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No 5 (2025)
- Year: 2025
- Published: 15.10.2025
- Articles: 11
- URL: https://bakhtiniada.ru/0235-0106/issue/view/20600
Articles
Effect of Adsorption of Halogenide Ions on the Capacity of Iridium Electrode in Molten Salts
Abstract
The adsorption activity of the iridium electrode in molten sodium, potassium and cesium chlorides and bromides, sodium and potassium iodides was estimated from the dependence of the shape and position of the capacitance curve on the cation-anion composition of the electrolyte, the AC frequency and temperature. The capacitance curves have a complex shape with two main minima and a maximum between them in the entire studied ranges of temperature, frequency and electric polarization. In some cases, one or two additional minimа appear on the curves between the main minima. The position of both the minima and maxima of the capacitance depends on the radius of the salt cation and anion. The dependence of the position of the main maximum of the capacitance on the radius of the cation and anion is presented at T=1093 K in the AC frequency range of 3·100–1·104Hz. According to this approach, the potential of the capacitance maximum of a solid metal electrode in ionic melts with specifically adsorbing anions can be considered as the critical potential of the adsorption phase transition. The segment of the capacitance curve ΔEfrom the cathodic capacitance minimum, which corresponds to the classical minimum capacitance, to the capacitance maximum can be considered as a range of potentials in which the change in the properties of the double electric layer obey the Gouy-Chapman-Stern model. With a further shift from the critical potential to the positive direction, the electrostatic adsorption mechanism turns into chemical adsorption, with the transfer of part of the anions from the salt phase to the electrode and the formation of complex compounds. The value ofΔEcan help to estimate the effect of specific adsorption of halide ions on the shape of the capacitance curve.
421-429
Random two-dimensional ensembles of polygonal particles: densification and statistical-geometric properties
Abstract
This study investigates the densities and statistical-geometric characteristics of random packings of regular polygons (with 3 to 21 vertices) on a plane. The initial ensemble was generated using the random sequential adsorption (RSA) method. A densification algorithm for the packing is proposed, which is a modification of the Lubachevsky-Stillinger (LS) method. The final ensemble was obtained by gradually increasing the linear dimensions of two-dimensional particles while keeping the density of the square «box» fixed. The statistical-geometric characteristics and packing density of the final ensemble (for a given number of polygon vertices) were found to be practically independent of the number of particles (for a total number of particles on the order of 10⁴ or more). Data on pair correlation functions were obtained, and the evolution of these functions was analyzed across a wide range of packing densities. At packing densities (area fraction occupied by particles) exceeding 0.65–0.70, characteristic features emerge in these functions, indicating a structural transition analogous to the glass transition in a system of hard disks. Further densification leads to partial «crystallization», which (at densities above 0.80) is clearly visible both in visualized images of the ensemble itself and in the correlation function plots. Overall, the evolution of correlation functions for hard disks and polygons (especially those with more than 6 vertices) exhibits several common patterns. The results of this study are in good agreement with those obtained in other studies using fundamentally different densification algorithms (e.g., sedimentation under gravitational force). This suggests that different algorithms for generating random 2D ensembles generally lead to similar outcomes. It appears that the general structural properties of random two-dimensional systems of convex particles are well reproduced across different generation methods (including computational and «physical» modeling).
430-443
Dependence of liquid metals radiation on normalized entropy in the fifth period
Abstract
This study presents a universal approach for describing thermal radiation of molten fifth-period d-metals (yttrium, zirconium, niobium, molybdenum, rhodium, palladium) using dimensional analysis based on Buckingham’s π-theorem. The key achievement is the reduction of complex mathematical descriptions of radiant heat flux density to a single dimensionless variable – the ratio of molar entropy to the universal gas constant (S/R).Critically, this approach significantly simplifies the analysis of radiative characteristics in liquid metals.Furthermore, the proposed methodology demonstrates remarkableuniversalityandreproducibilityacross the entire group of studied elements. The methodology involves flux normalization at a fixed S/R = 14 value, corresponding to the characteristic entropy disorder level of these metal melts. To account for temperature-dependent density variations, a reduced radiation flux is introduced, compensating for melt density changes with temperature. The logarithm of the ratio between reduced radiation flux and individual scale flux (defined for each metal at S/R = 14) follows an exponential dependence. The resulting universal correlation shows excellent consistency (R² ≥ 0.98) across all period elements, confirming its statistical significance. Predicted values calculated using this correlation agree well with both experimental measurements and approximated data, showing mean deviations of ~4.3%. Notably, the normalized scale flux exhibits periodic variations with increasing atomic number, mirroring the behavior of surface tension at melting points. This suggests a common structural-energy origin for both radiative and surface properties of molten metals. The developed approach enables reliable prediction of liquid d-metals’ emissivity in the absence of experimental data and provides a foundation for modeling complex multicomponent metallic systems. These results hold significant implications for metallurgy, materials science, and thermal physics applications, including alloy development and high-temperature process optimization.
444-454
Electron absorption spectra of saturated chlorine solutions in melts of alkaline metal chlorides depending on temperature
Abstract
Electronic absorption spectra of saturated chlorine solutions in molten alkali metal chlorides were recorded in the range from the melting point of the salt to 1000°C. An SF-26 spectrophotometer converted for high-temperature measurements was used to record the spectra. The illuminator was separated from the main body and a silite high-temperature furnace with windows was placed between the illuminator and the monochromator. Quartz optical cells with a absorbing layer thickness of 0.8, 1.0 and 1.5 mm were used to conduct the experiments. The thinnest cuvette (0.8 mm) was used to record the spectrum of dissolved chlorine in molten cesium chloride, since the solubility of chlorine in it is maximum and, accordingly, the optical density of such a melt is also maximum. It was found that in all salts the absorption spectrum consists of a single broad absorption band with a maximum in the region of 26000–28000 cm-1. In the range of 13000–8000 cm-1 absorption is practically absent. With increasing temperature, as well as when passing from sodium chloride to cesium chloride, the absorption maximum shifts to the region of lower energies. The solubility of chlorine in molten salts increases with increasing temperature, which indicates the endothermicity of the dissolution process. The thermodynamic characteristics of this process were calculated based on the solubility values. The process of dissolution of Cl2 in molten alkali metal chlorides is characterized by a positive change in entropy and enthalpy. This indicates the dissolution of chlorine not in the form of simple Cl2 molecules, but rather the formation of their associates with ions of the salt medium. With increasing temperature and transition in the series of salt-solvents from NaCl to CsCl, the change in Gibbs energy shifts toward smaller (more negative) values, which corresponds to an increase in the solubility of chlorine in the same direction. And in the same direction, both the physical and chemical (formation of ions) components of the total solubility of the gas increase. A conclusion is made about the predominant chemical mechanism of chlorine dissolution in molten alkali metal chlorides.
455-466
Investigation of Saturated Vapor Pressure of K–Pb Melts
Abstract
The saturated vapor pressure of liquid lead alloys with alkali metals has been studied only for lead alloys with lithium and sodium. In [1], the saturated vapor pressure of lead-lithium alloys (0.05 < xLi < 0.95) was studied in combination with massspectrometric measurements at 700–900 K. Fischer and Johnson studied lead-sodiumalloys using the quasi-static method (0.15 < xNa < 0.90 at 753–1271 K) and the entrainment method (xNa = 0.1, 0.2, and 0.3 at1126 K) [2]. Based on the data on the vapor pressure of the Pb-Na system, thermodynamic calculations of the activity and activity coefficients of sodium vapor were performed, taking into account steam dimerization [3]. When measuring pressure, it is important to determine the temperature, because the vapor pressure depends on it logarithmically. In this work, the pressure of saturated vapors of K–Pb melts in the range of lead concentrations 0.10–0.64 mol at temperatures of 890–1227 K was studied by the static tensimetric method with exemplary platinum-platinum-rhodium thermocouples. It was found that for all the studied compositions, the vapor pressure increases with increasing temperature and decreases with increasing lead concentration in the melt. The dependences in the coordinates of the logarithm of pressure on the reverse temperature are linear in the temperature range 1040–1227 K. Two linear sections were found on the dependences of the logarithm of saturated vapor pressure on the molar fraction of lead in the melt (NPb) obtained at 1073 and 1123 K. With NPb up to 0.35, the slope angle tangent is –0.4762 at 1073 K and –0.5044 at 1073 K. At NPb above 0.36, the slope is –3.0813 and –3.2244 at lower and higher temperatures, respectively. A sharp increase in slope with a high lead content in the melt can be explained by the formation of KPb (K4Pb4) intermetallic solutions, which reduces the vapor pressure of the melt components.
467-475
MICROHETEROGENITY OF LIQUID STEEL 12CR18NI9TI
Abstract
The microheterogeneity of liquid steel of 12Cr18Ni9Ti grade, as a complex alloy, was understood as a local inhomogeneity in the elemental composition. Anomalous behavior in the temperature dependence of the kinematic viscosity and electrical resistivity of the melt was attributed to the presence of these microheterogeneity. Temperature dependences of the kinematic viscosities and electrical resistivities of 12Cr18Ni9Ti steel samples, in the liquid state, were measured at various stages of the technological cycle. Measurements were conducted in both heating and subsequent cooling modes, over a temperature range of 1400–1730°C. It was observed that the temperature dependencies of the kinematic viscosity obtained in heating and cooling modes coincided over the entire temperature range. However, a difference in the volume per structural unit of viscous flow was noted for all the studied samples. The minimum volume value of the viscous flow structural unit (υ) was obtained for a sample taken after the addition of ferromanganese and titanium. There was a discrepancy in the temperature dependence of the electrical resistivity of the melt, obtained in the heating and cooling mode, which was accompanied by a decrease in the thermal coefficient of electrical resistivity for all samples studied. The largest decrease in the temperature coefficient of electrical resistivity was observed for the sample containing ferromanganese and titanium, indicating a maximum increase in free volume of the melt and, consequently, an increase in the distance between adjacent atoms. It is worth noting that this sample had the highest degree of supercooling during crystallization. The results obtained suggest that the introduction of a new technological step, which involves reloading the furnace and adding titanium after the first discharge, can lead to an improvement in the homogeneity of the molten metal and a potential decrease in the quality of the finished products. Based on these findings, recommendations have been made regarding the preparation of the molten steel for casting and solidification. In order to ensure the highest possible quality of cast products made from 12Cr18Ni9Ti steel, it is recommended to limit the casting process to the first melt, without reloading the furnace or adding titanium.
476-491
Geometrical limit of density for random ensembles of regular polygons
Abstract
The paper studies statistical and geometric properties of random two-dimensional ensembles of regular polygons (with the number of vertices n from 3 to 15), obtained by densification of “starting” sparse packings using the modified Lubachevsky-Stillinger algorithm (LS ). Pair correlation functions for the specified packings are in good agreement with the results of other works. The evolution of these functions during the transition from the initial to the final density values and partial “crystallization” of the ensembles is presented in the form of 3D graphs. A statistical-geometric function of the excluded area for an ensemble of particles is proposed and studied, which is well described by a simple relation: (η) = a + b · lnη, where η is the fraction of the area of the ensemble occupied by particles, a and b are coefficients. The point of intersection of the graph of this function with the curve describing the dependence of the average area of the Voronoi region from η, defines the geometric limit of density ηmaxfor a random ensemble of particles (polygons or hard disks). For the considered two-dimensional ensembles of regular polygons, the value of ηmaxdepends relatively weakly on the shape of the particles and lies within the range of 0.680 (15-gons) – 0.694 (triangles). As the number of vertices increases, ηmaxnaturally tends to that for a random ensemble of hard disks. The values of the maximum density for the latter are obtained by extrapolating the dependence ηmax(n), and directly by modeling the hard disk system. The indicated values are almost identical and are (respectively): 0.6793 ± 0.0001 and 0.6792 ± 0.0002.
492-506
Evaluation of the possibility of formation of low-melting high-entropy alloys of the Al-Zn-Bi-Pb-Sn-In-Ga-Sb system
Abstract
Solders with a low melting point are necessary to solve the problem of integration of microcircuits and the reliability of their packaging, as well as to reduce thermal loads. To develop the next generation of electronic components, it is necessary to develop technologies for producing low-temperature compounds. This problem can be solved by creating solders, including those made of high-entropy alloys, differing in that they are characterized by the formation of solid solutions. These materials must be resistant to fatigue loads, exhibit plasticity, and adhere to other metallic materials. To reduce their toxicity, it is necessary to eliminate lead, which is usually found in solders. This paper presents the results of calculations of melting temperature, thermal conductivity, size factorδr, generalized thermodynamic parameter Ω, electronegativity, valence electron concentration, enthalpy, entropy, Gibb’s energy of mixing and other properties and parameters for 56 variants of five-component alloys of equiatomic composition from low-melting elements: Al, Zn, Bi, Pb, Sn, In, Ga and Sb, including, lead. The HEAPS program was used for the calculation, taking into account the inaccuracy in this program of the melting temperatures of tin, antimony, and indium, which differ from the observed ones. The VEC values for In, Sn, and Sb have been clarified. Based on the analysis of the calculated data, the compositions of potentially high-entropy alloys (HES) have been identified. It is shown that all alloys containing lead, as well as GaBiZnSnIn, GaBiZnSbIn, and AlGaBiZnIn alloys, do not satisfy the values of the δr parameter. They can form multiphase solid solutions, intermetallic compounds (IMC), and bulk-amorphous metallic glasses. The remaining variants of lead-free HEA-solders satisfy most parameters and can form solid solutions, with only AlGaZnSnSb being single–phase, and all others being multiphase solid solutions. The accumulated relatively large array of experimental and theoretical data can provide clarification of the criteria for the formation of the structure and properties of lead-free wind farms, which are in demand in practice.
507-521
Thermal oxidative stability of Al-Mn-graphene composite material under thermocycles conditions
Abstract
Aluminum-graphene composite material was synthesized by direct chemical interaction of boron carbide with molten matrix of Al-Mn alloy (analogue of АА 3003 alloy) with 1.22 wt. % of manganese, in molten alkali halides media. Initial Al-Mn alloy consists from aluminum base with formation of minor intermetallic amounts of MnAl6, but in aluminum-graphene composite except of aluminum base by the means of XRD the additional formation of double carbide AlMn3С. The formation of aluminum carbides was never detected no in pure aluminum, neither in all its alloys which was studied earlier. It was shown that the formation of three-layered graphene with linear dimensions up to 50 µm with total carbon concentration 0.055 wt.% decreases the onset point from 657.6℃for alloy AA3003 till 648℃for aluminum-graphene composite and results in an additional small peak at 650.1℃, which may be due to graphene oxidation. The original alloy AA 3003 in the air flow increases the mass when heated to 700℃by 0.16%, and the aluminum-graphene composite by 0.14 % which indicates a more significant oxidation of the original alloy AA 3003 compared the aluminum-graphene composite material. The effect of introduction of graphene into a metal matrix on the thermal properties of the composite was investigated, including under conditions of thermal cycling – triple heating up to 750℃and cooling up to 300℃in the air. It was shown that when graphene is introduced in the content up to 0.04 wt.% it does not change the mass of composite during thermal cycling as well as original alloy, while an increase in content up to 0.05 wt.% leads to an increase in mass of composite. Therefore, the composite material Al-Mn-graphene with a content of graphene up to 0.04 wt.%, which has higher mechanical properties compared to the alloy can be successfully used as plates of heat and radiators, since it is not subject to oxidation during thermal cycling.
522-536
Solubility of CeO2 and Nd2O3 in LiCl-Li2O melts
Abstract
Modern development of the nuclear industry requires a solution for the problems of spent nuclear fuel (SNF) processing, increasing the degree of nuclear fuel burn up and separating of fission products (FP) from fissile materials (FM). A promising method for solving these problems is pyrochemical reprocessing of SNF, one of the stages of which is oxide deposition. For safety reasons, the study is conducted using FM and FM simulators, including cerium and neodymium. In this work, the dissolution of neodymium (III) and cerium (IV) oxides in lithium chloride-based melts were studied. In the LiCl-Li2O melt, with a Li2O content not more than 4 mol.%, the solubility of cerium oxide remains below the detection limit, and then it significantly increases reaching 8.4∙10-3and 2.4∙10-2mol.% at 5 and 9 mol.% Li2O respectively. In case of neodymium oxide its solubility in the LiCl-Li2O melt increases linearly from 1.5∙10-3mol.% at 2 mol.% Li2O to 6.4∙10-3mol.% at 9 mol.% Li2O. The time to reach the saturation state during the dissolution of neodymium oxide is several times less than the time to reach the saturation state during the dissolution of neodymium oxide (25 hours for Nd2O3versus 145 hours for CeO2). To analyze the mechanisms of cerium and neodymium oxides dissolution, the phase composition of the ceramic tablets of these oxides after the experiment, as well as optical absorption spectra of the obtained melts were studied. Taking into account these data the possible mechanisms of interaction of cerium and neodymium oxides with LiCl-Li2O melts (0–9 mol.%) were proposed. The dissolution of cerium oxide occurs in a two-stage process with the slow formation of intermediate insoluble cerium compounds followed by their transition to soluble forms LiCeO2(for Ce3+) and Li2CeO3(for Ce4+), whichcauses the slow kinetics and nonlinear dependence on the Li2O content. Neodymium oxide interacts with lithium oxide in the melt, forming a soluble lithium neodymate compound LiNdO2.
537-551
К 85-летию Владимира Антоновича Хохлова
553-554