Phase Equilibria Research Articles

First-principles thermodynamic investigation on the α phases in TiO and TiNb binary system.

O and Nb are two representative alloying elements of Ti to form high-temperature and corrosion resistance α Ti alloys. The investigation on the thermodynamic characteristics of α Ti-O and Ti-Nb has attracted much attention in recent years. However, in this regard, a satisfied experimental technique or modeling scheme is still yet to be developed due to the appearance of a variety of oxides in Ti-O and the mechanical instability present in Ti-Nb. Herein, we combined first-principles calculations with the cluster expansion method to investigate the ground-state characteristics for α Ti-O and α Ti-Nb systems. The atomic bonding interactions in these two systems were first revealed based on the calculated electronic structures. Afterward, the Debye-Grüneisen model and Monte Carlo simulations were employed together to investigate the thermodynamic properties of α phases in these two systems, and the effect of vibrational entropy on the order-disorder transition temperatures of the phases in α Ti-O system was first examined. A good agreement with experimentally reported phase boundaries is obtained in the Ti-Nb system by handling the mechanical instabilities introduced by the highly distorted structures. In addition, the cluster expansion coefficients for the Ti-O and Ti-Nb system offer a good starting point to investigate the phase equilibrium in Ti-Nb-O ternary alloy. We also believe the insights provided here would be helpful for those who would like to seek an efficient scheme they are confident with to investigate the phase thermodynamic properties of other hcp Ti-based alloys.

Extracellular volume fraction derived from dual-energy CT: a potential predictor for acute pancreatitis after pancreatoduodenectomy.

To investigate the value of extracellular volume (ECV) fraction and fat fraction (FF) derived from dual- energy CT (DECT) for predicting postpancreatectomy acute pancreatitis (PPAP) after pancreatoduodenectomy (PD). This retrospective study included patients who underwent DECT and PD between April 2022 and September 2022. PPAP was determined according to the International Study Group for Pancreatic Surgery (ISGPS) definition. Iodine concentration (IC) and FF of the pancreatic parenchyma were measured on preoperative DECT. The ECV fraction was calculated from iodine map images of the equilibrium phase. The independent predictors for PPAP were assessed by univariate and multivariable logistic regression analysisand receiver operating characteristic (ROC) curve analysis. Sixty-nine patients were retrospectively enrolled (median age, 60 years; interquartile range, 55-70 years; 47 men). Of these, nine patients (13.0%) developed PPAP. These patients had lower portal venous phase IC, equilibrium phase IC, FF, and ECV fraction, and higher pancreatic parenchymal-to-portal venous phase IC ratio and pancreatic parenchymal-to-equilibrium phase IC ratio, compared with patients without PPAP. After multivariable analysis, ECV fraction was independently associated with PPAP (odd ratio [OR], 0.87; 95% confidence interval [CI]: 0.79, 0.96; p < 0.001), with an area under the curve (AUC) of 0.839 (sensitivity 100.0%, specificity 58.3%). A lower ECV fraction is independently associated with the occurrence of PPAP after PD. ECV fraction may serve as a potential predictor for PPAP after PD. DECT-derived ECV fraction of pancreatic parenchyma is a promising biomarker for surgeons to preoperatively identify patients with higher risk for postpancreatectomy acute pancreatitis after PD and offer selective perioperative management. PPAP is a complication of pancreatic surgery, early identification of higher-risk patients allows for risk mitigation. Lower DECT-derived ECV fraction was independently associated with the occurrence of PPAP after PD. DECT aids in preoperative PAPP risk stratification, allowing for appropriate treatment to minimize complications.

Coeval formation and exhumation of metamorphic sole and ophiolite in the Saga ophiolitic mélange: Insights into subduction initiation of the Neo‐Tethys

AbstractSubduction initiation is recorded by upper plate magmatism and lower plate metamorphism, that is, supra‐subduction zone (SSZ) ophiolite–metamorphic sole pair. Here, we report geochemical and geochronological data as well as P–T calculations of amphibolites (metamorphic sole) and hornblende gabbros (SSZ ophiolite) from the Saga ophiolitic mélange in Tibetan Plateau. Amphibolites show trace element contents compatible with normal‐mid‐ocean ridge basalt (N‐MORB), indicating that the protolith of amphibolite formed in a MOR setting. Instead, hornblende gabbros show significant high field strength elements (HFSEs) negative anomalies, enriched large ion lithophile elements (LILEs) and high zircon εHf(t) values, suggesting they formed by fluid‐induced partial melting of a depleted mantle. Thermobarometry and phase equilibrium modelling suggest two stages of metamorphism for garnet–clinopyroxene amphibolites: (I) a peak metamorphic stage (~1.9 GPa and 1000°C) and (II) a retrograde metamorphic stage (1.1–1.6 GPa and 800–1000°C). Zircon U–Pb ages of amphibolite and hornblende gabbro are 128.8 ± 5.1 Ma and 128.1 ± 1.5 Ma, respectively, suggesting subduction initiation within the eastern Neo‐Tethys occurred no later than 128 Ma and SSZ ophiolite formed at ~128 Ma. Apatite U–Pb ages of amphibolite and hornblende gabbro are 121.8 ± 2.1 Ma and 117.5 ± 4.5 Ma, respectively. Titanite U–Pb age of amphibolite is 122.2 ± 1.5 Ma. Overall, our data suggest that the metamorphic sole and SSZ ophiolite were exhumed since 128–118 Ma, and finally exhumed into the ophiolitic mélange.

Benedict–Webb–Rubin–Starling Equation of State + Hydrate Thermodynamic Theories: An Enhanced Prediction Method for CO2 Solubility and CO2 Hydrate Phase Equilibrium in Pure Water/NaCl Aqueous Solution System

Benedict–Webb–Rubin–Starling Equation of State + Hydrate Thermodynamic Theories: An Enhanced Prediction Method for CO2 Solubility and CO2 Hydrate Phase Equilibrium in Pure Water/NaCl Aqueous Solution System

Liquid–Liquid Equilibrium Behavior of Ternary Systems Comprising Biodiesel + Glycerol and Triglyceride + Methanol: Experimental Data and Modeling

Having a comprehensive knowledge of phase equilibrium is advantageous for industrial simulation and design of chemical processes. For further acquisition of primary data to facilitate the separation and purification of waste oil biodiesel systems, a liquid–liquid equilibrium (LLE) tank is deployed for the ternary system of waste oil biodiesel + methanol + glycerin, thereby enhancing the precision and efficiency of the process. The phase equilibrium system was constructed under the influence of atmospheric pressure at precise temperatures of 303.15 K, 313.15 K, and 323.15 K. The equilibrium components of each substance were analyzed by employing high-temperature gas chromatography, a sophisticated analytical method that enables the identification and quantification of individual components of a sample. Moreover, the ternary liquid–liquid equilibrium data were correlated by implementing the NRTL and UNIQUAC activity coefficient models. Subsequently, the binary interaction parameters of the ternary system were derived by conducting regression analysis. The experimental data demonstrated that the presence of lower methanol content in the system resulted in nearly immiscible biodiesel and glycerol phases, which ultimately facilitated the separation of biodiesel and glycerol. Conversely, with the increase in methanol content, the mutual solubility of biodiesel and glycerol was observed to increase gradually. The results showed that the calculated values of the NRTL and UNIQUAC models aligned well with the experimental values. The root-mean-square deviations of the NRTL and UNIQUAC models at 313.15 K were 2.76% and 3.56%, respectively.

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.

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.

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.

Predictability of the radiological response to Yttrium-90 transarterial radioembolization by dynamic magnetic resonance imaging-based radiomics analysis in patients with intrahepatic cholangiocarcinoma

The study aims to investigate the predictability of the radiological response in intrahepatic cholangiocarcinoma (iCC) patients undergoing Yttrium-90 transarterial radioembolization (TARE) with a combined model built on dynamic magnetic resonance imaging (MRI)-based radiomics and clinical features. Thirty-six naive iCC patients who underwent TARE were included in this study. The tumor segmentation was performed on the axial T2-weighted (T2W) without fat suppression, axial T2W with fat suppression, and axial T1-weighted (T1W) contrast-enhanced (CE) sequence in equilibrium phase (Eq). At the sixth month MRI follow-up, all patients were divided into responders and non-responders according to the modified Response Evaluation Criteria in Solid Tumors. Subsequently, a radiomics score (rad-score) and a combined model of the rad-score and clinical features for each sequence were generated and compared between the groups. Thirteen (36.1%) patients were considered responders, and the remaining 23 (63.9%) were non-responders. Responders exhibited significantly lower rad-scores than non-responders (P < 0.050 for all sequences). The radiomics models showed good discriminatory ability with an area under the curve (AUC) of 0.696 [95% confidence interval (CI), 0.522–0.870] for the axial T1W-CE-Eq, AUC of 0.839 (95% CI, 0.709–0.970) for the axial T2W with fat suppression, and AUC of 0.836 (95% CI, 0.678–0.995) for the axial T2W without fat suppression. Radiomics models created by pre-treatment MRIs can predict the radiological response to Yttrium- 90 TARE in iCC patients with high accuracy. Combining radiomics with clinical features could increase the power of the test. Large-scale studies of multi-parametric MRIs with internal and external validations are needed to determine the clinical value of radiomics in iCC patients.