A Regular Solution Model for a Single-Phase High Entropy and Enthalpy Alloy

A regular solution, 3-component model suggested by J.L. Meijering in which binary interaction parameters were equal and positive has been extended to 5 and 6-component high entropy alloys (HEAs). On cooling, Meijering’s model develops miscibility gaps containing a low temperature eutectoid at the equiatomic composition. Similar behavior is found in this work on HEAs with the eutectoid temperature decreasing, while both the entropy and enthalpy are increasing, as additional components are added to the system. An equation for the chemical spinodal at the equiatomic composition is derived from the same thermodynamic model that was used to predict miscibility gaps. The spinodal temperature is at a cone point where multiple spinodal surfaces meet and is dominated by entropy. A proposal is made to categorize HEAs as having low, medium or high enthalpy. Low enthalpy HEAs are defined as having mixing enthalpies less than 1.25 kJ/mol, high enthalpy HEAs having mixing enthalpies greater than 2.9 kJ/mol, and medium HEA as between the extremes. A possible approach for designing high enthalpy HEAs is suggested to incorporate Meijering’s method of analyzing potential HEAs according to their individual binary interaction parameters instead of their total mixing enthalpy.     

Computation of Eutectic Concentrations and Temperature in Two-Component and Multicomponent Systems

The initial data for computation of eutectic temperature in two-component and multicomponent systems are the form of the binary phase diagrams and the melting temperatures of the components of the eutectic. The eutectic components can be pure elements, chemical compounds, or solid solutions with ultimate solubility. In salt systems these are oxides, salts, or their complexes. Statistical analysis of some phase diagrams of binary, ternary, and other multicomponent systems makes it possible to formalize the interrelation between the eutectic temperature and the melting temperature of eutectic components. The dependences obtained have been used for developing methods of direct and successive computation of eutectic temperature and concentration in two-component and multicomponent systems. In order to reduce the error the elements and their compounds have been classified according to the electron structure and physicochemical properties in accordance with the Periodic System. The methods developed have been used for determining the temperature and concentration conditions of a boronizing process ensuring a liquid crystal state of treated surfaces at saturation temperatures with the aim of formation of pseudoeutectic structures of boronized layers on nickel alloys and high-speed steels.     

Alloy design for high-entropy alloys based on Pettifor map for binary compounds with 1:1 stoichiometry

Pettifor map for binary compounds with 1:1 stoichiometry was utilized as an alloy design for high-entropy alloys (HEAs) with exact or near equi-atomicity in multicomponent systems. Experiments started with selecting GuGd binary compound with CsCl structure from Pettifor map, followed by its extensions by selecting the binary compounds with the same CsCl structure to CuDyGdTbY equi-atomic quinary alloy and to Cu₄GdTbDyY and Ag₄GdTbDyY quinary alloys and Cu₂Ag₂GdTbDyY senary alloy in sequence. X-ray diffraction revealed that CuDyGdTbY alloy was formed into a HEA with mixture of bcc, fcc and hcp structures, whereas the Cu₂Ag₂GdTbDyY HEA was a single CsCl phase. The results suggest a potential of Pettifor map for the development of HEAs by utilizing its information of crystallographic structures. The further analysis was performed for composition diagrams of multicomponent systems corresponding to simplices in a high dimensional space. The present results revealed that a strategy of equi-mole of compounds instead of conventional equi-atomicity also works for the development of HEAs.     

High-Entropy Alloys with a Hexagonal Close-Packed Structure Designed by Equi-Atomic Alloy Strategy and Binary Phase Diagrams

High-entropy alloys (HEAs) with an atomic arrangement of a hexagonal close-packed (hcp) structure were found in YGdTbDyLu and GdTbDyTmLu alloys as a nearly single hcp phase. The equi-atomic alloy design for HEAs assisted by binary phase diagrams started with selecting constituent elements with the hcp structure at room temperature by permitting allotropic transformation at a high temperature. The binary phase diagrams comprising the elements thus selected were carefully examined for the characteristics of miscibility in both liquid and solid phases as well as in both solids due to allotropic transformation. The miscibility in interest was considerably narrow enough to prevent segregation from taking place during casting around the equi-atomic composition. The alloy design eventually gave candidates of quinary equi-atomic alloys comprising heavy lanthanides principally. The XRD analysis revealed that YGdTbDyLu and GdTbDyTmLu alloys thus designed are formed into the hcp structure in a nearly single phase. It was found that these YGdTbDyLu and GdTbDyTmLu HEAs with an hcp structure have delta parameter (δ) values of 1.4 and 1.6, respectively, and mixing enthalpy (ΔH _mix) = 0 kJ/mol for both alloys. These alloys were consistently plotted in zone S for disordered HEAs in a δ-ΔH _mix diagram reported by Zhang et al. (Adv Eng Mater 10:534, 2008). The value of valence electron concentration of the alloys was evaluated to be 3 as the first report for HEAs with an hcp structure. The finding of HEAs with the hcp structure is significant in that HEAs have been extended to covering all three simple metallic crystalline structures ultimately followed by the body- and face-centered cubic (bcc and fcc) phases and to all four simple solid solutions that contain the glassy phase from high-entropy bulk metallic glasses.     

Experimental Investigation and Thermodynamic Calculation of the Phase Equilibria in the Bi-Cu-Zn Ternary System

The phase equilibria of the Bi-Cu-Zn ternary system has been firstly and comprehensively investigated by electron probe microanalyzer (EPMA) with equilibrated alloys. Two isothermal sections of the Bi-Cu-Zn ternary system at 500 and 650 °C were determined. Based on the experimental data of phase equilibria, the Bi-Cu-Zn ternary system was also thermodynamically optimized using the Calculation of Phase Diagrams (CALPHAD) method. The experimental result shows that Bi is almost insoluble in the Cu-Zn binary compounds and (Cu) phase. It is found that the critical temperatures of the miscibility gaps in the Bi-Cu and Bi-Zn binary systems gradually increase with the increasing of the third element Zn or Cu additions. Moreover, the composition range of the liquid miscibility gap gradually reduces with the temperature increasing.     

Thermodynamics of binary phase diagrams with a miscibility gap and a congruently melting compound and binary phase diagrams with two miscibility gaps

The thermodynamics of phase diagrams with a miscibility gap and a congruently melting compound and phase diagrams with two miscibility gaps are treated using the Hoch-Arpshofen solution model and the Schottky- Wagner disorder model. We extended the Schottky-Wagner disorder model to the liquid phase. In phase diagrams with two miscibility gaps, a liquid compound between the two miscibility gaps must be present to obtain consistent thermodynamic data. We treated the Rb-I₂, Au-Se, and Sn-S binary systems.     

Phase transformations in ternary monotectic aluminum alloys

Monotectic aluminum alloys are of interest for the development of new alloys for technological applications such as self-lubricating bearings. In contrast to the well-known binary phase diagrams, many of the ternary systems are not well established. Moreover, in a ternary monotectic alloy one may encounter the four-phase equilibrium L′+L″+solid₁+solid₂, whereas in a binary system only a three-phase equilibrium L′+L″+solid₁ is possible. This opens a window for generating entirely new monotectic microstructures. The basis for such developments is the knowledge of the ternary phase diagrams and the conditions under which such four-phase reactions or different extensions of the binary monotectic reactions may form. This work presents a systematic classification of monotectic ternary aluminum alloys, illustrated by real systems. The study employs thermodynamic calculations of the ternary phase diagrams. For more information contact Rainer Schmid-Fetzer, Institute of Metallurgy, Clausthal University of Technology, D-38678 Clausthal-Zellerfeld, Germany. Fax +49-5323-723120; e-mail schmidfetzer@tu-clausthal.de     

Thermodynamics of binary phase diagrams with a miscibility gap and a congruently melting compound and binary phase diagrams with two miscibility gaps

The thermodynamics of phase diagrams with a miscibility gap and a congruently melting compound and phase diagrams with two miscibility gaps are treated using the Hoch-Arpshofen solution model and the Schottky- Wagner disorder model. We extended the Schottky-Wagner disorder model to the liquid phase. In phase diagrams with two miscibility gaps, a liquid compound between the two miscibility gaps must be present to obtain consistent thermodynamic data. We treated the Rb-I₂, Au-Se, and Sn-S binary systems.     

Phase diagrams of advanced magnesium alloys containing Al,Ca, Sn,Sr, and Mn

In this paper an overview of the most relevant phase diagrams is given comprising the unconventional alloying elements Sn, Ca, and Sr, in reasonable combinations with Al and Mn in Mg alloys as a basis for advanced applications. The focus is on magnesium-rich partial projections of the liquidus surface of five ternary systems, relevant to technological applications for lightweight materials. All phase diagrams are calculated from a coherent thermodynamic multicomponent database for magnesium alloys. These calculations are validated by key samples in the pertinent subsystems, including extensive ternary assessments and also quaternary work. Isothermal sections of magnesium-rich phase diagrams of alloys with constant aluminum and manganese content at 500°C and 550°C are given for the two five-component systems: Mg-Al-Mn-Ca-Sr and Mg-Al-Mn-Ca-Sn.     

Constitution of delta-phase alloys of the system U-Zr-Ti

The ternary section between the intermediate δ-phase alloys of the U-Zr and U-Ti systems has been investigated. A constitutional diagram for the section, ranging from U-74 atomic pct Zr to U-35 atomic pct Ti, is proposed. Thermal, metallographic, and X-ray data were obtained for alloys in this composition range. The section exhibits features of a quasibinary system in that only one and two-phase regions were found at the temperatures investigated. No evidence for a three-phase region or a new phase, not found in the binary systems, was indicated. At elevated temperatures the three components exhibited complete solubility, to form the body-centered-cubic γ phase, decomposing at about 560°C to the U-Zr and U-Ti δ phases in an apparent eutectoid reaction.     

Phase Diagrams: The Beginning of Wisdom

This work presents a primer on “How to Read and Apply Phase Diagrams” in the current environment of powerful thermodynamic software packages. Advanced aspects in that context are also covered. It is a brief guide into using this cornerstone of knowledge in materials science and engineering and offers assistance in the proper interpretation of results obtained from state-of-the-art Calphad-type thermodynamic calculations. Starting from the very basics it explains the reading of unary, binary and ternary phase diagrams, including liquidus projections, isothermal and vertical phase diagram sections. Application examples are directly derived from these phase diagrams of Fe, Cu-Ni, Mg-Al, and Mg-Al-Zn. The use of stable and metastable phase diagrams and appropriate choices of state variables are explained for the relevant Fe-C and Fe-C-Si systems. The most useful concept of zero-phase fraction lines in phase diagram sections of multicomponent systems is made clear by coming back to the Cu-Ni and Mg-Al-Zn systems. Thermodynamic solidification simulation using the Scheil approximation in comparison to the equilibrium case is covered in context of multicomponent multiphase solidification and exemplified for Mg-Al-Zn alloys. The generic approach is directly applicable for all inorganic materials, but exemplified in this concise work for a small selection of metallic systems to highlight the interdependences among the phase diagrams. The embedded application examples for real material systems and various materials processes also emphasize the use of phase diagrams for the path from initial off-equilibrium state towards equilibrium.     

Design of High-Entropy Alloy: A Perspective from Nonideal Mixing

Since the advent in 2004, high-entropy alloys (HEAs) have been attracting a great deal of research interest worldwide. Being deemed as a major paradigmatic shift, the design of HEAs without base elements poses challenges to the existing thermodynamic models and theories that were long established for traditional alloys, one of which is related to the thermodynamic mechanisms for the formation of random solid solution in a concentrated multicomponent alloy. In this article, we discuss the design of HEAs from the perspective of correlated mixing (nonideal mixing of atoms with interatomic correlations). In a quantitative manner, we can show that the formation of a random solid solution in HEAs depends not only on the number of constituent elements but also on the alloy’s melting/processing temperature and on various interatomic correlations. Through the correlated mixing rule, we further demonstrate a strategy to screen out equiatomic alloys with the thermodynamic characteristics close to those of random solid solutions from an expanded library of 20 candidate elements.     

Calculations of phase diagrams in associated solution model

The development of an ideal associated solution model concerned with complexes of various compositions, sizes, and shapes is described. Such models were used earlier to calculate thermodynamic characteristics and the position of the liquidus line for binary eutectic systems as well as those having a stable compound in the solid phase. In all the cases, the model parameters were not adjusted but were estimated from melting temperatures of the components. The latest studies deal with the influence of arbitrary stoichiometry associates on the equilibrium thermodynamic properties of liquid alloys. The application of the model to eutectic systems and systems having an unlimited miscibility in solid and liquid states close to the liquidus has been considered. It was shown that if the difference in melting temperatures of the components was small, different types of fusibility diagrams were possible: eutectic diagrams, cigar-shaped diagrams, or diagrams with upper or lower azeotropic points. Peritectic transformations could take place if the difference in melting temperatures of the components were large.     

Effect of Cr on Microstructure and Properties of a Series of AlTiCr x FeCoNiCu High-Entropy Alloys

A series of AlTiCr _x FeCoNiCu (x: molar ratio, x = 0.5, 1.0, 1.5, 2.0, 2.5) high-entropy alloys (HEAs) were prepared by vacuum arc furnace. These alloys consist of α-phase, β-phase, and γ-phase. These phases are solid solutions. The structure of α-phase and γ-phase is face-centered cubic structure and that of β-phase is body-centered cubic (BCC) structure. There are four typical cast organizations in these alloys such as petal organization (α-phase), chrysanthemum organization (α-phase + β-phase), dendrite (β-phase), and inter-dendrite (γ-phase). The solidification mode of these alloys is affected by Chromium. If γ-phase is not considered, AlTiCr_0.5FeCoNiCu and AlTiCrFeCoNiCu belong to hypoeutectic alloys; AlTiCr_1.5FeCoNiCu, AlTiCr_2.0FeCoNiCu, and AlTiCr_2.5FeCoNiCu belong to hypereutectic alloys. The cast organizations of these alloys consist of pro-eutectic phase and eutectic structure (α + β). Compact eutectic structure and a certain amount of fine β-phase with uniform distribution are useful to improve the microhardness of the HEAs. More γ-phase and the microstructure with similar volume ratio values of α-phase and β-phase improve the compressive strength and toughness of these alloys. The compressive fracture of the series of AlTiCr _x FeCoNiCu HEAs shows brittle characteristics, suggesting that these HEAs are brittle materials.     

Al-Si-Fe三元系热力学计算与评估

利用Calphad技术和应用Pandat相图计算软件,重新评估了Al-Si-Fe体系液相投影图,550、727、800℃等温截面,以及不同成分合金在1 477℃时的液相混合焓。结果表明,计算所得相图及液相混合焓与实验数据相符,该工作建立的热力学模型及参数可作为外推建立Al-Zn-Si-Fe等高元体系数据库的基础,并对相关体系的材料设计工作具有重要的指导意义。     

Mo-RE二元合金相图的热力学数据库

利用CALPHAD方法,选择和建立合理的热力学模型,并结合相平衡及热力学性质的相关实验信息,对Mo-RE (RE: Ce, Pr, Nd, Sm, Eu, Tb, Ho, Er, Tm, Yb, Lu)各二元系相图进行了热力学优化与计算。其中,液相和端际固溶体相的Gibbs自由能采用亚正规溶体模型描述,气相的Gibbs自由能采用理想气体模型描述。计算结果与实验数据取得了良好的一致性,最终得到了一组自洽的合理描述Mo-RE二元系各相自由能的热力学参数,建立了Mo-RE (RE: Ce, Pr, Nd, Sm, Eu, Tb, Ho, Er, Tm, Yb, Lu)二元合金相图的热力学数据库。该热力学数据库可以提供相平衡及热力学性质等多种信息,为外推计算三元以及更多组元体系的相平衡提供理论基础,并为相关体系的合金设计及制备提供重要的理论指导。     

Thermodynamic analysis of alloys Ti–Al, Ti–V, Al–V and Ti–Al–V

Thermodynamic analysis of three binary Ti-based alloys: Ti–Al, Ti–V, and Al–V, as well as ternary alloy Ti–Al–V, is shown in this paper. Thermodynamic analysis involved thermodynamic determination of activities, coefficient of activities, partial and integral values for enthalpies and Gibbs energies of mixing and excess energies at four different temperatures: 2000, 2073, 2200 and 2273 K, as well as calculated phase diagrams for the investigated binary and ternary systems. The FactSage is used for all thermodynamic calculations.     

First-Principles Calculations and CALPHAD Modeling of Thermodynamics

Thermodynamics is the key component of materials science and engineering. The manifestation of thermodynamics is typically represented by phase diagrams, traditionally for binary and ternary systems. Consequently, the applications of thermodynamics have been rather limited in multicomponent engineering materials. Computational thermodynamics, based on the CALPHAD approach developed in the last few decades, has released the power of thermodynamics and enabled scientists and engineers to make phase stability calculations routinely for technologically important engineering materials. Within the similar time frame, first-principles quantum mechanics technique based on density functional theory has progressed significantly and demonstrated in many cases the accuracy of predicted thermodynamic properties comparable with experimental uncertainties. In this paper, the basics of the CALPHAD modeling and first-principles calculations are presented emphasizing current multiscale and multicomponent capability. Our research results on integrating first-principles calculations and the CALPHAD modeling are discussed with examples on enthalpy of formation at 0 K, thermodynamics at finite temperatures, enthalpy of mixing in binary and ternary substitutional solutions, defect structure and lattice preference, and structure of liquid, super-cooled liquid, and glass.     

The Solidification of Multicomponent Alloys

Various topics taken from the author’s research portfolio that involve multicomponent alloy solidification are reviewed. Topics include: ternary eutectic solidification and Scheil-Gulliver paths in ternary systems. A case study of the solidification of commercial 2219 aluminum alloy is described. Also presented are modifications of the Scheil-Gulliver analysis to treat dendrite tip kinetics and solid diffusion for multicomponent alloys.     

TCHEA1: A Thermodynamic Database Not Limited for “High Entropy” Alloys

In this paper we report a thermodynamic database which was developed by using the CALPHAD approach. The TCHEA1 database includes 15 chemical elements (Al, Co, Cr, Cu, Fe, Hf, Mn, Mo, Nb, Ni, Ta, Ti, V, W and Zr). It is suitable for the study of Bcc and Fcc HEA systems. The database is constructed based on the thermodynamic assessment of all binary systems and many key ternary systems where almost all possible metastable and stable phases are considered. It is extensively demonstrated in the present work that TCHEA1 gives satisfactory prediction on the phase equilibria in various HEA systems (quaternary to ennead) and wide temperature ranges (liquidus to subsolidus). Thermodynamic stability calculations of simple solid solutions (Bcc and Fcc) and intermetallics (sigma, Laves, μ-phase etc.) are validated against the available experimental information in as-cast or as-annealed state. Such CALPHAD database focusing on the modelling of Gibbs energy rather than entropy makes reliable predictions of thermodynamic equilibrium and phase transformation, no matter whether the alloy/system has high entropy or not. Cases with miscibility gap in liquid and solid solutions and second-order phase transition at low temperatures are demonstrated. With the volume data included, TCHEA1 is capable to predict the density and thermal expansion coefficient of HEAs as well. This thermodynamic database is also applicable in process simulations when used together with compatible kinetic databases.