Domain Growth Model Research Articles

Rough FTO electrode interface effect upon ferroelectric switching dynamics in Ag/P(VDF‐HFP)/FTO capacitor structures

AbstractRough FTO electrode interface effect upon the characteristic ferroelectric polarization parameters and switching dynamics in Ag/P(VDF‐HFP)/FTO junctions is systematically evaluated by varying electric field amplitude and frequency. Structural and microstructural studies confirm the ferroelectric phase formation of P(VDF‐HFP) on FTO surface. Tilted rectangular P‐E loops have been recorded in the applied fields ranging over 156.25–468.75 MV/m measured between 250 mHz and 5 Hz frequency ranges. Giant saturation of 21.7 μC/cm2 and remnant polarization of 34.9 μC/cm2 has been noted at low frequencies due to the influence of high electric field induced leakage currents. The coercive field, saturation and remnant polarization response with increase in electric field amplitude and frequency of the applied signal are well fitted with classic domain growth model proposed by Kolmogorov‐Avrami‐Ishibashi. A switching time scales of 32.2–693 ms has been observed for forward switching while for backward switching it is noted as 22.1–618.8 ms, when measured at frequencies from 5 Hz to 250 mHz. Furthermore, the tilted P‐E loops are attributed to the excessive leakage currents due to the high surface roughness of FTO bottom electrode.

Asymmetric Electrode Influence upon Ferroelectric Switching Dynamics in Ag/PVDF‐HFP/ITO Capacitor Structures

Asymmetric electrode (Ag and indium tin oxide (ITO)) influence upon ferroelectric switching dynamics in polyvinylidene fluoride-hexafluoropropylene (PVDF-HFP) thin films across Ag/PVDF-HFP/ITO capacitor structures is systematically investigated. Grazing incidence X-Ray diffraction (GI–XRD), atomic force microscopy (AFM), and UV–visible spectroscopy are utilized to comprehend the structural and microstructural characteristics of PVDF–HFP thin films upon ITO interface. Low voltage rectified and asymmetric current–voltage (I–V) curves reveal the varied barrier potential due to the asymmetric electrodes. Typical squared hysteresis loops along with uniform domain growth model are verified from quasi-static and dynamic ferroelectric loop measurements. Further, from low-frequency (10 and 15 mHz) quasi-static and dynamic (100–1000 Hz) triangular pulses, the switching time, domain dimension with respect to frequency, and amplitude of the electric field are separately evaluated and noted that smaller switching times when electron traverses from Ag to ITO electrode.

Structural, microstructural, and ferroelectric studies of polyvinylidene fluoride‐hexafluoropropylene (PVDF‐HFP) thin films in Ag/Cu/PVDF‐HFP/Cu capacitor structures

AbstractIn this article, the structural, microstructural, and ferroelectric characteristics of polyvinylidene fluoride‐hexafluoropropylene (PVDF‐HFP) thin films in Ag/Cu/PVDF‐HFP/Cu capacitor structures have been investigated. The bottom interfaces glass or Cu/glass influence upon the PVDF‐HFP thin‐film crystal structure and microstructure have been evaluated using grazing incidence X‐ray diffractometer and atomic force microscopy. Quasi‐static current–voltage loops, the polarization versus electric field loops measured at varied applied frequencies (100 mHz–1 Hz) and electric field amplitudes (2.5–27.5 MV/m) are utilized to comprehend the ferroelectric characteristics of PVDF‐HFP thin films. Furthermore, the observed linear dependency between coercive field and frequency is linked to the homogenous domain growth model proposed by Kolmogorov‐Avrami‐Ishibashi.

Relaxor behaviors enhance piezoelectricity in lead-free BiFeO3-BaTiO3 ceramics incorporated with a tiny amount of Bi(Mg1/2Ti1/2)O3 near the morphotropic phase boundary

The relaxor behaviors near the morphotropic phase boundary (MPB) can reduce the energy barrier for polarization rotation, which is an effective strategy to improve the piezoelectric properties of materials. In this work, the phase structure, microstructure, and piezoelectric properties of (0.69-x)Bi1.02FeO3-0.31BaTiO3-xBi(Mg1/2Ti1/2)O3 (0.00 ≤ x ≤ 0.08) ceramics were systematically studied. The addition of a tiny amount of Bi(Mg1/2Ti1/2)O3 was found to cause the phase to transform from R-phase-dominant ferroelectrics (FEs) to PC-phase-dominant relaxor ferroelectrics (RFEs). The dielectric and electrical data reveal that nonergodic relaxor ferroelectrics (NE-RFEs) near the MPB were favorable for domain switching, which contributed to the enhanced piezoelectric and electrostrain properties of d33 = 182 pC/N, TC = 475 °C, and S = 0.21% at x = 0.04. Finally, a model of domain growth induced by an electric field was proposed for FEs and NE-RFEs.

Domain patterning of non-polar cut lithium niobate by focused ion beam

The domain switching by ion beam irradiation of single-domain Y-cut plates of congruent lithium niobate doped by 5 mol% MgO was studied. Dot irradiation resulted in the formation of wedge-like domains grown along Z- polar direction. The nonlinear dependences of the domain sizes on irradiation conditions were obtained. The model of domain growth on non-polar cut was proposed in frame of kinetic approach. The absence of the domain merging along Z- polar direction was attributed to the deceleration of the forward growth by electrostatic interaction of the positive charges at the charged domain walls and injected positive ions.

Retention of intermediate polarization states in ferroelectric materials enabling memories for multi-bit data storage

A homogeneous ferroelectric single crystal exhibits only two remanent polarization states that are stable over time, whereas intermediate, or unsaturated, polarization states are thermodynamically instable. Commonly used ferroelectric materials however, are inhomogeneous polycrystalline thin films or ceramics. To investigate the stability of intermediate polarization states, formed upon incomplete, or partial, switching, we have systematically studied their retention in capacitors comprising two classic ferroelectric materials, viz. random copolymer of vinylidene fluoride with trifluoroethylene, P(VDF-TrFE), and Pb(Zr,Ti)O3. Each experiment started from a discharged and electrically depolarized ferroelectric capacitor. Voltage pulses were applied to set the given polarization states. The retention was measured as a function of time at various temperatures. The intermediate polarization states are stable over time, up to the Curie temperature. We argue that the remarkable stability originates from the coexistence of effectively independent domains, with different values of polarization and coercive field. A domain growth model is derived quantitatively describing deterministic switching between the intermediate polarization states. We show that by using well-defined voltage pulses, the polarization can be set to any arbitrary value, allowing arithmetic programming. The feasibility of arithmetic programming along with the inherent stability of intermediate polarization states makes ferroelectric materials ideal candidates for multibit data storage.

Discrete and continuous models for tissue growth and shrinkage

The incorporation of domain growth into stochastic models of biological processes is of increasing interest to mathematical modellers and biologists alike. In many situations, especially in developmental biology, the growth of the underlying tissue domain plays an important role in the redistribution of particles (be they cells or molecules) which may move and react atop the domain. Although such processes have largely been modelled using deterministic, continuum models there is an increasing appetite for individual-based stochastic models which can capture the fine details of the biological movement processes which are being elucidated by modern experimental techniques, and also incorporate the inherent stochasticity of such systems.In this work we study a simple stochastic model of domain growth. From a basic version of this model, Hywood et al. (2013) were able to derive a Fokker–Plank equation (FPE) (in this case an advection–diffusion partial differential equation on a growing domain) which describes the evolution of the probability density of some tracer particles on the domain. We extend their work so that a variety of different domain growth mechanisms can be incorporated and demonstrate a good agreement between the mean tracer density and the solution of the FPE in each case. In addition we incorporate domain shrinkage (via element death) into our individual-level model and demonstrate that we are able to derive coefficients for the FPE in this case as well. For situations in which the drift and diffusion coefficients are not readily available we introduce a numerical coefficient estimation approach and demonstrate the accuracy of this approach by comparing it with situations in which an analytical solution is obtainable.

Sub-aging in a domain growth model

We study analytically the aging dynamics of the O(n) model in the large-n limit, with conserved and with non-conserved order parameter. While in the non-conserved dynamics, the autocorrelation function scales in the usual way C(t,tw) = C(t/tw), in the case of a conserved order parameter, `multiscaling' manifests itself in the form C(t,tw) = C (h(t)/h(tw)), with a relaxation time growing more slowly than the age of the system (sub-aging), and h(t) a function growing faster than any length scale of the problem. In both cases, the effective temperature associated to the violation of the fluctuation theorem tends to infinity in the asymptotic limit of large waiting times.

Monte Carlo model of domain growth in ultrathin magnetic films with perpendicular anisotropy

A Monte Carlo simulation of the domain growth process in ultrathin magnetic films with strong perpendicular anisotropy is carried out to study the effect of local variations of the domain-wall coercivity on the rate of domain expansion. The algorithm used simulates domain growth as a thermo-activated or viscous process, depending on the value chosen for the applied field. The rate of thermo-activated domain expansion is found to increase gradually to a constant value, attained when the domain size is sufficiently large. The depinning transition is rather sharp and not as wide as the distribution width of domain-wall coercivities. It may therefore be difficult to derive accurate information on the coercivity distribution from the measurement of v(H) curves in materials such as Au/Co/Au films ( t Co=8 Å).

Magnetic domains and demagnetizing fields in FeTb thin films

The magnetic properties of 500 Å thick amorphous thin films with 0.16 < x < 0.35 have been studied experimentally. All films possess a strong perpendicular magnetic anisotropy (PMA) with an anisotropy constant . Using a polar Kerr microscope, the magnetic domain patterns in the samples with different values of the compositional parameter x were observed, revealing strong correlations between the domain shapes and the magnetic parameters of the films. In order to explain the experimental observations a micromagnetic model of domain growth on a two-dimensional hexagonal grid is developed. By means of an FFT algorithm with periodic boundary conditions an adequate description of the demagnetizing field distribution was achieved. The model allows us to calculate both the domain patterns and the hysteresis loops, showing good agreement with the experimental observations. Both the experimental and the theoretical studies demonstrate that the closeness to the compensation point is the decisive factor controlling the micromagnetic behaviour of the films.

Micromagnetics of Magnetic Multilayers

A new micromagnetic approach for multilayered films for magneto-optic (MO) recording has been developed. The model takes into account both the magnetization distribution from layer to layer along the film normal and the splitting into domains. This model is a generalization of the domain growth model, developed for amorphous films of ferrimagnetic alloys [2]. Here we present the basic ideas of the model and discuss some results of simulations on Fe/Tb-multilayers as well.

Domain models for aging in spin glasses

A simple domain growth model is shown to account for aging in spin glasses. It accounts quantitatively for the change in glass temperature with frequency. It is shown that percolation clusters present in disordered systems are responsible for the peak in ∂M/∂ ln t, where M is the magnetization, and t is the time.

Coarsening in the 1D Ising model evolving with Swendsen - Wang dynamics: an unusual scaling

We consider a simple model of domain growth: the zero-temperature 1D Ising model evolving according to the Swendsen - Wang dynamics. We find that in the long-time limit, the pair correlation function scales with a characteristic length increasing as the square of the average domain size. In that limit, a few large domains occupy almost all the space with many small domains between them. In contrast to the usual picture of coarsening, the average domain size here is not a characteristic length of the growth problem. Instead, one finds a power-law distribution for the sizes of large domains with a cut-off at a length which grows as the square of the average size of the domains.

A soluble model of domain growth in one-dimensional disordered systems

We introduce a new algorithm for domain growth in disordered systems at low temperatures based on the tendency for such a system to freeze into metastable states. We apply the algorithm to the d=1 random-bond Ising model for a variety of bond distributions. The analytical forms we obtain for the two-point correlation function and autocorrelation function agree well with numerical simulations of the model. These forms are not the same as those of the pure Ising model with Glauber dynamics.

Monte Carlo study of the temperature dependence of domain-growth kinetics in a system with a nonconserved order parameter and a zero-temperature equilibration fixed point.

We have investigated the relationship between the proportionality factor in the Lifschitz-Allen-Cahn scaling relation and the microscopic kinetics of nonequilibrium transport in a Monte Carlo model of domain growth in a two-dimensional, quenched, chemisorbed overlayer with a nonconserved order parameter and a zero-temperature equilibration fixed point. We have identified two components of the proportionality factor, which reflect the two temperature dependences of domain growth in this system. The primary temperature dependence arises from the rate of surface diffusion. In addition, we find a factor, \ensuremath{\alpha}, which decreases with increasing temperature due to the influence of thermal fluctuations. We also find that the proportionality factor has a time dependence, which arises from the rate of surface diffusion. We have found that this time dependence can influence the apparent form of the growth law. We discuss why the observed time dependence of diffusion should be a general phenomenon present in both simulations and experiments of domain growth in quenched systems.

Non-algebraic domain growth in binary alloys with quenched disorder

The authors present detailed numerical results from a computationally efficient cell dynamical system model of domain growth in binary alloys with quenched disorder. Their numerical results suggest that the domain growth law for the disordered case is compatible with (R)(t) approximately (1nt)x, where x has a weak dependence on the disorder amplitude. However, it is possible that their simulations do not access the true asymptotic regime. They also find that the scaled structure factor for the disordered case is independent of the amplitude of disorder and is the same as that for the pure system.

Domain growth in the random-field Ising model

We study a continuum random-field model of domain growth in quenched nonequilibrium systems. We derive an equation of motion for the interfaces separating domains and find approximate solutions for the growth laws in two and three dimensions. We find what may be a dynamical mechanism for the theoretical prediction that the lower critical dimension of this model is ${d}_{1}=2$. Our theoretical predictions can be tested experimentally or by computer simulation.

Observation of ordering kinetics in layered antiferromagnets by neutron scattering

The author presents a neutron scattering result on the time evolution of the magnetic order in quasi-two-dimensional dilute Ising antiferromagnetics Rb2CocMg1-cF4. The experiments described were performed for the observation of the time evolution of interplanar ordering following quenching to low temperature from a disordered high-temperature state. The results show that the (100) antiferromagnetic Bragg intensities increase with time as t1/2 at an early stage and as log t at a later stage. A characteristic dependence as a function of time was observed on a macroscopic time scale and the observed behaviour is in good agreement with recently developed statistical theory for a one-dimensional domain growth model.

Phase separation and coalescence in critically quenched isobutyric-acid—water and 2,6-lutidine—water mixtures

Light scattering was used to study phase separation in critically quenched mixtures of isobutyric-acid---water and 2,6-lutidine---water. The measurements spanned the time interval $10\ensuremath{\le}t\ensuremath{\lesssim}{10}^{3}$ s and quench depths from 0.7 to 9 mK. The parameters measured were ${k}_{m}(t)$, i.e., the photon momentum transfer at the angle of maximum scattering, and the ring intensity $I({k}_{m},t)$. The early-stage measurements of ${k}_{m}$ vs $t$ are in very good agreement with the calculations of Kawasaki and Ohta and with the coalescence model of domain growth, which gives ${k}_{m}\ensuremath{\propto}{t}^{\ensuremath{-}\ensuremath{\phi}}$, with $\ensuremath{\phi}=\frac{1}{3}$. In the late stage $\ensuremath{\phi}$ increases to unity in both systems. This implies that hydrodynamic effects control the rate of growth of the nucleating domains of size $l\ensuremath{\simeq}{k}_{m}^{\ensuremath{-}1}$. In both early and late stages, the intensity measurements are consistent with $I({k}_{m},t)\ensuremath{\propto}{l}^{3}$. The scattering experiments were supplemented by direct observation of domain growth with a microscope.

Coercive Field of Ferroelectric TGS and TGSe as a Function of Impressing Rate of Field

Calculations of the ferroelectric coercive field as a function of impressing rate of field have been made on the basis of a two-dimensional model of domain growth; a linear dependence of nucleus density on the applied fields and an anisotropy of sideways velocity of a domain wall motion are taken into account. Experimental results of coercive fields in TGS and TGSe which have been measured by the application of triangular fields are successfully explained by the present treatment. The contribution of newly created nuclei to the polarization reversal cannot be ignored in both crystals.