Kolmogorov-Avrami Model Research Articles

Grid pattern emerging from complex dynamics of defects.

The formation process and growth dynamics of the grid pattern, a cellular convective pattern in the electroconvection of nematic liquid crystals, are investigated. The grid pattern appears via a disordered state called defect turbulence with the increasing of an applied voltage. The averaged defect density increases with the applied voltage and then the defects that have been in the continuous process of creation and annihilation are frozen as grid cells forming domain structures. The area fraction of the grid domains is adopted as the order parameter. The temporal growth of the area fraction for the step voltage was also measured. By applying the Kolmogorov-Avrami model to the results, it is suggested that the growth dynamics of the grid domain is not primarily governed by domain growth, but by the local transition of the rolls to the cellular flow via preliminary grid structures that transiently appear.

Effect of Overcooling and Stoichiometry Deviations on Kinetics and Mechanism of Crystallization of As2Se3 Glass

A comparative study of the kinetics of massive bulk crystallization of As2Se3, As1.9Se3, and As2.1Se3 bulk glasses at 240°C is performed using the Kolmogorov–Avrami model. A theoretical analysis of the experimental dependences of the linear growth rate of As2Se3 crystals on temperature and viscosity of the As2Se3 glass is performed. It is shown that the dislocation growth of crystals in the form of spherulites appears to be probable in the As2Se3 glass under overcooling at ∆T = 30–135°С. For individual lamellar crystals As2Se3 with dislocation-free faces inside the spherulites, a growth mechanism with surface two-dimensional nucleation (2Dsg model) appears to be probable at ∆T = 75–135°С.

From early nucleation past the percolation threshold: Status of the Kolmogorov-Avrami theory on a cold Ising lattice.

A high-precision test of the Kolmogorov-Avrami (KA) model of "geometric" interactions between growing nuclei is performed for an Ising ferromagnet driven by Metropolis dynamics. As long as the interface boundaries of interacting nuclei are rough, the KA model is adequate for arbitrary large densities of the new phase, well beyond the percolation transition, as in the case of homogeneous nucleation. For a prenucleated system the KA description breaks down at sufficiently low temperature, when the length of a kinetically smooth interface exceeds the distance between seeds.

Exchange bias in defect-induced ferromagnetic SiC

Abstract In this paper, the observation of exchange bias in defective ferromagnetic SiC is presented. Two typical features of exchange bias are clearly observed: the shift of magnetic hysteresis upon field cooling and the training effect. A core-shell morphology particle model is employed to quantitatively analyze the exchange bias field dependence on the cooling field. Based on the model, the calculated anisotropy constant is 2.5 × 105 erg/cm3. The training effect can be described by the Kolmogorov-Avrami model, which is used for the classical exchange bias system. The appearance of exchange bias is the signature of the existence of an interface between ferromagnetic and antiferromagnetic layers or cores/shells.

Theoretical and experimental analysis of precipitation and solubility effects in lithium-sulfur batteries

A rate-dependent nucleation theory is developed to analyze the dependence of the capacity of lithium-sulfur (Li-S) batteries on discharge rates. The theory is based on expressing the nucleation rate of solid products in terms of the surface oversaturation of the precipitating species and rewriting the classical Kolmogorov-Avrami model in the form of a differential system of equations. By coupling this system of equations with the multicomponent transport equations we are able to explain qualitatively well the decrease of the specific capacity with increasing discharge rates and the characteristics of the discharge curves under variable discharge currents in Li-S batteries. Special attention is given to accurately determine the values of model parameters from experimental data, including the solubility constants of the solid products and the mobilities and diffusivities of the ions. The anodes of the batteries used in our analysis were made using Li foils and the cathodes were fabricated using freestanding carbon nanotube foams, on which solid sulfur was uniformly distributed to maximize the dissolution rate. The experimental data combined with the theoretical analysis show that the capacity limitation in our batteries is due to surface passivation by the final reaction products. In order to increase the specific capacity of Li-S batteries under normal discharge rates we conclude that it is better to avoid the solid precipitation of intermediate lithium polysulfides (LiPS) by using electrolytes with a high solubility of LiPS. In addition, it is better to use catalyst particles in the cathode that would promote the nucleation rate at specified locations. The number of catalyst particles should not be too small to avoid electrolyte oversaturation or too large to avoid the rapid passivation of the carbon surface with solid products.

Formation of self-assembled domain structures in single crystals of lithium tantalate with artificial dielectric layer

ABSTRACTThe polarization reversal was studied in single crystals of lithium tantalate with intermediate deviation from stoichiometric composition (([Li]/([Li]+[Ta]) = 48.9%) with and without surface photoresist layer. The switching current was analyzed according to the stages of domain structure evolution revealed during in situ visualization of domain kinetics. The characteristic times of the switching process were extracted by fitting of the experimental data using modified Kolmogorov-Avrami model. The formation of the self-assembled domain chains was observed during polarization reversal with photoresist dielectric layer on one polar surface.

Increase and Relaxation of Abnormal Conduction Current in Lithium Niobate Crystals with Charged Domain Walls

The increase and relaxation of the conduction current caused by formation of intergrown charged domain walls (CDW) during polarization reversal have been studied in stoichiometric lithium niobate. The 103-104 times increase of the conduction current was revealed in the temperature range 100-200°C. The current, measured during polarization reversal, consists of the conventional switching current and the conduction current along CDW dominating for T>200°C. The model based on the complex conductivity pathway along CDW was proposed. The current data were analyzed in terms of the Kolmogorov-Avrami model taking into account the input of the CDW conductivity.

Dynamic Simulation of Polarization Reversal Processes in Ferroelectric Crystals under Electron Beam Irradiation

The paper describes the results of dynamic simulation of electron beam-induced polarization reversal process in ferroelectrics with a focus on a fractal approach. The methods of fractal analysis were used to estimate the scaling characteristics of TGS-domain structure images and polarization switching current obtained with the SEM. The computer simulation results of domain configuration geometry and corresponding form of switching current are presented. Using modified Kolmogorov-Avrami model, the polarization current was determined taking into account differential equation with fractional derivative. The main features of simulation curve of polarization switching current correspond to experimental data observed.

Exchange bias relaxation in reverse magnetic fields

The time dependence associated with the so-called exchange bias in coupled polycrystalline ferromagnetic/antiferromagnetic films has been suspected as arising from antiferromagnetic domain dynamics. In this paper we present a quantitative description of the nucleation and growth of antiferromagnetic domains based on the Kolmogorov-Avrami model, which describes the time dependence of the exchange bias in all the systems for which data could be found.

A theory of polarization reversals in finite systems

Abstract A theory of polarization reversals in finite system is developed on the basis of the Kolmogorov-Avrami model. The observed size dependence of the switching time, which looks very peculiar at a glance, seems to be well explained by the present theory.

Intensity Oscillation of Reflection High-Energy Electron Diffraction(RHEED) by a Polynuclear Growth Model

Intensity oscillation of reflection high-energy electron diffraction (RHEED) is discussed under the light of an analytical solution obtained for polynuclear growth processes based on the Kolmogorov-Avrami model. According to the model, the RHEED intensity oscillations persist both for the one- and the two-dimensional cases, implying a steady growth.

A Model of Polarization Reversal in Ferroelectrics

The ferroelectric switching process has been studied on the basis of a one-dimensional discrete lattice model. The characteristics of the model is discussed in the relationship with the Kolmogorov-Avrami(KA) model. It has turned out that the features in the early stage of the polarization reversal in the present model coincides with what described by the KA model.