Thermodynamic Calculation Of Phase Equilibria Research Articles

The pH value influence on the waylandite-structured BiAl3(PO4)2(OH)6 compound formation under hydrothermal conditions

The present work has found that the rate of the waylandite-structured BiAl3(PO4)2(OH)6 compound formation under conditions of hydrothermal treatment at 200 °C of a suspension obtained at 25 °C as a result of the nanocrystalline hexagonal BiPO4 and the amorphous phase precipitation, increases in the 5 – 9 pH range specified for this water-salt suspension. The rate of this compound formation decreases under conditions of isothermal exposure of the initial suspension with pH 11. This is due to the increased solubility under these conditions of the amorphous phase, predominantly consisting of aluminum hydroxide. Thermodynamic calculation of phase equilibria at 200 °C in the BiAl3(PO4)2(OH)6-BiPO4-Al(OH)3-H2O(HNO3, NaOH) system showed that the BiAl3(PO4)2(OH)6 compound, resulting from the water-salt suspension treatment, is stable in the 4.2–11.7 pH range specified for this suspension. It was experimentally established that this compound is not formed under conditions of hydrothermal treatment of the suspension with the specified pH 3. This is consistent with the calculation results and is explained by the increased stability of nanocrystalline BiPO4 under these conditions.

Experimental determination and thermodynamic calculation of phase equilibria in Ag-Zr-Y system

The phase equilibria of the Ag-Zr-Y system at 800, 600 and 500 °C were investigated by means of X-ray diffraction (XRD) and scanning electron microscope (SEM) with energy dispersive X-ray spectrometry (EDS) techniques. The solubilities of Y in the Ag2Zr and AgZr phases and of Zr in the Ag51Y14, Ag2Y and AgY phases were measured, and no ternary compound was found in these isothermal sections. By means of the CALPHAD method, thermodynamic parameters of the Ag-Zr-Y system were assessed based on the experimental data from the present work and the literature. Substitutional solution model was used to describe the solution phases and sublattice models were used to describe binary compounds. A set of self-consistent and accurately described thermodynamic parameters of the Ag-Zr-Y system were obtained. The representative isothermal sections and liquidus projection were calculated, and the Hill reaction scheme of the Ag-Zr-Y system was constructed. The calculated results are in agreement with the experimental data.

Experimental investigation and thermodynamic calculation of phase equilibria in the ternary Fe-Si-Ta system

Two isothermal sections of the Fe-Si-Ta ternary system at 1100 °C and 900 °C in the whole composition range have been experimentally determined combined with EPMA and XRD techniques. Except for these known ternary G, E, and V phases, a new ternary compound named X was detected with the composition region about 27.1–29.9 at% Fe, 30.6–31.7 at% Ta and 39.5–41.2 at% Si. Si has an extensive solubility in the Fe2Ta phase, and the solubility of Fe in the Ta2Si phase tends to be parallel to the Fe-Si side. Based on the experimental results in this work, the Fe-Si-Ta ternary system has been assessed using the CALPHAD method. A set of reliable thermodynamic parameters for the Fe-Si-Ta system was obtained. The current thermodynamic description is in good agreement with available experimental data. The calculated liquidus projection and invariant reaction scheme in the Fe-Si-Ta ternary system were presented. The present work can provide essential experimental and thermodynamic data for the establishment of the G-phase strengthen alloy database.

Thermodynamic calculation of phase equilibria in the Al–Fe–Zn–O system

Abstract The thermodynamics of the phase equilibria in the Al–Fe–Zn–O quaternary system was studied using the calculation of phase diagrams method to understand the oxidation behavior of the Zn bath surface during galvanizing process. The thermodynamic parameters for the Gibbs energies of the different constituent phases in the binary and ternary systems relevant to this quaternary system were taken mainly from previous studies. In this study, the thermodynamic assessment of the Al2O3–ZnO system was carried out based on the available experimental data, and some modifications to the thermodynamic model and/or parameters for the Fe–Zn–O ternary system were made to maintain consistency with the thermodynamic descriptions of other binary and ternary systems, making up the Al–Fe–Zn–O quaternary system adopted in this study. The calculated results on the ternary and quaternary systems generally agreed with the available experimental results on phase equilibria. The set of thermodynamic parameters enabled us to calculate the phase equilibria in the Al–Fe–Zn–O quaternary system over the entire composition and temperature ranges.

Thermodynamic description and electrical conductivity of the Ge-In-Zn system: Experiments and modeling

The ternary Ge-In-Zn system is chosen for the study due to the importance of germanium-based alloys in the industry of electronic devices and their special application as memory materials. This ternary system has not been explored so far. In the current work, experimental techniques such as differential thermal analysis (DTA), scanning electron microscopy (SEM) with energy dispersive spectrometry (EDS), X-ray powder diffraction (XRD)and electrical conductivity tests were used for characterization of the prepared ternary Ge-In-Zn alloys. Investigated alloys were from four isothermal sections at 25, 100, 200 and 300 °C and three vertical sections Ge-InZn, In-GeZn, Zn-GeIn. The obtained results were compared with the results of thermodynamic calculation of phase equilibria based on the Calphad method. The calculation was performed by using thermodynamic parameters for constitutive binary systems. Good agreements between calculated phase diagrams and experimental data have been obtained without introducing ternary thermodynamic parameters. Based on that, calculations of liquidus projection and invariant reactions were performed.

Thermodynamic calculation of phase equilibria of rare earth metals with boron binary systems

Abstract In order to develop novel materials based on rare earth (RE) boride and/or transition metals, phase equilibria and thermodynamic information of the RE–B based alloys are indispensable. On the basis of experimental phase equilibria and thermodynamic properties, thermodynamic assessments of the RE–B (RE = La, Sm, Gd and Tb) binary systems were carried out by the CALPHAD (Calculation of Phase Diagram) method. Self-consistent parameters of the RE–B (RE = La, Sm, Gd and Tb) binary systems were obtained, which can be used to reproduce well the experimental data. Furthermore, in combination with the previous assessments of the RE–B binary systems in the literature, phase equilibria and thermodynamic properties of the RE–B (RE = La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm and Lu) binary systems are discussed systematically. The tendency of phase equilibria and thermodynamic information as a function of RE atomic number is demonstrated. In general, the enthalpy of mixing of liquid RE–B alloys and the enthalpy of formation of the RE–B intermetallic compounds become more and more negative with the increase in RE atomic number (except for La, Ce, Pr and Nd), while the phase transition temperatures for the RE–B intermetallic compounds increase gradually.

Structure and Properties of TiAl-Based Alloys Doped with 2 at.% Mo

Arc-melted Ti100–xMo2Alx alloys (where x is 44, 46, 48, and 50 at.% Al) that were produced from pure components were examined by X-ray diffraction and scanning electron microscopy with electron microprobe analysis (SEM/EDX). The melting points and solid-phase transformations were studied by differential thermal analysis (DTA) and the mechanical properties by fracture toughness, bending, and compression tests. The CALPHAD approach was used for thermodynamic calculation of phase equilibria in the composition region under study. The cast alloys mainly consist of a lamellar structure formed by lamellas of γ-TiAl and α2-Ti3Al phases with submicron thickness and a cubic Ti55Mo4–6Al39–40 phase of A2 type (β) or B2 type (β0). In the γ-TiAl-based alloys, molybdenum behaves as a low-melting dopant, enriching the grain periphery. The standard mechanical characteristics of the alloys were determined and their structural sensitivity was analyzed. All studied alloys demonstrate excellent high-temperature strength. The yield stress is 400–600 MPa in the temperature range 20–750°C. The strength slightly increases at 300 and 600°C under dynamic strain ageing. The strain hardening parameters were established over a wide range of test temperatures. The temperature dependence of the strain hardening coefficient and strain hardening index was analyzed for alloys in different phase and structural states. In the temperature range from 20 to 600°C, the strain hardening index and coefficient were found to vary slightly. The strain hardening index increased from n = 0.6 to n = 0.95 with aluminum content changing from 44 to 50 at.%, which indicates that the strain hardening mechanism changes with variation in the alloy phase constituents.

Thermodynamic calculation of phase equilibria in the Bi–Mg–Zn ternary system

AbstractOn the basis of the experimental phase equilibria of the Bi–Mg–Zn ternary system, the thermodynamic assessment of the Bi–Mg–Zn ternary system was carried out by means of the CALPHAD (CALculation of PHAse Diagram) technique. The Gibbs free energies of the solid solution phases (Rhombohedral_A7, Hcp_A3 and Hcp_Zn) were described by the substitutional solution model, and that of the liquid phase was described by the associate model with the constituent species Bi, Bi2Mg3, Mg and Zn. The non-stoichiometric compound, α-Bi2Mg3 as well as its high temperature allotrope β-Bi2Mg3 were described by the sublattice models, (Bi,Zn,Va)2(Mg,Zn)3 and (Bi,Zn)1(Bi,Zn,Va)3(Mg,Zn)6, respectively. In order to obtain a set of self-consistent thermodynamic data, the thermodynamic parameters of the phases, including liquid, α-Bi2Mg3 and β-Bi2Mg3, of the Bi–Mg–Zn ternary system were optimized while the thermodynamic data of other phases were adopted directly from the literature reports of the constituent binary systems. With this newly developed thermodynamic database, the CALPHAD results can well reproduce the experimental phase diagram information of the Bi–Mg–Zn ternary system. The solidification processes of a typical Bi–Mg–Zn alloy are calculated and analyzed using the phase equilibrium approach and the Gulliver–Scheil model in comparison with the experimental investigation.

High-throughput thermodynamic calculations of phase equilibria in solidified 6016 Al-alloys

In the present work, high-throughput calculation (HTC) method is performed to obtain the phase equilibria of solidified 6016 Al-alloys. The calculations of primary phase fraction, precipitates fraction and phase composition are realized based on the Scheil-Gulliver solidification model of Thermo-Calc software, and the entire composition ranges of standard 6016 Al-alloy is taken into account. A Python-based program called Automatic Execution and Extraction Tasks (AEET) is developed, it automatically generate the commands of calculations, execute the Thermo-Calc software and then extract the key data of output files. The obtained results are listed in an Excel file, which is convenient for the subsequent visualization analysis and machine learning. Several criteria are combined to filter the appropriate compositions of industrial 6016 Al-alloys, providing a valuable guidance to the experimentalists and avoiding unnecessary trial-and-error tests. This HTC approach is not limited to the solidification modelings; it can be extended to any kinds of thermodynamic and kinetic calculations.

A revised petrological model for subducted oceanic crust: Insights from phase equilibrium modelling

AbstractMany geological and geodynamical studies of metamorphism in subduction zones have relied upon worldwide compilations of modelled slab‐top pressure–temperature (P–T) conditions, although recent evaluation of such data sets suggests that these predictions are ~100–300°C colder at any given pressure than the conditions recorded by exhumed metamorphic rocks. As such, geochemical, petrological and geophysical interpretations formulated using such ‘cold’ assumptions may be subject to error and uncertainty. Here, we apply thermodynamic phase equilibrium calculations to forward‐model how phase assemblages, the P–T conditions of key devolatilization reactions and the effect of densification with depth vary for typical mid‐ocean ridge basalt (MORB) along these newly defined ‘hotter’ subduction zone geotherms for cold, warm and average environments. The depth and extent of devolatilization of MORB is strongly dependent on the geotherm along which the oceanic crust subducts. At the onset of subduction along a warm geotherm, metabasites contain ~3 wt% H2O and release ~45% of this fluid in a single pulse at ~20 km, correlating with chlorite and epidote breakdown. Below these depths, metamorphosed MORB will dehydrate incrementally due to gradual amphibole breakdown, becoming almost completely dehydrated at ~70 km. Oceanic crust subducting along an average geotherm will contain ~3.5 wt% of H2O at the onset of subduction and will release ~40% of the bulk‐rock H2O in two fluid pluses occurring at ~30 and 50 km, correlating with chlorite breakdown. Below these depths, gradual dehydration of ~50% of the bulk‐rock H2O due to amphibole breakdown leads to near‐complete dehydration at ~80 km. By contrast, in cold subduction zones, metamorphosed MORB will typically be H2O‐undersaturated and will dehydrate gradually at different depths, transporting ~0.6 wt% H2O to sub‐arc depths. As the volume of fluid released via these dehydration reactions differs strongly between cold, average and warm scenarios, different degrees of serpentinization of the mantle forearc are expected worldwide and thus, the efficacy of buoyancy‐driven exhumation should vary strongly in space and time. Metabasites subducting along a warm and average geotherm will liberate most of the fluids at shallower depths, suggesting that these lithologies might preferentially exhume, yet MORB subducting along cold geotherms will not dehydrate until greater depths, inhibiting its return to the surface. Critically, while we show that metabasites formed along warmer geotherms are denser than metabasites from colder geotherms at any equivalent depth, buoyancy‐driven exhumation provoked by fluids plays a notably more important role in exhumation potential than the overall bulk‐rock ‘metamorphic’ density. Furthermore, we show that lawsonite does not stabilize in average and warmer subduction zones, which provides a simple but important solution to the mismatch between its predicted abundance in experiments and its rarity in nature and argues against its use as a reliable petrogenetic indicator of subduction throughout deep geological time, as has been suggested by some recent studies.

Experimental Study of Phase Composition of B-Fe-Mn-V Alloys and Thermodynamic Calculations of Phase Equilibria in the B-Mn-V and B-Fe-Mn-V Systems

Phase compositions of B-Fe-Mn-V alloys were studied by several experimental methods (DTA measurement, X-ray diffractions, and scanning electron microscopy). Besides the experimental study of the quaternary system, thermodynamic modelling of the ternary B-Mn-V system by the Calphad method and thermodynamic calculations for the quaternary B-Fe-Mn-V system were performed. Calculations for the quaternary system are based on the ternary subsystems (B-Mn-V, B-Fe-V, B-Fe-Mn, and Fe-Mn-V). Boron is modelled as an interstitial element in all solid solutions of vanadium, manganese, and iron. Very good agreement between experimental results and thermodynamic calculations was achieved. The created thermodynamic database is suitable for thermodynamic calculations of phase diagrams for all the ternary subsystems and also for the B-Fe-Mn-V quaternary system.

Experimental Investigation and Thermodynamic Calculation of Phase Equilibria in the Mg-Pb-Sn Ternary System

The phase equilibria of the Mg-Pb-Sn ternary system were investigated using a combined method of electron probe microanalyzer and x-ray diffraction. Three isothermal sections of the Mg-Pb-Sn ternary system at 200, 300 and 400 °C were experimentally established. The phase equilibria of Mg-Pb-Sn ternary system were thermodynamically assessed by using CALPHAD (Calculation of Phase Diagrams) method on the basis of the presently determined experimental data. A consistent set of thermodynamic parameters has been derived for describing the Gibbs free energies of each solution phase and intermetallic compound in the Mg-Pb-Sn ternary system. The calculated phase diagrams and thermodynamic properties in the Mg-Pb-Sn ternary system are in good agreement with experimental data.

Enthalpy of formation of U3Si2: A high-temperature drop calorimetry study

U3Si2 is presently receiving consideration as a high density light water reactor fuel. A reliable knowledge of the formation enthalpy of U3Si2 not only helps study the thermal stability but also facilitate the modeling efforts by serving as a benchmark parameter for thermodynamic calculations of phase equilibria at high temperatures. Previous high temperature thermal analysis on U3Si2 laid the basis for us to conduct two types of high-temperature drop calorimetric measurements to determine its enthalpy of formation: oxide-melt drop-solution calorimetry and transposed temperature drop calorimetry, from which the results obtained are consistent. The determined standard enthalpy of formation of U3Si2 per mole atom, −33.2 ± 3.1 kJ/mol⋅at.%, is in good agreement with previously reported values obtained by other techniques. Our drop calorimetry methods will be used for thermodynamic studies of other U-Si compounds whose enthalpies of formation are not available.

Microstructure and functionality of a uniquely graded super duplex stainless steel designed by a novel arc heat treatment method

A novel arc heat treatment technique was applied to design a uniquely graded super duplex stainless steel (SDSS), by subjecting a single sample to a steady state temperature gradient for 10 h. A new experimental approach was used to map precipitation in microstructure, covering aging temperatures of up to 1430 °C. The microstructure was characterized and functionality was evaluated via hardness mapping. Nitrogen depletion adjacent to the fusion boundary depressed the upper temperature limit for austenite formation and influenced the phase balance above 980 °C. Austenite/ferrite boundaries deviating from Kurdjumov–Sachs orientation relationship (OR) were preferred locations for precipitation of σ at 630–1000 °C, χ at 560–1000 °C, Cr2N at 600–900 °C and R between 550 °C and 700 °C. Precipitate morphology changed with decreasing temperature; from blocky to coral-shaped for σ, from discrete blocky to elongated particles for χ, and from polygonal to disc-shaped for R. Thermodynamic calculations of phase equilibria largely agreed with observations above 750 °C when considering nitrogen loss. Formation of intermetallic phases and 475 °C-embrittlement resulted in increased hardness. A schematic diagram, correlating information about phase contents, morphologies and hardness, as a function of exposure temperature, is introduced for evaluation of functionality of microstructures.

Thermodynamic Calculation of Phase Equilibria in the Mn-RE (RE=Nd, Gd, Dy) Binary Systems

Ternary intermetallic compounds with rare earth elements and transition metals in the RE-Mn-X (X=Si, Ge, Sn etc.) ternary systems show interesting magnetic properties. As key sub-binary systems of the RE-Mn-X (X=Si, Ge, Sn etc.) ternary systems, the information of phase equilibria and thermodynamic properties of the Mn-RE (RE=Nd, Gd, Dy) binary systems are indispensable to explore the RE-Mn-X (X=Si, Ge, Sn etc.) alloys with better magnetic properties. In this work, the experimental data of phase equilibria and thermodynamic properties of the Mn-RE (RE=Nd, Gd, Dy) binary systems in the published literature were reviewed. Based on the available experimental information, thermodynamic calculation of phase equilibria of the Mn-RE (RE=Nd, Gd, Dy) binary systems was performed using the CALPHAD method. As a result, further experimental investigation and thermodynamic optimization would be still necessary in order to develop the self-consistent and compatible thermodynamic database of the RE-Mn-based alloy systems.

Microstructure and tensile and Charpy impact properties of reduced activation ferritic–martensitic steel with Ti

The influence of Ti, a low activation alloying element, on the microstructure and mechanical properties was investigated of reduced activation ferritic–martensitic (RAFM) steel containing Ti instead of Ta, The steel design with Ti was based on thermodynamic calculations of phase equilibria. All samples were normalized at 1000°C for 1h and tempered at 650°C and 750°C for 2h, which resulted in tempered martensite with M23C6 carbides and MX precipitates. Ti-added RAFM steel tempered at 650°C has fine M23C6 carbides and nano-sized (Ti,W)C particles with about 20nm, leading to a superior balance of strength and impact toughness, compared to the previous RAFM steels with Ta.

The influence of chemical composition on microstructure, hardness and electrical conductivity of Ag-Bi-In alloys at 100 °C

Considering possible applications and scarceness of literature data, Ag-Bi-In system was investigated in terms of microstructure, mechanical and electrical properties of ternary alloys from an isothermal section at 100oC. Based on the experimentally obtained results hardness and electrical conductivity of all ternary alloys from the ternary Ag-Bi-In system at 100oC were predicted. In addition, the selected isothermal section was further thermodynamically assessed and experimentally studied using scanning electron microscopy (SEM) with energy dispersive spectrometry (EDS), X-ray powder diffraction (XRD) analysis and light optical microscopy (LOM). Phase transition temperatures of alloys with overall compositions along vertical sections x(Ag)=0.5 as well as liquidus temperatures were experimentally determined by DTA. The experimentally obtained results were compared with literature data and with the results of thermodynamic calculation of phase equilibria based on CALPHAD method and corrected data for Ag-In binary system. Calculated liquidus projection, invariant equilibria and phase diagram of the Ag-Bi-In ternary system are presented as well.

Thermodynamic assessment and experimental study of the Al-Ag-Ga phase diagram

Ternary Al-Ag-Ga system was assessed both theoretically using thermodynamic calculations of phase equilibria based on CALPHAD method and experimentally using differential thermal analysis (DTA), scanning electron microscopy (SEM) combined with energy dispersive spectrometry (EDS) and X-ray powder diffraction (XRD) analysis. The calculated phase transition temperatures, isothermal sections at 300 and 500°C and liquidus surface projection were experimentally validated by experimental study of selected long-term annealed alloy samples with overall compositions along four vertical sections Al-Ag80Ga20, Al-Ag60Ga40, Ag-Al80Ga20 and Ag-Al60Ga40.

A new robust stability algorithm for three phase flash calculations in presence of water

Thermodynamic phase equilibrium calculations for systems containing water are inseparable parts of the compositional hydrocarbon reservoir simulation. In this regard, stability analysis of the phases for distinguishing the existing ones at specific pressures and temperatures is a principal part of such calculations. This study is aimed to develop a new stability algorithm with application to three phase flash calculations in the presence of brine. The developed scheme is capable of doing the phase behavior calculations in a more robust way compared to the other available algorithms. Henry's law is utilized to predict the aqueous phase properties, and a new initial guess is provided for three phase flash calculations that assures the convergence of the scheme. It is shown that the proposed procedure is able to handle the systems with high CO2 content while the available schemes in the literature fail.

Experimental investigation and thermodynamic calculation of phase equilibria in the Mg–Pb–Zn ternary system

The phase equilibria of the Mg–Pb–Zn ternary system were investigated using electron probe microanalysis (EPMA), back scattered electron (BSE) imaging and X-ray diffraction (XRD) methods. Three isothermal sections of the Mg–Pb–Zn ternary system at 200 °C, 300 °C and 400 °C were experimentally established. The phase equilibria of Mg–Pb binary and Mg–Pb–Zn ternary system were thermodynamically assessed by using CALPHAD (Calculation of Phase Diagrams) method on the basis of the presently determined experimental data. A consistent set of thermodynamic parameters has been derived for describing the Gibbs free energies of each solution phase and intermetallic compound in the Mg–Pb and Mg–Pb–Zn systems. The calculated phase diagrams and thermodynamic properties in the Mg–Pb and Mg–Pb–Zn systems are in good agreement with experimental data.