Кафедра "Прикладна математика" ДІІТ

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http://crust.ust.edu.ua/handle/123456789/691
ENG: Department "Applied Mathematics"

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Browsing Кафедра "Прикладна математика" ДІІТ by Author "Shtapenko, Eduard Ph."

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    Abnormal Effect of Changing the Wetting Angle in Non-Equilibrium Melt–Solid Metal Systems
    (G. V. Kurdyumov Institute for Metal Physics of the N.A.S. of Ukraine, Kyiv, 2024) Shtapenko, Eduard Ph.; Syrovatko, Yuliya V.
    ENG: The paper deals with the temperature dependence of the contact angle of wetting of a steel substrate with a liquid tin. The experiment shows that the wetting angle is decreased as the temperature rose, and the wettability of this system is improved. However, with the further increase in temperature, the contact angle is increased again that is an abnormal phenomenon. To explain this phenomenon and the process of contact-angle formation in general, we propose the quantum mechanical model based on the Wentzel-Kramers-Brillouin (WKB) conception. In this case, interaction of the melt ions with the substrate atoms is considered indirectly through the formation of a potential barrier with the linear dimensions determined by both the ratio of masses of the atoms of interacting metals and the temperature. From the WKB standpoint, at low temperatures, when the kinetic energy of a generalized particle with the reduced mass is less than the potential barrier, the wave function decays rapidly and, accordingly, the contact angle does not actually change. Quantitative and qualitative changes appear, when the kinetic energy of particles with the reduced mass exceeds the positive barrier values because of increase in temperature. Following the WKB conception, passage or reflection of a particle with the reduced mass over the barrier is determined by the integer or half-integer ratio of the de Broglie wavelength and linear dimensions of the potential barrier. Therefore, qualitative changes in the system, i.e., the wetting threshold and abnormal increase in the contact angle, are described by the processes associated with passage or reflection of a particle with the reduced mass over the barrier. Experimental and theoretical curves of dependences of both the contact angle and the work of adhesion versus temperature show similar dynamics.
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    Determination of Entropy and Debye Temperature of the Phases of Al-Cu-Co and Al-Ni-Co Decagonal Quasicrystals at the Normal and High Temperatures
    (OICC Press, Oxford, UK; Islamic Azad University, Tehran, Iran, 2025) Syrovatko, Yuliya V.; Shtapenko, Eduard Ph.; Syrovatko, Volodymyr
    ENG: This paper deals with determination of the entropy of quasicrystalline phases of Al-Cu-Co and Al-Ni-Co alloys by the information-and-statistical method at the temperature of 300 К. Scanned digital images of quasicrystals were processed with the use of this method. Statistical data of the multicomponent structure were divided into separate components of the normal distribution of parameters corresponding to certain phases. We calculated the Gaussian parameters on the basis that dependence of the logarithmic representation of the normal distribution function took the form of a quadratic function. It allowed us to find the mean-square deviation and to calculate the entropy of quasicrystalline phases at 300 К. The resulting values were further used to calculate the Debye temperature of the phases. Decagonal quasicrystals have anisotropic structure. It is assumed that anisotropy manifests itself in the difference of the dispersion laws in the xy plane and in the direction of the z axis, which is described by the model of anisotropic crystals. Using this model, we have found an expression describing the dependence of the entropy on the temperature and Debye temperature of the phases. From here, we calculated the Debye temperature of the phases. Next, using the Debye temperature values, we calculated the entropy of phases at higher temperatures. Therefore, with the use of the presented calculation methods, it is possible to determine the Debye temperature and the entropy of quasicrystalline phases that was done in our study for Al–Cu–Co and Al–Ni–Co quasicrystals.
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    Formation of Contact Interaction Zones during Infiltration of Composite Materials Depending on Binder Composition
    (Chuiko Institute of Surface Chemistry of NAS of Ukraine, Kyiv, 2025) Shtapenko, Eduard Ph.; Syrovatko, Yuliya V.; Levkovich, O. O.
    ENG: In the production of macro-heterogeneous composite materials with a metal matrix by the oven infiltration method, it is necessary to control the contact interaction processes occurring at the filler and binder interfaces. The width of the resulting contact interaction zones at the interfaces is an indicator of intensity of these processes. The intensity of contact interaction processes depends on many factors, including the binder alloy composition. The paper examines the effect of binder alloying components on the change in the surface tension of the binder alloy, and, so on the intensity of contact interaction processes occurring at the interfaces during infiltration of composite materials. Calculations of changes in the surface tension of iron-based binder upon alloying with C, P, B and Mo are presented using the formalism of the electrochemical interaction of regular solutions. The iron melt was considered as a solvent, while C, B, P and Mo were considered as dissolved components. It was taken into account that formation of an interface resulted in the appearance of unbalanced charges and energetic influence on the ions distributed in the melt. Adsorption of dissolved components on the filler surface decreased the surface tension of the binder. When estimating the thickness of the layer of excess ion concentration at the surface, we assumed that the binder surface tension depended on the number of adsorbed ions. Our calculations were expressed in accordance with the concept of mole equivalent. It is found that alloying of the Fe–C–B–P binder with Mo causes a decrease in the difference between the surface tension values of the alloyed binder and pure iron melt by 28.5 %, and, accordingly, 22.6 % reduction of thickness of the layer of excess ion concentration. The results obtained were compared with the results of experimental works with regard to composite materials with W–C fillers and iron binders alloyed with C, B, P, and Mo. It is determined that when the Fe–C–B–P binder is alloyed with Mo the width of contact interaction zones in the composite materials decreases by 15–20 %. Therefore, the results of calculations using the proposed method for changing the thickness of the layer of excess ions at the interfaces when alloying the binder correlate with the experimental data for changes in the width of contact interaction zones of composite materials.
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    Quantum-Mechanical Methodology for Determining the Temperature Dependence of Contact Angle in Melt–Solid Metal Systems
    (Oles Honchar Dnipro National University, Dnipro, 2024) Shtapenko, Eduard Ph.; Syrovatko, Yuliya V.; Voronkov, Eugene O. ; Mikhailova, Tetiana F.
    ENG: Aim. In order to determine the composite materials’ manufacturing process parameters, it is necessary to evaluate the stability of their structural components and determine the contact angle of wetting of the filler with the molten binder at the infiltration temperature. The development of a theoretical method for determining the dependence of the contact angle of wetting on temperature in melt – solid metal systems makes it possible to reduce the volume of experimental studies. Methods. The paper presents a quantum mechanical methodology for calculating the binding energy of interacting substances, as well as an experimental study of the dependence of the contact angle on temperature for tin – steel systems. The methodology is based on the calculation of the binding energy between atoms of interacting substances using density functional theory. Results. The calculations show an anomalous behavior of contact angle values for the tin–steel system with increasing temperatures. It means that, when the temperature increases, the values of the contact angle initially become lower, and later, in the temperature range of 450-510 °C, an increase in the contact angle is observed. The obtained theoretical and experimental data correlate well with each other. Conclusions. The appearance of extreme regions in the experimental and theoretical temperature dependences is associated with the thermal expansion of interatomic distances in the crystal lattice. The obtained theoretical and experimental data correlate well with each other and base on the thermal expansion of interatomic distances in the crystal lattice.