Simulation of the dynamics of the spatial domain structure of a ferroelectric triglycine sulfate crystal

The dynamics of a domain structure of order-disorder ferroelectrics similar to triglycine sulfate is considered. Starting from the Hamiltonian of the problem, a kinetic equation describing the polarization dynamics of ferroelectrics is derived. The results are analyzed and compared with the experimental data.     

Modeling of Seignette salt by a ferroelectric: Polarization lattices as a result of interaction with the acoustic subsystem

The dynamics of the domain structure observed in ferroelectrics with two dipoles per ferroelectric cell—analogues of the Seignette salt crystal—is studied. Kinetic equations for the mean values of pseudospin operators are derived based on the Hamiltonian of the problem. These equations are used to numerically study the evolution of the ferroelectric polarization as a function of the problem parameters for both transparent and polarized interfaces.     

Dynamics of the domain structure in ferroelectrics with an incommensurate phase

The dynamics of the domain structure of ferroelectrics with an incommensurate phase (like sodium nitrite) is considered. The polarization properties of these ferroelectrics are described using the pseudospin formalism. The equation for the polarization is numerically solved together with the equation for acoustic waves. The obtained results are analyzed for various values of the parameters of the crystal and different initial conditions. It is shown that, after a sufficiently large time, the domain structure of the crystal becomes localized.     

Investigation into the domain structure dynamics in ferroelectrics with an incommensurate phase

The domain structure dynamics in ferroelectrics with an incommensurate phase is studied. Sodium nitrite is considered to be a prominent representative of the above ferroelectrics. The polarization properties of these ferroelectrics are described using pseudospin formalism. A kinetic equation for describing polarization of ferroelectrics is derived using the Hamiltonian. This equation is numerically solved simultaneously with the sound-vibration equation. The results are analyzed for various crystal parameters and initial conditions. The crystal domain structure is shown to be localized for reasonably long times. This circumstance makes it possible to conclude that these domain-structure states are long-lived states of a soliton type. The importance of finding and describing these states is emphasized. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 66–70, August, 2006.     

Mathematical Modeling of the Polarization of Polycrystalline Ferroelectrics

General patterns of the polarization models of Rayleigh, Preisach, and Jiles–Atherton are found. The limiting dependence of the polarization is confirmed. A way of constructing it based on the energy criterion for domain switching for polycrystalline ferroelectrics with perovskite structure is proposed. Differential equations are constructed for determining the irreversible components of polarization and deformation, and large loops of dielectric hysteresis are calculated.     

Specific features in the permittivity of polycrystalline ferroelectrics: The role of Schottky regions

This paper reports on the results of investigations into the influence of Schottky regions formed in the vicinity of crystallite boundaries in polycrystalline ferroelectrics on their permittivity. The dependence of the dielectric properties of the Schottky regions on the orientation of the spontaneous polarization in the adjacent region of the crystallite is taken into consideration. It is demonstrated that nonmonotonic dependences of the permittivity and its relative change on the crystallite size under uniaxial compression are associated with the presence of the domain structure in polycrystalline ferroelectrics.     

Potts-Ising model for simulation of polarization switching in polycrystalline ferroelectrics

This paper proposes a scheme based on the Potts and Ising models for simulating polarization switching of polycrystalline ferroelectrics using the Monte Carlo method. The polycrystalline texture with different average grain size is produced from the Potts model. Then Ising model is implemented in the polycrystalline texture to produce the domain pattern and hysteresis loop. The domain patterns and hysteresis loops have been obtained for polycrystalline texture with different average grain size. From the results of domain pattern evolution process under an applied electric field using this scheme, an extended domain, which covers more than one grain with polarization aligned roughly in the same direction, has been observed during the polarization reversal. This scheme can well reproduce the basic properties of polycrystalline ferroelectrics and is a valuable tool for exploring the physical properties of polycrystalline ferroelectrics.     

Unusual domain evolution in semiconducting ferroelectrics: A phase field study

The effect of electrical conductivity on the domain evolution of semiconducting ferroelectrics is investigated using a phase field model which includes the drift of space charges. Phase field simulations show that the tail-to-tail 90° charged domain wall appears during the domain formation in the semiconducting ferroelectrics at zero field, which is prohibited in common insulating ferroelectrics. Due to the screening of polarization charges, the domain switching takes place through the motion of head-to-head 180° charged domain wall in the semiconducting single-domain ferroelectrics subjected to an electric field. Comparing to the insulating ferroelectrics, the semiconducting ferroelectrics have a lower speed of domain evolution due to the decrease of mobility of charged domain walls. The response of semiconducting ferroelectrics to a mechanical load is also found different from that of insulating ferroelectrics.     

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.     

Physical and mathematical modeling of the electron-beam-induced charging of ferroelectrics during the process of domain-structure switching

The results of modeling the dynamic charging processes that arise when ferroelectrics are under the action of an electron beam in a scanning electron microscope are presented. Implementation of the model is based on simultaneous solution of the continuity equation and Poisson equation with allowance for the radiation-stimulated intrinsic conductivity of the irradiated sample and with an initial charge distribution determined using the Monte Carlo method. The multidimensional boundary evolutionary problem is solved using grid methods. The model permits one to study the dynamics of the process of the electron-beam-induced charging of ferroelectrics. Estimates for the values of fields generated by charges accumulated during the irradiation process are presented for a set of modeling parameters corresponding to physical data obtained in experimental observations of the polarization switch for a ferroelectric lithium niobate crystal.     

Proton transport in ordered hydrogen-bonded solids

The proton transfer is considered in hydrogenbonded chains with asymmetric double-minimum potentials for proteons. The transport is described by the kinksoliton propagation in an energetically asymmetric double-well potential for a proton. The asymmetry can be caused by the spontaneous polarization in hydrogenbonded ferroelectrics, medium polarization in nonferroelectric hydrogen-bonded solids, crystallographic structure, geometry of the proton neighbourhood and internal electric field in biological macromolecules. The soliton dynamics of the system is analytically studied including the influence of a constant external electric field and damping mechanism. The velocity, energy, momentum and mobility of kinks are calculated.     

Domain pattern in ferroelectric triglycine sulphate using pyroelectric effect

A method to study domain structure in ferroelectrics, using pyroelectric effect is described. Variation of pyroelectric signal from the surface of a triglycine sulphate crystal plate has been studied by scanning the surface of the crystal with a low wattage He-Ne laser beam. The integrated pyroelectric signal is due to two components, namely, (1) the primary component arising out of the change in spontaneous polarization with temperature and (2) the delayed component arising out of the possible polarization reversal. The component of an electric field along the ferroelectric axis due to thermal hemisphere within the crystal plate formed by the laser beam has been calculated and shown to exceed coercive field, making polarization reversal possible. The delayed pyroelectric signal is a measure of polarization reversal within the patch illuminated and its observed variation over the surface yields information of the domain structure.     

Polarization response explored by joint Hamiltonian and stochastic approach

The effect of thermal fluctuations on systems modeled by anharmonic nonconservative Hamiltonians is investigated in the framework of interacting lattice cells each cell obeying to Langevin dynamics. Representative examples addressed to critical phenomena in ferroelectrics include polarization response of a single lattice cell, ergodicity breaking, and birth of a domain, and the effect of nonlocal electroelastic interaction all derived combining the Fokker–Planck, imaginary time Schrödinger, and symplectic integration techniques.     

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.     

Development of helical cholesteric structure in a nematic liquid crystal due to the dipole-dipole interaction

A nematic liquid crystalline phase is considered whose rod-like non-centrosymmetric molecules possess a permanent dipole moment. This phase is a “liquid ferroelectric” if all the molecules are oriented along the same “preferred” direction. It is shown that a liquid ferroelectric can not exist in a homogeneous nematic state. It is transformed into a more stable helical structure (the vector of the spontaneous polarization of such a structure rotates aroung the helical axis). There is a variety of domain structures for the specific case when the anisotropy coefficient of the polarization is equal to zero. Since each elementary dipole moment is rigidly bound to its molecule, the “preferred” alignment direction of the rod-like molecules as well as the polarization vector rotates with respect to the same axis in a helical manner. Therefore a nematic phase with a nonzero spontaneous polarization has a cholesteric structure. Its helical pitch is determined by the geometric size of the sample, the absolute value of the spontaneous polarization, and the elastic moduli. Apparently, we can consider some cholesteric phases to be liquid ferroelectrics with helical domain structure.     

Switching current noise and relaxation of ferroelectric domains

We simulate field-induced nucleation and switching of domains in a three-dimensional model of ferroelectrics with quenched disorder and varying domain sizes. We study (1) bursts of the switching current at slow driving along the hysteresis loop (electrical Barkhausen noise) and (2) the polarization reversal when a strong electric field was applied and back-switching after the field was removed. We show how these processes are related to the underlying structure of domain walls, which in turn is controlled by the pinning at quenched local electric fields. When the depolarization fields of bound charges are properly screened we find that the fractal switching current noise may appear with two distinct universal behaviors. The critical depinning of plane domain walls determines the universality class in the case of weak random fields, whereas for large randomness the massive nucleation of domains in the bulk leads to different scaling properties. In both cases the scaling exponents decay logarithmically when the driving frequency is increased. The polarization reverses in the applied field as a power-law, while its relaxation in zero field is a stretch exponential function of time. The stretching exponent depends on the strength of pinning. The results may be applicable for uniaxial relaxor ferroelectrics, such as doped SBN:Ce. Received 7 February 2002 / Received in final form 10 April 2002 Published online 9 July 2002     

Pulse-controlled generation and characterization of partially-switched multiple-value polarization states in PZT ceramics

This paper explores in depth the partially switched states of ferroelectrics, through macroscopic polarization measurements in conjunction with piezoresponse force microscopy, x-ray diffraction and dielectric characterization, with the ultimate purpose to explore their usefulness for unconventional multiple-value nonvolatile memory applications. We prove that it is possible to reproducibly generate analog levels of polarization in a Pb(Zr,Ti)O₃ ferroelectric ceramic capacitor and control them with electric pulses that stabilize unique domain patterns, compatible with those of adjacent states. Some of these states contain, in the same locations of the sample surface, areas with orientation of polarization vector opposite to that of the electric field that decides the analog polarization level, while others contain clamped domain structures with reduced piezoelectric activity. We argue that disclosing the complex relationships between the domain structures of the analog polarization states, as well as their dependence on write voltage parameters, might help to expand the multiple-value storage capability of ferroelectrics beyond what would be achievable on macroscopic scale.     

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.     

Temperature dynamics of triglycine sulfate domain structure according to atomic force microscopy and dielectric spectroscopy data

A hydrogen-containing ferroelectric triglycine sulfate (TGS) was comprehensively studied with an atomic force microscopy (AFM) and dielectric spectroscopy. The domain structure dynamics was in situ investigated with piezoresponse force microscopy (PFM) during heating and cooling the TGS crystal near phase transition. Relaxation dependencies of domain boundaries general perimeter and domain dimensions were obtained. TGS dielectric spectra measured at the frequency range from 10 to 10¹¹ Hz were analyzed on basis of significant contribution of conductivity into the dielectric response of ferroelectrics and a good agreement with the experimental data was received. It allows us to obtain more information about temperature dynamics of the domain structure.     

Lattice-scale domain wall dynamics in ferroelectrics

Ferroelectric domain walls are atomically thin, and consequently their dynamics are sensitive to the periodic potential of the underlying lattice. Despite their central role in domain dynamics, lattice-scale effects have never been directly observed. We investigate local domain dynamics in thin film ferroelectrics using atomic-force microscopy. Upon combined dc and ac electric driving, fluctuations in the local piezoresponse are observed. Fourier analysis of the fluctuations reveals the presence of narrow band and broad band noise, and Barkhausen jumps. The narrow band noise is attributed to dynamics associated with lattice-scale pinning and is reproduced by a simple physical model.