Thermodynamics and kinetics of the initial stages of polarization switching in ferroelectrics

The thermodynamics and kinetics of polarization switching in ferroelectrics are studied in the specific case of switching in intrinsic ferroelectrics with 180° domains. The initial stage of the switching in the region of weak metastability is analyzed. An expression relating the critical domain size to the switching field is derived. An equation describing the evolution of the size distribution function of the switched domains is obtained. Expressions for calculating the number of polarization switching nuclei as a function of the switching field are derived.     

Theory of switching of multiaxial ferroelectrics (the main stages)

The kinetics of switching of multiaxial ferroelectric crystals with 180° and 90° domains under conditions of normal and layer-by-layer domain growth is studied using the multidimensional theory of first-order phase transitions. The main stages of the process of switching of a multiaxial ferroelectric are considered under the assumption that repolarized cylinder-shaped domains grow three-dimensionally. A closed set of equations describing the kinetics of switching is derived with allowance for a change in repolarization in the course of the phase transition. Equations for the time-dependent switching current are derived. The main characteristics of switching are compared qualitatively with the experimental data on barium titanate.     

Thermodynamics and kinetics of switching of ferroelastic ferroelectrics at its initial stage

Thermodynamics and kinetics of switching of ferroelastic ferroelectrics (FFs) are studied at the initial (weak-metastability) stage. It is shown that in the switching of a uniaxial FF, the role of the electric field and mechanical stress simultaneously applied to the FF is analogous to that of supersaturation or supercooling of solutions and melts in the process of a conventional phase transition. The dependence of the critical size of a domain on the strength of the switching field is derived. In the space of domain sizes, the dependence of the steady flux of repolarized and redeformed nuclei on the applied field is determined and the time required for this steady flux to set in (latent time) and the time during which this flux is steady are estimated.     

Polarization switching kinetics in ferroelectrics

The switching kinetics in ferroelectrics in the bulk polarization switching stage and in the final stage of the process are studied. Consideration is given to the specific case of switching of intrinsic ferroelectrics with 180° domains. A complete system of equations describing the switching processes and taking into account the change in repolarization in the course of a phase transformation is derived. The solution of this system is found. All the main characteristics of the switching process are calculated; namely, the evolution of the domain size distribution function is revealed and the time dependences of the domain density and flux are determined. An expression describing the variation in repolarization with time is obtained. The mechanisms of domain growth are studied. An equation for calculating the switching current and its variation with time is derived. A method is proposed for determining a number of constants for ferroelectric crystals by studying the switching current evolution.     

High-energy QCD asymptotic behavior of photon-photon collisions

Complex quasienergy and level width are calculated for a weakly bound atomic state in an intense circularly polarized monochromatic laser field using the method suggested by Zel’dovich for the regularization of divergent integrals with the Gamow wave function. It is demonstrated that this method converges, and the conditions for its applicability are indicated. These results are used to discuss the accuracy of the semiclassical approximation in the problems of ionization theory.     

Switching of partially switched KNbO3 single crystals containing cooperatively ordered impurity dipoles

Switching studies have been carried out in partially switched KNbO₃ single crystals by observing switching transients and hysteresis loops. The crystals used contained ordered impurity dipoles that are active in nucleating domains around them. Partial initial switching was obtained by applying known compressive stress to the crystal by means of a spring. The partially switched nature was determined by recording the photograph of the crystal surface. The changed domain structure on the surface gave a clear idea of the extent of partial switching. As the compressive stress was gradually increased, the crystal showed increased initial mechanical switching through the mechanism of evaporation of domain walls associated with ordered impurity dipoles. The dipoles then switch systematically converting 90° domains with polar axes in the plane of plate into 60° domains with polar axes in the perpendicular pseudocubic {001} planes. The initial switching condition changes the switching characteristics as determined by hysteresis loops and switching transients. The results are interpreted in terms of domains in the crystal. If the dipole density is quite high, the effect of the dipoles becomes negligible, and the switching behaviour approximates that of a normal ferroelectric. The switching transients and the hysteresis loops in the crystals containing cooperatively ordered dipoles are basically different from the ones observed in normal ferroelectrics. The anomalous behaviour is detrimental to the use of material in device applications. Hence, it is shown that the switching transients and hysteresis loops provide a ready means of detecting the presence of these ordered impurity dipoles.     

Polarization switching kinetics in ferroelectrics in the region of strong metastability

The thermodynamics and kinetics of polarization switching in ferroelectrics are studied in the framework of the field theory in the vicinity of the critical point of first-order phase transitions. The study is exemplified by the switching of intrinsic ferroelectrics with 180° domains. An expression describing the dependence of the domain critical size on the switching field is derived. The switching process is studied at high switching fields. Relationships for calculating the field dependence of the number of switched domains are obtained.     

Non-equilibrium agglomeration of helium-vacancy clusters in irradiated materials

Abstract

Time evolution of non-equilibrium systems, where the probability density is described by a continuum Fokker-Planck (F-P) equation, is a central area of interest in stochastic processes. In this paper, a numerical solution of a two-dimensional (2-D) F-P equation describing the growth of helium-vacancy clusters (HeVCs) in metals under irradiation is given. First, nucleation rates and regions of stability of HeVCs in the appropriate phase space for fission and fusion devices are established. This is accomplished by solving a detailed set of cluster kinetic rate equations. A nodal line analysis is used to map spontaneous and stochastic nucleation regimes in the helium-vacancy (h-v) phase space. Growth trajectories of HeVCs are then used to evaluate the average HeVC size and helium content during the growth phase of HeVCs in typical growth instability regions.

The growth phase of HeVCs is modeled by a continuum 2-D, time-dependent F-P equation. Growth trajectories are used to define a finite solution space in the h-v phase space. A highly efficient dynamic remeshing scheme is developed to solve the F-P equation. As a demonstration, typical HFIR irradiation conditions are chosen. Good agreement between the computed size distributions and those measured experimentally are obtained.     

Exciton absorption at the initial stages of the formation of the CuCl phase in a glass

The fundamental absorption spectra of CuCl nanocrystals in glass samples are investigated in the energy range 3–4 eV at a temperature of 300 K with the aim of elucidating the kinetics of the initial stage of the formation of the CuCl phase in the glass. The CuCl phase is grown in the glass under stepwise annealing at temperatures of 500, 615, and 707°C. The kinetics of variation in the intensity and the shift of the maximum in the exciton absorption spectra of CuCl nanocrystals are studied in the course of annealing of the glass samples. It is established that, for all the temperatures under investigation, the formation of the CuCl phase begins with the transient stage that involves the fluctuation formation of supercritical nuclei of the CuCl nanomelt. At a temperature of 500°C, the transient stage gives way to the stage of a rapid increase in the number of supercritical nuclei of the CuCl phase. At temperatures of 615 and 707°C, the transient stage gives way to the stage of an intensive growth of nuclei without a considerable increase in their number. The number of nuclei formed during the transient stage at 707°C is smaller than that observed after the transient stage at 500°C by a factor of 24. However, the sizes of the nuclei formed at 707°C are larger than those observed after the transient stage at 500°C. This difference is explained by the fact that the diffusion length of Cu⁺ ions controlling the formation of the CuCl phase increases with increasing temperature. The experimental data on the kinetics of the formation of the new phase in the glass are in good agreement with the Zel’dovich-Frenkel classical theory of the formation of a new phase, which accounts for the stage of the formation of critical nuclei.     

Mechanism of Plastic Collapse of Nanosized Crystals with BCC Lattice under Uniaxial Compression

Within the dislocation–kinetic approach, based on the nonlinear kinetic equation for dislocation density, an attempt is made to consider the problem of a catastrophic plastic collapse of defect-free nanocrystals of metals with bcc lattice under their uniaxial compression with a constant deformation rate. Solutions of this equation were found in the form of moving waves, describing the dislocation multiplication process as the wave moves along the crystal from a local dislocation source. Comparison of the theory with the results of experiments on defect-free Mo nanocrystals showed that their ultrahigh strength at the initial stage of deformation is associated with a low rate of rise of crystal plastic deformation in comparison with the growth of its elastic component. The subsequent plastic collapse of crystal is caused by a sharp increasing the plastic component, ending with reaching the equality of elastic and plastic deformation rates.

     

On nonlinear effects in condensation models with continuous and discrete descriptions of nucleation

A set of nonlinear equations for the evolution of the condensate fraction is suggested. The diffusion approximation to the Zel’dovich equation is shown to be fundamentally inapplicable for describing nonlinear effects. A diffusion equation with the applicability domain free of limitations due to supersaturation smallness is derived.     

Weak detonation in mixtures of phlegmatized RDX with aluminum

The Zel’dovich theory predicts the possibility of realization of self-sustained weak detonation in systems with nonmonotonic energy release. The present paper describes experiments aimed at detecting such a regime of detonation in mixtures of phlegmatized RDX with PP-1 and PAP-2 aluminum powders. The mass fraction of aluminum was 20%. To examine the detonation regimes, 70-mm-in-diameter charges of these mixtures were initiated with powerful triangular pressure pulses, which gave rise to attenuating overdriven detonation waves. The pressure profiles were recorded at various distances from the initiation plane (from 10 to 80 mm). Specific features of the time evolution of the detonation wave profile indicative of the existence of a supersonic flow region arising not later than 0.15 μs behind the shock front were revealed. The supersonic character of the flow behind an intermediate C-J plane is an inherent characteristic of self-sustained weak detonation; i.e., direct experimental evidence for the existence of weak detonation in RDX-aluminum mixtures was obtained.     

Quantum graviton creation in a model universe

Quantization in the spatially inhomogeneous, anisotropic, Gowdy three-torus solution of Einstein's equations leads to the production of gravitons from empty space. The creation of pairs of gravitons occurs only in wave modes with wavelength exceeding the horizon size at an initial time. The final number of created gravitons in any mode is proportional to the number of causally unconnected regions at the initial time over the wavelength of that mode. At large times, graviton number is well defined since the solution is in WKB form. The creation process produces the anisotropic collisionless radiation identical to that discussed by Doroshkevich, Zel'dovich, and Novikov which characterizes the large time classical solution. Near the singularity, the model behaves like an empty Bianchi Type I universe at each point in space (local Kasner). The canonical methods of Arnowitt, Deser, and Misner yield a reduced Hamiltonian from which the classical equations of motion are obtained. The quantization of the rapidly varying gravitational field component resembles the procedures used by Parker or Zel'dovich et al. to study particle creation in curved spacetime.     

Kinetic approach for describing the fatigue effect in ferroelectrics

A new kinetic approach is proposed for explaining the fatigue effect in ferroelectrics. A self-consistent variation in the area and geometry of the switching region of a sample upon a cyclic switching accompanied by the formation and growth of kinetically frozen domains is considered. It is assumed that fatigue is due to self-organized formation of a spatially inhomogeneous internal bias field due to retardation of bulk screening of the depolarization field. Variations in the switching charge and in the amplitude of switching current, which are calculated with the help of computer simulation of domain kinetics upon cyclic switching, are in good agreement with experimental data obtained for thin lead zirconate-titanate (PZT) thin films.     

Theoretical study of the effect of the size of a high-energy proton beam of the Large Hadron Collider on the formation and propagation of shock waves in copper irradiated by 450-GeV proton beams

The interaction of 450-GeV protons with copper, which is the material of the collimators of the Large Hadron Collider, has been theoretically studied. A theoretical model for the formation and propagation of shock waves has been proposed on the basis of the analysis of the energy released by a proton beam in the electronic subsystem of the material owing to the deceleration of secondary particles appearing in nuclear reactions induced by this beam on the electronic subsystem of the material. The subsequent transfer of the energy from the excited electronic subsystem to the crystal lattice through the electron-phonon interaction has been described within the thermal spike model [I.M. Lifshitz, M.I. Kaganov, and L.V. Tanatarov, Sov. Phys. JETP 4, 173 (1957); I.M. Lifshitz, M.I. Kaganov, and L.V. Tanatarov, At. Energ. 6, 391 (1959); K. Yasui, Nucl. Instrum. Methods Phys. Res., Sect. B 90, 409 (1994)]. The model of the formation of shock waves involves energy exchange processes between excited electronic and ionic subsystems of the irradiated material and is based on the hydrodynamic approximation proposed by Zel’dovich [Ya.B. Zel’dovich and Yu.P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena (Nauka, Moscow, 1966; Dover, New York, 2002)]. This model makes it possible to obtain the space-time distributions of the main physical characteristics (temperatures of the ionic and electronic subsystems, density, pressure, etc.) in materials irradiated by high-energy proton beams and to analyze the formation and propagation of shock waves in them. The nonlinear differential equations describing the conservation laws of mass, energy, and momentum of electrons and ions in the Euler variables in the case of the propagation of shock waves has been solved with the Godunov scheme [S. K. Godunov, A.V. Zabrodin, M.Ya. Ivanov, A.N. Kraiko, and G.P. Prokopov, Numerical Solution of Multidimensional Problems in Gas Dynamics (Nauka, Moscow, 1976) [in Russian]]. The temperature, pressure, and specific internal energy have been calculated independently and separately for the ionic and electronic subsystems of the irradiated material. The formation of shock waves in copper has been simulated in the cylindrical geometry for various sizes and various types of the beam: for a needle beam (the distribution of protons in the beam is described by the Dirac delta function) and beams with a finite radius (0.3, 3, and 5 mm) with a Gaussian distribution of protons near the axis of the beam. The effect of the size and geometry of the proton beam, as well as of the form of the chosen boundary conditions, on the intensity of shock waves formed in copper and on change in their physicomechanical properties in the space and time has been revealed in the numerical simulation results.     

Formation and growth of CuCl phase nuclei in glass

In glass, the CuCl phase starts to form a certain time after the onset of supersaturation. As the temperature is increased, the transient period (stage of formation of critical nuclei) shortens and the growth kinetics of the CuCl phase switches from the first to second stage. The observed pattern of the CuCl phase growth kinetics is fully consistent with the Zel’dovich-Frenkel classical theory of new-phase formation. The delay time is determined by the radius of the critical nucleus (CuCl nanomelt) and the diffusion coefficient of the limiting component, the Cu⁺ ions. The radius of the critical nucleus is about 1 nm and does not vary within a broad temperature range. The activation energy for the CuCl phase growth process does not change in the transition from the formation of critical nuclei to the first and, subsequently, second stage.     

Distinct ferroelectric domain switching dynamics in epitaxial BiFeO3 (001) capacitors depending on the bias polarity

Understanding ferroelectric domain switching dynamics at the nanoscale is a great of importance in the viewpoints of fundamental physics and technological applications. Here, we investigated the intriguing polarity-dependent switching dynamics of ferroelectric domains in epitaxial BiFeO₃ (001) capacitors using transient switching current measurement and piezoresponse force microscopy. We observed the distinct behavior of nucleation and domain wall motion depending on the polarity of external electric bias. When applying the negative bias to the top electrode, the sideways domain wall motion initiated by only few nuclei was dominant to polarization switching. However, when applying the positive bias, most of domains started to grow from the pre-existed pinned domains and their growth velocity was much smaller. We suggest that the observed two distinct domain switching behavior is ascribed to the interfacial defect layer.     

Effect of low-symmetry mechanical stresses on the magnetic properties of iron borate

Low-(C ₃) symmetry mechanical stresses are used to induce an additional crystalline magnetic anisotropy in the basal plane of a FeBO₃ single crystal. The effect of the stress-induced anisotropy on the main magnetic properties of this weak ferromagnet is studied by a magnetooptic method. This additional anisotropy is shown to transform the initial 180° domain structure of iron borate into a structure with domain walls making an angle of ～ 120° with each other in the basal plane of the crystal. However, unlike in the ordinary 120° DW structure, the azimuthal angle of the spontaneous magnetization vectors in the arising domains varies along domain walls. It is found that the stress-induced transformation of the crystal’s domain structure significantly affects the shape of hysteresis loops recorded at quasi-static magnetization, increases the initial magnetooptic susceptibility, and makes the coercive force anisotropic.