Phase Equilibria Research Articles

Formation and phase equilibria of gas hydrates confined in hydrophobic nanoparticles

The promotion of gas hydrate formation is of fundamental importance to facilitate its great potential applications in, for example, gas separation, transportation and energy storage. The employment of Dry Water (DW), which is a powdery Pickering system composed of macro water droplets surrounded by stabilising hydrophobic nanoparticles, is considered an effective method for enhancing hydrate formation. The promotion mechanism underlying this observation, however, has yet to be well understood. In this work, the effect of DW on both formation kinetics and thermodynamic stability of gas hydrates was investigated using a micro differential scanning calorimetry (µDSC) in CH4 and CO2 hydrate systems, using two different hydrophobic nanoparticles. Distinctly shorter induction times and higher conversion ratios were observed for DW compared to bulk water. The DW system stabilised by more hydrophobic nanoparticles showed benefits in accelerating nucleation, while the other system, which consisted of smaller DW droplets, led to a superior enhancement of hydrate growth. Besides the effect on formation kinetics, it was also noted that DW influenced the µDSC hydrate dissociation peak characteristics, including melting points and melting peak shapes. This phenomenon suggested that the centre- and surface-droplet hydrates in DW may have different structures, due to the “hydrophobic effect” of the nanoparticles structuring the near-surface water, so exhibiting melting points corresponding to bulk hydrate or to a more structured surface hydrate (with raised melting point), respectively. To support this “hydrophobic effect” hypothesis, a series of hydrate and ice formation experiments were conducted in porous media having different hydrophobicity, the results of which demonstrated that hydrates adjoining confined hydrophobized surfaces, in other systems similar to DW, also displayed higher melting temperatures.

The experimental study on the (solid + liquid) phase Equilibria for {LiBr (1) + ionic liquid (2) + water (3)} systems

The paper presents experimentally determined (solid + liquid) phase diagrams in the {LiBr (1) + ionic liquid (2) + water (3)} systems. Interpretation of the results and comparison with the literature data for the {LiBr + water} enables the determination of the influence of the ionic liquid on the LiBr solubility in water. It is known that one of the disadvantages of an aqueous lithium bromide solution is the tendency to crystallize, especially with a higher concentration of lithium bromide in the solution. This is one of the problems in absorption refrigeration technology where the aqueous lithium bromide solution is a working fluid commonly used on an industrial scale. One of the possibilities for improving the properties of this system is the use of an additive increasing the solubility of LiBr in water. In this work, the following ionic liquids (ILs): N-(2-hydroxyethyl)ammonium glycolate, N,N-di(2-hydroxyethyl)ammonium glycolate, N,N-di(2-hydroxyethyl)-N-methylammonium glycolate, and N,N,N-tri(2-hydroxyethyl)-ammonium glycolate were considered as an addition to the conventional system. The (solid + liquid) phase diagrams were determined using the dynamic method. Liquid phase range was determined at the absorber operating temperature, T = 303.15 K, and compared to LiBr + water system.

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.

2.13 Ga Lawsonite/Barroisite-Bearing E-Morb Signature Metagabbro Associated with Spinel Metaperidotite from Itaguara (São Francisco Craton, Brazil): Oldest Blueschist-Facies Fragment of Oceanic Moho?

In close association with Paleoproterozoic retroeclogite and accretionary prism-related mica-quartz schist, a 2.13 Ga (metamorphic titanite U-Pb age) lawsonite/barroisite-bearing E-MORB signature metagabbro associated with spinel metaperidotite is found in the Itaguara Sequence from southern São Francisco craton, Brazil. Petrography and pressure-temperature equilibrium phase diagrams suggest that the metagabbro experienced blueschist-facies metamorphism, attaining peak metamorphic conditions at ~16 kbar and ~450 °C during subduction. The retrograde metamorphic path crossed epidote amphibolite-facies, in which the mineral assemblage found in metaperidotite (olivine, clinopyroxene, spinel, serpentine, chlorite, talc, and tremolite) was stable during a ca. 2.1 Ga continental collision-related exhumation that occurred between the Archean Campo Belo/Bonfim and Divinópolis complexes. This geological framework suggests that the metagabbro and adjacent spinel metaperidotite represent a subducted and exhumed blueschist-facies fragment of a Paleoproterozoic oceanic Mohorovičić (Moho) discontinuity, thus establishing the Itaguara metagabbro as the oldest-known occurrence of retrogressed blueschist and providing evidence for the activity of the modern-style plate tectonics more than 2 Gyr ago.

Thermodynamic re-optimization of the CaO–SiO2 system integrated with experimental phase equilibria studies

CaO–SiO2 is the key system in ferrous and non-ferrous metallurgy, ceramic manufacture, cement production, and other applications. A number of discrepancies and gaps in knowledge has been identified and resolved since the last thermodynamic optimization of this system. This study reports new experimental phase equilibria data measured using recent advances in equilibration, sample quenching, and Electron Probe X-ray Microanalysis (EPMA) technique. An updated self-consistent set of thermodynamic model parameters is provided. Most importantly, these updates are integrated with a complete re-assessment of the 20-component Cu–Pb–Zn–Fe–Ca–Si–O–S–Al–Mg–Cr–Na–As–Sn–Sb–Bi–Ag–Au–Ni–Co system directly relevant to applications in the ferrous and non-ferrous metallurgical industries. To obtain a large single set of model parameters, significant advances were made in the computational approach, with a focus on simultaneous parallel optimization of binary and ternary model parameters using an experimental dataset combining binary, ternary, and multicomponent information. The Modified Quasichemical Formalism is used for the liquid slag phase. Thermodynamic properties of solid phases and liquid endmembers are completely revised following the recommendations for the third generation of CALPHAD databases. Other notable changes include the revision of the melting temperature of CaO, justified by extrapolations from the multicomponent systems, as well as a physically realistic heat capacity function for metastable SiO2 below the glass transition temperature. These updated properties expand the areas of application of the database to amorphous and partially crystallized slags at ambient temperatures, such as thermodynamics and kinetics of leaching of toxic elements in an aqueous environment. The fundamental limitations of the existing Modified Quasichemical Formalism are also discussed, along with strategies for addressing them.

Enhanced age hardening response of a Mg-Y alloy by Ca addition at an elevated temperature

The effect of Ca addition on the age hardening response and precipitation behavior of a Mg-7Y-0.5Zr (wt%) alloy during isothermal aging at 350 ℃ has been studied by hardness test and high-angle annular dark-field scanning transmission electron microscopy. The addition of 0.6 wt% Ca can effectively enhance the age hardening response of Mg-7Y-0.5Zr alloy at 350 ℃, and the enhanced hardness is mostly attributed to the uniform precipitation of a novel strengthening precipitate phase, designated βp. The βp phase forms as plates on {101̅0}α planes. It has a Cd45Sm11-type structure (space group F4̅3m, lattice parameter a = 2.24 nm) and a composition of Mg5Y0.8Ca0.2. Its orientation relationship with the α-Mg matrix phase is such that [1̅11]βp // [21̅1̅0]α and (110)βp // (0001)α. After prolonged aging at 350 ℃, the metastable phase βp can transform in-situ to the equilibrium phase β-Mg24Y5 with a cube-to-cube orientation relationship. The βp → β phase transformation is associated with the transition of constituent atomic clusters and the re-distribution of selected atoms within clusters.

Modeling CO2 solubility in water using gradient boosting and light gradient boosting machine

The growing application of carbon dioxide (CO2) in various environmental and energy fields, including carbon capture and storage (CCS) and several CO2-based enhanced oil recovery (EOR) techniques, highlights the importance of studying the phase equilibria of this gas with water. Therefore, accurate prediction of CO2 solubility in water becomes an important thermodynamic property. This study focused on developing two powerful intelligent models, namely gradient boosting (GBoost) and light gradient boosting machine (LightGBM) that predict CO2 solubility in water with high accuracy. The results revealed the outperformance of the GBoost model with root mean square error (RMSE) and determination coefficient (R2) of 0.137 mol/kg and 0.9976, respectively. The trend analysis demonstrated that the developed models were highly capable of detecting the physical trend of CO2 solubility in water across various pressure and temperature ranges. Moreover, the Leverage technique was employed to identify suspected data points as well as the applicability domain of the proposed models. The results showed that less than 5% of the data points were detected as outliers representing the large applicability domain of intelligent models. The outcome of this research provided insight into the potential of intelligent models in predicting solubility of CO2 in pure water.

MaterialsMap: A CALPHAD-based tool to design composition pathways through feasibility map for desired dissimilar materials, demonstrated with resistance spot welding joining of Ag-Al-Cu

Assembly of dissimilar metals can be achieved by different methods, for example, casting, welding, and additive manufacturing (AM). However, undesired phases formed in liquid-phase assembling processes due to solute segregation during solidification diminish mechanical and other properties of the processed parts. In the present work, an open-source software named MaterialsMap, has been developed based on the CALculation of Phase Diagrams (CALPHAD) approach. The primary objective of MaterialsMap is to facilitate the design of an optimal composition pathway for assembling dissimilar alloys with liquid-phases based on the formation of desired and undesired phases along the pathway. In MaterialsMap, equilibrium thermodynamic calculations are used to predict equilibrium phases formed at slow cooling rate, while Scheil-Gulliver simulations are employed to predict non-equilibrium phases formed during rapid cooling. By combining these two simulations, MaterialsMap offers a thorough guide for understanding phase formation in various manufacturing processes, assisting users in making informed decisions during material selection and production. As a demonstration of this approach, a compositional pathway was designed from pure Al to pure Cu through Ag using MaterialsMap. The design was experimentally verified using resistance spot welding (RSW).

Effect of Adding Minor Cu Amounts on Stability of Constituent Phases in Al<sub>x</sub>CrFeMnNi High Entropy Alloy Microstructure

A family of AlxCuyCrFeMnNi (x=0, 0.15, 0.3, 0.6, 0.9 and y=0, 0.07, 0.14) high entropy alloys (HEA) were arc cast and then heat treated for 24h at 1100֯C-1150֯C followed by water quench. The microstructure of low Al alloys (Al0Cux and Al0.15Cux) consisted of FCC and BCC phases. Al0.3Cux showed an additional ordered precipitate phase. High Al alloys (Al0.6Cux and Al0.9Cux) consisted of two BCC phases rich in Cr-Fe and Ni-Al. In the present study, the phases formed in the microstructures were evaluated in light of valence electron concentration (VEC), Hume-Rothery (H-R) and degree of partitioning. Although VEC successfully predicts the impact of Al and Cu on the trend of FCC-BCC phase formation, the parameter does not accurately predict the structure of high Al alloys. A good agreement was observed between H-R rules prediction and the experiments which might be ascribed to the high temperature equilibrium phases developed by the heat treatment. As per these criteria, increasing Cu (up to 3at.%) and decreasing Al promote formation of solid solution phases. Adding minor amounts of Cu avoids the Cu partitioning that besets high Cu HEAs.

Low-temperature phase equilibria of the ternary Cu-In-Sn system at In-rich corner

Cu2In3Sn is one of the IMCs frequently observed in the joint between In-Sn solder and Cu. However, the ternary phase equilibria related to Cu2In3Sn and the crystal structure have been insufficiently investigated. In the present research, Cu-In-Sn phase equilibria and crystallographic structures were studied by means of synchrotron powder XRD, single-crystal XRD, SEM, EPMA, and DSC. Two isothermal sections at 100°C and 140°C were constructed. It is discovered that binary CuIn2 continuously extends to Cu(In0.76,Sn0.24)2 in the ternary field at 100°C, forming a Cu(In,Sn)2 single-phase region, and that the homogeneity range of Cu(In,Sn)2 shrinks from both the Sn-rich end and the Sn-lean end when the temperature increases. The labeling of Cu2In3Sn is discouraged since no separate Cu(In1-x,Snx)2 phase field was found.

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

This research combines industrial engineering principles with chemical process modeling to explore the capture of CO2 from natural gas under cryogenic conditions. The study specifically investigates the Solid-Vapor (S-V) phase equilibrium in a methane-carbon dioxide (CH4-CO2) system. The study employs Response Surface Methodology (RSM) to develop a robust model for predicting phase behavior in industrial gas separation processes. The model is validated using experimental data, offering enhanced operational insights into cryogenic CO2 capture in industrial applications. The developed RSM model is particularly valuable as it can predict the mole fractions of methane and CO2 at various temperatures and pressures in the solid-vapor region of phase equilibrium, where limited experimental data make it difficult to estimate these components accurately. The key contribution of this study is to validate the RSM model's available experimental data, and the model can further be used to predict the process conditions at which high methane composition (yCH4) can be achieved. The developed model showed good agreement when the results were compared with previous experimental studies. The utilization of chemical engineering data to forecast previously unknown conditions in gas separation processes broadens the scope of industrial process optimization in this work.

Experimental study of phase equilibria in Y–Co–Zr system at 600 °C and 800 °C

Phase equilibria of the Y–Co–Zr ternary system at 600 °C and 800 °C were studied for the first time using the diffusion couple technique and equilibrium alloy method with electron probe microanalysis (EPMA), scanning electron microscopy (SEM), and X-ray diffraction (XRD). The results reveal that the stable ternary intermetallic compounds were not found, while YCo2 and Co2Zr are formed a continuous solid solution phase (Y, Zr)Co2 with a Cu2Mg-type structure. The solid solubility of Zr in α-Y2Co17, YCo5, Y2Co7, α-YCo3, YCo and Y3Co at 800 °C was determined to be 5.6, 2.4, 9.4, 18.0, 1.4 and 1.4 at.%, respectively, while the solid solubility of Y in Co23Zr6, CoZr and CoZr3 was measured to be 6.4, 6.3 and 2.6 at.%. Meanwhile, the solid solubility of Zr in α-Y2Co17, YCo5, Y2Co7, α-YCo3, YCo, Y4Co3, Y3Co2, Y8Co5 and Y3Co at 600 °C was measured to be 4.4, 3.0, 9.4, 17.2, 1.6, 1.6, 1.9, 1.9 and 3.2 at.%, respectively, while the solid solubility of Y in Co23Zr6 and CoZr was measured to be 4.8 and 2.4 at.%. Two isothermal sections of the Y–Co–Zr ternary system at 600 °C and 800 °C were constructed finally. It provides the fundamental information for the development of high-performance Y–Co–Zr-based magnetic alloys.

New mixed inhomogeneous phase in vortical gluon plasma: First-principle results from rotating SU(3) lattice gauge theory

Using first-principle numerical simulations, we find a new spatially inhomogeneous phase in rigidly rotating Nc=3 gluon plasma. This mixed phase simultaneously possesses both confining and deconfining phases in thermal equilibrium. Unexpectedly, the local critical temperature of the phase transition at the rotation axis does not depend on the angular frequency within a few percent accuracy. Even more surprisingly, an analytic continuation of our results to the domain of real angular frequencies indicates a profound breaking of the Tolman-Ehrenfest law in the vicinity of the phase transition, with the confining (deconfining) phase appearing far (near) the rotation axis.

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.

Experimental and modeling investigations on CH4 hydrate phase equilibria in multi-ion “Haima” cold seep environment

CH4 hydrate formation represents a primary pathway for CH4 transformation within the deep-sea CH4 seepage environment, holding utmost significance for global carbon budget and marine hydrate resources distribution. As a typical active CH4 seeping, however, the influence characteristics of various ions in in-situ “Haima” cold seep on CH4 hydrate stability remains unclear. In this study, founded on the multiple ion components from the seawater of the “Haima” cold seep, the effects of salt ion categories and concentrations on CH4 hydrate phase equilibrium were investigated, and a thermodynamic model suitable for high-salinity deep-sea environment was proposed. Results indicated that, in higher concentration salt solutions (>3.45 wt%), hydrate stability was no longer solely governed by salinity, and significant differences among ion types were observed. The inhibitory strength of the ions on CH4 hydrate stability followed the order of Mg2+>Na+>Ca2+>Mn2+≈K+>Sr2+>Ba2+. The predicted CH4 hydrate phase equilibrium conditions from the proposed model exhibited strong agreement with both experimental results and data reported in the literature. The average absolute deviation of pressure (AADP) from the model prediction was 2.7% and 4.3% compared to the experimental and published literature data, respectively, which outperformed those of the CSMHYD model, Chen-Guo model and Hu-Lee-Sum correlation (4.7%–6.2%). In light of the marine temperature gradient and prediction results, it is estimated that CH4 hydrate could maintain stably below 600 m depth of the seawater in the cold seep area.

A Comprehensive Review of Distillation in the Pharmaceutical Industry

Distillation processes play a pivotal role in the pharmaceutical industry for the purification of active pharmaceutical ingredients (APIs), intermediates, and solvent recovery. This summary explores the fundamental principles governing distillation, including mass transfer and phase equilibrium concepts. It delves into various distillation methods employed in pharmaceutical engineering, encompassing fractional distillation, azeotropic/extractive distillation, steam distillation, vacuum distillation, membrane distillation, and molecular distillation. Recent advancements in distillation technology, such as process intensification, miniaturization, and integration with other separation processes, are highlighted. The current state of distillation in pharmaceutical engineering is discussed, addressing regulatory considerations, solvent selection, and recovery challenges. Future prospects emphasize the need for energy-efficient and sustainable processes, advanced distillation technologies, process modeling and optimization, continuous manufacturing integration, and interdisciplinary collaboration. These efforts aim to drive innovation and address the evolving needs of the pharmaceutical industry, ensuring the continued importance of distillation in the purification and separation of pharmaceutical compounds

Heat and mass transfer performance analysis of a vertical tubular ammonia/water bubble absorber based on CFD modeling

Bubble absorbers are highly efficient in mass transfer processes, but their popularization is limited by the risks associated with too much ammonia charging. In order to reduce the ammonia charge, it is essential to optimize the heat and mass transfer performance in the absorber. Existing models provide in-depth analysis of bubble motion and morphology, but insufficient attention has been paid to the concentration distribution and interfacial heat and mass transfer resistance. In this study, a two-dimensional axisymmetric vertical tubular ammonia/water bubble absorber was modeled based on Fluent and phase equilibrium, absorption heat data based on Aspen was imported. The relative deviations were 9%, 0.45%, and 4.1% in terms of the completely absorbed height, the liquid phase ammonia mass fraction, and the outlet temperature, respectively. The results showed that the mass transfer deterioration point was at the gas column closure and the heat transfer deterioration point was at the gas column contraction. Variable parameter studies have shown that turbulence effects at the gas–liquid interface can lead to enhancement and deterioration of local heat and mass transfer, which in turn cause local oscillations in the concentration and temperature profiles. While increasing the interphase mass transfer driving force promotes the interphase mass transfer process, it hinders the diffusion mass transfer process within the liquid phase. This effect is particularly pronounced in the absence of intense cooling, leading to an increase in the complete absorbed height.

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.

Numerical simulation study of natural gas hydrate extraction by depressurization combined with CO2 replacement

Utilizing depressurization combined with CO2 replacement for extracting natural gas hydrates (NGHs) is vital for sustainable energy and carbon sequestration. In this study, a NGH reservoir numerical model was developed to investigate the impacts of depressurization combined with CO2 replacement on hydrate extraction at a field scale. Findings reveal an increase in methane production with reduced bottom hole pressure. When the bottom hole pressure is 3.5 MPa, the methane production reaches its maximum at 1.71 × 106 m3. Methane hydrates near production and injection wells decompose first, with deeper hydrates decomposing more easily. Higher differential pressures between injection and production enhance methane extraction and CO2 hydrate formation. However, excessive pressure differential (1.5 MPa) can lead to CO2 breakthrough across reservoir barriers, adversely affecting the purity of methane. At 1800 d, the methane purity is only 36.2 %. Optimal methane extraction and CO2 sequestration occur at higher injection temperatures (9 °C) below the CO2 hydrate phase equilibrium temperature. Temperatures above this equilibrium adversely affect both processes. The study validates the feasibility of depressurization with CO2 replacement for extracting hydrates in the Shenhu area, offering theoretical guidance for synergistic offshore methane extraction and CO2 sequestration techniques.

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

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