Angular Frequency Research Articles

Simple pendulum: period dependent on amplitude of oscillation

In this study, with a pedagogical aim suited for the undergraduate, the differential equations of motion that characterize and determine the motion of a simple pendulum were obtained considering small and large amplitudes of oscillation. These differential equations were solved through differential equation solution methods, numerical, expansion of functions and integrations. The solutions obtained using the different methods were compared. It was possible to verify, both experimentally and theoretically, that for the oscillatory movement of the simple pendulum, its oscillation period increases and its angular frequency decreases with the increase of the oscillation amplitude. The validity range of the approximation for small ranges of motion was also determined. It was verified that the theoretical and experimental results present a good agreement for angles smaller than 55°. The experimental measurements were made with “a low-cost home-built” equipment.

Modified pure-viscoacoustic wave propagation and compensated reverse-time migration in transversely isotropic media

Previous studies demonstrated that seismic attenuation and anisotropy can significantly affect the kinematic and dynamic characteristics of wavefields. If these effects are not incorporated into seismic migration, the resolution of the imaging results will be reduced. Considering the anisotropy of velocity and attenuation, we derive a new pure-viscoacoustic wave equation to simulate P wave propagation in transversely isotropic (TI) attenuating media by combining the complex dispersion relation and modified complex modulus. Compared to the conventional complex modulus, the modified modulus is derived from the optimized relationship between angular frequency and wavenumber, which can improve the modeling accuracy in strongly attenuating media. Wavefield comparisons illustrate that our pure-viscoacoustic wave equation can simulate stable P wavefields in complex geological structures without S-wave artifacts and generate similar P wave information to the pseudo-viscoacoustic wave equation. During the implementation, we introduce two low-rank decompositions to approximate the real and imaginary parts and then use the pseudo-spectral method to solve this new equation. Since the proposed equation can simulate decoupled amplitude attenuation and phase dispersion effects, it is used to perform Q-compensated reverse-time migration (Q-RTM). Numerical examples demonstrate the accuracy and robustness of the proposed method for pure-viscoacoustic wavefield simulations and migration imaging in transversely isotropic attenuating media.

Acoustic characteristics and performance analysis of a solid-state thermoacoustic oscillator

Thermoacoustic instability in solids paves the way for the development of solid-state thermoacoustic (SSTA) engines with superior reliability. Acoustic characteristics with respect to the performance of SSTA oscillators are investigated, where growth ratio is taken as a performance metric. Numerical analyses show that the acoustic characteristics not only determine the temperature gradient direction for strengthening the oscillation, but also affect the maximum growth ratio. A high growth ratio is obtained at a low angular frequency and an acoustic field around 1/8 wavelength from the strain antinode. To realize appropriate acoustic characteristics, the angular frequencies and acoustic fields under different boundary conditions are studied, based on which the method to adjust the acoustic characteristics is discussed. This work aims to reveal the relationship between the acoustic characteristics and the performance of SSTA oscillators, and to provide new insights on adjusting the acoustic characteristics for improving SSTA oscillators.

SIMULATION AND RESEARCH OF SINGLE-PHASE SHORT CIRCUITS IN THE ELECTRICAL NETWORK

The purpose of this work is to model single-phase short circuits in a three-phase electrical network and identify their type by analyzing the angular frequency of the spatial vector. Recently, the saturation of electric networks with powerful non-linear loads, the introduction of conversion equipment and renewable energy sources lead to the need for systematic analysis and research of the quality of electric energy (QEE). One of the factors that significantly affect the operation of electrical equipment is short circuits. In the article, based on the developed model of the formation of QEE distortions, a single-phase short circuit in a three-phase electrical network is investigated by switching it to a single-phase system with two α-β projections and a zero-sequence voltage vector.
 Studies of the influence of the location of the short-circuit point on the voltage in the electrical network have shown that the difference in the distance from the point of damage to the load, type of short-circuit leads to varying degrees of voltage change. Conducted studies have shown that different types of malfunctions and parameters of the electrical network at the point of short circuit cause different disturbances in the electrical voltage in the power supply system. The presence of a short circuit of the same type at different locations leads to different voltage drops and overvoltages. Short-term changes in voltage are the most common distortions of the quality of electrical voltage in electrical networks. The simulation results based on the developed model are consistent with the theory and reliably simulate the change in voltage in the electrical network.
 In the future, the presented model can help in creating a basis for the identification and subsequent control measures of voltage change violations.

Energy and dissipation spectra of waves propagating in the inner surf zone

The spectral behaviour of random sawtooth waves propagating in the inner surf zone is investigated in this study. We show that the elevation energy spectrum exhibits a universal shape with an $\omega ^{-2}$ tendency in the inertial subrange and an exponential decay in the diffusive subrange ( $\omega$ being the angular frequency). A theoretical spectrum is derived based on the similarities between sawtooth waves in the inner surf zone and Burgers wave solutions. Very good agreement is shown between this theoretical spectrum and laboratory experiments covering a large range of incident random wave conditions. Additionally, an equation describing the universal shape of the dissipation spectrum is derived. It highlights that the dissipation spectrum is nearly constant in the inertial subrange, consistent with prior laboratory observations. The findings presented in this study can be useful to improve broken wave dissipation parametrizations in stochastic spectral wave models.

Rapid Semiconducting Supramolecular Mg(II)-Metallohydrogel: Exploring Its Potential in Nonvolatile Resistive Switching Applications and Antiseptic Wound Healing Properties.

An effective strategy was employed for the rapid development of a supramolecular metallohydrogel of Mg(II) ion (i.e., Mg@PEHA) using pentaethylenehexamine (PEHA) as a low-molecular-weight gelator in aqueous medium under ambient conditions. The mechanical stability of the synthesized Mg@PEHA metallohydrogel was characterized by using rheological analysis, which showed its robustness across different angular frequencies and oscillator stress levels. The metallohydrogel exhibited excellent thixotropic behavior, which signifies that Mg@PEHA has a self-healing nature. Field emission scanning electron microscopy and transmission electron microscopy images were utilized to explore the rectangular pebble-like hierarchical network of the Mg@PEHA metallohydrogel. Elemental mapping through energy-dispersive X-ray spectroscopy analysis confirmed the presence of primary chemical constituents in the metallohydrogel. Fourier transform infrared spectroscopy spectroscopy provided insights into the possible formation strategy of the metallohydrogel. In this work, Schottky diode structures in a metal-semiconductor-metal geometry based on a magnesium(II) metallohydrogel (Mg@PEHA) were constructed, and the charge transport behavior was observed. Additionally, a resistive random access memory (RRAM) device was developed using Mg@PEHA, which displayed bipolar resistive switching behavior at room temperature. The researchers investigated the switching mechanism, which involved the formation or rupture of conduction filaments, to gain insights into the resistive switching process. The RRAM device demonstrated excellent performance with a high ON/OFF ratio of approximately 100 and remarkable endurance of over 5000 switching cycles. RRAM devices exhibit good endurance, meaning they can endure a large number of read and write cycles without significant degradation in performance. RRAM devices have shown promising reliability in terms of long-term performance and stability, making them suitable for critical applications that require reliable memory solutions. Significant inhibitory activity against the drug-resistant Klebsiella pneumonia strain and its biofilm formation ability was demonstrated by Mg@PEHA. The minimum inhibitory concentration value of the metallohydrogel was determined to be 3 mg/mL when it was dissolved in 1% DMSO. To study the antibiofilm activity, an MTT assay was performed, revealing that biofilm inhibition (60%) commenced at 1 mg/mL of Mg@PEHA when dissolved in 1% DMSO. Moreover, in the mouse excisional wound model, Mg@PEHA played a crucial role in preventing postoperative wound infections and promoting wound healing.

Investigating the phase behaviour of binary suspensions of cellulose nanocrystals and montmorillonite with nonlinear rheology, SAXS and polarized optical microscopy

Using microscopy imaging techniques, X-ray scattering, and nonlinear rheological measurements, we have examined microstructural changes, and phase behavior of cellulose nanocrystals (CNC)/montmorillonite (MMT) composite colloidal systems. Fourier-transform (FT) rheology-stress decomposition methods, Lissajous-Bowditch plots, and other techniques are used to both qualitatively and quantitatively determine the various phases that the suspensions exhibit. In the MAOS (medium amplitude oscillatory shear) region, multiple scaling regions, as well as quadratic scaling regions are obtained. The dependence of the normalized third relative intensity (I3/1) values on angular frequency (ω) also provided new insights into how nonlinear parameters depend on the various CNC/MMT phases. These findings allow us to differentiate various phases exhibited by the composite system, including the isotropic, biphasic, and chiral nematic liquid crystalline (LC) phases. The CNC/MMT nanocomposite system exhibits a variety of liquid crystalline phases, which may contribute to improved mechanical properties for the system, including increased mixture strength, stiffness, and toughness because of the particle alignment in the LC phase. Additionally, the field of optics and photonics may find use for this nanocomposite system in the fabrication of sensors, polarizers, and optical films; energy storage applications where the aligned structures facilitate ion transport; and the formulation of paints and coatings where the strain stiffening and shear thinning behavior of the CNC/MMT composite system are critical.

Dielectric and electrocaloric properties of BCTZ composite with cobalt zinc ferrite nanoparticles

Dielectric and electrocaloric properties of a multiferroic composite constituted from Ba0.85Ca0.15Ti0.9Zr0.1O3 (BCTZ) and Co0.4Zn0.6Fe2O4 (CZF), chosen for their closely related transition temperatures, are reported. Dielectric characteristics of the composites in the 1 kHz−10 MHz angular frequency range are described by two Cole-Cole relaxation models (domain wall and charge carrier) whereas for frequency <1 kHz, it is explained by Maxwell-Wagner type interfacial polarization using Jonscher power law. The effect of CZF phase on the dipolar mechanisms as a function of CZF mole fraction and the temperature are discussed. The electrocaloric property of the composites is estimated indirectly by Maxwell thermodynamic relation.

A stable Q-compensated reverse-time migration method using a modified fractional viscoacoustic wave equation

Seismic wave propagation inside the earth is usually accompanied by amplitude dissipation and velocity dispersion. It is essential to accurately characterize these effects and make the corresponding compensations in seismic reverse-time migration (RTM) and the following interpretation. Due to the approximation of [Formula: see text] in the derivation, the conventional fractional viscoacoustic wave equation in strongly attenuative media is unsatisfactory. This paper develops a modified viscoacoustic wave equation by combining the relationship between angular frequency and complex wavenumber. The numerical simulation demonstrates its advantage of high accuracy in describing constant- Q effects, especially in strongly attenuative media with small Q values. A truncated Taylor-series expansion algorithm and a pseudospectral method are developed to solve this equation during wave propagation. To address the issue of numerical instability in Q-compensated RTM ( Q-RTM), a stabilized technology with regularization is further developed. Unlike the conventional filtering method implemented in the wavenumber domain, our approach only adds an explicit regularization term, which can be directly computed in the space domain. Furthermore, this regularization depends on velocities and quality factors, significantly improving its applicability in complicated structures. Noise-free data tests demonstrate that our Q-RTM method can effectively correct phase distortion, compensate for amplitude attenuation, and produce high-resolution migrated images without any cutoff-frequency artifacts caused by filtering. Noisy data experiments further verify the antinoise performance and robustness of our method.

Dielectric behavior and impedance spectroscopy of Niobium substituted Lanthanum based orthovanadates at high temperatures

We present the detailed study of the temperature dependent dielectric properties, impedance spectroscopy and electrical conductivity of LaV1−xNbxO4 (x=0–1) samples prepared by the solid-state reaction method. The dielectric constant (ϵr′) increases (decreases) with increase in the temperature (frequency); while, the magnitude of ϵr′ remains almost invariant (order of 104 at 100 Hz and 600 °C) with x. The single phase x=0 (monoclinic-monazite, P21/n) and x=1 (monoclinic fergusonite, I2/a) samples show the lower values of loss factor [tanδ= (4–8)] as compared to the x=0–0.8 samples [tanδ= (12–18)] having mixed tetragonal and monoclinic phases, which indicates the strong correlation between the crystal structure and the dielectric properties. The real part of impedance (Z′) decreases with both temperature and frequency, and the observed weak relaxation remains almost unaltered with x. The imaginary part of impedance (Z′′) shows strong relaxation peaks shifting towards higher temperatures with frequency, which is attributed to the effect of grains, grain boundaries, and electrodes in the samples. The activation energy of the relaxation process is estimated to be 0.8–1.0 eV for the x=0–0.6 samples, and ≈1.4 eV for the x=0.8; whereas the x=1 sample shows two values (≈0.5 eV and ≈1.0 eV) in the higher and lower temperature range, respectively. Further, the change in total conductivity with the angular frequency, which found to be in the range of 10−3 to 10−5 S/m, is fitted using the Jonsher power law. The analysis suggests the overlapping large polaron tunneling (OLPT) model for all the samples, whereas the x = 1 sample exhibit a transition near 480 °C and at higher temperatures it shows non-overlapping small polaron tunneling (NSPT) and quantum mechanical tunneling (QMT). This transition is corroborated by the tangent loss curves and may be associated with the change in structure.

Rotating Alfvén waves in rotating plasmas

Angular momentum coupling between a rotating magnetized plasma and torsional Alfvén waves carrying orbital angular momentum (OAM) is examined. It is demonstrated not only that rotation is the source of Fresnel–Faraday rotation – or orbital Faraday rotation effects – for OAM-carrying Alfvén waves, but also that angular momentum from an OAM-carrying Alfvén wave can be transferred to a rotating plasma through the inverse process. For the direct process, the transverse structure angular rotation frequency is derived by considering the dispersion relation for modes with opposite OAM content. For the inverse process, the torque exerted on the plasma is derived as a function of wave and plasma parameters.

Mathematical modeling and dynamic analysis of carbon fiber reinforced plastic shaft-disk-bearing system considering internal damping effect

The internal damping has significant influence on the dynamic characteristics of carbon fiber reinforced plastic drive shaft. In this paper, a dynamic model of the single-span multi-disk carbon fiber reinforced plastic shaft with elastic support is established based on layer-wise theory, damping specific capacity model, and Euler–Bernoulli beam theory. The model takes into account physical factors such as rigid body displacement caused by elastic support deformation, gyroscopic effect of concentrated mass disk, viscous internal damping of the carbon fiber reinforced plastic shaft, and lamination parameters. The model is used to analyze the natural angular frequency and critical instability speed of carbon fiber reinforced plastic shaft-disk-bearing system. The analysis results are compared with those obtained from the equivalent modulus beam theory, equivalent single layer theory, simplified homogenized beam theory, and quadrature element method. All the results demonstrate the accuracy of the proposed model, thereby validating its effectiveness. Furthermore, the model is utilized to investigate the influence of lamination parameters and mass ratio on the natural angular frequency and critical instability speed. This study provides valuable insights for the dynamics and stability design of the carbon fiber reinforced plastic shaft-disk-bearing system.

Effects of Hybrid POSS Nanoparticles on the Properties of Thermoplastic Elastomer-Toughened Polyamide 6.

In this study, polyamide 6 (PA6)/thermoplastic elastomer (TPE) blends were prepared to decrease the notch sensitivity of PA6 for automotive applications, and the morphological, rheological, mechanical, and thermal properties of PA6/TPE blends, which are partially miscible or immiscible depending on the TPE ratio, were significantly improved in the existence of polyhedral oligomeric silsesquioxane (POSS) nanoparticles with multiple reactive epoxy groups as compatibilizers. An unstable phase morphology was obtained with the addition of TPE into PA6 without POSS nanoparticles, whereas interfacial interactions between phases in the presence of POSS were enhanced as a result of a significant decrease in the average particle size from 1.39 to 0.41 μm. The complex viscosity value of the 70PA6/30TPE blend, which was 20 kPa/s-1 at 0.1 rad/s angular frequency, reached 380 kPa/s-1 with the addition of POSS due to the formation of long chains by the generation of graft and/or block copolymers, which resulted in a 65% increase in Young's modulus value. Most notably, the Izod impact strength of pure PA6, which was 10 kJ/m2, increased by 290% with the incorporation of POSS. It was confirmed by FTIR analysis that the reactive multiple epoxy groups of MultEpPOSS and EPPOSS nanoparticles react with the proper groups of PA6 and/or TPE, and also, a partial hydrogen bonding interaction occurs between PA6-TPE from the shifting of N-H and carbonyl peaks. In conclusion, it can be suggested that POSS nanoparticles can serve as highly effective compatibilizers for PA6/TPE blends and have potential commercial applications, especially in the automotive sector.

A trivalent ferrite ferrofluid compound’s rheological response to angular frequency, magnetic induction and shear induction of chain clusters

At low and high temperatures in the presence and absence of magnetic fields, the effects of shear rate, angular frequency, and shear strain on the rheological characteristics of zinc ferrite ferrofluid is investigated. Chemical co-precipitation was used to create a zinc ferrite ferrofluid that was then coated with oleic acid to improve the stability of the fluid’s particles and avoid particle agglomeration. We looked at the rheological characteristics caused by the induced magnetic field, such as the shear stress, complex viscosity, storage modulus, loss modulus, relaxation modulus, viscous torque, damping factor, and figure of merit. From the analysis of time dependent relaxation modulus, a steady-state rheological system is formed at time interval beyond 50 s. As the shear and complex viscosities increase with an increase in magnetic field and a decrease in temperature, obstruction to fluid flow is produced. When a rheological system operates at low angular frequency and high shear rate, high shear stress is loaded; when it operates at high angular frequency and low shear rate, low shear stress is loaded. In the absence of magnetic field, a low viscosity 0.425 Pa.s and shear force 46 Pa were formed, while high viscosity 8.140 Pas and shear stress 168 Pa were formed when magnetic field 1.000 Tesla was applied. The oscillatory mode test demonstrates a change in structure from solid to liquid due to the establishment of a crossover point between shear strain 55 and 64%, supporting the solid–liquid phase transition behavior. The damping analysis demonstrates that the system is in fact excessively dampened, and it may now be utilized to reduce vibrations in a system. The system is really overdamped showing a maximum damping factor 2.08, according to the damping study, and can therefore be used to reduce vibrations in other systems. The fluid exhibits non-Newtonian shear-thinning behavior as shear rates increase. A high viscous torque is created at low shear strain and high angular frequency, which leads to the creation of a strong rotating magnetic field.

IDENTIFICATION AND CLASSIFICATION OF SINGLE-PHASE VOLTAGE DIPS USING THE METHODOLOGY OF THE SPATIAL VECTOR OF ANGULAR FREQUENCY

A new method of identification and classification of voltage dips in a three-phase electric network is presented. The method is based on the representation of voltages of the electrical network by one complex variable - a spatial vector of the angular frequency. The main characteristics of the spatial vector, which are used to identify and classify dips, are the major and minor semi-axes, the angle of rotation of the formed ellipse. For balanced dips, the space vector goes in a circle in the complex plane with a radius equal to the voltage. For unbalanced dips, the spatial vector is an ellipse with parameters that depend on the phase of the voltage drop, the magnitude of the dip, and the phase angle shift.&#x0D; This method introduces a new level of accuracy and reliability in the analysis and classification of voltage dips, making it a tool for improving the quality of power supply and increasing the stability of electrical systems. The use of this method can help reduce the impact of unplanned interruptions in the supply of electricity to the enterprise and home, which is becoming a key task in the modern electricity sector.

Damped quantum drift Zakharov-Kuznetsov equation for a dissipative inhomogeneous partially degenerate plasma with quantizing magnetic field

Damped quantum drift Zakharov-Kuznetsov (DQDZK) equation is investigated in two dimensions for a spatially inhomogeneous and dissipative plasma with adiabatic electron trapping in the presence of quantizing magnetic field and partial degeneracy. Linear and nonlinear analysis is presented in detail. For the 2D case, it is observed that the angular frequency of linear drift ion acoustic wave (DIAW) exhibits a cut-off point that gets modified by Landau quantization and partial degeneracy of the trapped electrons. It is observed that the inclusion of ion-neutral collisions leads to the formation of DQDZK equation for the system under consideration. The DQDZK is solved analytically using the hyperbolic tangent method and a decaying solitary wave solution is obtained. It is shown that the effects of quantizing magnetic field, partial degeneracy, and obliqueness significantly modify the properties of the nonlinear drift ion acoustic structures. The results presented here can be gainfully employed to understand the linear and nonlinear wave propagation in dense degenerate plasmas present in astrophysical compact objects like white dwarfs and neutron stars.

Laser irradiation effects on the dielectric properties of zinc ferrite at room temperature

Zinc ferrite (ZF) nanomaterials were synthesised by the sol–gel auto-combustion method. Synchrotron-XRD confirms the formation of the pure F-d3m spinel structure whereas EDX reveals the composition of synthesised nano ZF. We investigated and compared the dielectric properties of un-irradiated pellet ZF-UI and irradiated pellets ZF-I1 (pulsed Nd:YAG laser dose of 1.2 W, λ = 1064 nm), ZF-I2 (pulsed Nd:YAG laser dose of 1.5 W, λ = 532 nm) and ZF-I3 (continuous AlGaAs diode laser of 4 W, λ = 808 nm) at room temperature. Dielectric constant (ε′) decreased prominently for ZF-UI while it decreased gradually for ZF-I1 and its decrement for ZF-I2 and ZF-I3 is very slow whereas dielectric constant (ε ″) decreased prominently for ZF-UI and ZF-I1while reduced slowly for ZF-I2 and ZF-I3 in the low-frequency region. ε′ becomes ∼69% for ZF-I1 and ∼9% for ZF-I2 and ZF-I3 at a higher frequency of 2 MHz whereas ε ″ for radiated samples becomes steady and nearly equitable at higher frequencies in comparison to that of ZF-UI in the measured frequency range of 10 kHz to 2 MHz. Dielectric loss (tan δ) of all irradiated samples has decreased and become ∼33% for ZF-I3, 43% for ZF-I2, nearly equal for ZF-I1 at 104 Hz and then decreased continuously up to 2 MHz when compared to tan δ for ZF-UI. The Jonscher power law has been fitted in measured ac conductivity (σ ac) with angular frequency (ω) graphs. DC conductivity (σ dc), temperature-dependent parameter B(T) and frequency exponent (n) have been extracted. σ dc for all irradiated samples has decreased and become nearly 51% for ZF-I1, 3% for ZF-I2 and 2% for ZF-I3 in comparison to that of ZF-UI whereas B(T) increased to 1.6 times for ZF-I3 and decreased to 0.7 times for ZF-I1 and 0.2 times for ZF-I2 while n shows slight decrement for ZF-I2 and ZF-I3. Interpretation from Cole–Cole plots for un-irradiated and irradiated pellets is in agreement with our investigations. These results suggest that the dielectric properties of ZF can be controlled and tuned by laser irradiation.

Structure of the streaming flow generated by a sphere in a fluid undergoing rectilinear oscillation

A solid body in a viscous fluid undergoing oscillatory motion naturally produces a steady secondary flow due to convective inertia. This phenomenon is embodied in the streaming flow generated by a sphere in an unbounded fluid executing rectilinear oscillations. We review the considerable literature on this canonical problem and summarise exact and asymptotic formulas in the small-amplitude limit. These analytical formulas are used to explore the characteristic flow structure of this problem and clarify previously unreported features. A single, toroidal-shaped vortex exists in each hemisphere regardless of the oscillation frequency, which can drive a counter-flow away from the sphere. The vortex centre moves monotonically away from the sphere with decreasing oscillation frequency, and engulfs the entire flow domain for $\beta \equiv \omega R^2/\nu &lt; 16.317$ , where $\omega$ is the angular oscillation frequency, $R$ the sphere radius, and $\nu$ the fluid kinematic viscosity. This seemingly abrupt change in flow structure at the critical frequency $\beta _{critical} =16.317$ , and its quantification, appear to have not been reported previously. We perform a direct numerical simulation of the Navier–Stokes equations, to (1) confirm existence of this critical frequency at finite amplitude, and (2) examine its variation with amplitude. This reveals a universal relationship between the critical frequency and oscillation amplitude, clarifying previous reports on the structure of this streaming flow. The critical frequency is shown to be identical for the streaming flow and the cycle-averaged particle paths, establishing that the critical frequency is accessible directly using standard measurements.

Analytical solutions to the precession relaxation of magnetization with uniaxial anisotropy

Based on the Landau–Lifshitz–Gilbert (LLG) equation, the precession relaxation of magnetization is studied when the external field H is parallel to the uniaxial anisotropic field H k. The evolution of three-component magnetization is solved analytically under the condition of H = nH k (n = 3, 1 and 0). It is found that with an increase of H or a decrease of the initial polar angle of magnetization, the relaxation time decreases and the angular frequency of magnetization increases. For comparison, the analytical solution for H k = 0 is also given. When the magnetization becomes stable, the angular frequency is proportional to the total effective field acting on the magnetization. The analytical solutions are not only conducive to the understanding of the precession relaxation of magnetization, but also can be used as a standard model to test the numerical calculation of LLG equation.

Enhancing NiZn ferrite properties through microwave sintering: A comparative study

The structural, microstructural, morphological, and electromagnetic properties of a micro- and nanostructured nickel–zinc ferrite ((Cu0.12Ni0.23Zn0.65)Fe2O4) were studied after sintering between 900 and 1100°C. The microparticulated ferrite (MICRO) was a commercial material, while the nanoparticulated ferrite (NANO) was obtained through high energy milling of the former. The effect of microwave heating (MW), compared to traditional infrared sintering (IR), was investigated.Microwave sintering successfully controlled the grain growth of both granulometries and produced sintered bodies with high relative densities (low porosity), small average grain size, narrow grain size distribution, and a high value of the complex magnetic permeability-imaginary part (μ″) for the MICRO ferrite. In the case of the NANO ferrite, microwave sintering yielded values similar to those obtained by conventional IR.Microwave sintering significantly affected the densification and grain growth processes for both granulometries studied. Additionally, reducing the granulometry of the starting ferrite powder had a noticeable impact on the microstructure and electromagnetic properties of the sintered ferrites, regardless of whether microwave or infrared radiation was used. However, the magnetic property (μ″) decreased when the particle size of the starting powder was reduced from micro to nanometric scale, irrespective of the sintering source. This observation is supported by our previously published mathematical models that establish relationships between the complex magnetic permeability, magnetization mechanisms, angular frequency, and ferrite microstructure.