Phase equilibria in the ternary Al-Sc-Mn system

Optical microscopy, electron microprobe analysis, and electrical resistivity measurements are used to study Al-Sc-Mn alloys containing up to 3 at % Sc and to 2.5 at % Mn. The boundaries of the Al-based solid solution are determined at 640, 600, and 400°C, and the isothermal section of the Al-rich portion of the Al-Sc-Mn system at 640°C is constructed. The Al-based solid solution is found to be in equilibrium with the ScAl₃ and MnAl₆ phases.     

Phase equilibria in the ternary system zirconium-molybdenum-carbon

Summary The system Zr-Mo-C was investigated by means of x-ray diffraction and microstructural analyses. Phase equilibria in the system at 1400 and 600°C were established (Fig. 1). The compound Mo₂C dissolves about 4 at.% Zr. The ZrC-base solid solution extends up to 90 mol.% Mo₃C₂. The hexagonal phase Mo₃C₂ may be stabilized at 1400°C and below by zirconium.     

Estimating terminal phase equilibria in ternary systems

Abstract

An analytical method for the estimation of terminal two-phase equilibria in ternary systems is presented. The method utilizes thermodynamic solution parameters, free energies of transformation of pure components and phase equilibria of the relevant binary systems.

At low solute concentrations or at higher concentrations in systems where solute interactions are weak, it is shown that ternary isotherms are characterized by approximately linear phase boundaries and constant solute partition coefficients.

The method has been employed to calculate several tie-lines of the 1510°C isotherm in the iron-rich comer of the Fe-Mn-S diagram. In this moderately rich solution system typifying fairly strong solute interaction, the curvature of the phase boundaries and variation of the partition coefficients throughout the two-phase region are found to be minimal (for the parameters used in the calculations).

Résumé

Cette communication fait part d'une méthode de calcul des lignes de conjugaison dans les régions terminales d'un diagramme de phases ternaire. La méthode utilise les paramètres thermodynamiques de solution, les énergies libres de transformation des composants, et les diagrammes de phases binaires qui limitent le diagramme ternaire.

On démontre que les isothermes sont linéaires et les coefficients de partage invariables lorsque les interactions entre solutés sont faibles.

La méthode a servi au calcul des lignes de conjugaison de la région fer δ + liquide du système Fe-Mn-S à 1510°C. On constate que la courbure des isothermes et la variation des coefficients de partage d'un bout à l'autre de la région bi-phasée sont minimes.     

Phase equilibria and intermetallic phases in the Ni-Si-Mg ternary system

The Ni-Si-Mg ternary phase diagram has been established after homogenization and slow cooling to room temperature. The chemical compositions of the alloys and their phases were obtained using fully quantitative energy dispersive X-ray spectroscopy (EDS) with standard spectrum files created from intermetallic compounds Mg₂Ni and Ni₂Si. The following intermetallic phases have been observed: (a) four new ternary intermetallic phases, designated as ν, ω, μ, and τ, (b) a ternary intermediate phase Mg(Ni,Si)₂ based on the binary MgNi₂ phase containing Si; (c) three ternary intermetallic phases, η, κ, and ζ, previously reported by the present authors;[10] and (d) Mg₂SiNi₃ (Fe₂Tb type),^[9] previously reported by Noreus et al. ^[8] The MgNi₆Si₆ phase, which was also previously reported,^[7] was not observed at the corresponding composition in the present work. However, the MgNi₆Si₆ phase reported as being of hexagonal symmetry (Cu₇Tb type),^[9] with the lattice parameters a=0.4948 nm and c=0.3738 nm, possibly corresponds to the μ phase (Mg(Si_0.48Ni_0.52)₇) discovered in the present work. The lattice structure of the newly discovered ω phase was determined with the help of the X-ray indexing program TREOR (developed by Werner et al. ^[13]) to be a hexagonal structure of the Ag₇Te₄ type ((Mg_0.52Ni_0.48)₇Si₄) with the lattice parameters a=1.3511 nm and c=0.8267 nm.     

Phase equilibria in Nb-Y-Si ternary system at 873 K

The isothermal section of the Nb-Y-Si ternary system at 873 K was investigated over the whole concentration range mainly by powder X-ray diffraction (XRD), scanning electron microscopy (SEM) and energy dispersive analysis (EDX). This isothermal section consisted of 10 single-phase regions, 17 two-phase regions, and 8 three-phase regions. The existence of the binary compounds, i.e., Y 5 Si 3 , Y 5 Si 4 , YSi, Y 3 Si 5 , YSi 2 , Nb 5 Si 3 and NbSi 2 at 873 K was confirmed. On the basis of XRD patterns, the structure types of Y 5 Si 4 , Y 3 Si 5 and YSi 2 were discussed. No ternary compound and no detectable solid solubility in the binary compounds were found.     

Phase equilibria in the ternary systems Zirconium-Vanadium-Boron,Zirconium-Niobium-Boron and Zirconium-Manganese-Boron

Summary The systems Zr-V-B, Zr-Nb-B, and Zr-Mn-B were investigated by the x-ray diffraction technique, and their phase equilibria at 900° C (Zr-V-B and Zr-Mn-B) and 1500° C (Zr-Nb-B) were established. Ternary compounds having an -phase structure were found in the systems Zr-V and Zr-Mn containing a small quantity of oxygen or nitrogen (a=12.153 A and 11.999 A, respectively). Solid solutions of zirconium in NbB and Nb₃B₂ were observed. The compound NbB dissolves 30 at. % Zr, and its lattice constants increase: a from 3.298 to 3.325 A, b from 8.722 to 8.813 A, and c from 3.164 to 3.175 A. The compound Nb₃B₂ dissolves 6 at. % Zr, and its lattice constants increase: a from 6.185 to 6.202 A and c from 3.281 to 3.295 A.Translated from Poroshkovaya Metallurgiya, No. 6(54), pp.49–52, June, 1967.     

Phase equilibria in the Mg-Al-Ca ternary system at 773 and 673 K

The isothermal sections of the Mg-Al-Ca ternary system at 773 and 673 K were determined by phase analysis with electron-probe microanalysis (EPMA) and transmission electron microscopy (TEM). The C36 phase exists between the C14 (Mg₂Ca) and C15 (Al₂Ca) phases, and its stoichiometry is close to Mg₂Al₄Ca₃. The α-Mg phase equilibrates with the C14 and C36 phases at 773 K, but with C14, C15, and β phases at 673 K, due to the decomposition of the C36 phase into C14 and C15 phases. These intermetallic phases have significant solid-solubility in the ternary system.     

Experimental studies on hydrogen solubility in liquid ternary iron-nickel-chromium alloys

The hydrogen solubilities in liquid ternary iron-nickel-chromium alloys have been experimentally determined by Sieverts’ method. The experimental data have been evaluated with the help of regression analysis (Gauß-Jordan) and using own published empirical equations (polynomials). With the help of experimentally determined hydrogen solubilities and the coefficients of the polynomials, the concentration dependencies of hydrogen solubilities, interaction coefficients, enthalpies and entropies of hydrogen solution have been determined. The hydrogen solubility increases with increasing temperature and with an increase in the nickel and chromium concentration. The results have been represented as isothermal planes. The hydrogen solubilities in liquid ternary iron-nickel-chromium alloys (x_Cr ≤ 50%) have been predicted with the help of “Central Atoms” model, assuming the concentration dependencies of the “model parameter λ” and selecting the value of the coordination number (Z’ = 10) for each of the “reference elements” iron or nickel. The comparison between the experimentally determined and the predicted hydrogen solubilities in iron-nickel-chromium alloys confirms that the prediction of hydrogen solubilities in liquid system iron-nickel-chromium can be qualitatively made over a wide range of alloy concentrations (x_Cr = 50%) with the aid of “Central Atoms” model and with the assumption of concentration dependencies of the “model parameter λ”.     

Effect of chromium on the hydrogen solubility in liquid ternary iron-cobalt-chromium alloys

The experimentally determined hydrogen solubilities (Sieverts’ method) in liquid iron–cobalt–chromium melts were described based on own already published empirical equations and applying the regression analysis (Gauß-Jordan). The experimental results are represented as perspective isothermal planes. Addition of chromium increases the hydrogen solubilities. The hydrogen solubility increases with increasing temperature. The concentration dependencies of the interaction coefficients, enthalpies and entropies of hydrogen solution were calculated from the experimentally determined hydrogen solubility. Assuming a concentration dependence of the model parameter “λ” of the “Central Atoms” model the hydrogen solubilities in ternary iron-cobalt-chromium (x_cr ≤ 20%) melts were predicted. These predictions were made using the own experimentally determined hydrogen solubilities of the binary system iron-cobalt (x_Co ≤ 100%) and iron–chromium (x_Cr ≤ 25%) with iron, and referred to the other two binary systems cobalt–iron (x_Fθ ≤ 100%) and cobalt–chromium (x_cr ≤ 20%) with cobalt as “reference element”. The predicted hydrogen solubilities were compared with the own experimentally determined hydrogen solubilities. The deviations between these two results are less than 2%.     

Phase equilibria in the ternary system Sc−Cr−C at subsolidus temperatures

Phase equilibria in the ternary system Sc−Cr−C were investigated by metallography, differential thermal analysis, x-ray diffraction, and electron probe microanalysis. A projection of the solidus surface was constructed for the first time. The nature of phase equilibria in the system is defined by the presence of two thermodynamically stable phases based on the compounds Sc₂CrC₃ (whose existence was confirmed) and ScC_1−x. The melting point of the alloys increases with increasing carbon concentration. Compositions in the 〈Cr〉+〈ScC_1−x〉+〈Sc〉 range have a minimum melting temperature equal to 1018±2°C, and the maximum melting temperature in the system, 1660±2°C, is found in alloys containing 〈Cr₃C₂〉+〈Sc₂CrC₃〉+C. Institute for Materials Science Problems. Ukrainian Academy of Sciences, Kiev. Translated from Poroshkovaya Metallurgiya, Nos. 3–4, pp. 18–26, March–April, 1997.     

Phase equilibria of the ternary Ni-Cr-Zr system and interfacial reactions in the Ni-Cr/Zr couples

The phase equilibria of the ternary Ni-Cr-Zr system and interfacial reactions in the Ni-Cr/Zr couples at 900 °C were determined. Fifty alloys were prepared from pure Ni, Cr, and Zr. The alloys were metallographically analyzed. Both X-ray diffraction and electron-probe microanalysis (EPMA) were carried out for structural identification and compositional analysis of phases formed in these alloys. At 900 °C, the Cr-Ni₁₀Zr₇ two-phase region divides the system into two halves. ZrCr₂(C14) exists in the Zr-Cr-Ni₁₀Zr₇ half, and the ZrCr₂ (C15) phase has an extensive ternary solubility. In the Cr-Ni₁₀Zr₇-Ni half, except for the Ni₇Zr₂ phase, most of the binary Zr-Ni compounds are in equilibrium with either Cr or Ni phase. Reaction-couple techniques were used for the interfacial reaction study. The reaction path was Zr/NiZr₂/NiZr/Ni₁₀Zr₇/Ni₂₁Zr₈/Cr/Ni-Cr alloy in the Ni-Cr/Zr couples examined in this study. The results indicate that Ni is the fastest-diffusing species, while Cr is the slowest one.     

On the solubility of aluminum in cryolitic melts

The solubility of aluminum in NaF-AlF₃-Al₂O₃ melts with various additives was found to increase with increasing NaF/AlF₃ molar ratio (CR) and increasing temperature and to decrease with additions of A1₂O₃, CaF₂, MgF₂, and LiF to the melts. With the use of literature data for the activities of NaF and A1F₃ in cryolitic melts, three dissolution reaction models were found to give a good fit to the experimental solubility data. According to the most probable of these models the total concentration of dissolved aluminum (aluminum and sodium species) is given by c_Al = c_Na(diss) + c_AlF2- + c_Al2F3- + c_Al3F4- + c_Al4F5- In NaF rich melts, aluminum will dominantly dissolve as sodium, while at cryolite ratios commonly used in aluminum electrowinning (CR = 2.25 to 2.7) the AlF _-2 ^- -ion is the predominant dissolved metal species. Other species (A1₂F₃ ^-, A1₃F₄-, A1₄F₅-) were found to be of some significance only in melts with high excess A1F₃ (CR < 2).     

On the solubility of aluminum in cryolitic melts

The solubility of aluminum in NaF-AlF₃-Al₂O₃ melts with various additives was found to increase with increasing NaF/AlF₃ molar ratio (CR) and increasing temperature and to decrease with additions of A1₂O₃, CaF₂, MgF₂, and LiF to the melts. With the use of literature data for the activities of NaF and A1F₃ in cryolitic melts, three dissolution reaction models were found to give a good fit to the experimental solubility data. According to the most probable of these models the total concentration of dissolved aluminum (aluminum and sodium species) is given by c_Al = c_Na(diss) + c_AlF2- + c_Al2F3- + c_Al3F4- + c_Al4F5- In NaF rich melts, aluminum will dominantly dissolve as sodium, while at cryolite ratios commonly used in aluminum electrowinning (CR = 2.25 to 2.7) the AlF _-2 ^- -ion is the predominant dissolved metal species. Other species (A1₂F₃ ^-, A1₃F₄-, A1₄F₅-) were found to be of some significance only in melts with high excess A1F₃ (CR < 2).     

Phase equilibria in the Mg?Al?Ca ternary system at 773 and 673 K

The isothermal sections of the Mg−Al−Ca ternary system at 773 and 673 K were determined by phase analysis with electron-probe microanalysis (EPMA) and transmission electron microscopy (TEM). The C36 phase exists between the C14 (Mg₂Ca) and C15 (Al₂Ca) phases, and its stoichiometry is close to Mg₂Al₄Ca₃. The α-Mg phase equilibriates with the C14 and C36 phases at 773 K, but with C14, C15, and β phases at 673 K, due to the decomposition of the C36 phase into C14 and C15 phases. These intermetallic phases have significant solid-solubility in the ternary system.     

Phase equilibria in the Mg?Al?Ca ternary system at 773 and 673 K

The isothermal sections of the Mg−Al−Ca ternary system at 773 and 673 K were determined by phase analysis with electron-probe microanalysis (EPMA) and transmission electron microscopy (TEM). The C36 phase exists between the C14 (Mg₂Ca) and C15 (Al₂Ca) phases, and its stoichiometry is close to Mg₂Al₄Ca₃. The α-Mg phase equilibriates with the C14 and C36 phases at 773 K, but with C14, C15, and β phases at 673 K, due to the decomposition of the C36 phase into C14 and C15 phases. These intermetallic phases have significant solid-solubility in the ternary system.     

On the geometrical representation of phase equilibria

In order to achieve a rational and optimal representation of thermodynamic information in a two-dimensional plot for multicomponent systems, three types of equilibrium phase dia-grams are investigated with regard to their topology. These three types are 1) diagrams in which the coordinates are given by two generalized thermodynamic potential functions ; 2) diagrams in which one generalized thermodynamic potential function is replaced by a ratio of conjugate extensive variables; 3) diagrams in which both generalized thermody-namic potential functions are replaced by ratios of conjugate extensive variables. In the second part of this investigation, the general considerations are used to calculate and construct phase diagrams of ternary systems of the kindA-B-X. It is shown that the pro-posed representations, especially the ones using logp X ₂-n _A/(n _A +n _B ) as generalized thermodynamic potential and conjugate extensive variable coordinates (which are topo-logically analogous to the well knownT- x _i -diagrams of binary systems) allow conclusions of practical importance to be drawn. The ternary systems discussed in detail are Co-Ni-O, Ag-Cu-Cl, Cu-Ni-S, Pb-Sn-Cl, Ag-Sb-S, Mg-Ni-O, Fe-Cr-O, and Fe-Ni-O.     

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.