Application of Wilson’s method to the calculation of thermodynamic properties of liquid ternary metallic systems from the data on boundary binary systems

et al. 2022

Rationale The Sm2O3‐ZrO2‐HfO2 system is a promising base for the development of a wide spectrum of new refractory materials. Reliable data on thermodynamic properties in this system are of significant importance for planning the preparation and application of high‐temperature ceramics. Especially, they can be useful for calculation of the unknown phase equilibria in this system. Methods The thermodynamic properties of the Sm2O3‐ZrO2‐HfO2 system were studied by the high‐temperature mass spectrometric method. The samples in the system under consideration synthesized by the solid‐state method were vaporized from a tungsten twin effusion cell using a MS‐1301 magnetic sector mass spectrometer. Ionization of the vapor species effusing from the cell was carried out by electrons at an energy of 25 eV. Results It was shown that, at temperatures below 2500 K, the main vapor species over the ceramics based on the Sm2O3‐ZrO2‐HfO2 system were SmO, Sm, and O corresponding to vapor composition over pure Sm2O3. The SmO, Sm, and O partial vapor pressures over the samples and the Sm2O3 activities were obtained in the temperature range 2319–2530 K. This allowed the excess Gibbs energy values to be determined. For comparison, the excess Gibbs energies in the Sm2O3‐ZrO2‐HfO2 system were also calculated by the semi‐empirical Kohler, Toop, Redlich‐Kister, and Wilson methods and optimized by the statistical thermodynamic Generalized Lattice Theory of Associated Solutions (GLTAS). Conclusions The thermodynamic data calculated by the semi‐empirical approaches at 2423 K were shown to be lower than the experimental values. However, the Toop and Wilson methods were found to be useful for evaluation of the excess Gibbs energy values at the Sm2O3 mole fraction less and higher than 0.32, respectively. The self‐consistent thermodynamic description of the Sm2O3‐ZrO2‐HfO2 system was derived at high temperatures by optimization of the experimental results using the GLTAS.

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: The Semi-empirical Approachesmentioning

confidence: 99%

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High‐temperature mass spectrometric study of the thermodynamic properties in the Sm₂O₃‐ZrO₂‐HfO₂ system

Каблов

et al. 2022

“…In the present study, semi‐empirical approaches that enable the excess Gibbs energy of a ternary system to be determined based on the corresponding values in the binary systems were used. Among these approaches, at least two types can be distinguished: polynomial and geometrical methods 53 . One example of each type was considered in the current investigation.…”

Section: Methodsmentioning

confidence: 99%

“…It should be mentioned that polynomial and geometrical methods are based on the assumption that the thermodynamic properties in a ternary system are completely dependent on the contributions from the binary systems. This means that the pair interactions of components are not altered significantly when a third component is added to a binary system, and that ternary interactions do not contribute noticeably to the thermodynamic description of a ternary system 53,54 …”

Section: Methodsmentioning

confidence: 99%

Mass spectrometric study of ceramics in the Sm₂O₃‐ZrO₂‐HfO₂ system at high temperatures

Лопатин

et al. 2021

Rationale Systems containing zirconia, hafnia, and rare earth oxides are indispensable in various areas of high‐temperature technologies as a basis of ultra‐high refractory ceramics. Exposure of these materials to high temperatures may result in unexpected selective vaporization of components or phase transitions in the condensed phase leading to changes in physicochemical properties. Consequently, reliable application of the ceramics based on systems such as Sm2O3‐ZrO2‐HfO2 is impossible without data on its vaporization processes and thermodynamic properties, which may be used to predict the physicochemical characteristics of the ultra‐high refractory ceramics. Methods Ceramics based on the Sm2O3‐ZrO2‐HfO2 system were obtained by solid‐state synthesis and characterized by X‐ray fluorescence and X‐ray phase analyses. The vaporization and thermodynamics of the system considered were examined by the high‐temperature mass spectrometric method using a MS‐1301 magnetic sector mass spectrometer with a tungsten twin effusion cell. Vapor species effusing from the cell were ionized by electrons with an energy of 25 eV. Results The main vapor species over the Sm2O3‐ZrO2‐HfO2 system were shown to be SmO, Sm, and O at a temperature of 2373 K, indicating selective vaporization of Sm2O3 from the samples. The partial pressures of these vapor species and the Sm2O3 activities were determined in the Sm2O3‐ZrO2‐HfO2 system and allowed the excess Gibbs energies to be evaluated. These excess Gibbs energy values were compared with the results obtained by the semi‐empirical and statistical thermodynamic approaches. Conclusions The data obtained in this study showed negative deviations from the ideal behavior in the Sm2O3‐ZrO2‐HfO2 system at 2373 K. The results calculated according to the semi‐empirical methods and statistical thermodynamic Generalized Lattice Theory of Associated Solutions were in agreement with each other. Thus, this evidenced the desirability of further experimental investigation of the Sm2O3‐ZrO2‐HfO2 system by the high‐temperature mass spectrometric method.

High‐temperature mass spectrometric study of thermodynamic properties in the TiO₂–Al₂O₃–SiO₂ system and modeling

Shemchuk

et al. 2022

Rationale The TiO2–Al2O3–SiO2 system is the base for various glass–ceramic materials, which have great practical value for a large number of modern technologies. Many TiO2–Al2O3–SiO2 materials are synthesized or applied at high temperatures, which justifies the relevance of the present study. Methods The samples in the TiO2–Al2O3–SiO2 system were synthesized using the method of induction melting in a cold crucible. The thermodynamic properties of the TiO2–Al2O3–SiO2 system were studied using the Knudsen effusion mass spectrometric method. The derived thermodynamic functions were optimized within the generalized lattice theory of associated solutions (GLTAS) approach and compared with the results of calculation using the semiempirical Kohler, Muggianu, Toop, Redlich–Kister, and Wilson methods based on the corresponding data in the binary systems. Results The SiO2 selective vaporization from the samples under study was shown at temperatures above 1940 K. The thermodynamic properties in the TiO2–Al2O3–SiO2 system, including the TiO2–SiO2 system, were obtained in the temperature range 1965–2012 K and were optimized using GLTAS to obtain the consistent concentration dependences of the component activities and excess Gibbs energies. Conclusions Positive deviations from the ideal behavior were observed in the TiO2–Al2O3–SiO2 system at high temperatures. Comparison of these values with the results of the modeling based on the GLTAS approach allowed the recommendations regarding the optimal semiempirical methods for the excess Gibbs energy calculation in different concentration ranges to be made.