Pub Date : 2025-01-23DOI: 10.1134/S0036029524701829
E. V. Nikolaeva, A. L. Bovet, I. D. Zakiryanova
The electrical conductivity of LiF–KF–NaF (FLiNaK) molten system was measured in the temperature range 480–777°C. The comparison of the obtained experimental data on molten FLiNaK with the available data for individual, double and ternary fluoride melts containing KF, NaF and LiF was carried out. The resulting dependence of electrical conductivity on molar volume of the system demonstrates that at 867°C and Vm larger than 23 cm3/mol the specific electrical conductivity is practically independent on molar volume and respectively on the molten mixture composition. The electrical conductivity of FLiNaK–CeF3 molten systems with the cerium fluoride additions ranging from 0 to 25 mol % was measured depending on both the temperature and concentration of CeF3. In addition, the electrical conductivity of 0.85 FLiNaK–0.15CeF3–Li2O molten system with Li2O additions up to 2.3 mol % was measured. The investigation demonstrates that the addition of cerium fluoride and oxide results in a decrease of the electrical conductivity of the fluoride molten system.
{"title":"Electrical Conductivity of Fluoride and Oxyfluoride Molten Systems Based on FLiNaK","authors":"E. V. Nikolaeva, A. L. Bovet, I. D. Zakiryanova","doi":"10.1134/S0036029524701829","DOIUrl":"10.1134/S0036029524701829","url":null,"abstract":"<p>The electrical conductivity of LiF–KF–NaF (FLiNaK) molten system was measured in the temperature range 480–777°C. The comparison of the obtained experimental data on molten FLiNaK with the available data for individual, double and ternary fluoride melts containing KF, NaF and LiF was carried out. The resulting dependence of electrical conductivity on molar volume of the system demonstrates that at 867°C and <i>V</i><sub>m</sub> larger than 23 cm<sup>3</sup>/mol the specific electrical conductivity is practically independent on molar volume and respectively on the molten mixture composition. The electrical conductivity of FLiNaK–CeF<sub>3</sub> molten systems with the cerium fluoride additions ranging from 0 to 25 mol % was measured depending on both the temperature and concentration of CeF<sub>3</sub>. In addition, the electrical conductivity of 0.85 FLiNaK–0.15CeF<sub>3</sub>–Li<sub>2</sub>O molten system with Li<sub>2</sub>O additions up to 2.3 mol % was measured. The investigation demonstrates that the addition of cerium fluoride and oxide results in a decrease of the electrical conductivity of the fluoride molten system.</p>","PeriodicalId":769,"journal":{"name":"Russian Metallurgy (Metally)","volume":"2024 4","pages":"916 - 923"},"PeriodicalIF":0.4,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108821","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-23DOI: 10.1134/S0036029524701908
A. V. Abramov, I. B. Polovov, A. F. Gibadullina, R. R. Alimgulov, A. I. Trubcheninova, M. S. Karabanalov
Abstract—The influence of the composition of nickel alloys on the mechanism of their corrosion in NaCl–KCl-based chloride melts has been analyzed. Nickel alloys NIMONIC 80A alloy, VDM Alloy 718, INCONEL alloy C-276 with different compositions of the matrix and alloying additives have been selected as the investigated materials. The corrosion rates of these alloys in NaCl–KCl and NaCl–KCl + UCl4 salt systems after exposure for 100 h at 750°C has been found. It has been shown that NIMONIC 80A alloy containing high-chromium excess phases is subjected to intergranular corrosion after only 30 hours of contact with NaCl–KCl. It has been demonstrated that continuous nonuniform corrosion is the main reason for damage of VDM 718 alloy (which also has excess phases in the microstructure) after 100 h of exposure in NaCl–KCl. Although prominent secondary-phase grain-boundary chainlike precipitates arise in INCONEL C-276 alloy at 750°C, its surface exhibits continuous uniform damage. From data obtained it was concluded that secondary phases arising in VDM 718 alloy and INCONEL C-276 alloy serve as cathodes of galvanic microcouples. Therfore intergranular corrosion (IGC) on the surface of these alloys has not been observed. It has been shown in a series of special experiments that in uranium-containing chloride melt, the corrosion rate rises by many times and the type of surface damage becomes basically the same—continuous nonuniform.
{"title":"Influence of the Composition of Nickel Alloys on the Mechanism of Their Corrosion in NaCl–KCl-Based Chloride Melts","authors":"A. V. Abramov, I. B. Polovov, A. F. Gibadullina, R. R. Alimgulov, A. I. Trubcheninova, M. S. Karabanalov","doi":"10.1134/S0036029524701908","DOIUrl":"10.1134/S0036029524701908","url":null,"abstract":"<p><b>Abstract</b>—The influence of the composition of nickel alloys on the mechanism of their corrosion in NaCl–KCl-based chloride melts has been analyzed. Nickel alloys NIMONIC 80A alloy, VDM Alloy 718, INCONEL alloy C-276 with different compositions of the matrix and alloying additives have been selected as the investigated materials. The corrosion rates of these alloys in NaCl–KCl and NaCl–KCl + UCl<sub>4</sub> salt systems after exposure for 100 h at 750°C has been found. It has been shown that NIMONIC 80A alloy containing high-chromium excess phases is subjected to intergranular corrosion after only 30 hours of contact with NaCl–KCl. It has been demonstrated that continuous nonuniform corrosion is the main reason for damage of VDM 718 alloy (which also has excess phases in the microstructure) after 100 h of exposure in NaCl–KCl. Although prominent secondary-phase grain-boundary chainlike precipitates arise in INCONEL C-276 alloy at 750°C, its surface exhibits continuous uniform damage. From data obtained it was concluded that secondary phases arising in VDM 718 alloy and INCONEL C-276 alloy serve as cathodes of galvanic microcouples. Therfore intergranular corrosion (IGC) on the surface of these alloys has not been observed. It has been shown in a series of special experiments that in uranium-containing chloride melt, the corrosion rate rises by many times and the type of surface damage becomes basically the same—continuous nonuniform.</p>","PeriodicalId":769,"journal":{"name":"Russian Metallurgy (Metally)","volume":"2024 4","pages":"974 - 984"},"PeriodicalIF":0.4,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108823","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-23DOI: 10.1134/S0036029524701969
G. M. Zirnik, S. A. Sozykin, D. A. Uchaev, A. S. Chernukha, I. A. Solizoda, S. A. Gudkova, D. A. Vinnik
Abstract—A sol–gel method is developed to synthesize ternary indium–gallium–zinc oxide using tartaric acid as an organic complexing agent. The synthesized samples were examined by X-ray diffraction and transmission and scanning electron microscopy. Summarizing the consistent results of these research methods, we can state that the sizes of the particles composing the synthesized samples depend on the synthesis temperature: agglomerates of nanoparticles form at the lowest of synthesis temperatures, and micron-sized particles are detected after sintering at 900°C. The crystallinity of the samples increases with the synthesis temperature. All samples have no impurity crystalline phases and exhibit a uniform indium, gallium and zinc distribution over the sample volume.
{"title":"Preparation and Synthesis of Polycrystalline InGaZnO4 via Tartaric Acid Mediated Sol–Gel Method","authors":"G. M. Zirnik, S. A. Sozykin, D. A. Uchaev, A. S. Chernukha, I. A. Solizoda, S. A. Gudkova, D. A. Vinnik","doi":"10.1134/S0036029524701969","DOIUrl":"10.1134/S0036029524701969","url":null,"abstract":"<p><b>Abstract</b>—A sol–gel method is developed to synthesize ternary indium–gallium–zinc oxide using tartaric acid as an organic complexing agent. The synthesized samples were examined by X-ray diffraction and transmission and scanning electron microscopy. Summarizing the consistent results of these research methods, we can state that the sizes of the particles composing the synthesized samples depend on the synthesis temperature: agglomerates of nanoparticles form at the lowest of synthesis temperatures, and micron-sized particles are detected after sintering at 900°C. The crystallinity of the samples increases with the synthesis temperature. All samples have no impurity crystalline phases and exhibit a uniform indium, gallium and zinc distribution over the sample volume.</p>","PeriodicalId":769,"journal":{"name":"Russian Metallurgy (Metally)","volume":"2024 4","pages":"1022 - 1027"},"PeriodicalIF":0.4,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108931","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-23DOI: 10.1134/S0036029524701611
A. G. Davydov, V. A. Elterman
In view of ever-increasing interest of the industry in multicomponent salt solutions, those engaged in physical chemistry are facing a problem of deriving equations of state that could correctly predict the density of liquid electrolytes in a wide range of temperatures and concentrations. Such an equation of state must take into account not only main contributors to the pressure but also significant second-order effects due to the electron shell polarizability in ions. In this study, an equation of state that considers the interaction of ionic charge with induced dipoles involving a thermodynamic perturbation theory (based on the model of charged hard spheres) has been applied to construct the temperature dependences of the density of molten lithium, sodium, and potassium halides. Using this equation of state, we have managed to fairly accurately describe main features in the variation of the melt density with temperature and composition. In passing from fluorides to chlorides, the densities of considered melts first slightly decrease near melting points and then rise as bromides and iodides are substituted for chloride anions. This is in complete agreement with experimental data. For all salts, the discrepancy between calculated and experimental dependences was no greater than ten percent. The best agreement was observed for bromide and chloride melts, which is qualitatively explained in the text. In general, it has been shown that calculation data are in good qualitative and quantitative agreement with published results in respect that calculations were performed using only tabulated values of ionic radii and polarizabilities.
{"title":"Equation of State for Characterizing the Density of Lithium, Sodium, and Potassium Molten Halides","authors":"A. G. Davydov, V. A. Elterman","doi":"10.1134/S0036029524701611","DOIUrl":"10.1134/S0036029524701611","url":null,"abstract":"<p>In view of ever-increasing interest of the industry in multicomponent salt solutions, those engaged in physical chemistry are facing a problem of deriving equations of state that could correctly predict the density of liquid electrolytes in a wide range of temperatures and concentrations. Such an equation of state must take into account not only main contributors to the pressure but also significant second-order effects due to the electron shell polarizability in ions. In this study, an equation of state that considers the interaction of ionic charge with induced dipoles involving a thermodynamic perturbation theory (based on the model of charged hard spheres) has been applied to construct the temperature dependences of the density of molten lithium, sodium, and potassium halides. Using this equation of state, we have managed to fairly accurately describe main features in the variation of the melt density with temperature and composition. In passing from fluorides to chlorides, the densities of considered melts first slightly decrease near melting points and then rise as bromides and iodides are substituted for chloride anions. This is in complete agreement with experimental data. For all salts, the discrepancy between calculated and experimental dependences was no greater than ten percent. The best agreement was observed for bromide and chloride melts, which is qualitatively explained in the text. In general, it has been shown that calculation data are in good qualitative and quantitative agreement with published results in respect that calculations were performed using only tabulated values of ionic radii and polarizabilities.</p>","PeriodicalId":769,"journal":{"name":"Russian Metallurgy (Metally)","volume":"2024 4","pages":"757 - 762"},"PeriodicalIF":0.4,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108964","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-23DOI: 10.1134/S0036029524701702
A. S. Russkih, T. V. Osinkina, E. M. Zhilina, V. P. Chentsov, S. A. Krasikov
The surface properties and the density of melting products significantly influence the separation of metallic and slag phases in a metallothermic process and correspondently influence the formation of a final alloy as an ingot. There are poor data in the literature on surface and interfacial properties of aluminum–titanium alloys containing rare refractory metals. The aim of this work is to study the surface and volumetric properties of contacting phases using experimental and computational methods and to analyze the revealed dependences. The interaction of a base Al–Ti alloy containing tantalum, niobium, and vanadium up to 4 at % with an oxide slag. The surface tension and the density of a metallic melt are determined by the sessile drop method. These properties in oxide melts are studied using the maximum pressure in a gas bubble. The interfacial tension between the metal and the slag is estimated using an equation, which takes into account the experimental values of the surface tension of the contacting phases and the contact angle. Our calculations and measurements show that the surface tension and the density of Al–Ti–(1.5–3) at % Nb and Al–Ti–(0.6–1.2) at % Ta alloys decrease as temperature increases. According to the experimental data, the interfacial tension between the metal and the slag is 922–1035 mJ/m2, which implies good separation of the metallic and slag phases in combination with a significant difference in the densities of these phase (from 5 to 6 g/cm3). The revealed tendency in changing the interfacial tension and the adhesion indicates a positive influence of Ta, Nb, and V on the separation of the metallic and oxide phases when these elements are introduced into a Ti–Al alloy. The data obtained in this work allow us to conclude that, in the case when a base Al–Ti alloy containing up to 4 at % tantalum, niobium, and vanadium is melted, a metallic phase will form at the crucible bottom and will be well separated from an oxide phase and the crucible material.
{"title":"Effect of Ta, Nb, and V on the Interfacial Interaction of Al–Ti Alloys with an Oxide Melt","authors":"A. S. Russkih, T. V. Osinkina, E. M. Zhilina, V. P. Chentsov, S. A. Krasikov","doi":"10.1134/S0036029524701702","DOIUrl":"10.1134/S0036029524701702","url":null,"abstract":"<p>The surface properties and the density of melting products significantly influence the separation of metallic and slag phases in a metallothermic process and correspondently influence the formation of a final alloy as an ingot. There are poor data in the literature on surface and interfacial properties of aluminum–titanium alloys containing rare refractory metals. The aim of this work is to study the surface and volumetric properties of contacting phases using experimental and computational methods and to analyze the revealed dependences. The interaction of a base Al–Ti alloy containing tantalum, niobium, and vanadium up to 4 at % with an oxide slag. The surface tension and the density of a metallic melt are determined by the sessile drop method. These properties in oxide melts are studied using the maximum pressure in a gas bubble. The interfacial tension between the metal and the slag is estimated using an equation, which takes into account the experimental values of the surface tension of the contacting phases and the contact angle. Our calculations and measurements show that the surface tension and the density of Al–Ti–(1.5–3) at % Nb and Al–Ti–(0.6–1.2) at % Ta alloys decrease as temperature increases. According to the experimental data, the interfacial tension between the metal and the slag is 922–1035 mJ/m<sup>2</sup>, which implies good separation of the metallic and slag phases in combination with a significant difference in the densities of these phase (from 5 to 6 g/cm<sup>3</sup>). The revealed tendency in changing the interfacial tension and the adhesion indicates a positive influence of Ta, Nb, and V on the separation of the metallic and oxide phases when these elements are introduced into a Ti–Al alloy. The data obtained in this work allow us to conclude that, in the case when a base Al–Ti alloy containing up to 4 at % tantalum, niobium, and vanadium is melted, a metallic phase will form at the crucible bottom and will be well separated from an oxide phase and the crucible material.</p>","PeriodicalId":769,"journal":{"name":"Russian Metallurgy (Metally)","volume":"2024 4","pages":"818 - 826"},"PeriodicalIF":0.4,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-23DOI: 10.1134/S0036029524701672
O. V. Volkova, V. V. Zakharov, E. A. Il’ina, B. D. Antonov, A. A. Pankratov
Abstract—The discharge characteristics of heat activated batteries (HABs) containing NiCl2–NiF2 mixtures as a positive electrode are studied. For the current density range from 0.25 to 1.5 A cm–2, this cathodic material is characterized by stable electrical characteristics in a temperature range of 480–600°C. The optimum composition of the cathodic mixture for the discharge conditions of HAB cells under study is determined. The reduction products of the NiCl2–NiF2 cathodic mixtures are studied by X-ray diffraction (XRD), scanning electron microscopy (SEM), and simultaneous thermal analysis (STA). The components of the cathodic mixture are reduced via the two-electron electrochemical reaction. The reduction products are metallic nickel and lithium halides. Lithium salts form solid solutions based on lithium chloride. Nickel forms the dendrite sponge that grows during HAB cell discharge and shifts deep inside the positive electrode. Pores of the dendrite sponge are filled with the salt fraction with a melting point of 470–490°C. The melting point of the salt fraction predetermines the lower boundary of the working temperature range of the HAB cell under study.
{"title":"Electroreduction of Nickel(II) Chloride and Nickel(II) Fluoride Mixtures in a Heat Activated Battery","authors":"O. V. Volkova, V. V. Zakharov, E. A. Il’ina, B. D. Antonov, A. A. Pankratov","doi":"10.1134/S0036029524701672","DOIUrl":"10.1134/S0036029524701672","url":null,"abstract":"<p><b>Abstract</b>—The discharge characteristics of heat activated batteries (HABs) containing NiCl<sub>2</sub>–NiF<sub>2</sub> mixtures as a positive electrode are studied. For the current density range from 0.25 to 1.5 A cm<sup>–2</sup>, this cathodic material is characterized by stable electrical characteristics in a temperature range of 480–600°C. The optimum composition of the cathodic mixture for the discharge conditions of HAB cells under study is determined. The reduction products of the NiCl<sub>2</sub>–NiF<sub>2</sub> cathodic mixtures are studied by X-ray diffraction (XRD), scanning electron microscopy (SEM), and simultaneous thermal analysis (STA). The components of the cathodic mixture are reduced via the two-electron electrochemical reaction. The reduction products are metallic nickel and lithium halides. Lithium salts form solid solutions based on lithium chloride. Nickel forms the dendrite sponge that grows during HAB cell discharge and shifts deep inside the positive electrode. Pores of the dendrite sponge are filled with the salt fraction with a melting point of 470–490°C. The melting point of the salt fraction predetermines the lower boundary of the working temperature range of the HAB cell under study.</p>","PeriodicalId":769,"journal":{"name":"Russian Metallurgy (Metally)","volume":"2024 4","pages":"798 - 804"},"PeriodicalIF":0.4,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-23DOI: 10.1134/S0036029524701933
A. G. Fedyushkina, D. V. Ponomareva, E. I. Timoschuk, I. B. Polovov, A. I. Trubcheninova, A. V. Abramov, R. R. Alimgulov
Abstract—The results of interaction between medium and fine grained raphite and carbon-carbon composite material (CCCM) and LiF-NaF-KF (FLiNaK) at 750°C are presented. The efficiency of using coatings based on low- and high-temperature pyrocarbon to prevent the penetration of the molten salt into the carbon material volume is evaluated. The corrosion rates of these classes of carbon materials in the molten salt are determined.
{"title":"Interaction of Various Classes of Carbon Materials with the Molten FLiNaK Salt","authors":"A. G. Fedyushkina, D. V. Ponomareva, E. I. Timoschuk, I. B. Polovov, A. I. Trubcheninova, A. V. Abramov, R. R. Alimgulov","doi":"10.1134/S0036029524701933","DOIUrl":"10.1134/S0036029524701933","url":null,"abstract":"<p><b>Abstract</b>—The results of interaction between medium and fine grained raphite and carbon-carbon composite material (CCCM) and LiF-NaF-KF (FLiNaK) at 750°C are presented. The efficiency of using coatings based on low- and high-temperature pyrocarbon to prevent the penetration of the molten salt into the carbon material volume is evaluated. The corrosion rates of these classes of carbon materials in the molten salt are determined.</p>","PeriodicalId":769,"journal":{"name":"Russian Metallurgy (Metally)","volume":"2024 4","pages":"999 - 1004"},"PeriodicalIF":0.4,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108909","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-23DOI: 10.1134/S003602952470174X
E. A. Titova, L. V. Toropova, D. V. Alexandrov
Abstract—A convective boundary integral equation has been obtained to describe nonisothermal solidification from a binary melt/solution. The convective boundary integral is derived in three-dimensional and two-dimensional cases and is verified for fixed surface shapes, namely, a paraboloid of revolution, an elliptical paraboloid, and a parabolic cylinder. These surface shapes correspond to needle and lamellar dendrites growing in a liquid-phase flow uniformly flowing onto a crystal. The convective boundary integral equation for dendrites having the shape of a paraboloid of revolution and a parabolic cylinder is shown to give exactly the same dependence of supercooling on the Peclet, Reynolds, and Prandtl numbers as the direct solution to a boundary-value differential problem. A thermal-concentration boundary integral has been verified at various impurity concentrations in a liquid. The results are numerically compared, since the analytical forms of the solutions are different. Another approach to verification is to reduce the new integral equation to the well-known solutions by limiting transitions. The convective boundary thermal-concentration equation is shown to transform into a convection-free equation at the liquid flow velocity tending to zero. The convective boundary integral is calculated for the growth of a parabolic dendrite in an incident ideal liquid flow. The dependences of the supercooling at the dendritic surface on the Peclet number, which were constructed for convection in an ideal liquid and a viscous liquid in the Oseen approximation, nearly coincide for metals and metal alloys but differ sharply for organic materials and aqueous solutions. A parameter that determines the need to take viscosity into account is found. This parameter is the Prandtl number, which has an order of 10–2 for metals and 101 for aqueous solutions. The Prandtl number allows us to compare the following two different heat transfer mechanisms: a diffusion mechanism and energy transfer via viscous friction. In metals, the Prandtl number is small due to a low viscosity and a high thermal conductivity, and the diffusion mechanism of heat transfer prevails. Therefore, a much simpler ideal liquid model can be used instead of a viscous liquid model can be sued for metallic alloys.
{"title":"Curved Solidification Front Dynamics in Melts with Convection","authors":"E. A. Titova, L. V. Toropova, D. V. Alexandrov","doi":"10.1134/S003602952470174X","DOIUrl":"10.1134/S003602952470174X","url":null,"abstract":"<p><b>Abstract</b>—A convective boundary integral equation has been obtained to describe nonisothermal solidification from a binary melt/solution. The convective boundary integral is derived in three-dimensional and two-dimensional cases and is verified for fixed surface shapes, namely, a paraboloid of revolution, an elliptical paraboloid, and a parabolic cylinder. These surface shapes correspond to needle and lamellar dendrites growing in a liquid-phase flow uniformly flowing onto a crystal. The convective boundary integral equation for dendrites having the shape of a paraboloid of revolution and a parabolic cylinder is shown to give exactly the same dependence of supercooling on the Peclet, Reynolds, and Prandtl numbers as the direct solution to a boundary-value differential problem. A thermal-concentration boundary integral has been verified at various impurity concentrations in a liquid. The results are numerically compared, since the analytical forms of the solutions are different. Another approach to verification is to reduce the new integral equation to the well-known solutions by limiting transitions. The convective boundary thermal-concentration equation is shown to transform into a convection-free equation at the liquid flow velocity tending to zero. The convective boundary integral is calculated for the growth of a parabolic dendrite in an incident ideal liquid flow. The dependences of the supercooling at the dendritic surface on the Peclet number, which were constructed for convection in an ideal liquid and a viscous liquid in the Oseen approximation, nearly coincide for metals and metal alloys but differ sharply for organic materials and aqueous solutions. A parameter that determines the need to take viscosity into account is found. This parameter is the Prandtl number, which has an order of 10<sup>–2</sup> for metals and 10<sup>1</sup> for aqueous solutions. The Prandtl number allows us to compare the following two different heat transfer mechanisms: a diffusion mechanism and energy transfer via viscous friction. In metals, the Prandtl number is small due to a low viscosity and a high thermal conductivity, and the diffusion mechanism of heat transfer prevails. Therefore, a much simpler ideal liquid model can be used instead of a viscous liquid model can be sued for metallic alloys.</p>","PeriodicalId":769,"journal":{"name":"Russian Metallurgy (Metally)","volume":"2024 4","pages":"846 - 862"},"PeriodicalIF":0.4,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-23DOI: 10.1134/S0036029524701660
A. G. Davydov, V. A. Elterman
Abstract—The temperature dependences of the densities of molten rubidium and cesium halides are described for the first time in terms of a statistical theory of liquid. The equation of state used in this work allows us to take into account the contribution of charge–dipole interactions between ions in melts using a charged hard sphere model. This version of the equation of state is obtained using a thermodynamic perturbation theory in combination with the virial theorem, which connects expressions for various contributions to internal energy and fluid pressure. The calculation results are shown to be qualitatively and quantitatively consistent with experimental data on the temperature dependences of the densities of molten rubidium and cesium halides. The errors in calculating the densities range from 1 to 10% when only standard tabular values of ion radii and polarizabilities are used. We also present and analyze the main trends in changes in the hard sphere, Coulomb, and charge–dipole contributions to the pressure of the molten salts as functions of temperature and chemical composition. These contributions are found to decrease when the melts are heated and when the cation and anion radii in the salt compositions increase. The contribution caused by the interactions of point ion charges and induced dipoles in the melts under consideration is shown to be about 10% of the Coulomb contribution. Thus, it increases in the melt density, which, in turn, causes better agreement of the calculation results with the available experimental data.
{"title":"Calculation of the Temperature Dependences of the Densities of Liquid Rubidium and Cesium Halides with Allowance for the Charge–Dipole Contribution to the Melt Pressure","authors":"A. G. Davydov, V. A. Elterman","doi":"10.1134/S0036029524701660","DOIUrl":"10.1134/S0036029524701660","url":null,"abstract":"<p><b>Abstract</b>—The temperature dependences of the densities of molten rubidium and cesium halides are described for the first time in terms of a statistical theory of liquid. The equation of state used in this work allows us to take into account the contribution of charge–dipole interactions between ions in melts using a charged hard sphere model. This version of the equation of state is obtained using a thermodynamic perturbation theory in combination with the virial theorem, which connects expressions for various contributions to internal energy and fluid pressure. The calculation results are shown to be qualitatively and quantitatively consistent with experimental data on the temperature dependences of the densities of molten rubidium and cesium halides. The errors in calculating the densities range from 1 to 10% when only standard tabular values of ion radii and polarizabilities are used. We also present and analyze the main trends in changes in the hard sphere, Coulomb, and charge–dipole contributions to the pressure of the molten salts as functions of temperature and chemical composition. These contributions are found to decrease when the melts are heated and when the cation and anion radii in the salt compositions increase. The contribution caused by the interactions of point ion charges and induced dipoles in the melts under consideration is shown to be about 10% of the Coulomb contribution. Thus, it increases in the melt density, which, in turn, causes better agreement of the calculation results with the available experimental data.</p>","PeriodicalId":769,"journal":{"name":"Russian Metallurgy (Metally)","volume":"2024 4","pages":"827 - 833"},"PeriodicalIF":0.4,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109045","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-23DOI: 10.1134/S0036029524701714
A. G. Davydov, V. A. Elterman
Abstract—Because of great difficulties in conducting high–temperature experiments to measure the thermal effects in molten salts, the information accumulated to date on the temperature dependences of the heat capacities even for the simplest subclass of salt melts, namely, alkali metal halides, cannot make an answer about the existence and reliability of trends in decreasing or increasing the heat capacities of melts with temperature. Most data on the heat capacities of molten halides are presented in handbooks as temperature-independent quantities. Therefore, to reveal trends in temperature-induced changes in the heat capacities of melts, it is advisable to turn to theoretical analysis methods. In this work, we develop a version of a thermodynamic perturbation theory and apply it to describe the temperature dependences of the heat capacities of a number of halide melts. The model of taking into account charge–dipole interactions using a system of comparing charged hard spheres, which was tested earlier in calculating the enthalpies of alkali-halide melts, is applied to calculate the isobaric heat capacities of molten cesium fluoride, chloride, bromide, and iodide in the temperature range 200 K above their melting temperatures. A combination of a mean spherical model of charged hard spheres of different diameters and the first correction caused by point-charge-induced dipoles to the interionic interaction of molten salts is shown to be a good basis for qualitative and quantitative agreement with experimental data on heat capacities within a few percent. In addition, the proposed model is found to predict a weak monotonic decrease in the heat capacities of melts upon heating in all cases of cesium halides.
{"title":"Calculation of the Heat Capacities of Molten Cesium Halides Using Thermodynamic Perturbation Theory","authors":"A. G. Davydov, V. A. Elterman","doi":"10.1134/S0036029524701714","DOIUrl":"10.1134/S0036029524701714","url":null,"abstract":"<p><b>Abstract</b>—Because of great difficulties in conducting high–temperature experiments to measure the thermal effects in molten salts, the information accumulated to date on the temperature dependences of the heat capacities even for the simplest subclass of salt melts, namely, alkali metal halides, cannot make an answer about the existence and reliability of trends in decreasing or increasing the heat capacities of melts with temperature. Most data on the heat capacities of molten halides are presented in handbooks as temperature-independent quantities. Therefore, to reveal trends in temperature-induced changes in the heat capacities of melts, it is advisable to turn to theoretical analysis methods. In this work, we develop a version of a thermodynamic perturbation theory and apply it to describe the temperature dependences of the heat capacities of a number of halide melts. The model of taking into account charge–dipole interactions using a system of comparing charged hard spheres, which was tested earlier in calculating the enthalpies of alkali-halide melts, is applied to calculate the isobaric heat capacities of molten cesium fluoride, chloride, bromide, and iodide in the temperature range 200 K above their melting temperatures. A combination of a mean spherical model of charged hard spheres of different diameters and the first correction caused by point-charge-induced dipoles to the interionic interaction of molten salts is shown to be a good basis for qualitative and quantitative agreement with experimental data on heat capacities within a few percent. In addition, the proposed model is found to predict a weak monotonic decrease in the heat capacities of melts upon heating in all cases of cesium halides.</p>","PeriodicalId":769,"journal":{"name":"Russian Metallurgy (Metally)","volume":"2024 4","pages":"793 - 797"},"PeriodicalIF":0.4,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}