggests the free charge motion that may be related to ac conductivity relaxation, whereas the large values of ε’ at lower frequencies may be associated with hopping conduction. Moreover, with increase in frequency, the ε’ and ε” terms becomes al- most parallel at higher temperatures. This type of beha- vior is reported in other conducting ion dielectrics  and is associated with ion hoping as the dominant me- chanism of dielectric relaxation .