Within the framework of the theory of thermodynamics, a method for determining the electro-optical coefficients is proposed. It is shown that for all ferroelectrics the symmetry of which admits a diagonal susceptibility, the ratio of some electro-optical coefficients is expressed in terms of the ratio of susceptibilities. For barium titanate, the dependence of the electrooptical coefficients on the electric field has been revealed and studied. It is shown that large values of the electro-optical coefficients of barium titanate are associated with a nonlinear dependence of the dielectric susceptibility on the electric field.

The electro-optic coefficients of ferroelectric materials were obtained by Landau thermodynamic theory. It is proved that if the permittivity tensor is diagonal, then some ratios of the electro-optical coefficients are equal to the ratios of its diagonal components. The dependence of electro-optic coefficients on the external electric field for single-crystal barium titanate was studied and discussed. It is shown that electro-optic coefficients are rather high for barium titanate due to a non-linear response of dielectric susceptibility to electric field strength.

The method of thermomigration of liquid zones based on aluminum makes it possible to create complex structures of closed channels with boundaries formed from p-n junctions in single-crystal silicon wafers. The channels are characterized by the uniformity of their properties, and the pn junctions are characterized by their sharpness. Such structures are used in high-current electronics, photovoltaics, and microelectromechanical converters. Volumetric deformation inside and outside the channel due to alloying of silicon with aluminum leads to the formation of mechanical stresses. The equilibrium shape of the channels formed at high temperatures is determined by the minimum elastic energy and depends on the material parameters and geometry of the structure. Within the framework of the linear theory of elasticity, the behavior of elastic energy during the formation of the structure of thermomigration channels at high temperatures doped with aluminum in a single-crystalline (001) cut disk was studied. The simulation was performed using the finite element method in the COMSOL Multiphysics mathematical package. The study was carried out for practically important structures in which the direction of the edges is oriented along the diagonal of the square. Only such structures do not have breaks during the process of thermomigration. Based on the calculation results, it was revealed that the minimum elastic energy corresponds to structures with different crystalline orientations inside the channel and outside it – in the main silicon matrix. The direction of the crystalline axes inside the channel, corresponding to the minimum elastic energy, is rotated by 45 degrees in the plane of the disk relative to the direction of the axes of the main matrix of the silicon crystal. In addition, calculations showed that with such a turn, the shape of the channels changes. The minimum elastic energy corresponds not to vertical structures, but to inclined ones. The angle of inclination of the pyramids depends on the width of the channels and the distance between them.

The electro-mechanical properties of a ferroelectric film of barium strontium titanate (BST) film located on a silicon substrate depend on applied external strain. A significant dependence is observed for concentrations close to values, where a phase transition for the ferroelectric film occurs. A model of single-crystal BST film near the phase transition under uniaxial strain is studied by the thermodynamic theory of phase transitions. The material properties of the film obtained by the model are used for numerical study of the excitation of Rayleigh’ acoustic waves on the surface of the film-substrate heterostructure. Shifting the extrema of S-parameters, characterizing the efficiency of excitation of surface acoustic waves, is shown under the applied strain. The change of S-parameters for the first three resonances determined principally by the geometry of the interdigital electrodes is presented. The largest shift of resonant frequency is observed in a case of the second resonance that corresponds to Sezava wave.

For single-walled carbon nanotubes (SWCNTs) with a length of 1-50 nm, the surface plasmon-polariton (SPP) resonance is within the terahertz frequency range; therefore, SWCNT lattices can be used to design frequency-selective surface (FSS). The numerical model of electromagnetic wave diffraction on a two-dimensional periodic SWCNT lattice can be described by an integro-differential equation of the second-order with respect to the surface current along SWCNT. The equation can be solved by the Bubnov-Galerkin method. Frequency dependence of reflecting and transmitting electromagnetic waves for FSSs near the SPP resonance are studied numerically. It is shown that the resonances are within the lower-frequency part of the terahertz range. Also, we estimate the relaxation frequency of an individual SWCNT and demonstrate the applicability of the Kubo formula for graphene conductivity to array of strips similar in size with SWCNTs under consideration.

The excitation of surface acoustic waves (SAWs) on the surface of the ferroelectric film [barium strontium titanate (BST)] located on the dielectric substrate (silicon) was studied theoretically. We found that the most effective SAW excitation takes place when spontaneous polarization occurs in the film plane and the wave propagates along the direction adjacent to the direction of the spontaneous polarization vector. Based on a nonlinear model of phase transitions in solid BST solutions, the dependency of the material constants of piezo-effect equations on the misfit strain with a fixed concentration was obtained numerically. The effect of various misfit strains on SAW characteristics was studied for the film located on single-crystal silicon. It was shown that the effectiveness of SAW excitation increases as the misfit strain nears the boundary of phase transition.

A method is proposed to control the properties of thin ferroelectric films under forced strain due to the differences in crystal lattice parameters and thermal expansion coefficient between the film and substrate materials. The control method is based on applying additional mechanical strain to the substrate. A single-crystal Ba $$_{x}$$ Sr $$_{1 -x}$$ TiO $$_{3}$$ film model is studied within the framework of phenomenological theory using the Landau potential. It is shown that additional uniaxial strain of the substrate in the Ba $$_{x}$$ Sr $$_{1-x}$$ TiO $$_{3}$$  film changes the material constants of the film. Abnormal change occurs at strains close to the values at which the phase state of the film changes. The generation of surface acoustic waves is studied. The modeling results indicate the possibility of controlling the excitation of surface acoustic waves in the film–silicon substrate heterostructure.

The possibility of the development of MEMS devices based on the tunable ferroelectric film Ba 0.8 Sr 0.2 O 3 properties under uniaxial deformation was studied theoretically. The thermodynamic model of the phase transitions for the film under uniaxial stress was constructed. The behavior of the material constants for the film in various phase states was investigated. The propagation properties of the surface acoustic wave (SAW) under the uniaxial stress were studied for the film located on the single-crystal silicon substrate. It was shown that the SAW resonance frequency changes within 3 MHz for the frequency of 274 MHz, and 9 MHz for the frequency of 512 MHz.

We investigated the epitaxial Bi4Ti3O12 (BTO) thin films with different thicknesses on a (0 0 1) MgO substrate with a Ba0.4Sr0.6TiO3 buffer layer (4 nm). The crystallographic axis [1 0 0] of Bi4Ti3O12 film is rotated on degrees relative to [1 0 0] MgO axis. When the thickness of Bi4Ti3O12 film is less than 40 nm, the unit cell of the film is compressed in the normal to the interface plane direction. In cases of large film thicknesses, the sign of strain changes and correspondingly the unit cell is stretched. Switched spontaneous polarization in the interface plane with 180 degrees domain structure occurs at 10 nm film thickness and increases with a thickness up to 55 C cm (2). Changes in the Raman spectra of the Bi4Ti3O12 films indicates to increase of monoclinic distortion of the film unit cell in comparison with the bulk unit cell. The anisotropy of in-plane dielectric properties and the effect of internal strain on dielectric properties for the Bi4Ti3O12 films are confirmed by the study of the dielectric characteristics of the films.

We study theoretically two-dimensionally periodic gratings of plasmonic strips on substrates which contain dielectric and plasmonic layers. The developed electrodynamic model is based on solving the vector integro-differential equation of diffraction by three-dimensional dielectric bodies by the Galerkin method. It is shown that at the resonant frequencies of the surface plasmon polariton, these structures absorb almost 100% of the energy of the incident radiation in a wide wavelength range. The use of nonmetal plasmonic materials makes it possible to create a wideband absorber of infrared waves.

The frequency dependence of scattering parameters of interdigital surface acoustic wave transducers placed on ferroelectric barium titanate (BaTiO3) epitaxial film in c-phase coated over magnesium oxide has been studied using the finite-element method (FEM) approach along with the perfectly matched layer (PML) technique. The interdigital transducer which has a comb-like structure with aluminum electrodes excites the mechanical wave. The distance between the fingers allows tuning the frequency properties of the wave propagation. The magnesium oxide is taken as the substrate. The two-dimensional model of two-port surface acoustic wave filter is created to calculate scattering parameters and to show how to design the fixture in COMSOL (TM). Some practical computational challenges of finite element modeling of SAW devices in COMSOL (TM) are shown. The effect of lattice misfit strain on acoustic properties of heterostructures of BaTiO3 epitaxial film in c-phase at room temperature is discussed in present article for two low-frequency surface acoustic resonances.

Piezoelectric effect equations have been derived by linearizing the nonlinear equations of state of a thin film existing in a paraelectric phase in the presence of an external electrical field (induced piezoelectric effect). The behavior of the piezoelectric and elastic constants of thin films of a solid barium–strontium titanate solution BST065 (x = 0.65) in a planar field at different misfit strain values has been studied numerically.

In the present work, the effect of grain size distribution on the diffraction profile shape is inspected via analysis of the mutual ratio of Lorentz and Gauss components in pseudo‐Voigt function which is used for simulating X‐ray profiles of nanoparticles. As established from the plotted dependences, the error in the average Pt nanoparticles size determination reaches 56% and the discrepancy between calculated Pt nanoparticle surface areas attains 60%. Furthermore, the determination error becomes greater with increasing the Lorentz contribution to pseudo‐Voigt function, or, in fact, with enlarging particle size distribution. The empirically found electrochemical surface area of Pt/C electrocatalyst is compared with that evaluated from XRD data using the Scherrer formula and particle size distribution data analysis.

Developing the novel electric field tunable, reconfigurable, adaptive and frequency-agile microwave devices with specific properties involves technological and scientific activities in the studying of material properties. Measurements of its properties could be a difficult and expensive issue, especially when it concerns thin-film ferroelectrics. Their electromechanical properties change significantly under applied DC bias field. The material coefficients of barium strontium titanate thin films are still unknown; therefore, it is expedient to carry out their calculations. In the present paper, the linear equations of piezoelectric effect have been written for thin barium strontium titanate films under DC bias electric field in paraelectric phase (induced piezoelectric effect) based on the grand potential of Landau theory of phase transitions. The dependence of material constants for thin films of Ba0.65Sr0.35TiO3 (BST65) on the applied planar field at different lattice misfit strains has been studied for this phase. All induced piezoelectric moduli show extreme behavior during field alteration. Elastic moduli show similar abnormal behavior. The alterations increase as misfit strain is approaching the critical value.

НЕКОТОРЫЕ ОСОБЕННОСТИ ПОВЕДЕНИЯ ПОВЕРХНОСТНЫХ АКУСТИЧЕСКИХ ВОЛН В ТОНКИХ ПЛЕНКАХ ТИТАНАТА БАРИЯ

The effect of a bias electric field on the material coefficients of Ba 0.8 Sr 0.2 O3 (BST08) thin films was studied. The material constants are derived from piezoelectric effect equations by the linearization of nonlinear phenomenological state equations. The numerical results are obtained for the case of BST08 film with a misfit strain value equal to −4×10 −3 located on a cubic substrate for the (001) cut plane in the electric field up to 5×10 7 V/m applied along [100] direction in the film plane. The electromechanical coupling coefficient k 11 reaches a maximum under applied electric field.