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.     

Considerations on the Kaufman approach to binary phase diagram calculation

The Kaufman approach to phase equilibria involving primarily the fcc, bcc and hcp phases was examined outside the Group Nos. 4 to 10 range where it is customarily employed. The “stability parameters” (ΔH and ΔS of transformation) for most elements in the Group Nos. 1 to 3 region were found to fit satisfactorily the correlation curves of stability parametervs group no.; some of the parameters for Al, Be, Mg and Ti, however, did not. The rare earth parameters fit well in the Group No. 3.5 position they were expected to occupy. A sample phase diagram calculated between two Group 1 elements was in good agreement with experiment. Phase boundaries of fcc +bcc regions adjacent to terminal solid solutions in several Group 1/Group 2 and Group 1/Group 3 systems, on the other hand, were quite unsatisfactory. This difficulty was traced to the high, positive regular solution constants calculated for both phases. Such constants were shown to result from the downward concavity of a plot of enthalpy of vaporizationvs Group No. in the Nos. 1 to 3 region; in the Nos. 4 to 10 range this plot is concave upward.     

Considerations on the Kaufman approach to binary phase diagram calculation

The Kaufman approach to phase equilibria involving primarily the fcc, bcc and hcp phases was examined outside the Group Nos. 4 to 10 range where it is customarily employed. The “stability parameters” (ΔH and ΔS of transformation) for most elements in the Group Nos. 1 to 3 region were found to fit satisfactorily the correlation curves of stability parametervs group no.; some of the parameters for Al, Be, Mg and Ti, however, did not. The rare earth parameters fit well in the Group No. 3.5 position they were expected to occupy. A sample phase diagram calculated between two Group 1 elements was in good agreement with experiment. Phase boundaries of fcc +bcc regions adjacent to terminal solid solutions in several Group 1/Group 2 and Group 1/Group 3 systems, on the other hand, were quite unsatisfactory. This difficulty was traced to the high, positive regular solution constants calculated for both phases. Such constants were shown to result from the downward concavity of a plot of enthalpy of vaporizationvs Group No. in the Nos. 1 to 3 region; in the Nos. 4 to 10 range this plot is concave upward.     

相图计算在TiAl基金属间化合物结构设计中的应用

为加速高性能TiAl基金属间化合物的研发，以相图热力学计算结果为基础，研究合金化元素Nb、W、B和热处理温度、冷却速度对TiAl基金属间化合物的相转变、微观结构的影响。研究结果表明：对成分为Ti-45Al—7Nb-0．4W-0．15B（原子百分比）的TiAl基金属间化合物在1450℃进行均匀化退火处理，高温下的α相经炉冷可以得到完全由α2／γ片层团构成的较为粗大的全片层组织；在1235℃进行均匀化热处理可以获得细小的双态组织。上述关键性的热处理实验和微观结构分析证实了理论计算结果的可行性。     

Thermodynamic properties of liquid Cd-Pb-Sn solutions and analytical calculation of the phase diagram

Abstract

The relative partial thermodynamic properties of Cd in liquid Cd-Pb-Sn alloys have been investigated in the temperature range 680–840K by an emf technique. Data have been represented by general , power series expansions in the composition variables, and the liquidus surfaces when Cd or Sn are the primary crystallization products have been calculated analytically.

Résumé

Les propriétés thermodynamiques partielles du cadmium dans les alliages Cd-Pb-Sn liquide ont été étudiées dans une fourchette de température comprise entre 680 et 840K par la mesure de force électromotrice. Les données sont représentées par un développement en série des variables de composition. Les surfaces du liquidus ont été calculces analytiquement dans le cas où le cadmium ou l' étain est le produit prima ire de cristallisation.     

On the iron-carbon phase diagram

Experimental results that are obtained by electron microscopy, X-ray diffraction, and carbide analysis and indicate the precipitation of carbon atoms clusters in a hypereutectoid steel during its annealing above the eutectoid temperature are presented. These results are compared to the reported data in order to construct a new Fe-C phase diagram, where cementite forms below the eutectoid temperature due to the tendency of the Fe-C system toward ordering and carbon unbound to iron precipitates above this temperature in the form of clusters or graphite particles due to the tendency of this system toward phase separation.     

Low-temperature extension of the lehrer diagram and the iron-nitrogen phase diagram

Iron layers are nitrided in mixtures of ammonia and hydrogen at low temperatures, using a thin nickel caplayer as a catalyst. In the coordinate field of inverse temperature vs nitriding potential, we determined the boundaries between areas in which the α, γ′, or ε phases are in thermal equilibrium. Using these data, the Fe-N phase diagram is extended from 350 °C to 240 °C and extrapolated down to 200 °C. The α, γ′, and ε phases probably coexist in a triple point in the Lehrer diagram around 214 °C.     

On the Mn-MnS phase diagram

Using a DTA technique the melting point of pure MnS has been determined to 1655 ±5°C. The monotectic temperature in the Mn-MnS system was found to be 1570 ±5°C. With these new data a thermodynamic analysis of the Mn-MnS system was carried out applying a previously developed thermodynamic model.     

Calculation of the titanium-aluminum phase diagram

The Ti-Al phase diagram has been calculated by optimization of Gibbs energies with respect to phase diagram and thermochemical data.T ₀ curves, the locus of compositions and temperatures where the Gibbs energies of the liquid and one of the solid phases are equal, have been calculated over the entire composition range. In order to assure physically reasonable extrapolations of theT ₀ curves of the ordered phases far from their equilibrium stability ranges, the Bragg-Williams approximation was used to provide start values for the empirical optimizations. This approximation led to good convergence of the optimizations, and only small deviations from the Bragg-Williams Gibbs energies were needed to obtain excellent agreement with experimental data.     

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     

The Dy-Zn phase diagram

The dysprosium-zinc phase diagram has been investigated over its entire composition range by using differential thermal analysis, (DTA) metallographic analysis, X-ray powder diffraction, and electron probe microanalysis (EPMA). Seven intermetallic phases have been found and their structures confirmed. DyZn, DyZn₂, Dy₁₃Zn₅₈, and Dy₂Zn₁₇ melt congruently at 1095 °C, 1050 °C, 930 °C, and 930 °C, respectively. DyZn₃, Dy₃Zn₁₁, and DyZn₁₂ form through peritectic reactions at 895 °C, about 900 °C and 685 °C, respectively. Four eutectic reactions occur at 850 °C and 30.0 at pct Zn (between (Dy) and DyZn), 990 °C and 60.0 at pct Zn (between DyZn and DyZn₂), 885 °C and 76.0 at pct Zn (between DyZn₃ and Dy₃Zn₁₁), and 875 °C and 85.0 at pct Zn (involving Dy₁₃Zn₅₈ and Dy₂Zn₁₇). The Dy-rich end presents a catatectic equilibrium; a degenerate invariant effect has been found in the Zn-rich region. The phase equilibria of the Dy-Zn alloys are discussed and compared with those of the other known RE-Zn systems (RE=rare earth metal) in view of the regular change in the relative stabilities of the phases across the lanthanide series     

Thermodynamics and phase relationships of transition metal-sulfur systems: Part III. Thermodynamic properties of the Fe-S liquid phase and the calculation of the Fe-S phase diagram

An associated solution model is applied to describe the thermodynamic behavior of Fe-S liquid. This model assumes the existence of ‘FeS’ species in addition to Fe and S in the liquid. With two solution parameters for each of the binaries Fe-‘FeS’ and ‘FeS’-S, this model accounts for the compositional dependence of the thermodynamic properties of Fe-S liquid from pure Fe to pure S over a wide range of temperature. The binary Fe-S does not contribute significantly to the excess Gibbs energy of the liquid due to the rather small dissociation constant of ‘FeS’ to Fe and S. Using this model for the liquid phase and a defect thermodynamic model for the pyrrhotite phase, the Fe-S phase diagram is calculated. The calculated diagram is in excellent agreement with the experimental data, accounting for the range of homogeneity of pyrrhotite at all temperatures. Both the thermodynamic and phase diagram data are obtained from the literature. Formerly Post-Doctoral Research Associate, Materials Department, College of Engineering and Applied Science, University of Wisconsin-Milwaukee.     

The neodymium-gold phase diagram

The Nd-Au phase diagram was studied in the 0 to 100 at. pct Au composition range by differential thermal analysis (DTA), X-ray diffraction (XRD), optical microscopy (LOM), scanning electron microscopy (SEM), and electron probe microanalysis (EPMA). Six intermetallic phases were identified, the crystallographic structures were determined or confirmed, and the melting behavior was determined, as follows: Nd₂Au, orthorhombic oP12-Co₂Si type, peritectic decomposition at 810 °C; NdAu, R.T. form, orthorhombic oP8-FeB type, H.T. forms, orthorhombic oC8-CrB type and, at a higher temperature, cubic cP2-CsCl type, melting point 1470 °C; Nd₃Au₄, trigonal hR42-Pu₃Pd₄ type, peritectic decomposition at 1250 °C; Nd₁₇Au₃₆, tetragonal tP106-Nd₁₇Au₃₆ type, melting point 1170 °C; Nd₁₄Au₅₁, hexagonal hP65-Gd₁₄Ag₅₁ type, melting point 1210 °C; and NdAu₆, monoclinic mC28-PrAu₆ type, peritectic decomposition at 875 °C. Four eutectic reactions were found, respectively, at 19.0 at. pct Au and 655 °C, at 63.0 at. pct Au and 1080 °C, at 72.0 at. pct Au and 1050 °C, and, finally, at 91.0 at. pct Au and 795 °C. A catatectic decomposition of the (βNd) phase, at 825 °C and ≈1 at. pct Au, was also found. The results are briefly discussed and compared to those for the other rare earth-gold (R-Au) systems. A short discussion of the general alloying behavior of the “coinage metals” (Cu, Ag, and Au) with the rare-earth metals is finally presented.     

The Nd-Zn phase diagram

Metallographie, thermal, and X-ray techniques were used to determine the phase relations in the Nd-Zn system. Eight compounds, three eutectics and a eutectoid were found. The compounds NdZn, NdZn₂, and Nd₂Znn melt congruently at 923°, 925°, and 981°C respectively. The compounds Nd₃Zn₁₁, NdZn_4.46, and Nd₃Zn₂₂ undergo peritectic decomposition at 870°, 902°, and 950°C respectively, while NdZn₃ undergoes peritectoid decomposition at 849°C. The eutectics occur at 12 wt pct Zn and 630°C, 38 wt pct Zn and 868°C, and 56 wt pct Zn and 854°C. The eutectoid occurs at 4 wt pct Zn and 622°C. The existence of a NdZn₁₂ phase of the SmZn₁₂ type structure has been confirmed. An allotropie transformation between the tetragonal NdZn₁₁ structure and the hexagonal NdZn₁₂ defect structure is proposed.     

Liquidus surface of the Mg-Sm-Tb phase diagram

Differential thermal, electron microprobe, and X-ray diffraction analyses and metallography are used to study Mg-Sm-Tb alloys containing up to 30% Sm or Tb. Polythermal sections and the solidification surface of the Mg-Sm-Tb phase diagram are constructed for the Mg-rich region. In the composition range under study, nonvariant transition-type equilibrium L + Mg₂₄Tb₅ = (Mg) + Mg₄₁Sm₅ is found to exist at a temperature of 539°C.