Thermodynamic Properties Of Liquid Alloys Research Articles

Application of CALPHAD Method for Predicting of Concentration Range of Amorphization of Transition Metals Melts

Early, the efficiency of the CALPHAD (Calculation of Phase Diagrams) method to a targeted search for compositions of amorphous alloys has been shown. The method for predicting the ranges of amorphization is based on the calculation of diagrams of metastable phase transformations between supercooled melts and boundary solid solutions on the base of pure elements. In this work, the model parameters for thermodynamic properties of liquid alloys and boundary solid solutions were summarized in a self-consistent database for the multicomponent Cu–Fe–Ni–Ti–Zr–Hf system. Such database for the multicomponent system is based on a common set of model parameters for boundary binary and ternary systems. This database was used to predict the concentration ranges of amorphization for the quinary Cu–Fe–Ni–Ti–Zr, Cu–Fe–Ni–Ti–Hf and boundary ternary and quaternary systems. The results of calculations are presented along sections in quaternary and quinary systems. The ternary and quaternary equiatomic alloys along with high entropy CuFeNiTiZr and CuFeNiTiHf alloys are trapped into prognosed composition ranges of amorphization. Predicted composition space of amorphization for melts of the Fe–Ni–Ti–Zr system is shown on the concentration tetrahedron. Based on the obtained results, a new criterion for predicting the concentration regions of amorphization of multicomponent melts is proposed, according to which the presence of a sufficient content of metals that are electron acceptors and donors is a chemical factor that affects the thermodynamic stability of melts and determines their glass-forming ability. For multicomponent melts of the Cu–Fe–Ni–Ti–Zr–Hf system the concentration ranges of amorphization correspond to the simultaneous fulfillment of the conditions xFe + xNi + xCu > 0.25 and xTi + xZr + xHf > 0.15, where Fe, Ni, and Cu are electron acceptors and Ti, Zr, and Hf are electron donors.

Thermodynamic Modeling of the Ag-Cu-Sn Ternary System

In this work, combined with previous assessments of the Ag-Cu, Ag-Sn and Cu-Sn binary systems, thermodynamic modeling of the Ag-Cu-Sn ternary system was performed using the CALPHAD method using the reported phase diagram data and thermodynamic data. The solution phases including Liquid, fcc, bcc, hcp, bct(Sn) and diamond(Sn) were modeled as substitutional solutions and their excess Gibbs energies were expressed by the Redlich–Kister–Muggianu polynomial. The solubility of the third element in binary intermetallic compounds was not taken into account due to the fact that ternary solubilities for most of the binary compounds are not significant. Thermodynamic properties of liquid alloys, liquidus projection, several vertical sections and isothermal sections were calculated, which were in reasonable agreement with the reported experimental data. Finally, a set of self-consistent thermodynamic parameters formulating the Gibbs energies of various phases in the Ag-Cu-Sn ternary system was obtained.

Glass-forming ability of Ni-Zr-Al alloys: the interplay of thermodynamic and geometric factors

ABSTRACT Despite decades of intensive rehearses, we still lack robust and physically clear methods to discover new metallic alloys with high glass-forming ability (GFA). Different empirical criteria proposed to estimate GFA have limited applicability. Here we address the impact of thermodynamic and geometric factors on GFA of Ni-Zr-Al alloys. Using the ideal associated solution model, we calculated the Gibbs energy and the mixing enthalpy of the system and compared the results with available experimental and theoretical data. The results show that the model used is a good approximation for calculating the thermodynamic properties of liquid alloys if both binary and ternary compounds are explicitly taken into account. However, we conclude that it is hardly possible to address GFA of Ni-Zr-Al alloys using only thermodynamic properties. We test a few different criteria, proposed in the literature, and show that they also fail to explain GFA in the system. Then, we propose new parameters based on Gibbs mixing energy and effective difference in atomic radii, which allows localising the composition domain corresponding to the best GFA in Ni-Zr-Al alloys. Our findings open up the prospects to develop reliable theoretical methods for discovering new metallic glasses.

Lithium–Tellurium System: Thermodynamic and Electrochemical Studies and Prospects for Use in Chemical Current Sources

Published data on the lithium–tellurium phase diagram and on thermodynamic properties of liquid alloys and solid phases formed are summarized and comprehensively analyzed in connection with prospects for using tellurium and its compounds and composites in various energy conversion systems involving lithium. The results of studying the thermodynamic properties of lithium tellurides by different methods are compared. The results of the main studies dealing with the use of tellurium in chemical current sources (CCSs) of various designs are briefly considered.

Modelling thermodynamic properties of binary Cu–Eu and ternary Al–Cu–Eu melts

Model calculations of the whole set of thermodynamic properties of liquid alloys for the binary Cu–Eu and ternary Al–Cu–Eu systems have been performed. Authors used the ideal associated solution model (IAS model) for calculation of the entropies and excess Gibbs energies of mixing for these systems. The binaries were given as the Redlich-Kister polynomials. The thermodynamic properties for the ternary system are described using the Redlich-Kister-Muggianu formalism. A comparison of the surfaces of excess Gibbs energy and entropy of mixing for liquid Al–Cu–Eu alloys at 1350 K demonstrates that the ordering related to the formation of rather strong associates in the Al–Eu system significantly affects the concentration dependence of the excess Gibbs energy of mixing in the liquid phase at this temperature.

МОДЕЛЮВАННЯ ТЕРМОДИНАМІЧНИХ ВЛАСТИВОСТЕЙ РОЗПЛАВІВ ПОТРІЙНОЇ СИСТЕМИ Ge-Mn-Gd

In the present work, the Gibbs energies of mixing of liquid alloys of the Ge-Mn-Gd ternary system were determined, which was made on the basis of an analysis of published data on the thermodynamic properties of liquid alloys of boundary binary systems that form the ternary Ge-Mn-Gd, as well as on the basis of the model calculations in these binary systems. To determine the activities of the components, the Gibbs energies of mixing, and the enthalpies of mixing of liquid alloys of the Ge-Mn(Gd) systems, for which alloying process is accompanied by significant heat release, an ideal associated solution model was applied. For the melts of the Mn-Gd system, which are characterized by rather insignificant exothermic effects, a model of regular solutions was used. The surface of the Gibbs energy of mixing for the alloys of the Ge-Mn-Gd ternary system has been determined on the basis of the concentration dependences of the Gibbs energies of mixing obtained for constituent binary systems under the assumption of additivity of pair interactions using the Redlich-Kister-Muggianu method. The obtained topology of the Gibbs energy isolines projections is compared with the thermochemical properties of liquid alloys of this system that we have determined earlier. A comparative analysis of the topology of these surfaces in the Ge-Mn-Gd system led to the conclusion that the surfaces of ΔG and ΔmH monotonically decrease from the manganese-rich angle of the diagram towards the Ge-Gd side of the concentration triangle. The minimum value of the thermodynamic characteristics of mixing of the ternary liquid alloys corresponds to the composition, which coincides with the composition of the most stable intermetallic compound in the Ge-Gd system. From the course of isolines of free energies and integral enthalpies of mixing, one can also conclude about the influence of a short-range order, existed in the Ge-Mn system near the composition with a mole fraction of mangan greater than 0.7, on the properties of ternary alloys in the vicinity of this composition. Thus, the topology of isolines and the large exothermic values of the obtained thermodynamic properties allow us to make a reasonable conclusion that the strong interaction between unlike components inherent in the Ge-Gd system in the solid state is also maintained for liquid alloys of the Ge-Mn-Gd system.

Thermodynamic Analysis of Alloys in Sodium–Tellurium System in Liquid and Solid States

The whole set of available data on the thermodynamic properties of liquid alloys and solid phases in the sodium–tellurium system is considered, beginning from the first study in 1970 and till the recent reports in 2015. The application of the sodium–tellurium system in chemical power cells is discussed.

Lithium–selenium and sodium–selenium systems: Thermodynamic properties and prospects for use in chemical current sources

Data on phase diagrams and thermodynamic properties of liquid alloys and solid phases in the lithium–selenium and sodium–selenium systems are summarized and discussed. The main lines of research in the field of using these systems in chemical current sources, in accordance with publications of the years 2013–2016, are discussed.

Bismuth-indium system: thermodynamic properties of liquid alloys

Bismuth-indium system: thermodynamic properties of liquid alloys

Thermodynamic Properties of Binary Al–Ce and Ce–Fe Alloys

The mixing enthalpies of liquid alloys in the binary systems Al–Ce (at 1540 K in the composition range 0.7 < x Ce < 1) and Ce–Fe (at 1830 K in the entire composition range) are determined by calorimetry. The thermodynamic properties of liquid alloys are calculated in the entire composition range using the model of ideal associated solutions. The thermodynamic activities of components show large negative deviations from the ideal solution for the Al–Ce melts and small ones for the Ce–Fe melts. The mixing enthalpies correspond to exothermic effects. The minimum values of the mixing enthalpies of liquid alloys are −45.8 ± 2.2 kJ/mol at x Ce = 0.37 for the Al–Ce system (1870 K) and −1.0 kJ/mol at x Ce = 0.36 for the Ce–Fe system (1830 K).

Application of Molecular Interaction Volume Model for Phase Equilibrium of Sn-Based Binary System in Vacuum Distillation

Based on the molecular interaction volume model (MIVM), the activities of components of Sn-Sb, Sb-Bi, Sn-Zn, Sn-Cu, and Sn-Ag alloys were predicted. The predicted values are in good agreement with the experimental data, which indicate that the MIVM is of better stability and reliability due to its good physical basis. A significant advantage of the MIVM lies in its ability to predict the thermodynamic properties of liquid alloys using only two parameters. The phase equilibria of Sn-Sb and Sn-Bi alloys were calculated based on the properties of pure components and the activity coefficients, which indicates that Sn-Sb and Sn-Bi alloys can be separated thoroughly by vacuum distillation. This study extends previous investigations and provides an effective and convenient model on which to base refining simulations for Sn-based alloys.

Application of MIVM for Pb-Sn System in Vacuum Distillation

The activity coefficients of components of the Pb-Sn binary alloy system were calculated based on the molecular interaction volume model (MIVM). A significant advantage of this model lies in its ability to predict the thermodynamic properties of liquid alloys using only two binary infinite activity coefficients. Based on the MIVM, the vapor-liquid phase equilibrium of the Pb-Sn alloy system in vacuum distillation has been predicted using the activity coefficients of Pb and Sn. The results showed that the content of tin in the vapor phase was 0.008 wt pct, while in the liquid phase, it was 83 wt pct at 1173 K (900 °C); it reached 0.022 wt pct in the vapor phase, while in the liquid phase, it was 92 wt pct at 1223 K (950 °C); and it was 0.052 wt pct in the vapor phase, while in the liquid phase, it was 97.88 wt pct at 1273 K (1000 °C). The content of tin in the vapor phase increased with the distillation temperature increasing. Experimental investigations into the separation of Pb and Sn from the Pb-Sn alloy by vacuum distillation were carried out for the proper interpretation of the results of the model. The influence of the distillation time (20 to 80 minutes) and the distillation temperatures of 1173 K, 1223 K, and 1273 K (900 °C, 950 °C, and 1000 °C) on the separating effect was also studied. The experimental results showed that the content of tin in the vapor phase was 0.085 wt pct, while in liquid phase, it was 83 wt pct under the operational conditions of distillation temperature of 1173 K (900 °C), evaporation time of 20 minutes, and chamber pressure of 20 Pa; it reached 0.18 wt pct in the vapor phase, while in the liquid phase, it was 92 wt pct at 1223 K (950 °C), 20 minutes, and 20 Pa; and it was 0.35 wt pct in the vapor phase, while in the liquid phase, it was 97.88 wt pct at 1273 K (1000 °C), 20 minutes, and 20 Pa. In all these experiments, it was observed that the content of tin in the vapor phase increased as the distillation time and temperatures were increased. The experimental results are in good agreement with the predicted values of the MIVM for the Pb-Sn binary system.

Thermodynamic behavior of polyvalent solutes in solid silver: System Ag–Sb

An electrochemical cell is used to measure the activity of Sb in α-Ag–Sb alloys as a function of temperature and composition. The results are consistent with known thermodynamic properties of liquid alloys and the phase diagram. Thermodynamic factor derived from diffusion measurements on solid alloys is also in harmony with the results of this study. The excess chemical potential of Sb increases gradually with composition for dilute alloys. Slope of the curve become steeper with increasing concentration, suggesting strong solute–solute repulsion. The results are discussed in comparison with earlier measurements on the systems Ag–X, where X is an element with same isoelectronic core structure as Ag. Solute–solute repulsion is found to increase with the difference in valency between the solute and the solvent, or with the number of excess electrons donated by the solute to the conduction band of Ag.

Application of molecular interaction volume model in vacuum distillation of Pb-based alloys

A method is presented for calculating the separation coefficients of Pb–Au and Pb–Sn alloys in vacuum distillation based on molecular interaction volume model (MIVM). A significant advantage of the model lies in its ability to predict the thermodynamic properties of liquid alloys using only binary infinite activity coefficients. The calculated results of Pb–Ag, Pb–Au, Pb–Sb, Pb–Sn and Sb–Sn show good agreement with experimental data in literature. It shows that the prediction effect of the proposed method is of better stability and reliability because the MIVM has a good physical basis.

Calculation of phase equilibrium in vacuum distillation by molecular interaction volume model

Phase equilibrium of Pb–Au and Pb–Sn systems in vacuum distillation have been predicted based on molecular interaction volume model (MIVM). A significant advantage of the model lies in its ability to predict the thermodynamic properties of liquid alloys using only binary infinite activity coefficients. The calculated activity coefficients are compared with experimental data showing good agreement with each other. This shows that the prediction effect of the proposed method is of better stability and reliability because the MIVM has a good physical basis.

Thermodynamic properties of Al-Y system melts

The thermochemical properties of Al-Y melts were determined by isoperibolic calorimetry. It was established that the minimal value of integral mixing enthalpies is equal to −40.8 + 0.4 kJ/mol at 1770 K and xY = 0.41. The thermodynamic properties of liquid alloys were modeled by the developed procedure using the coordinates of a liquidus line in the phase diagram of the Al-Y system, and by the theory of ideal associated solutions. The component activities exhibit high negative deviations from the Raoult law. The Gibbs energies of mixing of Al-Y melts have a minimum of −30.6 kJ/mol at xY = 0.48.

Thermodynamic description of the Au–Ag–Pb ternary system

Combined with previous assessments of the Au–Ag, Ag–Pb and Au–Pb binary systems, thermodynamic description of the Au–Ag–Pb ternary system has been performed using the CALPHAD method and Thermo-calc ® software package on the basis of the reported experimental information. The solution phases, including liquid and fcc_A1, are modeled as substitutional solutions, of which the excess Gibbs energies are expressed by the Redlich–Kister–Muggianu polynomial. The solubility of Ag in the Au–Pb intermediate compounds, Au 2Pb, AuPb 2 and AuPb 3, is not taken into account due to the lack of experimental data. Thermodynamic properties of liquid alloys, liquidus projection and several vertical sections of this ternary system have been calculated, which are in reasonable agreement with the reported experimental data. Finally, a set of self-consistent thermodynamic parameters formulating the Gibbs energies of various phases in the Au–Ag–Pb ternary system has been obtained in the present work.

Thermodynamic properties of liquid alloys of the Ni-Hf system

By the method of calorimetry in isoperibolic conditions are determined integral and partial mixing enthalpies of liquid alloys of the Ni-Hf system at 1770 ± 5 K. Defined that liquid Ni-Hf alloys are formed with allocated large quantity of heat. The analysis of own and literary data has allowed to establish for mixing enthalpies of binary Ni-Hf liquid alloys dependence on temperature. With use of the Schroder equation are calculated the activities of studied alloys components from co-ordinates of liquidus line of the phase diagram of this system. Between calculated and experimentally established values of melts components activities of the Ni-Hf system is observed only qualitative consent. Are also calculated ΔG and ΔS of liquid Ni-Hf alloys.

Thermodynamic assessment of the Cu-Ti-Zr system. III. Cu-Ti-Zr system

The CALPHAD method is used for the thermodynamic assessment of the Cu-Ti system that bounds the ternary Cu-Ti-Zr system, which is capable of forming amorphous alloys. The self-consistent parameters of thermodynamic models of the phases are obtained from data on the phase equilibria and thermodynamic properties of liquid alloys and intermetallic compounds. The Gibbs energy of the liquid phase is described using the associated ideal solution model. To describe the thermodynamic properties of the Cu4Ti and CuTi intermetallic compounds with homogeneity range, sublattice models are used. The calculated phase diagram of the system and the thermodynamic properties of the phases are in good agreement with experimental data.

Thermodynamic assessment of the copper-hafnium system

The thermodynamic properties of phases and phase equilibria in the Cu-Hf system are described with the CALPHAD method. The set of self-consistent model parameters is based on the thermodynamic properties of liquid alloys, intermetallic compounds, and phase equilibria. The excess Gibbs energy of the liquid phase is described using an ideal associated solution model. The models of thermodynamic properties are used to describe possible metastable transformations such as glass formation in rapid quenching from the melt, formation of bulk amorphous alloys, and formation of supersaturated terminal solid solutions.