Magnetic contributions to the thermodynamic functions of alloys and the phase equilibria of Fe-Ni system below 1200 K

A generalized approach is proposed to calculate the magnetic contribution to the thermodynamic functions of alloys. This approach is applied successfully to the Fe-Ni binary system. The predicted magnetic specific heat of the fcc phase at 75 at. Pct Ni is in agreement with the experimental data within the accuracies of the data and the predicted values. The magnetic contributions to the Gibbs energies of the fcc and bcc phases for the Fe-Ni alloys obtained from this approach are added to the nonmagnetic portion of the Gibbs energies. The nonmagnetic portion of the Gibbs energy of the fcc phase is obtained from extensive thermochemical data at high temperatures as discussed in the paper immediately following this one. The total Gibbs energies of the fcc, bcc, and the orderedγ′-(FeNi₃) phases are then used to calculate/predict phase equilibria of the Fe-Ni binary at temperatures lower than 1200 K. The calculated equilibria are in agreement with available experimental data. In addition, a irascibility gap of the fcc phase at low temperatures is predicted, resulting in the formation of a monotectoid equilibrium at 662 K as given below: {fx1361-02} The existence of the miscibility gap is due to the magnetic Gibbs energy term of the fcc phase which is composition dependent. Experimental results reported in the literature support the predicted miscibility gap.     

A thermodynamic analysis of the phase equilibria in the Fe-Mn-S system

The experimental information on the phase equilibria in the Fe-Mn-S system is meager. An attempt has now been made to predict these phase equilibria by extrapolation of the free energy properties from the binary sides. The crucial point is the choice of a thermodynamic model for the liquid phase which could apply to the whole range of composition. Such a model is suggested. The calculations show some encouraging agreement with the experimental information available and they yield a better understanding of some aspects of the formation of FeS during the solidification of steel, containing manganese.     

Experimental study of phase equilibria and thermodynamic optimization of the Fe-Zn-O system

The Fe-Zn-O phase diagram in air was studied over the temperature range from 900 °C to 1500 °C. The compositions of the phases in quenched samples were obtained by electron probe X-ray microanalysis (EPMA). This experimental technique is not affected by zinc losses resulting from vaporization of zinc at high temperatures. The model for the spinel solid solution was developed within the framework of the compound-energy formalism (CEF). The choice of parameters of the CEF and the sequence of their optimization can have a major influence on the predictions in multicomponent phases. These choices can only be made rationally by reference to the specific model being represented in the CEF. This is discussed for the case of the two-sublattice spinel model. In the limiting case, the proposed model reduces to the model by O’Neill and Navrotsky for spinels. When the CEF is used in combination with the equation of Hillert and Jarl to describe the magnetic contribution to thermodynamic functions of a solution, it is necessary to assign certain values of magnetic properties to all pseudocomponents and to magnetic interaction parameters to obtain the most reasonable approximation of the magnetic properties of a solution. It was shown how this can be done based on very limited experimental data. The same equations can be used when the Murnaghan or the Birch-Murnaghan equation is combined with the CEF to describe the pressure dependence of thermodynamic functions. The polynomial model was used to describe the properties of wustite and zincite, and the modified quasichemical model was used for the liquid slag. All thermodynamic and phase-equilibria data on the Fe-O and Fe-Zn-O systems were critically evaluated, and parameters of the models were optimized to give a self-consistent set of thermodynamic functions of the phases in these systems. All experimental data are reproduced within experimental error limits. These include the thermodynamic properties of phases (such as specific heat, heat content, entropy, enthalpy, and Gibbs energy); the cation distribution between octahedral and tetrahedral sites in spinel; the oxygen partial pressure over single-phase, two-phase, and three-phase regions; the phase boundaries (liquidus, solidus, and subsolidus); and the tie-lines.     

A thermodynamic analysis of the copper-lead-sulfur system at 1473 K

A consistent set of thermodynamic activities in the Cu-Pb-S system is derived at 1473 K from a knowledge of the high-temperature phase relations, the boundary binary thermodynamics and the estimated limiting activity coefficients of sulfur in copper-lead melts. Within the uncertainty limits, the derived values in the present study and the experimental values of Azuma,et al, for the activity of Pb are in good accord. The tie-line distribution in the lead-rich portion of the ternary miscibility gap has been slightly modified to be consistent with the thermodynamic properties of the lead-sulfur system.     

A thermodynamic analysis of the copper-lead-sulfur system at 1473 K

A consistent set of thermodynamic activities in the Cu-Pb-S system is derived at 1473 K from a knowledge of the high-temperature phase relations, the boundary binary thermodynamics and the estimated limiting activity coefficients of sulfur in copper-lead melts. Within the uncertainty limits, the derived values in the present study and the experimental values of Azuma,et al, for the activity of Pb are in good accord. The tie-line distribution in the lead-rich portion of the ternary miscibility gap has been slightly modified to be consistent with the thermodynamic properties of the lead-sulfur system.     

Co-Cr系相平衡的热力学计算和fcc相的磁性诱导相分离

Two-phase equilibria between the ferromagnetic fcc and the paramagnetic fcc phase from 800 ℃ to 900 ℃ in the Co-rich region have been detected by the diffusion couple technique. Two phase separation region of the fcc has been confirmed along the Curie temperature. The phase equilibria including the present results and the thermodynamic data of the Co-Cr system reported in the literature were analyzed on the basis of the thermodynamic evaluation. A set of thermodynarnic values for the liquid, fcc, hcp, bcc, sigma phases was obtained. The calculated phase equilibria were in good agreement with most of the experimental data.     

A thermodynamic analysis of the iron-nitrogen system

An attempt is made to rationalize and bring into mutual agreement different types of information on the phase equilibria in the Fe-N system by applying simple thermodynamic models to the individual phases. The attempt was successful except for some information regarding the ∈ phase. As a result, equations and curves describing the various phase equilibria are recommended.     

A thermodynamic analysis of the iron-nitrogen system

An attempt is made to rationalize and bring into mutual agreement different types of information on the phase equilibria in the Fe-N system by applying simple thermodynamic models to the individual phases. The attempt was successful except for some information regarding the ∈ phase. As a result, equations and curves describing the various phase equilibria are recommended.     

A thermodynamic analysis of the Fe-Mn-C system

The experimental information on the solid state phase equilibria in the Fe−Mn−C system was analyzed in thermodynamic terms. Gibbs free energy of each phase was described by a regular or subregular solution model and the numerical values of the parameters were determined. The results were used to calculate isothermal sections between 873 and 1373 K. They show a reasonable agreement with all the experimental information available.     

A thermodynamic analysis of the copper-sulfur system

An associated solution model is applied to describe the thermodynamic behavior of Cu-S liquid. This model assumes the existence of ‘Cu₂S’ species in addition to Cu and S in the liquid. With two solution parameters for each of the binaries Cu-‘Cu₂S’ and ‘Cu₂S’-S, this model accounts for the compositional dependence of the thermodynamic properties of Cu-S liquid from pure Cu to pure S over a wide range of temperature. The binary Cu-S does not contribute significantly to the excess Gibbs energy of the liquid due to the rather small dissociation constant of ‘Cu₂S’ to Cu and S. Using this model for the liquid phase, a statistical thermodynamic model for the digenite phase, and appropriate thermodynamic equations for the other phases, the Cu-S phase diagram is calculated. The calculated diagram is in excellent agreement with the experimental data, accounting for the range of homogeneity of digenite at all temperatures. Formerly with the Materials Department, University of Wisconsin-Milwaukee Formerly Professor of Materials Engineering and Associate Dean for Research of the Graduate School of the University of Wisconsin-Milwaukee.     

An analysis of the phase equilibria in the Fe−FeS system

Applying a previously developed thermodynamic model to available experimental data from different phase equilibria in the Fe−FeS system, an attempt has been made to reconcile the results from different investigations. Analytical expressions for the free energy of the individual phases are recommended.     

Phase transformations and phase equilibria in the Fe-N system at temperatures below 573 K

The phase transformations of homogeneous Fe-N alloys of nitrogen contents from 10 to 26 at. pct were investigated by means of X-ray diffraction analysis upon aging in the temperature range from 373 to 473 K. It was found that precipitation of α″-Fe₁₆N₂ below 443 K does not only occur upon aging of supersaturated α (ferrite) and α′ (martensite), but also upon transformation of γ′-Fe₄N_1-z and ɛ-Fe₂N_1-x (<20 at. pct N). No α″ was observed to develop upon aging of γ(austenite). Therefore, it is proposed that γ′ is a stable phase at temperatures down to (at least) 373 K. Phase formation upon annealing at low temperatures is apparently governed by the (difficult) nucleation and (slow) growth of new Fe-N phases: α″ forms as a precursor for α because of slow nitrogen diffusion, and nitrogen-enriched ɛ develops as a precursor for γ′ because of a nucleation barrier.     

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.