Influence of the RE₂O₃ (RE = Y, Gd) and CaO nanoadditives on the electromagnetic properties of nanocrystalline Co_0.2Ni_0.3Zn_0.5Fe₂O₄

2.1 Synthesis

Co_0.2Ni_0.3Zn_0.5Fe₂O₄ nanoparticles were produced by the polyol method starting from Fe (III) chloride and the acetates of M(II) (M = Co, Ni, and Zn) as precursors and diethyleneglycol as a solvent (Huili et al., 2015a). Stoichiometric nanoparticles were obtained by optimizing four synthetic parameters including the hydrolysis ratio (h), the acetate ratio (τ_Ac), and the Zn ratio (τ_Zn), defined by the molar ratios of water/metal, acetate/M²⁺, and Zn²⁺/Fe³⁺, respectively, and the refluxing duration (t). The values of the four parameters h, τ_Ac, τ_Zn, and t, were found to be ≈1, 3.66, 0.5, and 3 h, respectively. The above cited optimized synthetic parameter values found for Co_0.2Ni_0.3Zn_0.5Fe₂O₄ were adopted for the preparation essays of Y₂O₃, Gd₂O₃, and CaO powders using the polyol method. The respective precursors of the oxides are Y(CH₃CO₂)₃ (Sigma-Aldrich; 99.9%), Gd(CH₃CO₂)₃ (Sigma-Aldrich; 99.9%), and CaCO₃ (Sigma-Aldrich; 98.5%). All chemicals were used as received. In a typical experimental procedure, an appropriate amount of each precursor and 62.5 mL of diethyleneglycol were added to a round bottom three-necked flask 250 mL capacity to reach a nominal concentration of the associated cation of 0.2 M. Then, appropriate amounts of distilled water and anhydrous sodium acetate (Sigma-Aldrich; 99%) were added to adjust the hydrolysis and the acetate molar ratios to the values ≈1 and 3.66, respectively. The resulting mixture was then refluxed at boiling temperature under mechanical stirring for 3 h. After slow cooling, the obtained precipitate was washed with ethanol under vigorous sonication with intermittent centrifugation. Finally the precipitate was dried overnight in air at 60 °C. Importantly, we also note that unlike the ferrite phase which was obtained without any further heat treatment, formation of crystalline Y₂O₃, Gd₂O₃ and CaO required subsequent calcinations of their associated as-produced powders (the dried precipitates). Further details on the calcination conditions will be given in the results and discussion section.

2.2 Characterization techniques

The structure and phase purity of the produced powders were examined by X-ray diffraction (XRD) using a BRUKER D8 ADVANCE diffractometer equipped with a copper anode (λ_CuKα = 1.540/1.544 Å). XRD powder pattern indexing was carried out with McMaille program (Le Bail, 2004) and the unit cell parameters were refined by the Rietveld method (Rietveld, 1969) using the FULLPROF program (Carvajal, 1998). The average crystallite size was inferred from the broadening of the XRD diffraction peaks applying the Scherrer formula (Scherrer, 1918). Instrumental broadening was estimated from Cagliotti plots (Cagliotti et al., 1958) using a polycrystalline silicon as standard. IR characterization was carried out on a Nicolet UR 200 FT–IR spectrometer using the ATR technique over the range 400–4000 cm⁻¹ with a resolution of 4 cm⁻¹. The particle morphology was observed by a FEI QUANTA 200 transmission electron microscope (TEM) operating at 200 kV with a probe diameter of 200 nm. A small quantity of the powder was ultrasonically dispersed in ethanol, then a drop of the suspension was deposited on a carbon coated copper grid and the solvent was evaporated at room temperature. TEM images were recorded at different magnifications at randomly selected areas of sample and the average particle size was obtained by measurements of at least 100 particles. dc magnetic measurements were conducted on a Quantum Design PPMS VSM magnetometer. The sintered powders were compacted inside capsules to prevent physical movement during the experiments. The hysteresis loops were measured with magnetic field cycling in the ±30 kOe range at 300 K. The temperature dependence of the spontaneous magnetization was recorded between 50 and 330 K under a constant magnetic field of 20 kOe. The collected data were corrected from the diamagnetic contribution and were presented in the cgs–emu g⁻¹ units. The collected data were corrected from the diamagnetic contribution of the sample holder and were presented in cgs–emu g⁻¹ units. The dielectric response of the sintered pellets was measured in the heating mode from 105 °C to 400 °C using TEGAM 6192 ALF impedance analyzer in the frequency range 10 Hz–13 MHz. Electrical equivalent circuits of the sintered pellet were simulated using Zview program (Johnson, 2005). The as-produced ferrite and the as-produced additives (Y₂O₃, Gd₂O₃ or CaO) were individually pre-annealed in air at 500 °C for 4 h in order to remove the organic species grafted onto the nanoparticles surface (Huili et al., 2015a). Then, an appropriate mass of the resulting ferrite powder was then mixed with a small quantity (5 wt.%) of each additive. Each mixture was then well ground using agate mortar and then uniaxially compacted under 7 tons cm⁻² pressure resulting in disk–shaped pellet of about 13.0 mm diameter and 1.5 mm thickness. The pelletized powders were then heated in air for two hrs at 1000 °C in a programmable muffle furnace followed by a slow cooling to room temperature. Hereafter, for the sake of simplicity, the sintered pellets will be sometimes denoted as undoped ferrite, ferrite/Y₂O₃, etc., for the sintered pure ferrite Co_0.2Ni_0.3Zn_0.5Fe₂O₄ and the sintered 5 wt.% Y₂O₃ dopped ferrite, etc., respectively. Finally, the surfaces of the pellets were coated by silver paste in order to ensure a good and uniform contact with the incoming current wires.

3.1 Phase and microstructure analyses

The phase and microstructure analyses of the as-prepared ferrite and its corresponding annealed one at 1000 °C were reported elsewhere (Huili et al., 2015b). The XRD patterns are indexed in a spinel-type structure with no evidence of any foreign phase, indicating, in particular, a high thermal stability of the sintered ferrite. Crystallites of both powders were found to be in the nanometer scale. The mean crystallite size in the as-produced ferrite and its associated sintered powder were found be at around 2 nm and 86 nm, respectively. Figs. 1–3 show the XRD patterns of the as-synthesized powders of the pure additives and their associated ones calcinated at different conditions as well as those of ferrite/additives powders sintered at 1000 °C. The JCPDS Bragg positions of Y₂O₃, Gd₂O₃, and CaO standards are also plotted for comparison. One can observe that for the as-prepared powders of Y₂O₃ and Gd₂O₃, the diffraction patterns are poorly resolved, indicating the possibility the formation of amorphous intermediate phase and/or ultrasmall nanoparticles. At the annealing temperature 500 °C, appears the signature of both phases Y₂O₃ (JCPDS card No. 088-1040) and Gd₂O₃ (JCPDS card No. 043-1014) with broad XRD peaks indicating the formation of ultrafine crystallites. With the increase in annealing temperature, the diffraction peaks are expected to become more intense and sharper in accordance with an increase in crystallinity and crystallite size. The mean crystallite size (〈L_XRD〉) of Y₂O₃ and Gd₂O₃ annealed at 1000 °C was found to be at around 81 nm and 108 nm, respectively. Table 1 gathers selected structural and structural parameters of the produced powder oxides annealed at 1000 °C. Additionally, at 1000 °C all the observed peaks of the produced RE₂O₃ (RE = Y, Gd) were assigned to the cubic structure of the reference oxides without any detectable extra phase indicating in particular highly thermally stable oxides. The refined lattice parameters (Table 1) of RE₂O₃ (RE = Y, Gd) annealed at 1000 °C were found to be in excellent agreement with those reported elsewhere (Baldinozzi et al., 1998; Zachariasen, 1927). Fig. 3 shows the XRD patterns of the as-prepared CaO and the associated annealed powder at 1000 °C along with standard JCPDS data of calcium oxide and calcium carbonate (calcite allotrope). It can be observed that the as-prepared powder consists of pure calcite (JCPDS card No. 5-586) indicating the chemical inertness of the major phase precursor (calcite) toward the polyol solvent. Additionally, a close look of the XRD pattern of the as-produced revealed the disappearance of an impurity initially found with the precursor. We also note that a number of attempts varying the hydrolysis ratio, the acetate ratio, and the refluxing time remained unsuccessful for the preparation of the expected oxide. On the other hand, the annealed powder at 1000 °C as expected reveals the formation of pure calcium oxide (JCPDS card No. 78-0649) through a well-known thermal decomposition of calcium carbonate. In CaO powder the mean crystallite size is notably larger than in the other additives, and it is of about 270 nm. The XRD patterns of the sintered ferrite/additives show the signature of the two components of each powder indicating in particular the occurrence of neither solid solution (there’s no shift of diffraction peaks) nor detectable other new phases i.e. each component of the sintered materials retains its chemical and structural identity. The relatively moderate sintering conditions (1000 °C, 2 h) compared to the conventionally adopted for the sintering of bulk ferrites (>1200 °C, >12 h) could be the main reason for the absence of any detectable solid-state reaction between the additives and the ferrite phase. However, the co-sintering of the ferrite and the additives phases may affect their microstructure in comparison with their own microstructure. The microstructural features of each component of the ferrite/additives powders were estimated (Table 1). Except for the CaO phase whose size was surprisingly found to be reduced to about the half, the mean crystallite size and the strain of the component phases of each sintered powder are found to be similar to those calculated for the isolated phases. In order to get more information about the powder morphology of the additives Y₂O₃, Gd₂O₃, and CaO, TEM analysis was performed (Fig. 4(a–c)). As can be clearly seen from TEM images and the associated histograms, the grains of RE₂O₃ (RE = Y, Gd) show important irregularity in the size and the shape with a high degree of agglomeration. Those of Y₂O₃ are relatively more regular with polygonal plate-shaped nanoparticles of six or higher sides and a mean particle size (the average size for each particle was calculated by measuring the largest and the smallest length) of about 87 nm. On the other hand CaO powder consists of roughly spherical, slightly agglomerated nanoparticles with a particle size ranging from about 90 to 180 nm and an average diameter of 126 nm. The FT-IR spectroscopy was used to elucidate the surface functionality and the vibrational modes of the inorganic core of the as-prepared additives (Fig. 5). The IR spectra of the solvent diethyleneglycol and as-prepared Y₂O₃ annealed at 1000 °C are also recorded for comparison. As expected the IR spectrum of the as-prepared CaO powder shows a very strong absorption band at around 1430 cm⁻¹ and two sharp ones centered at 1430, 880, and 713 cm⁻¹ arising from the stretching modes of carbonate ion (Miller and Wilkins, 1952). For the as-prepared powders of RE₂O₃ (RE = Y, Gd), the IR spectra in the region above 750 cm⁻¹ show characteristics of the main chemisorbed species including hydroxyl groups, polyol, and acetate ions (Huili et al., 2015a). For instance, we noticed the presence of the alkyl-substituted ether, C–O–C, bridging and secondary alcohol, C–O, stretching bands (1150–1050 cm⁻¹) of the polyol as well as the characteristic acetate, COO, symmetric ν_s (weak and broad at 1407–1440 cm⁻¹) and asymmetric ν_as (strong and broad at 1622–1650 cm⁻¹) stretching bands. These assignments are supported by the presence of a couple of sharp bands located at 2920/2880 cm⁻¹ associated with C-H vibrations (ν_as/ν_s CH₂). It is worth noting that the organic species detected on RE₂O₃ particles are completely absent in the case of the as-prepared CaO sample thus supporting the XRD results. Another important point is to be noted that the IR bands associated with the capping agents are much more pronounced with the as-prepared Y₂O₃ than the observed for as-prepared Gd₂O₃. The result can be explained on the basis of the difference in the specific surface of the particles of the two samples; the smaller the particle size, the larger the surface area is, and therefore the larger the amount of grafted organic species on its surface is. The last result supports the XRD microstructure analyses results found for the two sintered samples. For the annealed two oxides at elevated temperatures the organic species are expected todepart from the particles surface through a combustion reaction. The result can be clearly seen for the typical IR spectrum of the as-prepared Y₂O₃ powder annealed at 1000 °C which revealed the complete disappearance of the IR features of the organic. Additionally, for both the as-prepared Gd₂O₃ and the as-prepared Y₂O₃ powder annealed at 1000 °C appeared at low frequencies two broad intense bands in the range 600–400 cm⁻¹. The absorption bands are characteristic of the rare earth oxides RE₂O₃ (including Y₂O₃) cubic oxides (Baun and Mc Devitt, 1963). Further, as can be deduced from IR study, unlike the as-prepared Y₂O₃, appearance of characteristic bands for the as-prepared Gd₂O₃ in the range 600–400 cm⁻¹ confirms the possibility of one-pot synthesis of the last oxide without any further heat treatment. However, as pointed out above, XRD demonstrated that the Gd₂O₃ core is of amorphous nature since no diffraction peaks were detected and subsequent annealing is just required for promoting its crystallization. Furthermore, it is interesting to note that the vibrational frequency (≈533 cm⁻¹) observed for sintered Y₂O₃ is notably higher than that observed for Gd₂O₃ (≈506 cm⁻¹). The result can be correlated with RE-O bonding length; the oxide with the larger RE-O bond length, i.e. with the larger cations radius (Gd³⁺) is expected to exhibit the lower stretching frequency IR band.

Close

Figure 1

XRD patterns of the as-prepared sample obtained from the preparation of Y₂O₃ and associated powders annealed at different conditions in comparison with the reference Y₂O₃ (JCPDS card No. 88-1040). The XRD peaks of the spinel-type ferrite phase (JCPDS card No. 52-0278) are indicated by the symbol (+). For the as-prepared powder, the only peak observed at around 27° indicated by (^*) is due to the sample holder.

Export to PPT

Close

Figure 2

XRD patterns of the as-prepared sample obtained from the preparation of Gd₂O₃ and the associated powders annealed at different conditions in comparison with the reference Gd₂O₃ (JCPDS card No. 43-1014). The XRD peaks of the spinel-type ferrite phase (JCPDS card No. 52-0278) are indicated by the symbol (+).

Export to PPT

Close

Figure 3

XRD patterns of the as-prepared sample obtained from the preparation of CaO and the associated powder annealed at 1000 °C in comparison with the references calcite (JCPDS card No. 05-0586) and calcium oxide (JCPDS card No. 017-0912). (^*) unassigned peak due to a minor unknown impurity in CaCO₃ precursor (Sigma-Aldrich; 98.5%). The XRD peaks of the spinel-type ferrite phase (JCPDS card No. 52-0278) are indicated by the symbol (+).

Export to PPT

Close

Figure 4

TEM images for Y₂O₃ (a), Gd₂O₃ (b), and CaO (c), sintered at 1000 °C with their corresponding particle size distribution histograms.

Export to PPT

Close

Figure 5

IR spectra of the as-prepared produced powders. The IR spectra of the solvent diethyleneglycol and as-prepared Y₂O₃ annealed at 1000 °C are also recorded for comparison. The grid lines are a guide for eyes.

Export to PPT

3.2 Magnetic properties

The isothermal hysteresis loops of the three ferrite/additives measured at 300 K are presented in Fig. 6. As can be noted, there is no hysteresis features (neither remanence nor coercivity), indicating a superparamagnetic behavior of the materials at ambient temperature. In small ferromagnetic or ferrimagnetic single domain particles, superparamagnetism occurs above the so-called blocking temperature, T_B, because of weakly interacting and thermal fluctuations of the spins of the nanoparticles. The thermal effects allow flips of spins between the easy magnetization axes which lead to near zero–coercivity and increase in saturation magnetization (Pileni, 2001). Below T_B the thermal fluctuation does not dominate and the superparamagnetic nanosized particles cannot rotate freely but freeze in random orientations leading to high–coercive fields. The saturation magnetization, M_sat, values gathered in Table 2 are determined by extrapolating a linear fitting of M vs 1/H data to 1/H = 0. As expected the saturation magnetization of the ferrite/additives is quite similar to each other and doesn’t differ significantly from that of the pure sintered ferrite owing to the low fraction (5%) of the additives in the materials. The slight decrease of M_sat observed for the ferrite/additives in comparison with the undoped ferrite (Table 2 and the zoom-view in Fig. 6), is possibly attributed to the very weak ferromagnetism and diamagnetism at room temperature of nanosized Gd₂O₃ and Y₂O₃ (Bud’ko and Canfield, 2006; Zhu et al., 2012) and CaO, respectively. It is worth noting that dissolution of any of the Gd³⁺, Y³⁺, or Ca²⁺ cations in the spinel-like structure, even at very low concentration should appreciably alter the magnetization of the ferrite material. For instance, it is reported that entrance of Gd³⁺ and Y³⁺ at low concentration, respectively enhanced and reduced the saturation magnetization of CoFe₂O₄ (Yan et al., 1998). Therefore any assumption of incorporation of the above mentioned cations in the spinel-type lattice can be ruled out. Decay of magnetization with temperature and the Curie temperature of spinel ferrites are of vital important parameters from technological applications’ point of view. To get a quantitative description we measured the temperature dependence of the spontaneous magnetization, M_sp (Fig. 7). For nanostructured ferrites, below the Curie temperature M_sp vs T can be well fitted with a modified Bloch’s law function (Abdallah et al., 2014).

Close

Figure 6

Dc M-H hysteresis loops measured at 300 K for ferrite/Y₂O₃, ferrite/Gd₂O₃, and ferrite/CaO, sintered at 1000 °C. The inset is a zoom-view at high fields. The data of undoped ferrite were reported by us in a previous work (Huili et al., 2015b).

Export to PPT

Close

Figure 7

Spontaneous magnetization, M_sp vs temperature measured at 20 kOe for ferrite/Y₂O₃, ferrite/Gd₂O₃, and ferrite/CaO, sintered at 1000 °C. The inset is a zoom-view around 220 K showing the goodness of fit to the modified Bloch’s law.

Export to PPT

3.3 Electrical and dielectric study

The electrical and dielectric properties of the sintered Co_0.2Ni_0.3Zn_0.5Fe₂O₄ doped with 5 wt.% of Y₂O₃, Gd₂O₃, and CaO were studied by complex impedance spectroscopy as a function of temperature and frequency.

The following are useful equations for the determination of a number of electrical/dielectric quantities based on the measured real (Z′) and imaginary (Z″) components of the complex electrical impedance (Z^∗) of the electrical system (pellet + electrode + …).

The real (ε′) and the imaginary (ε″) parts of the complex dielectric constant, ε^∗ ( ${\epsilon }^{\ast }={\epsilon }^{\prime }+j{\epsilon }^{″}$ ), and applying the following relations:

The dielectric loss factor (tan δ) is calculated from the ratio of ε″ to ε′:

• f, the frequency of the applied external electrical field.

• ω = 2πf, the angular frequency.

$C_0=\frac{{\epsilon }_{0}S}{t}\text{,}$ the free space capacitance of a parallel-plate capacitor with separation t and face area S those of the studied pellets.

The complex electrical modulus, M^∗, is defined as the inverse of complex permittivity:

Taking account of the above cited relations, the real (M′) and the imaginary (M″) parts of the complex electrical modulus can be calculated as follows:

The dc conductivity, σ_dc, can be calculated applying the following formula:

The percentage porosity was also calculated according to the relation:

Close

Figure 8

Cole–Cole diagrams measured at selected temperatures for (a) undoped ferrite, (b) ferrite/Y₂O₃, (c) ferrite/Gd₂O₃, and (d) ferrite/CaO, sintered at 1000 °C. The red thin solid line denotes the simulated diagrams and the inset is the equivalent electrical circuit using Zview program.

Export to PPT

Close

Figure 9

Arrhenius plots of Co_0.2Ni_0.3Zn_0.5Fe₂O₄ and its associated doped samples sintered at 1000 °C. In the X-axis labeling the symbol T is the absolute temperature expressed in Kelvin.

Export to PPT

Close

Figure 10

Frequency dependence of ac conductivity, σ_ac, measured at selected temperatures for (a) undoped ferrite, (b) ferrite/Y₂O₃, (c) ferrite/Gd₂O₃, and (d) ferrite/CaO, sintered at 1000 °C.

Export to PPT

Close

Figure 11

Frequency dependence of the real part of the electric modulus, M′, measured at selected temperatures for (a) undoped ferrite, (b) ferrite/Y₂O₃, (c) ferrite/Gd₂O₃, and (d) ferrite/CaO, sintered at 1000 °C.

Export to PPT

Close

Figure 12

Frequency dependence of the imaginary part of the electric modulus, M″, measured at selected temperatures for the undoped ferrite, Co_0.2Ni_0.3Zn_0.5Fe₂O₄, and its associated doped samples sintered at 1000 °C.

Export to PPT

As can be noticed, for a given sample, as the temperature increases, f_r shifts toward higher frequencies implying a decrease in the relaxation time consequence of thermal activation of charge carriers. In addition, f_r was found to be higher with the doped samples. Further it depends on the nature of doping oxide. The high relaxation frequency (>13 MHz) is observed with CaO doping. It is important to note that the trend in f_r correlates the ac and dc conductivities trends observed for the studied samples; the higher the relaxation frequency is the larger conductivity will be. The last conclusion allows giving another way for the explanation and prediction of the ac and dc conductivities trends.

Frequency dependence of the imaginary dielectric constant, ε“, and dielectric loss factor, tan δ, at selected temperatures are shown in Figs. 13 and 14. It is clear that all the studied samples exhibit dielectric dispersion where the both ε” and tan δ decrease rapidly with increasing frequency of the applied field. Beyond a certain critical value of frequency, the dielectric properties become almost constant. The above dielectric dispersion is a general trend observed for all ferrites. It is explained on the basis on the two polarization mechanisms (Maxwell, 1973; Wagner, 1913; Shinde et al., 2008; Sarah and Suryanarayana, 2003): (i) electrons exchange between the Fe³⁺ and Fe²⁺ ions at octahedral sites and (ii) space charge polarization due to the presence of an inhomogeneous dielectric structure. For mechanism (i) which is expected to play the dominant role, the polarization occurs through a mechanism similar to the conduction process; the exchange of electrons between the Fe³⁺ and Fe²⁺ ions at octahedral sites may lead to the local displacement of electrons in the direction of the field applied and these electrons determine the polarization. Moreover, owing to the comparatively greater polarizability of the Fe²⁺ ions which have a greater number of electrons than the Fe³⁺ ions, it can be understood that variation in dielectric constant of ferrites strongly correlated with the variations in the concentration of Fe²⁺ ions. At low frequencies, the polarization can follow the applied field and therefore a high dielectric constant and loss factor are recorded. With the increase in frequency, ε“ and tan δ decreased substantially and reached an almost constant value beyond certain frequency of external field (see Fig. 13). This can be explained by the fact that beyond a critical frequency the hopping frequency of the electron exchange between Fe²⁺ and Fe³⁺ cannot follow the alteration of ac electric field. Mechanism (ii) suggested as outlined before that the sample can be modelized by the M-W model consisting of a heterogeneous structure containing well conducting grains separated by highly resistive thin grain boundaries. This causes localized accumulation of charge under the applied electric field which builds up space charge polarization. Hence a high value of dielectric constant is expected at low frequency (Shinde et al., 2008; Ajmal and Maqsood, 2007). The electron reverses their direction with the increase in field reversal frequency of electric field. The chances of electron accumulation at grain boundaries decreased thereby decreasing polarization. Therefore, the dielectric features ε” and tan δ decrease with rise in frequency and reach almost constant value as is observed. For our samples the lowest value of tan δ is observed for the composition Co_0.2Ni_0.3Zn_0.5Fe₂O₄/Y₂O₃ and it is found to be remarkably lower than that reported for the unsubstituted undoped bulk ferrite, Ni_0.5Zn_0.5Fe₂O₄ (Huili et al., 2014; Shokrollahi and Janghorban, 2007). The improved electrical/dielectric properties obtained for the Y₂O₃ doped ferrite can be attributed to a number of interdependent factors including the curtailing of the Fe²⁺ ions, the better compositional stoichiometry, the moderate sintering conditions, and fine grained pre- and post-sintered component materials. The low loss values at higher frequencies show the potential applications of these materials, especially the Y₂O₃ doped material in high-frequency microwave devices. As shown in Fig. 14, the CaO doped ferrite, exhibited an additional peak at about 35 kHz. The phenomenon is known as ferromagnetic resonance. It has been observed with other ferrites (Singh et al., 2011; Khan et al., 2014; Junaid et al., 2016; Iqbal et al., 2014). Ferromagnetic resonance can be observed if an ion has two equilibrium states separated by a potential barrier, and the jumping probability of both ions will be the same. The frequency that changes the position of ion is called the natural frequency of that ion (f_N). When both the natural and external applied frequencies were the same, then the maximum electrical energy was transferred to the oscillating ions and then the power loss increased resulting in the resonance phenomenon. In our case, since ferromagnetic resonance was observed only with the ferrite/CaO, it can be suggested that the calcium ions in their crystal lattice occupy two energetically equal equilibrium states separated by a potential barrier.

Close

Figure 13

Frequency dependence of the imaginary part of dielectric permittivity, ε″, for (a) undoped ferrite, (b) ferrite/Y₂O₃, (c) ferrite/Gd₂O₃, and (d) ferrite/CaO, sintered at 1000 °C.

Export to PPT

Close

Figure 14

Frequency dependence of the loss factor, tan δ, measured at 123 °C for Co_0.2Ni_0.3Zn_0.5Fe₂O₄/additives sintered at 1000 °C. The inset is a zoom-view at high frequencies.

Export to PPT