This chapter summarizes the progress that has been made in the study of high-entropy alloy (HEA) systems and the process-structure-property relationships that define them. It describes the various ways HEAs can be strengthened and explains how alloying elements influence tensile and yield strength, fracture toughness, and fracture strength. It discusses the stages of plastic deformation in HEAs and the role of dislocations and twinning in the evolution of microstructure. It reviews some of the work that has been done on fatigue behaviors and the methods developed to assess fatigue performance. It discusses the influence of defects on fatigue life, the effect of temperature and grain size on fatigue-crack propagation, and the role of nanotwinning in crack-growth retardation. It describes the methods used to produce HEAs in bulk and powder form and to apply them as protective coatings and films. It also identifies potential applications based on properties such as strength, hardness, density, wear resistance, high-temperature stability, and biocompatibility.

This chapter, presented in a question-and-answer format, covers many practical aspects of high-entropy alloys (HEAs). It provides clear and concise answers to more than 50 questions, imparting knowledge on alloying elements, heat treatments, diffusion mechanisms, phase formation, lattice distortion, crystal and grain structures, structure-property relationships, microstructure control, and characterization methods. It likewise explains how to calculate the effect of strengthening processes on the mechanical properties of HEAs and offers insights on how to balance strength, ductility, and density for specific applications. It also provides information on twinning behaviors, stacking faults, elastic properties, coating and film deposition methods, manufacturing challenges, and the use of computational techniques for alloy design.

This chapter describes the basics of energy and entropy and “free energy.” Fundamentals of internal energy U , the enthalpy H , entropy S , free energies G , and F of a substance are presented. The chapter also presents the thermal vibration model to promote a better understanding of the U , S , and F of the crystal. It covers basic concepts of thermodynamics of magnetic transition and discusses the role and the meaning of magnetic transition in iron and steel. The chapter concludes with a general discussion on an amorphous phase from a thermodynamic viewpoint.

This chapter explains how the principles of chemical thermodynamics are used in the construction and interpretation of phase diagrams. After a brief review of the laws of thermodynamics, it describes the concept of Gibbs free energy and its application to transformations that occur in single-component and binary solid solutions. It then examines the relationship between the free energy of a solution and the chemical potentials of the individual components. It also explains how to account for the heat of mixing using quasi-chemical models, discusses the effect of interatomic bond energies and chemical potentials, and shows how the equilibrium state of an alloy can be obtained from free-energy curves.

This chapter explains the idea of solution theory and the nature of mixed materials. The chapter considers approximation of free energy by the regular solution model and sublattice model. It discusses chemical potential and nonrandom distribution based on the interactions between solute atoms.

This chapter presents abbreviations and symbols used for soldering.

This chapter covers the analytical methods developed to characterize ordering phenomena in crystal structures. The chapter gives examples of ordering phenomena and discusses models for long-range ordering, such as the Bragg-Williams-Gorsky (B-W-G) model, and for short-range ordering. Examples of ordering and phase separation due to ordering by the B-W-G model are described. The chapter includes an appendix covering the effect of phase separation inversion type.

This appendix is intended as a guide for expressing weights and measures in the base, supplementary, and derived Systeme International d'Unites.

This chapter provides a fundamental understanding of beryllium reduction thermodynamics as a prerequisite for subsequent chapters on extraction, chemical processing, and corrosion. It examines a number of reduction methods along with a potential refining process, highlighting the challenges encountered with each.