The charge distribution and spillover of oxygen atoms in nanostructured CeO2-In2O3 systems have been studied. The interaction of nanoobjects (nanoparticles or nanoclusters) i.e. the spillover of oxygen atoms from catalytically active CeO2 nanoclusters to In2O3 nanoparticles, results in an increase in the inhomogeneity of the radial electron density distribution in the nanoparticles. This in turn increases the resistance of the CeO2-In2O3 system in air relative to pure In2O3. It is shown here that the spillover of oxygen atoms in the two-component system (CeO2-In2O3) causes a shift of the maximum in the temperature dependence of the sensor response to hydrogen towards lower temperatures and a significant enhancement of the sensor response compared to one-component system (In2O3). The theoretical model developed agrees well with the published experimental data on the sensor response in In2O3 and CeO2-In2O3 systems.

This study discusses the conditions for the occurrence of two-dimensional superconductivity under the action of an electric field on an La 2 – x Sr x CuO 4 plate at a temperature lower than the maximum temperature of the superconducting transition, but when the concentration of charge carriers falls outside the superconductivity range. The study is carried out for a lanthanum-strontium cuprate plate at various hole concentrations, as well as temperature, and potential differences. A quasi-two-dimensional superconducting layer arises near the surface of the plate. The thickness of the superconducting layer is several angstroms and independent of the field strength in the range investigated. The thickness depends only on the concentration of holes and temperature. In addition, the distance of the superconducting layer from the edge of the plate is found to be a function of all three factors. The conditions used for conducting the experiment are also formulated.

Показано, что при воздействии электрического поля на пластинку высокотемпературного сверхпроводника при определенных условиях может возникнуть квазидвумерная сверхпроводимость. Это происходит, если в отсутствие электрического поля при температуре меньше максимальной температуры сверхпроводящего перехода концентрация носителей в пластине находится вне области существования сверхпроводимости. Изучение проведено для пластины лантан-стронциевого купрата при различных концентрациях дырок, температурах и разностях потенциалов. Оказалось, что квазидвумерный сверхпроводящий слой возникает вблизи поверхности пластины. Толщина сверхпроводящего слоя составляет несколько ангстрем и в исследованном диапазоне не зависит от величины поля. Его толщина зависит лишь от концентрации дырок и температуры. В то же время расстояние сверхпроводящего слоя от края пластины является функцией всех трех факторов. Сформулированы условия проведения эксперимента.

This paper deals with the mathematical modeling of the electronic structure of semiconductor particles. Mathematically, the task is reduced to a joint solution of the problem of free energy minimization and the set of chemical kinetic equations describing the processes at the surface of a nanoparticle. The numerical modeling of the sensor effect is carried out in two steps. First, the number of charged oxygen atoms on the surface of the nanoparticle NO− is determined. This value is found by solving a system of nonlinear algebraic equations, where the unknowns are the stationary points of this system describing the processes on the surface of a nanoparticle. The specific form of such equations is determined by the type of nanoparticles and the mechanism of chemical reactions on the surface. The second step is to calculate the electron density inside the nanoparticle (nc(r)), which gives the minimum free energy. Mathematically, this second step reduces to solving a boundary value problem for a nonlinear integro-differential equation. The calculation results are compared with experimental data on the sensor effect.

A model is built of the sensory process in sensors based on CeO 2 –In 2 O 3 nanocomposites. It is shown there is an increase in the response to hydrogen and a shift in the maximum of the sensory curve to lower temperatures with respect to the single system In 2 O 3 . It is established that the obtained results correspond to experimental data in the literature.

Abstract The theory of occurrence of superconductivity in the plate of high-temperature superconductor under electric field vertical to it, when the carrier concentration lies outside of the region of existence of superconductivity at the temperature T < $$T_{{\text{c}}}^{{\max }}$$ , was developed. The calculation was carried out for the layer of lanthanum strontium cuprate under the fields of 10^–1 V/nm ≥ E ≥ 10^–2 V/nm at various temperatures and hole concentrations. It was demonstrated that the quasi-two-dimensional superconducting layer of several Angstrom in thickness occurs near surface of the plate, moreover thickness of this layer does not depend on magnitude of the field, and depends only on temperature and on hole concentration.

The study investigates the possible origin of electric field effect on the rate of chemical reactions. The geometry of the considered problem mirrors the shape of surface roughness elements as well as the tip of a scanning tunneling microscope (STM) used to study the peculiarities of chemical reaction in an external electrostatic field. The results show that the actual field near truncated cone acting on the chemical system significantly exceeds the average external field. It is shown that in the calculation of the effect of electric field on the rate of chemical reactions, the increase in the electric field near nanoscale protrusions of the metal surface, in particular, near the STM needle, should be taken into account. These results are used to study the Diels-Alder reaction under the influence of electric field.

The theory of occurrence of superconductivity in the plate of high-temperature superconductor under electric field vertical to it, when the carrier concentration lies outside of the region of existence of superconductivity at the temperature T < $$T_{{\text{c}}}^{{\max }}$$, was developed. The calculation was carried out for the layer of lanthanum strontium cuprate under the fields of 10–1 V/nm ≥ E ≥ 10–2 V/nm at various temperatures and hole concentrations. It was demonstrated that the quasi-two-dimensional superconducting layer of several Angstrom in thickness occurs near surface of the plate, moreover thickness of this layer does not depend on magnitude of the field, and depends only on temperature and on hole concentration.

The electric field and charge distributions in a nanosized truncated metal cone in a strong electric field have been found. The geometry of the problem corresponds to surface roughness elements and a scanning tunneling microscope tip. The electron density along the cone axis is shown to change dramatically, by tens of percent. The field penetrates deep into the metal tip to distances of the order of a nanometer. The position of the Fermi level near the upper base of the cone changes noticeably. The barrier through which the electrons are tunneled upon entry into or exit from the tip is shown to be asymmetric and to depend on the sign of the external electric field.

The theory is developed of sensory response to reducing gases of nanostructured semiconductor oxides such as In2O3 with large concentration of electrons in the conduction band. The charge distribution in nanoparticles is determined by the functional relationship between the density of negative and positive charges inside the nanoparticles and electrons on the surface. The capture of conduction electrons by adsorbed oxygen atoms causes redistribution of electrons in the nanoparticles, thereby decreasing the near-surface electron density and the conductivity of the system. Thus, there is a functional relationship between negative charge on the surface and charge structure inside the nanoparticle, which has to be considered. The conditions for the association-dissociation reactions of oxygen molecules on the surface also change. On adsorption of a reducing gas, the O- ions react with the gas molecules and the electrons are released into the volume of the nanoparticles. The conductivity of the system thereby increases, which constitutes the sensory effect. The radial distributions of the conduction electrons and electrostatic potential in a nanoparticle are here calculated as a function of the hydrogen concentration in the ambient air. A kinetic scheme is developed of chemical reactions corresponding to the above sensory mechanism, and the associated equations are solved. As a result, the theoretical functional relationships of sensitivity to temperature and hydrogen concentration are established. The theoretical results are in good agreement with the experimental data.

A theory of sensor response on reducing gases of nanoscale-structured semiconducting oxides with the high concentration of conduction-band electrons has been developed (modeled on In2O3). The distribution of charges in nanoparticles is determined by the functional relationship of the density of negative and positive charges in nanoparticles and electrons on their surface. The capture of conduction electrons by adsorbed oxygen atoms causes electron redistribution in nanoparticles, such that the near-surface density of electrons and the conductivity of the system decrease. In this case, the conditions of the association and dissociation of oxygen molecules on the surface also change. During the adsorption of reducing gases (H2, CO), atomic oxygen ions react with them and electrons are released that enter bulk nanoparticles. The conductivity of the system increases, which corresponds to the sensor effect. A kinetic scheme of chemical reactions, which corresponds to the that described above, has been plotted and corresponding equations were solved. As a result, theoretical dependences of the sensitivity of sensor on the temperature and pressure of hydrogen were found, which agree well with experimental curves at qualitative and quantitative level.

The dependence of a sensor’s response to hydrogen on the temperature and hydrogen pressure in an indium oxide nanostructured film is measured. A theory of sensor’s response to reducing gases in nanostructured semiconducting oxides with high concentrations of electrons in the conduction band is developed (using the example of In2O3). It is shown that the capture of conduction electrons by adsorbed oxygen redistributes the electrons in nanoparticles and reduces the surface electron density and the conductivity of a system; the conductivity is proportional to the electron density in nanoparticle contacts, i.e., to the surface electron density. It is found that atomic oxygen ions react with reducing gases (H2, CO) during adsorption of the latter: electrons are released and enter the volumes of nanoparticles; the conductivity of the system grows, creating the sensory effect. Using a model developed earlier to describe the distribution of conduction electrons in a semiconductor nanoparticle, a kinetic scheme corresponding to the above scenario is built and corresponding equations are solved. As a result, a theoretical dependence of a sensor’s sensitivity to temperature is found that describes the experimental data well.

This paper presents a joint experimental and theoretical investigation of sensor response of nanostructured In2O3 semiconductor thin films containing a large concentration of conduction electrons. The capture of the conduction electrons by oxygen adsorbates from air causes redistribution of the electrons inside the nanoparticles, resulting in reduction of the subsurface electron density, and the drop of the conductivity of nanoparticle thin films. When CO and H-2 reduced gas analytes are introduced to the system, their reaction with previously adsorbed negative atomic oxygen ions O- releases electrons back to the nanoparticles, producing a noticeable increase of thin-film conductivity, which constitutes the sensor effect. This work presents a kinetic model of such processes, which allows us to a quantitative description of the sensor effect including dependence of sensor sensitivity on temperature. Concurrently, experiments are performed to quantify the sensor response by nanostructured In2O3 thin film as a function of temperature and hydrogen concentration upon addition of hydrogen gas to the gas medium. The measured response is described well by the theoretical model developed in this work.

Обсуждена взаимосвязь эмпирических параметров известной формулы Гавриляка–Негами с физическими характеристиками металлсодержащих наноструктурированных композитов. Рассмотрение проводится на основе нефеноменологической теории комплексной диэлектрической проницаемости указанных материалов. Оказалось, что абсолютные величины и температурная зависимость эмпирических параметров во многом зависят от энергии электронов в ловушках, расположенных вокруг металлических наночастиц. При этом, если частотная зависимость диэлектрической проницаемости в области максимумов неплохо описывается эмпирической формулой, то с интерпретацией температурной зависимости дело обстоит гораздо хуже, и придавать эмпирическим параметрам какой-либо физический смысл не стоит.

The relationship between the empirical parameters of the Havriliak–Negami formula with the physical characteristics of metal nanostructured composites is discussed. The analysis is based on a non-phenomenological theory of the complex permittivity of these materials. It turns out that the absolute values and temperature dependence of the empirical parameters are largely dependent on the energy of the electrons in traps located around metal nanoparticles. While the frequency dependence of the permittivity near the maximum is closely described by the empirical formula, the interpretation of the temperature dependence encounters serious difficulties, with the empirical parameters having no physical sense.

We develop a theory that allows considering and describing the development of multiparticle correlations in paramagnetic spin systems. We show that in crystals with many equivalent nearest neighbors around a spin in a lattice, an infinite system (of size ∼ 1023) of coupled differential equations for time correlation functions describing multiparticle correlations is reducible to the diffusion equation with an imaginary diffusion coefficient. The equation can be solved analytically in the lowest-order approximation of the theory. The equation obtained in the next approximation must be solved numerically because a discontinuity of the diffusion coefficient appears. The obtained results agree well with experimental data. The observed mutual similarity of the calculated time correlation functions and several other characteristic features appearing in the spin system dynamics are consequences of the development of dynamical chaos.

The previously developed theory of sensor response is validated by detailed comparison with experiment. For this purpose, new experiments are performed to investigate the sensitivity of semiconductor tin dioxide (SnO2) nanostructured thin films with average nanoparticle diameter approximate to 120 nm as a function of temperature and concentration of analyte hydrogen gas. Concurrently, the sensor properties are calculated at experimental conditions by taking into account the increase of surface chemical reactions with temperature as well as subsequent dominance of desorption over adsorption processes at high temperatures. Comparative analysis of temperature and nanoparticle size dependence of sensor response is also performed using experimental data from other groups. Qualitative agreement between experiment and theory is achieved.