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Multicomponent phase space has been shown to consist of an enormous number of materials with different compositions, the vast majority of which have never been made or investigated, with great potential, therefore, for the discovery of exciting new materials with valuable properties. At the same time, however, the enormous size of multicomponent phase space makes it far from straightforward to identify suitable strategies for exploring the plethora of potential material compositions and difficult, therefore, to be successful in discovering desirable new materials. Unfortunately, all our knowhow and understanding has been developed for materials with relatively few components in relatively limited proportions, with most of our scientific theories relying essentially on linear assumptions of component dilution and independence that no longer apply in concentrated multicomponent materials. Trial and error, controlled substitution, parameterisation, thermodynamic modelling, atomistic modelling and machine learning techniques have all been employed as methods of exploring multicomponent phase space, with varying levels of success, but ultimately none of these techniques has proved capable of delivering consistent or guaranteed results. This paper provides an overview of the different techniques that have been used to explore multicomponent phase space, indicates their main advantages and disadvantages, and describes some of their successes and failures. [ABSTRACT FROM AUTHOR]

The parallel tangent method widely applied to predict the composition and driving force to form a nucleus from an oversaturated solution is extended in this paper. The parallel tangent method is shown to (i) Over-estimates the composition difference between the first nucleus and the parent phase, (ii) Neglects the composition dependence of interfacial energies and (iii) Neglects the composition dependence of probability to form embryos prior to nucleation. New model equations are developed here for the composition dependence of the interfacial energies and probability to form the embryos as function of nucleus composition at given matrix composition. The most probable composition of the first nucleus is found at the maximum of the driving force of nucleation extended by the new model equations. The success of the extended method is demonstrated for an Al-Fe liquid alloy with 0.3 w% of Fe to predict the first nucleating intermetallic phases upon cooling after nucleation of the fcc phase. It is shown that although the prediction based on the parallel tangent method contradicts experimental observations, the prediction based on our extended method agrees with them. [ABSTRACT FROM AUTHOR]

Thermodynamic description of the ZrO2-MgO-MnOx was derived for the first time using available experimental data on phase relations in air and protective gas atmosphere. Solid solution phases were modelled using compound energy formalism. The liquid phase was described by the modified two-sublattice model for ionic liquid. Solubility of ZrO2 was modelled in cubic spinel and MgO-MnO solid solution (halite structure) and therefore the Gibbs energies of Zr-containing endmembers were introduced. Ternary interaction parameters were introduced for halite, cubic spinel and cubic ZrO2 to reproduce the stabilization of cubic ZrO2 at temperatures below its stability in bounding systems and stabilization of cubic spinel at temperatures above its stability limit in the bounding systems. The obtained thermodynamic database was used to interpret results of differential thermal analysis. [ABSTRACT FROM AUTHOR]

The addition of vanadium (V) to the representative Co-Cr-Fe-Mn-Ni high-entropy alloy (HEA) system is attracting attention expecting a large solid solution hardening effect. For the design of V-added HEAs, prediction of the sigma (σ) phase formation has been mainly issued because it affects a significant influence on the mechanical properties. Although the CALculation of PHAse Diagram (CALPHAD) approach can be a good tool for prediction of phase structures, robust thermodynamic database is still required for an accurate prediction of V-added HEA systems. The present work aims at providing a thermodynamic description for the Cr-Fe-Ni-V HEA system, focusing on the thermodynamic stability of the σ phase. A parameterization technique which minimizes the number of fitting parameter and simplifies the extension into higher-order systems is proposed and applied to the σ phase with multiple sublattice during modelling the Cr-Ni-V and Fe-Ni-V systems. The reliability of the developed thermodynamic description for the Cr-Fe-Ni-V quaternary system is experimentally confirmed by designing, fabricating and analysing the phase structures of a series of Cr-Fe-Ni-V HEAs. [ABSTRACT FROM AUTHOR]

Phase equilibria of the TiO-AlO system were investigated experimentally using XRD, SEM/EDX and DTA methods. Temperature stability limits of the aluminum titanate (AlTiO) were detected. The thermodynamic parameters of the liquid phase as well as solid solution phases were assessed by CALPHAD approach using obtained experimental results. The thermodynamic data for the Ti-Al, Al-O and Ti-O systems and available experimental data for the Ti-Al-O system were critically evaluated and optimized to develop database of the Ti-Al-O system. [ABSTRACT FROM AUTHOR]

Thermodynamic descriptions of the Fe-Si-P system is developed in the frame of a new Fe-X-P (X = Al, Cr, Cu, Mn, Mo, Si, Ni, Si, Ti) database. The thermodynamic parameters of the binary sub-systems, Fe-Si, Fe-P and Si-P, are taken from the earlier assessments and those of the Fe-Si-P system are optimized in this study using the experimental thermodynamic and phase equilibrium data of the literature. The solution phases of the system (bcc_A2, fcc_A1, dia_A4, liquid) are described with the substitutional solution model. The compounds are treated either with the sublattice model (FeSi-H, FeP and FeP) either as stoichiometric phases (FeP, FeSi, FeSi, FeSi, FeSi-L, SiP, SiP and FeSiP). No solubility of Fe neither Si in the white P-phase has been modeled. The correlation between the calculated and the experimental thermodynamic and phase equilibrium data is reasonably good. [ABSTRACT FROM AUTHOR]

Thermodynamic descriptions of the Fe-Al-P system and its binary sub-systems, Fe-Al and Al-P, are developed in the frame of a new Fe-X-P (X = Al, Cr, Cu, Mn, Mo, Nb, Ni, Si, Ti) database. The thermodynamic parameters of the binary Fe-P system are taken from an earlier assessment and those of the Fe-Al, Al-P and Fe-Al-P systems are modified (Fe-Al, Al-P) or optimized (Fe-Al-P) in this study, using experimental thermodynamic and phase equilibrium data from the literature. The solution phases of the system (liquid, bcc_A2 and fcc_A1) are described with the substitutional solution model. The compounds are treated either as stoichiometric (AlFe, AlFe, AlFe, AlFe, FeP, AlP) or as semi-stoichiometric phases (FeP and FeP). Good or reasonable correlation has been obtained between the calculated and the experimental thermodynamic and phase equilibrium data. [ABSTRACT FROM AUTHOR]

A thermodynamic description of the Fe-Ti-P system is developed in the frame of a new Fe-X-P (X = Al, Cr, Cu, Mn, Mo, Ti, Ni, Ti, Si) database. The adjustable parameters of the binary sub-systems (Fe-P, Fe-Ti and Ti-P) are taken, in general, from earlier assessments (slightly modifying the Ti-P description) and those of the ternary system are optimized in this study using literature experimental thermodynamic and phase equilibrium data. The solution phases of the system (Liquid, bcc_A2, fcc_A1 and hcp_A3) are described with the substitutional solution model. The Fe-Ti and the Ti-P compounds (FeTi, FeTi, TiP, TiP, TiP, TiP, TiP and TiP) are treated as stoichiometric phases. The same is true for the ternary phase FeTiP and for the white-P phase. Continuous solubility has been accepted between the isomorphic compounds FeP and TiP. The titanium solubility in the FeP phase has also been taken into account. Good or reasonable agreement between the calculated and the experimental thermodynamic and phase equilibrium data was obtained. This conformity has been shown by means of a number of graphical and numerical comparisons. [ABSTRACT FROM AUTHOR]

Thermodynamic descriptions of the Fe-Nb-P system and its binary sub-system, Fe-Nb, are developed in the frame of a new Fe-X-P (X = Al, Cr, Cu, Mn, Mo, Nb, Ni, Si, Ti) database. The thermodynamic parameters of the binary sub-systems, Fe-P and Nb-P, are taken from earlier assessments and those of the Fe-Nb-P and Fe-Nb systems are optimized in this study using literature experimental thermodynamic and phase equilibrium data. The solution phases of the system (i.e. bcc_A2, fcc_A1, Liquid) are described with the substitutional solution model. The phase Mu (FeNb) has been modeled as (Fe,Nb)(Nb), while FeP and FeNbP, have been modeled both as (Fe,Nb)(P). All other phases (FeNb, FeP, FeP, NbP, NbP, NbP, NbP, FeNbP, FeNbP, (P)) are treated as stoichiometric. The assessment of this system needs improvement but more experimental information has to be available. [ABSTRACT FROM AUTHOR]

Thermodynamic descriptions of the Fe-Mo-P system and its binary sub-system, Mo-P, are developed in the frame of a new Fe-X-P (X = Al, Cr, Cu, Mn, Mo, Nb, Ni, Si, Ti) database. The thermodynamic parameters of the binary sub-systems, Fe-Mo and Fe-P, are taken from earlier assessments (modifying slightly the Fe-Mo description) and those of the Fe-Mo-P and Mo-P systems are optimized in this study using experimental thermodynamic and phase equilibrium data available in the literature. The solution phases (i.e., bcc_A2, fcc_A1, Liquid) are described with the substitutional solution model. The binary compounds: FeMo, FeP, MoP and MoP, are treated as stoichiometric phases, while for FeP and FeP two-sublattice models accounting for the dissolution of Mo were applied. Some intermetallic compounds (Mu, R and Sigma) are described with three-sublattice models. [ABSTRACT FROM AUTHOR]

Thermodynamic description of the Fe-Ni-P system is developed in the frame of a new Fe-X-P (X = Al, Cr, Cu, Mn, Mo, Nb, Ni, Si, Ti) database. The thermodynamic parameters of the binary sub-systems, Fe-Ni and Fe-P, are taken from earlier assessments. Those of the Ni-P and the Fe-Ni-P systems are optimized in this study using literature experimental thermodynamic and phase equilibria data. The solution phases of the ternary system (liquid, bcc_A2 and fcc_A1) are described with the substitutional solution model. The most of the phosphides (FeP, NiP-H, NiP-L, NiP-H, NiP-L) as well as the white-P-phase are treated as stoichiometric. Continuous solubility has been accepted between the two couples of isomorphic phases: FeP and NiP, and FeP and NiP. Good or reasonable correlation was obtained between the calculated and the experimental thermodynamic and phase equilibrium data. [ABSTRACT FROM AUTHOR]

Thermodynamic descriptions of the Fe-Mn-P system and its binary sub-system, Mn-P, are developed in the frame of a new Fe-X-P (X = Al, Cr, Cu, Mn, Mo, Nb, Ni, Si, Ti) database. The thermodynamic parameters of the binary sub-systems, Fe-Mn and Fe-P, are taken from the latest earlier assessments. Those of the Fe-Mn-P and Mn-P systems are optimized in this study using literature experimental thermodynamic and phase equilibrium data. The solution phases of the system are described with the substitutional solution model and the phosphides are treated as stoichiometric phases or semi-stoichiometric phases of the (A,B)C type described with the two-sublattice model. The formation of a miscibility gap in the liquid phase, at high P-contents is predicted. [ABSTRACT FROM AUTHOR]

A thermodynamic description of the Fe-Cr-P system is developed in the frame of a new Fe-X-P (X = Al, Cr, Cu, Mn, Mo, Nb, Ni, Si, Ti) database. The thermodynamic parameters of the binary sub-systems, Fe-Cr, Fe-P and Cr-P, are taken from earlier assessments slightly modifying the Fe-P and Cr-P descriptions, and those of the ternary system are optimized in this study using the experimental thermodynamic and phase equilibrium data from the literature. The solution phases are described using a substitutional solution model. The phosphides are treated as semi-stoichiometric phases of the type (A,B)C. The intermetallic Sigma phase is described with a three-sublattice model. [ABSTRACT FROM AUTHOR]

Experimental determination of thermodynamic and thermophysical properties of both solid and, in particular, liquid alloys at high temperatures is often technically difficult or even impossible, and therefore theoretical models can be used to estimate missing property values. Preliminary inspection of the literature related to the Cr-Nb-Re system and its binary subsystems reveals mainly theoretical results obtained in the framework of different theories, but the corresponding experimental property data are still sparse. The energetics of mixing in liquid Cr-Nb, Cr-Re and Nb-Re systems has been analysed through the study of the concentration dependence of various thermodynamic, surface (surface tension and surface composition) and structural properties (concentration fluctuations in the long-wavelength limit and chemical short-range order parameter) by the first or the quasi-chemical approximation for regular solutions, developed by Bhatia and Singh, in the framework of statistical mechanical theory in conjunction with the quasi-lattice theory. The results obtained for these binary systems have been extended to study the thermodynamics and surface properties of ternary Cr-Nb-Re liquid alloys. [ABSTRACT FROM AUTHOR]

Thermodynamic description of the Fe-Cu-P system is developed within the frame of a new Fe-X-P (X = Al, Cr, Cu, Mn, Mo, Nb, Ni, Si, Ti) database. The thermodynamic parameters of the binary sub-systems, Fe-Cu, Fe-P and Cu-P, are taken from earlier assessments. Those of the Fe-Cu-P system are optimized in this study using the experimental thermodynamic and phase equilibrium data from the literature. The solution phases of the system are described using the substitutional solution model and the phosphides are treated as stoichiometric or semi-stoichiometric phases of the type (A,B)C. [ABSTRACT FROM AUTHOR]

The C-Cr-Fe-Ni-O system has recently been studied with the intention to thermodynamically describe the influence of oxygen on high alloyed steels. In this study the ternary Fe-Mn-O system is assessed and part of the binary Mn-O system is reassessed. α- and β-hausmannite (Mn3O4) were earlier described as stoichiometric phases, but are here described using the compound energy formalism with a four sublattice model to be consistent with the preceding study of the Cr-Fe-Ni-O spinel. The liquid phase is assessed using the ionic two-sublattice model. Good agreement between calculated and experimental values is achieved. [ABSTRACT FROM AUTHOR]