Thermodynamic Database Research Articles

Phase equilibria in the low-TiO2 part of the CaO–MgO–SiO2–Al2O3–TiO2 system at a fixed MgO/CaO mass ratio of 0.2 and Al2O3/SiO2 mass ratio of 0.4

Adding titanium oxide has become a common practice in modern blast furnace operating procedures. The blast furnace slag is based on the CaO–MgO–Al2O3–SiO2–TiO2 low titanium slag system rather than CaO–MgO–Al2O3–SiO2 system. Phase equilibria in the CaO–SiO2–Al2O3–MgO–TiO2 system in the low-TiO2 part have been experimentally determined by means of high temperature equilibration and quenching technique followed by electron probe X-ray microanalysis. Introducing a small quantity of titanium-bearing materials can lower the liquidus temperature. The TiO2 content in the slag should be controlled below 4.6 wt%, otherwise it will enter the perovskite phase region where the liquidus temperatures increases rapidly. The compositions of the solid solutions corresponding to the liquidus have been precisely measured and should be utilized for developing the thermodynamic database.

Experimental investigation and thermodynamic modelling of WC-Fe-Ni-Co-Cr cemented carbides

This work investigates the effect of Cr addition into the FeCoNi binder phase of the cemented carbides (WC-FeCoNi) using experimental and computational techniques. Liquid phase formation temperatures and C contents of WC-Fe-Ni-Co-Cr alloys were used as experimental results. Based on this, a thermodynamic modelling was conducted on the W-C-Fe-Ni-Co-Cr system using the CALPHAD (CALculation of PHAse Diagrams) approach. Taking into account the experimental and theoretical results, it was shown that the error in the solidus and liquidus temperatures were lower in the database generated in this work in comparison to the commercial thermodynamic databases for steels and cemented carbides. Using the database developed in the present work, the experimental data can be well reproduced.In addition, the maximum solubility of Cr to avoid the formation of Cr-rich carbides was also deduced from this study.

Biosolid Gasification Performance Prediction Using a Stoichiometric Thermodynamic Model.

The gasification process can recover energy from biosolids produced in wastewater treatment. This paper developed a stoichiometric thermodynamic equilibrium model for biosolid gasification based on the biosolid properties, thermodynamic database, and equilibrium constants. If the calculation result showed that the quantity of char was negative, the quantity of char was put to zero, and the simulation was carried out again. The model was first verified by woody gasification under isothermal conditions, and the influence of a given temperature on biosolid gasification was simulated. The model further investigated the effects of different feedstock types, moisture contents, equivalence ratios, and reaction extensions on the adiabatic temperature, exergy efficiency, and syngas properties under autothermal conditions. The four factors were all the main factors for adiabatic temperature. The exergy efficiency depended more on the operation conditions than on the feedstock type. The H2 concentration of the dry syngas in biosolid gasification exhibited a curve both against the given temperature under isothermal conditions and against the moisture content under autothermal conditions.

Experimental Validation of Property Models and Databases for Computational Superalloy Design

Computational superalloy development is a powerful alternative to the conventional experimental approach. Based on thermodynamic databases and the CALPHAD method, it is possible to estimate the properties of a large number of potential alloys and select the most promising ones. However, the accuracy of the databases and complementary property models can be unsatisfying. The accuracy of two mass density and lattice parameter models and the TTNI8 and TCNI10 databases is analyzed in detail on the experimental basis of computationally optimized single‐crystalline superalloys. Various properties are measured and compared to the results of the property models and databases. Neither of the databases is superior to the other and especially the solvus temperature is not accurately described in both. The new mass density model, a linear regression based on the molar mass, is more reliable for low‐density alloys. Both lattice parameter model versions slightly overestimate the room‐temperature lattice parameter. The lattice parameter, however, is more accurately calculated using the new model version. The results of this study can be readily used to improve a multicriteria alloy optimization tool for computational superalloy design.

Experimental determination and thermodynamic reassessment of the Al–Cr–Ru ternary system

The isothermal sections at 950 °C and 1150 °C of Al–Cr–Ru ternary system were determined experimentally by equilibrium alloy method, combined with X-ray diffraction, scanning electron microscopy and energy-dispersive spectrometric. Nine and eight three-phase equilibria were confirmed at the 950 °C and 1150 °C isothermal sections of the Al–Cr–Ru ternary systems, respectively. The liquids surface projection of the Al–Cr–Ru ternary system was determined by identifying the microstructures of the as-cast alloys, and seven primary solidification regions were determined in the liquids surface projection. Besides, the ternary compound τ2 was identified as end-centered monoclinic structure by transmission electron diffraction analysis. The lattice parameters of the τ2 phase are a = 0.5175 nm, b = 1.7532 nm, c = 0.5150 nm and α = γ = 90°, β = 79.167°. Based on the available data of the Al–Cr–Ru ternary system and related binary systems, thermodynamic reassessment of the Al–Cr–Ru ternary system was performed using the Calculation of Phase Diagram approach. A new thermodynamic database for the Al–Cr–Ru ternary system was obtained, and the experimental data are consistent well with the calculated results.

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.

Effect of Nb and B on the Precipitation Behaviors in Al-Ti-Nb Balanced-Ratio Ni-Based Superalloy: A Phase-Field Study

In this paper, quantitative two-dimensional (2-D) phase-field simulations were performed to gain insight into the effects of B and Nb for Al-Ti-Nb balanced-ratio GH4742 alloys. The microstructure evolution during the precipitation process was simulated using the MICRESS (MICRostructure Evolution Simulation Software) package developed in the formalism of the multi-phase field model. The coupling to CALPHAD (CALculation of PHAse Diagram) thermodynamic databases was realized via the TQ interface. The morphological evolution, concentration distribution, and thermodynamic properties were extensively analyzed. It is indicated that a higher Nb content contributes to a faster precipitation rate and higher amounts and the smaller precipitate size of the γ′ phase, contributing to better mechanical properties. The segregation of the W element in γ′ precipitate due to its sluggish diffusion effect has also been observed. Higher temperatures and lower B contents accelerate the dissolution of boride and reduce the precipitation of borides. With the increased addition of B, the formation of borides may have a pinning effect on the grain boundary to hinder the kinetic process. In addition, borides are prone to precipitate around the interface rather than in the bulk phase. Once the M3B2 borides nucleate, they grow in the consumption of γ′ phases.

Quantitative Microstructure Prediction of Powder High-Temperature Alloy during Solution Heat Treatment and Its Validation

Heat treatment, particularly solution heat treatment, is a critical process in the preparation of powder metallurgy superalloys, where the cooling process significantly impacts the microstructure. This study, based on thermodynamic and kinetic databases as well as the precipitation mechanism of strengthening phases, delves into the influence of cooling process, especially the cooling path, on the material’s microstructure. The results indicate that under slow cooling rates, the precipitated phases are more likely to exhibit a multimodal size distribution, while under rapid cooling rates, a unimodal distribution may form. The average cooling rate does not consistently accurately reflect the growth of the precipitated phases; even with the same average cooling rate, different cooling paths can lead to significant differences in the size of the precipitates. To accurately predict the size of the precipitates, it is necessary to consider the specific cooling process. Constant cooling rate experiments designed for the study and the dissection testing of full-size turbine discs produced in manufacturing validated the calculated results of the precipitates. Therefore, optimizing cooling through simulation calculations can effectively and accurately control the precipitates, thereby obtaining a microstructure that can meet performance requirements.

Integrated experimental and thermodynamic modeling study of slag-matte-metal equilibrium in the Pb–Fe–O–S–Si-(Al, Ca, Zn) systems at 1100–1200 °C

Integrated experimental and thermodynamic modeling study was undertaken to characterize the effect of Al, Ca and Zn on the partitioning of elements between the slag, matte and metal phases in the Pb–Fe–O–S–Si-(Al), (-Ca), and (-Zn) systems in equilibrium with tridymite at 1100–1200 °C. The experimental methodology involved closed system equilibration in sealed ampoules, quenching and electron probe X-ray microanalysis (EPMA) of compositions of phases. FactSage thermodynamic database obtained by combining earlier assessments of sub-systems was used to plan the targeted experiments, and the results of new experiments were used to improve the thermodynamic database. Important effects were revealed for the conditions of the present study: CaO decreases the concentration of Pb and S in slag; Al2O3 has small effect on Pb in slag, but significantly decreases the concentration of S in slag; ZnO has small effect on Pb in slag, but increases the concentration of S in slag. These experimentally measured effects were reproduced by the model.

Thermodynamic properties and revised Helgeson-Kirkham-Flowers equations of state parameters of the hydrated and dehydrated monomeric silica species at t = 0.01–600oC, P = 1–3000 bars, ρH2O = 0.35–1.1 g cm−3, and Im= 0 m

The thermodynamic properties and revised Helgeson-Kirkham-Flowers equations of state (r-H-K-F EoS) parameters of the hydrated (Si(OH)4(aq), SiO(OH)3– and SiO2(OH)22−) and corresponding dehydrated (SiO2(aq), HSiO3− and SiO32−) monomeric silica species are important to describe the pH, composition, temperature, and pressure dependence of formation/breakdown reactions of all silicon-bearing compounds globally. Experimental log10 equilbrium constant, K values describing the formation reactions of these hydrated and dehydrated monomeric silica species were therefore compiled from the literature, extrapolated to zero ionic strength by specific ion interaction theory as required and used to derive their thermodynamic properties and r-H-K-F EoS parameters.Consideration of all formation reactions in the same study provides a collective, internally consistent update to the thermodynamic properties and r-H-K-F EoS parameters of the monomeric silica species that are able to provide satisfactory matches to the available experimental log10 K values at t = 0.01–600oC, P = 1–3000 bars, ρH2O = 0.35–1.1 g cm−3, and zero ionic strength. These temperature and pressure limits comfortably bracket t = 0.01–100oC and P = 1–270 bars relevant to the geological disposal of radioactive wastes at depths of up to 1 km.Updates to the thermodynamic properties of silicon-bearing compounds in all of the available geochemical thermodynamic databases are necessary, especially if reaction properties are used or given. Internal consistency between the hydrated and dehydrated species means that the hydrated species alone can be used as entries in geochemical thermodynamic databases.

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.

Thermodynamic Simulation Calculations of Phase Transformations in Low-Aluminum Zn-Al-Mg Coatings.

This study delves into the formation, transformation, and impact on coating performance of MgZn2 and Mg2Zn11 phases in low-aluminum Zn-Al-Mg alloy coatings, combining thermodynamic simulation calculations with experimental verification methods. A thermodynamic database for the Zn-Al-Mg ternary system was established using the CALPHAD method, and this alloy's non-equilibrium solidification process was simulated using the Scheil model to predict phase compositions under varying cooling rates and coating thicknesses. The simulation results suggest that the Mg2Zn11 phase might predominate in coatings under simulated production-line conditions. However, experimental results characterized using XRD phase analysis show that the MgZn2 phase is the main phase existing in actual coatings, highlighting the complexity of the non-equilibrium solidification process and the decisive effect of experimental conditions on the final phase composition. Further experiments confirmed that cooling rate and coating thickness significantly influence phase composition, with faster cooling and thinner coatings favoring the formation of the metastable phase MgZn2.

Measurement of Diffusion Coefficients and Assessment of Atomic Mobilities in HCP Mg-Ag-Sn Alloys

Reliable thermodynamic and kinetic databases are essential for designing and developing novel magnesium (Mg) alloys for elevated-temperature applications in the automotive and aerospace industries. This study investigated diffusion behaviors of HCP Mg-Ag-Sn alloys by four sets of three diffusion couples annealed at 450, 500, and 550 °C, respectively. Interdiffusion and impurity diffusion coefficients at the three annealing temperatures were extracted using the forward-simulation method. The determined diffusion coefficients, combined with prior results in the literature, were then used to assess atomic mobilities for the HCP phase of the Mg-Ag-Sn system. This assessment was conducted using the DICTRA and the TCMG5 thermodynamic database within the Thermo-Calc software. Comprehensive comparisons between calculated and experimental diffusion coefficients yielded an excellent agreement. The atomic mobilities were also further validated by appropriate predictions of concentration profiles and diffusion paths observed in independent diffusion couple experiments performed at 525 °C for 18 hrs. It has been found that the addition of Sn and Ag both increase the diffusivity of Ag in HCP Mg and Sn in HCP Mg in the stable temperature range of HCP Mg, respectively. This improved understanding of the kinetics in the Mg-Ag-Sn ternary system is essential for controlling diffusion-dependent properties such as coarsening and, therefore, the mechanical properties of Mg-Ag-Sn alloys at elevated temperatures.

L12 nanoparticle-strengthened CoNi-based superalloy with ultrahigh yield stress developed using CALPHAD method

In this study, a Co-30Ni-10Ti-2Ta-3Al (30Ni3Al) alloy with high γ′ phase dissolution temperature (1215°C), excellent mechanical properties, and low density (8.46 g/cm3) was developed based on the thermodynamic database of Co-based high-temperature alloys established by our group. Compositional design and microstructure control were achieved through the utilization of thermodynamic phase diagrams and phase fractions. It is found that the addition of 2 at.% Ta significantly improves the γ′ phase fraction and solvus while maintaining a suitable working window. However, a rafting trend of γ′ phase was observed as heat treatment for a long time at 750°C. By introducing 3 at.% Al and 30 at.% Ni into the optimized Co-10Ti-2Ta master alloy, the rafting of the γ′ phase was effectively suppressed. Benefiting from the fine, stable, high volume fraction γ′/γ microstructure, the 30Ni3Al alloy demonstrates compressive yield strengths of approximately 1487±7 MPa and 1319±13 MPa at room temperature and 600°C, respectively. The superb mechanical property at high temperatures can be attributed to the work-hardening effect resulting from the interactions of superattice stacking faults in γ′ phase.

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

Thermodynamic descriptions of the CaO–Al2O3 and CaO–Al2O3–SiO2 systems over the whole composition and temperature ranges

AbstractThe CaO–Al2O3–SiO2 system is a fundamental system in aluminosilicate materials, and its thermodynamic description provides key information for ceramic design, cement production, slag tapping, and geological prediction. However, the existing thermodynamic calculations for the CaO–Al2O3 system show inaccurate heats of formation for the compounds and consequently a decomposition of the CA2 (CaO⋅2Al2O3) phase at a low temperature. Besides, the solid solutions in anorthite and cristobalite have never been considered in the previous thermodynamic assessments for the CaO–Al2O3–SiO2 system. Therefore, thermodynamic reassessments of the CaO–Al2O3 and CaO–Al2O3–SiO2 systems are carried out in the present work using the CALculation of PHAse Diagram method, considering the solid solution in anorthite and cristobalite for the first time. The anorthite and cristobalite phases are modeled based on the individual mechanism of solid solution, with the anorthite described by (Ca+2, Va)1(Al+3, Si+4)2(Si+4)2(O−2)8 and the cristobalite described by (Va, Ca+2)1(Si+4, Al+3)2(O−2)4. The present assessment solves the above issues and provides consistent thermodynamic descriptions for the liquid and solid phases. Based on the established thermodynamic database, a Scheil solidification simulation is carried out for a cement clinker and the variations of mass fractions of the phases as well as the composition of liquid during Scheil cooling are calculated. The present work guides the design of relevant materials and lays an essential foundation for the establishment of the thermodynamic database of multicomponent aluminosilicate materials.

Thermodynamic modelling of alkali-silica reactions in blended cements

Experiments and field observations have shown that supplementary cementitious materials (SCMs) mitigate the risk of alkali-silica reaction (ASR) in Portland cement blends, but this is difficult to describe thermodynamically due to the lack of appropriate thermodynamic database information, and challenges in defining the kinetic factors. This paper examines how four well-known SCMs (namely ground granulated blast furnace slag, silica fume, metakaolin, and fly ash) mitigate ASR, by using a multi-stage simulation and a newly extended thermodynamic database. Calcium hydroxide consumption by SCM hydration, dilution of available alkalis, and alkali binding in calcium-alkali-aluminosilicate hydrate solid solutions, play pivotal roles in understanding the influence of SCMs in ASRs. Blending aluminium-rich SCMs in ASR-prone systems appears to act by preventing the dissolution of reactive silica in aggregates rather than by suppressing the formation of ASR products. This paper provides new thermodynamic insights into the mechanisms by which SCMs enhance concrete durability against ASR.

Combined experimental and CALPHAD investigation of equimolar AlCoCrFeNiX (X=Mo,Ta,W) High-Entropy Alloys

Aiming to evaluate the effect of refractory metal additions to a quinary AlCoCrFeNi High-Entropy Alloy (HEA), three novel equimolar AlCoCrFeNi-X (X = Mo, Ta, W) HEAs were designed, arc-melted, annealed, and characterized by SEM-EDS, XRD and microhardness measurements. CALPHAD thermodynamic calculations were exploited to design compositions and thermal treatments of the selected HEAs as well as to predict constitution and interpret microstructure of the samples. On the other hand, the experimental results contributed to the validation of the in-house built GHEA thermodynamic database (including the Al, Co, Cr, Fe, Ni, Mo, Ta, W elements) used for the calculations. No TCP intermetallic was found to form in the quinary AlCoCrFeNi alloy. However, the formation of σ, Laves-C14 and μ phases was observed in the samples containing Mo, Ta, and W, respectively, in agreement with the most accepted VEC-based phases stabilization criteria. The addition of the refractory metals led to a microhardness increase for all the investigated alloys. Overall, good agreement was observed between experiments and calculations, especially for compositional trends and phase amounts, allowing the database validation and supporting its applicability to phase equilibria simulation in the six-component HEAs belonging to the Al–Co–Cr–Fe–Ni-X (X = Mo, Ta, W) systems.

Development of a consistent geochemical model of the Mg(OH)2–MgCl2–H2O system from 25°C to 120°C

The formation of magnesium chloride-hydroxide salts (magnesium hydroxychlorides) has implications for many geochemical processes and technical applications. For this reason, a thermodynamic database for evaluating the Mg(OH)2–MgCl2–H2O ternary system from 0 °C–120 °C has been developed based on extensive experimental solubility data. Internally consistent sets of standard thermodynamic parameters (ΔGf°, ΔHf°, S°, and CP) were derived for several solid phases: 3 Mg(OH)2:MgCl2:8H2O, 9 Mg(OH)2:MgCl2:4H2O, 2 Mg(OH)2:MgCl2:4H2O, 2 Mg(OH)2:MgCl2: 2H2O(s), brucite (Mg(OH)2), bischofite (MgCl2:6H2O), and MgCl2:4H2O. First, estimated values for the thermodynamic parameters were derived using a component addition method. These parameters were combined with standard thermodynamic data for Mg2+(aq) consistent with CODATA (Cox et al., 1989) to generate temperature-dependent Gibbs energies for the dissolution reactions of the solid phases. These data, in combination with values for MgOH+(aq) updated to be consistent with Mg2+-CODATA, were used to compute equilibrium constants and incorporated into a Pitzer thermodynamic database for concentrated electrolyte solutions. Phase solubility diagrams were constructed as a function of temperature and magnesium chloride concentration for comparisons with available experimental data. To improve the fits to the experimental data, reaction equilibrium constants for the Mg-bearing mineral phases, the binary Pitzer parameters for the MgOH+ — Cl− interaction, and the temperature-dependent coefficients for those Pitzer parameters were constrained by experimental phase boundaries and to match phase solubilities. These parameter adjustments resulted in an updated set of standard thermodynamic data and associated temperature-dependent functions. The resulting database has direct applications to investigations of magnesia cement formation and leaching, chemical barrier interactions related to disposition of heat-generating nuclear waste, and evaluation of magnesium-rich salt and brine stabilities at elevated temperatures.

Thermodynamic Assessment of the P2O5-Na2O and P2O5-MgO Systems.

Knowledge about the thermodynamic equilibria of the P2O5-Na2O and P2O5-MgO systems is very important for controlling the phosphorus content of steel materials in the process of steelmaking dephosphorization. The phase equilibrium and thermodynamic data of the P2O5-Na2O and P2O5-MgO systems were critically evaluated and re-assessed by the CALPHAD (CAlculation of PHAse Diagram) approach. The liquid phase was described by the ionic two-sublattice model for the first time with the formulas (Na+1)P(O-2, PO3-1, PO4-3, PO5/2)Q and (Mg+2)P(O-2, PO3-1, PO4-3, PO5/2)Q, respectively, and the selection of the species constituting the liquid phase was based on the structure of the phosphate melts. A new and improved self-consistent set of thermodynamic parameters for the P2O5-Na2O and P2O5-MgO systems was finally obtained, and the calculated phase diagram and thermodynamic properties exhibited excellent agreement with the experimental data. The difference in the phase composition of invariant reactions from the experimentally determined values reported in the literature is less than 0.9 mol.%. The present thermodynamic modeling contributes to constructing a multicomponent oxide thermodynamic database in the process of steelmaking dephosphorization.