Isoplethal Sections Research Articles

Thermodynamic modeling of the Hf-Ta-O system for the design of oxidation resistant HfC-TaC ceramics

An improved understanding of the oxidation resistance of HfC-TaC ultra-high temperature ceramics (UHTCs) is developed through modeling of the phase equilibria in the Hf-Ta-O system and HfO2-Ta2O5 isoplethal section. CALculation of PHAse Diagrams (CALPHAD) thermodynamic models of the systems are developed in conjunction with experimental data from the literature and first-principles calculations. Density functional theory (DFT) calculations accurately describe thermodynamic properties of binary oxides in the Hf-Ta-O system and predict cation disorder in Hf(n-5)/2Ta2On. The ternary modeling includes revised models of the Hf–O system and existing models of the Ta–O and Hf–Ta systems. The Hf(n-5)/2Ta2On ternary oxide series is modeled as three entropically stabilized solid solutions with disordered cation sublattices that increase in stability with structure size. Hf4Ta2O13 is considered a metastable phase based on the present models and phase diagram, consistent with the lack of experimental data supporting its stability. The calculated phase diagrams improve upon prior ones and predict optimal thermal resistance of HfC-TaC ceramics at compositions between 3HfC-1TaC and 4HfC-1TaC.

Alloying Elements in Intermetallic γ‐TiAl Based Alloys – A Review on Their Influence on Phase Equilibria and Phase Transformations

Intermetallic γ‐TiAl based alloys are innovative structural materials dedicated to applications in the automotive and aeronautic industries. Especially their low density, high specific yield strength, and excellent resistance against creep and oxidation make them a suitable choice for structural high‐temperature components in combustion engines. However, further improvement of their properties and processability is required to conquer new application areas and facilitate cost‐effective production. While the incorporation of additional alloying elements is a promising possibility, their effects on the phase transformations and phase equilibria need to be considered rigorously. In this context, this review provides a detailed survey of the research work on the influence of technically important alloying elements on the Ti–Al phase diagram. First, an introduction to the fundamentals of the phase transformations in γ‐TiAl based alloys and the consequences of changed cooling conditions, relevant for example to the latest developments within the field of processing, is given. Afterward, the alloying elements, categorized with respect to their stabilization effect, are discussed and their particularities are highlighted. Topics covered include established ternary phase diagrams and isoplethal sections, the stabilization of additional phases as well as the influence of alloying elements on the microstructure of modern engineering intermetallic γ‐TiAl based alloys.

CALPHAD-guided design of Mg-Y-Al alloy with improved strength and ductility via regulating the LPSO phase

This work performed a CALPHAD-guided design strategy to develop high strength-ductility Mg–Y–Al alloy by taking advantage of the strengthening effect of the LPSO phase and the ductilizing effect of the α-Mg matrix. To achieve this goal, the LPSO phase content and the Y content in the α-Mg matrix were quantitatively optimized via calculations of the isoplethal section and phase fraction diagrams. Based on this, three typical Mg-Y-Al alloys without the LPSO phase and with varying LPSO contents were designed. The strength of the alloys was significantly improved by the introduction of the LPSO phase and the increase in its content. However, the ductility of the alloy was maintained while increasing the LPSO content. Through analyzing the strengthening and ductilization mechanisms, it was revealed that the LPSO phase can strengthen the extruded alloys by refining the dynamic recrystallized grain size, exerting a short-fiber-like strengthening effect, and dislocations strengthening effect by hindering <c+a> dislocations movements. The ductile α-Mg phase with considerable Y content can effectively withstand plastic strain by operating multiple slips during the deformation, significantly improving the ductility of the material. The results of this study inspired the development of an effective design strategy to produce high strength-ductility Mg-Y-Al alloys by quantitatively optimizing the LPSO phase and Y contents in the α-Mg matrix, as well as to design high-performance Mg alloys for engineering demands in the future.

Experimental study and thermodynamic modelling of the ternary system Fe–Ni–Si with re-modelling of the constituent binary systems

The present paper reports on the thermodynamic modelling of the complete ternary Fe–Ni–Si system based on key experimental results and information reported in literature. The key experiments were performed to verify phases and phase fractions in selected ternary Fe–Ni–Si alloys using samples in the as-cast state as well as annealed samples. Chemical compositions of the samples were analysed by Energy Dispersive X-Ray Spectroscopy. Microstructure characterization was performed by Scanning Electron Microscopy and Electron Backscatter Diffraction techniques. Phase transformation temperatures were determined by Differential Scanning Calorimetry operated in the Differential Thermal Analysis mode. Calculations performed using proposed thermodynamic description reproduce experimental data well, including data from available literature. In particular, the Fe-rich corner of the Fe–Ni–Si system has been modelled in detail, with emphasis on the A2 and B2 phase fields. The developed ternary database was used to compute phase diagrams and thermodynamic properties of the constituent binary systems as well as selected isothermal and isopleth sections. Due comparison with commercially available and previously modelled thermodynamic descriptions is presented and discussed.

CALPHAD-guided alloy design of Sn–In based solder joints with multiphase structure and their mechanical properties

A CALPHAD-guided alloy design and the corresponding key experiments method were performed to study the microstructure-mechanical properties relationships for Sn–In based solder alloys with In content ranging from 0 to 52 wt %. Based on a calculated Sn0.7Cu–Sn52In isoplethal section phase diagram, six compositions (Sn52In, 42In, 35In, 18In, 8In and Sn0.7Cu) were selected with different phases such as β-In3Sn, γ-InSn4, β-Sn and β-Sn(In). The phase fractions of alloys acquired from experimental microstructures are consistent with calculated values. Their phase fractions differ and the order of hardness values is β-Sn(In) > β-Sn > γ-InSn4 > β-In3Sn, leading to an increase in strength and a decrease in ductility with the reduction of In content. Strengths of low In content alloys of 18In and 8In containing β-Sn(In) and γ-InSn4 phase are higher compared with high In content alloys of Sn52In, 42In and 35In containing γ-InSn4 and β-In3Sn phases. Meanwhile, elongations of low In content alloys are better than that of 42In and 35In alloys. Thus, the best strength and ductility combination can be achieved by low ln contents alloys. This work can provide a new strategy for the development of Sn–In based alloys via CALPHAD-guided design of phase types and fractions.

The High-Temperature Cu-Fe-S System: Thermodynamic Analysis and Prediction of the Liquid–Solid Phase Range

Thermodynamic modeling of the Cu-Fe-S liquid solution is carried in the framework of the modified quasichemical model. The manifold nature of Cu-Fe-S liquid solutions from highly metallic via sulfur-rich to pure liquid sulfur is described by one single Gibbs energy expression at 1 bar total pressure. The model predictive ability of an asymmetric versus symmetric approach is thermodynamically analyzed with respect to the extrapolation scheme from the binary subsystems into the ternary system. Without the need of adjustable ternary parameters predictions of sulfur potentials for the liquid phase are in line with experimental data available in the literature. High-temperature pyrrhotite optimized via the compound energy formalism and Cu-Fe-S alloy phases are taken into consideration to predict phase equilibria with the liquid solution. Four isothermal and four isoplethal sections demonstrate promising agreement between a large stock of experimental data and prediction.

The phase diagram of the MnTe–SnTe–Sb2Te3 ternary system and synthesis of the iso- and aliovalent cation-substituted solid solutions

The phase diagram of the MnTe–SnTe–Sb2Te3 quasi-ternary system was studied and the new isovalent cation substituted Mn1-xSnxSb2Te4 and Mn1-xSnxSb4Te7 (x = 0 ÷ 1) solid solutions series were revealed along the aliovalent (Sb1-x-yMnxSny)2Te3 and Sn1-x-yMnxSbyTe (x = 0 ÷ 1) solid solutions. The phase relationships were established experimentally using differential thermal analysis (DTA), powder X-ray diffraction (PXRD), and scanning electron microscopy (SEM). The liquidus surface projection, an isothermal section at 500 °C, and the phase diagrams of the five isopleth sections have been constructed. Based on the obtained phase diagrams, the optimization of synthesis conditions was performed to approach the most rational design of the prepared solid solutions. The synthesized Mn1-xSnxSb2Te4 and Mn1-xSnxSb4Te7 solid solution phases were characterized and revealed that by increasing Sn content in both the solid solution series, the a- and c crystal lattice parameters increase linearly following Vegard's law.

Experimental Phase Equilibria and Isopleth Section of 8Nb-TiAl Alloys

The 8Nb isopleth section of a Ti-Al-Nb system is experimentally determined based on thermal analysis and thermodynamic calculation methods to obtain the phase transformation and equilibrium relations required for material design and fabrication. The phase transus and relations for the 8Nb-TiAl system show some deviations from the calculated thermodynamic results. The ordered βo phase transforms from the disordered β/α phases at 1200–1400 °C over a large Al concentration range, and this transformation is considered to be an intermediate type between the first- and second-order phase transitions. Moreover, the βo phases are retained at the ambient temperature in the 8Nb-TiAl microstructures. The ωo phase transforms from the highly ordered βo phase, rather than from α2 or βo with a low degree of atom ordering B2 (LOB2) structure, with Al concentration of 32–43 at% at approximately 850 °C. From the experimental detection, the transition of the ωo phase from the βo phase is considered to be a further ordering process.

Thermodynamic modelling of the Al–Co–Mn system

In the present work, the Al–Co–Mn ternary system is thermodynamically modelled using the Calphad approach. In the modelling, experimental data such as liquidus, solidus, tie lines, and phase boundaries are included. An order–disorder model is used to describe the bcc and B2 phases. The bcc/B2 description was modified in the binary Al–Co system to improve the fit of bcc/B2 equilibria in the ternary system. The thermodynamic models of Al5Co2, M-Al13Co4, γ1, and γ2 intermetallic phases were modified to include the third element to reflect the solubility of this element in the ternary system. The ternary phase T-AlCoMn is described as a stoichimetric compound. Ternary interaction parameters for liquid, bcc, β-Mn, and hcp were optimized, using all the relevant experimental data in the literature. Calculated isothermal and isoplethal sections are compared with experimental data. A comparison between modelling and experimental measurements showed a good agreement between the present results and experiments.

Experimental Study of High Temperature Phase Equilibria in the Iron-Rich Part of the Fe-P and Fe-C-P Systems

During the solidification of steel, phosphorus strongly segregates in the interdendritic liquid phase. In the continuous casting process, even low levels of P may have a detrimental effect on the final product quality. However, phosphorus is partly added up to 0.10 wt pct to improve the mechanical properties of advanced steel grades nowadays, e.g., High-Strength Interstitial-Free (HSIF). To provide new experimental data for the development of thermodynamic databases and solidification models for P alloyed steel grades, phase equilibria in the Fe-P and Fe-C-P key systems were studied up to 1550 °C using differential scanning calorimetry (DSC) and high temperature laser scanning confocal microscopy (HT-LSCM). Special focus was placed on solid/liquid equilibrium temperatures in the Fe-rich part of the binary Fe-P system between 0.025 and 9 wt pct P. In the ternary system, three isoplethal sections with 0.10 mass pct. P, 0.20 mass pct. C and constant mass percent ratio P/C of 2 were investigated. In the latter section, HT-LSCM observations were linked with DSC signals to optically identify present phase stabilities. Particularly at [pct P] < 1, significant differences between performed measurements and calculated phase equilibrium temperatures using thermodynamic assessments from the literature were identified. In all ternary sections, the experiments indicate less influence of P on the hypo-peritectic range compared to the thermodynamic calculations.

Solid-Liquid Equilibria for Hexafluorophosphate-Based Ionic Liquid Quaternary Mixtures and Their Corresponding Subsystems.

The present work describes an experimental study and the thermodynamic modeling for the solid-liquid phase diagram of an ionic liquid quaternary system constituted by hexafluorophosphate ([PF6]-) as the common anion and by 1-methyl-3-propylimidazolium ([C3mim]+), 1-methyl-1-propylpyrrolidinium ([C3mpyrr]+), 1-methyl-3-propylpyridinium ([C3mpy]+), or 1-methyl-1-propylpiperidinium ([C3mpip]+) as the cations. The Modified Quasichemical Model was used to model the liquid solution, and the Compound Energy Formalism was used for the relevant solid solutions. The liquidus projections of the four ternary subsystems (1) [C3mim][PF6]-[C3mpip][PF6]-[C3mpyrr][PF6], (2) [C3mpy][PF6]-[C3mpip][PF6]-[C3mpyrr][PF6], (3) [C3mpip][PF6]-[C3mpy][PF6]-[C3mim][PF6], and (4) [C3mpyrr][PF6]-[C3mpy][PF6]-[C3mim][PF6] were predicted using a standard symmetric (for systems 3 and 4) or asymmetric (for systems 1 and 2) interpolation method. In order to test the accuracy of the thermodynamic model, two isoplethal sections were experimentally measured in each of the four ternary systems using differential scanning calorimetry. Overall, agreement was very satisfactory, not requiring fitting of any ternary interaction parameters for the liquid solution model. In each of the four calculated ternary liquidus projections, the region of composition corresponding to room temperature ionic liquid mixtures was determined. The global minimum of the liquidus temperature in the complete composition space was calculated to be about -16 °C, with a mole percentage composition of (33.8% [C3mpyrr][PF6] + 33.9% [C3mpy][PF6] + 32.3% [C3mim][PF6]).

Sn-3.0Ag-0.5Cu/Sn-58Bi composite solder joint assembled using a low-temperature reflow process for PoP technology

Package-on-Package (PoP) is a popular technology for fabricating chipsets of accelerated processing units. However, the coefficient of thermal expansion mismatch between Si chips and polymer substrates induces thermal warpage during the reflow process. As such, the reflow temperature and reliability of solder joints are critical aspects of PoP. Although Sn58Bi is a good candidate for low-temperature processes, its brittleness causes other reliability issues. In this study, an in-situ observation was performed on composite solders (CSs) made of an Sn-3.0Ag-0.5Cu (SAC305) solder and an Sn58Bi solder that were mixed during reflow at temperatures of 170 °C (CS-170), 180 °C (CS-180), and 190 °C (CS-190). The volumes of the mixed-solder regions were in the order of CS-190 > CS-180 > CS-170. A calculated Sn58Bi-SAC305 isoplethal section of the Sn-Ag-Cu-Bi quaternary system was employed to elucidate the melting behavior of CS-190. CS-190 with Sn cyclic twin boundary and Bi phase preferred orientation of [0001] was demonstrated by electron backscatter diffraction. Moreover, Cu/CS-190/Cu joints with a shear strength of 46 MPa were formed. CS-190 can reduce the brittleness of SnBi solder owing to the reduced solid-solution hardening with the decrease in the Bi content. These factors can improve the reliability of PoP technology.

The Bi2Se3–Bi2Te3–BiI3 system: Synthesis and characterization of the BiTe1-xSexI solid solutions

This paper describes the phase relationships and ternary solubility of the binary and ternary compounds in the Bi2Se3–Bi2Te3–BiI3 system. Differential thermal analysis (DTA), powder X-ray diffraction (PXRD) and scanning electron microscope equipped with energy dispersive X-ray spectrometer (SEM-EDS) were main tools for experimental investigations of the equilibrated samples of the system. This system is found to be quasi-ternary plane of the quaternary Bi–Se–Te–I system. An isothermal section at 300 K, a liquidus surface projection and four isopleth sections of the system were plotted based on experimental and literature data. The existence of the BiTe1-xSexI solid solutions series (γ1 and γ2) in the wide range of composition of BiSeI–BiTeI section was revealed and characterized. No new quaternary compound was found in the system. The primary crystallization fields and homogeneity range of all the existing phases, as well as character and temperature of all the non- and monovariant equilibria of the system were determined.

Thermodynamic constitution of the Al–Cu–Ni system modeled by CALPHAD and ab initio methodology for designing high entropy alloys

The Al–Cu–Ni system has been thermodynamically assessed over the whole composition and temperature range based on a critical literature review. The L12 and B2 phases, in conjunction with their disordered counterparts, are described using partitioning models. Ab initio calculations were performed to support the assessment of these phases. A set of self-consistent thermodynamic parameters for describing the Gibbs energy of individual phases was obtained. The assessment was validated by comparing various calculations such as invariant reaction equilibria, thermochemical properties, isothermal and isoplethal sections with all available experimental data. The Al–Cu–Ni ternary is a vital subsystem of many high entropy alloys (HEAs), which can probably be attributed to the existence of stable ordered and disordered FCC and BCC structures. In near-equiatomic compositions of this ternary system, the phase formation and equilibrium and non-equilibrium solidification curves were calculated using the present thermodynamic description. The phase competitions and their impacts on the design of HEAs are discussed, e.g. the relative stability of the disordered FCC and BCC for dual-phase HEAs, and the equilibria between disordered FCC_A1 and ordered B2 phases for ductile high strength HEAs.

Liquid–Liquid–Solid Equilibria in the Ternary System Water–Phosphoric Acid–Cyclohexane at 25 and 35 °C: Stability Domain of Hemihydrate and Anhydrous Phosphoric Acid

The water–phosphoric acid–cyclohexane ternary system was studied at 25 and 35 °C under atmospheric pressure, and the binodal curve was determined by the cloud-point method. In addition, the isoplethic section between 2H3PO4·H2O–cyclohexane was investigated using a Tammann diagram based on the thermal analysis of different samples with the determination of hemihydrate melting temperature. The concentration of phosphoric acid and cyclohexane was assayed by volumetric titration and gas chromatography, respectively; the amount of water was calculated by the material balance equation. The miscibility between phosphoric acid and cyclohexane was found to be very low with the appearance of a three-phase stability domain liquid–liquid–solid by the presence of phosphoric acid crystals: hemihydrate (2H3PO4·H2O) and anhydrous phosphoric acid (H3PO4).

The phase equilibria in the Tl-S-I system and electrical properties of the Tl6SI4 and TlS compounds

The phase equilibria in the ternary Tl-S-I system were investigated experimentally by means of powder X-ray diffraction (PXRD) and differential thermal analysis (DTA). Five isopleth sections, liquidus surface projection and room temperature isothermal section were constructed based on experimental data. dc-and ac-electric properties of the TlS and Tl6SI4 crystals were studied within the temperature and frequency ranges from 120 K to 300 K and from 50 kHz to 35 MHz, respectively. The hopping mechanism for charge transfer over the localized states near the Fermi level was established at low temperatures and high frequencies for these compounds. The density and energy scatter of the states which are located in the vicinity of the Fermi level as well as the average time and distances of jumps were estimated for the title compounds.

Phase Equilibria in the Tl4PbTe3-Tl9SmTe6-Tl9BiTe6 Section of the Tl-Pb-Bi-Sm-Te System.

Phase equilibria in the section Tl4PbTe3-Tl9SmTe6-Tl9BiTe6 of the Tl-Pb-Bi-Sm-Te system were determined by combination of differential thermal analysis, powder X-ray diffraction methods as well as microhardness measurements. The phase diagrams of the boundary systems Tl4PbTe3-Tl9SmTe6, Tl9SmTe6-Tl9BiTe6, isothermal section at 820 and 840 K, some isopleth sections and as well as liquidus and solidus surfaces projections, were plotted. Unlimited solid solutions, which crystallize in Tl5Te3 structure type were found in the system at the solidus temperatures and below.

Interrupted heating DTA for liquidus temperature determination of Ag–Cd–In alloys

An Ag–Cd–In alloy is used as the control rod material in most pressurized water reactors. Despite this important application, the phase diagram of the Ag–Cd–In ternary system remains largely unknown especially the phase equilibria involving the liquid phase in the Cd- and In-rich regions. In this work, the 60 at.% In isopleth section is investigated by differential thermal analysis (DTA). The results of the classical protocol at constant heating and cooling rates are compared with those obtained using an interrupted heating DTA (IHDTA) method. It is shown that this last protocol allows to strongly reduce the uncertainty on the liquidus temperature determination.

Experimental Study of the Tl4PbTe3-Tl9TbTe6-Tl9BiTe6 Section of the Tl-Pb-Bi-Tb-Te System

The aim of the present study was to determine the phase relations in the Tl4PbTe3-Tl9TbTe6-Tl9BiTe6 section of the Tl-Pb-Bi-Tb-Te system. Based on a set of the methods of the physicochemical analysis (differential thermal analysis, powder X-ray diffraction method as well as microhardness measurements), the phase diagram of the Tl4PbTe3-Tl9TbTe6 boundary system, some isopleth sections, liquidus and solidus surfaces projections, as well as isothermal sections at 840 and 860 K, were plotted. Unlimited solid solutions with the Tl5Te3 structure (δ-phase) were found in the system, which are of interest as a thermoelectric materials.

The YbTe-SnTe-Bi2Te3 system

The phase diagram of the YbTe-SnTe-Bi2Te3 system was experimentally investigated by using differential thermal analysis (DTA), powder X-ray diffraction (PXRD) and scanning electron microscopy (SEM-EDS) techniques. Four isothermal sections at 300, 800, 900 and 1000 K, the liquidus surface projection, as well as four isopleth sections were constructed from experimental results. Three different solid solubility fields based on SnTe, YbTe and Bi2Te3, respectively, were observed at 300 and 800 K. No new quaternary compound was detected in the system. The primary crystallization fields and homogeneity ranges of the phases as well as the types and coordinates of all the non- and monovariant equilibria were determined. It was also revealed that the solid solution α2 based on YbTe is a major phase in the distribution of phase areas in the subsolidus.