Phase Equilibria Research Articles

Effect of high pressure synthesis conditions on the formation of high entropy oxides

High entropy materials are often entropy stabilized, meaning that the configurational entropy from multiple elements sharing a single lattice site stabilizes the structure. In this work, we study how high-pressure synthesis conditions can stabilize or destabilize a high entropy oxide (HEO). We study the high-pressure and high-temperature phase equilibria of two well-known families of HEOs: the rock salt structured compound (Mg,Co,Ni,Cu,Zn)O, including some cation substitutions, and the spinel structured compound (Cr,Mn,Fe,Co,Ni)3O4. Syntheses were performed at various temperatures, pressures, and oxygen activity levels, resulting in dramatically different synthesis outcomes. In particular, in the rock salt HEO, we observe the competing tenorite and wurtzite phases and the possible formation of a layered rock salt phase while the spinel HEO is highly susceptible to partial decomposition into a mixture of rock salt and corundum phases. At the highest tested pressures, 15 GPa, we discover the transformation of the spinel HEO into a metastable modified ludwigite-type structure with the nominal formula (Cr,Mn,Fe,Co,Ni)4O5. The relationship between the synthesis conditions and the final reaction product is not straightforward. Nonetheless, we conclude that high-pressure conditions provide an important opportunity to synthesize high entropy phases that cannot be formed any other way.

High-pressure mafic granulite and supracrustal rocks in the southern Hengshan area, North China Craton: Metamorphic P-T-t evolution and geotectonic significance

Amphibolite- to granulite-facies rocks are widely distributed in the Hengshan Complex, middle Trans-North China Orogen, and the high-pressure (HP) mafic granulite has been recently identified in the southern Hengshan area. The HP mafic granulite and amphibolite occur as rootless tectonic boudins/lenses within the TTG (tonalite–trondhjemite–granodiorite) gneiss/metapelite, indicative of typical “block-in-matrix” texture of metamorphic-tectonic mélange. Three to four generations of metamorphic mineral assemblages that correspond to the prograde (M1), peak (M2), and retrograde (M3-M4) stages, are recognized in these rocks. Conventional geothermobarometry and phase equilibrium modeling yield peak P–T conditions of 10.8–13.8 kbar/754–799 °C for the HP mafic granulite and 7.3–9.0 kbar/690–725 °C for the supracrustal rocks, respectively. A clockwise P–T path with near-isothermal decompression (ITD) and subsequent near-isobaric cooling (IBC) segments is reconstructed for the HP mafic granulite, indicating a dynamic subduction–collision–exhumation process that unfolded during an orogenic event. Secondary ion mass spectrometry (SIMS) U-Pb dating of zircon yields metamorphic ages of ca. 1.91–1.83 Ga, representing the long-lived tectono-metamorphic event caused by collision between the Eastern and Western Blocks along the Trans-North China Orogen. It is hypothesized that the tectono-metamorphic mélange in the area originated from the tectonically juxtaposition of metamorphic rocks that had diverse protoliths, different peak P–T conditions and discrepant metamorphic ages. This complexity may be a hallmark of Paleoproterozoic orogens, drawing intriguing parallels with the intricate characteristics observed in Phanerozoic orogenic belts.

IMPROVING THE ACCURACY OF CALCULATING THE SUPER-COMPRESSIBILITY COEFFICIENT OF HELIUM BASED ON STATE EQUATIONS

To date, the Russian gas industry is developing a large number of deposits with a high helium content in the composition of the extracted gas, such as Chayandinskoye, Kovyktinskoye, Yaraktinskoye oil and gas condensate fields. Helium has never before been the object of detailed study during gathering and treatment, but today helium is an important resource that is used in many fields: military industry, medicine, shipbuilding, laser technology, space technology. The high demand for the component of the extracted gas has created requirements for the creation of a technology for separating it from gas. In addition, helium is a «cold» gas due to the weak interaction of its molecules, so it is difficult to model phase equilibrium at extremely low temperatures. As a result, improving the simulation of condensation of a helium mixture is undoubtedly an urgent task of the industry today. The purpose of the study is to increase the accuracy of calculating the thermodynamic properties of helium based on one of the modifications of the Peng-Robinson equation of state for thermobaric conditions corresponding to helium liquefaction processes.As the methods used in this work, a software module for calculating the selection of the Peneloux correction in the Java programming language was implemented. The results are tested on known experimental data, as well as a specialized software product for calculating the thermodynamic properties of fluids.The features of calculating the superconductivity coefficient of helium based on the cubic equation of state are presented. The optimal range of the Peneloux correction for the Peng-Robinson equation of state has been found, as well as an approximation formula that allows us to find the correction in the low temperature region. The results obtained will allow us to calculate the thermodynamic properties of helium with high accuracy. This will allow us to predict the volume of production and condensation of helium from natural gas, which is certainly an important task for the development of the country's economy.

Phase equilibria and crystallographic structure of clathrate hydrate formed with carbon dioxide and cyclohexanone

This paper reports the phase equilibrium and crystallographic data of the hydrate formed in the CO2 + cyclohexanone + water system. We measured the phase equilibrium condition and conducted the powder X-ray diffraction measurements. The formation of the structure II hydrate in the system of CO2 + cyclohexanone + water was observed at the temperature from 270.0 K to 275.6 K, under the pressure from 0.62 MPa to 1.70 MPa.At 270.0 K – 275.6 K and 0.62 MPa – 1.70 MPa, the structure II hydrate formed, and the phase equilibrium condition alleviated in the system of CO2 + cyclohexanone + water, while the hydrate formed at 276.5 K - 280.7 K and 2.02 MPa – 3.33 MPa, displayed structure I and cyclohexanone acted as an inhibitor. Equilibrium conditions were measured using the isochoric method, revealing different p-T slopes at high and low temperatures. The high-temperature slope closely resembled that of structure I CO2 hydrate reported previously. We continuously monitored temperature and pressure during the structural phase transition, resulting in a slope change. To directly determine the hydrate structure, PXRD measurements were conducted on two samples: one from the high-temperature side and the other from the low-temperature side. The sample from the high-temperature side exhibited structure I with a lattice constant of 11.8749 (9) Å at 153 K, while the low-temperature sample displayed structure II with a lattice constant of 17.443(1) Å at 153 K.

Rigorous modelling and optimization of hybrid absorption-adsorption separation process of H2/CH4 using ZIF-8/glycol/water slurry

Efficient separation of H2/CH4 is vitally important for the hydrogen energy system. To guide the scale-up of the separation technique using the ZIF slurry, the rigorous modelling and optimization of the separation process of H2/CH4 using ZIF-8/glycol/water slurry is conducted. A rigorous phase equilibrium model is proposed to describe the hybrid absorption-adsorption with liquid film permeation. Next, the MESH (Material balance, phase Equilibrium, Summation, Heat balance) equations for mass transfer units, modelling and multi-objective optimization of the full separation process are established. The effect of operation pressure and gas-slurry volume ratio on product purity, recovery ratio and unit energy consumption are investigated. Results show that the calculated solubilities of pure/binary components are in good agreement with the experiment data. The feed gas (H2/CH4: 70: 30) can be enriched to be (H2/CH4: 99: 1) with the H2 recovery ratio of 99.5 % and the total unit energy consumption reaches 0.2492 kW·h/Nm3 (feed gas).

Exploring equilibrium conditions in liquid metal dealloying of powders by in situ synchrotron X-ray diffraction

Liquid metal dealloying is a recently developed method to elaborate micro and nano-porous materials. It consists in the selective dissolution of an alloying element from a precursor alloy by immersing it in a liquid metal bath. In this paper, we monitor the dealloying reaction of Invar (Fe65Ni35) powders in liquid Mg using in situ synchrotron X-ray diffraction. Rietveld refinement of the diffraction spectra enables quantifying the evolution of different crystalline phases throughout the process, thereby gaining new insights into the kinetics, phase equilibria, and the role of intermetallics on the reaction. These results are systematically compared to post mortem observations of dealloyed samples, showing a good agreement between both techniques. In particular, we show that adjusting the thermodynamic conditions of the reaction (temperature, FeNi/Mg ratio) enables to tailor the microstructure of the dealloyed powders, by modifying the dealloyed fraction to achieve core–shell structures, and altering the composition of ligaments.

A method for calculating two-phase equilibrium: Constrained gray prediction evolutionary algorithm with a surrogate model based on quadratic interpolation

Traditional methods, including direct solution methods based on Newton's method and indirect solution methods based on thermodynamic principles, are the mainstream methods used to solve the volume-temperature flash calculation (called NVT-flash), even though they suffer from drawbacks such as sensitivity to initial value and complexity of derivative calculations. A constrained backtracking search algorithm (CBSA), proposed in 2024, was the first and only metaheuristic algorithm to successfully tackle the NVT-flash problem, which overcomes shortcomings of traditional methods. Considering the advantages of metaheuristic algorithms, a constrained gray prediction evolutionary algorithm with a surrogate model based on quadratic interpolation (CGPE-QI) is proposed in this paper to deal with the NVT-flash problem. CGPE-QI considers total Helmholtz free energy as the objective function, moles vector, and volume of a single phase as variables. Constraints to solve the NVT-flash problem are addressed by using a direct search method and an exterior point method. Numerical experiments on two-phase equilibrium of pure substance and mixtures are carried out employing CGPE-QI. Experimental results are the same as those obtained by traditional methods, which confirms that CGPE-QI can effectively tackle the NVT-flash problem and possesses energy decay property. In particular, the results demonstrate that CGPE-QI is more competitive than CBSA in terms of convergence speed, stability, and calculation cost. CGPE-QI proposed in this paper is the second metaheuristic algorithm to successfully solve the NVT-flash problem, illustrating that metaheuristic algorithms have great potential in solving phase equilibrium calculation problems.

Thermodynamic modeling and process evaluation of advanced ionic liquid-based solvents for CO2/CH4 separation

Carbon capture technology is a prospective strategy to address the increasing concentration of CO2 in the atmosphere, with the core challenge of developing new cost-effective processes. In this work, the energy analysis and economic evaluation were conducted based on rigorous thermodynamic models and the process simulation results of a novel chemical absorption-dominated hybrid solvent which consists of functional ionic liquid of choline triazole ([Cho][Triz]) and sulfolane (TMS) to separate CO2 from shale gas. The solubility of CO2 and CH4 in different solvents were calculated using phase equilibrium model including the NRTL activity coefficient equation, the RK equation of state, chemical reaction equilibrium equations, and the mass balance equation. The physical properties of the ionic liquid-based solvent systems were calculated with empirical equations which was corrected using experimental data. The results obtained from the thermodynamic models exhibited good agreement with experimental data. Subsequently, the established models and the parameters obtained were embedded into Aspen Plus for further analysis. The total CO2 capture energy consumption of 1.65 GJ·t−1 CO2 and the cost of 48.07 $·t−1 CO2 were achieved using the new solvent when the mass fraction of IL was 60 wt%. Compared with the commercial 30 wt% MDEA carbon capture process, it reduced the energy consumption and economic cost of 64.16 % and 45.59 %, respectively.

Playing lato–lato is difficult and this is why

Lato–lato, a pendulum-based toy gaining popularity in Indonesian playgrounds, has sparked interest with competitions centered around maintaining its oscillatory motion. While some find it easy to play, the challenge lies in sustaining the oscillation, particularly in maintaining both ‘up and down collisions.’ Through a Newtonian dynamics numerical analysis using Python (code by ChatGPT), this study identifies two equilibrium phases—phase 1, characterized by normal pendulum motion, and phase 2, the double collision mode—using the driven oscillation model. In addition, further analysis and discussion are done using the obtained numeric data. The difficulty in remaining in phase 2 highlights the intricate hand-eye coordination required, shedding light on the toy’s appeal and the skill it demands.

Tectono-thermal Evolution of the Proterozoic Mahakoshal Belt along the Northern Margin of Central Indian Tectonic Zone: Constraints from Geochemistry, Phase Equilibria Modelling and in-situ Monazite Dating from a Metapelite Sequence around Jabalpur

ABSTRACT In this contribution, geochemical signatures and petrological evolution of a folded sequence of mica schist from the Jabalpur area of the Mahakoshal Belt in the northern Central Indian Tectonic Zone (CITZ) are described. Multiple tectonic discrimination diagrams incorporating both major and trace element concentrations have constrained back-arc settings for deposition of the sedimentary units. S1 foliation formation marks the beginning of the M1 metamorphic stage. In contrast, the later M2 metamorphic event resulted in garnet and andalusite formation during heating at 2-3 kbar, followed by staurolite-sillimanite, garnet-staurolite assemblages at peak P-T conditions of 5.4 kbar, 550-600°C. Textural evidence suggests that M2 is pre-syn tectonic to D2 deformation, resulting in formation of the NE-SW trending S2 axial planar foliation. From the isopleth thermobarometry, a clockwise P-T path with near-isothermal decompression has been determined for M2. Similar results have been obtained from conventional thermo-barometry performed on multiple samples. Monazite dating (EPMA) of one of the samples suggests 1.9 Ga, age for D1-M1 event. M2 is correlated with the younger age population of monazites yielding 1.5 Ga. A clockwise P-T path constrained for M2 suggests collisional tectonics along the northern margin of the CITZ, as recorded from its southern margin.

Exploring C3F8 as a gaseous structure H hydrate former: Implications for hydrate-based greenhouse gas separation and recovery

Octafluoropropane (C3F8) is a fluorinated gas (F-gas) known for its high global warming potential. In this study, the role of C3F8 as a novel gaseous structure H (sH) hydrate former was investigated. By employing a comprehensive methodology involving thermodynamic, crystallographic, and spectroscopic analyses, the successful encapsulation of C3F8 into the large cages of sH hydrates was unveiled for the first time. The incorporation of C3F8 into sH hydrates was inferred from a shift in the thermodynamic hydrate phase equilibria, and unequivocal evidence of successful C3F8 encapsulation was obtained using powder X-ray diffraction, 13C nuclear magnetic resonance, and Raman spectroscopy. The findings showed that C3F8 overcame the conventional limitations associated with sH hydrate formers, which are predominantly liquid and solid substances, thereby significantly expanding the scope of potential gaseous sH hydrate formers. This advancement not only enhances the fundamental understanding of gas hydrate formers but also opens up new avenues for hydrate-based technologies, particularly in the separation and recovery of large-size F-gases, which have substantial environmental implications.

Atomistic insights into the reentrant phase-transitions in polyuracil and polylysine mixtures.

The phase separation of protein and RNA mixtures underpins the assembly and regulation of numerous membraneless organelles in cells. The ubiquity of protein-RNA condensates in cellular regulatory processes is in part due to their sensitivity to RNA concentration, which affects their physical properties and stability. Recent experiments with poly-cationic peptide-RNA mixtures have revealed closed-loop phase diagrams featuring lower and upper critical solution temperatures. These diagrams indicate reentrant phase transitions shaped by biomolecular interactions and entropic forces such as solvent and ion reorganization. We employed atomistic simulations to study mixtures with various RNA-polylysine stoichiometries and temperatures to elucidate the microscopic driving forces behind reentrant phase transitions in protein-RNA mixtures. Our findings reveal an intricate interplay between hydration, ion condensation, and specific RNA-polylysine hydrogen bonding, resulting in distinct stoichiometry-dependent phase equilibria governing stabilities and structures of the condensate phase. Our simulations show that reentrant transitions are accompanied by desolvation around the phosphate groups of RNA, with increased contacts between phosphate and lysine side chains. In RNA-rich systems at lower temperatures, RNA molecules can form an extensive pi-stacking and hydrogen bond network, leading to percolation. In protein-rich systems, no such percolation-induced transitions are observed. Furthermore, we assessed the performance of three prominent water force fields-Optimal Point Charge (OPC), TIP4P-2005, and TIP4P-D-in capturing reentrant phase transitions. OPC provided a superior balance of interactions, enabling effective capture of reentrant transitions and accurate characterization of changes in solvent reorganization. This study offers atomistic insights into the nature of reentrant phase transitions using simple model peptide and nucleotide mixtures. We believe that our results are broadly applicable to larger classes of peptide-RNA mixtures exhibiting reentrant phase transitions.

Phase equilibria of SiO2–Al2O3–Fe3O4-5 wt.% CaO system at 1400 °C in air relevant to the production of continuous basalt fibers: Emphasis on spinel solid solution phase

A long-term foundational study aimed at developing a thermodynamic database for continuous basalt fiber systems is in progress. In this work, the equilibrium phase relations of the SiO2–Al2O3–Fe3O4-5 wt.% CaO system at 1400 °C in air atmosphere were determined experimentally using the equilibrium-quenching technique. Subsequent analyses were conducted using Electron Probe Micro-Analysis (EPMA), X-ray Diffraction (XRD), and Scanning Electron Microscopy (SEM) to validate the experimental results and further investigate the microstructural characteristics. The results revealed a single liquid region and three distinct two-phase regions as Liquid-Cristobalite, Liquid-Mullite solid solution, and Liquid-Spinel solid solution. Additionally, two three-phase regions were identified as liquid-cristobalite-mullite solid solution, and liquid-mullite solid solution-spinel solid solution. This work contributes to a deeper understanding of the phase behavior during the melting of basalt ore systems, which is crucial for optimizing their production and enhancing their applications.

Effects of High Al Content on the Phase Constituents and Thermal Properties in NiCoCrAlY Alloys.

MCrAlY (M = Ni and/or Co) metallic coatings are essential for the protection of hot-end components against thermal and corrosion damage. Increasing the Al content is considered a feasible solution to improve the high-temperature performance of MCrAlY coatings. In this paper, the effects of high Al contents (12-20 wt.%) on the phase constituents and cast microstructures in MCrAlY alloys were studied by high-energy X-ray diffraction and electron microscopy techniques combined with phase equilibria calculations. High Al content improved the stability of β, σ, and α phases. Meanwhile, an evolution of the cast microstructure morphology from a dendrite structure to an equiaxed grain structure was observed. The thermal properties were analyzed, which were closely related to the phase constituents and solid-to-solid phase transitions at evaluated temperatures. This work is instructive for developing high-Al-content MCrAlY coatings for next-generation thermal barrier applications.

Development of a customized computer Program for the construction of ternary diagram for liquid-liquid extraction process

The Liquid-Liquid Extraction (LLE) is a liquid-liquid phase mass transfer process in which solute chemicals are transferred between two immiscible or partially miscible liquids due to difference in solubility of the solutes in the two liquids. The phase equilibrium relationships are generally inconvenient to handle algebraically, therefore, LLE computational analyses are usually made graphically. Manual construction of ternary diagram becomes cumbersome, tedious and time consuming when used for a process that requires large number of stages. Therefore, the aim of this work was to develop a customized computer package for the ternary diagram. The customized computer package for the ternary diagram construction was achieved with the use of fuzzy inference system toolbox and primitive line function in MATLAB. The computer program was test-run using data from literature to determine theoretical number of stages for a given LLE separation process. The result compared well with the existing literature result.

Phase equilibria of Fe3O4–Cr2O3–CaO system: experimental measurements and thermodynamic calculations

Phase equilibria of Fe3O4–Cr2O3–CaO system: experimental measurements and thermodynamic calculations

Testing the TTG–Metabasite Connection in the Southern Superior Province: an Integrated Geochemical, Isotopic, and Petrogenetic Modelling Approach

Abstract Archean cratons are dominated by tonalite–trondhjemite–granodiorite (TTG) suites, the products of crustal differentiation that formed early continental crust. These rocks may have been primarily generated by partial melting of hydrated basaltic crust in a variety of settings including subduction zones or the deep lithosphere. Sources are mainly inferred from examination of TTGs alone, as potential source rocks are rarely exposed. In the southern Superior Province, Canada, the Kapuskasing Uplift exposes an important crustal cross-section with upper- to middle-crustal TTGs and lower-crustal metabasites, which show evidence of having produced trondhjemitic anatectic melt. Here, we test the hypothesis that these metabasites were the source of the Mesoarchean to Neoarchean TTGs in the Kapuskasing Uplift by combining phase equilibrium and melt trace element modelling with whole-rock and zircon Lu–Hf isotope analysis and geochronology (garnet Lu–Hf and zircon U–Pb) of metabasic samples. By comparison of the results with existing data from TTGs in the Kapuskasing Uplift, we determined that the metabasites are plausible source rocks for the TTGs. The Lu–Hf systematics of the metabasites and TTGs are the most robust evidence of a genetic connection. Modelling results support an increase in TTG source depth over time. New geochronological data constrain partial melting of metabasite and crystallization of anatectic melt between ca. 2685 Ma and ca. 2600 Ma, coeval with crystallization of only the youngest TTGs. Overall, these results indicate a complex history of intracrustal differentiation in the Kapuskasing Uplift, with partial melting of two isotopically distinct lower-crustal metabasic sources at different times and depths.

Cryogenic Process Optimization for Natural Gas Purification: Predictive Modeling of Methane–CO2 Solid–Vapor Phase Equilibrium Using Response Surface Methodology

Cryogenic Process Optimization for Natural Gas Purification: Predictive Modeling of Methane–CO₂ Solid–Vapor Phase Equilibrium Using Response Surface Methodology

Understanding the origins of reversible and hysteretic pathways of adsorption phase transitions in metal-organic frameworks

Phase behavior of nanoconfined fluids adsorbed in metal–organic frameworks is of paramount importance for the design of advanced materials for energy and gas storage, separations, electrochemical devices, sensors, and drug delivery, as well as for the pore structure characterization. Phase transformations in adsorbed fluids often involve long-lasting metastable states and hysteresis that has been well-documented in gas adsorption–desorption and nonwetting fluid intrusion-extrusion experiments. However, theoretical prediction of the observed nanophase behavior remains a challenging problem. The mesoscopic canonical, or mesocanonical, ensemble (MCE) is devised to study the nanophase behavior under conditions of controlled fluctuations to stabilize metastable and labile states. Here, we implement and apply the MCE Monte Carlo (MCEMC) simulation scheme to predict the origins of reversible and hysteric adsorption phase transitions in a series of practical MOF materials, including IRMOF-1, ZIF-412, UiO-66, Cu-BTC, IRMOF-74-V, VII, and IX. The MCEMC method, called the gauge cell method, allows to produce Van der Waals type isotherms with distinctive swings around the phase transition regions. The constructed isotherms determine the positions of phase equilibrium and spinodals, as well as the nucleation barriers separating metastable states. We demonstrate the unique capabilities of the MCEMC method in quantitative predictions of experimental observations compared with the conventional grand canonical and canonical ensemble simulations. The MCEMC method is implemented in the open-source RASPA and LAMMPS software packages and recommended for studies of adsorption behavior and pore structure characterization of MOFs and other nanoporous materials.

Understanding shape selectivity effects of hydroisomerization using a reaction equilibrium model.

We study important aspects of shape selectivity effects of zeolites for hydroisomerization of linear alkanes, which produces a myriad of isomers, particularly for long chain hydrocarbons. To investigate the conditions for achieving an optimal yield of branched hydrocarbons, it is important to understand the role of chemical equilibrium in these reversible reactions. We conduct an extensive analysis of shape selectivity effects of different zeolites for the hydroisomerization of C7 and C8 isomers at chemical reaction equilibrium conditions. The reaction ensemble Monte Carlo method, coupled with grand-canonical Monte Carlo simulations, is commonly used for computing reaction equilibrium of heterogeneous reactions. The computational demands become prohibitive for a large number of reactions. We used a faster alternative in which reaction equilibrium is obtained by imposing chemical equilibrium in the gas phase and phase equilibrium between the gas phase components and the adsorbed phase counterparts. This effectively mimics the chemical equilibrium distribution in the adsorbed phase. Using Henry's law at infinite dilution and mixture adsorption isotherm models at elevated pressures, we calculate the adsorbed loadings in the zeolites. This study shows that zeolites with cage or channel-like structures exhibit significant differences in selectivity for alkane isomers. We also observe a minimal impact of pressure on the gas-phase equilibrium of these reactions at typical experimental reaction temperatures 400-700K. This study marks initial strides in understanding the reaction product distribution for long-chain alkanes.