Thermodynamic Database Research Articles

Phase relations at 1573 K and 1673 K and thermodynamic assessment of ZrO2-SrO-BaO system

The thermodynamic database of ZrO2-SrO-BaO system was essential for the development of high-stability refractories. Thirteen samples were prepared using the solid-state reaction method to investigate the isothermal sections of ZrO2-SrO-BaO system at 1573 K and 1673 K. Four solid solution phases, (Ba, Sr)ZrO3, (Ba, Sr)2ZrO4, (Ba, Sr)3Zr2O7, and (Ba, Sr)4Zr3O10, were identified. Based on the re-assessment of SrO-BaO sub-binary system, a self-consistent thermodynamic database of ZrO2-SrO-BaO system was obtained. Calculated isothermal sections at 1573 K and 1673 K and liquidus projection showed good agreement with existing experimental data. Finally, a potential refractory (Sr0.06, Ba0.94)ZrO3 with better stability was designed using the thermodynamic database of ZrO2-SrO-BaO system.

CALPHAD modeling of [formula omitted]- carbide dual ordering in Fe-Al-C ternary alloys

A novel four-sublattice model for the κ phase, denoted as (Fe, Al)3(Fe, Al)1(C, Va)1(C, Va)3 was proposed to improve the thermodynamic prediction, such as equilibrium composition, phase stability of κ-carbide in Fe-Al-C system. The sublattice model explains the transformation from the disordered FCC solid solution to the ordered κ-carbide via concurrent ordering of substitutional and interstitial atoms. The dual ordering model can restrict the irregular contribution of configurational entropy arising at 20 at% C composition, which is an issue with the existing thermodynamic databases. For the CALPHAD assessment, κ-carbide was considered as a single, individual phase that is in equilibrium with the liquid, austenite (γ), ferrite (α) or other intermetallic and carbide phases in the Fe-Al-C system. The formation energy calculated from density functional theory (DFT) showed that Fe3Al–L12 phase is energetically more favorable than the Fe3AlC–E21 phase, and C atoms in sublattice IV are not energetically favorable at all. The assessed parameters provided better accuracy than the existing database in the calculations of isothermal sections, liquidus projection, invariant reactions, and low-temperature phase compositions. The model is highly suitable for the low temperature (<800 °C) phase predictions. Thus, the improved Fe-Al-C model lays the foundation for the thermodynamic and kinetic studies of κ-carbide for designing new Fe-Mn-Al-C alloys and optimizing the heat treatment processes.

A Thermodynamic and Kinetic‐Based Argon Oxygen Decarburization Process Model and Validation with Plant Data

Argon oxygen decarburization (AOD) is one of the most dynamic and complex processes in stainless steel production. Along with a lot of metallic additions, oxygen (O2), argon (Ar), or nitrogen (N2) gas is blown into the reactor to produce complex stainless‐steel grades. Typically, a hit‐and‐trial method approach is followed in the plant to optimize the critical process parameters for producing any new grades or optimizing the existing ones. In this regard, a mathematical model of the process coupled with robust thermodynamic databases is adopted to optimize the process. As discussed in the manuscript, most of the previous models explain the decarburization patterns by assuming a critical carbon (C) content to justify the change in decarburization rate from surface oxidation due to high O2 flow rates at high C levels to liquid phase mass transfer of C at low C levels. In the current study, decarburization patterns are described without any assumption of critical C content. The modeling results are validated against the plant data for a standard 316L grade in a 150 ton AOD converter. Next, the model parameters are implemented as it is for grades 439 and 321 and the AOD model is used as a predictive tool for these grades.

Pressure and Temperature Estimation in Greenschist‐Facies Metapelites: An Example From the Variscan Belt in Sardinia

ABSTRACTPhase equilibrium modelling is a powerful method for obtaining pressure–temperature (P–T) estimates in metapelites; however, the advantages, disadvantages, and limitations of applying this technique to greenschist‐facies pelites have received little attention. This study uses two greenschist‐facies metapelites from the Nappe Zone in Sardinia (Italy) to examine differences between currently available thermobarometric techniques. First, this work compares P–T estimates from chlorite–K‐white mica–quartz–water and K‐white mica–quartz–water multiequilibrium approaches, the latter integrated with previously published Tmax results from Raman spectroscopy on carbonaceous material. Consistent P–T conditions are retrieved from these methods for both samples, with P–T estimates suggesting a difference in peak metamorphic conditions between the Internal and External Nappe Zones of Sardinia (peak P–T conditions of 0.6–0.8 GPa, 420°C°C–450°C and 0.4–0.5 GPa, 370°C°C–400°C for the Internal and External Nappes, respectively). Second, phase equilibrium modelling was used to assess the ability of six different sets of solution models, alongside their associated thermodynamic datasets, to constrain P–T conditions in the same samples, which are characterized by high‐variance mineral assemblages. Significant differences were found between the six thermodynamic databases, and important discrepancies were recognized between the observed and predicted mineral assemblages and compositions (e.g., Si in K‐white mica). In only one sample, three databases were able to predict the observed natural assemblage. The compositional isopleths for K‐white mica, from the same databases, do not intersect, offering no assistance in constraining P–T conditions. However, one database predicted chlorite's natural composition, yielding a P–T estimate consistent with multiequilibrium methods: ~0.9 GPa, ~350°C°C–400°C for the Internal Nappe Zone and ~0.5 GPa, ~300°C°C–350°C for the External Nappe Zone. Although P–T conditions constrained using calculated isopleths from greenschist‐facies metapelites and databases optimized for modelling low‐grade to medium‐grade pelitic systems may be reliable, they should be applied cautiously and compared with estimates from inverse and independent approaches.

Phase Field Simulation Study of the β′ Precipitation Phase of Mg-Gd-Y Alloys

Abstract The key reinforcing precipitation phase in the aging precipitation sequence of Mg-Gd-Y alloys is the bamboo-leaf-like substable β′ phase, which can effectively inhibit the crystal base slip to enhance the age-hardening response of magnesium alloys. In this work, a phase field model of the aging precipitation process of Mg-Gd-Y ternary alloys was created by combining the phase field method and thermodynamic database. The microstructure evolution of the β′ precipitated phase in the isothermal aging process of Mg-Gd-Y alloys was simulated, and the impact of anisotropic parameters on the precipitated phase’s morphology was examined. Finally, the effect of Gd content on the β′ phase in the Mg-Gd-Y alloys was disclosed from the standpoint of the kinetics. β′ precipitation phase precipitation mechanism of Mg-Gd-Y alloys from the kinetic point of view. The results show that the anisotropic elastic energy and the interfacial energy work together to influence the shape of the β′ precipitation phase. Gd content increases lead to refined grains, an increase in the volume fraction of the Mg-Gd-Y alloy β′ precipitated phase, and a greater aspect ratio of the precipitated phase.

Micromechanical testing and microstructure analysis of as-welded and post-weld heat-treated Ti-6Al-4V alloy

The microstructural evolutions and variations in mechanical performance of electron beam welded (EBW) Ti-6Al-4V (Ti64) alloy have been investigated. The effects of heat treatment on the microstructure of welded samples have been studied after post-welding solution treatment and ageing. The martensitic phase α′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\alpha }{\\prime}$$\\end{document} has been confirmed using transmission electron microscopy (TEM). Electron backscatter diffraction (EBSD) has been used to investigate the phase and grain morphology. Results showed that the martensitic α′ phase coarsened, the size of heat-affected zone (HAZ) changed and grains in the base materials (BMs) had grown after the post-weld heat treatments (PWHT). The tensile behaviour of electron beam welded Ti64 has been investigated using in situ tensile testing monitored by optical microscopy. The deformation and failure were directly revealed during the in situ tensile process. Results showed that the EBW Ti64 samples have different failure locations after receiving different post-weld heat treatments. The relationship between the post-weld heat treatments, microstructural evolution and mechanical properties of EBW Ti64 were investigated. Thermodynamic databases were used to predict mechanical properties—including the yield strengths—of the titanium alloy for different grain sizes, representing different post-weld heat treatment operations, and these were embedded into a finite element modelling framework to simulate the tensile testing specimens to understand the mechanical fields experienced such as stresses and strains, just prior to failure.

Thermodynamic calculation-assisted design of 500 MPa high performance steel by machine learning

In order to rationally design Q500 low-alloy wind power steel with stable microstructure and properties within a large cooling rate range, this study proposed a design system that utilizes thermodynamic database, machine learning (ML), and the multi-objective genetic optimization algorithm (MOGA). Thermodynamic calculation has been used to obtain a large amount of data on phase fractions and mechanical properties for various chemical composition at different cooling rates. By comparing the predictive capabilities of different ML models, the deep neural network (DNN) and MOGA were combined to design Q500 wind power steel. Subsequently, three groups of designed chemical compositions were appropriately selected for verification. The results indicate that the yield strength of the experimental steel was over 500 MPa, and the maximum error in microstructure and mechanical property prediction was 5.0%. The prediction results demonstrated the rationality of the composition design framework. Meanwhile, the method of combining the material database and ML proposed in this study can also be applied to the design of other low-alloy steels.

Enhancing the Accuracy and Generality of the Debye–Grüneisen Model: Optimizing the Volume Dependence for Accurate Predictions Across Varied Compositions

In this work, we have introduced an optimized Debye-Grüneisen model that revolutionizes the determination of the Debye temperature and Grüneisen parameters. Unlike conventional methods, our model requires only the 0 K energy volume data for a material as input, eliminating the need to determine the bulk modulus and its pressure derivative, which often pose challenges due to numerical uncertainties. This unique feature sets our model apart from existing approaches and streamlines the process, enabling accurate predictions of thermal expansion behavior across various materials. To demonstrate its effectiveness, we showcase its excellent agreement with measured coefficients of thermal expansion (CTE) for the nickel-cobalt-chromium-aluminum-yttrium (Ni-Co-Cr-Al-Y) bond-coating system. Additionally, we apply our approach by conducting a high-throughput search for potential bond-coating materials among 90,000 compositions within the aluminum-cobalt-chromium-iron-nickel (Al-Co-Cr-Fe-Ni) system. From this extensive search, four compositions are synthesized, and the measured CTE values agree very well with theoretical predictions, hence validating our approach. The current optimized Debye-Grüneisen model combined with Density Functional Theory (DFT)-based thermodynamic database enables reliable and efficient high-throughput calculations of CTE of Ni-based alloys without expensive phonon calculations.

Phase equilibria and thermodynamic analysis of liquid–liquid immiscibility in the system SiO2–Na2O–MoO3

AbstractPhase equilibrium experiments were carried out in the SiO2–Na2O–MoO3 system at 1200ºC and 1000ºC. We found that immiscible phase region in this system is narrower than that reported previously. By combining phase relationship and thermodynamic data and assuming associate species model, interaction parameters to describe enthalpy of mixing of SiO2–Na2O–MoO3 liquid were optimized by CALPHAD methodology. The thermodynamic database can be applied to thermodynamic calculations of silicate systems containing molybdenum, such as the vitrification process of high-level radioactive waste.

Laboratory-Scale Implementation of Standardized Reconstituted Geothermal Water for Electrochemical Investigations of Carbon Steel Corrosion

Currently, the demand for heat production by geothermal energy is increasingly strong amid the controversy surrounding non-renewable forms of energy. In France, the Dogger aquifer in the Paris Basin (DAPB) produces saline geothermal waters (GWs) that are hot (70–85 °C), anaerobic, and slightly acidic (pH 6.1–6.4), and are characterized mainly by the presence of Cl−, SO42−, CO2/HCO3−, and H2S/HS. These GWs are corrosive, while the well casings used are carbon steel. GWs have been continuously treated since the 1990s by corrosion inhibitors at the bottom of production wells to reduce water–steel interactions and scaling issues. Electrochemical experiments to optimize inhibitors were carried out on site, protected from the ambient atmosphere, with actual geothermal water, using water tapping at the wellhead. Currently, carbon steel corrosion/scaling, corrosion inhibition phenomenology, and kinetics evaluation remain important challenges. These issues are, of course, linked to the durability of installations. The novelty of our work consists of our validation of a modus operandi that properly reproduces, at the laboratory scale, operating conditions similar to those encountered on the types of geothermal installations. Particular attention was paid to characterizing waters and gases from 13 production wellheads that were modelled with PhreeqC® Version 3 hydrogeochemical software and the Thermoddem thermodynamic database for implementing standardized reconstituted geothermal water (SRGW), a well-balanced water representative of the major elements and dissolved gases of actual DAPB geothermal waters. The developed electrochemical setup enabled us to analyze corrosion mechanisms such as those observed on site and to investigate corrosion inhibition using petrosourced and biosourced inhibitors. The modus operandi constitutes a reference for further investigations, at the laboratory scale, of corrosion inhibition. These investigations may include screening and optimizing the formulas of petrosourced and biosourced inhibitors for use in DAPB waters.

Formation kinetics and equilibrium thermodynamics study on the Bi2O3-TiO2 system for synthesis of the bismuth titanate ceramics

Formation kinetics and equilibrium thermodynamics are fundamental knowledge for predicting microstructure and properties during materials processing and utilization. This work prepared high purity Bi12TiO20, Bi4Ti3O12 and Bi2Ti4O11 compounds and characterized these compounds by in-suit X-ray diffraction, scanning electron microscope, energy dispersive spectrometer as well as calorimetry. Based on the experimental data obtained in this work and the literature, a thermodynamic description of the Bi2O3–TiO2 system was carried out, a thermodynamic database as well as the calculated phase diagram of the system was provided. The discrepancy between the present calculation with the experimental data were discussed, the formation kinetics of the compounds was explained and the bismuth titanate ceramics with tailored structure and specific physical properties were sintered.

Development and Applications of a Thermodynamic Database for Multicomponent Cu Alloys

Development and Applications of a Thermodynamic Database for Multicomponent Cu Alloys

Effect of molybdenum addition on precipitate coarsening kinetics in Inconel 740H: A phase-field study

Inconel 740H (IN740H) has emerged as an important candidate for the advanced ultra-supercritical (AUSC) steam turbines due to its superior microstructural stability and creep resistance under service conditions. In the present work, we have reparameterized a multicomponent Ni-based superalloy (IN740H) into an equivalent ternary Ni-Al-Mo superalloy, based on the partitioning coefficients of the elements, using the thermodynamic database (CALPHAD). We use this thermodynamic description to employ a quantitative phase-field model to assess the long-term stability of γ′ precipitates in IN740H utilizing GPU-based supercomputing architecture. The assessment helps us to enhance our understanding of the effect of the atomic diffusivity of Mo on coarsening kinetics of the γ′-precipitates in equivalent ternary Ni-Al-Mo superalloy. Investigation reveals that our phase-field model can accurately predict the experimentally observed coarsening kinetics in IN740H.

Enhancing Large Language Model Comprehension of Material Phase Diagrams through Prompt Engineering and Benchmark Datasets

Large Language Models (LLMs) excel in fields such as natural language understanding, generation, complex reasoning, and biomedicine. With advancements in materials science, traditional manual annotation methods for phase diagrams have become inadequate due to their time-consuming nature and limitations in updating thermodynamic databases. To overcome these challenges, we propose a framework based on instruction tuning, utilizing LLMs for automated end-to-end annotation of phase diagrams. High-quality phase diagram images and expert descriptions are collected from handbooks and then preprocessed to correct errors, remove redundancies, and enhance information. These preprocessed data form a golden dataset, from which a subset are used to train LLMs through hierarchical sampling. The fine-tuned LLM is then tested for automated phase diagram annotation. Results show that the fine-tuned model achieves a cosine similarity of 0.8737, improving phase diagram comprehension accuracy by 7% compared to untuned LLMs. To the best of our knowledge, this is the first paper to propose using LLMs for the automated annotation of phase diagrams, replacing traditional manual annotation methods and significantly enhancing efficiency and accuracy.

Liquid AlCoCrFeNi and AlCoCrFeNiX (X = Mo, Ta) high-entropy alloys on graphite: Wetting, reactivity and CALPHAD modelling

Wettability and interfacial reactivity with graphite of three equimolar High-Entropy Alloys (HEAs), namely AlCoCrFeNi (HEA-base), AlCoCrFeNiMo (HEA-Mo) and AlCoCrFeNiTa (HEA-Ta), were investigated for the first time, aiming to support industrial sectors involving liquid-phase processing routes. Isothermal high-temperature wettability tests were performed at 1400 °C for HEA-base and HEA-Mo, and at 1580 °C for HEA-Ta. The samples were then analysed by SEM-EDS. Based on the in-house-built GHEA thermodynamic database, CALPHAD calculations were used to simulate and discuss liquid-solid interactions occurring at high temperatures as well as transformations taking place in the samples during cooling. HEA-base wetted the graphite well after 5 min and the wetting behaviour significantly improved for HEA-Mo after the same contact time. HEA-Ta, after initial melting and wetting stage, solidified due to high-melting phases formation. All the graphite/HEA samples formed refractory carbides. For HEA-base and HEA-Mo, such carbides were found homogeneously dispersed in the whole drop. In HEA-Ta, TaC formed a compact layer separating two liquids of different compositions, with only one of these being in contact with the graphite substrate. The here proposed combination of experiments and thermodynamic calculations allowed to understand and discuss both high-temperature reactivity and evolution of the systems over cooling. Overall, a remarkable agreement between equilibrium calculations and experimental findings was observed for these complex dynamic systems.

The MOOSE fluid properties module

The Fluid Properties module within the Multiphysics Object-Oriented Simulation Environment (MOOSE) is used to compute fluid properties for numerous applications, ranging from nuclear reactor thermal hydraulics to geothermal energy. Those applications drove the development of the module to enable numerous different fluid equations of states, property lookups with primitive and conserved flow variable to cater to pressure and density-driven solvers, and an object-oriented design facilitating expansion and maintenance. Each fluid property is implemented in its own class but inherits capabilities such as automatic differentiation, automated out-of-bounds handling or variable conversion capabilities. This paper presents the module, its design, its user and developer interface, its content in terms of fluids and properties, and several of its applications showing its major role in the MOOSE simulation ecosystem. Program summaryProgram title: MOOSE Fluid Properties moduleCPC Library link to program files:https://doi.org/10.17632/cwzhsyp6pd.1Developer's repository link:https://github.com/idaholab/moose/tree/next/modules/fluid_propertiesLicensing provisions: LGPLProgramming language: C++, PythonNature of problem: The simulation of thermal hydraulics of advanced nuclear reactor systems, such as heat pipe micro-reactors or molten-salt cooled pebble bed reactors, requires a wide variety of discretizations of the fluid flow equations, from 1D thermal hydraulics to computational fluid dynamics at various levels of fidelity, with a wide variety of coolants. Applications are developed within the MOOSE C++ framework by Argonne and Idaho National Laboratories to simulate these reactors for research and design purposes. These applications (Sockeye, SAM, others) rely on MOOSE for the computation of fluid properties. The fluid properties module contains properties for most advanced nuclear reactor coolants, including an interface to the Molten Salt Thermodynamics Database (MSTDB) developed by Oak Ridge National Laboratory. Single phase, two phase, and gas mixtures fluid properties are computed by the module.Solution method: The fluid properties module includes numerous numerical methods to support the wide range of applications, notably forward automatic differentiation, conversion methods between pressure and density-driven variable sets, spline-based table lookups which are the current state of the art for the fast computation of fluid properties. The integration with MOOSE facilitates uncertainty quantification with regards to the fluid properties and optimization studies with regards to the fluid composition.

A new model framework of laser powder bed fusion by integrating a powder-scale model with a thermodynamic database

Laser powder bed fusion (LPBF) has been increasingly practised in powder-based additive manufacturing industries, yet the fundamentals including multiphase flow and phase change were not well understood. This work develops a powder-scale computational fluid dynamics-discrete element method-volume of fluid (CFD-DEM-VOF) model integrated with a temperature-dependent thermodynamic database to simulate the multiphase flow with phase change in the LPBF process. The integrated model is validated by comparing prediction results with the experimental measurements. Several LPBF cases with different laser powers, track numbers, and hatch distances are numerically studied. The simulation results demonstrate that the model can capture the key phenomena and key features in the LPBF process observed experimentally, including temperature distribution and morphology of molten tracks. The results also show the random configuration of the powders leads to the asymmetrical distribution of the temperature in the molten pool. The laser beam with a lower power density causes pore defects in the transition zone of the laser track because of partially melted particles, causing a rough molten surface. Incorporating an overlap between two molten tracks is crucial for enhancing the surface quality and mitigating issues such as discontinuity and particle adherence along the track edge. This model provides a cost-effective solution for comprehending and optimizing multiphase flow and phase change phenomena within the LPBF process in additive manufacturing.

Critical Evaluation and Thermodynamic Optimization of the Cr–P and Cr–Fe–P Systems

Existing thermodynamic descriptions of the whole Cr–Fe–P system are insufficiently accurate for understanding the thermodynamic behavior of the Cr–Fe–P materials during the manufacturing process. To construct a more precise and consistent thermodynamic database of the Cr–Fe–P system, thermodynamic modeling of the Cr–P and Cr–Fe–P systems was conducted using the CALculation of PHAse Diagrams (CALPHAD) approach based on critical evaluation of the experimental data. The modified quasichemical model and compound energy formalism were employed to describe the liquid and solid solutions, respectively. The Gibbs energies of stoichiometric compounds Cr3P(s), Cr2P(s), CrP(s), and CrP2(s) were carefully determined based on reliable experimental data. The ternary (Cr,Fe)3P, (Cr,Fe)2P, and (Cr,Fe)P phosphides were modeled as solid solutions considering mutual substitution between Cr and Fe atoms. In addition, the phase equilibria of BCC_A2 and FCC_A1 solutions and the liquid phase of the ternary Cr–Fe–P system were also optimized for more accurate descriptions of existing phase equilibria and thermodynamic properties data. As an application of the present database, the experimentally unexplored thermodynamic properties and phase diagrams of the Cr–Fe–P system are predicted.

Al-Fe-Si-Zr жүйесінің фазалық құрамын сапалық және санды есептеу

The calculation and optimization of the composition was carried out using the Thermo- Calc software product. The Thermo-Calc program generates state diagrams based on the dependence of chemical potentials on temperature. In the TTAL5 thermodynamic database of the Thermo-Calc program, the calculation of the effect of alloying elements contained in a solid solution of Al for alloys of the selected chemical composition was carried out. Taking into account the mixing energy, the minimum equation of free energy for all phases is solved. Here it is possible to obtain a suitable phase composition by forming the Al-Fe-Si-Zr phase in the concentration range of iron and Silicon 0.3-0.5% and 0.1-0.3%. Based on the calculated data, the validity of the calculated data regarding the use of scrap aluminum products as the main raw material for smelting heat-resistant conductive alloys of high strength has a positive effect on the economic component of the production process.

Analysis of the effect of citrate on radionuclide retention on portlandite

We analysed how citrate (CIT), a chelating agent potentially present in radioactive waste disposals, affects the mobility of four radionuclides (RN): 63Ni, 233U, 152Eu, 238Pu in portlandite, an important hydrated phase of cement, a commonly used material for waste isolation.Portlandite was synthetized in the laboratory and showed high purity and grain size of few μm. This solid, buffers the pH to 12.5 and shows high adsorption capability for the studied RNs: 152Eu and 238Pu exhibited the highest adsorption (Kd ∼1·105 mL g−1) and 233U the lowest (Kd ∼8·102 mL g−1). CIT adsorption was also experimentally evaluated by batch sorption experiments and electrophoretic (ζ-potential) measurements: a non-lineal sorption behaviour was observed, with Kd values decreasing (from ∼1·103 mL g−1) as CIT concentration increased up to 1·10−2 M, according to portlandite sorption sites saturation.In the presence of CIT, a marginal decrease for 233U adsorption in portlandite was observed, one order of magnitude reduction for 63Ni, while 238Pu and 152Eu adsorption decreased significantly. The calculated sorption reduction factors (SRF) for the four RN in the presence of CIT at a concentration of 5·10−3 M were: 2.4, 9.7, 37 and 50.9 for 233U, 63Ni, 238Pu, and 152Eu, respectively.According to the available thermodynamic databases, low complexation between CIT and RN is predicted at pH = 12.5, thus the RN adsorption decrease in the presence of CIT must be attributed to the organic adsorption on portlandite. However, current thermodynamic are still incomplete for this ligand and this pH range and this limits a precise interpretation of the experimental data.