MORPHOLOGY AND COMPOSITION OF THE INTERFACE BOUNDARY OF SODIUM CHLORIDE SINGLE CRYSTALS WITH LEAD

Методами электронной микроскопии и рентгеноспектрального анализа исследована межфазная граница раздела жидкого свинца с хлоридом натрия после охлаждения и разрыва контакта. На поверхностях разрыва образцов обнаружено накопление поверхностно-активных примесей, содержащихся как объеме свинца, так и в хлориде натрия. Как показывают результаты рентгеноспектрального анализа, содержание примесей на поверхности подложки хлорида натрия превышает объемное содержание на несколько порядков. На поверхности свинца также наблюдается значительное накопление примесей кремния и индия. В исследованных образцах наблюдается анизотропия растекания жидкого свинца по поверхности монокристаллов хлорида натрия. Линия разрыва, затвердевшей капли свинца с монокристаллической поверхностью хлорида натрия ориентации (110), заметно отклоняются от круга. Кроме того, на электронно-микроскопическом изображении межфазной поверхности свинца после отрыва от подложки хлорида натрия ориентации (100), наблюдаются участки в виде «сигары», в которых обнаружено накопление примесей. Данные участки имеют ориентации, совпадающие с кристаллографическим направлением подложки. The interface between liquid lead and sodium chloride after cooling and breaking the contact was investigated by the electron microscopy and X-ray spectral analysis. Accumulation of surface-active impurities, contained both in the bulk of lead and in sodium chloride was found on the fracture surface of the samples. As shown by the results of the X-ray diffraction analysis, the content of impurities on the surface of the sodium chloride substrate exceeds the bulk content by several orders of magnitude. A significant accumulation of silicon and indium impurities is also observed on the lead surface. Anisotropy of spreading of liquid lead over the surface of sodium chloride monocrystals is observed in the studied samples. The separation line of a solidified lead droplet on the surface of sodium chloride with orientation (110) deviates noticeably from a circle. In addition, on the electron microscopic image of the lead interface after detachment from the substrate of sodium chloride of orientation (110), there are areas in the form of a «cigar», in which the accumulation of impurities was detected. The orientation of these regions coincides with the crystallographic direction of the substrate.

An Optimal Fourth-Order Finite Difference Scheme for the Helmholtz Equation Based on the Technique of Matched Interface Boundary

In this paper, a new optimal fourth-order 21-point finite difference scheme is proposed to solve the 2D Helmholtz equation numerically, with the technique of matched interface boundary (MIB) utilized to treat boundary problems. For the approximation of Laplacian, two sets of fourth-order difference schemes are derived firstly based on the Taylor formula, with a total of 21 grid points involved. Then, a weighted combination of the two schemes is employed in order to reduce the numerical dispersion, and the weights are determined by minimizing the dispersion. Similarly, for the discretization of the zeroth-order derivative term, a weighted average of all the 21 points is implemented to obtain the fourth-order accuracy. The new scheme is noncompact; hence, it encounters great difficulties in dealing with the boundary conditions, which is crucial to the order of convergence. To tackle this issue, the matched interface boundary (MIB) method is employed and developed, which is originally used to accommodate free edges in the discrete singular convolution analysis. Convergence analysis and dispersion analysis are performed. Numerical examples are given for various boundary conditions, which show that new scheme delivers a fourth order of accuracy and is efficient in reducing the numerical dispersion as well.

Structural stability for the Boussinesq equations interfacing with Darcy equations in a bounded domain

A priori bounds were derived for the flow in a bounded domain for the viscous-porous interfacing fluids. We assumed that the viscous fluid was slow in $\Omega _{1}$ Ω 1 , which was governed by the Boussinesq equations. For a porous medium in $\Omega _{2}$ Ω 2 , we supposed that the flow satisfied the Darcy equations. With the aid of these a priori bounds we were able to demonstrate the result of the continuous dependence type for the Boussinesq coefficient λ. Following the method of a first-order differential inequality, we can further obtain the result that the solution depends continuously on the interface boundary coefficient α. These results showed that the structural stability is valid for the interfacing problem.

О токовой зависимости эффективности инжекции и относительном вкладе скорости эмиссии и внутренних оптических потерь в насыщение ватт-амперной характеристики мощных импульсных лазеров (λ=1.06 мкм)

The results of numerical simulation of the current dependence of the injection efficiency in the active area of the laser based on separate confinement heterostructures are presented. The feature of the transfer of charge carriers through isotype N-n heterotransitions on the interface boundary of waveguide and active areas is shown. Using the classic dependencies of the Drude-Lorentz theory, the cross-section of electrons and holes for the GaAs waveguide was evaluated. The resulting values of σe= 1.05∙10-18 cm2 and σp= 1.55∙10-19 cm2 and current dependencies of the injection efficiency allowed to determine the root-cause reason for the pulse power saturation of semiconductor lasers. It has been established that saturation of power-current characteristics is dominated by holes escape from the active region to the waveguide and internal optical losses are lower confinement factors.

APPROXIMATE ANALYTICAL SOLUTION OF THE PROBLEM OF CONJUGATE HEAT TRANSFER BETWEEN THE BOUNDARY LAYER AND THE ANISOTROPIC STRIP

Optimization of technological processes in metallurgy related to transfer and use of heat energy makes more complicated demands for calculation of heat exchange. Therefore, the work, the approximate analytical method for solving the conjugate problems of viscous gas-dynamic boundary layer and thermal conductivity in the anisotropic strip, has been developed. The paper uses modern numerical methods for solving differential equations in partial derivative and analytic methods on the basis of an integral transform of Fourier and Laplace. Boundary equations have been solved analytically with certain simplifications, and the problem of anisotropic heat conduction has been solved analytically. The heat flows are determined analytically by the longitudinal variable at the interface boundary. It has been established that temperature increase of the external surface contributes to that all factors directly impacting on the magnitude of heat flows act towards their reduction. The analytical solution for the problem of thermal conductivity in the anisotropic strip with a general type of anisotropy when the heat flows from the boundary layer are determined at the boundaries is obtained. The conducted research for the temperature of external boundary and heat flow from gas to it demonstrates that with increasing the degree of longitudinal anisotropy the surface temperature of the strip downstream increases from increasing longitudinal heat conduction An original conjugation method using the continuous heat flows, and temperatures at the interface boundary is found. The numerical results for the heat flows and temperatures at the interface boundary have been obtained and analyzed.