Phase equilibria, phase formation and solidification microstructure in Sm-Fe-Ti alloys via experimental determination and thermodynamic calculation

The goal of this study is to carry our detailed thermodynamic analysis of FeMn fluxless smelting process in submerged arc furnaces (SAF) using realistic plant data and compare the calculation results with industrial outcomes. Modern thermodynamic databases FactSAGE was deployed to assess equilibria inside separate phases and between them at 1400-1800°C for two FeMn78 alloys with different phosphorus content. Phases (metal, slag and gas) compositions were calculated with metal recovery value for manganese as well as through-recovery of manganese in both working slag and metal. It was found that temperature of the process 1500-1525°C predicts maximal recovery of manganese into the alloy. The outcomes allowed combination of blended manganese agglomerates, ores, return tails to be efficiently composed and converted into materials streams, which can be fed into the thermodynamic calculations. Such approach allows flexibility to optimize different scenarios in high-carbon ferromanganese fluxless smelting. The correlation of the calculations with industrial plant outcomes was found to be very good. The method gives a good basis to check behavior of different components and elements in the furnace, distribution of them between the phases (gas, metal, slag) and identify the pathways for improvement of the process leading to higher yield and quality. With the same thermodynamic database parameter similar approach can be used for other manganese ferroalloys.

The article deals with the features of mineral composition of gold-bearing waste from the gold concentration plant. The tailings material consists primarily of a finely dispersed, silty fraction. The structure of the accumulated tailings resembles a layered pie: three horizons of different compositions are distinguished. They were formed during the processing of mixed, and primary (sulfide) ores oxidized in different years. The most common ore minerals in the tailings dump deposits are pyrrhotite, arsenopyrite, pyrite, stibnite, magnetite, and iron hydroxides. In addition, native bismuth, native gold, bismuth and tellurium sulfides, scheelite, and secondary antimony and arsenic minerals (valentinite, tripugiite, and scorodite) are also noted.The composition of the tailings dump’s recirculating water and sludge was studied. Vertical variability in the chemical composition of the tailings storage facility’s recycled waters was established. Sharp variability in water composition is observed at depths of 6–8 meters. To study the direction and rate of dissolution and precipitation of substances in the liquid phase of the tailings dump field experiments were conducted. During the experiments, samples of minerals and man-made materials including rubber, sulfur, mercury amalgam on copper, copper, steel, graphite, native gold in quartz, pyrite and pyrrhotite, arsenopyrite were placed in recycled sludge water at various depths to be extracted in batches with the exposure times of 1, 2, and 3 months. The experiment revealed the etching traces of native gold and a diverse range of newly formed mineral phases including gypsum, iron hydroxides, scorodite, iron and manganese cyanides, copper sulfates and thiocyanates, and others. The Selector-Windows software package was selected for physicochemical modeling of the hypergene processes occurring in the tailings sludge waters. The Selector-Windows software package features a system of built-in thermodynamic databases and a module for generating models of varying complexity and architecture. Performed thermodynamic modeling using the software package allowed the authors to calculate the parameters and direction of technogenic processes occurring in the concentration tailings, determine the elemental and ionic composition, Еh-pH parameters of forming solutions, crystallizing minerals, and their associations as well as to propose a mechanism for secondary gold concentrations in the silt fraction of tailings.

A numerical model is introduced in which the thermodynamic diffusion approach resulting from irreversible thermodynamics is consistently applied. Unlike Fick's approach that relies on concentration gradients, the thermodynamic approach employs the actual driving force for diffusion, which is the gradient of a component's thermodynamic activity. Utilizing CalPhaD programs to extract component activities from thermodynamic databases, a numerical calculation method was developed and implemented using CUDA C++, in order to apply the thermodynamic model. The model's effectiveness was evaluated using the binary aluminum‐iron system, starting from pure metal diffusion couples and simulating interdiffusion until complete mixing under varying conditions. It is shown that the thermodynamic model accurately predicts phase changes and the formation of intermetallic phases using only a singular global diffusion coefficient valid for both components and all phases. The model's application to complex geometries is demonstrated on the alloying of an interpenetrating composite.

Abstract The increasing demand for cleaner energy carriers has intensified interest in liquid fuel blends containing oxygenated compounds such as alcohols and glycol ethers. These additives improve combustion efficiency and reduce environmental impact. In this work, excess molar enthalpies were determined for a binary mixtures (ethanol + 1-propanol; diethylene glycol monoethyl ether + 1-propanol; and ethylene glycol monophenyl ether + ethanol) as well as for four ternary mixtures: diethylene glycol monomethyl ether (1) + 1-propanol (2) + ethanol (3), diethylene glycol monoethyl ether (1) + 1-propanol (2) + ethanol (3), ethylene glycol monomethyl ether (1) + 1-propanol (2) + ethanol (3), and ethylene glycol monophenyl ether (1) + 1-propanol (2) + ethanol (3). Measurements were obtained with a quasi-isothermal flow calorimeter at 298.15 K and 313.15 K under 0.1 MPa, conditions representative of typical industrial applications. The experimental data were then correlated using the Redlich–Kister equation for the binary system and the NRTL, UNIQUAC, and modified UNIFAC (Dortmund) models for the ternary systems, enabling evaluation of both mixture behavior and model accuracy. The findings expand the thermodynamic database for alcohol- and glycol ether-based blends and provide benchmarks for simulation and design in energy and petrochemical processes.

ABSTRACT Key phase diagram studies of Li 2 O–V 2 O 5 , K 2 O–V 2 O 5 , and Rb 2 O–V 2 O 5 systems were conducted using X‐ray diffraction and differential thermal analysis within Pt crucibles. The XRD results confirmed the existence of stoichiometric phase Li 4 V 34 O 87 in the Li 2 O–V 2 O 5 system. In the K 2 O–V 2 O 5 system, the melting temperatures of K 2 V 8 O 21 and KVO 3 were experimentally determined to be 532.4°C and 516.5°C, respectively. The eutectic reaction between liquid, Rb 3 V 5 O 14 , and RbVO 3 in the Rb 2 O–V 2 O 5 system was identified at 496°C with a composition of 42 mol% Rb 2 O. The modified quasichemical model (MQM), which accounts for the short‐range ordering of the second‐nearest neighbors of cations in molten oxide solutions, was employed to describe the liquid phase, and compound energy formalism (CEF) was applied to model the Li 1+X V 3 O 8 solid solution at elevated temperatures. Thermodynamic modeling of the R 2 O–V 2 O 5 (R = Li, Na, K, Rb, and Cs) systems was developed using the CALculation of PHAse Diagrams (CALPHAD) methodology. The experimental data across the entire composition range of the R 2 O–V 2 O 5 systems were successfully reproduced, and thermodynamic properties for all solid and liquid phases within all binary systems were obtained. The developed thermodynamic database was further applied to simulate vanadium extraction processes, with the optimal operation windows.

The thermochemistry of the Cu–Ni–S system largely determines the recovery of nickel, copper, and platinum group metals from sulfide ores and the production of nickel speiss in polymetallic recycling through lead bullion route. This study evaluates the accuracy of the FactSage 8.3 FTsulf thermodynamic database for predicting phase equilibria and element distribution within this system and provides data for further model improvements. Existing experimental data from literature were critically assessed against model predictions, identifying key areas where data were either lacking or controversial. New experiments were designed in these areas. Experimental investigation focused on two key areas: the matte-metal miscibility gap at 1100 and 1200 °C, and the solubility of copper sulfide in the β-Ni 3 S 2 solid phase, often referred to as high-temperature heazlewoodite. The experimental method of equilibration and quenching, followed by Electron Probe X-ray Microanalysis (EPMA) was refined to apply it for highly fluid matte and liquid metal phases. While the FactSage 8.3 FTsulf database generally agreed with most literature data, our results revealed a systematic underestimation of the nickel distribution coefficient, ratio of wt.% Ni in liquid Cu 2 S-rich matte to wt.% Ni in liquid copper metal. The solubility of copper sulfide in the β-Ni 3 S 2 solid phase was underestimated by the model compared to the experimental results of this study. These findings will inform future thermodynamic model optimizations and contribute to a broader research program focused on characterizing phase equilibria, heat balance, and elemental distribution in complex nickel-, copper-, and lead-based polymetallic processes. • Assessed FactSage 8.3 FTsulf for Cu-Ni-S phase equilibria/element distribution • Focused experiments on matte-metal miscibility gap and β-Ni 3 S 2 non-stoichiometry • Model underestimated Ni distribution coefficient in matte/metal phases. • Cu 2 S solubility in β-Ni 3 S 2 solid phase was also underestimated. • Findings support improvement of thermodynamic models for polymetallic processes

Phase equilibria and thermodynamic modeling of the Ge-Te-Bi ternary system

In this study, the orientation-dependent solidification behavior of CMSX-4 single-crystal superalloy welds was systematically investigated using phase-field simulations. A multiphase-field model implemented in MICRESS, coupled with CALPHAD-based thermodynamic and mobility databases, was employed to simulate weld solidification under gas tungsten arc welding (GTAW) conditions. The numerical model was validated by comparing the simulated primary dendrite arm spacing (PDAS) with experimental observations, showing good agreement. Initial crystallographic misorientations of 0° and 15° were introduced to represent epitaxial single-crystal and high-angle polycrystalline solidification, respectively. The results reveal that, although the mushy zone range remains nearly identical for both orientations, the morphology and continuity of residual liquid at the terminal stage of solidification differ significantly. For the epitaxially grown condition (0°), residual liquid is distributed in a discontinuous droplet-like form due to early dendrite arm coalescence. In contrast, high-angle misorientation (15°) delays dendrite coalescence, leading to the formation of continuous liquid films enriched with solute elements such as Hf. This continuous liquid film provides an effective pathway for crack initiation and propagation, resulting in a substantially higher BTR. These findings demonstrate that the solidification cracking susceptibility of single-crystal superalloy welds is governed primarily by the morphology of residual liquid during the final stage of solidification rather than by the mushy zone range itself. The present study provides a mechanistic framework for understanding BTR variation in single-crystal superalloy welds and offers critical insights for controlling epitaxial growth and improving weldability in repair welding and additive manufacturing applications.

Modeling water-rock interactions in underground environments requires the use of thermodynamic databases that account for the complexity of groundwater chemical compositions under relevant pressure and temperature conditions. A key issue concerning saline groundwaters is their high ionic strength, which are often not reliably calculated and calls for the use of specific thermodynamic approaches. Among such approaches, the Pitzer model appears to be one of the most promising. However, its applicability to underground fluids is limited by the fact that the values of its numerous parameters are only known for a subset of chemical systems and, more particularly, are often missing for trace elements and at temperatures other than 25 °C. This paper describes a new way to develop a relevant thermodynamic database to account for the trace elements in these types of deep environments. It combines two in-house databases: Thermoddem, which relies on the B-dot Extended Debye-Hückel activity model, and PhreeSCALE, which uses the Pitzer formalism. The resulting Hy brid Pi tzer- T hermoddem (HyPiT) thermodynamic database (TDB) integrates a simplified Pitzer model to account for major and trace elements. Based on a series of recent works ( Simoes et al., 2017a , 2017b , 2016 ), the Pitzer binary interaction parameters, β (0) and β (1) and their first derivative with respect to temperature (d β (0) /dT and d β (1) /dT) are determined for simulating the first order interactions between trace elements and major species. The HyPiT database is successfully applied to different geochemical systems relevant to underground environments. They include (i) the solubility of gypsum in NaCl and sea-type brines of varying ionic strength at temperatures between 0 and 25°C, (ii) the solubility of barite in NaCl brines at 25, 60 and 80°C, (iii) the solubility of calcite in 0.1 and 4 M NaCl brines for temperatures and pressures up 250°C and 1450 bars, respectively, (iv) the solubility of amorphous silica up to 150°C in various single electrolyte solutions, namely HCl, NaCl, MgCl 2 , HNO 3 , NaNO 3 , Na 2 SO 4 , and MgSO 4 . Particular attention is also given to the modeling of iron-bearing systems such as the speciation of Fe III in LiCl solutions up to 20 mol/kg. • We considered all the comments made by the reviewer. As the revisions are minor, we have nothing to highlight here. • We are grateful to the reviewer and the associate editor for their support.

ABSTRACT Phase equilibria in the Y 2 O 3 –Ta 2 O 5 system play an important role in the development of new materials for thermal barrier coating (TBC) applications, with higher thermal stability resulting in more efficient gas turbines with reduced exhaust gas emissions. Therefore, the development of a consistent thermodynamic database for this oxide system is invaluable for faster and more sustainable material development. In this work, four different sample compositions were prepared by co‐precipitation reactions, and the heat capacities of the orthorhombic Y 3 TaO 7 (Y 1‐ x Ta x O 1.5+ x with x = 0.26 and x = 0.29) and the hexagonal YTa 7 O 9 phases, both with homogeneity ranges, were experimentally measured in the temperature range from 200 to 1373 K using differential scanning calorimetry (DSC). The obtained results, together with literature data on phase equilibria and experimental thermodynamic values, have been used to assess the thermodynamic description of the Y 2 O 3 –Ta 2 O 5 system applying the CALPHAD approach.

Abstract The Thermodynamic Reference Database (THEREDA) is designed for geochemical calculations in the context of repositories for radioactive waste under high-saline conditions. For this purpose, it adopts the Pitzer ion-interaction approach. THEREDA is currently the only database worldwide that allows comprehensive polythermal calculations (up to at least 100 °C) of the hexary system of the oceanic salts Na-K-Mg-Ca-Cl-SO 4 -H 2 O, including acids, bases, and CO 2 /carbonates. Its validity is documented primarily, yet not exclusively, by application to solubility data. THEREDA’s potential to predict the development of the geochemical environment, e.g. in the event of an intrusion of solution, constitutes a prerequisite for the engineering design of a nuclear waste repository with regard to the selection and placement of plug and sealing system components. The focus of THEREDA lies on the calculation of solubilities of radionuclides (actinides, fission and activation products), chemotoxic and matrix elements e.g., canister materials, and compounds having an impact on the overall geochemical milieu in the near field of a repository under high-saline conditions. Special features of THEREDA besides its focus on high-saline solutions are procedures for testing prior to any release combined with intercode-comparison, extensive and publicly available validation against published experimental data, and systematic application of a scheme to mark data with regard to quality, reliability, and origin. Traceability of data and validated experimental results to published sources is also emphasised. This documentation is in part realised in ready-to-use parameter files for users, and in part on the website ( www.thereda.de ). Another feature is the possibility for operation of THEREDA by several institutions in a net-worked manner. To highlight THEREDA’s potential, examples for applications of the database are given. Additionally, ongoing efforts for the further development of THEREDA are described in the outlook at the end of this article. • Thermodynamic database for high-saline solutions using the Pitzer approach • Ready-to-use parameter files for PHREEQC and Geochemist’s Workbench • Used for nuclear waste management and geochemical modeling regarding nuclear waste disposal • Covering brines, oceanic salts, actinides, fission products, heavy metals, cement phases • Calculation of polythermal solid-liquid phase equilibria, solubility, speciation

A global assessment of the geochemistry of carbonate mineral formation and the dynamics of calcite precipitation in alkaline lakes

To satisfy the needs of an ever-growing population, it is imperative to cope with the extended demand for copper. To do so, copper makers mostly rely on pyrometallurgical processes that are characterized by emitting hazardous gases and solid wastes, and by the fact that these processes are energy demanding. Additionally, copper makers face the issue of processing leaner ore bodies or exploiting mineral deposits already overexploited or about to end their productivity cycle. These problems compromise the sustainable production of copper. Because of that, this study focuses on the leading technology in use to assess and identify possible solutions in order to improve the efficiency of energy usage and to decrease the amount of wastes generated in copper pyrometallurgy. To do so, reliable thermodynamic databases and Sankey diagrams were used to determine possible improvements. For example, it is determined that by increasing the mass ratio of Fe/Cu in the mineral feedstock may result in increasing the copper content in the matte, and thus reducing the exergy flows, resulting in improved energy usage. Another positive impact is that using oxygen-enriched air with higher copper concentrations could decrease SO2 emissions by nearly 25%. Among other detrimental environmental issues, they entail.

Abstract Magnesium oxychloride cement (MOC) is recognized for its superior mechanical performance and environmental benefits. Yet, the phase evolution of MOC in aggressive environments, particularly with chloride and sulfate exposure, remains insufficiently understood. A novel thermodynamic database with self‐consistency is constructed in this study to reveal the degradation mechanism of hardened MOC paste exposed to solutions of NaCl, CaCl 2 , Na 2 SO 4 , MgSO 4 , and natural brine environments, accounting for both chemical attack and leaching effects. The predicted phase assemblages are validated through x‐ray diffraction data from published sources and additional experiments. The results reveal that MOC degradation in saline media is governed by three interrelated factors: (i) leaching dominates the degradation process, with chemical attack playing a secondary role; (ii) chloride/sulfate concentrations dictate the thresholds for phase transformation; and (iii) reaction pathways and secondary phase evolution are shaped by the competition between Ca 2+ /Na + and Mg 2+ ions. The present work delivers novel thermodynamic perspectives on MOC degradation and lays a theoretical foundation for its optimization in marine and saline environments.

Thermodynamic properties of MgCl 2 -MgSO 4 and CaCl 2 -CaSO 4 binary systems hold significant importance in the exploration of potential phase change materials for thermal energy storage applications. This study aims to elucidate the phase diagrams and thermodynamic properties of the eutectic mixtures within these systems, employing experimental techniques such as Differential Thermal Analysis (DTA) and Differential Scanning Calorimetry (DSC). Through comprehensive experimental investigations, the phase diagrams of the MgCl 2 -MgSO 4 and CaCl 2 -CaSO 4 systems were meticulously delineated, revealing the eutectic compositions and transition temperatures. Specifically, the eutectic composition for MgCl 2 -MgSO 4 was proposed to be 28.0 mol% MgSO 4 with a melting temperature of 663 ± 5 °C, while for the CaCl 2 -CaSO 4 system it was found to be at 14.0 mol% CaSO 4 and 722 ± 5 °C. Additionally, the enthalpy of fusion of these eutectic mixtures was for the first time determined, providing crucial insights into their thermal behaviour. They are 38.2 ± 1.0 kJ/mol for the Mg-containing system and 30.2 ± 0.4 kJ/mol for the Ca-containing system, respectively. The experimental data obtained in this study served as the foundation for the development of a new Gibbs energy dataset, which is essential for conducting thermodynamic calculations. The utilisation of this dataset enables accurate predictions of thermodynamic properties across the entire composition and temperature ranges of the systems under investigation. • An experimental analysis of the binary systems MgCl 2 -MgSO 4 and CaCl 2 -CaSO 4 was conducted using DTA/TG and DSC. • Experimental phase diagrams covering the whole composition range were obtained by DTA in sealed platinum tubes. • DSC measurements on eutectic mixtures provided C p data and enthalpy of fusion. • The thermodynamic database was significantly improved and updated based on the present experimental results. • The calculated phase diagrams and thermodynamic properties showed good agreement with the experimental data.

Thermodynamic database of quaternary Al-Si-Mg-Sb system and its application in the design of Sb-modified Al-Si-Mg casting alloys

Abstract In this work, seven RE–Cu (RE = Ce, Pr, Sm, Eu, Tb, Er and Lu) binary systems were optimized using the CALPHAD method based on the reported experimental data. The liquid phase and terminal solid solution phases were modeled using the substitutional solution model, while the intermetallic compounds were treated as stoichiometric compounds. Self‐consistent thermodynamic parameters of seven RE–Cu binary systems were obtained, which can be used to reproduce the experimental results including phase diagram and thermodynamic properties. Furthermore, in combination with the reported assessments of six RE–Cu (RE = La, Nd, Gd, Dy, Ho, and Yb) binary systems, phase equilibria, and thermodynamic properties of 13 RE–Cu (RE = La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Yb, and Lu) binary systems were examined systematically. Generally, it was observed that as the RE atomic number increases, the formation temperatures of the RE–Cu intermetallic compounds increase gradually, and the enthalpy of mixing of liquid RE–Cu alloys and the enthalpy of formation of the RE–Cu intermetallic compounds become increasingly negative. These results provide a comprehensive set of thermodynamic parameters for the RE–Cu binary systems, which will serve as a crucial foundation for developing a thermodynamic database of RE–Cu‐based alloys.

Abstract The equilibrium phase relations between metallic copper and silica-saturated FeO–CaO–SiO 2 –(Na 2 O, Al 2 O 3 ) slags were investigated at 1200 °C and p O2 from 10 −7.0 to 10 −4.5 atm. An advanced experimental technique was employed, involving high-temperature isothermal equilibration in controlled CO–CO 2 –N 2 gas atmospheres, followed by quenching in ice-water mixtures. Quantitative measurements of the equilibrated phase compositions were conducted using electron probe X-ray microanalysis. The equilibrium compositions of metal and slag were displayed as a function of p O2 , and the copper solubilities in three different slags were compared and discussed in the context of fire refining. The experimental results were compared with data from the literature as well as thermodynamic databases of MTDATA and FactSage thermodynamic software. This study enhances the understanding of slag chemistry in copper anode furnace refining, contributing to the optimization of industrial fire refining operations.

Abstract This study investigates the heat capacities of intermetallic phases, specifically Ni 3 Fe, Ni 3 Mn, Ni 3 Ti, NiMn and TiAl, using differential scanning calorimetry (DSC), and enthalpy increments of Ni 3 Ti, NiMn and TiAl by means of drop calorimetry. The experimentally derived heat capacities of the respective phases are described using an Extended-Einstein model (EE-model). The experimental data, the fitted heat capacities, and literature data are in good agreement. The study also assesses the reliability of the heat capacities using enthalpy increments measured between 680 and 890 K. Experimental heat capacity data for ordered binary intermetallic phases are crucial thermophysical properties for constructing multicomponent thermodynamic databases which support computational materials design.