Maxwell-Wagner Model Research Articles

Room temperature variation in dielectric and electrical properties of Mn doped SnO2 nanoparticles

Pure and Mn doped SnO2 nanoparticles of the composition MnxSn(1-x)O2 where (x = 0.0, 0.03, 0.05, 0.07) were synthesized by sol gel auto combustion method. Structural studies performed by XRD and EDS suggest that the crystal system remains pure rutile with a tetragonal structure even after the doping of Mn. The EDS analysis reveals that both Sn and Mn elements are present in the sample which confirmed the successful doping of Mn in the SnO2 host structure. The identification of the various chemical bonds present in the pure and Mn doped samples has been carried out through Fourier Transform Infrared spectroscopy. FTIR spectrum has been recorded in solid phase using KBr pellets technique in the regions of 4000–400 cm-1. The complex dielectric constant, complex impedance, and a.c. conductivity have been studied as function of frequency and composition using LCR meter. Dielectric constant and loss was found to decrease with the increase in frequency and the obtained results have been explained on the basis of Maxwell-Wagner model. A.C. conductivity was found to increase with the increase in frequency due to hopping between charge carriers. It increases with the increase in dopant level which may be due to the free electron density and crystalline size.

Effects of LaNiO3 interlayer on the microstructures and electrical properties of Ba0.9Sr0.1Ti0.99Mn0.01O3 multilayer

The aim of this work was to investigate the effects of low-resistivity interlayer on the physical properties of periodic Ba0.9Sr0.1Ti0.99Mn0.01O3 (BSTM) multilayers prepared by a chemical solution deposition method. A LaNiO3 (LNO) layer was inserted into the periodic BSTM multilayer artificially to form a sandwiched configuration of BSTM/LNO/BSTM. The capacitances at low frequencies (<100 kHz) of the sandwiched multilayer are significantly enhanced compared to that of the pure BSTM multilayer. The space charge accumulated at the LNO layer was proposed to explain the enhancement based on Maxwell-Wagner (M-W) model. However, LNO interlayer leads to an increase in the leakage current. A non-Ohmic conduction region is observed for BSTM/LNO/BSTM multilayer when the electric field exceeds 100 kV/cm. The results offer a new approach to achieve dielectric films with high dielectric constant.

Dielectric Properties of New Cd&lt;sub&gt;1-3x&lt;/sub&gt;Dy&lt;sub&gt;2x&lt;/sub&gt;[]&lt;sub&gt;x&lt;/sub&gt;MoO&lt;sub&gt;4&lt;/sub&gt; Molybdates (where 0 &amp;lt; x ≤ 0.2)

New scheelite type Cd1-3xDy2x[]xMoO4solid solution, where 0.0098 ≤ x ≤ 0.2 and [] denotes the cationic vacancies, was investigated by using UV-vis-NIR and dielectric spectroscopies at room temperature and in the temperature range 77-400 K, respectively. These studies showed the optical band gap energy Eg above 3.4 eV and relative low dielectric permittivity: εr ~ 6.0, 9.5, 7.0 and 8.2 for the x parameter 0.0098, 0.0839, 0.1667 and 0.2000, respectively. εr slightly decreases with increasing frequency and slightly increases at higher temperatures. All samples showed the maximum permittivity in the temperature range of 250-350 K. The loss tangent exhibited similar behaviour and its maximum value did not exceed 0.25. These results are discussed in a context of the shallow trap levels and the Maxwell-Wagner model.

Dielectric responses in polycrystalline rare-earth iron garnets

Rare-earth iron garnets (RIG, R = Y, Tb and Lu) were sintered at 1350 °C. Their crystal structures were refined by the Rietveld method, which showed that the oxygen coordination polyhedra were highly distorted. X-ray photoelectron spectroscopy revealed a similar Fe2+/Fe3+ ratio (∼27/73) in different RIGs. The origins of dielectric responses were identified by cross examination of the permittivity, modulus and impedance presentations. Fitting experimental data with the Debye-type and Maxwell-Wagner models revealed that the dielectric relaxation at room temperature was dominated by the Debye-type process but as temperature increased, the Maxwell-Wagner effect gradually took over. The static permittivity was 750, 785 and 2653 for YIG, TbIG and LuIG, respectively. The particularly large permittivity of LuIG arose from a large difference between the distortions of FeO6 and FeO4 in the structure and therefore, a large dipole moment was created when electron hopping between the octahedral and tetrahedral sites took place.

Structural and complex impedance spectroscopic studies of Mg-substituted CoFe2O4

In this work, we present the effect of Mg substitution on the structural and impedance spectroscopic characteristics of Co1−xMgxFe2O4 (x=0.0, 0.3, 0.6, 0.9 and 1.0) samples, prepared by sol-gel auto-combustion method. As-burnt and fluffy powder samples were grinded and subsequently calcined at 600°C for 6h to change single phase cubic spinel structure, as confirmed by X-ray diffraction. The data obtained from diffraction was also utilized to perform Rietveld's refinement which provided detailed information on the structural changes occurred during the substitution. Frequency and temperature dependent electrical, and impedance studies were performed using an impedance analyzer in a wide frequency and temperature range. The behavior of characteristic dielectric parameters has been investigated using Maxwell-Wagner's model and Koop's theory. The impedance plot was used to define electro-active regions of the prepared samples, useful in modelling an equivalent circuit for each region. Frequency dependent Nyquist plot revealed the effect of grain, grain boundaries and electrode effect. Samples exhibited distinct grain and grain boundary contributions to the conductivity. Temperature dependent electrical characterization revealed that samples had negative temperature coefficient of resistance. The binding energies at different temperatures have also been estimated.

Sol-gel auto combustion synthesis, electrical and dielectric properties of Zn1−xCoxO (0.0 ≤ x ≤ 0.36) semiconductor nanoparticles

In the present work, Co2+ ion doped zinc oxide nanoparticles Zn1−xCoxO (x = 0.00, 0.06, 0.12, 0.18, 0.24, 0.30 and 0.36 mol) were synthesized by sol-gel auto combustion method. The effects of heavily doped Co2+ ion concentration on the structural, electrical and dielectric properties were studied. The prepared nanoparticles were characterized by X-ray diffraction technique (XRD), transmission electron microscopy (TEM), selected area diffraction pattern (SAED) and Fourier transform infrared spectroscopy (FT-IR). The X-ray diffraction analysis revealed the formation of single phase having hexagonal wurtzite structure along with secondary phase (Co3O4). TEM analysis clearly showed the small agglomeration and spherical shape of nanoparticles. SAED pattern also confirms the hexagonal wurtzite structure with single crystalline nature. FTIR analysis showed the vibrational frequency band position of Zn–O shifted to higher frequency band with Co2+ ion increasing host semiconductor nanoparticles. The temperature dependent (300–400 K) DC resistivity of samples was studied by the standard two probe method. DC electrical resistivity was found to increase with increasing Co2+ content in ZnO matrix. The dielectric properties of pure and Co2+ doped ZnO nanoparticles were studied as a function of frequency and composition using the LCR–Q meter. All the dielectric parameters show dispersion and decreases with increase in Co2+ content. The observed dielectric behavior is explained on the basis of Maxwell–Wagner model and Koops phenomenological theory.

Investigation of the Role of Ce3+ Substituted Ions on Dielectric Properties of Co-Cr Ferrites Prepared by Co-precipitation Method

A series of a CoCr0.04CexFe1.96−xO4 spinel ferrite system with 0 ≤ x ≤ 0.1 (in steps of 0.02) has been synthesized by the co-precipitation technique. The synthesized samples were characterized using a Fourier transform infrared spectroscope (FT-IR), Raman spectroscopy, a scanning electron microscope (SEM), and dielectric measurements. The typical FT-IR spectrum of the samples annealed at 850°C exhibited two frequency bands due to the formation of octahedral (B-site) and tetrahedral (A-site) clusters of metal oxide, respectively. The SEM images showed the spherical morphology of synthesized material and confirmed the grain size in the range of (0.33–0.44) μm. The decrease of permittivity with the increase of frequency in the range of 1 MHz to 3 GHz follows the Maxwell–Wagner model. Moreover, the Ce3+substituted materials have smaller values of loss tangent and dielectric constant especially for x = 0.10, which is favorable for the applications where low losses are desired. The value of ac (alternating current) conductivity increases with an increase in the frequency and decreases with Ce3+ substitution, which reflects the hopping mechanism at respective sites. Such characteristics of these materials may be suitable␣for potential applications such as electromagnetic attenuation materials, switching applications, and microwave devices.

Characterization and frequency-thermal response of electrical properties of Cu nanoferrite prepared by sol–gel method

In this paper, we have synthesized copper ferrite nanocrystals using sol–gel method. X-ray diffraction (XRD) analysis confirms that the ferrite has cubic spinal structure and shows Jahn–Teller effect. Also, scan electron microscope (SEM) image demonstrates that grains are nano size order. We showed that the dielectric properties are compatible with the Maxwell–Wagner model and phenomenological Koop's theory. Loss tangent and conductivity of the ferrite have been measured to have small values of 2.4 and 2×10−7S/m, respectively at room temperature and at 12Hz. Conductivity has been investigated in terms of localized hopping mechanism and good obedience of Jonscher's law was observed. Variation of activation energy was studied and showed a transition temperature of 443°K. The electrical modulus shows relaxation of interfacial polarization with relaxation time of 0.318ms at 24°C and 15.9μs at 72°C. In Impedance spectroscopy, we observed the effects of grain and grain boundary. By increasing temperature, capacity and conduction would increase which show easier polarization process and a semiconducting behavior. Also, relaxation times are shifted to smaller values to represent increasing the electrons mobility.

Structural, electrical, and optomagnetic tweaking of Zn doped CoFe2−xZnxO4−δ nanoparticles

Nanoparticles of pure and Zn doped CoFe2O4 of the composition CoFe2−xZnxO4−δ (x=0, 0.05, 0.10, 0.15) have been successfully synthesized by microwave gel combustion. The microstructural and compositional analyses were carried out by X-ray diffraction, Scanning Electron Microscopy. The crystallite size was found to increase with the increase in the Zn content. The dielectric constant (ε) and A.C. conductivity were studied as a function of frequency and temperature and were explained on the basis of Maxwell–Wagner model and electron hopping respectively. The energy band gap was found to decrease gradually with Zn doping. The magnetic measurements, depicts an increase in magnetization with the increase in Zn concentration, which in turn shows a strong dependency on the particle size. The magnetic hysteresis loop confirms the ferromagnetic nature.

Effects of Pr-contents on the structural, magnetic and high frequency parameters of M-type hexagonal ferrites synthesized by sol–gel method

A series of M-type hexagonal ferrite having chemical formula Ba0.75Ca0.25PrxFe12−2xO19 (x = 0.00, 0.50, 1.00, 1.50, 2.00) were prepared by using sol–gel auto combustion technique. These samples were firstly calcined at 900 °C for 3 h and finally sintered at 1150 °C for 5 h. The effects of Pr-contents on the structural, magnetic, and electrical properties of M-type hexaferrite have been studied. The structure and morphology of the samples were studied by X-ray diffraction (XRD) and scanning electron microscopy respectively. Vibrating sample magnetometer was also used in order to study the magnetic properties of these ferrites. XRD patterns show that the samples have single phase M type Ba-hexagonal structure for x = 0.0, 0.5, 1.0 whereas at higher Pr concentrations (x = 1.5, 2.0) some peaks of Fe2O3 appear as second phase. The large value of coercivity (>1 kOe) for all the samples shows that these ferrites are permanent magnets and exhibit the hard magnetic behavior. The variation of AC conductivity and resistivity as a function of frequency could be explained on the basis of Koop’s Phenomenological theory and Maxwell–Wagner model. The observed variation in dielectric constant can be described on the basis of space charge polarization and hopping conduction between Fe+3 and Fe+2. The dispersion observed in the dielectric loss was due to Maxwell–Wagner interfacial type polarization and Koop’s phenomenological theory.

Dielectric, complex impedance and electrical conductivity studies of the multiferroic Sr2FeSi2O7-crystallized glass-ceramics

In this paper, the Sr2FeSi2O7-crystallized glass-ceramics was successfully prepared by conventional melt casting followed by heat treatment method in the SrO–Fe2O3–SiO2–B2O3 glass system. The XRD, SEM and EDS results show that the crystalline Sr2FeSi2O7 is obtained with uniform microstructures and its grain size around 0.5–0.7 μm. The magnetization hysteresis (M−H) loop of the glass-ceramics exhibits typical ferromagnetic behavior with saturation magnetization values Ms = 10.527 emu/g and coercive field Hc = 210.462 Oe. In addition, some electric characteristics of (dielectric, impedance and conductivity) of the glass-ceramics have been investigated in a wide rang of frequency (20 Hz–2000 kHz) and temperature (220–440 °C) ranges. The dielectric dispersion phenomenon in ε′ and ε'' with frequency can be explained by Maxwell–Wagner model. Moreover, the complex impedance measurement provides a clear rationalization of the Maxwell–Wagner type of relaxation, namely crystalline phase and glassy phase contributions. The step-like feature of ac conductivity, plateau and dispersive regime can be explained by the Jump Relaxation Model (JRM) and dc conductivity is found to obey the Arrhenius law. The temperature dependence of n is investigated to explain the conduction mechanism in the different parts, which is attributed to the CBH model in Part-1 and the OLPT model in Part-2. The investigations of both complex impedance and conductivity show the NTCR character of the sample.

Effect of Mn2+ substitution on structural, magnetic, electric and dielectric properties of Mg–Zn ferrites

In this work, Mn substituted Mg–Zn spinel ferrites having general formula Zno.4Mg0.6−xMnxFe2O4 (0≤x≤0.30) have been synthesized by oxalate precursor chemical method and investigated their structural, magnetic and electric properties. X-ray diffraction (XRD) is used to study the crystal structure of synthesized materials. XRD study reveals the formation of polycrystalline cubic spinel lattice structure without any impurity phase having crystallite size in the range from 39.97nm to 45.62nm. Scanning electron micrographs revealed, increase in grain size (D) with increase in Mn2+ content up to x=0.10; then it decreases for x>0.10. Energy dispersive x-ray analysis (EDAX) confirms the presence of Mg2+, Mn2+, Fe3+, Zn2+ and O2− ions as per the stoichiometry. The magnetic moment (nB), with Mn2+ substitution is found to increase initially up to x=0.10 and then it deceases with further Mn2+ substitution. The observed variation in the magnetic moment (nB) is explained by considering the variation of saturation magnetization, anisotropy constant, density values and exchange interaction. The d.c. electrical resistivity decreased with increase in temperature in accordance with semiconducting behavior. Furthermore, the conductivity was found to obey the Arrhenius relation with a change in slope at critical temperature (i.e. the Curie temperature). The increase in d.c. resistivity is attributed to the hindering of Verwey mechanism between Fe2+⇔Fe3+ ions and Mn2+⇔Mn3+. The dielectric constant (ε′) measurement revealed the dielectric dispersion behavior in accordance with the Maxwell–Wagner model and Koops phenomenological theory, which is responsible for conduction and polarization. The dielectric characteristics (ε′, ε″ and tanδ) exhibit dispersion due to Maxwell–Wagner type interfacial polarization. The values of dielectric constant (ε′) and a.c. resistivity (ρac) exhibit highest magnitude at x=0.10 and decreases further with Mn2+ substitution.

Organic double layer element driven by triboelectric nanogenerator: Study of carrier behavior by non-contact optical method

By using optical electric-field-induced second-harmonic generation (EFISHG) technique, we studied carrier behavior caused by contact electrification (CE) in an organic double-layer element. This double-layer sample was half suspended in the open air, where one electrode (anode or cathode) was connected with a Cu foil for electrification while the other electrode was floated. Results showed two distinct carrier behaviors, depending on the (anode or cathode) connections to the Cu foil, and these carrier behaviors were analyzed based on the Maxwell–Wagner model. The double-layer sample works as a simple solar cell device. The photovoltaic effect and CE process have been proved to be two paralleled effects without strong interaction with each other, while photoconductivity changing in the sample can enhance the relaxation of CE induced charges. By probing the carrier behavior in this half-suspended device, the EFISHG technique has been demonstrated to be an effective non-contact method for clarifying the CE effect on related energy harvesting devices and electronics devices. Meanwhile, the related physical analysis in this letter is also useful for elucidating the fundamental characteristic of hybrid energy system based on solar cell and triboelectric nanogenerator.

Structural and Dielectric Studies of Gd Doped ZnO Nanocrystals at Room Temperature

Gadolinium doped Zinc oxide (Zn1–xGdxO) nanocrystals with different percentage of Gd content (x = 0, 0.2, 0.4, 0.6, 0.8) have been prepared by the solid state reaction method. The structural, mor-phological and chemical studies of the samples were performed by X-ray diffraction (XRD), Scanning electron microscope (SEM) and Energy dispersive X-ray (EDX) analysis. The XRD spectra confirm that all the samples have hexagonal wurtzite structure. Decrease in average crystallite size with an increase in Gd concentration is observed in XRD. SEM images show that the grain size of undoped ZnO is larger than the Gd doped ZnO, specifying the hindrance of grain growth upon Gd doping. The chemical composition of the samples was confirmed using Energy dispersive X-ray (EDX) analysis. The variation of dielectric constant (εr), dielectric loss (tan δ) and AC conductivity as a function of frequency is studied at room temperature in a frequency which ranges from 100 Hz - 4.5 MHz by using LCR Hi TESTER. All the samples exhibit the normal dielectric behavior, i.e. decreases with increase in frequency which has been explained in the light of Maxwell-Wagner model. The dielectric constant and dielectric loss can be varied intensely by tuning Gd concentration in Zn1–xGdxO compounds.

Enhancing pyroelectric and ferroelectric properties of PVDF composite thin films by dispersing a non-ferroelectric inclusion La2O3 for application in sensors

Thin films consisting of non-ferroelectric inclusions of La2O3 dispersed in a polymer matrix of polyvinylidene difluoride (PVDF) were prepared by the spin-coating method. It was found that the pyroelectric coefficient and remanent polarization of the composites were significantly improved to reach 42μC/m2K and 84mC/m2, respectively. The enhancement of the measured coefficients in the composites can be achieved by introducing a very small amount (3wt%) of La2O3. The figure of merit for material sensitivity, FD has also improved from 69 to 86μC/m2K1. A local field in the inclusion site was shown to facilitate the poling procedure. A simple Maxwell–Wagner model in which the dc conductivity of the inclusion site was taken into consideration showed a good agreement with the obtained pyroelectric and ferroelectric properties.

Polyol synthesis of Mn3+ substituted Fe3O4 nanoparticles: Cation distribution, structural and electrical properties

In this study, MnxFe2−xO4 (x=0.0, 0.2, 0.4, 0.6, 0.8 and 1.0) nanoparticles were synthesized by polyol route and the effect of Mn3+ substitution on structural and dielectric properties of Fe3O4 was studied. X-ray powder diffraction (XRD) patterns confirmed the single spinel ferrite phase formation (Rietveld analysis). Crystallite size of the synthesized materials lie in the range of 12–25nm as calculated X-ray diffraction patterns using Scherrer’s formula. The microstructural features were examined by SEM images. Cation distribution calculations confirmed Fe3+ ions have both tetrahedral and ochedral site preferences whereas Mn3+ ions mostly occupies tetrahedral A-site. The ac electrical and dielectric properties of Mn3+ ion substituted Fe3O4 nanoparticle show that there were significant changes in both conductivity and complex permittivity as well as dielectric loss tangent as Mn3+ ion concentration is varied from zero to unity. It is clearly seen that conductivity increases with increase in temperature which may be due to increase in hopping capability of charge carriers at higher temperatures. Detailed evaluation of analysis reveals that at higher frequencies there is less effect of temperature on conductivity which can be interpreted on the basis of interfacial, dipolar, ionic and electronic polarization as detailed above section in explanation of variation of dielectric loss. The dielectric permittivity shows dielectric behavior can be clarified on the basis of Koop’s interpretations in accordance with two layer Maxwell–Wagner model by accounting for surface charges. The electrical and dielectric properties, i.e. ac/dc conductivity, real/complex dielectric permittivity, and dielectric loss (tan δ) decrease with Mn3+ ion doping in some aspects.

Engineering of the frequency dependence of the ferroelectric properties of thin film Pt/Ba0.5Sr0.5TiO3/Pt structures

Engineering of a frequency dependent permittivity can be of interest for various sensor application. In this work a strong modification of the frequency dependence of the ferroelectric properties is achieved via a controlled diffusion of the metal electrode (Pt) into the ferroelectric layer ((Ba,Sr)TiO3). For this purpose a series of Ba0.5Sr0.5TiO3 layers is deposited onto Pt coated sapphire at various temperatures range from 660°C to 760°C. Using an additional Pt top electrode, the electronic properties of the resulting capacitors are investigated via frequency dependent cryoelectronic measurements. The structure and stoichiometry of the layers are analyzed via X-ray and Rutherford backscattering spectrometry, respectively. The analysis of the permittivity and loss tangent shows a strong frequency dependence of the permittivity in a small region of the deposition temperatures (680–710°C), i.e. the permittivity changes from εeff≃600 at low frequency to εeff≃20 at high frequency. This behavior is caused by a partial diffusion of Pt into the ferroelectric layer and can be explained by the Maxwell–Wagner model.

Investigation of super-exchange interactions in BaHoxFe12−xO19 (0.1≤x≤0.4) nanohexaferrites and exploration at ultra high frequency region

BaHoxFe12−xO19 (x=0.1, 0.2, 0.3, 0.4) nanohexaferrites were successfully synthesized for the first time by sol–gel auto-combustion technique. X-ray diffraction (XRD), transmission electron microscopy (TEM) and energy dispersive X-ray analysis (EDAX) were utilized to investigate the different structural parameters and elemental composition. Incorporation of Ho3+ ions increased the dc resistivity while a decrease in the saturation magnetization (Ms), 66.68–57.08emu/g, followed by decrease in Curie temperature (766.83–758.15K), exchange integral (J), and anisotropy was observed. The obtained values of Ms were found to be very high as compared to the values reported in the bulk form. The dielectric constant (ε′) and dielectric loss tangent (tanδ) were investigated as a function of frequency and the behavior is explained on the basis of Maxwell–Wagner model and Koop׳s theory. Additionally, a maiden attempt was made to explore the BaHoxFe12−xO19 nanohexaferrites at ultra-high frequencies and observed ultra-low magnetic loss (0.004–0.01) and dielectric loss (0.004–0.06).

Microwave Dielectric and Magnetic Properties of Co-Zn Ferrites

The dielectric permittivity, loss tangent, in the frequency range 1MHz to 1.8 GHz and hysteresis loop parameters at room temperature were studied on a series of Zn substituted cobalt ferrites with general formula Co1-xZnx Fe2O4 where (x=0.0, 0.2, 0.4, 0.6, 1.0.). The experimental results indicate that the Zn substitution affects all these parameters. The observed dispersion in dielectric permittivity with frequency is in accordance with Maxwell-Wagner model. The high temperature sintering is used to synthesize these materials via solid state reaction route and these samples were characterized by X-ray diffractometer (XRD), vibrating sample magnetometer (VSM). The saturation magnetizations (MS) Hc and Mr of the Particles were measured at room temperature. Here for the smaller dopent concentration Ms increases with increasing in the Zn content this can explained on the basis of increased number of magnetic ions in the spinel lattice, at some point Ms decrease because of the difference between the magnetic moment of Fe2+ and Zn2+, the magnetic moment of the A sub lattice will increases and the moment of the B sub lattice will decrease. The variation of crystalline shape ellipsoid is correlated with variation of dielectric constant.

Electrical Behavior of Tb-Mn Substituted Y-Type Hexa-ferrites for High-Frequency Applications

Single phase nanostructured Tb-Mn substituted Y-type hexaferrites with composition Sr2Co2−x Mn x Tb y Fe12−y O22 (x = 0.0–1, y = 0.0–0.1) have been synthesized by the normal microemulsion technique. X-ray diffraction patterns reveal the formation of Y-type hexagonal single phase. The crystallite size, calculated by Scherer’s formula, is found in the range of 30–48 nm, which is well suitable for obtaining good signal-to-noise ratio in high density recording media. The enhancement in direct current resistivity has been attributed to the reduction in Fe3+ ions at octahedral sites. The Arrhenius plots show that there are two conduction mechanisms operating in the synthesized materials: in the ferri-region, the conduction is due to electrons, whereas in the para-region, it is due to polaron hopping phenomena. The calculated values of activation energy in the para-region are greater than 0.40 eV, which clearly suggests that the conduction phenomenon is due to hopping of polarons. Variation of dielectric constant with frequency depicts that the dielectric constant initially decreases with increase in frequency, while at higher frequency it decreases slowly. The dielectric results are in agreement with the Maxwell–Wagner model. Both the resonance and relaxation peaks at high frequency have been observed in dielectric loss and tan δ data. It has been noted that such types of peaks appear when hopping frequency becomes equal to that of the external applied field. The high values of resistivity and low dielectric loss make these materials best candidates for high frequency applications.