Invariant Reaction Temperatures Research Articles

Thermodynamic modeling of the Mg–Nd–Sr ternary system with key experimental investigation

The phase equilibria in the Mg-rich region of the Mg–Nd–Sr ternary system at 300 and 350 °C were established using equilibrated-sample method. Powder X-ray diffraction (XRD) technique and scanning electron microscopy (SEM) equipped with energy-dispersive spectroscopy (EDS) were used for phase composition determination. Four three-phase equilibria and four two-phase equilibria have been experimentally determined at both isothermal sections of 300 and 350 °C. The phase equilibria relationships in the Mg-rich side were studied. The major invariant reaction temperatures of vertical sections with 80 at. % Mg and 10 at. % Sr were determined with differential scanning calorimetry (DSC) test. Moreover, thermodynamic modeling of Mg–Nd–Sr ternary system has been carried out by CALPHAD method based on the present key experimental results. The liquid solution was described using the modified quasi-chemical model in the pair approximation (MQMPA). The compound energy formalism (CEF) was used for the solid phases. The present obtained thermodynamic database of Mg–Nd–Sr ternary system will provide an important support for the Mg-based biodegradable implant development.

Ho–Co and Ho-Co-Fe phase diagrams

Phase equilibria in the Ho-Co-Fe ternary and the boundary binary Ho–Co systems are investigated using differential thermal analysis, scanning electron microscopy, electron-probe microanalysis, and X-ray diffraction. Based on the experimental results, the binary Ho–Co phase diagram was revised resulting in confirmation of the general features of the previously published phase diagram, except for the mode of formation of the Ho3Co compound. The temperatures of most invariant reactions were adjusted. The ternary Ho-Co-Fe phase diagram was constructed over the whole concentration range. The liquidus and solidus projections, Scheil reaction scheme and isothermal sections at 1250, 1200 and 1000 °C are presented. The most prominent feature of this system is existence of three continuous solid solutions Ho2(Co,Fe)17, Ho(Co,Fe)3 and Ho(Co,Fe)2, which define the character of the solidus projection. Other binary compounds have significant solubility of third component. Among them Ho6Fe23 has a widest homogeneity range and dissolves up to 28.0 at.% Co at all studied temperatures. All intermetallic phases are linear phases in terms of holmium. Five four-phase invariant reactions are found. One of them is of eutectic type and four ones are of U-type. Four invariant three-phase eutectic equilibria are present in the system.

Experimental determination of phase diagram involving silicides in the Fe-Si binary system

The phase diagram of the Fe-Si binary system was precisely determined using FE-EPMA/WDS and thermal analysis of DSC. It was confirmed that the concentration ranges of the β-Fe2Si and ζα-FeSi2 phases are slightly narrower and shifted toward higher Fe concentrations compared with the literature, and the other iron-silicide phases have low but certain concentration ranges less than 1 at%. The A2/B2/D03 order-disorder transition and Curie temperatures in the BCC phases exhibited concentration dependences consistent with those temperatures reported by Meco and Napolitano, and the Curie temperatures of the α”-Fe3Si (D03) alloys deviated higher from the extrapolated values of the α-Fe (A2) phase with increasing Si content and bent at the stoichiometric composition of 25 at%Si. Invariant reaction temperatures were mostly coincident with those of the phase diagram in the literature, except for the peritectoid temperature of the η-Fe5Si3 phase, whereas a small discrepancy was revealed in the solidus and liquidus lines.

A thermodynamic description of the B–Co system: modeling and experiment

Abstract The B–Co system is investigated via thermodynamic modeling and experiments. In the modeling section, all of the experimental phase diagram and thermodynamic data available from the literature were critically reviewed and assessed by using thermodynamic models for the Gibbs energies of individual phases. In the experimental section, 6 key alloys were prepared by arc melting Co slug and B pieces and annealing at 900 °C for 9 days. Water-quenched samples were analysed by using X-ray diffraction, optical microscopy, electron probe microanalysis and differential thermal analysis techniques. The measured invariant reaction temperatures are: 1136 ± 2 °C for Liquid (L) ↔ (αCo) + Co3B, 1157 ± 2 °C for L + Co2B ↔ Co3B, 1263 ± 2 °C for L ↔ Co2B + CoB, and 1358 ± 2 °C for L ↔ CoB + B. A consistent thermodynamic data set for the B–Co system is finally obtained by considering the present experimental results and reliable literature data. Comparisons between the calculated and measured phase diagram and thermodynamic quantities show that all of the accurate experimental information is satisfactorily accounted for by the thermodynamic description.

A re-examination of the liquidus surface of the Al–Fe–Ti system

Abstract The liquidus surface of the Al –Fe –Ti system has been reexamined. 34 different alloys have been studied by differential thermal analysis, and the temperatures of invariant reactions have been determined. By examining the as-cast samples by optical microscopy, X-ray diffraction and energy-dispersive spectrometry in a scanning electron microscope, the crystal structures and chemical compositions of the primary phases and two-phase aggregates have been established. In some cases, additional investigations were carried out in the transmission electron microscope. From the combined results of these investigations the solidification paths of the alloys were established leading to a revised representation of the liquidus surface of the Al –Fe –Ti system. A reaction scheme has been set up which shows phase equilibria that are consistent with previous solid-state isothermal sections.

Experimental investigation of the U-rich region and thermodynamic re-assessment of the U–Ti system

• The eutectoid reactions in the U-rich region were experimentally determined. • The congruent reaction γ(U,Ti) →δ-U 2 Ti was experimentally re-investigated. • The phase diagram of U-Ti system was thermodynamically re-assessed. • A set of more rational thermodynamic parameters were obtained. • A new two-phase region αU + βU was predicted. The U–Ti binary system was investigated via experimental measurements and thermodynamic modeling. In order to clarify the disputed phase equilibria of the U–Ti system, 11 alloys with different contents of Ti were prepared by arc melting. The investigated Ti content covers the U-rich portion within the composition range from 1 at.% Ti to 33.3 at.% Ti. All samples were annealed at the temperatures of 640, 720 and 730 °C, and then analyzed by optical microscopy, X-ray diffraction, scanning electron microscopy, energy dispersive X-ray spectroscopy and differential scanning calorimeter. The phase equilibria associated with γ(U,Ti), αU, βU, and δ-U 2 Ti were experimentally determined in detail. The reaction temperature and composition of the invariant reaction γ(U,Ti) → βU + δ-U 2 Ti were precisely determined, and the invariant reaction temperature of the reaction βU→ αU + δ-U 2 Ti was updated. The solid solubility of Ti in αU at low temperatures was also revised by experiments. The temperature and the enthalpy of transition δ-U 2 Ti to γ(U,Ti) were newly measured by the differential scanning calorimeter. Finally, a set of self-consistent thermodynamic parameters were obtained by taking into account the present experimental findings and reliable literature data using CALPHAD (Calculation of phase diagrams) technique, and all calculated results are in good agreement with the experimental ones.

Experimental investigation and thermodynamic assessment of the Mn–Zr system

The Mn–Zr binary system has been investigated via experimental measurements and thermodynamic calculations. In order to investigate phase equilibria in the Mn–Zr system, five alloys were prepared by arc melting under vacuum. All alloys were examined by means of X-ray diffraction, scanning electron microscopy and electron probe microanalysis after annealing at 650 °C for 70 days or 950 °C for 30 days. The homogeneity range of ZrMn2 was determined to be from 25.0 to 33.2 at.% Zr at 950 °C and from 26.7 to 34.3 at.% Zr at 650 °C. The solubility of Mn in (αZr) was 1.6 at.% Mn, while that of Zr in (αMn) was 0.2 at.% Zr at 650 °C. The invariant reaction temperatures of liquid → ZrMn2 + (βZr) and (βZr) → ZrMn2 + (αZr) were determined to be 1131 and 785 °C, respectively. A thermodynamic assessment of the Mn–Zr system was conducted by taking into account the present experimental results and reliable literature data. The calculated results using the presently obtained parameters can well reproduce the experimental data.

The Cu–Te system: Phase relations determination and thermodynamic assessment

The Cu–Te binary system is of a significant interest due to the existence of Cu2Te superionic conductor in the thermoelectric application. The phase equilibria have been investigated by means of experiment and thermodynamic modeling. Based on the critical literature review on the available phase diagram and thermodynamic data, 16 crucial alloys are prepared and the phase relations in the as-cast and annealed status analyzed using X–ray diffraction (XRD) and electron probe microanalysis (EPMA). Moreover, a simultaneous differential scanning calorimetric and thermogravimetric (DSC–TG) analyses technique is utilized to confirm temperatures of invariant reactions, as well as the polymorphic transitions in the intermetallic compounds Cu2Te, Cu4Te3 and CuTe. There are five variants in the Cu2Te. A thermodynamic optimization of the Cu–Te system is then conducted with the support of the assessed literature data and the present experimental results. The liquid phase is described by the associate model due to the chemical short–range order and Cu2Te, Cu4Te3 and CuTe are treated as stoichiometric compounds in the present optimization. A set of self–consistent thermodynamic parameters are finally constructed. The present calculations are in good agreement with the available experimental data.

Experimental phase diagram, thermodynamic modeling and solidified microstructure in the Mo–Ni–W ternary system

In this work, the isothermal section at 900 °C, a liquidus projection and invariant reaction temperatures in the Mo–Ni–W ternary system were established using X-ray diffraction (XRD), Differential Scanning calorimeter (DSC) and electron probe micro-analysis (EPMA). Based on the experimental phase diagram data from the present work and the literature, the Mo–Ni–W system was assessed by means of the CALPHAD (CALculation of PHAse Diagrams) method. The liquid, fcc-(Ni), bcc-(Mo) and bcc-(W) phases were described with a regular solution model. The sub-lattice models were used to express Gibbs energies of the intermediate phases of MoNi3, MoNi, (Mo, W)Ni4, WNi and W2Ni. The present modeling covers the entire composition and an extensive temperature ranges of the Mo–Ni–W ternary system, and a set of self-consistent thermodynamic parameters were finally obtained. Comprehensive comparisons between the calculated and measured phase diagram data show that most experimental information is satisfactorily accounted for by the present thermodynamic description. Scheil solidification simulations for a few representative as-cast alloys were performed. It was found that the solidified microstructures can be reasonably described by the Scheil simulation. The liquidus projection and reaction scheme of the Mo–Ni–W system were generated by the presented modeling.

Phase diagram of Bi–In–Se ternary system

Bi–In–Se ternary system is of thermoelectric application interests and its phase diagrams are fundamentally important. Experimental measurements and Calphad-type thermodynamic modeling are carried out to determine the phase diagrams of the Bi–In–Se ternary system. Bi–In–Se ternary alloys are prepared. The equilibrium phases at 250 °C and their primary solidification phases are determined. No ternary compound is observed. The primary solidification phases are Bi2Se3, Se, In2Se3, In6Se7, InSe, In4Se3, In, ε, BiIn2, Bi3In5, BiIn, Bi, and (Bi2)m(Bi2Se3)n. In the Bi–In–Se isothermal section at 250 °C, there are seven tie-triangles which are Liquid+(Bi)+InSe, Liquid + In4Se3+InSe, (Bi)+Bi6Se7+InSe, (Bi)+In6Se7+In2Se3, (Bi)+(Bi2)m(Bi2Se3)n + In2Se3, Bi2Se3+(Bi2)m(Bi2Se3)n + In2Se3 and Liquid + In2Se3 +Bi2Se3. The temperatures of invariant reactions are determined by thermal analysis, and the reaction scheme is determined. Calphad-type thermodynamic modeling of the Bi–In–Se ternary system is carried out based on the thermodynamic models of the three binary constituent systems, and experimental results of isothermal sections and liquidus projection. The calculated and experimentally determined Bi–In–Se phase diagrams are in good agreement.

DTA measurements in the ternary Ag-Au-Ga system

In this work, the ternary Ag-Au-Ga system was studied experimentally by differential thermal analysis (DTA). The measurements were carried out along two chosen cross-sections determined by the ratio of mole fractions XAg/XGa=1:1 and XAu/XGa=1:1 by applying Pegasus 404 apparatus form Netzsch. The experiments were performed at three rates: 1 K min-1, 5 K min-1, and 10 K min-1. Next, the obtained experimental results were used to estimate the temperatures of liquidus by applying extrapolation to a zero rate. Moreover, the temperatures of invariant reactions and other phase transformations were investigated from DTA measurements which were carried out with the rate 1 K min-1. Finally, the experimental results were compared with the isopleths obtained from the prediction and calculation of the phase diagram which were done by using CALPHAD method. The experimental data obtained in this work are in good agreement with the calculation results.

The Co–Ti system revisited: About the cubic-to-hexagonal Laves phase transformation and other controversial features of the phase diagram

The Co–Ti system is one of the important systems for the development of Co-based superalloys and it is the only binary Co-X system where the characteristic, fine-scaled γ/γ′ microstructures (fcc-Co with fcc L12-ordered TiCo3) can form. Surprisingly, the phase relations and invariant reaction temperatures in the Co-rich part of the system are not very well established and there are fundamental inconsistencies between different versions of the phase diagram. Crucial points such as the type of formation reaction of the γ′ phase TiCo3 from the melt are unclear. The system is not only of high scientific interest because of the presence of the γ/γ’ microstructure, but also due to the occurrence of two different, stable polytypes of the Laves phase TiCo2 (hexagonal C36 and cubic C15 type). The phase fields of these two polytypes should be separated by a two-phase field the existence of which however has never been clearly proven. A re-investigation of the Co-rich part of the phase diagram (0–50 at.% Ti) including all invariant reactions as well as the liquidus, solidus, and solvus lines was performed by not only making use of equilibrated alloys but also applying diffusion couples.

Experimental investigation and thermodynamic modeling of the Fe−Si−Zr system

The Fe−Si−Zr alloys have attracted considerable interests in recent decades. It is important to study this ternary phase diagram for experimental design. In this paper, the Fe−Si−Zr ternary system is investigated by combining the experiments and thermodynamic calculations. Liquidus surface projection of the Fe−Si−Zr system is characterised using X-ray powder diffraction (XRD), scanning electron microscopy (SEM) with energy dispersive spectrometer (EDS) and differential thermal analysis (DTA). The liquidus projection of this ternary system is constructed by identifying primary crystallization phases and invariant reaction temperatures in the as-cast alloys. Eleven different primary solidification regions are observed. Based on the experimental results of this work and the data from the previous work in the literature, the thermodynamic calculation of the Fe−Si−Zr system is performed using CALPHAD (CALculation of PHAse Diagrams) technique. A set of self-consistent thermodynamic parameters of the Fe−Si−Zr system is obtained. The calculated results are in good agreement with the experimental data. This study provides a set of reliable thermodynamic parameters to the Fe-based thermodynamic database, and a cost-effective tool to design experiments and manufacturing processes.

Comparative Analysis of the Ternary Al–Si–X and Al–Cu–X (X = Sn, Pb, Bi, Cd, In) Systems in the Aluminum Alloy Range

Thermodynamic calculations are used to study the phase compositions of Al–Si–X and Al–Cu–X alloys, where X is a low-melting metal (Sn, Pb, Bi, Cd, In). Poly- and isothermal sections are used to determine the temperatures of invariant monotectic reactions. The formation of globular low-melting phase inclusions in heating at 500°C is found by experimental techniques.

Liquidus Projection and Thermodynamic Modeling of a Sn-Ag-Zn System

Sn-Ag-Zn alloys are promising Pb-free solders. In this study, the Sn-Ag-Zn liquidus projection was determined, and the Sn-Ag-Zn thermodynamic modeling was developed. Various Sn-Ag-Zn alloys were prepared. Their as-cast microstructures and primary solidification phases were examined. The invariant reaction temperatures of the ternary Sn-Ag-Zn system were determined. The liquidus projection of the Sn-Ag-Zn ternary system was constructed. It was found that the Sn-Ag-Zn ternary system has eight primary solidification phases: e2-AgZn3, γ-Ag5Zn8, β-AgZn, ζ-Ag4Sn, (Ag), e1-Ag3Sn, β-(Sn) and (Zn) phases. There are eight ternary invariant reactions, and the liquid + (Ag) = β-AgZn + ζ-Ag4Sn reaction is of the highest temperature at 935.5 K. Thermodynamic modeling of the ternary Sn-Ag-Zn system was also carried out in this study based on the thermodynamic models of the three constituent binary systems and the experimentally determined liquidus projection. The liquidus projection and the isothermal sections are calculated. The calculated and experimentally determined liquidus projections are in good agreement.

Thermodynamic Study and Re-optimization of the Au-Ga Binary System

Activities of gallium in the liquid Au-Ga alloys were determined using galvanic cells with the solid oxide electrolyte. The cells of the type:AuxGa(1-x)//ZrO2+Y2O3//Fe,FeO\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$${\\text{Au}}_{x} {\\text{Ga}}_{(1 - x)} //{\\text{ ZrO}}_{2} + {\\text{Y}}_{2} {\\text{O}}_{3} //{\\text{ Fe}},\\,{\\text{FeO}}$$\\end{document}were used in the temperature range from 1050 to 1273 K, and for four alloy compositions xGa = 0.2, 0.4, 0.6 and 0.8. From the measured e.m.f.’s the activity of gallium was derived, which taken together with the recently measured heat of mixing provided precise description of the thermodynamic properties of the liquid phase. This study was supplemented with DTA experiments which were performed for three alloy compositions, namely 0.15, 0.25 and 0.40 gallium mole fraction. The results of these experiments verified with temperature of respective invariant reactions. Finally, present results, taken together with the information existing in the literature, were used for the calculation of the optimized Au-Ga phase diagram. ThermoCalc software was applied to complete these calculations.

Experimental determination of phase equilibria of Al-rich portion in the Al–Fe binary system

Al-rich portion of the Al–Fe binary phase diagram was determined by conventional heat-treatment for equilibration, the diffusion couple method and thermal analysis. Equilibrium compositions are mostly coincident with the generally accepted phase diagram in the literature up to 1000 °C, except the solubility range of θ-Fe4Al13 phase. The solubility ranges of the η-Fe2Al5 and the θ-Fe4Al13 phases were confirmed to increase and incline to the Fe-rich side with increasing temperature. Phase boundaries and the eutectoid composition of the ε-Fe5Al8 phase were determined from the diffusion couple method and heating curves of DSC measurement, which were slightly shifted to a higher Fe concentration. Transformation temperatures of liquidus, solidus and invariant reactions determined from heating curves of DSC measurement were mostly lower than those in the phase diagram evaluated by Kattner and Burton. An invariant reaction related to the formation of the θ-Fe4Al13 phase was confirmed as the peritectic reaction of Liquid + η-Fe2Al5 = θ-Fe4Al13 in this study taking equilibrium compositions of the η-Fe2Al5 + θ-Fe4Al13 phases and solidus temperatures of the θ-Fe4Al13 phase into consideration.

Experimental investigation and thermodynamic assessment of Nd–H and Nd–Ni–H systems

A coupled experimental investigation and thermodynamic study of the Nd–Ni–H system have been carried out and the self-consistent thermodynamic database on this system has been obtained. High pressure differential scanning calorimetry (HP-DSC) is used to determine the temperature of reaction NdNi5H3↔NdNi5+1.5H2 in the pressure range of 3.01–11.01MPa H2. The thermodynamic functions for Nd–H system are developed based on the critical assessment of the equilibrium pressure PH2 over sample at 600–800°C, invariant reaction temperatures and hydrogen solubilities in Nd. Two sets of thermodynamic functions for Nd–Ni–H system are provided because two sets of models for NdNi5, NdNi5H3 and NdNi5H6 are adopted. The NdNi5, NdNi5H3 and NdNi5H6 are modeled as separated phases in parameter set 1 and described as a single phase in parameter set 2. The calculated decomposition temperatures of NdNi5H3 and NdNi5Ni6 at different pressures agree well with the experimental data. However, the thermodynamic description of parameter set 1 is recommended through comparing the calculated pressure–temperature–composition (PCT) curves with the experimental results. In addition, the obtained thermodynamic database of Nd–Ni–H system is applied to analyze the hydriding process of Nd–Ni alloys.

Liquidus projection of Cu–In–Se photovoltaic material system

Cu–In–Se (CIS) and its based alloys are among the most important solar cell materials. However, there are only limited Cu–In–Se phase equilibria data available. This study determines the liquidus projection of the Cu–In–Se system. Cu–In–Se alloys were prepared from pure constituent elements. The primary solidification phases of as-cast Cu–In–Se alloys were determined. The univariant lines of Cu–In–Se liquidus projection were constructed according to the experimental results determined in this study, those in the literature and the phase diagrams of its three binary constituent systems. There are 15 primary solidification phases in the ternary Cu–In–Se liquidus projection: β1-Cu2Se, Cu, β2-Cu4In, γ-Cu7In3, η′-Cu2In, Cu11In9, In, In4Se3, InSe, In6Se7, In2Se3, Se, CuSe2, CuSe and CuInSe2 phases. A large miscibility gap extends from the Cu–Se side to the In–Se side. There are 16 ternary invariant reactions in this Cu–In–Se liquidus projection involved in the liquid phase. The temperatures of invariant reactions were determined using differential thermal analysis.

Experimental investigation and thermodynamic calculation of the Mg–Mn–Ni system

Based on the critical review of the ternary Mg–Mn–Ni system, 12 alloys were prepared using a powder metallurgy method in a glove box. The isothermal section of the Mg–Mn–Ni system at 400°C was determined. Ternary compound τ (Mg3MnNi2) was confirmed in the present work. In order to obtain the phase transition temperatures, differential scanning calorimetry (DSC) was applied to the selected alloys using sealed Ta crucibles. The invariant reaction temperatures for two invariant reactions in the Mg-rich corner were measured. Considering the experimental data from present work and literature, the Mg–Mn–Ni system was optimized and a set of thermodynamic parameters was obtained. Calculated results fit well with the experimental data.