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.     

Thermodynamic analysis of the iron-copper system I: The stable and metastable phase equilibria

Thermodynamic and phase diagram data in the Fe-Cu system are evaluated. For the liquid and fcc phases, the Margules-type of equations is used. For the bcc phase, the same type of equation is used to describe the non-magnetic contribution to the Gibbs energy. In addition, a magnetic term is included. Using the thermodynamic equations derived from equilibrium data, the stable and metastable equilibria of this system are calculated. Agreement between the calculated and experimental phase diagram is good except for temperatures higher than 1720 K. For these temperatures, the calculated liquidus tends to be higher. The possibility of supercooling which may account for some of the lower temperatures measured should not be excluded. The calculated metastable miscibility gap of the liquid phase also agrees with the experimental data.     

Application of thermodynamics of heterogeneous phase equilibria to the construction of the Fe-Si-O ternary phase diagram

Based on the thermodynamic principles of phase rule and heterogeneous equilibria, the ternary phase diagram for the system Fe-SiO in the range of temperatures from 1730 to 1200° has been constructed with more attention paid to temperatures above 1515° and towards the iron corner of the diagram. The system is characterized by a region of three liquids above 1730° which reduces to two-liquids regions at lower temperatures. Several three-phase and four-phase reactions occur in this system on cooling, at various temperatures. Near the iron corner a eutectic reaction occurs at a fixed temperature in which delta iron co-precipitates with cristobalite from liquid iron containing silicon and oxygen. At lower temperatures the system is characterized by an invariant reaction involving liquid iron, delta iron, cristobalite and liquid oxide. For oxygen rich melts, solidification terminates on the Fe-0 binary with the monotectic precipitation of delta iron and liquid oxide. This paper was presented at the Centennial Meeting of the AIME Conference, New York, 1971.     

Use of Flory’s approach for assessing the phase diagram of zinc-bismuth (Zn-Bi) system

In an attempt to check the suitability of Flory’s approach for assessing the miscibility gap in binary monotectic systems, Zn-Bi has been chosen. Using Flory’s approach for the liquid phase and experimental data for the existing solid phases, the computer generated phase diagram locates the monotectic point at 689.5 K (416.5 °C) and 0.6 at. % Bi. The critical point is located at 877.4 K (604.4 °C) and 13.96 at. % Bi.     

The Fe-Cu system: A thermodynamic evaluation

Thermochemical and phase diagram data in the Fe-Cu system have been critically evaluated by using phenomenological models for the Gibbs energy of various phases. A set of thermodynamic parameters more consistent with most of the selected experimental data than previous assess-ments has been obtained by a computerized least-squares method. Stable and metastable phase equilibria,T ₀ curves, and thermodynamic properties are calculated with the optimized param-eters. The calculated liquid/face-centered cubic (fcc)T ₀ curve and metastable liquid spinodal seem to permit an accurate prediction of maximum solid solubility obtained upon melt quenching in this system.     

The thermodynamics of tetrataenite and awaruite: A review of the Fe-Ni phase diagram

There are two well-known ordered ferromagnetic intermetallic compounds in the iron-nickel system: tetrataenite, FeNi, and awaruite, FeNi₃. Their thermodynamic properties are established from the various stable and metastable equilibria in which they are involved, and a review to make this data accessible is appropriate. The Fe-Ni phase diagram shows a paramagnetic face-centered cubic phase (gamma) with well-measured properties over the entire composition range from 1184 to 1662 K. Its properties can be extrapolated to lower temperatures, and known stable and metastable equilibria are used to establish models for the thermodynamic properties of the ferromagnetic alpha phase, a high-temperature paramagnetic alpha phase, a paramagnetic gamma-ordered Fe₃Ni phase, the ferromagnetic disordered gamma phase, and both ordered ferromagnetic gamma phases, tetrataenite, FeNi, and awaruite, FeNi₃. The overestimate of Chuang et al. for the entropy of ordering in awaruite is corrected. The standard enthalpies at 298.15 K of tetrataenite (0.5 FeNi) and awaruite (0.25 FeNi₃) are −1170 and −3560±1000 J mol⁻¹. The corresponding standard entropy values are 35.7 and 33.3±3 J mol⁻¹ K⁻¹. All the second-order transitions are accurately modeled and the full phase diagram is calculated. The spinodal regions and metastable equilibria responsible for the complex behavior on cooling of alloys with mole fractions of nickel between 0.26 and 0.40 are described in detail.     

Experimental Phase Equilibria Studies of the Pb-Fe-O System in Air,in Equilibrium with Metallic Lead and at Intermediate Oxygen Potentials

The phase equilibria information on the Pb-Fe-O system is of practical importance for the improvement of the existing thermodynamic database of lead-containing slag systems (Pb-Zn-Fe-Cu-Si-Ca-Al-Mg-O). Phase equilibria of the Pb-Fe-O system have been investigated: (a) in air at temperatures between 1053 K and 1373 K (780 °C and 1100 °C); (b) in equilibrium with metallic lead at temperatures between 1053 K and 1373 K (780 °C and 1100 °C); and (c) at intermediate oxidation conditions for the liquid slag in equilibrium with two solids (spinel + magnetoplumbite), at temperatures between 1093 K and 1373 K (820 °C and 1100 °C). The high-temperature equilibration/quenching/electron probe X-ray microanalysis technique has been used to accurately determine the compositions of the phases in equilibrium in the system. The Pb and Fe concentrations in the phases were determined directly; preliminary thermodynamic modeling with FactSage was used to estimate the ferrous-to-ferric ratios and to present the results in the ternary diagram.     

Experimental Investigation and Thermodynamic Calculations of the Bi-Ge-Sb Phase Diagram

A phase diagram of the Bi-Ge-Sb ternary system was investigated experimentally by differential thermal analysis (DTA), scanning electron microscopy with energy-dispersive X-ray spectroscopy (SEM-EDS), and X-ray powder diffraction (XRD) methods and theoretically by the CALPHAD method. The liquidus projection; invariant equilibria; and three vertical sections, Sb-Bi_0.5Ge_0.5, Ge-Bi_0.5Sb_0.5, and Bi-Ge_0.5Sb_0.5, as well as isothermal sections at 773 K and 373 K (500 °C and 100 °C), were predicted using optimized thermodynamic parameters for constitutive binary systems from the literature. In addition, phase transition temperatures of the selected samples with compositions along calculated isopleths were experimentally determined using DTA. Predicted isothermal sections at 773 K and 373 K (500 °C and 100 °C) were compared with the results of the SEM-EDS and XRD analysis from this work. In both cases, good agreement between the extrapolated phase diagram and experimental results was obtained. Alloys from the three studied vertical sections were additionally analyzed using the Brinell hardness test.     

Thermodynamic Modeling of the Al-Ti-V Ternary System

The sub-binary systems Al-Ti, Ti-V, and Al-V are reviewed and adopted from the previous assessments, the thermodynamic analysis of the Al-Ti-V ternary system is performed by the CALPHAD approach, and a set of self-consistent thermodynamic parameters of the ternary system are obtained. Furthermore, the isothermal sections of this system at 1073 K, 1173 K, 1273 K, 1373 K, and 1473 K (800 °C, 900 °C, 1000 °C, 1100 °C, and 1200 °C) and the ternary invariant equilibria are calculated and compared with the corresponding experimental data, and all are in good agreement with most of the experimental results. Thus, the optimized thermodynamic parameters in this study may provide more accurate guidance to develop the new alloys involving it.     

The thermodynamic properties and phase diagram of the zinc-lead system

A Gaussian plus Krupkowski formalism is used to represent the phase diagram, boiling point data, and the thermodynamic properties of the zinc-lead system. The high shear technique of Esdaile and Siviour 1 was adapted for measurements of the monotectic conditions and the boundaries of the liquid miscibility gap. The monotectic conditions were found to be 690.94 ± 0.02 K and 1.017 ± 0.005 wt pct Pb, 0.323 ± 0.002 at. pct Pb.     

Activity Measurements of Mg in the Ternary Cu-Mg-Si System Using Thermogravimetric Knudsen Effusion Method

The high vapor pressure of Mg in comparison with Cu and Si enables the use of thermogravimetric Knudsen effusion method (KEM) to determine the thermodynamic properties of binary Cu-Mg, Mg-Si, and ternary Cu-Mg-Si alloys. In the current study, the weight loss of solid Mg with time has been determined at different constant temperatures between 705 K and 788 K (432 °C and 515 °C) by using KEM, and from these diagrams, the sublimation rate of Mg was calculated. By introducing the sublimation rates into the equation derived from the kinetic gas theory, the enthalpy change of sublimation reaction of Mg at the experimental temperatures was calculated to be 147.5 ± 6.5 kJ mol^?1, which is close to the 143.8 ± 0.5 kJ mol^?1 calculated using the thermodynamic data available in the literature. Similar procedure was also applied to the binary Cu-Mg, Mg-Si, and ternary Cu-Mg-Si alloys where the activities of Mg with respect to the Mg wt pct with W _Cu:W _Si = 20:80 were calculated. The diversion points in the activity–composition diagrams gave the phase boundary compositions in the phase diagrams. The phase boundary compositions of Mg in the alloys determined using KEM were in good agreement with the known binary and the constructed ternary phase diagram using FactSage thermochemical software and databases.     

Thermodynamics and phase diagram of the Fe-C system

A critical review of published data provides a fairly accurate knowledge of the thermodynamic properties of all of the phases of the system Fe-C that are stable or metastable at atmospheric pressure. Selected data are shown as tables and equations. A proposed phase diagram differs only slightly from others recently published but has the following features. Peritectic compositions and the α-γ equilibrium are shown to agree with measured values of the activity of iron in the solid and liquid solutions and the thermodynamic properties of pure iron. Of all the reported carbides of iron only two may be studied under equilibrium conditions. The solubilities of cementite and of χ-carbide in α-Fe are deduced from measured equilibria. Both are metastable at all temperatures with respect to graphite and its saturated solution in iron. The χ-carbide becomes more stable than cementite below about 230° Certain published data on ε-carbide permit an estimate of its free energy as a precipitate during the aging process.     

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

A Study of equilibria in the Fe-Cr-Ni-Mo-C-N system at 1273 K

The phase equilibria in the Fe-rich corner of the Fe-Cr-Ni-Mo-C-N system have been studied at 1273 K using a sealed capsule technique to measure the C and N activities and the electron microprobe to measure the compositions of the individual phases following identification by X-ray analysis. Some of the new information was combined with previous assessments of the Fe-Cr-N, Fe-Ni-N, and Fe-Cr-Ni systems and a new assessment of the Cr-Ni-N system in order to assess the thermodynamic properties of the Fe-Cr-Ni-N system. A set of parameters is obtained, based mainly upon experimental information from 1273 K (1000 °C) and 1473 K (1200 °C), which can be used for calculations of the Fe-Cr-Ni-N phase diagram in this temperature range. Isothermal sections are presented and show reasonable agreement with experimental data not used in the assessment. The thermodynamic analysis is restricted to the Fe-Cr-Ni-N system, but some experimental data are also presented for alloys containing Mo and C. Formerly with Royal Institute of Technology, Stockholm.     

A thermodynamic analysis and calculation of the Fe-Ni-Cr phase diagram

Phase diagrams of Fe-Ni-Cr are calculated as a function of temperature from the liquid phase down to 500 K using thermodynamic values of the pertinent phases. These phases are the liquid, fcc, bcc, sigma, and γ^′-FeNi₃ phases. Not only the thermodynamic values calculated from the models for the various phases are in agreement with experimental data available in the literature, the calculated phase diagrams are also in agreement with experimental data over a wide range of temperature. Below 1123 K, no conventional phase diagram data are available in the literature due to kinetic difficulties. However, the calculated diagram is able to explain the results obtained when the alloys are subjected to electron irradiation. Deceased, was with the Department of Metallurgical and Mineral Engineering, University of Wisconsin.