Showing papers in "Calphad-computer Coupling of Phase Diagrams and Thermochemistry in 1991"
TL;DR: In this article, the authors present the data for the condensed phases of 78 elements as currently used by SGTE (Scientific Group Thermodata Europe) as a sound basis for the critical assessment of thermodynamic data, thereby, perhaps, limiting unnecessary duplication of effort.
Abstract: Thermodynamic data for the condensed phases of 78 elements as currently used by SGTE (Scientific Group Thermodata Europe) are tabulated. SGTE is a consortium of seven organisations in Western Europe engaged in the compilation of a comprehensive, self consistent and authoritative thermochemical database for inorganic and metallurgical systems. The data are being published here in the hope that they will become widely adopted within the international community as a sound basis for the critical assessment of thermodynamic data, thereby, perhaps, limiting unnecessary duplication of effort. The data for each phase of each element considered aie presented as expressions showing, as a function of temperature, the variation of (a) G-HSER, the Gibbs energy relative to the enthalpy of the “Standard Element Reference” ie the reference phase for the element at 298.15 K and (b) the difference in Gibbs energy between each phase and this reference phase (ie lattice stability). The variation of the heat capacity of the various phases and the Gibbs energy difference between phases are also shown graphically. For certain elements the thermodynamic data have been assessed as a function of pressure as well as temperature. Where appropriate a temperature— pressure phase diagram is also shown.
Throughout this paper the thermodynamic data are expressed in terms of J mol−1. The temperatures of transition between phases have been assessed to be consistent with the 1990 International Temperature Scale (ITS90).
4,116 citations
TL;DR: In this article, a modification of the excess Gibbs energy expression of the original model is suggested, which retains the original compatibility and also extends it to multicomponent systems, and is shown to be compatible to many different models for binary systems.
Abstract: A two-sublattice model for liquids was recently presented. This model was compatible to many different models for binary systems. However, for multicomponent systems it was found that this compatibility breaks down. A slight modification of the excess Gibbs energy expression of the original model is suggested in this paper which retains the original compatibility and also extends it to multicomponent systems.
161 citations
TL;DR: In this article, a thermodynamic analysis of phase equilibria in the V-N binary system has been carried out, where the thermodynamic parameters for each phase were evaluated on the available experimental data, by using thermodynamic models for the Gibbs energy.
Abstract: A thermodynamic analysis of phase equilibria in the V-N binary system has been carried out. The thermodynamic parameters for each phase were evaluated on the available experimental data, by using thermodynamic models for the Gibbs energy. Most of the experimental information was well reproduced by the present set of thermodynamic descriptions. However, some uncertainty still attaches to the nature of the γ(fcc) phase, and the need of further experimental investigations is emphasized.
138 citations
TL;DR: In this paper, a thermodynamic evaluation of the Cr-N, Fe-N and Mo-N systems using a two sublattice model for the solid phases and a subregular solution for the liquid is presented.
Abstract: A thermodynamic evaluation of the Cr-N, Fe-N, Mo-N and Cr-Mo-N systems using a two sublattice model for the solid phases and a subregular solution model for the liquid is presented. A set of parameters describing the Gibbs energies of the various phases is given, and the calculated phase diagrams are presented and compared with various types of experimental data.
133 citations
TL;DR: In this paper, the authors extend the data set to include tantalum by performing CALPHAD analyses of the fifteen binary systems based on the heats of formation estimated by Niessen et al.
Abstract: Previous papers in the current series provide descriptive information concerning one hundred twenty binary system composed of boron, carbon, aluminum, silicon, titanium, vanadium, chromium, manganese, iron, cobalt, nickel, copper, niobium, molybdenum and tungsten. The current work extends the data base to include tantalum by performing CALPHAD analyses of the fifteen binary systems based on the heats of formation estimated by Niessen et al. and Colinet et al.
79 citations
TL;DR: In this paper, a thermodynamic analysis of phase equilibria in the Fe-N-V system has been carried out on the basis of the established three binary descriptions and selected ternary experimental data.
Abstract: A thermodynamic analysis of phase equilibria in the Fe-N-V system has been carried out on the basis of the established three binary descriptions and selected ternary experimental data. The two-phase equilibrium between austenite and VN phase was treated as a portion of the miscibility gap in the fcc phase. A set of isothermal sections was presented in the whole range of compositions. Some thermodynamic analysis was carried out on the solubility products of VN in ferrite and austenite.
41 citations
TL;DR: In this article, a sequential Bayesian parameter estimation technique is proposed to ensure that a minimum of experimental thermodynamic and phase diagram data suffices for the calculation of excess functions which are comparable in accuracy and precision with quantities obtained by conventional methods.
Abstract: A sequential Bayesian parameter estimation technique ensures that a minimum of experimental thermodynamic and phase diagram data suffices for the calculation of excess functions which are comparable in accuracy and precision with quantities obtained by conventional methods. In addition, the new algorithm provides a feedback between data evaluation and experimental design. Typical applications of the proposed method are illustrated by several examples.
37 citations
TL;DR: In this paper, the phase boundaries in ternary, quaternary and even higher order nickel-base superalloys are calculated by the cluster variation method (CVM) which utilizes the tetrahedron approximation and the phenomenological Lennard-Jones pair interaction potential.
Abstract: The γ′/γ equilibrium phase boundaries in ternary, quaternary and even higher order nickel-base superalloys are calculated by the cluster variation method (CVM) which utilizes the tetrahedron approximation and the phenomenological Lennard-Jones pair interaction potential. The potential parameters are first estimated from thermochemical data and /or semi-empirical formulae on cohesive energies and lattice parameters of binary alloys or compounds. Some of these values are adjusted by a small amount to obtain better agreement with the phase bpundaries In lower order alloys reported in the literature. These paramter values are shown to reproduce γ′/γ equilibrium phase compositions, γ′ volume fraction and misfit between the two lattices etc. in higher order alloys close to experimental observation in the temperature range from 750 to 1250°C. Hence, this method may be applicable to the designing of engineering nickel base superalloys in which the improvement of high temperature performance is effected by multiple alloying additions.
36 citations
Abstract: The thermodynamic properties of rankinite, Ca 3 Si 2 O 7 , are reeassessed in order to fit information from the ternary Al 2 O 3 -CaO-SiO 2 system.
28 citations
TL;DR: In this paper, the Gibbs free energies of the ZrO 2 -MgO system have been evaluated using the selected phase diagram data from the literature and an optimal set of thcrmodynamic functions for this system has been obtained.
Abstract: The experimentally determined phase diagram data in the ZrO 2 -MgO system have been critically evaluated. An optimal set of thcrmodynamic functions for this system has been obtained using the selected phase diagram data from the literature. The Gibbs free energies are described by the following models: a regular solution model for the liquid and tetragonal ZrO 2 solid solution, and a subregular solution model for cubic ZrO 2 solid solution. The terminal solid solutions based on monoclinic ZrO 2 and MgO are treated as pure oxides in view of the negligible solubilities. A consistent set of parameters describing the system is presented, and comprehensive companions with the experimental data are made. It is shown that most of the experimental information is satisfactorily accounted for by the present thermodynamic description.
28 citations
TL;DR: In this article, the excess Gibbs energy difference between the liquid and the mixed crystalline state, having space group P2 1 a with Z=2, of binary p-dihalobenzene systems (halo = Cl, Br, I) can be represented, as a function of temperature and mole fraction of the second component (the one with the larger molar volume), by the formula ΔG E (T,X) = A(1 − T θ ) ×(1−X)[1+B( 1−2X)]
Abstract: The excess Gibbs energy difference between the liquid and the mixed crystalline state, having space group P2 1 a with Z=2, of binary p-dihalobenzene systems (halo = Cl, Br, I) can be represented, as a function of temperature and mole fraction of the second component (the one with the larger molar volume), by the formula ΔG E (T,X) = A(1 − T θ ) ×(1−X)[1+B(1−2X)] The constant θ is a characteristic temperature; for the family of p-dihalobenzene systems it has the value 500 K. The constant B, which is a measure of the asymmetry of the thermodynamic mixing properties of a system, can be given as B = 0.2. The other binary characteristic, the constant A, stands in relation to the coefficient of crystalline isodimorphism em. The latter expresses the degree of geometrical similarity of the unit cells of the two pure components. The relation between A and em is A = −62(1−em) kJ.mol−1
TL;DR: In this paper, the phase diagram and thermodynamic properties of the Mn-V and Fe-Mn-V systems are analyzed by the use of thermodynamic models, and reasonable descriptions of the systems are obtained based on some estimation.
Abstract: The phase diagram and thermodynamic properties of the Mn-V and Fe-Mn-V systems are analysed by the use of thermodynamic models. Though experimental information is very limited, reasonable descriptions of the systems are obtained based on some estimation.
TL;DR: In this paper, the Gibbs free energies of formation for the V2C and VC carbides were derived from the experimental data and all the thermodynamic data used in calculation of phase diagrams were presented.
Abstract: The thermodynamic data for all the phases in the V-C and Fe-V systems were optimized from experimental thermodynamic and phase equilibrium data. The calculated phase diagrams of the V-C and Fe-V systems and the Gibbs free energies of formation for the V2C and VC carbides were in good agreement with corresponding experimental data. All the thermodynamic data used in calculation of phase diagrams are presented.
TL;DR: In this paper, the authors have refined the thermodynamic description of the Fe-V system, incorporating some recent thermochemical data which were not used by earlier authors in optimization, and the most recent SGTE recommendations for the lattice stability parameters of elements are employed.
Abstract: In this work, we have refined the thermodynamic description of the Fe-V system, incorporating some recent thermochemical data which were not used by earlier authors in optimization. The most recent SGTE recommendations for the lattice stability parameters of elements are employed. The calculated thermochemical properties and phase diagram are compared with experimental results. An improved phase diagram for the system is presented.
TL;DR: In this paper, the authors provide descriptive information concerning one hundred thirty six binary systems composed of boron, carbon, aluminum, silicon, titanium, vanadium, chromium, manganese, iron, cobalt, nickel, copper, niobium, molybdenum, tantalum and tungsten.
Abstract: Previous papers in the current series provide descriptive information concerning one hundred thirty six binary systems composed of boron, carbon, aluminum, silicon, titanium, vanadium, chromium, manganese, iron, cobalt, nickel, copper, niobium, molybdenum, tantalum and tungsten. This data base has been employed to calculate isothermal sections in the Ta-Ni-Mo, Ta-Nb-Al, Ta-Nb-Cu, Ta-Cu-Ni, Ta-W-Ti, Ta-Al-Fe and Ta-Al-Ni systems for comparison with limited experimental data.
TL;DR: This paper fitted the thermodynamic functions for most of the binary metallic solutions tabulated by Hultgren et al. to a three-term solution model and used this model to reproduce much of the tabular data in this compilation as well as calculating values for the partial and integral functions for any composition and temperature.
Abstract: We have fitted the thermodynamic functions for most of the binary metallic solutions tabulated by Hultgren et al. to a three term solution model. From these results it is possible to reproduce much of the tabular data in this compilation as well as calculating values for the partial and integral functions for any composition and temperature. We have also identified a problem in the consistency of some of the original error estimates and have offered a resolution.
TL;DR: In this article, a thermodynamic assessment of the solid-liquid phase diagram in the system thianaphthene+naphthalene was made, where the phase diagram is an example of crossed isodimorphism: two each other crossing solid liquid loops give rise to a three phase equilibrium.
Abstract: A thermodynamic assessment was made of the solid-liquid phase diagram in the system thianaphthene+naphthalene The phase diagram is an example of crossed isodimorphism: two each other crossing solid-liquid loops give rise to a three-phase equilibrium (in this case eutectic) The information used consisted of experimental liquidus data, the thermodynamic melting properties of the pure components and the excess Gibbs energy of the liquid state The latter was derived from vapour-pressure data; it is given by GEliq(T=372 K,X) = X(1-X)[306 - 180(1−2X) + 267(1−2X)2] Jmol−1 The calculated excess Gibbs energy of the solid state with the naphthalene structure is GEsol(T=325 K,X) = X(1–X)[1762 - 568(1–2X) + 732(1–2X)2 - 349(1–2X)3] Jmol−1 The values of the initial distribution coefficients are: − at the thianaphthene side k00 = 0749 − at the naphthalene side k00 = 0196
TL;DR: In this article, the eutectic between spinel and corundum is shown to be well above the temperature reported by Rankin and Merwin, and the value of 57.65 ± 8 kJ mol−1 for the heat of fusion of MgO is confirmed.
Abstract: Spinel, MgAl2O4, dissolves excess AlO1.5 or MgO, so its thermodynamic properties must be known as functions of composition. These functions have been determined directly from published experimental data and from various lattice models. They are then expressed as a table of Redlich-Kister power series coefficients. Once the solids are modelled, the MgO-AlO1.5 liquids are fitted using the known phase equilibria data. The li'quid behavior is close to subregular, but five Redlich-Kister coefficients are required to fit the eutectic on the MgO side and the melting point of spinel. It is shown that the accepted MgO-AlO1.5 phase diagram is in error: the eutectic between spinel and corundum is well above the temperature reported by Rankin and Merwin. The value of 57.65 ± 8 kJ mol−1 for the heat of fusion of MgO is confirmed.
TL;DR: In this article, a thermodynamics-based, computer-aided analysis was used to design an optimum composition of the β-phase dispersion for the crack-tip transformation toughening.
Abstract: The most important factors affecting the dispersed-phase transformation toughening in the gamma- TiAl intermetallic by a dispersion of the beta phase are the stability of the dispersion, the transformation volume change and the β/γ chemical compatibility. A thermodynamics-based, computer-aided analysis was used to design an optimum composition of the β-phase dispersion for the crack-tip transformation toughening. It is found that such an optimum composition exists in the ternary Ti - Al - V system.
TL;DR: In this paper, a polynomial-of-composition (POC) method was proposed for the treatment of excess molar volume of liquid in the presence of pressure on the liquid at about 0.85mol NaIO3.
Abstract: Based on the advanced thermodynamic models, the optimized thermodynamic data for these two systems were derived from experimental phase dragrams. In optimization the excess molar volume of liquid was represented by a polynomial of composition and optimized by the combination of the two experimental phase diagrams. The calculated and experimental phase diagrams were in good agreement. This indicated the present method for treatment of excess molar volume is reasonable. The calculated results showed that the application of pressure on the present system restrains the formation of short range order of atoms in the liquid at about x = 0.85mol NaIO3.
TL;DR: In this paper, a model was developed for coarsening kinetics of M2C carbides and subsequently applied to optimize the composition of high Co-Ni steels with respect to the overaging resistance during secondary hardening.
Abstract: A model has been developed for coarsening kinetics of M2C carbides and subsequently applied to optimize the composition of high Co-Ni steels with respect to the overaging resistance during secondary hardening. The model accounts for both effects of multicomponent diffusion and precipitate shape anisotropy. It is found that W additions to high Co-Ni steels significantly reduces the coarsening rate constant. Calculations for two W-free 14Co-10Ni steels at a typical tempering temperature of 783K reveals a beneficial effect of the Cr substitution with Mo, in a good agreement with available experimental data.
TL;DR: In this article, the relation between the Darken's excess stability and phase diagram has been revealed and the behavior of the excess stability curve over the entire composition range has been described quantitatively in terms of the formulae presented in this paper based on the knowledge of phase diagram.
Abstract: The relation between the Darken's excess stability and phase diagram has been revealed and the behavior of the excess stability curve over the entire composition range has been described quantitatively in terms of the formulae presented in this paper based on the knowledge of phase diagram. In order to judge if a positive peak will appear in the stability curve at the composition corresponding to an intermediate compound, a criterion inequality has been suggested. All of them have been successfully applied to alloys and slag systems.
Journal Article•
TL;DR: The new model, called the Entity Model is based on the concept of entity which was defined recently and provides model parameters which are common for all systems where it is applicable, which makes it the simplest model available apart from the Raoultian but more widely applicable than the latter.
Abstract: A new model is presented to describe the thermodynamic nature of metallic solutions This model, called the Entity Model is based on the concept of entity which was defined recently, It makes excellent predictions fora number of binary metallic solutions. It provides model parameters which are common for all systems where it is applicable. This distinguishes it from the other models where parameters are system specific, except in the case of the Raoultian model. This makes the new model the simplest model available apart from the Raoultian but more widely applicable than the latter.