Rayleigh Law Research Articles

The Rayleigh law in silicon doped hafnium oxide ferroelectric thin films

A wealth of studies have confirmed that the low‐field hysteresis behaviour of ferroelectric bulk ceramics and thin films can be described using Rayleigh relations, and irreversible domain wall motion across the array of pining defects has been commonly accepted as the underlying micro‐mechanism. Recently, HfO2 thin films incorporated with various dopants were reported to show pronounced ferroelectricity, however, their microscopic domain structure remains unclear till now. In this work, the effects of the applied electric field amplitude, frequency and temperature on the sub‐coercive polarization reversal properties were investigated for 10 nm thick Si‐doped HfO2 thin films. The applicability of the Rayleigh law to ultra‐thin ferroelectric films was first confirmed, indicating the existence of a multi‐domain structure. Since the grain size is about 20–30 nm, a direct observation of domain walls within the grains is rather challenging and this indirect method is a feasible approach to resolve the domain structure. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)

Speckle-intensity correlations of photons scattered by cold atoms

The irradiation of a dilute cloud of cold atoms with a coherent light field produces a random intensity distribution known as laser speckle. Its statistical fluctuations contain information about the mesoscopic scattering processes at work inside the disordered medium. Following up on earlier work by Assaf and Akkermans [Phys. Rev. Lett. 98, 083601 (2007)], we analyze how static speckle-intensity correlations are affected by an internal Zeeman degeneracy of the scattering atoms. It is proven on general grounds that the speckle correlations cannot exceed the standard Rayleigh law. On the contrary, because which-path information is stored in the internal atomic states, the intensity correlations suffer from strong decoherence and become exponentially small in the diffusive regime applicable to an optically thick cloud.

The dynamics of a vapor embryo in a superheated liquid (characteristics of the initial growth period)

The initial period of growth of a vapor bubble of near-critical size is studied analytically and numerically. It is demonstrated that the dynamic effects resulting from the hydrodynamics of radial liquid motion are decisive in the problem under consideration. An analytical solution for the problem is obtained, and the asymptotic solution branches are investigated. It is concluded that the dynamic inertial-controlled Rayleigh law of bubble growth is a degenerate solution branch that is applicable at sufficiently large growth times. It is demonstrated that the effect of viscous forces degenerate both in the initial period of bubble growth and for large growth times. These forces may exert a significant influence on the bubble growth dynamics only at the intermediate growth stages. The effect of viscosity is maximized in the region of near-spinodal superheating even in the case of liquids with a relatively low viscosity. For example, the corrections for the effect of viscosity in water reach hundreds of percent. The formula for estimating the duration of the initial bubble growth period (within which the viscous forces may be neglected) is derived based on the asymptotic solution. Interpolation design formulas that satisfy the needed passages to the limit are proposed. It is found that that there exists a peculiar “incubation period” of bubble growth, within which the bubble growth is not very fast. The duration of this period depends on the extent of influence of surface tension forces. The formulas for calculating the duration of this “incubation” period are derived. It is demonstrated that this duration remains finite even when the surface tension effects become degenerate.

Statistical models of the wave field of a random aperture antenna

The method of statistical imitation simulation (SIS) is applied to analyze the characteristics of the electromagnetic field produced by a random aperture antenna (RAA) excited by a harmonic signal with a preassigned distribution of amplitude and phase errors. In the study, SIS models of the orthogonal and quadrature components of the RAA field intensity vector and its scalar E are considered. As the conditions for the applicability of the central limit theorem of the probability theory are fulfilled, these models approach standard models (the normal law, the Rayleigh and Rice laws, the distribution of the scalar of a multidimensional vector with normal components).

Non-180° domain contributions in Bi0.5(Na0.82K0.18)0.5TiO3 lead-free piezoelectric thick films

Piezoelectric responses of Bi0.5(Na0.82K0.18)0.5TiO3 (NKBT) ceramic films with thickness of 10–100μm have been studied in a wide range of ac electric field and frequency. By the Rayleigh law fit, the typical irreversible Rayleigh coefficient, α, for piezoelectric response is 39.69±0.41×10−18m2V−2, which is much larger than that of the piezoelectric thin films, indicating significantly enhanced non-180° domain wall motions in NKBT thick films. The logarithmic frequency dependence of the piezoelectric response is associated with domain wall pinning in NKBT thick films, and the frequency dispersion increases with increasing ac field amplitude, which is attributed to the relaxation of non-180° domains.

Vertical evolution of potential energy density and vertical wave number spectrum of Antarctic gravity waves from 35 to 105 km at McMurdo (77.8°S, 166.7°E)

AbstractWe report the first characterization of potential energy densities and vertical wave number spectra of Antarctic gravity waves (GWs) from 35 to 105 km, derived from Fe lidar temperature measurements at McMurdo (77.8°S, 166.7°E) in 2011–2013 winters. For GWs with periods of 2–10 h, the potential energy density per unit volume (Epv) decreases by 2 orders of magnitude from 35 to 105 km, while that per unit mass (Epm) increases from several to hundreds of J/kg. Epm increases with a mean scale height of ~10.4 km in the Rayleigh region (35–65 km) and of ~13.2 km in the Fe region (81–105 km), and of particular interest is the inferred severe dissipation in between (65–81 km). Overall, the vertical evolutions of Epv and Epm indicate considerable wave energy loss from the stratosphere to the lower thermosphere. The vertical wave number spectra exhibit power law forms for vertical wavelengths λz < ~10 km. The mean spectral slope in the spectral range of 2–10 km is about −2.55 and −2.26 in the Rayleigh and Fe regions with standard deviations of 0.36 and 0.38, respectively. Large variations in the power spectral densities (PSDs) are seen for λz > 10 km in 35–60 km. PSDs increase by 1 order of magnitude from the stratosphere to the lower thermosphere. Using higher temporal resolution data to include 0.5–2 h waves increase Epm by ~25–45% and increase PSDs of 2–5 km waves by a factor of 2 and of >10 km waves by less than 50%.

Dielectric and Ferroelectric Behaviors of (100)-Oriented 0.9Pb(Sc0.5Ta0.5)O3-0.1PbTiO3 Thin Films

0.9Pb(Sc0.5Ta0.5)O3-0.1PbTiO3 (PSTT10) thin films were deposited on Si(1 0 0) substrate with a LaNiO3 buffer layer by RF magnetron sputtering technique and post annealed by a two-steps rapid thermal annealing method. Dielectric, ferroelectric behaviors and surface morphology of the films were analyzed. The films show good ferroelectric and dielectric properties which is similar to the PSTT5 thin films. The leakage current behavior of the films is according with Ohm law in a low electric field region, while it satisfies a space-charge limited conduction in a medium electric field region. With the increasing of frequency, the dielectric constant decrease and the dielectric loss increase, which shows a typical relaxor behavior. The dielectric constant of the films in low frequency band can be explained as Rayleigh law. The films exhibits crack free and uniform surface, with roughness of about 17 nm.

Effect of feature size on dielectric nonlinearity of patterned PbZr0.52Ti0.48O3 films

Lead zirconate titanate, PZT (52/48), thin films with a PbTiO3 seed layer were patterned into features of different widths, including various sizes of squares and 100 μm, 50 μm, and 10 μm serpentine designs, using argon ion beam milling. Patterns with different surface area/perimeter ratios were used to study the relative importance of damage produced by the patterning. It was found that as the pattern dimensions decreased, the remanent polarization increased, presumably due to the fact that the dipoles near the feature perimeter are not as severely clamped to the substrate. This investigation is in agreement with a model in which clamping produces deep wells, which do not allow some fraction of the spontaneous polarization to switch at high field. The domain wall mobility at modest electric fields was investigated using the Rayleigh law. Both the reversible, εinit, and irreversible, α, Rayleigh coefficients increased with decreasing serpentine line width for de-aged samples. For measurements made immediately after annealing, εinit of 500 μm square patterns was 1510 ± 13; with decreasing serpentine line width, εinit rose from 1520 ± 10 for the 100 μm serpentine to 1568 ± 23 for the 10 μm serpentine. The irreversible parameter, α, for the square patterns was 39.4 ± 3.2 cm/kV and it increased to 44.1 ± 3.2 cm/kV as the lateral dimension is reduced. However, it was found that as the width of the serpentine features decreased, the aging rate rose. These observations are consistent with a model in which sidewall damage produces shallow wells that lower the Rayleigh constants of aged samples at small fields. These shallow wells can be overcome by the large fields used to measure the remanent polarization and the large unipolar electric fields typically used to drive thin film piezoelectric actuators.

A calculation method for initial magnetization curve under constant magnetization based on time-space transformation

It is of great significance to research on methods for obtaining the initial magnetization curve, the important magnetic property of ferromagnetic materials. In the existing methods, a time-varying magnetic field is adopted as the excitation field. To obtain the initial magnetization curve, magnetic field and induced magnetic flux density in the specimen have to be measured step-by-step as the excitation field changes, and this is inefficient. Thus, a calculation method for initial magnetization curve based on time-space transformation is proposed in this paper. In this method, an elongated rod or a circular ring is used as the specimen. A spatially varying magnetic field generated by constant magnetization is utilized as the excitation field. The strength of the excitation field changes with the spatial positions of the specimen. Under the action of the excitation field, the magnetic field strength within the specimen is calculated by means of the responding magnetic field strength on the surface of the specimen according to the continuity of the tangential magnetic field strength. While, based on the Gauss' law for magnetism, the law of approach to saturation and the basic equation of magnetization curve in Rayleigh region, the induced magnetic flux density within the specimen can be calculated from the responding magnetic flux density on the surface of the specimen. After obtaining the magnetic field strength and magnetic flux density in the specimen, the initial magnetization curve can be obtained. To verify theoretically the correctness of the method, simulations are carried out with an elongated rod and a circular ring. In experiments, a spatially varying magnetic field generated by DC coils is applied on the specimen as the excitation field. The initial magnetization curve calculated from the magnetic field strength and magnetic flux density on the surface of the specimen is similar to the known initial magnetization curve. Experimental results also show that when adopting an elongated rod rather than a circular ring as the specimen, this calculation method for initial magnetization curve is simpler and the error in the results is smaller, which are different from those obtained by existing measurement methods for initial magnetization curve. In addition, in order to study the influence of the limiting factors in practical applications of the calculated results, further research is conducted based on the simulation data. Results show that when choosing a proper elongated rod as the specimen, the initial magnetization curve can be calculated from the magnetic field strength and magnetic flux density on the surface of the specimen under the constant magnetization, also the induced magnetic field flux in the specimen does not have to be measured by the encircling detecting coil which makes this method easy to operate. Namely, this method is feasible in practice. This paper may be a theoretical guidance for exploring new measurement methods for initial magnetization curve.

Effect of Sn content on dielectric, piezoelectric and ferroelectric properties for Pb(Zr0.35Ti0.65)1−xSnxO3 ceramics near morphotropic phase boundary

ABO3 perovskite structure Pb(Zr0.35Ti0.65)1−xSnxO3 (PZST) piezoelectric ceramics were synthesized by conventional solid state reaction method with the compositions near tetragonal to rhombohedral morphotropic phase of boundary (MPB). The influences of Sn content on dielectric, piezoelectric and ferroelectric properties of PZST piezoceramics were investigated while Zr/Ti ratio was fixed. With increasing Sn content, the c/a ratios and Curie temperatures TC decrease monotonically. Rayleigh law was explored to evaluate the piezoelectric behaviors as a function of loading electric field strength. Both Rayleigh coefficients αd and dinit′ are increased with increasing Sn content, indicating that Sn content considerably increase the mobility of domain walls and also the piezoelectric nonlinear responses.

Estimation of Radar Cross-Section in Rayleigh, MIE, and Optical Regions by the 2-D-FDTD Simulation

In this paper, the far-field electromagnetic fields were calculated by using near-field/far-field (NF/FF) transformation technique from the near field finite-difference time domain (FDTD) data obtained by total field/scattering field (TF/SF) formulation. To evaluate the effectiveness of scattering mechanisms depending on the frequency used, the target geometry and the electrical properties, first of all simple shapes such as a square cylinder, a circular cylinder, and an equilateral triangle, were studied. It has been shown that the radar cross section (RCS) calculations can be done in Rayleigh, Mie, and optical regions by the 2-D FDTD simulation. Finally, the RCS behavior of an aircraft model composed of simple shapes as ellipse and triangle are investigated for different illuminations and different frequencies.

Anomalous optical forces on the anisotropic Rayleigh particles.

We investigate the optical forces on the radially anisotropic spheres from an incident plane wave based on our generalized full-wave scattering theory and the Maxwell stress tensor integration techniques. We demonstrate that the optical force on the Rayleigh sphere with radial anisotropy does not always obey the well-known Rayleigh's law F~k04a(6) (where k(0) is the wave number and a is the radius of the sphere), but could be anomalous with the laws such as F~k00a(2), F~k0-2a(0), and F~k08a(10) under certain conditions. Therefore, the optical force on the anisotropic Rayleigh spheres is enhanced at the electric dipole resonance, and may be further increased by tuning the anisotropic parameters. On the contrary, the optical forces on the anisotropic spheres can be largely reduced for anisotropic spheres with electromagnetic transparency.

Temperature dependence of the intrinsic and extrinsic contributions in BiFeO3-(K0.5Bi0.5)TiO3-PbTiO3 piezoelectric ceramics

This contribution focuses on the use of modified Rayleigh law as a technique for determining the intrinsic and extrinsic (reversible/irreversible) contributions to the piezoelectric effect up to 150 °C across a broad compositional space, augmenting previous understanding of the BiFeO3-(K0.5Bi0.5)TiO3-PbTiO3 system. At room temperature, a mechanistic explanation of the correlation between crystal symmetry, i.e., tetragonal spontaneous strain, xs, and the Rayleigh relations using Landau theory is provided. The intrinsic response was found to be heavily dependent upon the tetragonal xs, whereby an optimisation between polarization and permittivity was elucidated, leading to enhanced piezoelectric charge coefficients. A c/a ratio of ∼1.041 was identified at which the room temperature intrinsic and extrinsic effects were at a maximum; a dinit of 183 × 10−12 m/V and Rayleigh coefficient of 59 × 10−18 m2/V2 were measured, resulting in the largest piezoelectric charge coefficients. The piezoelectric charge coefficient d33, intrinsic and extrinsic contributions of these materials were all found to increase up to 150 °C while adhering to the Rayleigh model. The reversible extrinsic component of the total reversible response, dinit, was calculated to be relatively minor, 4.9% at room temperature, increasing to 12.1% at 150 °C, signifying its increasing influence to the piezoelectric effect, as domain wall motion is thermally activated. Hence, the phenomenological interpretation provided here may be used as a roadmap to elucidate the origins of the temperature dependence of the piezoelectric effect.

Influence of Li doping on domain wall motion in Pb(Zr0.52Ti0.48)O3 films

Li-doped PbZr0.52Ti0.48O3 (PZT) films were utilized to study the effect of A-site acceptor dopants on the mobility of ferroelectric domain walls. For chemical solution-deposited PZT films 2 μm in thickness doped with 1–3 mol% Li, the low-field dielectric permittivity remained between 1200 and 1300. With increasing Li concentration, the reversible Rayleigh constants einit increased from 1080 for undoped PZT films to 1240 for the films doped with 3 mol% Li, while the irreversible Rayleigh parameter showed a peak value at 1 mol% Li doping.

Achieving Both High d 33 and High Q m for the Pb(Zr0.26Sn0.26Ti0.48)1−x Fe x O3−x/2 Ternary System for Use in High-Power Ultrasonic Transducers

For applications in high power ultrasonic transducers, both high piezoelectric coefficients d 33 and high mechanical quality factor Q m are essential. In this work, acceptor-doped Pb(Zr0.26Sn0.26Ti0.48)1−x Fe x O3−x/2 ferroelectric ceramics with compositions near the morphotropic phase boundary were prepared by routine solid-state reaction. By introducing Fe3+ ion into the perovskite crystal lattices, defect dipoles resulting from Fe3+ ions and oxygen vacancies are formed, pinning extrinsic domain wall motion, and hence increasing Q m but reducing d 33. It was found that substitution with 0.5 mol% Fe3+ resulted in high d 33 (390 pC/N) and high Q m (540). The nonlinear dielectric responses of these ceramics were evaluated on the basis of the Rayleigh law. Both Rayleigh coefficients, $$\alpha$$ and $$\kappa_{\rm{init}},$$ are reduced by doping with the acceptor ion Fe3+, indicating that the intrinsic contribution and reversible domain wall mobility are both reduced.

Temperature-dependent polarization back-switching and dielectric nonlinearity in PbZr0.4Ti0.6O3 ferroelectric thin films

Temperature-dependent domains back-switching behavior and nonlinear dielectric response were studied in 200 nm fresh and aged PbZr0.4Ti0.6O3 thin films to compare domain walls motion under large and small signals. Expected thermally activation of domains back-switching and dielectric nonlinearity were observed at low temperature, however, abnormal thermally inhibited behavior occurred at higher temperatures. Such phenomenon was found in both fresh and aged films and the ageing process magnified such thermally inhibited effect. Analyzing nonlinear dielectric response with Rayleigh law suggested that the interaction between domain walls and pinning centers was strengthened at high temperature especially after ageing. Promoted pinning effect by rising temperature could reduce dielectric loss and this is practical for high temperature applications of ferroelectrics.

Extended Brauer model for ferromagnetic materials: analysis and computation

Purpose – The purpose of this paper is to develop a fast and accurate analytic model function for the single-valued H-B curve of ferromagnetic materials, where hysteresis can be disregarded (normal magnetization curve). Nonlinear magnetoquasistatic simulations demand smooth monotone material models to ensure physical correctness and good convergence in Newton's method. Design/methodology/approach – The Brauer model has these beneficial properties, but is not sufficiently accurate for low and high fields in the normal magnetization curve. The paper extends the Brauer model to better fit material behavior in the Rayleigh region (low fields) and in full saturation. Procedures for obtaining optimal parameters from given measurement points are proposed and tested for two technical materials. The approach is compared with cubic spline and monotonicity preserving spline interpolation with respect to error and computational effort. Findings – The extended Brauer model is more accurate and even maintains the computational advantages of the classical Brauer model. The methods for obtaining optimal parameters yield good results if the measurement points have a distinctive Rayleigh region. Originality/value – The model function for ferromagnetic materials enhances the precision of the classical Brauer model without notable additional simulation cost.

Rayleigh Region in Amorphous and Nanocrystaline FINEMET Alloy

Magnetization processes in ferromagnetic materials can be described in four ways, reversible and irreversible domain wall (DW) motion, rotation of the vector of magnetic polarization, and paraprocess in high magnetic elds. The process of reversible DW motion is characteristic for the range of small exciting magnetic elds the Rayleigh region (RR). The dependence of magnetic polarization J in this region, called also the region of initial susceptibility (permeability), on the magnetic eld strength H can be expressed by the following equation

Calcium and titanium isotopic fractionations during evaporation

Isotope fractionations associated with high temperature evaporation provide important constraints on the physicochemical processes that affected planetary materials at the birth of the solar system. Previous evaporation experiments have focused on isotopic fractionation of moderately to highly volatile elements. Here, we investigate the isotope fractionation behavior of two highly refractory elements, calcium and titanium, during evaporation of perovskite (CaTiO3) in a vacuum furnace. In our experiments, isotope fractionation during evaporation follows the Rayleigh law, but not the commonly used exponential law, with the dominant evaporating species being Ca(g) and TiO2(g). If isotope fractionations in early solar system materials did follow the Rayleigh law, the common practice of using an exponential fractionation law to correct for mass-dependent fractionation in the study of mass-independent fractionations may introduce significant artificial isotope anomalies.

Non-linear behavior of coercivity to the maximum applied magnetic field in La substituted nanocrystalline cobalt ferrite

The magnetic properties of nanocrystalline cobalt ferrite could be tuned with substituting small amount of non-magnetic rare earth cation at Fe site in cobalt ferrite. The variation in magnetic parameter of samples could also be obtained by measuring its anhysteretic magnetization curve without tailoring its chemical composition. The magnetic parameters such as coercivity, remanent magnetization and saturation magnetization critically depend upon different values of external magnetic fields. In the present study, the anhysteretic magnetization curve of the samples CoFe2−xLaxO4 (x=0.025, 0.05, 0.075 and 0.1) has been recorded and response of coercivity to different maximum values of applied field has been investigated. It has been observed that the response of coercivity to different maximum values of applied field shows non-linear behavior. The analysis of the response of coercivity to different values of applied field in low field regime has been carried out with the help of Rayleigh laws. The analysis of the plot yields significant information about magnetic anisotropy.