Liquidus Surface Research Articles

Performance of uncertainty-based active learning for efficient approximation of black-box functions in materials science.

Obtaining a fine approximation of a black-box function is important for understanding and evaluating innovative materials. Active learning aims to improve the approximation of black-box functions with fewer training data. In this study, we investigate whether active learning based on uncertainty sampling enables the efficient approximation of black-box functions in regression tasks using various material databases. In cases where the inputs are provided uniformly and defined in a relatively low-dimensional space, the liquidus surfaces of the ternary systems are the focus. The results show that uncertainty-based active learning can produce a better black-box function with higher prediction accuracy than that by random sampling. Furthermore, in cases in which the inputs are distributed discretely and unbalanced in a high-dimensional feature space, datasets extracted from materials databases for inorganic materials, small molecules, and polymers are addressed, and uncertainty-based active learning is occasionally inefficient. Based on the dependency on the material descriptors, active learning tends to produce a better black-box functions than random sampling when the dimensions of the descriptor are small. The results indicate that active learning is occasionally inefficient in obtaining a better black-box function in materials science.

Thermal analysis and modeling of phase equilibria in the NaCl–NaBr–Na2WO4 system

The phase complex of a three-component system of sodium chlorides, bromides and tungstates was studied for the first time using experimental and theoretical methods. It was found that the liquidus surface of the system consists of the crystallization fields of NaBr, Na2WO4, Na3ClWO4 compounds and NaClxBr1–x solid solutions. The differential thermal method of physico-chemical analysis (DTA) revealed the compositions and melting points of eutectic in the quasi–binary and three–component systems NaBr–Na3ClWO4 and NaCl–NaBr–Na2WO4, respectively. To establish the nature of the physico-chemical interaction in the system, three compositions were studied in the secondary triangle NaCl–NaBr–Na3ClWO4 by the DTA method, thermal effects of tertiary crystallization were not recorded on the DTA curves of these compositions, which is proof of the absence of a non-invariant composition in the NaCl–NaBr–Na3ClWO4 simplex. To determine the composition and melting point of the nonvariant composition located in the NaBr–Na2WO4–Na3ClWO4 simplex, a polythermal section located in the field of crystallization of sodium bromide and a nonvariant section emerging from the crystallization pole of sodium bromide passing through the point of joint crystallization of sodium chloride and the compound, with a constant decrease in the content of sodium bromide in the studied compositions before the onset of non-invariant crystallization process. The composition of the three-component eutectic of ED in molar percentages, crystallizing at 560оC with the following component content, has been determined: 7.5% NaCl; 38.5% NaBr; 54% Na2WO4. Based on data on the melting temperatures of the initial salts, compositions and crystallization temperatures of two- and three-component systems, a 3D-model of the “composition–temperature” phase complex in the temperature range 500–700оC was formed using theoretical methods. On the basis of the model, the isotherms of the liquidus surface and the T–x diagram of the polythermal section for which experimental studies were conducted was constructed. Also, as an example of using a 3D-model, the composition of the equilibrium phases released during cooling of an arbitrarily selected figurative point in the temperature range from 700 to 500оC. was calculated.

Integrated experimental and thermodynamic modelling study of phase equilibria in the “CuO0.5”-PbO-CaO system in equilibrium with Cu/Pb metal

Phase equilibria studies were undertaken on the “CuO0.5”-PbO-CaO system in equilibrium with Cu/Pb metal as part of the integrated experimental and thermodynamic modelling study of phase equilibria in the Cu-Pb-Zn-Fe-Ca-Si-Al-Mg-O-S-(As, Sn, Sb, Bi, Ag, Au, Ni, Cr, Co and Na) gas/oxide liquid/matte/speiss/metal/solids system in support of the development and optimisation of pyrometallurgical processes. The equilibration and quenching technique followed by the electron probe X-ray microanalysis (EPMA) was used in the present study. The primary phase fields of massicot (PbO), copper plumbite (Cu2PbO2), cuprite (Cu2O) and lime (CaO) were experimentally characterised. The experimental data obtained in the present study, as well as available literature data on the phase equilibria and thermodynamics of the “CuO0.5”-PbO-CaO system in equilibrium with Cu/Pb were used for the optimisation of the model parameters of the discussed system in agreement with the Cu-Pb-Zn-Fe-Ca-Si-Al-Mg-O-S-(As, Sn, Sb, Bi, Ag, Au, Ni, Cr, Co and Na) gas/oxide liquid/matte/speiss/metal/solids system to obtain a self-consistent set of parameters of the thermodynamic model for all phases. The predicted liquidus surface of the “CuO0.5”-PbO-CaO system was presented for the first time in the complete range of temperatures and compositions.

Phase equilibria in the system BaO–TiO2

AbstractThe system BaO–TiO2 is technically important because it contains multiple dielectric and ferroelectric phases, including the important BaTiO3, which is one of the most widely studied dielectric perovskites owing to its dual piezoelectric and ferroelectric properties. The present work revises the subsolidus phase equilibria data by synthesizing previous phase equilibria data and new experimental results using high‐temperature (600°–1300°C) and long‐term (≤336 h) equilibration, coupled with analytical work based principally on room‐temperature X‐ray diffraction. The resultant phase diagram is given in both mole and weight percents, extending from the liquidus surface (not investigated) to absolute zero temperature (for inclusion of the previously excluded crystallographic and ferroelectric phase transformations). The major features include (1) correction of four eutectoid and three peritectoid reactions and corresponding temperatures, (2) indication of inferred partial solid solubilities, (3) clarification of the BaTiO3 solid solubility homogeneity regions, and (4) specification of some invariant point compositions on the liquidus surface.

Liquid state property and rapid peritectic solidification of refractory Mo-33.3 at.% Zr alloy under electrostatic levitation condition

The thermophysical properties and rapid solidification mechanism of liquid Mo-33.3 at.% Zr peritectic alloy were investigated by electrostatic levitation technique, which attained a maximum undercooling of 387 K (0.16 TL). At its liquidus temperature, the density, surface tension, viscosity and solute diffusion coefficient of this refractory alloy were determined as 8.14 g/cm3, 1.60 N/m, 11.32 mPa·s and 1.41 × 10−9 m2/s, respectively. The primary (Mo) dendrite growth started from multi-point nucleation, while its growth velocity agreed well with the prediction of LKT/BCT dendrite growth theory and reached an upper value of 43 mm/s. The subsequent peritectic transition was characterized by a power-law kinetics relation between the nominal growth velocity of peritectic Mo2Zr phase and peritectic undercooling, displaying a maximum velocity of 46 mm/s. The increase of liquid undercooling facilitated the completion of peritectic transition and refined the microstructure of residual primary (Mo) phase, thus enhancing the Vickers hardness of this alloy gradually up to 1190.9 HV at the maximum undercooling.

Liquid-Solid Phase Diagrams for Lithium-Ion Battery Electrolytes in the Ternary Space and Beyond

Although practical lithium-ion battery electrolytes generally utilize two or more solvents in addition to the dissolved lithium salt, liquid-solid phase diagrams have, as far as the authors know, only been reported for binary single-solvent electrolytes. This precludes rational design of low freezing point liquid electrolyte mixtures. We herein present a thermodynamic framework to draw out ternary electrolyte liquidus surfaces using the comprising binary liquid-solid equilibria data and limited ternary data measured via calorimetry. LiPF6 in liquid carbonate mixtures are here studied. The introduced thermodynamic framework also allows evaluation of the thermodynamic factor, which appears in the context of transport parameter measurements.

Experimental Determination of the Isothermal Sections and Liquidus Surface Projection of the Co–V–Zr System

Experimental Determination of the Isothermal Sections and Liquidus Surface Projection of the Co–V–Zr System

Liquidus surface projection and isothermal section at 1500 °C of (Mo-5Nb)-Ti-C pseudo-ternary system

The liquidus surface projection and isothermal section at 1500 °C of the (Mo-5Nb)-Ti-C pseudo-ternary system were experimentally determined. X-ray diffraction analysis and scanning electron microscopy in conjunction with electron-probe microanalysis were carried out to analyze the solidification behavior and phase constituents. The replacement of 5 at.% Mo with Nb was found to negligibly affect the solidification path or the formation of new phases. However, the quasi-peritectic point U2 shifted closer to the (Mo-5Nb)-C border in the liquidus surface projection than in the Mo-Ti-C system. The BCC single-phase region, BCC + TiC two-phase region, and BCC + Mo2C + TiC three-phase region were determined in the isothermal section at 1500 °C. The replacement of 5 at.% Mo with Nb was found to expand the BCC + TiC two-phase region and narrow the BCC + Mo2C + TiC three-phase region by stabilizing the TiC phase. Therefore, the addition of Nb to the Mo-Ti-C system expanded the compositional range of the BCC + TiC two-phase region, leading to variable properties of TiC-dispersed BCC-based alloys and BCC-TiC cermets.

Experimental investigations of 9 mol.% Mo5SiB2 isopleth phase diagram in Mo–Mo5SiB2–TiC pseudo-ternary system

The present work focuses on gaining a systematic understanding of the microstructure variation and solidification reactions of alloys in the Mo-rich portion of the Mo–Mo5SiB2(T2)–TiC pseudo-ternary system. A series of MoSiBTiC alloys with 9 mol% T2 were selected from the vicinity of the Mo–TiC binary and Mo–Mo5SiB2(T2)–TiC ternary eutectic point to carefully examine the solidification pathway and phase diagram. The solidification reaction temperature of the alloys was detected via an ultra-high-temperature thermal analysis method using blackbody radiation. Solidification was observed in situ using an electromagnetic levitation (EML) apparatus, and the microstructure evolution of solidified EML samples under different thermal histories was characterized. The results provide an experimentally based reassessment of the liquidus surface projection. The primary Moss phase region is shown to be larger than indicated in previously reported data, and a Mo2B primary region should exist in the triangle. As the main result of the investigation of the solidification pathway of a series of MoSiBTiC alloys, an isopleth phase diagram with 9 mol.% T2 in Mo–Mo5SiB2(T2)–TiC pseudo-ternary system is presented.

Experimental determination and thermodynamic optimization of the Nb–V–Zr system

A comprehensive thermodynamic description for each phase is essential for designing of the novel Zr-based nuclear materials. The construction of the experimental liquidus surface projection and isothermal section of the Nb–V–Zr system was established through analyzing solidification microstructures and phase constituents. The stability of the τ phase with C14-structure was established by investigating the composition range of Nb in τ, which was measured to be between 19.8 and 40.5 at.% at 1473 K. The solubility of Nb in λ2 with the C15-type was ∼ 16.9 at.% at 1473 K. The liquidus surface projection showed primary solidification areas of bcc(Nb,V,Zr), λ2 and τ. The thermodynamic parameters were derived combining the CALPHAD method with experimental results from phase diagram data in this work and the literatures. Solution phases, including liquid, bcc, and hcp, were regarded as substitutional solutions. Considering the crystal structures and solid solubility of intermetallic compounds, λ2 and τ were modeled as (Nb,V,Zr)2(Nb,V,Zr) using two-sublattice model. A set of self-consistent thermodynamic parameters of the Nb–V–Zr system was obtained, which will provide theoretical guidance for the design of Zr-based nuclear materials.

EXPERIMENTAL STUDY OF THE PHASE EQUILIBRIA IN THE SnTe–Sb2Te3–Te SYSTEM

Phase equilibria of the SnTe–Sb2Te3–Te portion of the Sn–Sb–Te ternary system have been experimentally investigated using differential thermal analysis (DTA), powder X-ray diffraction (XRD), and microstructural analysis methods. Based on the measured experimental results and literature information, isothermal sections at 500 K, liquidus surface projection, and several vertical sections of the phase diagram were plotted. The 500 K phase diagram of this system consists of 2 single-phase regions, 2 two-phase regions, and 3 three-phase regions. The liquidus surface projection is represented by the primary crystallization fields of 5 phases. The primary crystallization fields of all phases, the types, and coordinates of non- and monovariant equilibria were determined. Obtained experimental data can be valuable input for design for Sn–Sb–Te-based alloys

Experimental investigation and thermodynamic description of the Co–Mo–Ta system

38 annealed and 30 as-cast alloys were investigated to construct the isothermal sections at 1273 and 1473 K and the liquidus surface projection of the Co–Mo–Ta system by SEM/EDS and XRD methods. The three-phase regions Co3Mo+λ3+μ and fcc(Co) + Co3Mo+λ3 at 1273 K, and the three-phase region fcc(Co)+λ3+μ at 1473 K, were determined. In the liquidus surface projection, eight primary solidification phase regions, fcc(Co), bcc(Mo, Ta), σ, μ, λ1, λ2, λ3 and CoTa2, and five invariant reactions, liq.→fcc(Co)+λ3+μ, liq.→λ1+λ3+μ, liq.+λ2→λ1+λ3, liq.+CoTa2→μ+bcc(Mo, Ta) and liq.+bcc(Mo, Ta)+σ→μ, were obtained. On the basis of the experimental results, the Co–Mo–Ta system was evaluated to obtain a set of self-consistent thermodynamic parameters by CALPHAD method.

About the Alkemade Theorem and the Limits of its Applicability for the Construction of Ternary Liquidus Surfaces

The Alkemade theorem goes back to a very fundamental paper on the graphical description of thermodynamic equilibrium problems from 1893 (van Rijn van Alkemade in Z Phys Chem 11: 289-327, 1893). It is one of the most helpful implements for the construction of the liquidus surface of ternary phase diagrams. In its original form, it allows to find the direction of falling or increasing temperature along the monovariant reaction lines forming the boundaries of the primary crystallization fields. The theorem is valid for systems with any number of phases; however, its geometrical construction rule is only defined for the case of stoichiometric phases and it is not clear how to apply the theorem in the case of phases with extended homogeneity ranges. Some examples from a ternary, transition-metal-based system containing phases with large homogeneity ranges are presented, and the usefulness and limits of applicability of the theorem are discussed.

PHASE RELATIONS IN THE Bi2-Bi2Se3-Bi2Te3 SYSTEM AND CHARACTERIZATION OF SOLID SOLUTIONS

Phase relations in the Bi2–Bi2Se3–Bi2Te3 system were determined experimentally using differential thermal analysis (DTA), X-ray diffraction (XRD), and scanning electron microscopy (SEM). Based on the experimental results, a solid-phase equilibria diagram at room temperature, a projection of the liquidus surface, and several polythermal sections of the phase diagram were constructed. The regions of primary crystallization and phase homogeneity, types, and coordinates of non- and monovariant equilibria were determined. Continuous solid solutions along the Bi8Se9–Bi8Te9, BiSe–BiTe, and Bi4Se3–Bi4Te3 sections, as well as wide areas of solid solutions based on other bismuth selenides and tellurides, were found. The established phase diagrams can be used for the synthesis of solid solutions of a given composition and the growth of their single crystals by directional crystallization from solution-melts

Selezen А.О., Piskach L.V. INTERACTION IN THE QUASI-TERNARY Tl2Se–CdSe–SnSe2 SYSTEM

Selezen А.О., Piskach L.V. INTERACTION IN THE QUASI-TERNARY Tl2Se–CdSe–SnSe2 SYSTEM

Phase equilibria in the quasi–ternary Li<sub>2</sub>O–Mn<sub>2</sub>O<sub>3</sub>–Eu<sub>2</sub>O<sub>3</sub> system

Series of samples of quasi–ternary Li2O–Mn2O3 – Eu2O3 system, synthesized from of precursors subjected to preliminary mechanochemical activation and annealed in air at temperatures of 700–1100°C have been systematically studied by powder X–ray diffraction(pXRD) and thermal analysis (TG–DSC) methods. The possibility of substituting Mn for Eu for the LiMn2–xEuxO4 spinel phase is estimated. Within the framework of the Li–Mn–Eu concentration triangle, a subsolidus isobaric diagram and a projection of the liquidus surface of the Li–Mn–Eu–O system were constructed using models of polythermal phase diagrams of the LiEuO2–LiMnO2 and LiEuO2–LiMn2O4 sections. The temperatures of eutectic equilibria with the participation of three crystalline phases and a melt were determined.

Hypoeutectic Liquid-Solid Phase Diagrams for Ternary Lithium-Ion Battery Electrolytes.

One of the current efforts of Li-ion battery technology research is to enable the operation of lithium-ion batteries in low temperature environments (<0 °C). However, the ternary phase diagrams of liquid electrolytes commonly used in lithium-ion cells are generally unknown. We herein study the liquidus surface of a ternary liquid electrolyte─up to 1 m LiPF6 in ethylene carbonate and ethyl methyl carbonate. We find that literature electrochemical and thermodynamic measurements of the composing binary electrolytes, in addition to limited ternary liquidus data, can be used to recover the liquidus surface via appropriate mixing terms.

Melting Processes of Pelitic Rocks in Combustion Metamorphic Complexes of Mongolia: Mineral Chemistry, Raman Spectroscopy, Formation Conditions of Mullite, Silicate Spinel, Silica Polymorphs, and Cordierite-Group Minerals

Melted rocks (clinkers and paralavas) of the Mongolian combustion metamorphic (CM) complexes were formed during modern and ancient (since the Quaternary) wild-fires of brown coal layers in the sedimentary strata of the Early Cretaceous Dzunbain Formation. According to XRD, Raman spectroscopy, and SEM-EDS data, cordierite, sekaninaite, indialite, ferroindialite, silica polymorphs, mullite, Fe-mullite, anhydrous Al-Fe-Mg silicate spinel (presumably new mineral), and other phases were identified. It has been established that isomorphic impurity of potassium in the cordierite-group minerals does not correlate with their crystal structure (hexagonal or orthorhombic). Indialite and ferroindialite retained their hexagonal structure in some fragments of the CM rocks, possibly due to the very fast cooling of local zones of sedimentary strata and the quenching of high-temperature K-rich peraluminous melt. Clinkers, tridymite–sekaninaite, and cristobalite–fayalite ferroan paralavas were produced by partial melting of Fe-enriched pelitic rocks (mudstone, siltstone, and silty sandstone) in a wide temperature range. The formation of mullite, Fe-mullite, and Al-Fe-Mg silicate spinel in clinkers developed from dehydration–dehydroxylation and incongruent partial melting of Fe-enriched pelitic matter (Al-Mg-Fe-rich phyllosilicates, ‘meta-kaolinite’, and ‘meta-illite’). Large-scale crystallization of these minerals in the K-rich peraluminous melts occurred, presumably, in the range of T &gt; 850–900 °C. The subsurface combustion of coal layers heated the overburden pelitic rocks from sedimentary strata to T &gt; 1050 °C (judging by the formation of cordierite-group minerals) or locally till the melting point of detrital quartz grains at T &gt; 1300 °C and, possibly, till the stability field of stable β-cristobalite at T &gt; 1470 °C. Ferroan paralavas were formed during the rapid crystallization of Fe-rich silicate melts under various redox conditions. From the analysis of the liquidus surface in the Al2O3–FeO–Fe2O3–SiO2 major-oxide system, it follows that the least high-temperature (&lt;1250 °C) and the most oxidizing conditions occurred during the crystallization of mineral assemblages in the most-enriched iron silicate melts parental for cristobalite–fayalite paralava.

Modeling of temperature-concentration ranges of phase stability and liquidus surface in the ternary Fe–P–C system and phase composition experimental study

This paper reports thermodynamic properties and phase equilibria in the iron-phosphorus-carbon system for developing a technology for smelting ferrophosphorus as well as for utilizing them in the processes of phosphorus-alloying of metals. According to the results of thermodynamic calculations, we plotted a ternary Fe–P–C phase equilibrium diagram (liquidus surface) in the form of graphical dependences, which indicate the concentration fields of phase coexistence. The results of simulation allowed finding out five nonvariant points, three of which are new: E1 eutectic (teutectic=12170С), U1 peritectic (tperitectic=10950С), and Е3 eutectic (teutectic=3380С). The experimental studies of the phase composition of ferrophosphorus showed that the phosphorus microstructure is represented by Fe3P phosphide, Fe3C carbide, and carbophosphide eutectic. We carried out the thermodynamic calculation of the temperature-concentration ranges of phase stability in the Fe–P–C system that are at equilibrium with the smelts of both the carbon solid solutions and phosphorus ones in - and -iron, FeP, Fe2P, Fe3P phosphides, and graphite. In this study, three previously unknown nonvariant equilibria have been determined: a eutectic equilibrium at 1216.580C; a peritectic one with a transformation point at 1095.190C; and a eutectic one at a temperature of 337.510C. In experiments, we obtained an equilibrium concentration of carbon which decreases in the Fe–P–C system when the content of phosphorus increases. The research findings largely reveal special features of preparation of ferrophosphorus by carbon reduction of phosphorites.

Phase Equilibria in the Quasi-Ternary System Cu2Se-In2Se3-CuI and the Crystal Structure of the AIBIII2XVI3YVII Compounds, Where AI-Cu, Ag; BIII-Ga; XVI-Cl, Br, I; YVII-S, Se, Te

The quasi-ternary system Cu2Se-In2Se3-CuI has been investigated by x-ray diffraction and differential thermal analysis. The isothermal section at 770 K and the liquidus surface projection of the system have been built. For the first time, the primary crystallization regions, and the coordinates of the invariant and monovariant equilibria have been determined. In the system, the regions of the solid solutions based on the binary, ternary, and quaternary compounds have been investigated. The formation of the CuIn2Se3I quaternary compound, which melts congruently at 1213 K and has a homogeneity region of 15 and 9 mol.% CuI within the composition triangle has been established. For the first time, the crystal structures of CuGa2Te3I and AgGa2Te3Br compounds have been studied using a powder method. They crystallize in the tetragonal symmetry, Space Group I-4, a = 5.9147(4) Å, c = 11.952(2) Å for CuGa2Te3I; a = 6.2977(3) Å, c = 11.9473(7) Å for AgGa2Te3Br compound, respectively. The connection of their structures with the structures of the defective diamond-like semiconductors has been discussed.