Phase equilibria and thermodynamics of binary copper systems with 3d-metals. I. The copper-scandium system

Thermodynamic assessment of the Cu-Sc system was carried out using the CALPHAD method. A set of self-consistent model parameters was obtained with the usage of the information about phases equilibria and thermodynamic. Gibbs energy for the liquid phase was assessed within the framework of the model of ideal associated solution. Optimized model parameters make it possible to reproduce satisfactorily the phase diagram and thermodynamic values. Analysis of the relative thermodynamic stability of supercooled melts and competing crystalline phases let us to predict their glass forming ability by rapid quenching from the liquid state. __________ Translated from Poroshkovaya Metallurgiya, Nos. 3–4(448), pp. 43–55, March–April, 2006.     

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.     

Thermodynamic assessment of the Cu-Ti-Zr system. II. Cu-Zr and Ti-Zr systems

The thermodynamic assessment of the Cu-Zr and Ti-Zr systems is carried out using the CALPHAD method. The Gibbs energy of Cu-Zr liquid alloys is described by the ideal associated solution model. The excess Gibbs energy of Ti-Zr liquid alloys and Cu-Zr and Ti-Zr solid solutions is descried by models with Redlich-Kister polynomials. The Gibbs energy of Cu-Zr intermetallic compounds is described by models taking into account their formation enthalpy and entropy. A set of self-consistent parameters of the models is obtained using data on phase equilibria and thermodynamic properties of the phases. The calculated phase diagrams of the systems and values of thermodynamic properties of the phases are in good agreement with experimental information. The relative thermodynamic stability of supercooled liquid alloys and competitive crystal phases of the Cu-Zr system are analyzed.     

Thermodynamics of Liquid Alloys and Metastable Phase Transformations in the Copper - Titanium System

We have used solution calorimetry at temperatures of 1573 K and 1873 K over broad concentration ranges to study the mixing enthalpy of Cu - Ti liquid alloys. The molar mixing enthalpies of the system are significant negative values. We have established the temperature dependence of the molar mixing enthalpies of the system: there is an increase in their exothermicity as the temperature is lowered. The significant negative mixing enthalpies of the system allow us to conclude that the chemical bonds are localized in the studied melts and consequently associates form. We tested this conclusion within ideal associated solution theory, which describes well the results obtained with a set of CuTi and CuTi₂ associates. Using the model obtained, we have calculated the excess thermodynamic functions of mixing (enthalpy, Gibbs free energy, heat capacity) for the liquid alloys. We estimated the Gibbs energies of fcc, bcc, and hcp solutions in the system by the CALPHAD method, using data from the initial sections of the phase diagrams and from the corresponding thermodynamic data. We have calculated the metastable phase equilibria between the limiting solid solutions and the liquid or supercooled liquid phase. It was shown that for the supercooled liquid and the amorphous phase, a broad concentration range of relative thermodynamic stability can be obtained. The concentration range of amorphization of Cu - Ti melts corresponds to the position of the metastable liquidus line and the T₀ line at temperatures close to the temperature range of amorphous solidification. __________ Translated from Poroshkovaya Metallurgiya, Nos. 5–6(443), pp. 67–80, May–June, 2005.     

Thermodynamic Properties and Phase Equilibria of Nd–Ni Alloys

Isoperibolic calorimetry has been used for the first time to determine the mixing enthalpies of binary Nd–Ni liquid alloys in the range 0 < xNi < 0.5 at 1733 K and range 0.55< xNi < 1 at 1773 K. The binary Nd–Ni melts are characterized by significant negative mixing enthalpies with a minimum of –33.9 ± 0.8 kJ/mole at xNi = 0.63 and 1750 K. In the temperature range studied (1733–1773 K), the mixing enthalpies of the melts are described by polynomial ΔH = xNi (1 – xNi )× × (–75.32 – 103.41 xNi + 273.45$$ {x}_{Ni}^2 $$ – 817.02$$ {x}_{Ni}^3 $$ +548.58$$ {x}_{Ni}^4 $$). The ideal associated solution (IAS) model was used to calculate the activities of components, molar fractions of associates, Gibbs energies, and mixing entropies using our ΔH and $$ \varDelta \overline{H}i $$ and literature data on the formation enthalpy of nickelides and the Nd–Ni phase diagram. All intermediate phases were considered stoichiometric, with zero excess heat capacity. Five associates were selected for the calculation: Nd2Ni, NdNi, NdNi2, NdNi3, and NdNi5. Most of them agree in composition with the intermetallides in this system. Only one of them does not exist in solid state. This is associate Nd2Ni, whose composition is close to that of the Nd7Ni3 intermetallide. The activities of the Nd–Ni melt components show high negative deviations from ideal solutions. Associates of simplest composition, NdNi and NdNi2, are predominant in the melts. The mixing entropies of Nd–Ni liquid alloys are negative (minimum value is close to –6.4 J/mole · K). All our thermodynamic properties indicate that there is strong energy of interaction between Ni and Nd. The liquidus curves of the Nd–Ni system were calculated using the IAS model parameters.     

A thermodynamic analysis of the Pb−S system and calculation of the Pb−S phase digram

An associated solution model is used to describe the thermodynamic properties of the liquid phase in the Pb−S system, where the existence of ‘PbS’ species is assumed in addition to ‘Pb’ and ‘S’. The liquid is now considered as a pseudo-ternary solution of ‘Pb’, ‘S’, and ‘PbS’ in which the concentrations of the species are related by an equilibrium constant. The thermodynamic properties of the intermediate phase, PbS, are described by a point-defect model. The doubly ionized vacancies on the Pb and the S sites are considered to be the dominant defects and the nonstoichiometry is caused by the excess of vacancies on either site. The parameters of these models are obtained by simultaneous optimization of the available thermodynamic and phase equilibria data. The Pb−S phase diagram is then calculated, using these thermodynamic models, and compared with the experimental data.     

Thermodynamic description for concentrated metallic solutions using interaction parameters

The integral molar excess Gibbs energy of a multicomponent system is expressed in terms of interaction parameters, from which the analytical formulae of the activity coefficients of the solutes and solvent, as Eqs. [23] and [24], were deduced. This approach, named the ε approach, is able to describe quantitatively the thermodynamic properties of multicomponent systems. It features thermodynamic consistency, high accuracy, and a rather small influence of the higher-interaction parameters on the thermodynamic properties of metallic solutions. A simple modification to the first-order interaction parameters extends the ε approach, to be applicable to systems with strong interactions between components at both low and concentrated levels.     

Thermodynamic study and the phase diagram of the Mg-Sn system

By means of concentration cells of the following type, Mg (l)MgCl2 in (LiCl-KCl)_eut (l)Mg-Sn (1), the partial thermodynamic data of Mg in Mg-Sn liquid solutions have been obtained in the composition range of 0.1 ≤X _Mg ≤ 0.75 and at temperatures from 950 to 1100 K. These values are compared with thermodynamic data reported in the literature and used for the evaluation to obtain a complete set of thermodynamic functions for phase diagram calculations and for further interpretation by the associate model. This model, which accepts the existence of ‘Mg₂Sn as-sociates’ in the liquid alloys, enables calculations of viscosity by Kucharski’s method corre-lating properly with experimental data. Mutual correlations between thermodynamic properties, physical properties, structure, and the phase diagram of the Mg-Sn system were shown to in-dicate a maximum chemical short-range order close to the composition Mg2Sn.     

Thermodynamics and phase relationships of transition metal-sulfur systems: Part III. Thermodynamic properties of the Fe-S liquid phase and the calculation of the Fe-S phase diagram

An associated solution model is applied to describe the thermodynamic behavior of Fe-S liquid. This model assumes the existence of ‘FeS’ species in addition to Fe and S in the liquid. With two solution parameters for each of the binaries Fe-‘FeS’ and ‘FeS’-S, this model accounts for the compositional dependence of the thermodynamic properties of Fe-S liquid from pure Fe to pure S over a wide range of temperature. The binary Fe-S does not contribute significantly to the excess Gibbs energy of the liquid due to the rather small dissociation constant of ‘FeS’ to Fe and S. Using this model for the liquid phase and a defect thermodynamic model for the pyrrhotite phase, the Fe-S phase diagram is calculated. The calculated diagram is in excellent agreement with the experimental data, accounting for the range of homogeneity of pyrrhotite at all temperatures. Both the thermodynamic and phase diagram data are obtained from the literature. Formerly Post-Doctoral Research Associate, Materials Department, College of Engineering and Applied Science, University of Wisconsin-Milwaukee.     

Electromotive Force Measurements in the Ternary System Bi-In-Zn

The thermodynamic properties of the ternary Bi-In-Zn system were determined with the electromotive force (EMF) method using a liquid electrolyte. Four different cross sections with constant In/Bi ratios of 1:2, 1:1, 2:1, and 9:1 were applied to measure the thermodynamic properties of the ternary system in the temperature range between the liquidus temperature of the alloys and 973 K (700 °C). Zinc was added in steps of 5 at. pct from 5 to 90 pct. The partial free energies of Zn in liquid Bi-In-Zn alloys were determined as a function of concentration and temperature. The integral Gibbs free energy and the integral enthalpy of the ternary system at 873 K (600 °C) were calculated by Gibbs–Duhem integration. The ternary interaction parameters were evaluated using the Redlich–Kister–Muggianu polynomials.     

On the decomposition of solid solutions of magnesium in aluminum

A nonequilibrium version of measuring the electromotive force during a continuous decrease in the temperature at a rate of 5–7 °C/min is used to study the thermodynamic properties of solid solutions of magnesium in aluminum. The studies show that the abrupt change in the potential of an alloy containing 20–30 mol % Mg at 370–380°C reliably correlates with the decomposition of the solid solution formed at 450°C.     

Phase equilibria of the Al-Li binary system

The solid + liquid phase equilibria between α-Al and β-AlLi were determined using differential thermal analysis (DTA), metallography, and chemical analysis. Boron nitride (BN), which was found to be inert to these alloys, was used as the container. These measurements were carried out in order to resolve the discrepancies reported in the literature. The α-Al+β-AlLi eutectic temperature and composition were determined to be 600 °C±1 °C and 25.8±0.5 at. pct Li. Using these data and data reported in the literature concerning the phase equilibria and thermodynamic properties, thermodynamic models for all the phases were obtained by optimization. The thermodynamic values obtained for the β-AlLi phase describe not only the phase equilibria, but also yield structural defect data in agreement with measured values. The assessed enthalpies of formation, excess entropies of formation, and entropies of melting for all the intermetallic phases obtained are compared with empirical correlations when experimental data are not available. In addition to the stable diagram, a metastable diagram involving the δ′-Al₃Li is also calculated from the thermodynamic models. The calculated diagram is in good agreement with the experimental data.     

Features of solid solution formation with a fluorite type structure in the system ZrO2-HfO2-Y2O3 with different synthesis methods

X-ray phase, petrographic, and thermal analysis methods are used to study the properties of solid solutions with a fluorite type structure in the ternary system ZrO₂-HfO₂-Y₂O₃ in relationship to preparation method: mixing of the original powders followed by solid-phase sintering and melting in solar furnaces; hydrothermal synthesis of nanocrystalline powders followed by solid-phase sintering. It is shown that in specimens whose composition lies at the isoconcentrate of 10 mole% Y₂O₃ a single phase forms independent of preparation method, i.e. a solid solution with a fluorite type structure. The azeotrope, situated at the liquidus of the limiting binary system ZrO₂-Y₂O₃ in the region of fluorite-like solid solutions, affects the melting temperature of ternary solid solutions and the lattice parameters of specimens after melting in a solar furnace. __________ Translated from Poroshkovaya Metallurgiya, Nos. 1–2(447), pp. 3–11, January–February, 2006.     

Thermodynamic properties of solid Ni-Zn alloys by atomic absorption

Atomic absorption spectroscopy was used to determine the vapor pressure of zinc in equilibrium with α,β ₁, and γ-phase Ni-Zn alloys. This technique is based upon measurement of the attenuation of a resonance line of zinc of wavelength 3076Å. Thermodynamic activity, relative partial molar enthalpy and entropy, and excess properties of zinc were calculated. Lattice parameters were also measured for the alloys from Debye-Scherrer patterns, and trends in the thermodynamic data were correlated with composition variation in the lattice parameters. Thermodynamic properties in all three phases showed negative deviation from ideality. All three phases showed a large, negative excess entropy. An attempt was made to partition the thermodynamic properties of the α-phase alloys into magnetic, vibrational, and electronic contributions, and a model based on the rigid band approximation was applied to the excess free energy of zinc. Thermodynamic properties of the β₁ alloys were found to be in good agreement with a model based on a substitutional defect in the equiatomic alloy. Thermodynamic behavior of the γ-phase alloys was correlated with magnetic susceptibility and lattice effects—behavior in this electron compound seems complex. Magnetic contributions due to destruction in the alloys of the magnetic moment of nickel appear to make a strong contribution to the entropy of alloys in this system. Leave as Professor of Metallurgy Department of Materials Science, Washington State Univ.     

Thermodynamic assessment of the Nb-N system

The phase equilibrium and thermodynamic information of the Nb-N system was reviewed and assessed by using thermodynamic models for the Gibbs energy of individual phases. Although there was a large amount of experimental information of the system, heat capacity data of the Nb₂N and NbN were not available either in low or high temperatures. In the present study, low-temperature heat capacity and the^o S ₂₉₈ values were estimated using estimated entropy Debye temperatures. Only the Nb₂N (hcp) and NbN (fcc) nitrides were considered to be the true binary phases and were included in the present evaluation in addition to the N₂ gas, liquid, andα-solid solution (bcc). Three thermodynamic models were used: a two-sublattice model for the solid solution phases, a substitutional model for the liquid phase, and an ideal-gas model for the N₂ gas. The model parameters were evaluated by fitting to the selected data by means of a computer program. A consistent set of parameters was obtained which satisfactorily described most of the experimental and estimated data.     

An experimental and thermodynamic study of the Fe-Cr-C-N system at 1273 K

The thermodynamic properties of the Fe-Cr-C-N system at 1273 K (1000 °C) have been evaluated using old and new information. The binary systems are well established. The Fe-Cr-C system is fairly well established, but some experiments were performed in this study in order to establish theα/γ/M₂₃C₆ equilibrium. The Fe-Cr-N system was evaluated in a parallel study. In the Fe-C-N system the properties of theα andγ phases are well established. No direct information from the Cr-C-N system was used. In order to establish the properties of the quaternary system some experiments were made by equilibrating a set of Fe-Cr-C-N alloys at 1273 K, using a sealed capsule technique. After quenching, the carbon and nitrogen activities were evaluated by analyzing the specimens, which were completely austenitic. Phase equilibria in other specimens were studied by microprobe measurements and X-ray phase identification. When the quaternary system was evaluated thermodynamically, it was found that all the experimental information could be reasonably well accounted for without introducing new parameters for the quaternary system. However, it was necessary to evaluate the properties of the metastableε-Cr₂C phase in order to fit the quaternary experimental information. The phase diagram was calculated from the evaluated thermodynamic properties. A number of sections are presented for direct comparison with the experimental data. Formerly with Royal Institute of Technology, Stockholm.     

Interaction of Yttrium,Lanthanum, and Samarium Oxides at 1600°C

Phase equilibria and structural transformations in the La2O3–Y2O3–Sm2O3 system at 1600°C were studied by X-ray diffraction and petrography over the entire composition range. Solid solutions based on the hexagonal (A) modification of La2O3, cubic (C) modification of Y2O3, and monoclinic (B) modification of La2O3 (Sm2O3) were found to form in the system. The starting materials were La2O3, Sm2O3, and Y2O3 (99.99 %) powders. The samples were prepared from nitrate solutions with subsequent evaporation and decomposition at 800ºC for 2 h. The samples were subjected to heat treatment in three stages: at 1100°C (for 2464 h), at 1500°C (for 50 h), and then at 1600°C (for 10 h) in furnaces with Fechral (H23U5T) and Superkanthal (MoSi2) heating elements, respectively. The isothermal section of the La2O3–Y2O3–Sm2O3 phase diagram at 1600°C is characterized by three single-phase (A-La2O3, B-La2O3 (Sm2O3), C-Y2O3) and two-phase (A + B, B + C) regions. The ordered phase of perovskite-type was not found at 1600°C in this system. An infinite series of solid solutions based on the monoclinic modification of B-La2O3 (Sm2O3), which occupies the largest area of the isothermal section, forms in the system. Yttrium oxide stabilizes the total mutual solubility of lanthanum and samarium oxides. The lattice parameters of the B phase decrease, the lattice volume increases with the addition of a heavier ion, and the lattice of solid solutions based on the B modification of rare earth metal oxides becomes more densely packed with higher yttrium oxide. The lattice parameters of the B phase lattice vary from a = 1.3988 nm, b = 0.3774 nm, and c = 0.8427 nm in the single-phase sample containing 15 mol.% Y2O3–42.5 mol.% La2O3– 42.5 mol.% Sm2O3 to a = 1.3806 nm, b = 0.3709 nm, and c = 0.8312 nm in the two-phase sample containing 45 mol.% Y2O3–27.5 mol.% La2O3–27.5 mol.% Sm2O3.     

Thermodynamics of theβ’-NiZn intermetallic phase exhibiting the CsCl-structure

The thermodynamic activity, partial molar entropy and partial molar enthalpy of zinc have been calculated based on the measurement of partial pressure of zinc above eleven β’-NiZn alloys exhibiting the CsCl-type of structure over the temperature interval 1042 to 1159 K, using the dew-point method. Good correlations are found between theory and experiment for all three partial quantities. Furthermore, from these results and the recently reported data on the f.c.c. terminal solid solutions, the corresponding partial quantities of nickel in β’-NiZn alloys are computed as well as the integral quantities. It is found that the thermal entropy of this phase remains constant with composition, an assumption used by Chang and co-workers in deriving the theoretical equations to account for the compositional variations of the thermodynamic properties for this type of ordered phase. A similar analysis is also made for the thermodynamic properties of the low-tempe rature form of the equi-atomic phase exhibiting the face-centered tetragonal superlattice structure.