Thermodynamics and phase relationships of transition metal-sulfur systems: I. The cobalt-sulfur system

Thermodynamic activity of sulfur in the Co₄S₃±y, Co₉S₈ and C0₁-y, phases was determined as a function of composition over the temperature interval, 875 to 1168 K, using a gas equilibration technique. The data obtained in the present study as well as those reported in the literature are evaluated to yield thermodynamic equations of state for all the intermediate phases. Several forms of the Co-S phase diagram are presented. Formerly Research Assistant, Materials Department, College of Engineering and Applied Science, University of WisconsinMilwaukee     

Thermodynamics and phase relationships of transition metal-sulfur systems: I. The cobalt-sulfur system

Thermodynamic activity of sulfur in the Co₄S_3±y , Co₉S₈ and Co_1−y phases was determined as a function of composition over the temperature interval, 875 to 1168 K, using a gas equilibration technique. The data obtained in the present study as well as those reported in the literature are evaluated to yield thermodynamic equations of state for all the intermediate phases. Several forms of the Co−S phase diagram are presented. Y. O. CHEN, formerly Research Assistant, Materials Department, College of Engineering and Applied Science, University of Wisconsin-Milwaukee     

Thermodynamics and phase relationships of transition metal-sulfur systems: IV. thermodynamic properties of the Ni-S liquid phase and the calculation of the Ni-S phase diagram

An associated solution model is applied to describe the thermodyanmic properties of the liquid Ni-S phase. This model assumes the existence of ‘NiS’ (l) species in the liquid in addition to Ni(l) and S(l). With two solution parameters for the binaries Ni-‘NiS’ and ‘NiS’-S, this model is able to describe the thermodynamic behavior of the liquid phase over a wide range of temperature and composition. Using this model for the liquid phase, a statistical thermodynamic model for the monosulfide phase and empirical thermodynamic equations for β₁-Ni₃S₂ and β₂-Ni₄S₃, the Ni-S phase diagram is calculated. The calculated diagram is in excellent agreement with the available experimental data with the exception that the eutectic composition for the equilibrium L₁ + δ + η and those of the two liquids for the equilibriumL ₁ + L ₂ + η differ from the experimental data by more than 2 at. pct S. Formerly Post-Doctorl Research Associate, University of Wisconsin-Milwaukee is now Lecturer, Department of Metallurgical Engineering, Indian Institute of Technology, Kanpur, India     

Phase constitution of the Ni−Cr−S alloy system between 600° and 850°C

The diffusion couple method and electron probe microanalysis have been used to determine the ternary isotherms of Ni?Cr?S at 600°, 700°, 800°, and 850°C for sulfur compositions lying below 60 at. pct. It has been found that the solid and liquid phases Ni_3+x S₂ have a very shallow penetration into the diagram whereas the Ni_1?x S, Cr₃S₄, and Cr₂S₃ phases penetrate very deeply into the diagram. The phase compositions NiCr₂S₄ and NiCrS₃ have been detected near the limit of the latter two phase fields. The binary phases Cr₂S₃, Cr₃S₄, Cr₅S₆, Cr₇S₈, and CrS have all been identified and their existence ranges and free energies of formation have been established at 700°C. The phase diagram observed and proposed is consistent with the sequence of free energies of formation of nickel and chromium sulfides.     

Physicochemical laws of the interaction of nickel aluminides with alloying elements: II. Interaction of nickel aluminides with alloying elements and/or interstitial phases

The Ni-Al-X (X is an interstitial element or phase) phase diagrams are analyzed to reveal systems that can be used as the basis for designing promising alloys and natural composites based on nickel aluminides reinforced by interstitial phases (natural composites I). The most thermally stable materials are shown to be heterophase alloys and composite materials (CMs) located in the eutectic-type (including degenerate eutectic) pseudobinary sections of ternary or multicomponent phase diagrams. They exhibit insignificant (or zero) dissolution of interstitial phases at operating temperatures and the absence of an intense interaction between CM components (natural composites II). Natural composites I based on the NiAl-or Ni₃Al-interstitial phase alloys produced upon cooling from a melt can be reinforced by the refractory thermally stable rigid interstitial phases, namely, borides and carbides, that are present in pseudobinary sections in equilibrium with these nickel aluminides, since the elements forming these phases dissolve completely in matrix melts and the mutual solubility of these phases in the solid state is low. Such borides are TiB₂ and HfB₂ in equilibrium with β-NiAl, and such carbides are, e.g., TiC and HfC in equilibrium with β-NiAl and La₂C₃, NbC, and TaC in equilibrium with γ′-Ni₃Al. Natural composites II should be produced using solid-phase methods (NiAl with AlN, Y₂O₃, Al₂O₃) or a combination of methods, where a refractory interstitial phase of the Al₂O₃ or Y₂O₃ type is solid and the intermetallic NiAl or Ni₃Al matrix is liquid. NiAl-TiB₂ (HfB₂), NiAl-Al₂O₃ (Y₂O₃), and Ni₃Al-La₂C₃ (NbC, TaC) composites are considered as examples.     

Critical evaluation and optimization of the thermodynamic properties and phase diagrams of the CaO-Al2O3, Al2O3-SiO2, and CaO-Al2O3-SiO2 systems

All available thermodynamic and phase diagram data have been critically assessed for all phases in the CaO-Al₂O₃, Al₂O₃-SiO₂, and CaO-Al₂O₃-SiO₂ systems at 1 bar pressure from 298 K to above the liquidus temperatures. All reliable data for the binary systems have been simultaneously optimized to obtain, for each system, one set of model equations for the Gibbs energy of the liquid slag and all solid phases as functions of composition and temperature. The modified quasichemical model was used for the slag. With these binary parameters and those from the optimization of the CaO-SiO₂ system reported previously, the quasichemical model was used to predict the thermodynamic properties of the ternary slag. Two additional small ternary parameters were required to reproduce the ternary phase diagram and ternary activity data to within experimental error limits. The calculated optimized phase diagram and thermodynamic properties are self-consistent and are the most reliable currently available estimates of the true values.     

Investigation of the surface of the liquidus of the Fe-Ni-S system at X s<0.51

Methods of thermal analysis, X-ray, optical, and electron microscopy were used to study the liquidus surface of the Fe-Ni-S system in the field of 35 to 51 at. pct sulfur. The FeS-NiS, FeS-Ni₃S₂, Fe_0.55S_0.45-Ni_0.55S_0.45, and Fe_0.61S_0.39-Ni_0.61S_0.39 sections and some additional samples were examined. A microscopic study of the samples slowly cooled and annealed enabled referring of all the samples to the fields of primary crystallization of the monosulfide solid solution (Fe _x Ni_1−x )S_1+y (MSS), the Fe-Ni solid solution with the γ-Fe structure (TN), and the (Fe _x Ni_1−x )_3±y S₂ heazlewoodite solid solution (HZSS). The data, obtained by a method of derivative thermal analysis, have been used to describe analytically the MSS and HZSS surface of primary crystallization. Previous results were used together with our own data to construct the TN surface of primary crystallization. These parts of the liquidus surface have been approximated by polynomial equations, the coefficients of which were determined by the least-squares method. As a result of the absence of experimental data in the δ-Fe-based solid-solution primary crystallization field, this liquidus part is approximated on the basis of the Fe-S and Ni-Fe phase diagram data. The equations are used to construct the boundaries between various areas of phase primary crystallization, to define the coordinates of a triple point, and to construct isotherms.     

The relative stabilities of Cr23C6/ Cr7C3/ and Cr3C2 and the phase relationships in ternary Cr-Mo-C system

The thermodynamic properties of CrC_6/23, CrC_3/7, CrC_2/3, and MoC_1/2 reported in the literature have been correlated with the relative stabilities of these carbide phases derived from ternary phase diagrams. On the basis of the free energy of formation for one of the carbides and the free energy changes for the various equilibria occurring in ternary Mo-Cr-C system at 1300°C, free energies of formation for the stable and unstable carbide phases have been obtained. Using this free energy data, a calculated ternary Mo-Cr-C phase diagram is presented which agrees well with the experimentally determined one.     

A Phase-Field Model for Phase Transformations in Glass-Forming Alloys

A phase-field model is proposed for phase transformations in glass-forming alloys. The glass transition is introduced as a structural relaxation, and the competition between the glass and crystalline phases is investigated. The simulations are performed for Cu-Zr alloys, employing thermodynamic and kinetic parameters derived from reported thermodynamic modeling and molecular dynamics simulation results,[1?C3] respectively. Four distinct phase fields are treated with a multi-phase-field approach, representing the liquid/glass, Cu₁₀Zr₇, CuZr, and CuZr₂ phases. In addition, a continuum-field method is applied to the liquid to accommodate the liquid?Cglass transformation. The combined phase-field approach is used to investigate the glass formation tendency, and critical cooling rates are estimated and compared with the reported experimental values.     

Critical evaluation and optimization of the thermodynamic properties and phase diagrams of the MnO-TiO2, MgO-TiO2, FeO-TiO2, Ti2O3-TiO2, Na2O-TiO2, and K2O-TiO2 systems

All available thermodynamic and phase diagram data have been critically assessed for all phases in the MnO-TiO₂, MgO-TiO₂, FeO-TiO₂, Ti₂O₃-TiO₂, Na₂O-TiO₂, and K₂O-TiO₂ systems at 1 bar pressure from 298 K to above the liquidus temperatures. All reliable thermodynamic and phase diagram data have been simultaneously optimized to obtain, for each system, one set of model equations for the Gibbs energy of the liquid slag as a function of composition and temperature and equations for the Gibbs energies of all compounds as functions of temperature. The modified quasichemical model was used for the molten slag phases.     

Determination of the isothermal sections of the Al-Ni-Si ternary system at 750 °C and 850 °C

The phase equilibria of the Al-Ni-Si ternary system at 850 °C and 750 °C have been investigated using scanning electron microscopy (SEM) and electron-probe microanalysis (EPMA). Isothermal sections at 850 °C and 750 °C were constructed based on experimental data from 53 alloys heat treated at 850 °C for 1200 hours and at 750 °C for 1440 hours, respectively. The phase equilibria among the following intermetallics and solid-solution phases are described: Ll₂-Ni₃(Al,Si), B2-NiAl, Ni₅Si₂, δ-Ni₂Si, ϑ-Ni₂Si(τ ₄), Ni₃Si₂, NiSi, NiSi₂, Ni₂Al₃, NiAl₃, Ni₂AlSi(τ ₂), Ni₃Al₆Si(τ ₃), Ni₁₆AlSi₉(τ ₅), the fcc solid solution, and the diamond (Si) phase. In addition, a phase, temporarily designated as Ni₅(Al,Si)₃(τ ₆), was observed for the first time at both 750 °C and 850 °C. This phase is probably the stabilization of Ni₅Al₃ by Si to higher temperatures than the binary Ni₅Al₃, which is only stable at <∼700 °C.     

Microstructure of AI2O3 fiber-reinforced superalloy (INCONEL 718) composites

Composites of INCONEL 718 alloy reinforced with either single-crystal (SAPHIKON) or polycrys-talline (Du Pont's FP) A1₂O₃ fiber were fabricated by pressure casting. Optical and transmission electron microscopy were used to characterize the microstructure of the composites and to determine the nature of the fiber/matrix reaction. The widely dispersed fibers in the SAPHIKON-fiber-reinforced composite had no influence on the solidification of the matrix. Six phases, γ-Ni₃Al, γ'-Ni₃Nb, δ-Ni₃Nb, TiC, NbC, and Laves, were present in the matrix of the composite. The last three phases were formed during solidification and the others precipitated during subsequent cooling. The high density of fibers in the FP-fiber-reinforced composite led to a more uniform microstructure within the matrix. Only three phases,γ″-Ni₃Nb, NbC, and Laves, were identified. Diffusion of Ti into the A1₂O₃ fiber resulted in preferential grain growth in the FP fiber in areas adjacent to the fiber/matrix interface. The fiber/matrix bond strength in shear in the SAPHIKON-fiber-reinforced composite was in excess of 150 MPa.     

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.     

Equilibres liquide-solide dans le systeme Ni-B-Si dans la region riche en nickel

The ternary system Ni-Si-B has been studied experimentally in the range (B + Si) < 45 at.%. This system was established by means of differential thermal analysis, X-ray diffraction, scanning and transmission electron microscopy. The main findings are reported: the end of solidification in the Ni-rich corner is the ternary eutectic: Ni(α)-Ni₃B-δNi₆Si₂B; in this composition range, δNi₆Si₂B decomposes during cooling; two ternary quasiperitectic reactions are observed for higher B and Si levels; the βNi₃Si and δ Ni₆Si₂B phases occur by peritectic reactions from γNi₅Si₂. The crystallisation paths and the resulting structures are always complex when γNi₅Si₂ appears as primary phase.     

Solid-State displacement reactions between selected metals and sulfides

Displacement reactions between sulfides and metals in the solid state are studied and compared with the resultant morphologies previously observed in oxide-metal displacement reactions. Sufficient thermodynamic and diffusion data were available only for the theoretical prediction of product morphology for the Fe-Ni₃S₂ reaction couple. Experiments substantiated the theoretical prediction of an aggregate morphology for this couple at 600°C. The growth of the product zone for the Fe-Ni₃S₂ reaction couple obeyed parabolic kinetics. The experimentally observed morphologies for Co-Ni₃S₂, Fe-Co₄S₃, Mn-Crs, Nb-Cu.₂S, Cr-Cu₂S, Cr-Ni₃S₂, and Mn-Cu₂S reaction couples are also reported and rationalized.     

Thermodynamics of the solid Ni-S system

Published measurements of sulfur vapor pressure were used to determine thermodynamic properties of the solid Ni-S system above 800 K. They were Gibbs-Duhem integrated to estimate the formation properties of stoichiometric Ni₃S₂, NiS, and NiS₂. Statistical thermodynamics was applied to find partition functions, interaction energies, and free energies to find possible atom arrangements in Ni_3±x S₂ and Ni_1−x S. Theoretical calculations indicated that nickel vacancies may exist in quasichemical order in the former phase and randomly in the latter phase. A strong indication was that Ni_3±x S₂ should have a sulfur bcc structure with nickel atoms distributed in octahedral sites having a Ni₅S₄ configuration. The possible existence of sulfur vacancies was theoretically investigated.     

Computer analysis of phase diagrams and thermodynamic properties of cryolite based systems: Part II. The AIF3-CaF2-LiF,AIF3-CaF2-NaF,and CaF2-LiF-NaF systems

A computer-assisted critical analysis of available phase diagrams and thermodynamic data of the ternary AlF₃-CaF₂-NaF, AlF₃-CaF₂-LiF, and CaF₂-NaF-LiF systems up to 30 mol pct A1F₃, as well as of all binary subsystems was performed. Optimized mathematical expressions for the thermodynamic properties of all phases were obtained. In the case of the binary mixtures, the use of the F0rland equivalent fractions was shown to reduce the number of coefficients needed to represent analytically the enthalpies of mixing. The Conformai Ionic Solution Theory was applied with success to describe the thermodynamic properties of these ternary charge-asymmetrical systems. The binary and ternary phase diagrams were calculated and compared, wherever possible, with experimental investigations.     

Phase relations in the Mo-Si-C system relevant to the processing of MoSi2-SiC composites

Phase relations in the Mo-Si-C system were evaluated at 1200 °C and 1600 °C within the composition range delimited by the phases Mo₅Si₃, MoSi₂, Mo_≤5Si₃C_≤1, and SiC. The evaluation included estimation of possible equilibria from known thermodynamic data of the binary phases as well as experimental work. For the experimental evaluation, high-purity powders were hot-pressed, heat-treated, and characterized by X-ray diffraction and electron microprobe analysis. It is shown that MoSi₂ is in equilibrium with Mo_≤5Si₃C_≤1 at 1600 °C, as previously established by Nowotnyet al, (Monatsh. Chem., 1954, vol. 85, pp. 255-72), and at 1200 °C, in contrast to the Mo₅Si₃-SiC equilibrium reported by van Looet al. (High Temp.- High Press., 1982, vol. 14, pp. 25-31). The thermodynamic estimation suggests that these phase relations should extend to lower temperatures in the range of compositions investigated. Thus, the third phase in silicon-lean MoSi₂-SiC composites should be the Nowotny phase (Mo_≤5Si₃C_≤1) instead of Mo₅Si₃. The Gibbs free energy of formation at 298 K of the idealized compound Mo₅Si₃C is estimated as -40.2 kJ/mol.