Phase Diagrams Of Multicomponent Systems Research Articles

Machine learning assisted predictions of multi-component phase diagrams and fine boundary information

A phase diagram is a critical tool in materials science, but establishing it often requires a large number of experiments, especially for multi-component systems. In this work, we propose a machine learning strategy to accurately predict the phase diagram for the multi-component ferroelectric system (Ba1−x−yCaxSry)(Ti1−u−v−wZruSnvHfw)O3 by combining classification and regression methods. Based on literature data, we construct by classification a diagram that maps composition and temperature to the phase, and identify octahedral factor, Matyonov-Batsanov electronegativity, the ratio of valence electron number to nuclear charge and core electron distance (Schubert) for the A site and B site cations as the dominant physical descriptors. A neural network (NN) regression model is adopted to accurately predict phase transition temperatures, i.e. the phase boundaries, so that a phase diagram can be established in composition space. In the region of phase boundaries, the relative proportions of coexisting phases are also estimated by their prediction probability. The predicted phase labels, location boundaries and coexisting phase proportions are experimentally validated for the ceramic (Ba0.96Ca0.02Sr0.02)(Ti0.98−xZr0.02Hfx)O3. Our work provides an effective approach to establish phase diagrams for multi-component systems and also predict fine boundary information.

Phase equilibrium in binary La2O3-Dy2O3 and ternary CeO2-La2O3-Dy2O3 systems

Cerium oxide doped with oxides of rare earth elements is a multifunctional material, a wide range of uses which is associated with its unique physicochemical properties. Phase diagrams of multicomponent systems are the physicochemical basis for the creation of new materials with improved characteristics.In this work, phase equilibria in ternary CeO2–La2O3–Dy2O3 and binary La2O3–Dy2O3 systems in the whole concentration range were studied. No new phases have been identified in these systems. An isothermal section of the phase diagram of the CeO2–La2O3–Dy2O3 system at a temperature of 1500 °С is constructed. No new phases have been detected in the system. It was found that in the studied ternary system solid solutions are formed on the basis of (F) modification of CeO2 with structure of fluorite type, monoclinic (B), cubic (C) and hexagonal (A) modifications of Ln2O3.In the La2O3–Dy2O3 binary system (1500–1100 °С) three types of solid solutions are formed: based on hexagonal modification A-La2O3, monoclinic modification B-Dy2O3 and cubic modification C-Dy2O3 separated by two-phase fields (A+B) and (B+C), respectively. The boundaries of the regions of homogeneity of solid solutions based on A-La2O3 are determined by compositions containing 35–40, 20–25, 15–20 mol% Dy2O3 at 1500, 1250, 1100 °C, respectively. From the obtained data it follows that the solubility of Dy2O3 in the hexagonal modification of lanthanum oxide is 39 mol% at 1500 °C, 23 mol. % at 1250 °C and 16 mol% at 1100 °C. The limits of existence of solid solutions based on monoclinic B-modification are determined by compositions containing 30–35, 65–60 (1250 °С), 35–40, 55–60 (1100 °С) 40–45, 70–75 (1500 °C) mol% Dy2O3.In the studied system, with a decrease in temperature from 1500° to 1100°C, there is a decrease in the solubility of La2O3 in the crystal lattice of cubic solid solutions of C-type from 16 to 10 mol%.

Alloy thermodynamics via the Multi-cell Monte Carlo (MC)2 method

From the Bronze Age to the Iron Age to the modern era, alloys have been closely tied to human civilization. Alloy design is still one of the most active fields of materials research to respond to the ever-changing needs of the modern global society. At the heart of designing new alloys, is the knowledge of phase equilibria and the underlying thermodynamics. Most of the modern alloys have more than two or three components, but the phase diagrams for multicomponent systems either do not exist or are partially explored. Here, we discuss how a computational approach can help fill this knowledge gap. We present a review of our Monte-Carlo-based method which allows, for the first time, the direct simulation of coexisting phases in many-component crystalline systems. It is universally applicable across materials classes and enables a wide range of applications.

TRIANGULATION OFTHE Cu-Sb-Se SYSTEM

Thermoelectric technologies allow the direct conversion of waste heat into electricity. A new strategy for finding promising thermoelectric materials is to study the phase diagrams of multicomponent systems. Analysis of recent investigations indicates high perceptivity of Cu2Se phase, due to abnormally low values of the thermal conductivity and high values of electrical conductivity. Other thermoelectric materials based on copper have attractive properties, such as: diamond-like compounds, argyrodites, oxiselenides, tetrahedron-type compounds and others. Due to this a more detailed investiation of the Cu–Sb–Se system are actually. An important step in the study of the system is the determination of quasi-binary sections by carrying out the triangulation. For this purpose, the quasi-binarity of sections in the ternary Cu–Sb–Se system at a temperature of 523 K was determined by X-ray diffraction analysis. Since the annealing temperature in the synthesis process is 523 K, six binary Cu2Se, CuSe, CuSe2, Cu1.6Sb0.4, Cu2Sb, Sb2Se3 and three ternary compounds CuSbSe2, Cu3SbSe3, Cu3SbSe4 took part in the triangulation of the system. Analysis of the early studies showed the presence of three quasi-binary sections in the Cu–Sb–Se system: Cu2Se – Cu3SbSe3, Cu3SbSe3 – CuSbSe2 and CuSbSe2 – Sb2Se3, and the character of the remaining 12 sections requires experimental studies. The quasi-binary section of Cu2Se-Sb2Se3 divides the general system of Cu-Sb-Se into two subsystems: Cu2Se-Sb2Se3-Se (30 intersection points) and Cu-Sb-Sb2Se3-Cu2Se (13 intersection points). To optimize the process of triangulation, it was decided to carry out it in stages: synthesis and study of the point in the most informative phase field with following separation and exclusion of quasi-binary and non-quasi-binary sections. Such approach makes it possible to reduce the number of syntheses and the number of used substances. Phase analysis was performed by comparing experimental and calculated from the literature powder patterns of phases present in the systems Cu2Se-Sb2Se3-Se and Cu-Sb-Sb2Se3-Cu2Se. The obtained results indicate that in the subsystem Cu2Se-Sb2Se3-Se has seven stable sections, all of which are based on the ternary compound Cu3SbSe4. In the Cu-Sb-Sb2Se3-Cu2Se subsystem, 5 quasi-binary sections are stable: three based on binary Cu2Se and two sections based on ternary compounds CuSbSe2 and Cu3SbSe3.

Determining Multi-Component Phase Diagrams with Desired Characteristics Using Active Learning.

Herein, we demonstrate how to predict and experimentally validate phase diagrams for multi‐component systems from a high‐dimensional virtual space of all possible phase diagrams involving several elements based on small existing experimental data. The experimental data for bulk phases for known systems represents a sampling from this space, and screening the space allows multi‐component phase diagrams with given design criteria to be built. This approach uses machine learning methods to predict phase diagrams and Bayesian experimental design to minimize experiments for refinement and validation, all within an active learning loop. The approach is proven by predicting and synthesizing the ferroelectric ceramic system (1‐ω)(Ba0.61Ca0.28Sr0.11TiO3)‐ω(BaTi0.888Zr0.0616Sn0.0028Hf0.0476O3) with a relatively high transition temperature and triple point, as well as the NiTi‐based pseudo‐binary phase diagram (1‐ω)(Ti0.309Ni0.485Hf0.20Zr0.006)‐ω(Ti0.309Ni0.485Hf0.07Zr0.068Nb0.068) designed for high transition temperature (ω ⩽ 1). Each phase diagram is validated and optimized through only three new experiments. The complexity of these compounds is beyond the reach of today's computational methods.

LASSI: A lattice model for simulating phase transitions of multivalent proteins.

Many biomolecular condensates form via spontaneous phase transitions that are driven by multivalent proteins. These molecules are biological instantiations of associative polymers that conform to a so-called stickers-and-spacers architecture. The stickers are protein-protein or protein-RNA interaction motifs and / or domains that can form reversible, non-covalent crosslinks with one another. Spacers are interspersed between stickers and their preferential interactions with solvent molecules determine the cooperativity of phase transitions. Here, we report the development of an open source computational engine known as LASSI (LAttice simulation engine for Sticker and Spacer Interactions) that enables the calculation of full phase diagrams for multicomponent systems comprising of coarse-grained representations of multivalent proteins. LASSI is designed to enable computationally efficient phenomenological modeling of spontaneous phase transitions of multicomponent mixtures comprising of multivalent proteins and RNA molecules. We demonstrate the application of LASSI using simulations of linear and branched multivalent proteins. We show that dense phases are best described as droplet-spanning networks that are characterized by reversible physical crosslinks among multivalent proteins. We connect recent observations regarding correlations between apparent stoichiometry and dwell times of condensates to being proxies for the internal structural organization, specifically the convolution of internal density and extent of networking, within condensates. Finally, we demonstrate that the concept of saturation concentration thresholds does not apply to multicomponent systems where obligate heterotypic interactions drive phase transitions. This emerges from the ellipsoidal structures of phase diagrams for multicomponent systems and it has direct implications for the regulation of biomolecular condensates in vivo.

Structurally driven asymmetric miscibility in the phase diagram of W-Ti

Phase diagrams for multi-component systems represent crucial information for understanding and designing materials but are very time consuming to assess experimentally. Computational modeling plays an increasingly important role in this regard but has been largely focused on systems with matching lattice structures and/or stable boundary phases. Here, using a combination of density functional theory calculations, alloy cluster expansions, free energy integration, and Monte Carlo simulations, we obtain the phase diagram of W-Ti, a system that features metastable boundary phases on both sides of the phase diagram. We find that the mixing energy on the body-centered cubic (BCC) lattice is asymmetric and negative with a minimum of about -120 meV/atom, whereas for the hexagonal closed packed (HCP) lattice the mixing energy is positive. By combining these data with a model for the vibrational free energy, we propose a revision of the W-rich end of the phase diagram with a much larger solubility of Ti in BCC-W than previous assessments. Finally, by comparison with the W-V and W-Re system we demonstrate how strongly asymmetric phase diagrams can arise from a subtle energy balance of stable and metastable lattice structures.

Invariant Equilibria in Multicomponent Systems

The translation method for predicting and constructing equilibrium phase diagrams of multicomponent systems is developed based on the compatibility of structural elements of partial constituent (n-component) systems and the general (n + 1)-component system with account for the requirements of the Gibbs phase rule. The invariant equilibrium states in the five-component system NaCl–KCl–MgCl2–CaCl2–H2O at 25°C are studied. This multicomponent system features the options of invariant equilibria where one and the same composition of equilibrium solid phases can be in equilibrium with saturated solutions of differing concentrations. Therefore, this invariant equilibrium is to be reflected in the diagram as a geometric (invariant) image that has a dimension (it may be conventionally referred to as a quasi-point) and not by a point. The dimension of this image is determined by the concentration bounds of components in the equilibrium saturated solution.

Using symmetry to elucidate the importance of stoichiometry in colloidal crystal assembly

We demonstrate a method based on symmetry to predict the structure of self-assembling, multicomponent colloidal mixtures. This method allows us to feasibly enumerate candidate structures from all symmetry groups and is many orders of magnitude more computationally efficient than combinatorial enumeration of these candidates. In turn, this permits us to compute ground-state phase diagrams for multicomponent systems. While tuning the interparticle potentials to produce potentially complex interactions represents the conventional route to designing exotic lattices, we use this scheme to demonstrate that simple potentials can also give rise to such structures which are thermodynamically stable at moderate to low temperatures. Furthermore, for a model two-dimensional colloidal system, we illustrate that lattices forming a complete set of 2-, 3-, 4-, and 6-fold rotational symmetries can be rationally designed from certain systems by tuning the mixture composition alone, demonstrating that stoichiometric control can be a tool as powerful as directly tuning the interparticle potentials themselves.

Phase transformations in oxides above 2000°C: experimental technique development

ABSTRACTThe oxidation of boride and carbide-based ultra-high-temperature ceramics is the primary limiting factor for their use as aerodynamic surfaces. Understanding the behaviour of the oxides that can result from oxidation of metal borides and carbides at very high temperatures is essential to optimise and tailor the performance of these materials; yet experimental thermodynamic and structural data for refractory oxides above 2000°C are mostly absent. The following techniques that can be applied to fill this gap are discussed: (i) commercial ultra-high-temperature differential thermal analysis for investigation of phase transformations and melting in inert environments to 2500°C, (ii) a combination of laser heating with a splittable nozzle aerodynamic levitator for splat quenching and drop calorimetry from temperatures limited only by sample evaporation, (iii) synchrotron X-ray and neutron diffraction on laser-heated aerodynamically levitated oxide samples for in situ observation of phase transformations in variable atmospheres, refinement of high-temperature structures and thermal expansion. Recent experimental findings include anomalous thermal expansion of the defect fluorite phase of YSZ, thermodynamics of pyrochlore–fluorite transformation from high-temperature structure refinements, and measurement of thermal expansion to the melting temperatures and fusion enthalpies of Zr, Hf, La, Yb and Lu oxides. These methods provide temperatures, enthalpies and volume change for phase transformations above 2000°C, which are required for thermodynamic assessments and calculation of phase diagrams of multicomponent systems.

Isobaric Vapor-Liquid Phase Diagrams for Multicomponent Systems with Nanoscale Radii of Curvature.

At any given temperature, pressure, and composition, a compound or a mixture of compounds will exist either in a single phase, whether solid, liquid, or vapor, or in a combination of these phases coexisting in equilibrium. For multiphase systems, it is known that the geometry of the interface impacts the equilibrium state; this effect has been well-studied in single component systems with spherical interfaces. However, multicomponent phase diagrams are usually calculated assuming a planar interface between phases. Recent experimental and theoretical work has started to investigate the effect of curved interfaces on multicomponent phase equilibrium, but these analyses have been limited to isothermal conditions or to a portion of the isobaric phase diagram. Herein, we consider complete vapor-liquid phase diagrams (both bubble and dew lines) under isobaric conditions. We use Gibbsian composite-system thermodynamics to derive the equations governing vapor-liquid equilibrium for systems with a spherical interface separating the phases. We validate our approach by comparing the predicted nitrogen/argon dew points with reported literature data. We then predict complete isobaric phase diagrams as a function of radius of curvature for an ideal methanol/ethanol system and for a nonideal ethanol/water system. We also determine how the azeotropic composition of ethanol/water changes. The effect of curvature on isobaric phase diagrams is similar to that seen on isothermal phase diagrams. This work extends the study of curved-interface multicomponent phase equilibrium to isobaric systems, expanding the conditions under which nanoscale systems, such as nanofluidic systems, shale gas reservoirs, and cloud condensation nuclei, can be understood.

Phase Equilibria in Multicomponent Water–Salt Systems

The translation method of determining phase equilibria and construction of phase diagrams for multicomponent systems was applied to investigate the phase equilibria in two quaternary Na, NH4//SO4, Cl–H2O (at 100 °C, 10 °C) and Na2SO4–K2SO4–MgSO4–H2O (at 35 °C) and three quinary Li, K//Cl, CO3, B4O7–H2O (at 0 °C), Na, K//Cl, SO4, B4O7–H2O (at 50 °C), and Na, K//Cl, CO3, B4O7 – H2O (at 25 °C) water–salt systems. The comprehensive closed phase equilibria diagrams for each of the systems were constructed at the relevant temperatures. The constructed diagrams for the quinary systems were fragmented into trivariant crystallization volumes for each of the available individual solid phases in the systems. The available experimental results on each of the three investigated quinary systems compose only a portion of the phase equilibria data obtained by us using the techniques of translation method. Comparison of our results with the available literature data for the two quinary Li, K//Cl, CO3, B4O7–H2O (at 0 °C) a...

Properties of Puma and Buksol lubricants modified by inorganic additives of binary polyphosphates

Results of investigations of tribotechnical and physicochemical properties of plastic lubricants, which are based on Puma and Buksol and used in heavy duty friction units of railway equipment, are presented. The search for new multipurpose polymeric additives of the inorganic nature was carried out based on physicochemical studies of phase diagrams of multicomponent systems. The influence of Puma and Buksol with the synthesized additives on characteristics of the process of friction is studied. Judgments about the mechanism of antifrictional and antiwear effect during work with these greases are stated. The base of this mechanism is the interaction of flexible links of anions of polyphosphate chains with a surface of metal. As a result, the layer of secondary structures is formed on the surface that protects the metal from wear.

Phase stability in nanoscale material systems: extension from bulk phase diagrams

Phase diagrams of multi-component systems are critical for the development and engineering of material alloys for all technological applications. At nano dimensions, surfaces (and interfaces) play a significant role in changing equilibrium thermodynamics and phase stability. In this work, it is shown that these surfaces at small dimensions affect the relative equilibrium thermodynamics of the different phases. The CALPHAD approach for material surfaces (also termed "nano-CALPHAD") is employed to investigate these changes in three binary systems by calculating their phase diagrams at nano dimensions and comparing them with their bulk counterparts. The surface energy contribution, which is the dominant factor in causing these changes, is evaluated using the spherical particle approximation. It is first validated with the Au-Si system for which experimental data on phase stability of spherical nano-sized particles is available, and then extended to calculate phase diagrams of similarly sized particles of Ge-Si and Al-Cu. Additionally, the surface energies of the associated compounds are calculated using DFT, and integrated into the thermodynamic model of the respective binary systems. In this work we found changes in miscibilities, reaction compositions of about 5 at%, and solubility temperatures ranging from 100-200 K for particles of sizes 5 nm, indicating the importance of phase equilibrium analysis at nano dimensions.

Multicomponent salt systems: Methodology, studies, achievements, and promises. Proceedings of the 68th Kurnakov readings, Moscow, 2009

AvtoKMIMS, an automated integrated methodology for studying multicomponent systems, has been developed. It includes a general study algorithm using software for modeling phase complexes and newgeneration differential thermal analysis equipment for performing single confirming experiments. AvtoK-MIMS rapidly and rationally obtains accurate information from the phase diagrams of multicomponent systems, thus giving impetus to create innovative materials and technologies.

Principles of crystal growth of intermetallic and oxide compounds from molten solutions

We present a tutorial on the principles of crystal growth of intermetallic and oxide compounds from molten solutions, with an emphasis on the fundamental principles governing the underlying phase equilibria and phase diagrams of multicomponent systems.

Modelling of phase diagrams and thermodynamic properties using Calphad method – Development of thermodynamic databases

The Calphad method is very important method for the modelling of thermodynamic properties and phase diagrams of multicomponent systems. The method is based on a semi-empirical approach and sequential modelling from simpler to more complicated systems. Therefore reliable experimental data are necessary for the description of the thermodynamic and phase properties of unary and binary systems. Basic principles of the method will be described in this paper, especially from the point of view of preparing the reliable theoretical thermodynamic description of simpler systems, which allow reliable prediction and assessment of higher order systems.The thermodynamic data, describing assessed binary and ternary systems are collected in the form of the thermodynamic databases, which allow (together with proper software) the prediction of properties for multicomponent systems corresponding to real materials. The software packages, based on Calphad method, are currently the only theoretical tools, applicable for complex materials as steels, superalloys, etc.The thermodynamic databases and outputs of the theoretical calculations are also important for many other applications and multi-scale simulations. They serve as input for phase field simulations, diffusion processes modelling, phase transformations, material properties and structure morphology development, including the processes on interface.

CALPHAD formalism for Portland clinker: thermodynamic models and databases

The so-called CALPHAD method is widely used in metallurgy to predict phase diagrams of multi-component systems. The application of the method to oxide systems is much more recent, mainly because of the difficulty of modelling the ionic liquid phase. Since the 1980s, several models have been proposed by various communities. Thermodynamic databases for oxides are available and still under development. The purpose of this article is to discuss the distinct approaches of the method for the calculation of multi-component systems for Portland cement elaboration. The article gives a state of the art of the most recent experimental data and the various calculations for the CaO–Al2O3–SiO2 phase diagram. A literature review of the three binary sub-systems leads to main conclusions: (i) discrepancies are found in the literature for the selected experimental data, (ii) the phase diagram data in the reference books are not complete and up to date and (iii) the two-sublattices model and the modified quasichemical model can be equally used for the modelling of the aluminates liquid. The predictive feature of the CALPHAD method is illustrated using the CaO–Al2O3–SiO2 system with the two-sublattices model: extrapolated (predicted) and fully-assessed phase diagrams are compared in the clinkering zone of interest. The recent application of the predictive method for the calculations of high-order systems (taking into account Fe2O3, SO3, CaF2, P2O5,…) shows that the databases developed with the two-sublattices model and the modified quasichemical model are no longer equivalent.

Application of microevaporators to dynamic exploration of the phase diagram

We present a detailed investigation of the functioning of microevaporators using numerics and analytical arguments. We first present a way to neatly control stationary gradients of solutes in a microfluidic channel. These gradients display exact exponential or Gaussian shapes depending on a Péclet number (Pe) that compares the mobility of the solute to the convection in the microevaporator. Then, we focus on the regimes of filling where solutes are continuously accumulated toward the tip of the microevaporator, and we give an analytical description on how they concentrate at the tip of the channel depending on Pe; we also evidence and stress the significant role of transient regimes in the mechanisms at work. Finally, we detail how to use these devices to explore dynamically phase diagrams of multicomponent systems.

Development of an alternative, time and cost saving method of creating pseudoternary diagrams using the example of a microemulsion

This article describes a new, time and material-saving method (Phase Diagram by Micro Plate Dilution (PDMPD) method) for creating pseudoternary phase diagrams for micro- and nanoemulsions. The PDMPD method enables the creation of ternary phase diagrams of multi-component systems. The method has been tested for the development of formulations of microemulsions. In principle this method makes it possible to determine the stability, long time stability and the phase and solubility behaviour of all liquid to semi-solid phase mixtures, and homogeneous or heterogeneous phase regions, and the effect of substances on the multi-component system. Compared with the traditional titration method (drop method), the PDMPD method enables a more exact status description of multi-component mixtures and the regions of microparticular systems in pseudoternary diagrams and offers the possibility of examining the dilution stages simultaneously and retrospectively on just one microplate.