Phase Equilibria Research Articles

Re-investigation of the Phase Equilibria and Thermodynamic Assessment of the Mg-Sm Binary System

Re-investigation of the Phase Equilibria and Thermodynamic Assessment of the Mg-Sm Binary System

Computer Simulation of Three-Phase Equilibria for Some Water/n-Alkane Binary Systems.

In this work, the vapor-liquid-liquid equilibrium (VLLE) of the water/n-pentane, water/n-hexane, water/n-octane, and water/n-decane binary systems is calculated by computer simulation using the NVT-Gibbs ensemble (in the version of three simulation boxes) combined with the configurational bias Monte Carlo method. The combination of both methods, the molecular potential models used, and the simulation details allowed us to calculate the triphasic equilibrium properties of the systems studied: the densities of the three phases in equilibrium, their compositions, and potential energies. In previous works, these simulations were not carried out at a temperature range nor water/n-alkanes systems simulated in this work, probably because they are highly nonideal systems; so, to the best of our knowledge, this is the first time that this phenomenon is studied in detail. The results from VLLE simulations of the water/n-pentane system for temperatures from 343.2 to 435 K, the water/n-hexane system for temperatures from 373.11 to 473.15 K, the water/n-octane system for temperatures from 310.9 to 500 K, and for the water/n-decane system for temperatures from 374.15 to 525 K are reported here. The temperature range was selected in concordance with the experimental data available for an adequate study of the VLLE simulation results. The subcritical densities (vapor and liquid rich in n-alkane phases) at various temperatures fit well with the scaling law and the law of rectilinear diameters, allowing the estimation of upper critical end point temperature and density of the VLLE. The simulation results show a good prediction with experimental data reports in the literature.

Experimental Investigation of Phase Equilibria in the Al–Mo–Hf Ternary System at 400 °C and 600 °C

This study investigates the phase equilibria of the Al-Mo-Hf ternary system at 400 °C and 600 °C using X-ray diffraction (XRD) and electron probe microanalysis (EPMA/WDS) techniques. Seven three-phase and five two-phase regions were identified at 400 °C, while eight three-phase and four two-phase regions were identified at 600 °C. Despite variations in the solid solubility ranges of certain compounds, the distribution of phase zones in the isothermal cross-section remained consistent at both temperatures. Using the experimental results and logical deductions, isothermal cross-sections were constructed for the Al-Mo-Hf ternary system at 600 °C and 400 °C.

Advances in CALPHAD Methodology for Modeling Hydrides: A Comprehensive Review

AbstractHydrides enable handling hydrogen at low pressure and near room temperature, offering higher volumetric densities than compressed or liquid hydrogen and enhancing safety. The CALPHAD method, rooted in the principles of thermodynamics, offers a systematic approach for predicting phase equilibria and thermodynamic properties in multicomponent materials. This comprehensive review paper aims to provide a detailed overview of the application of the CALPHAD method in the realm of metallic and complex hydrides. After an introduction to the fundamental thermodynamic aspects of hydrides, key elements of applying the CALPHAD method to model metal-hydrogen systems and complex hydrides are discussed. Subsequently, recent publications are reviewed, highlighting key findings and recent progresses in the field. Finally, the challenges that must be overcome to achieve further progress in this area are explored.

Thermodynamic Assessment of the P2O5-Na2O and P2O5-MgO Systems

Knowledge about the thermodynamic equilibria of the P2O5-Na2O and P2O5-MgO systems is very important for controlling the phosphorus content of steel materials in the process of steelmaking dephosphorization. The phase equilibrium and thermodynamic data of the P2O5-Na2O and P2O5-MgO systems were critically evaluated and re-assessed by the CALPHAD (CAlculation of PHAse Diagram) approach. The liquid phase was described by the ionic two-sublattice model for the first time with the formulas (Na+1)P(O−2, PO3−1, PO4−3, PO5/2)Q and (Mg+2)P(O−2, PO3−1, PO4−3, PO5/2)Q, respectively, and the selection of the species constituting the liquid phase was based on the structure of the phosphate melts. A new and improved self-consistent set of thermodynamic parameters for the P2O5-Na2O and P2O5-MgO systems was finally obtained, and the calculated phase diagram and thermodynamic properties exhibited excellent agreement with the experimental data. The difference in the phase composition of invariant reactions from the experimentally determined values reported in the literature is less than 0.9 mol.%. The present thermodynamic modeling contributes to constructing a multicomponent oxide thermodynamic database in the process of steelmaking dephosphorization.

UNIFAC PREDICTION OF VAPOR LIQUID EQUILIBRIA INVOLVING GAMMA-VALEROLACTONE DERIVATIVE SYSTEMS

Researchers have studied the hydrogenation of Gamma-Valerolactone (GVL) over Ru/C to produce 2-methyltetrahydrofuran (2-MTHF), a biomass-based platform chemical with potential as a biofuel and green solvent. Other byproducts of this reaction include 2-butanol (2-BuOH), 2-pentanol (2-PeOH), and 1,4-pentanediol (1,4-PDO). In this study, UNIFAC activity coefficient models were used to predict the vapor-liquid equilibrium of several systems included in the process to explain the phase behavior which is important in purification process. The accuracy of the UNIFAC model is tested by comparing the experimental boiling points for the binary system of 2-propanol + 1-butanol and the vapor-liquid equi-librium of the GVL + 2-MTHF system. From this comparison, the Root Mean Square Deviation (RMSD) values for the boiling point measurements are obtained to be 3.153%, and for the liquid and vapor phases in the vapor-liquid equilibrium measurements, the RMSD values are 1.934% and 0.298% respectively. These RMSD values indicate the level of accuracy of the UNIFAC model in representing the experimental data for both boiling point measurements and vapor-liquid equilibrium phase behavior. The prediction results of vapor-liquid equilibrium data for GVL derivative systems showed that the 2-BuOH + 2-MTHF system does form an azeotrope when the mol fraction of 2-BuOH is 0.0031 at 79.780C. The calculation was performed using ChemCAD commercial software for chemical process modeling and simulation

EXPERIMENTAL STUDY OF THE PHASE EQUILIBRIA IN THE SnTe–Sb2Te3–Te SYSTEM

Phase equilibria of the SnTe–Sb2Te3–Te portion of the Sn–Sb–Te ternary system have been experimentally investigated using differential thermal analysis (DTA), powder X-ray diffraction (XRD), and microstructural analysis methods. Based on the measured experimental results and literature information, isothermal sections at 500 K, liquidus surface projection, and several vertical sections of the phase diagram were plotted. The 500 K phase diagram of this system consists of 2 single-phase regions, 2 two-phase regions, and 3 three-phase regions. The liquidus surface projection is represented by the primary crystallization fields of 5 phases. The primary crystallization fields of all phases, the types, and coordinates of non- and monovariant equilibria were determined. Obtained experimental data can be valuable input for design for Sn–Sb–Te-based alloys

Transferable Anisotropic Mie Potential Force Field for Alkanediols.

The development of force fields for polyfunctional molecules, such as alkanediols, requires a careful account of different average intramolecular conformations for gas states compared to dense liquid states, where intra- and intermolecular hydrogen bonds compete. In the present work, the transferable anisotropic Mie (TAMie) potential is extended to 1,n-alkanediols. Using the convention that intramolecular nonbonded interactions up to and including the third neighbor are excluded, all force field parameters developed previously for 1-alcohols were transferred to 1,5-pentanediol and beyond, with good agreement with experimental phase equilibrium data. To obtain trans-gauche ratios of 1,2-ethanediol and 1,3-propanediol that are consistent with experimental results, the propensities for intra- and intermolecular hydrogen bonds had to be balanced. This was achieved by parameterizing the intramolecular dihedral energy functions governing the O-C-C-O and O-C-C-C angles while intramolecular charge-charge interactions were active. All partial charges belonging to a functional group are collected in a charge group and all interactions among two charge groups are evaluated even if they are separated by less than three bonds. With this approach, it is possible to apply the nonbonded parameters from 1-alcohols to alkanediols without further refinement. The agreement with experimental phase equilibrium and shear viscosity data is of similar quality as for the 1-alcohols and the trans-gauche ratio agrees with literature results from spectroscopic measurements and ab initio calculations.

Phase equilibria of the Na2O‐TiO2‐SiO2 system between 900 and 1600°C in air

AbstractThe Na2O‐SiO2‐TiO2 system is important for the glass, ceramic, and metallurgical industries. Its features provide information on the composition and melting temperature to be utilized during the production of glass and ceramic and during the processing of TiO2‐bearing material in the metallurgical industry. The liquidus temperatures between 900 and 1600°C in the ternary system at saturation of solid SiO2, TiO2, Na2Ti6O13, Na2SiTiO5, and Na2Ti3O7 were measured using the equilibration‐quenching energy‐dispersive X‐ray spectroscopy/Electron Probe Microanalyzer technique. A wide range of liquidus compositions were obtained with Na2O between 0 and 41.7 mol% in the SiO2‐ and TiO2‐rich regions. The present study provides liquidus data at 1500 and 1600°C for the first time. Liquidus temperatures at various double saturations were also obtained in the present investigation to determine univariant lines in the phase diagram. The present experimental data were compared with previous investigations and computed phase diagrams. The data obtained in the present investigation can be employed to optimize the thermodynamic properties and phase diagrams of the Na2O‐SiO2‐TiO2 system.

Solid–Liquid Phase Equilibria of the Aqueous Ternary System Containing Lithium Borate and Calcium Borate at T = (298.2, 323.2, and 348.2 K)

Solid–Liquid Phase Equilibria of the Aqueous Ternary System Containing Lithium Borate and Calcium Borate at <i>T</i> = (298.2, 323.2, and 348.2 K)

Experimental and thermodynamic assessment of the Cu–In system

Owing to the low melting temperature and excellent mechanical properties, In is considered a potential low-temperature solder. However, the interfacial reaction between In and Cu substrates is still unclear, specifically regarding the stability of CuIn2. Although CuIn2 was often observed at the Cu–In thin film after long-term aging below 100 °C, it is considered as a metastable phase and has not been added into the Cu–In phase diagram yet. In this study, the stability of CuIn2 and the peritectoid reaction Cu11In9 + In → CuIn2 were established using the Cu/In diffusion couple, Cu–In alloy phase equilibria, and decomposition investigation of CuIn2. The peritectoid temperature was determined to be in the range of 110–105 °C. Finally, thermodynamic assessment was conducted based on the experimental data and the revised Cu–In phase diagram.

CALPHAD-Based Modeling and Experimental Validation of Silicon Effect on the Solidification Behavior of Novel SiNb Cast Irons

AbstractThe low oxidation resistance of SiMo ductile cast irons used as exhaust manifold material at high temperatures necessitates the development of new generation ductile cast iron compositions. New alloy designs can be made using CALPHAD methodology, and solidification sequence, segregation and critical phase transformation temperatures can be determined, especially for the solidified bulk materials. Thus, in commercial practicality, castable compositions with a raised A1 temperature can be obtained. In this study, novel SiNb cast irons with varying silicon contents were developed as candidate materials for exhaust manifolds. Solidification sequence, microsegregation, phase transformations, equilibrium phases of hypereutectic compositions containing 4 to 7 wt pct Si were calculated by CALPHAD-based modeling. The bulk materials of the studied compositions were cast as Y blocks and metallurgical analyzes were carried out. Studies revealed that; (i) in the ferritic matrix of the cast irons, graphite, Nb-rich carbides and some pearlite existed, (ii) pearlite formation was due to the negative segregation of silicon and positive segregation of manganese during solidification, (iii) as silicon content increased the amount of silicon dissolved in ferrite phase increased in the solidified structure and as a result pearlite formation decreased at the cell boundaries, and amount of vermicular graphite increased, (iv) depending on the silicon content the critical A1 temperature varied between 860 °C to 1013 °C and these values were higher than that of SiMo cast iron. All these findings revealed that SiNb cast irons had phase stability at higher temperatures compared to SiMo cast iron.

Thermodynamic Modeling of the Au-Ge-X (X = In, Sb, Si, Zn) Ternary Systems.

In this study, the CALPHAD approach was employed to model the thermodynamics of the Au-Ge-X (X = In, Sb, Si, Zn) ternary systems, leveraging experimental phase equilibria data and previous assessments of related binary subsystems. The solution phases were modeled as substitutional solutions, and their excess Gibbs energies were expressed using the Redlich-Kister polynomial. Owing to the unavailability of experimental data, the solubility of the third elements in the Au-In, Au-Sb, and Au-Zn binary intermetallic compounds was excluded from consideration. Additionally, stable ternary intermetallic compounds were not reported in the literature and, thus, were not taken into account in the present thermodynamic calculations. Calculations of liquidus projections, isothermal sections, and vertical sections for these ternary systems have been performed, aligning with existing experimental findings. These thermodynamic parameters form a vital basis for creating a comprehensive thermodynamic database for Au-Ge-based alloys, which is essential for the design and development of new high-temperature Pb-free solders.

Dynamically selected steady states and criticality in non-reciprocal networks

We consider a simple neural network model, evolving via non-linear coupled stochastic differential equations, where neural couplings are random Gaussian variables with non-zero mean and arbitrary degree of reciprocity. Using a path-integral approach, we analyse the dynamics, averaged over the network ensemble, in the thermodynamic limit. Our results show that for any degree of reciprocity in the couplings, two types of criticality emerge, corresponding to ferromagnetic and spin-glass order, respectively. The critical lines separating the disordered from the ordered phases is consistent with spectral properties of the coupling matrix, as derived from random matrix theory. As the non-reciprocity (or asymmetry) in the couplings increases, both ordered phases diminish in size, ultimately resulting in the disappearance of the spin-glass phase when the couplings become anti-symmetric. We investigate non-fixed point steady-state solutions for uncorrelated interactions. For such solutions the time-lagged correlation function evolves according to a gradient-descent dynamics on a potential, which depends on the stationary variance. Our analysis shows that in the spin-glass region, the variance dynamically selected by the system leads the correlation function to evolve on the separatrix curve, limiting different realizable steady states, whereas in the ferromagnetic region, a fixed point solution is selected as the only realizable steady state. In the spin-glass region, stationary solutions are unstable against perturbations that break time-translation invariance, indicating chaotic behaviour in large single network instances. Numerical analysis of Lyapunov exponents confirms that chaotic behaviour emerges throughout the spin-glass region, for any value of the coupling correlations. While negative correlations increase the strength of chaos, positive ones reduce it, with chaos disappearing for reciprocal (i.e. symmetric) couplings, where marginal stability is attained. On the other hand, in finite size non-reciprocal networks, fixed points and limit cycles can arise in the spin-glass region, especially close to the critical line. Finally, we show that chaos is suppressed when the strength of external noise exceeds a certain threshold. Intriguing analogies between chaotic phases in non-equilibrium systems and spin-glass phases in equilibrium are put forward.

Thermodynamic assessment of the phase diagrams of calcite and CaO–CaCO3 system

The study of phase equilibria in the Ca–C–O system is complicated by the decomposition of one of the intermediate compounds, calcite. Experimental studies present an ambiguous interpretation of the results, which contain conflicting information about the phase diagrams of calcite and the CaO–CaCO3 system at pressures up to 100 MPa. Thermodynamic modelling has been used in this study for the determination of phase equilibria in these systems. Using reliable experimental phase diagram data, the thermodynamic properties of calcite and CaCO3(liq) were corrected to take into account the pressure influence. This resulted in an accurate reproduction of the experimental data on calcite phase equilibria and made it possible to construct a model of the CaO–CaCO3 system phase diagram taking into account the calcite decomposition. It will allow to further modelling of more complex processes involving calcite in the pressures range up to 30 MPa and temperatures up to 1800 K.

Permeability anisotropy analysis of two-phase flow during hydrate dissociation process

Natural gas hydrate (NGH) is a versatile and energy source. But in the actual extraction process, NGH in the reservoir will be out of phase equilibrium conditions and dissociate. This will induce alterations in permeability characteristics of reservoir and will exert a significant influence on the assessment of hydrate reservoir capacity. In the research, an innovative CT triaxial system was used to obtain the micro-structure of sediment specimen during hydrate dissociation. The anisotropy of absolute permeability (k), capillary pressure (Pc) and relative permeability (kr) were also analyzed using the pore network model (PNM). As demonstrated by the results, k increases gradually in all three directions during the dissociation. Pc gradually decreases. The degree of anisotropy of both Pc and gas-water relative permeability (krg and krw) gradually decreases. The impact of hydrate dissociation on the kr anisotropy during primary gas flooding surpasses that observed during secondary water flooding. As hydrate saturation decreases, the krw increases and the krg decreases in the horizontal directions. The krw does not change significantly and the krg increases in the vertical direction. Along the length of the sample, the distribution of hydrate and pore space exhibits heterogeneity across the sections. This inhomogeneous distribution will lead to anisotropy in permeability.

Revealing microstructural degradation mechanism induced by interdiffusion between Amdry365 coating and IN792 superalloy

Metallic coatings are widely employed to improve the oxidation resistance of superalloys. However, the interdiffusion between the metallic coatings and the superalloys leads to microstructural degradation in both. Some of the underlying degradation mechanisms are still elusive, e.g., the γ′ (Ni3Al) phase depletion in superalloys, where a large amount of γ′ precipitates are dissolved in the γ matrix even though the incoming Al from coatings indeed increases the Al content. Here, we investigated the interdiffusion behavior between the Amdry365 coating and the IN792 superalloy at 1100 °C, using multiple microscopic techniques and thermodynamics calculations. Our results showed an excellent agreement between experiments and thermodynamics simulations, indicating the dominant role of Al on the initial diffusion-induced phase transitions. We proposed the Al-Cr interference effect to account for the pile-up behavior of Cr and the reduced Al content near the coating/superalloy interface. The local phase equilibrium calculations revealed that the γ′ depletion in the superalloy is primarily attributed to the loss of γ′-forming elements, such as Ta and Ti. Our findings opened up an avenue for studies on the superalloy/coating interdiffusion, contributing to reducing this damaging impact

Phase equilibrium data prediction and process optimization in butadiene extraction process

In response to the lack of reliable physical parameters in the process simulation of the butadiene extraction, a large amount of phase equilibrium data was collected in the context of the actual process of butadiene production by acetonitrile. The accuracy of five prediction methods, UNIFAC, UNIFAC-LL, UNIFAC-LBY, UNIFAC-DMD, and COSMO-RS, applied to the butadiene extraction process was verified using partial phase equilibrium data. The results showed that the UNIFAC-DMD method had the highest accuracy in predicting phase equilibrium data for the missing system. COSMO-RS predicted multiple systems showed good accuracy. And a large number of missing phase equilibrium data were estimated using the UNIFAC-DMD method and COSMO-RS method. The predicted phase equilibrium data were checked for consistency. The NRTL-RK and UNIQUAC thermodynamic models were used to correlate the phase equilibrium data. Industrial device simulations were used to verify the accuracy of the thermodynamic model applied to the butadiene extraction process. The simulation results showed that the average deviations of the simulated results using the correlated thermodynamic model from the actual values were less than 2% compared to that using the commercial simulation software Aspen Plus and its database. The average deviation was much smaller than that of the simulations using the Aspen Plus database (>10%), indicating that the obtained phase equilibrium data are highly accurate and reliable. The best phase equilibrium data and thermodynamic model parameters for butadiene extraction are provided. This improves the accuracy and reliability of the design, optimization and control of the process, and provides a basis and guarantee for developing a more environmentally friendly and economical butadiene extraction process.

Mapping the application research on machine learning in the field of ionic liquids: A bibliometric analysis

The aim was to gain a deep understanding of the research status and application of machine learning in the field of ionic liquids, and to identify the research hotspots and frontiers. Co-occurrence analysis, co-citation analysis, key literature citation temporal analysis and emerging word analysis were used. The results show that the knowledge base of applying machine learning in the field of ionic liquids can be divided into three parts: fundamental properties and application research, thermodynamics and phase equilibrium research, and the combination of machine learning with computational chemistry methods. The research hotspots mainly include the prediction and optimization of properties, the prediction of phase behavior, and research on machine learning algorithms. The current research frontiers in applying machine learning in the field of ionic liquids include the prediction of ionic liquid performance, the structure-property relationships of ionic liquids, and the optimization and design of ionic liquid processes.

Tectono-metamorphic interaction of upper mantle peridotites and lower crustal units during continental rifting in the western Betic Cordillera

Recent geological mapping conducted in the Ronda Peridotites (Betic Cordillera, S Spain) has revealed a systematic field correlation between lower crustal metamorphic units and different tectono-metamorphic domains of the ultramafic massif. Mylonitic and highly tectonized Spl ± Grt peridotites (i.e., Grt-Spl mylonite and Spl tectonite domains), which are considered to be derived from a thick continental lithosphere, are in contact with garnet-bearing gneisses (i.e., kinzigites) of the Jubrique unit along a narrow but continuous mylonitic shear zone. Phase equilibrium calculations indicate that the metamorphic rocks of the Jubrique unit are consistent with an initial continental setting characterized by normal crustal thicknesses, which underwent two melting events. The first melting occurred at 0.9–1.0 GPa / 770–800 °C and resulted in 13 %melt, while the second one took place at shallower crustal conditions (0.4–0.5 GPa and 710–765 °C) and led to more restricted melt production (2–3 %melt). In contrast, the Spl ± Pl peridotites (Pl-tectonite domain), which are stable only at shallowest mantle levels within a highly extended continental lithosphere, are consistently found exposed in contact with heterogeneous granites and migmatites of the Guadaiza unit. According to new thermodynamic modeling, the Guadaiza metamorphic rocks record a single melting event characterized by a theoretical melt production of 6 to 11 % at the base of a very thin continental crust (ca. 0.3 GPa and 675–710 °C). This process was likely facilitated by influx of external water, necessary to generate high melt fractions observed in the diatexites. The systematic correlation observed between crustal metamorphic units, consistently overlaying the mantle rocks, and specific ultramafic domains of the Ronda massif, suggests that their juxtaposition primarily resulted from the severe extension of the continental lithosphere.U-Pb radiometric dating of zircons from gneisses, migmatites, and heterogeneous granites in the middle crustal rocks of the Guadaiza unit indicates that extensional processes, crustal anatexis, and melt stagnation occurred at around 280 Ma. Comparison of these new radiometric ages with previous results from the Jubrique unit suggests that a Permian high-temperature / low- to medium-pressure event uniformly affected the crustal units over the Ronda Peridotites. This event coincided with the formation of characteristic ultramafic mineral assemblages within the Ronda massif and provides evidence for the interaction between upper mantle rocks and lower- to mid-crustal metamorphic rocks during this period.