Development Of Thermodynamic Database Research Articles

Critical evaluation and thermodynamic assessment of the Al2O3–TiO2–CaO ternary system

Knowledge about the thermodynamic equilibria of the Al2O3–TiO2–CaO system is important for the design of refractory and ceramic materials. The Al2O3–TiO2, Al2O3–CaO and CaO–TiO2 binary systems were reoptimized and the Al2O3–TiO2–CaO ternary system was assessed by CALPHAD (CAlculation of PHAse Diagram) approach due to the reliability of phase diagram and thermodynamic property data. The liquid phase was described by the ionic two-sublattice model with the formula (Al+3,Ti+2,Ti+3,Ca+2)P(O−2,AlO1.5,Va,O,TiO2)Q. A set of self-consistent thermodynamic parameters for the Al2O3–TiO2–CaO ternary system was finally obtained, reproducing well the phase diagram and thermodynamic properties, predicting the Ca4Ti3O10 primary crystallization field. The present thermodynamic description is of interest for the design of refractory and ceramic materials as well as the development of thermodynamic databases for multicomponent aluminosilicate system.

Development of thermodynamic database of the Mn‐RE (RE = rare earth metals) binary systems

Development of thermodynamic database of the Mn‐RE (RE = rare earth metals) binary systems

Fundamental Issues Identified for Thermodynamic Description of Molten Salt Systems

Thermodynamic modeling of the molten salt systems is critical in the design of advanced nuclear power plants, materials recycling, and many other important clean energy applications. As one of the most capable computational thermodynamic approaches, the CALPHAD (Calculation of Phase Diagrams) method has been widely used for multicomponent thermodynamic database development and further support more physics-based modeling. Although considerable CALPHAD modeling efforts for molten salt systems have been made, we found that no evaluation has been performed regarding the unary thermodynamic models for the molten salt systems despite the fact that more than one pure substance database is available for the CALPHAD modeling. Therefore, the thermodynamic descriptions of the pure salts should be critically evaluated to ensure a high-fidelity molten salt thermodynamic database. In this work, we comprehensively analyzed some selected molten salts using different available thermodynamic descriptions from two databases as an example. One is the SSUB database released by the SGTE (Scientific Group Thermodata Europe), and the other is the FactPS database from the FactSage. The significant discrepancies observed in the thermodynamic description between the existing CALPHAD pure substance databases and experiments call for an urgent effort to improve.

Critical Evaluation and Thermodynamic Optimization of the Cu-Zn, Cu-Se and Zn-Se Binary Systems

In our study, a complete review of the literature, critical evaluation and thermodynamic assessment of the Cu-Zn, Cu-Se and Zn-Se binary systems were carried out. The modified quasi-chemical model (MQM) was applied to describe the Gibbs energy of the liquid phase. The Gibbs energies of all intermetallic compounds and terminal solid solutions were described using the compound energy formalism (CEF) model. The re-optimization of the Cu-Zn binary system was carried out by considering the ordered bcc_B2 crystal structure of the β’ phase. Moreover, the β and δ phases in the Cu-Zn binary system with the same bcc_A2 crystal structure were modeled as one single phase in the present work. A self-consistent thermodynamic database was constructed for the Cu-Zn, Cu-Se and Zn-Se binary systems, work that formed part of a comprehensive thermodynamic database development project researching zinc-based biodegradable materials.

Development of accurate chemical thermodynamic database for geochemical storage of nuclear waste. Part III: Models for predicting solution properties and solid-liquid equilibrium in cesium binary and mixed systems

The models described in this study are of high importance in the development of thermodynamic database needed for nuclear waste geochemical storage as well as for technology for extracting cesium resources from saline waters. In this study we developed new not concentration restricted thermodynamic models for solution behavior and solid-liquid equilibrium in CsF-H2O CsOH-H2O and Cs2SO4-H2O systems at 25 °C. To parameterize models we used all available experimental osmotic coefficients data for whole concentration range of solutions and up to saturation point. The new models are developed on the basis of Pitzer ion interactions approach. The predictions of new developed here models are in excellent agreement with experimental osmotic coefficients data (ϕ) in binary solutions from low to extremely high concentration (up to 21.8 mol.kg-1 for CsOH-H2O and up to 35.6 mol.kg-1 for CsF-H2O). The previously developed by Christov by Christov and co-authors and by other authors Pitzer approach based thermodynamic models for five (5) cesium binary systems (CsCl-H2O CsBr- H2O CsI-H2O CsNO3-H2O and Cs2SeO4- H2O) are tested by comparison with experimental osmotic coefficients data and with recommendations on activity coefficients (γ±) in binary solutions. The models which give the best agreement with (ϕ)- and (γ±) -data from low to high concentration up to m(sat) are accepted as correct models which can be used for solubility calculations in binary and mixed systems and determination of thermodynamic properties of precipitating cesium solid phases. The thermodynamic solubility products (ln Kosp) and the Deliquescence Relative Humidity (DRH) of solid phases precipitating from saturated cesium binary solutions (CsF(cr) CsCl(cr) CsBr(cr) CsI(cr) CsOH(cr) CsNO3(cr) Cs2SO4(cr) and Cs2SeO4(cr)) have been determined on the basis of evaluated and accepted binary parameters and using experimental solubility data. The reported mixing parameters [θ(Cs M2+) and ψ(Cs M2+ X)] evaluated by solubility approach for 15 cesium mixed ternary systems (CsCl-MgCl2-H2O CsBr-MgBr2-H2O CsCl-NiCl2-H2O CsBr-NiBr2-H2O CsCl-MnCl2-H2O CsCl-CoCl2-H2O CsCl-CuCl2-H2O CsCl-CsBr-H2O CsCl-RbCl-H2O Cs2SO4-CoSO4-H2O Cs2SeO4-CoSeO4-H2O Cs2SO4-NiSO4-H2O Cs2SeO4-NiSeO4-H2O Cs2SO4-ZnSO4-H2O and Cs2SeO4-ZnSeO4-H2O) are tabulated.

Thermodynamic modeling of the Al-Co-Cr-Fe-Ni high entropy alloys supported by key experiments

Al-Co-Cr-Fe-Ni alloys have been modeled by computational thermodynamics according to the CALPHAD approach using literature data and results of a few key experiments performed in this work. As a result, an Al-Co-Cr-Fe-Ni thermodynamic database has been developed, based on the thermodynamic assessments of all the binary and ternary subsystems and the addition of a few quaternary interaction parameters. The assessment was supported by ESPEI (Extensible Self-optimizing Phase Equilibria Infrastructure), a tool for thermodynamic database development within the CALPHAD method. Computed phase equilibria in the quinary system are in good agreement with experimental data from the literature and the present experiments.

A comparative study of two-phase equilibria modeling tools: MORB equilibrium states at variable pressure and H2O concentrations

AbstractPhase equilibria modeling is a powerful petrological tool to address both forward and inverse geological problems over a broad range of crustal and upper mantle conditions of pressure (P), temperature (T), composition (X), and redox (fO2). The development of thermodynamic databases, relatively realistic activity−composition (a−X) relations for solids, melts and fluids, pressure-volume-temperature (PVT) equations of state (EOS), and efficient numerical algorithms represent an inflection point in our ability to understand the nexus between tectonics and petrogenesis. While developed—and typically applied in isolation—by either metamorphic or igneous petrologists, some of the published thermodynamic models have overlapping P-T-X calibration ranges, which enables comparisons of model outcomes for similar conditions within the range of applicability. In this paper, we systematically compare the results of two such models that are routinely used for calculating phase equilibria in melt-bearing systems: rhyolite-MELTS (Gualda et al. 2012; Ghiorso and Gualda 2015) and the metabasite set of Green et al. (2016) using the thermodynamic database ds62 (Holland and Powell 2011) (hereafter denoted as “HPx-mb16”). We selected a N-MORB composition and modeled closed system equilibrium phase relations as a function of temperature at 0.25 and 1 GPa for N-MORB with 0.5 and 4 wt% H2O. Our results show that phase relations exhibit some key differences that, in some instances, impact geological inferences. For example, clinopyroxene and plagioclase stabilities are expanded to higher temperatures in HPx-mb16 compared to predictions from rhyolite-MELTS. Orthopyroxene and olivine are stable in greater proportions and at wider temperature ranges in rhyolite-MELTS compared to HPx-mb16. Importantly, HPx-mb16 predicts amphibole in all runs presented here, whereas amphibole is only predicted at high-P–high-H2O (1 GPa and 4 wt% H2O) in rhyolite-MELTS, and in lesser amounts. Garnet stability is systematically expanded at higher temperatures, and the proportion is greater in rhyolite-MELTS. In addition to phase assemblage differences, phase compositions may differ. For example, plagioclase anorthite content is systematically higher in HPx-mb16 (for the same set of conditions), whereas garnet Mg# is higher in rhyolite-MELTS. Calculated amphibole compositions are substantially different between the two models as well. Liquid compositions also show important differences. High-T liquids are generally similar in SiO2 contents but diverge at lower temperatures; in these cases, HPx-mb16 liquids are SiO2-depleted compared to those produced by rhyolite-MELTS. Liquids are also systematically and substantially more mafic in HPx-mb16, and alumina and the alkali concentrations are relatively different and show different trends as a function of temperature at constant pressure. Overall, liquid compositions show the greatest differences near the solidus. Differences in modal abundances of phases and liquid compositions influence liquid trace-element signatures, and these differences can affect geological interpretations. Finally, a comparison between melting experiments of basaltic bulk composition and both thermodynamic models shows that rhyolite-MELTS better reproduces the higher temperature experiments, whereas HPx-mb16 better reproduces the lower temperature experiments. We discuss these and other similarities and differences to highlight the strengths and limitations of each model and to recognize that modeling results have important implications for interpretations of geologic processes. We recognize that our results are informed by a small subset of calculations over a limited range of conditions—but encourage further comparisons over a wider range of conditions and compositions.

Thermodynamically Informed Nuclear Fuel Codes—A Review and Perspectives

A number of codes are used to predict various aspects of nuclear fuel performance and safety, ranging from conventional fuel performance codes to simulate normal operating conditions to integral engineering codes to simulate severe accident behaviour. There has been a number of reportings in the open literature of nuclear fuel codes being informed by thermodynamic calculations, ranging from the use of simple thermodynamic correlations to direct coupling of equilibrium thermodynamic software. Progress in expanding predictive capabilities have been reported, which also includes advances in thermodynamic database development to better capture irradiated fuel. However, this progress has been accompanied by several challenges, including effective coupling of different types of physical phenomena in a practical manner and doing so with a reasonable increase in computational expense. This review paper will summarize previous experiences reported in the open literature in coupling thermodynamic calculations with nuclear fuel codes and applications, identify current challenges and limitations, and offer some perspectives for the community to consider moving forward.

CALPHAD: Method for calculation of finite temperature thermodynamic properties for magnetic allotropes—Case study on Fe, Co and Ni

A method for calculation of finite temperature thermodynamic properties for magnetic allotropes has been developed. The developed method is based on quasi-harmonic approximations using the Debye–Grüneisen model. Electronic contributions are included and magnetic disordering contributions are added with the empiric model often used in CALPHAD (CALculation of PHAse Diagrams) databases. The developed method also includes two new ways to estimate the Debye temperature (θD(V0)) which enables calculation of finite temperature thermodynamic properties also for allotropes that are dynamically unstable at 0 K. Also a new CALPHAD approach for estimation of Curie- (TC) or Néel- (TN) temperatures is presented. The developed method was used to calculate Gibbs energy as a function of temperature (G(T)) and isobaric heat capacity as a function of temperature (CP(T)) for the body-centred-cubic (bcc), the face-centred-cubic (fcc) and the hexagonal-closed-packed (hcp) allotropes of Fe, Co and Ni. The results were compared with the SGTE Unary database. By using the developed method the phase transitions in Fe and Co were predicted. The calculations of the metastable allotropes fcc-Fe, hcp-Fe and bcc-Ni in this work indicates that the descriptions of these allotropes in the SGTE Unary database need to be updated, especially regarding the magnetic parameters. Furthermore, contradictory to previously reported results in literature, the calculations in this work show that the magnetic ground state structure of fcc-Fe is the double layer antiferromagnetic structure (AFM-D) and not a spin-spiral. The final conclusion is that by using the developed method it is possible to calculate finite temperature thermodynamic properties, not only, for stable and metastable magnetic allotropes, but also for magnetic allotropes that are dynamically unstable at 0 K, which is very important for the development of thermodynamic databases.

Thermodynamic modeling of the Al–Nb–V system

In the present work, the Al–Nb–V ternary system was thermodynamically modeled using the compound energy formalism (CEF) within the framework of the CALPHAD method and supported by ab initio calculations, which we report here for the first time. The thermodynamic descriptions of the Al–Nb, Al–V and Nb–V binary systems were taken from literature. Since it is not clear which is the best Al–V assessment available in the literature, three sets of thermodynamic parameters with three different thermodynamic descriptions of the Al–V system are proposed. End-member energies of Nb3Al and Nb2Al were obtained from first-principles electronic-structure calculations following the density functional theory (DFT). The optimized ternary parameters were based on experimental isothermal sections and liquidus projections data. The three sets of thermodynamic parameters show good agreement with experimental data. The new assessments successfully describe the miscibility gap between NbAl3 and VAl3 close to the Al–Nb system, the V solubility in Nb3Al, the tie-triangles Nb2Al-NbAl3-BCC and NbAl3-BCC-V5Al8, and the tie-lines between Nb3Al and BCC. In this sense, our work provides self-consistent thermodynamic descriptions of the Al–Nb–V system which can be used for the development of thermodynamic databases of higher order systems for refractory high-entropy alloys (RHEAs).

Correction to: Thermodynamic Database Development for the ZrO2-MgO-MnOx System

Correction to: Thermodynamic Database Development for the ZrO2-MgO-MnOx System

Erratum to: ESPEI for efficient thermodynamic database development, modification, and uncertainty quantification: application to Cu–Mg—CORRIGENDUM

In regards to the original publication of this article[1], the authors would like to correct the following: the opening sentence of the caption for Figure 5a should read “Corner plot (a) of the parameters in the liquid phase.”

Computational Thermodynamic Calculations: FactSage from CALPHAD Thermodynamic Database to Virtual Process Simulation

The CALPHAD-type computational thermodynamic databases have been developed since 1970. Several commercial computational thermodynamic software equipped with comprehensive and accurate thermodynamic databases and fast Gibbs energy minimization routine are widely used in the design of new materials and the optimization of materials processing. In this study, the FactSage software, which is the most frequently accessed software in high temperature materials processing, is briefly overviewed. The current databases and on-going directions of the thermodynamic database development are discussed. Application examples of FactSage thermodynamics databases to steel processing from the iron ore sintering process to the final metallic coating process are presented. Lastly, the most recent and future application of the FactSage thermodynamic databases to virtual steelmaking process simulations for the so-called industry 4.0 (smart factory) is highlighted.

Experimental Study of High Temperature Phase Equilibria in the Iron-Rich Part of the Fe-P and Fe-C-P Systems

During the solidification of steel, phosphorus strongly segregates in the interdendritic liquid phase. In the continuous casting process, even low levels of P may have a detrimental effect on the final product quality. However, phosphorus is partly added up to 0.10 wt pct to improve the mechanical properties of advanced steel grades nowadays, e.g., High-Strength Interstitial-Free (HSIF). To provide new experimental data for the development of thermodynamic databases and solidification models for P alloyed steel grades, phase equilibria in the Fe-P and Fe-C-P key systems were studied up to 1550 °C using differential scanning calorimetry (DSC) and high temperature laser scanning confocal microscopy (HT-LSCM). Special focus was placed on solid/liquid equilibrium temperatures in the Fe-rich part of the binary Fe-P system between 0.025 and 9 wt pct P. In the ternary system, three isoplethal sections with 0.10 mass pct. P, 0.20 mass pct. C and constant mass percent ratio P/C of 2 were investigated. In the latter section, HT-LSCM observations were linked with DSC signals to optically identify present phase stabilities. Particularly at [pct P] < 1, significant differences between performed measurements and calculated phase equilibrium temperatures using thermodynamic assessments from the literature were identified. In all ternary sections, the experiments indicate less influence of P on the hypo-peritectic range compared to the thermodynamic calculations.

Development of Thermodynamic Database for Performance Assessment of Geological Disposal of High-level Radioactive Waste and TRU Waste

高レベル放射性廃棄物や地層処分相当TRU廃棄物などの地層処分システムの性能を評価することを目的として，廃棄体が地下水に接触したあとの放射性核種の溶解および錯生成挙動を評価するために使用する熱力学データベース(TDB)が国内外で整備されている。本報告では，経済協力開発機構原子力機関(OECD/NEA)が実施している国際プロジェクトを中心に，わが国および欧米各国で整備されているTDBを概説する。

Experimental Study and Thermodynamic Calculations of the Distribution of Ag, Au, Bi, and Zn Between Pb Metal and Pb–Fe–O–Si slag

The present article continues the series reviewing the thermochemistry of complex multicomponent pyrometallurgical systems. The recovery of multiple metals through the Pb-based primary and recycling processes is an economic driving force for the circular economy of the future. In this study, equilibrium distributions of Ag, Au, Bi, and Zn between PbO–FeO–Fe2O3–SiO2 silica saturated slag and Pb metal phases were investigated experimentally, using high-temperature equilibration followed by rapid quenching. The measurement of phase compositions was done using microanalytical methods. Electron Probe X-ray Microanalysis (EPMA) was applied for those elements which present at relatively high concentrations. The Laser Ablation Inductively Coupled Plasma Mass Spectrometry (LA-ICP-MS) was used to measure very low concentrations of Ag and Au in slag. The starting mixtures of materials were planned using FactSage software and preliminary thermodynamic database to target specific proportions of phases and concentrations of Pb in slag after the achievement of equilibrium. Measured slag/metal distribution coefficients follow the sequence Zn ≫ Ag > Bi ≫ Au. Newly obtained results were critically assessed and used to improve the thermodynamic database. Integration between experiments and thermodynamic database development permits cross-analysis of distribution coefficients obtained in the present study with the parallel measurements of distribution in copper-based systems. The liquid slag phase was described using a two-sublattice Modified Quasichemical Model (MQM). Single sublattice MQM was applied for the liquid metal phase.

ESPEI for efficient thermodynamic database development, modification, and uncertainty quantification: application to Cu–Mg

Abstract

Comprehensive analysis of thermodynamic properties of calcium nitrate

Thermodynamic properties of calcium nitrate are of interest for development of thermodynamic databases, which can be applicable for thermal energy storage technologies. In the present work thermodynamic properties of Ca(NO3)2, i.e. heat capacity (Cp) and enthalpy of fusion, were determined experimentally. The enthalpy of fusion of Ca(NO3)2 (33.4 ± 1 kJ/mol) was measured in a closed Pt-crucible at the melting temperature 823 K for the first time. The heat capacity of Ca(NO3)2 was measured in the temperature range from 143 K to 723 K by three different differential scanning calorimeters. High temperature X-ray diffraction was used for determination of the temperature dependence of volume from 298 K to 723 K. Combination of heat capacity and volume allowed us to calculate the molar volume at 0 K and to obtain the thermal expansion. The Grüneisen parameter and bulk modulus were deduced from combination of the available ab initio values of Cv and the values of Cp as well as the thermal expansion obtained in this work. This methodology allowed us to perform a comprehensive analysis of experimental values and first principal calculations. A complete thermodynamic dataset for solid and liquid Ca(NO3)2 has been derived.

Distributions of Ag, Bi, and Sb as Minor Elements between Iron-Silicate Slag and Copper in Equilibrium with Tridymite in the Cu-Fe-O-Si System at T = 1250 °C and 1300 °C (1523 K and 1573 K)

New experimental data on the distributions of silver (Ag), bismuth (Bi), and antimony (Sb) between liquid iron-silicate slag and liquid copper metal in equilibrium with tridymite in the Cu-Fe-O-Si system at T = 1250 °C and 1300 °C (1523 K and 1573 K) have been obtained. The experimental methodology involved high-temperature equilibration, rapid quenching of the equilibrated phases, followed by direct measurement of the equilibrium phases with electron probe X-ray microanalysis (EPMA) for measurement of major element concentrations and laser ablation inductively coupled plasma mass spectrometry (LAICPMS) for the measurement of minor element concentrations. The 4-point test approach was employed to confirm the achievement of chemical equilibrium in the current study. Open-system equilibration on quartz substrates in controlled gas atmospheres (CO/CO2/Ar) and closed-system equilibration in sealed quartz ampoules were used. The new experimental data resolve significant discrepancies found in previous studies and can be used as input for the development of thermodynamic databases for copper-making processes.

Development of thermodynamic databases in the system U–Zr–Ce–Cs–Fe–B–C–I–O–H for application to simulating phase equilibria in severe nuclear accidents

ABSTRACTIn case of severe nuclear accidents involving melt down of nuclear fuels at high temperatures, it is of considerable importance to accurately evaluate the highly-volatizing behavior of fission products (FPs) over multicomponent debris. Particularly, cesium (Cs)- and iodine (I)- bearing chemical species are regarded as notable FPs. In the present work, the authors have generated original thermodynamic databases for the system U–Zr–Ce–Cs–Fe–B–C–I–O–H featuring Cs- as well as I-bearing subsystems, which are contained in oxide, iodide, and metal (including borides and carbides) sub-databases. It has been confirmed that the phase diagrams calculated by the present set of the databases reproduce the corresponding literature data well in various kinds of subsystems of the above multicomponent system. The present set of databases has subsequently been applied to simulate phase equilibria and volatizing behavior of Cs- and I-including species, respectively, in multicomponent debris under specific temperature and atmospheric conditions corresponding to severe nuclear accidents.