Microstructures and properties of high-entropy alloys

The chemical, physical, and mechanical characteristics of nickel-based superalloys are reviewed with emphasis on the use of this class of materials within turbine engines. The role of major and minor alloying additions in multicomponent commercial cast and wrought superalloys is discussed. Microstructural stability and phases observed during processing and in subsequent elevated-temperature service are summarized. Processing paths and recent advances in processing are addressed. Mechanical properties and deformation mechanisms are reviewed, including tensile properties, creep, fatigue, and cyclic crack growth. I. Introduction N ICKEL-BASED superalloys are an unusual class of metallic materials with an exceptional combination of hightemperature strength, toughness, and resistance to degradation in corrosive or oxidizing environments. These materials are widely used in aircraft and power-generation turbines, rocket engines, and other challenging environments, including nuclear power and chemical processing plants. Intensive alloy and process development activities during the past few decades have resulted in alloys that can tolerate average temperatures of 1050 ◦ C with occasional excursions (or local hot spots near airfoil tips) to temperatures as high as 1200 ◦ C, 1 which is approximately 90% of the melting point of the material. The underlying aspects of microstructure and composition that result in these exceptional properties are briefly reviewed here. Major classes of superalloys that are utilized in gas-turbine engines and the corresponding processes for their production are outlined along with characteristic mechanical and physical properties.

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Nickel-Based Superalloys for Advanced Turbine Engines: Chemistry, Microstructure and Properties

Magnesium alloys have received an increasing interest in the past 12 years for potential applications in the automotive, aircraft, aerospace, and electronic industries. Many of these alloys are strong because of solid-state precipitates that are produced by an age-hardening process. Although some strength improvements of existing magnesium alloys have been made and some novel alloys with improved strength have been developed, the strength level that has been achieved so far is still substantially lower than that obtained in counterpart aluminum alloys. Further improvements in the alloy strength require a better understanding of the structure, morphology, orientation of precipitates, effects of precipitate morphology, and orientation on the strengthening and microstructural factors that are important in controlling the nucleation and growth of these precipitates. In this review, precipitation in most precipitation-hardenable magnesium alloys is reviewed, and its relationship with strengthening is examined. It is demonstrated that the precipitation phenomena in these alloys, especially in the very early stage of the precipitation process, are still far from being well understood, and many fundamental issues remain unsolved even after some extensive and concerted efforts made in the past 12 years. The challenges associated with precipitation hardening and age hardening are identified and discussed, and guidelines are outlined for the rational design and development of higher strength, and ultimately ultrahigh strength, magnesium alloys via precipitation hardening.

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Precipitation and Hardening in Magnesium Alloys

The objective of this review is to study interfacial reactions between pure Sn or Sn-rich solders, and common base metals used in Pb-free electronics production. In particular, the reasons leading to the observed interfacial reactions products and their metallurgical evolution have been analyzed. Results presented in the literature have been critically evaluated with the help of combined thermodynamic–kinetic approach based on the concept of local equilibrium and microstructural knowledge. The following conclusions have been reached: Firstly, the formations of intermetallic compounds in solid/liquid reaction couples are primarily controlled by the dissolution processes of base metals. Other factors that need be considered are the thermodynamic driving force for the formation of intermetallic compounds, their structures and concentration profiles in liquid. Secondly, annealing of solder interconnections in solid state can drastically change the microstructures formed in the solid/liquid reactions, especially if only one of the components in the solder takes part in the interfacial reactions. Thirdly, additional elements can have three major effects on the binary reactions between a base metal and Sn: (i) they can increase or decrease the reaction/growth rates, (ii) the additives can change the physical properties of the phases formed, and (iii) they can form additional reaction products or displace the binary equilibrium phases by forming new reaction products. Finally, if the local stable or metastable equilibrium is established at the interface, stability information together with kinetic considerations can provide a feasible approach to analyze interfacial reactions, which can have significant impact on the reliability of soldered electronics assemblies.

Interfacial reactions between lead-free solders and common base materials

The phase-field method is reviewed against its historical and theoretical background. Starting from Van der Waals considerations on the structure of interfaces in materials the concept of the phase-field method is developed along historical lines. Basic relations are summarized in a comprehensive way. Special emphasis is given to the multi-phase-field method with extension to elastic interactions and fluid flow which allows one to treat multi-grain multi-phase structures in multicomponent materials. Examples are collected demonstrating the applicability of the different variants of the phase-field method in different fields of materials science.

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Phase-field models in materials science

This paper provides a consistent thermodynamic data set for the whole Cr–Nb–Ni ternary system via thermodynamic modeling. All of the experimental phase diagram data available from the literature are critically reviewed and assessed using thermodynamic models for the Gibbs energies of individual phases. The ternary liquid and (Ni) phases are described with a regular solution model. The two-sublattice model is used to model the binary phases NbCr 2 (HT), NbCr 2 (LT), NbNi 3 , and Nb 6 Ni 7 . In order to reproduce the measured solid solubilities in the ternary system and to reduce the number of adjustable parameters, the third element is assumed to be anti-site atoms in only one sublattice. Optimal thermodynamic parameters are obtained by considering reliable literature data. Comprehensive comparisons between calculated and measured phase diagrams show that all the accurate experimental information is satisfactorily accounted for by the present thermodynamic description. The thermodynamic parameters obtained can also describe the diffusion paths observed for the diffusion couples between Nb and several Cr–Ni alloys annealed at 1002  ∘ C.

A thermodynamic modeling of the Cr–Nb–Ni system

A methodology was presented for determining the interdiffusion coefficients of phases formed in a ternary diffusion couple using the measured growth rates and the concentration profiles across the couple Using this methodology the interdiffusion coefficients of the TNi 3 GaAs phase were obtained from several GaAs/Ni couples Assuming the cross-intrinsic diffusion coefficients to be negligible, relationships between intrinsic diffusion coefficients and interdiffusion coefficients were derived, and values were obtained for the three intrinsic diffusion coefficients of the T-phase The intrinsic diffusivity for Ni was the largest and that for arsenic the smallest These data were rationalized in terms of the structure of the T-phase

On the determination of diffusion coefficients in multi-phase ternary couples

The Huntington-McCombie-Elcock (HME) and antistructure bridge (ASB) mechanisms proposed for B2 intermetallic compounds are reviewed. By using a thermodynamic argument, the HME mechanism is shown to be operative near the stoichiometric composition. On the other hand, the ASB mechanism is shown to be important at compositions away from stoichiometry. A combination of these two mechanisms is able to describe the compositional dependences of the experimentally determined self-diffusion coefficients for several B2 intermetallic compounds. By using conclusions drawn from these two mechanisms, it is further shown that the compositional dependences of the activation energies and pre-exponential factors are related to the partial molar enthalpies and entropies of the component elements. The frequently observed decreases in the activation energy and pre-exponential factor with deviations from stoichiometry are in accord with the corresponding decreases in the partial molar enthalpy and entropy. The extensive experimental data for NiAl are used to verify these relations.

Diffusional behavior in B2 intermetallic compounds

An associated solution model is used to describe the thermodynamic properties of the liquid phase in the Pb−S system, where the existence of ‘PbS’ species is assumed in addition to ‘Pb’ and ‘S’. The liquid is now considered as a pseudo-ternary solution of ‘Pb’, ‘S’, and ‘PbS’ in which the concentrations of the species are related by an equilibrium constant. The thermodynamic properties of the intermediate phase, PbS, are described by a point-defect model. The doubly ionized vacancies on the Pb and the S sites are considered to be the dominant defects and the nonstoichiometry is caused by the excess of vacancies on either site. The parameters of these models are obtained by simultaneous optimization of the available thermodynamic and phase equilibria data. The Pb−S phase diagram is then calculated, using these thermodynamic models, and compared with the experimental data.

A thermodynamic analysis of the Pb−S system and calculation of the Pb−S phase digram

A thermodynamic method is developed for determining the activities of all three component elements along a ternary miscibility gap from a knowledge of the line distributions and the pertinent binary thermodynamic properties. The thermodynamic treatment outlined is particularly applicable when the ternary miscibility gap lies close to one of the boundary binaries. Its usefulness is demonstrated by successfully deriving the activities in the ternary system Cu-Pb-O at 1473 K. The method presented is of general applicability to ternary systems consisting of two metals and a nonmetal such as oxygen, sulfur or selenium.

Y. A. Chang

Papers

A thermodynamic modeling of the Cr–Nb–Ni system

On the determination of diffusion coefficients in multi-phase ternary couples

Diffusional behavior in B2 intermetallic compounds

A thermodynamic analysis of the Pb−S system and calculation of the Pb−S phase digram

A thermodynamic method for determining the activities from ternary miscibility gap data: The Cu-Pb-O system