Distribution function of the random field and polar properties of the relaxor ferroelectric films

The model for calculation of relaxor ferroelectrics thin films properties is proposed. The basis of the model is the theory of random field. This field is originated from the chemical disorder allowing for influence of the film surfaces, which destroys the polar long-range order and transform it into mixed state of ferroelectric glass (FG) or dipole glass (DG). The spatial profiles and averaged over coordinate inside the film values of properties of relaxor ferroelectric film were calculated with the random field distribution function. As an example the dependence of the order parameter on film thickness, temperature and distribution function characteristics was obtained. The critical thickness and temperature of the size-driven phase transition from FG to DG state as a function of the film and distribution function characteristics were calculated.Comment: 12 pages, 8 figure

Kostant--Kumar polynomials and tangent cones to Schubert varieties for involutions in AnA_n, F4F_4 and G2G_2

Let $G$ be a reductive complex algebraic group, $T$ a maximal torus of $G$, $B$ a Borel subgroup of $G$ containing $T$, $\Phi$ the root system of $G$ w.r.t. $T$, $W$ the Weyl group of $\Phi$. Denote by \Fo = G/B the flag variety, by $X_w$ the Schubert subvariety of \Fo associated with an element $w\in W$, and by $C_w$ the tangent cone to $X_w$ at the point $p = eB$. Then $C_w$ is a subscheme of the tangent space T_pX_w\subseteq T_p\Fo. Suppose $w$, $w'$ are distinct involutions in $W$. Using the so-called Kostant--Kumar polynomials, we show that if every irreducible component of $\Phi$ is of type $A_n$, $F_4$ or $G_2$, then $C_w$ and $C_{w'}$ do not coincide.Comment: 15 page

Theory of the size effect of the properties of the relaxor ferroelectric films

For the first time we proposed the model for the calculations of the relaxor ferroelectrics films properties in the framework of the random field theory. We took into account the misfit strain between film and substrate as well as surface piezoelectric effect that causes built-in electric field in the strained films. In the statistical theory framework we calculated random field distribution function with the electric dipoles and monopoles as the field sources. It was shown that with thickness decrease the mean field decreases, while the width of the distribution function increases. This leads to the additional smearing of the phase transition in the films in comparison to the bulk relaxors. As an example the dependence of the order parameter and dielectric susceptibility on the film thickness, temperature and random fields distribution function parameters was obtained. For free standing film the existence of critical thickness of relaxor state transformation into glassy state was predicted. Contrary to this the appearance of misfit strain induced ferroelectric phase appeared to be possible for some pairs film-substrate. We have shown that susceptibility temperature maximum shift with frequency in relaxor ferroelectric thin films obeys Vogel-Fulcher law with parameters dependent on film thickness. For the first time the analytical dependences of freezing temperature decreases and activation energy on the thickness was obtained, namely freezing temperature decreases and activation energy increases with film thickness decrease. Obtained results quantitatively agree with the available experimental data for PbMg1/3Nb2/3O3 relaxor thin films.Comment: 18 pages, 6 figure

Surface and size effect on fluctuations correlation in nanoparticles with long-range order

Surface and size effect on the order parameter fluctuations and critical phenomena in the intensively studied 3D-confined nanosized systems with long-range order was not considered theoretically, while the calculations for bulk samples and thick films were performed long ago. Since widely used magnetic resonance, diffraction and scattering methods collect information about both macro- and nanosystems via the structural factors, which are directly related with fluctuations correlator, analytical expressions for the correlation function of the order parameter fluctuations seem extremely necessary for quantitative analyses of the experimental data broad spectrum. In the letter we solve the vital problem within Landau-Ginzburg-Devonshire phenomenological approach for the particles of arbitrary shape and consider concrete examples of the spherical and cylindrical ferroic nanoparticles. Allowing for the strong surface energy contribution, analytical expressions derived for Ornstein-Zernike correlator of the long-range order parameter fluctuations in 3D-confined system, dynamic generalized susceptibility, relaxation times and correlation radii discrete spectrum are principally different from those known for bulk system. Besides the great importance of the fluctuations correlation function for the analyses of scattering and magnetic resonance experimental spectra, proposed expression for fluctuations strength defines the fundamental limit of phenomenological theory applicability for 3D-confined nanosystems.Comment: 15 pages, 2 figures, 1 appendi

On Lagrange Theory of Shells of Revolution

The new linear theory of elastic shells is presented in this paper. This theory is free from various logical imperfections, that may be found in the approaches of earlier researchers. On the base of this theory the equations of shells of revolution are built. The equations of cylindrical shell are compared by a number of properties with the equations of other researchers and with elasticity equations of 3-dimensional tube. Important quality decisions are stated.Comment: 19 pages, 4 figure

Theoretical Description of Ferroelectric and Pyroelectric Hysteresis in the Disordered Ferroelectric-Semiconductor Films

We have modified Landau-Khalatnikov approach and shown that both the polar lattice and the screened charged defects determine the response of disordered ferroelectric-semiconductors. This system exhibits the spatially inhomogeneous switching under the external field while Landau-Khalatnikov model describes homogeneous switching with the sharp pyroelectric coefficient peak near the thermodynamic coercive field value. Our model gives more realistic pyroelectric hysteresis loop shape without any peaks near the coercive field and describes both qualitatively and quantitatively typical Pb(Zr,Ti)O_3 and (Sr,Ba)Nb_2O_6 films pyroelectric hysteresis loops.Comment: 25 pages, 7 figure

Parallel generator of qq-valued pseudorandom sequences based on arithmetic polynomials

A new method for parallel generation of $q$-valued pseudorandom sequence based on the presentation of systems generating logical formulae by means of arithmetic polynomials is proposed. Fragment consisting of $k$-elements of $q$-valued pseudorandom sequence may be obtained by means of single calculation of a single recursion numerical formula. It is mentioned that the method of the "arithmetization" of generation may be used and further developed in order to protect the encryption gears from cryptographic onset, resulting in the initiating of mass hardware failures. The achieved results may be widely applied to the realization of perspective high-performance cryptographic facilities for information protection.Comment: 8 pages, 3 figure

Ballistic conductivity of graphene channel with p-n junction on ferroelectric domain wall

We study the impact of the ferroelectric domain wall on the ballistic conductance of the single-layer graphene channel in the heterostructure graphene / physical gap / ferroelectric film using Wentzel-Kramers-Brillouin approximation. Both self-consistent numerical modeling of the electric field and space charge dynamics in the heterostructure and approximate analytical theory show that the domain wall contact with the surface creates p-n junction in graphene channel. We calculated that the carriers' concentration induced in graphene by uncompensated ferroelectric dipoles originated from the spontaneous polarization abrupt near the surface can reach the values of 1019 m-2 order, which is in two orders higher than it can be obtained for the gate doped graphene on non-ferroelectric substrates. Therefore we predict that graphene channel with the p-n junction caused by ferroelectric domain wall would be characterized by rather high ballistic conductivity.Comment: 22 pages, 4 figures, and a Supplement with 2 figures and 1 tabl

Hadron Probing of the Deuteron Structure at Short Distances in Deuteron Breakup Reactions

We discuss deuteron $A(d,p)X$ breakup and cumulative pion production $A(d,\pi)X$ in the framework of constituent quark model of the deuteron. We demonstrate that consideration of the Pauli principle at the quark level, as well as multiple scattering, affect drastically cross section and polarization observables of these reactions and provide good description of the experimental data.Comment: Talk given at XVI European Conference on Few-Body Problems in Physics; 4 Latex pages + 5 PostScript figures. A few misprints are correcte

Appearance of ferroelectricity in thin films of incipient ferroelectric

The consideration of size-induced ferroelectric-paraelectric phase transition for conventional and incipient ferroelectrics thin films with perovskite structure was carried out in phenomenological theory framework of Ginsburg-Landau-Devonshire. The more general form of surface free energy expansion that includes intrinsic surface stress tensor, surface piezoelectric effect and electrostriction as well as quadratic and quartic powers of surface polarization has been considered. The analytical expressions for thickness dependence of transition temperature was derived both for the conventional and incipient ferroelectrics. It was shown that although there is no ferroelectricity in the bulk incipient ferroelectrics it appears in thin film for the negative extrapolation length that is realized e.g. at positive surface stress coefficient and negative or zero misfit strain. In our consideration we came to the conclusion about thickness induced ferroelectricity in incipient ferroelectrics KTaO3 at room temperature for the thin enough films. The similar surface effects can influence strongly on the phase transitions in the thin films of another incipient ferroelectrics, SrTiO3.Comment: 19 pages, 5 figures, 2 appendices, to be submitted to Physica Status Solidi, two new figures are added to this version, misprints are correcte