Dynamic Hysteresis Behavior Research Articles

Dynamic hysteresis and scaling behavior for Pb(Zr,Ti)O3 ceramics

The dynamic hysteresis of Nb-doped Pb(ZrxTi1−x)O3 (PZT, 0.40 ≤ x ≤ 0.60) ceramics with different phase structures was investigated as functions of frequency f and electric field amplitude E0. When E0 grows over ∼1.5 times of coercive field Ec, all the loops become well saturated and their scaling relations of hysteresis area ⟨A⟩ against f and E0 can be expressed with an identical form as ⟨A⟩∝f0.01E00.10 for either tetragonal phase or morphotropic phase, which is in good agreement with our previous result of rhombohedral PZT [Chen et al., J. Appl. Phys. 114, 244101 (2013)]. The results indicate that ferroelectrics with fairly distinct domain structures could have similar dynamic hysteresis and scaling behavior at high-E0 region.

Identical scaling behavior of saturated dynamic hysteresis in rhombohedral lead zirconate titanate bulk ceramics

The scaling behaviors of dynamic hysteresis were investigated in serial rhombohedral Nb-doped Pb(Zr1-xTix)O3 (PZT) bulk ceramics as a function of frequency (f) and field amplitude (E0). Three distinct regions were plotted including linear loops, minor loops, and saturated loops with an increase of E0. When the external fields were over ∼1.5 times of coercive field (Ec), the scaling relations of saturated loops for these PZT ceramics could be expressed with an identical form as hysteresis area ⟨A⟩ ∝ f 0.01E00.10, which indicated that similar ferroelectric systems with different compositions could display a uniform scaling law under high-E0 and low-f regions.

Temperature scaling behavior of dynamic hysteresis for (K,Na)NbO3 lead-free ferroelectric films

The temperature scaling of the ferroelectric hysteresis was first investigated in (K,Na)NbO3 films grown on SrRuO3/SrTiO3 over a temperature range from 100 K to 340 K. The power-law temperature scaling relations were obtained for ⟨A⟩, Pr, and Ec in the two distinguished temperature regions, separated by T ∼ 245 K. It was observed that ⟨A⟩ and Pr had a similar temperature dependence, compared with Ec. With increasing T, ⟨A⟩ and Pr decreased in the first region, and increased in the second region. While Ec decreased in the whole temperature range, but with different decrease rate in the two temperature regions.

Dynamic magnetic properties of the kinetic cylindrical Ising nanotube

The nature (time variation) of response magnetizations m(wt) of the kinetic cylindrical Ising nanotube in the presence of a periodically varying external magnetic field h(wt) is studied by employing the effective-field theory (EFT) with correlations as well as the Glauber-type stochastic dynamics. We have determined the time variations of m(wt) and h(wt) for various temperatures, and investigated the dynamic magnetic hysteresis behavior. Temperature dependence of the dynamic magnetizations, hysteresis loop areas and correlations are investigated in order to characterize the nature (first- or second-order) of the dynamic transitions as well as to obtain the dynamic phase transition temperatures. We also present the dynamic phase diagrams in the three different planes and compare the results of the equilibrium and nonequilibrium states. The phase diagrams exhibit dynamic tricritical, isolated critical, multicritical and triple points. The results are in good agreement with some experimental and theoretical results.

Linear temperature scaling of ferroelectric hysteresis in Mn-doped Pb(Mn1/3Sb2/3)O3-Pb(Zr,Ti)O3 ceramic with internal bias field

The temperature scaling of dynamic hysteresis was investigated in Mn-doped Pb(Mn1/3Sb2/3)O3-Pb(Zr,Ti)O3 ceramic with internal bias field. A set of simple linear temperature scaling relations were established for hysteresis area 〈A〉, coercivity Ec, and internal bias field Ei, which are different from the power-law scaling relationships for the soft and hard PZT ceramics. The proposed scaling relation between 〈A〉 and T can be predicted by the temperature dependent response of Ec and vice versa. It is suggested that the thermal deaging which related to the redistribution of the preferentially oriented defect dipoles is responsible for these dynamic hysteresis behaviors.

A Neural Network Modeling of Stress Behavior in Nonlinear Magnetostrictive Materials

Using accurate magnetostriction simulation models during the various design stages of their related devices can positively contribute to the enhancement of their precision. These models are indispensable to different crucial computational activities such as those dealing with active vibration damping devices and optimum clamping stresses for transformer sheets. In this paper, we present a new contribution for the dynamic hysteresis behavior of magnetostrictive materials. To do this, we have used a neural network to model the relationship between the elongation λ and the magnetization M for different loads σ. The derivative of λ according to M is then calculated numerically and integrated in the Jiles–Atherton model for calculating the hysteresis loops.

An energy-based dynamic loss hysteresis model for giant magnetostrictive materials

This paper addresses the development of a magneto-elastic coupling dynamic loss hysteresis model for giant magnetostrictive materials (GMMs). Considering the eddy current loss and anomalous loss, a dynamic constitutive model is proposed to predict the dynamic hysteresis behavior of GMMs. The model is validated by comparing the predicted results with experiments. At first, the frequency effect and anisotropy effect on the domain distribution can be obtained. Moreover, the magnetostriction cannot return to the initial value near the coercive field as the magnetization does with the increasing frequency. It can be explained that the domain distribution changes with the increasing energy loss. The model is benefit for the design and control of GMMs actuators.

A Novel Fractional Order Model for the Dynamic Hysteresis of Piezoelectrically Actuated Fast Tool Servo

The main contribution of this paper is the development of a linearized model for describing the dynamic hysteresis behaviors of piezoelectrically actuated fast tool servo (FTS). A linearized hysteresis force model is proposed and mathematically described by a fractional order differential equation. Combining the dynamic modeling of the FTS mechanism, a linearized fractional order dynamic hysteresis (LFDH) model for the piezoelectrically actuated FTS is established. The unique features of the LFDH model could be summarized as follows: (a) It could well describe the rate-dependent hysteresis due to its intrinsic characteristics of frequency-dependent nonlinear phase shifts and amplitude modulations; (b) The linearization scheme of the LFDH model would make it easier to implement the inverse dynamic control on piezoelectrically actuated micro-systems. To verify the effectiveness of the proposed model, a series of experiments are conducted. The toolpaths of the FTS for creating two typical micro-functional surfaces involving various harmonic components with different frequencies and amplitudes are scaled and employed as command signals for the piezoelectric actuator. The modeling errors in the steady state are less than ±2.5% within the full span range which is much smaller than certain state-of-the-art modeling methods, demonstrating the efficiency and superiority of the proposed model for modeling dynamic hysteresis effects. Moreover, it indicates that the piezoelectrically actuated micro systems would be more suitably described as a fractional order dynamic system.

Scaling behavior of dynamic hysteresis in relaxor ferroelectric 0.67Pb(Mg1/3Nb2/3)O3–0.33PbTiO3 ceramics

The scaling behaviors of dynamic ferroelectric hysteresis in the relaxor ferroelectric 0.67Pb(Mg1/3Nb2/3)O3–0.33PbTiO3 (PMNT67/33) ceramics near the morphotropic phase boundary (MPB) and other PMNT systems out of MPB region were investigated. The scaling relation of hysteresis area 〈A〉 against frequency f and field amplitude E0 for minor loops takes the form of 〈A〉∝f−0.2391E04.8779; while for the saturated loops, it is 〈A〉∝f 0.0401E00.5722. The scaling relations of PMNT67/33 ceramics are significantly different from those of other ferroelectrics, and the results of the analysis indicate that domain reversal in it is much more sensitive to the change of E0 at low electric field and responses more quickly to f at high electric field than other normal ferroelectrics. The coexistence of rhombohedral (R), monoclinic (M) and tetragonal (T) phases near the MPB and the polar nanoregions seems to play the key role in the dynamic behavior of the domain reversal in relaxor PMNT67/33 ceramics.

Hysteresis Properties of Magnetic/Non-Magnetic (M/NM) Multilayers: Monte Carlo Investigation

In this work, Monte Carlo simulation was used to model the dynamic hysteresis behavior of magnetic/non-magnetic multilayers in the framework of Heisenberg model using the spin-flip algorithm. The purpose is to investigate the hysteresis properties while varying the direction of external applied magnetic field and temperature taking account interface composition of magnetic/non-magnetic atoms. From the results, with thermal variation and interface composition, the simulated hysteresis loops change significantly due to the competition between magnetic anisotropy in magnetic films and the presence of isolated clusters at the interface.

Dynamic Hysteresis and Scaling Behavior of Energy Density in Pb0.99Nb0.02[(Zr0.60Sn0.40)0.95Ti0.05]O3 Antiferroelectric Bulk Ceramics

The evolution of dynamic hysteresis of lead zirconate titanate stannate antiferroelectric bulk ceramics at various frequencies (f) and field amplitudes (E0) has been investigated systematically. A series of asymmetrical minor loops were observed when the working fields were slightly lower than the forward switching field EAF. As E0 increased above EAF, symmetrical double loops appeared and their energy densities w against f and E0 were found to be fit the scaling behavior as w f−0.02(E0 − Ec)0.08, where Ec representing the threshold field is designated as EAF. The study is helpful to application of antiferroelectrics as energy‐storage capacitors.

Flow-controlled expiration discloses PEEP-dependent dynamic hysteresis of the pressure-volume loop

Hysteresis of the pressure-volume loop is a measure for the additional energy that is required during inspiration to recruit and inflate additional alveoli. The hysteresis area is usually constructed using data from a low-flow inflation/deflation maneuver; that is, from a quasi-static situation that the lung never sees during ongoing ventilation. However, during the dynamic conditions of mechanical ventilation the hysteresis area is biased by resistive pressure portions. Therefore we uncoupled flow and volume by linearizing expiratory flow (flow-controlled expiration). This enabled calculation of compliance separately for inspiration and expiration. We hypothesized that the volume-dependent intratidal compliance profiles differ between inspiration and expiration, describing a dynamic hysteresis behavior.

Dynamic magnetic hysteresis behavior and dynamic phase transition in the spin-1 Blume–Capel model

The nature (time variation) of response magnetization m(wt) of the spin-1 Blume–Capel model in the presence of a periodically varying external magnetic field h(wt) is studied by employing the effective-field theory (EFT) with correlations as well as the Glauber-type stochastic dynamics. We determine the time variations of m(wt) and h(wt) for various temperatures, and investigate the dynamic magnetic hysteresis behavior. We also investigate the temperature dependence of the dynamic magnetization, hysteresis loop area and correlation near the transition point in order to characterize the nature (first- or second-order) of the dynamic transitions as well as obtain the dynamic phase transition temperatures. The hysteresis loops are obtained for different reduced temperatures and we find that the areas of the loops are decreasing with the increasing of the reduced temperatures. We also present the dynamic phase diagrams and compare the results of the EFT with the results of the dynamic mean-field approximation. The phase diagrams exhibit many dynamic critical points, such as tricritical (•), zero-temperature critical (Z), triple (TP) and multicritical (A) points. According to values of Hamiltonian parameters, besides the paramagnetic (P), ferromagnetic (F) fundamental phases, one coexistence or mixed phase region, (F+P) and the reentrant behavior exist in the system. The results are in good agreement with some experimental and theoretical results.

Frequency Dependence of the Ferroelectric-Hysteresis Phase-Diagram: Monte Carlo Investigation

In this work, Monte Caro simulation was used to investigate the dynamic hysteresis behavior of 2 dimensional DIFFOUR model with varying field amplitude, field frequency and temperature over extensive ranges. Metropolis algorithm and Ising spins with variable magnitude were used in the simulation. The period average polarization was used as a dynamic order parameter in specifying dynamic ordered and disordered states. Fourth order cumulant of the period average polarization was then used to extract the dynamic critical temperature for constructing the dynamic phase diagram. It was found that the dynamic phase transition curves strongly depend on the field frequency. At higher frequency, the system requires higher level of field amplitude (electrical driving work) or higher environmental temperatures (thermal fluctuation) for a transition from dynamic ferroelectric to dynamic paraelectric phases. Consequently, the hysteresis shape at fixed temperature and field amplitude can be of either asymmetric or symmetric depending on the field frequency. This work therefore illustrates prominent and interesting behavior of the ferroelectric system under the perturbation of external field and temperature.

Hysteresis scaling relations in polycrystalline BaTiO 3 bulk ceramics

The scaling behaviors of the dynamic ferroelectric hysteresis of polycrystalline BaTiO 3 bulk ceramics were investigated. To enhance the accuracy of prediction, not only sets of the scaling relation of hysteresis area 〈 A〉 against frequency f and field amplitude E 0 were established, but also were sets of scaling relation of remnant polarization ( P r ) and coercive field ( E C ) against frequency f and field amplitude E 0. All scaling relations of hysteresis parameters, 〈 A〉, P r , and E C , displayed obviously the inter-correlation between f- and E 0-exponents in both sub-coercive field and above coercive field conditions. By first approximation, the scaling relations took a form of A ∝ f − 0.39 E 0 1.06 , P r ∝ f − 0.18 E 0 0.47 , and E C ∝ f − 0.33 E 0 0.46 above the coercive field condition; whereas the scaling relations in the form of A ∝ f − 0.55 E 0 3.40 , P r ∝ f − 0.43 E 0 1.73 , and E C ∝ f − 0.27 E 0 1.35 were obtained under a sub-coercive field condition. The frequency observation range affected directly the scaling exponents. Over the same frequency range, the scaling relations obtained in this study are generally comparable to previously reported scaling behavior in BaTiO 3 single crystals, as well as in other polycrystalline bulk ceramics, suggesting that materials (both single and polycrystalline) with similar domain switching mechanisms should have comparable dynamic hysteresis and scaling behavior.

The use of fractional derivation in modeling ferroelectric dynamic hysteresis behavior over large frequency bandwidth

The present article proposes a dynamical model to obtain ferroelectric hysteresis dynamics based on fractional derivatives. The consideration of a fractional derivative term widely increases the frequency bandwidth of the accuracy of the traditional hysteresis models. As a consequence, the model is suited for successfully taking into account the well-known scaling relations of the ferroelectric hysteresis area, ⟨A⟩, versus the frequency, f, and field amplitude, E0. Under low frequency excitation, simulation tests provided good results regarding the comparison of the fractional model, experimental results and the well-known nonentire power law ⟨A⟩∞f1/3E02/3 (where ⟨A⟩ represents the hysteresis loop area). These results were followed by comparing the hysteresis area obtained from the fractional model with that from the well known scaling relations as f→∞, and the results were proposed as validation of the high frequency behavior. Next, the model was tested on large frequency bandwidths (>6 decades) and validated with success using the comparison between simulation tests and the only experimental results available in literature obtained in such conditions by Liu et al. [J. Phys.: Condens. Matter 16, 1189 (2004)] for BNT thin film samples.

Thermal and electrical behavior of polyimide/silica hybrid thin films

AbstractSilica‐containing polyimide films were prepared by sol‐gel technique using a poly(amic acid) and tetraethoxysilane. The poly(amic acid) was synthesized by solution polycondensation reaction of 4,4′‐oxydiphthalic anhydride with 2,6‐bis(3‐aminophenoxy)benzene and an aminosilane coupling agent, 3‐aminopropyltriethoxysilane. The properties of these films, such as water vapors sorption capacity, dynamic contact angles and contact angle hysteresis, thermal, and electrical behavior have been evaluated with respect to their structure. The polymer films exhibited good thermal stability having the initial decomposition temperature above 450°C, glass transition temperature in the range of 223−228°C, and low‐dielectric constant in the range of 2.64−3.16. Two subglass transitions, γ and β, were evidenced by dynamic mechanical analysis and dielectric spectroscopy. The surface morphology and the roughness were investigated by atomic force microscopy and scanning electron microscopy. POLYM. ENG. SCI., 2010. © 2009 Society of Plastics Engineers

Sub-coercive field dynamic hysteresis in morphotropic phase boundary composition of Pb(Zr 1/2Ti 1/2)O 3–Pb(Zn 1/3Nb 2/3)O 3 ceramic and its scaling behavior

Sub-coercive field dynamic ferroelectric hysteresis of a morphotropic phase boundary composition of the PZT–PZN ceramic was investigated under influence of the compressive stress. The scaling relation of hysteresis area 〈 A 〉 against frequency f, field amplitude E 0 , and stress σ took a form of 〈 A − A σ = 0 〉 ∝ f − 0.33 E 0 3.75 σ 0.32 , which is not different significantly to that of other PZT–PZN compositions with pure tetragonal or rhombohedral structure, as well as to that of soft and hard PZT bulk ceramics. This study suggested that the domain structures, not ceramic compositions, played a key role in controlling dynamic hysteresis behavior of ferroelectric materials.

Stress-Dependent Scaling Behavior of Sub-Coercive Field Dynamic Hysteresis in Pb(Zr1/2Ti1/2)O3–Pb(Zn1/3Nb2/3)O3 Ceramic Systems

Stress dependence and scaling behavior of sub-coercive field dynamic ferroelectric hysteresis were investigated in (1-x)PZT-(x)PZN bulk ceramics, where x = 0.1, 0.2, 0.3, 0.4, and 0.5. The results shown that hysteresis area < A >, remnant polarization (P r ), and coercive field (E C ) increase with increasing of field amplitude (E 0), while decrease with increasing of frequency and compressive stress similar to previous investigations in bulk ceramics. The scaling relations of hysteresis area < A > against frequency f, field amplitude E 0, and stress σ for the minor loops took a form of < A–A σ = 0> ∝ f α E 0 β σγ with range of (−0.42) to (−0.34), (3.32) to (4.03), and (0.19) to (0.38) for exponents α, β, and γ, respectively, depending on compositions, which are very similar to that of soft and hard PZT bulk ceramics. This study suggests that the domain structures play a key role in controlling dynamic hysteresis behavior of ferroelectric materials.

Monte Carlo simulation on thickness dependence of hysteresis properties in Ising thin-films

In this work, Monte Carlo simulation was used to model the dynamic hysteresis behavior of ferromagnetic Ising thin-films using the spin-flip algorithm. The purpose is to investigate the thickness dependence of ferromagnetic hysteresis properties while varying frequency and amplitude of the external field. From the results, with increasing the films thickness, the calculated hysteresis properties significantly change due to the stronger ferromagnetic coupling in thicker films. In addition, the universal power law relations among the hysteresis properties, the thickness and the field parameters were found. The scaling exponents were also reported which agree well with a previous experiment on ferromagnetic thin-films.