Limiting Distribution of Frobenius Numbers for n=3n=3

The purpose of this paper is to give a complete derivation of the limiting distribution of large Frobenius numbers outlined in earlier work of J. Bourgain and Ya. Sinai and fill some gaps formulated there as hypotheses.Comment: 13 page

Regular and irregular shaped isolated domains in uniaxial ferroelectrics

The equipment of the Ural Center for Shared Use “Modern nanotechnology” Ural Federal University was used. The research was made possible by Russian Science Foundation (Grant 14-12-00826)

Humidity effects on tip-induced polarization switching in lithium niobate

Interest to ferroelectric materials has been increased significantly in last decades due to development of new generation of nonlinear optical and data storage devices. Scanning probe microscopy (SPM) can be used both for study of domain structures with nanoscale spatial resolution and for writing the isolated nanodomains by local application of the electric field. Tip-induced switching in the ambient still needs experimental investigations and theoretical explorations. Here we studied influence of the value of relative humidity in the SPM chamber on the process of tip-induced polarization switching. This phenomenon was attributed to existing of the water meniscus between tip and the sample surface in humid atmosphere. Presented results are important for further complex investigations of the ferroelectric materials and their applications.Comment: 15 pages, 5 figures, Submitted to Applied Physics Letter

Fatigue effect in ferroelectric crystals: Growth of the frozen domains

The model of the fatigue effect during cyclic switching caused by growth of the frozen domain area with charged domain walls has been proposed. It was claimed on the basis of the previous experimental results that for switching in increasing field the frozen domain area started to grow at the given sub-threshold field value and stopped at the threshold field. The influence of the shape and frequency of the field pulses used for cyclic switching has been considered. The uniaxial ferroelectric stoichiometric lithium tantalate single crystals produced by vapor transport equilibration with record low value of coercive field have been chosen as a model material for experimental verification of the model. The formation of the charged domain walls as a result of cyclic switching has been revealed by analysis of the domain images obtained by optical and Raman confocal microscopy. It has been shown that the fatigue degree is equal to the fraction of the frozen domain area. The experimental dependence of the switched charge on the cycle number has been successfully fitted by modified Kolmogorov-Avrami formula. The experimentally observed frequency independence of fatigue profile for rectangular pulses and frequency dependence for triangular pulses has been explained by proposed model. © 2012 American Institute of Physics

Polarization reversal and jump-like domain wall motion in stoichiometric LiTaO 3 produced by vapor transport equilibration

The polarization reversal and domain structure evolution has been studied in stoichiometric lithium tantalate prepared by vapor transport equilibration process. The first in situ visualization of domain kinetics has demonstrated the jump-like motion of few strictly oriented plane domain walls, which leads to short isolated current pulses in the switching current data. The proposed model of jump-like domain wall motion caused by interaction with pinning centers representing the areas with increased value of the threshold field is based on the effect of retardation of bulk screening. The derived formulas were applied successfully for analysis of the field dependence of the total switching time. The durations of wall jumps and wall stays (rest times) extracted from the switching current data are analyzed separately. The deceleration of the wall motion velocity during jump is controlled by the trail of residual depolarization field produced by bound charges and screening charges in the area behind the wall. The duration of the rest time is governed by the bulk screening of residual depolarization field. The value of Hurst exponent 0.75 obtained by fractal analysis of the switching current data has confirmed the essential influence of prehistory on the domain wall motion. The measurements of the coercive field by switching in bipolar triangular pulses in wide range of the field ramp rate have allowed us to extract the record low value of coercive field 60 V/mm for quasi-static polarization reversal. © 2012 American Institute of Physics

Domain shape instabilities and dendrite domain growth in uniaxial ferroelectrics

The effects of domain wall shape instabilities and the formation of nanodomains in front of moving walls obtained in various uniaxial ferroelectrics are discussed. Special attention is paid to the formation of self-assembled nanoscale and dendrite domain structures under highly non-equilibrium switching conditions. All obtained results are considered in the framework of the unified kinetic approach to domain structure evolution based on the analogy with first-order phase transformation. This article is part of the theme issue ‘From atomistic interfaces to dendritic patterns’. © 2018 The Author(s) Published by the Royal Society. All rights reserved.14-12-00826Data accessibility. This article has no additional data. Authors’ contributions. V.Ya.S. and A.R.A. wrote this in a joint effort. Competing interests. We declare we have no competing interests. Funding. The authors acknowledge support by the Russian Scientific Foundation (grant no. 14-12-00826). Acknowledgements. It is a pleasure to acknowledge the helpful discussions with A.L. Korzhenevskii and E.L. Rumyantsev. The equipment of the Ural Center for Shared Use ‘Modern nanotechnology’ UrFU was used

Field induced evolution of regular and random 2D domain structures and shape of isolated domains in LiNbO₃ and LiTaO₃

The shapes of isolated domains produced by application of the uniform external electric field in different experimental conditions were investigated experimentally in single crystalline lithium niobate LiNbO3 and lithium tantalate LiTaO3. The study of the domain kinetics by computer simulation and experimentally by polarization reversal of the model structure using two-dimensional regular electrode pattern confirms applicability of the kinetic approach to explanation of the experimentally observed evolution of the domain shape and geometry of the domain structure. It has been shown that the fast domain walls strictly oriented along X directions appear after domain merging

Domain shape in uniaxial ferroelectrics

The variety of domains shapes appeared in uniaxial ferroelectrics will be presented, classified and described systematically. The obtained experimental results will be discussed using unified kinetic approach based on the analogy between domain structure evolution and growth of new phase during first-order phase transformations.The equipment of the Ural Center for Shared Use "Modern nanotechnology" UrFU was used. The research was made possible in part by the Ministry of Education and Science of the Russian Federation (state task 3.4993.2017/6.7)

Study of ferroelectric domain structure by scanning probe microscopy

Будет систематически изложено каким образом различные методы сканирующей зондовой микроскопии используются для визуализации сегнетоэлектрических доменов с высоким пространственным разрешением, исследования доменной структуры, локального переключения и создания микро- и нанодоменных конфигураций.Application of various methods of the scanning probe microscopy for visualization of the ferroelectric domains with high spatial resolution, investigation of the domain structure, local switching and creation of the micro- and nanodomain patterns will be presented systematically.Работа выполнена с использованием оборудования УЦКП «Современные нанотехнологии» УрФУ