Temperature Dependent Dielectric Measurements Research Articles

Enhanced oxygen ion conductivity in Ba3W1+xV1−xO8.5+x/2 (− 0.2 ≤ × ≤ 0.2) hexagonal perovskite derivative compounds

Abstract A series of hexagonal perovskite derivative compounds Ba3W1+x V1−x O8.5+x/2 (x = − 0.2, − 0.1, 0, 0.1, 0.2) with varying oxygen content was synthesized by high-temperature solid-state reaction route and characterized using X-ray diffraction, SEM–EDX, Raman spectroscopy, XPS, and dielectric spectroscopy. All samples were isostructural, having features of both palmierite and 9R hexagonal perovskite. The unit cell volume showed a continuously decreasing trend with increasing oxygen content. The XPS studies showed no deviation of oxidation states of W6+ and V5+ and hence confirmed that the oxygen stoichiometry is solely controlled by the W to V ratio in the samples. The presence of both octahedral MO6 and tetrahedral MO4 units in all samples was inferred from temperature-dependent Raman spectroscopic studies. The translational and rotational motion of MO4 tetrahedra are appreciably affected by temperature. The dc conductivity was obtained directly from the complex ac conductivity derived from temperature-dependent dielectric measurements. It was found that the dc conductivity increases when the composition deviates from x = 0.0, i.e., W:V = 1:1. An estimate of the ion mobility and mobile ion concentration was obtained using the Almond-West formalism. The conductivity was found to be significantly higher in W-rich compounds (x > 0), and the ion mobility was also correspondingly higher. It could be inferred that the compositional dependence of unit cell parameters, particularly a- or b-axis, and the oxygen stoichiometry, play crucial roles in governing the ionic conductivity of these hexagonal perovskite derivatives.

Temperature-dependent dielectric measurements of polypyrrole/zinc cobalt oxide nanocomposites by impedance spectroscopy

Temperature-dependent dielectric measurements of polypyrrole/zinc cobalt oxide nanocomposites by impedance spectroscopy

Studies on the compositional dependent structural and electrical properties of CaTiO3-modified K0.5Na0.5NbO3 piezoelectric system

Lead-free piezoelectric ceramics of (1 − x)K0.5Na0.5NbO3-xCaTiO3 were fabricated, and their crystal structure, microstructure, and electrical properties were systematically studied. Rietveld refinement of the x-ray diffraction data and Raman spectroscopic analyses revealed a composition-dependent structural phase transition: three phase transitions, namely, from a pure orthorhombic phase for x ≤ 0.02 to a mixed phase of orthorhombic and tetragonal phases (0.03 ≤ x ≤ 0.08) and finally another mixed phase of tetragonal + cubic for x = 0.10 and 0.15 at room temperature (RT). The morphological study reveals a decrease in grain size along with a more uniform distribution of grains as the concentration of CaTiO3 (CT) increases; notably, a homogeneous distribution of grains is observed for x = 0.05. The temperature-dependent dielectric properties show two phase transitions, from orthorhombic to tetragonal (TO-T) and tetragonal to cubic (TC), for unmodified K0.5Na0.5NbO3 (KNN). However, both the phase transition temperatures (TO-T and TC) decrease, and the transition peaks broaden with an increase in CT substitution, and for x > 0.06, the TO-T shifted below RT. The broadening of the transition peak at TO-T may be due to the relaxation behavior. Among the prepared samples, the 5 mol. % CT-modified KNN shows the optimum electrical properties (d33 = 114 pC/N, ɛr = 412, and 2Pr = 15.25 μC/cm2) at RT. The enhanced electrical properties for x = 0.05 are due to the coexistence of orthorhombic and tetragonal phases, facilitating easy polarization rotation and flattening of the free energy profile. A phase diagram has been constructed based on the information gathered from the temperature-dependent dielectric measurements, RT x-ray diffraction, and Raman spectroscopy data and is discussed in detail.

Synergistic homovalent and heterovalent substitution effects on piezoelectric and relaxor behavior in lead-free BaTiO3 ceramics

Synergistic homovalent and heterovalent substitution effects on piezoelectric and relaxor behavior in lead-free BaTiO3 ceramics

Universal Dielectric Response in Electronically Correlated Functional Oxides CaCu3Ti4O12, LaFeO3, YFe0.5Cr0.5O3 and their Nanocomposites: A Comparative Study

AbstractCaCu3Ti4O12 (CCTO), LaFeO3 (LFO) and YFe0.5Cr0.5O3 (YFCO) were synthesized via conventional sol–gel auto–combustion method using citric acid as gelling agent. The X‐ray diffraction analysis revealed the phase purity of the samples. The energy dispersive X‐ray (EDX) analysis confirms the stoichiometry of the pristine phases. The average particle size obtained from the field emission Scanning electron microscopy (FE−SEM) images revealed that CaCu3Ti4O12 exhibits a broad range of particle size starting from a couple of hundreds of nanometer to micrometer, whereas that for LaFeO3 and YFe0.5Cr0.5O3 are about 110 nm and 50 nm, respectively. We have fabricated the new composites: CCTO–LFO, CCTO–YFCO and LFO–YFCO. The grain sizes of the composite phases are consistent with the pristine phases as they are prepared by at lower sintering temperatures and duration. The dielectric properties of these ceramic composites were compared to those of the pristine phases. The temperature and frequency dependent dielectric measurements reveal a wide range of dielectric constant with moderate tan δ values. The temperature dependent dielectric constant of the investigated samples varies from 100 to 1500 at room temperature and the data have been analyzed using universal dielectric response (UDR) model.

Temperature-dependent dielectric relaxation measurements of (acetamide + K/Na SCN) deep eutectic solvents: Decoding the impact of cation identity via computer simulations.

The impact of successive replacement of K+ by Na+ on the megahertz-gigahertz polarization response of 0.25[fKSCN + (1 - f)NaSCN] + 0.75CH3CONH2 deep eutectic solvents (DESs) was explored via temperature-dependent (303 ≤ T/K ≤ 343) dielectric relaxation (DR) measurements and computer simulations. Both the DR measurements (0.2 ≤ ν/GHz ≤ 50) and the simulations revealed multi-Debye relaxations accompanied by a decrease in the solution static dielectric constant (ɛs) upon the replacement of K+ by Na+. Accurate measurements of the DR response of DESs below 100MHz were limited by the well-known one-over-frequency divergence for conducting solutions. This problem was tackled in simulations by removing the zero frequency contributions arising from the ion current to the total simulated DR response. The temperature-dependent measurements revealed a much stronger viscosity decoupling of DR times for Na+-containing DES than for the corresponding K+ system. The differential scanning calorimetry measurements indicated a higher glass transition temperature for Na+-DES (∼220K) than K+-DES (∼200K), implying more fragility and cooperativity for the former (Na+-DES) than the latter. The computer simulations revealed a gradual decrease in the average number of H bonds (⟨nHB⟩) per acetamide molecule and increased frustrations in the average orientational order upon the replacement of K+ by Na+. Both the measured and simulated ɛs values were found to decrease linearly with ⟨nHB⟩. Decompositions of the simulated DR spectra revealed that the cation-dependent cross interaction (dipole-ion) term contributes negligibly to ɛs and appears in the terahertz regime. Finally, the simulated collective single-particle reorientational relaxations and the structural H-bond fluctuation dynamics revealed the microscopic origin of the cation identity dependence shown by the measured DR relaxation times.

Achieving giant field-induced strain in BS-modified BNKT lead-free ferroelectric ceramics

Achieving giant field-induced strain in BS-modified BNKT lead-free ferroelectric ceramics

Mild chemistry synthesis of ultrathin Bi2O2S nanosheets exhibiting 2D-ferroelectricity at room temperature.

Modern technology demands miniaturization of electronic components to build small, light, and portable devices. Hence, discovery and synthesis of new non-toxic, low cost, ultra-thin ferroelectric materials having potential applications in various electronic and optoelectronic devices are of paramount importance. However, achieving room-temperature ferroelectricity in two dimensional (2D) ultra-thin systems remains a major challenge as conventional three-dimensional ferroelectric materials lose their ferroelectricity when the thickness is brought down below a critical value owing to the depolarization field. Herein, we report room-temperature ferroelectricity in ultra-thin single-crystalline 2D nanosheets of Bi2O2S synthesized by a simple, rapid, and scalable solution-based soft chemistry method. The ferroelectric ground state of Bi2O2S nanosheets is confirmed by temperature-dependent dielectric measurements as well as piezoelectric force microscopy and spectroscopy. High resolution transmission electron microscopy analysis and density functional theory-based calculations suggest that the ferroelectricity in Bi2O2S nanosheets arises due to the local distortion of Bi2O2 layers, which destroys the local inversion symmetry of Bi2O2S.

High-temperature giant dielectric switching in an organic-inorganic hybrid material.

With the increasing research on giant dielectric materials, there is growing interest in the development of switching materials with giant dielectric properties. In this study, a novel organic-inorganic hybrid material (Et3NC2H4Br)FeCl4 was synthesized. It was characterized through differential scanning calorimetry (DSC) and in situ temperature-dependent powder X-ray diffraction (PXRD), which determined its phase transition temperature (TC) to be 362 K. Temperature-dependent dielectric measurements revealed that the material exhibited switchable dielectric properties, with the real part of the dielectric constant exceeding 106 at 500 Hz and a dielectric switching ratio surpassing 103. The ratio refers to the ratio between the high dielectric state and the low dielectric state of a step-like dielectric anomaly. Single-crystal X-ray diffraction (SCXRD) analysis confirmed that the material crystallized in the P21/c space group with a zero-dimensional structure. The optical bandgap, determined through UV-visible spectroscopy, was calculated to be 2.62 eV. Additionally, analysis using Hirshfeld surfaces and 2D fingerprint plots revealed that the predominant intermolecular interactions are H⋯Cl and H⋯H interactions. This study is anticipated to provide insights and hope for the design and application of high-temperature giant dielectric switching materials.

Orthorhombic-tetragonal phase coexistence and enhanced piezoelectric properties at room temperature in Zn and Ta modified (Ba0.95Ca0.05)(Zr0.05Ti0.95)O3 ceramics through the synergistic effect of lattice distortion.

This study provides a fundamental understanding of the enhanced piezoelectric properties in ABO3 perovskite based lead-free piezoelectric materials. For this we synthesized (Ba0.95Ca0.05)(Zr0.05Ti0.95-x (Zn1/3Ta2/3) x )O3((1 - x)BCZT-(x)ZT) (x = 0.00, 0.005, 0.01, and 0.02) solid solutions exhibiting high piezoelectric response. The (1 - x)BCZT-xZT materials are synthesized by a high-temperature solid-state ceramic reaction method by varying x in the full range (x = 0.00-0.02). In-depth exploratory research is performed on the structural, dielectric, ferroelectric, and piezoelectric properties of (1 - x)BCZT-(x)ZT ceramics. The formation of perovskite structure for all ceramics without the presence of any impurity phases is confirmed by X-ray diffraction (XRD) analyses, which also reveals that the Ca2+, Zr4+, Zr2+ and Ta5+ are well dispersed within the BaTiO3 lattice. For all (1 - x)BCZT-(x)ZT ceramics, thorough investigation of phase formation and phase-stability using XRD, Rietveld refinement, Raman spectroscopy, and temperature-dependent dielectric measurements provide conclusive evidence for the coexistence of orthorhombic + tetragonal (Amm2 + P4mm) phases at room temperature. The steady transition of Amm2 crystal symmetry to P4mm crystal symmetry with increasing x content is also demonstrated by Rietveld refinement data and related analyses. The c/a ratio of the tetragonal phase greatly influenced the electric properties of the ceramics. The c/a ratio of the tetragonal phase increases from 1.0112 for x = 0 to 1.0157 for x = 0.005 and subsequently decreases to 1.0038 for x = 0.02. When the c/a of the tetragonal phase reaches its maximum value, the ceramic with x = 0.005 has the best piezoelectricity (d 33 ∼ 297 pC N-1). The calculated degree of relaxation (γ) increases with the increase in BZT content, indicating that the BCZT-xBZT ceramics are ferroelectric materials with diffuse phase transition. Main dielectric, piezoelectric and ferroelectric parameters of (1-x)BCZT-xZT ceramics were optimized around x = 0.005 with a high piezoelectric coefficient (d 33 = 297 pC N-1), a remnant polarization (P r = 7.58 μC cm-2), spontaneous polarization (P s = 10.25 μC cm-2) and a high dielectric constant (ε max,T c = 4449 at T c and 2330 near RT) at 1 kHz, indicating promising applications for lead-free piezoelectric ceramics.

Tailoring the structural, optical, electrical and multiferroic properties of Sm1-xRxFeO3 (x = 0.0 and 0.5; R = Pr, Nd, and Gd) and their synergistic photocatalytic activity

Tailoring the structural, optical, electrical and multiferroic properties of Sm1-xRxFeO3 (x = 0.0 and 0.5; R = Pr, Nd, and Gd) and their synergistic photocatalytic activity

Structural and dielectric properties of Y3+ doped SrTiO3: a novel anode materials for solid oxide fuel cell

An ongoing and elusive task is to create single phase anode materials for solid oxide fuel cells (SOFC). Compared to the typical Ni-YSZ cermet anode, perovskite oxide based anode material has a number of benefits. Here, we present the structural and electrical characteristics of Y3+ doped SrTiO3 ceramics that are used as the anode in solid oxide fuel cells. The samples with nominal composition x = 0 and 0.05 were synthesized by high energy ball milling. The powder X-ray diffraction pattern reveals that the synthesized samples crystallize into cubic crystal structure with space group Pm3m for both the compositions. The samples were sintered at a temperature of 1300 °C for 6h. The sintered density of the samples was found to be greater than 97%. The temperature dependent dielectric measurement studies reveal that dielectric constant increases with yttrium doping and shows relaxer behavior. A higher dielectric constant and electrical conductivity was observed for the Y-doped sample which fulfill the basic requirement for anode materials of solid oxide fuel cells.

Structural, Optical, Relaxor and Transport Properties of a Nanocrystalline Double Perovskite: Ba2(FeMo)O6

The paper presents a synthesis (solid-state. reaction) and characterization of a lead-free double perovskite oxide Ba2(FeMo)O6 ceramic. The initial analysis using X-ray diffraction revealed that the material has a cubic crystal symmetry with a micro-lattice strain of 0.000824 and an average crystallite size of 62[Formula: see text]nm. The microstructural features and elemental composition of the prepared polycrystalline sample were examined using scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDX). The SEM micrograph, EDX spectrum and elemental mapping show distinctly grown grains with well-defined grain boundaries, purity and distribution pattern of the grains, respectively. Raman scattering spectroscopy is a valuable tool for studying the vibrational modes to get information about structural and chemical properties of materials. The optical properties of the material were investigated using UV–Vis spectroscopy, which provides various parameters including energy bandgap for different technological applications. The electrical behavior of the synthesized double perovskite was examined through frequency- and temperature-dependent dielectric measurements as well as impedance spectroscopy. The electrical conduction in the material followed Jonscher’s power law and is supported by a thermally activated conduction mechanism. The analysis of electrical resistance versus temperature confirms negative temperature coefficient of resistance nature and can be used as NTC thermistors. The study of polarization-electric field loop opens up the possibility of the ferroelectric nature of the studied sample and also measures energy storage density, energy loss density and efficiency for searching different potential applications related to sensors. Overall, the results suggest its potential for various technological applications, such as in sensors and devices requiring specific electrical behavior or ferroelectric properties.

High-entropy (Na0.2Bi0.2Ba0.2Sr0.2Zn0.2)TiO3 ceramics with enhanced energy storage density and reliable stability

High-entropy (Na0.2Bi0.2Ba0.2Sr0.2Zn0.2)TiO3 ceramics with enhanced energy storage density and reliable stability

Quenching-driven advancements in functional properties of high-temperature lead-free Sc, Ga modified 0.67BiFeO3-0.33BaTiO3 relaxor ceramics

Quenching-driven advancements in functional properties of high-temperature lead-free Sc, Ga modified 0.67BiFeO3-0.33BaTiO3 relaxor ceramics

Investigation on structural, optical and electrical properties of BiFeO3:ZnO nano–micro particles–matrix composite

A new class of materials called matrix-nano composites has the ability to meet the needs of modern advanced applications and technology. To prepare the BiFeO3:ZnO composite, BiFeO3 nanoparticles were prepared using a low–cost sol–gel method, to which ZnO in its micron-sized form was added in varying concentrations of 5%, 10%, and 15%. The structural, morphological, and optical properties of the pure and composite materials were characterized using XRD, FESEM, EDAX, PL spectra, and UV-Visible spectroscopy. The dielectric properties of the pristine and composites were investigated at room temperature. The a.c. conductivity fit with Jonscher's power law and CBH model described the charge conduction behaviour in all pure and composite materials. The temperature-dependent dielectric and loss measurements showed a temperature dependent relaxation process. UV-vis and PL characterization show that the composite materials exhibited improved charge separation efficiency and wider band gaps with increasing BFO content.

Enhanced Piezoelectric, Ferroelectric, and Electrostrictive Properties of Lead-Free (1-x)BCZT-(x)BCST Electroceramics with Energy Harvesting Capability.

Next-generation electronics and energy technologies can now be developed as a result of the design, discovery, and development of novel, environmental friendly lead (Pb)-free ferroelectric materials with improved characteristics and performance. However, there have only been a few reports of such complex materials' design with multi-phase interfacial chemistry, which can facilitate enhanced properties and performance. In this context, herein, novel lead-free piezoelectric materials (1-x)Ba0.95 Ca0.05 Ti0.95 Zr0.05 O3 -(x)Ba0.95 Ca0.05 Ti0.95 Sn0.05 O3 , are reported, which are represented as (1-x)BCZT-(x)BCST, with demonstrated excellent properties and energy harvesting performance. The (1-x)BCZT-(x)BCST materials are synthesized by high-temperature solid-state ceramic reaction method by varying x in the full range (x = 0.00-1.00). In-depth exploration research is performed on the structural, dielectric, ferroelectric, and electro-mechanical properties of (1-x)BCZT-(x)BCST ceramics. The formation of perovskite structure for all ceramics without the presence of any impurity phases is confirmed by X-ray diffraction (XRD) analyses, which also reveals that the Ca2+ , Zr4+ , and Sn4+ are well dispersed within the BaTiO3 lattice. For all (1-x)BCZT-(x)BCST ceramics, thorough investigation of phase formation and phase-stability using XRD, Rietveld refinement, Raman spectroscopy, high-resolution transmission electron microscopy (HRTEM), and temperature-dependent dielectric measurements provide conclusive evidence for the coexistence of orthorhombic + tetragonal (Amm2 + P4mm) phases at room temperature. The steady transition of Amm2 crystal symmetry to P4mm crystal symmetry with increasing x content is also demonstrated by Rietveld refinement data and related analyses. The phase transition temperatures, rhombohedral-orthorhombic (TR-O ), orthorhombic- tetragonal (TO-T ), and tetragonal-cubic (TC ), gradually shift toward lower temperature with increasing x content. For (1-x)BCZT-(x)BCST ceramics, significantly improved dielectric and ferroelectric properties are observed, including relatively high dielectric constant εr ≈ 1900-3300 (near room temperature), εr ≈ 8800-12900 (near Curie temperature), dielectric loss, tan δ ≈ 0.01-0.02, remanent polarization Pr ≈ 9.4-14 µC cm-2 , coercive electric field Ec ≈ 2.5-3.6kV cm-1 . Further, high electric field-induced strain S ≈ 0.12-0.175%, piezoelectric charge coefficient d33 ≈ 296-360 pC N-1 , converse piezoelectric coefficient ≈ 240-340 pm V-1 , planar electromechanical coupling coefficient kp ≈ 0.34-0.45, and electrostrictive coefficient (Q33 )avg ≈ 0.026-0.038 m4 C-2 are attained. Output performance with respect to mechanical energy demonstrates that the (0.6)BCZT-(0.4)BCST composition (x = 0.4) displays better efficiency for generating electrical energy and, thus, the synthesized lead-free piezoelectric (1-x)BCZT-(x)BCST samples are suitable for energy harvesting applications. The results and analyses point to the outcome that the (1-x)BCZT-(x)BCST ceramics as a potentially strong contender within the family of Pb-free piezoelectric materials for future electronics and energy harvesting device technologies.

Unveiling a hidden multiferroic state under magnetic fields in BaHoFeO4

In this paper, we report field-induced ferroelectricity in ${\mathrm{BaHoFeO}}_{4}$ in a narrow range of applied magnetic fields ($1.5\phantom{\rule{4.pt}{0ex}}\text{T}\ensuremath{\le}H\ensuremath{\le}5\phantom{\rule{4.pt}{0ex}}\text{T}$). Magnetization measurements reveal three magnetic anomalies, the first one at ${T}_{N}^{\text{Fe}}\ensuremath{\sim}52.8$ K, the second one at ${T}_{{N}_{2}}\ensuremath{\sim}36.4$ K, and the third one at ${T}_{N}^{\text{Ho}}\ensuremath{\sim}6.8$ K, corresponding to the antiferromagnetic ordering of ${\mathrm{Fe}}^{3+}$, a possible spin structure change of ${\mathrm{Fe}}^{3+}$, and the antiferromagnetic ordering of ${\mathrm{Ho}}^{3+}$ sublattices, respectively. Surprisingly, the heat capacity data did not show any anomaly at ${T}_{N}^{\text{Fe}}$ but exhibited a broad maximum at ${T}_{N}^{\text{Ho}}$. Below 40 K, isothermal magnetization measurements indicate a metamagnetic transition at 1.5 T. The temperature-dependent dielectric measurements performed below 1 T reveal two anomalies, around 6 and 36 K, corresponding to ${\mathrm{Ho}}^{3+}$ ordering and a possible change in the magnetic phase of the Fe sublattice. These anomalies disappear at higher magnetic fields, and a different dielectric anomaly appears above the metamagnetic transition with a broad asymmetric peak around 13 K (${T}_{P}$), which shifts to higher temperatures, reaches a maximum under 2 T, and then is suppressed further on increasing the magnetic field up to 9 T. A switchable electric polarization appears below 25 K and above the metamagnetic transition field ($H\ensuremath{\ge}1.5$ T). Intriguingly, the polarization disappears above 5 T. The presence of electric polarization in intermediate magnetic fields and its strong magnetic field dependence are interesting and make this material unique.

Temperature-dependent dielectric measurements and structural properties of barium stannate (BaSnO3)

Cubic perovskite BaSnO3, synthesized by solid-state reaction method, was structurally characterized using temperature-dependent X-ray and Raman spectroscopy studies along with room temperature neutron diffraction analysis. Here, we report the effect of temperature on the structural parameters of BaSnO3 in correlation with dielectric properties. Sample homogeneity and elemental composition were studied by scanning electron microscopy and energy dispersive X-ray spectroscopy methods. The compound maintains cubic symmetry even at high temperatures and exhibits gradual increase in unit cell volume owing to thermal expansion. To understand high temperature phase transition, if any, and capacitance behavior, high temperature dielectric measurements were carried out. High value of dielectric constant was obtained at low frequencies as the temperature was increased, which may be due to the presence of oxygen vacancies or the lone-pair effect.

The role of Pr3+, Pr3+-Y3+ and Pr3+-Y3+-Dy3+ ions substitutions on the electrical and dielectric properties of NiCo nanospinel ferrites

This study investigated the electrical and dielectric features for NiCo (Ni0.5Co0.5Fe2O4) NSFs, Pr-NiCo (Ni0.5Co0.5Pr0.1Fe1.9O4) NSFs, PrY-NiCo (Ni0.5Co0.5Pr0.1Y0.1Fe1.8O4) NSFs and PrYDy-NiCo (Ni0.5Co0.5Pr0.1Y0.1Dy0.1Fe1.7O4) NSFs have been synthesized hydrothermally. The microstructure of all compositions was characterized thru XRD, SEM, EDX, TEM and HR-TEM. XRD analyses proved the formation of cubic structure and the absence of any impurity. The cubic morphologies of all products have been confirmed by HR-TEM and SEM measurements. The chemical composition presented by EDX was matched with the predicted chemical composition. Temperature (T) and frequency (f) dependent electrical and dielectric measurements were made to evaluate ac/dc conductivities, dielectric constant/losses, and dissipation factor as well as Cole-Cole plots of impedance functions for all NiCo NSFs substituted with Pr3+, Pr3+Y3+ and Pr3+Y3+Dy3+-ions. The ac conductivity measurements confirmed that it obeyed power law rules, largely dependent on the ion substitutions in the host NiCo NSFs. The dielectric constant of NiCo NSFs leads to the usual dielectric distribution, which is strongly influenced by substituted Pr3+, Pr3+-Y3+ and Pr3+-Y3+-Dy3+ ions. Impedance analysis indicated that the conduction mechanisms in all samples were mainly due to grain-to-grain boundaries. The variation in dispersion factors with frequency, like Koop's phenomenological model, is generally attributable to the conduction mechanism in ferrites.