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Introduction to High-Entropy Materials

The advancements of human civilization are largely determined by the materials and tools that were manufactured and mastered by humans. During the Stone Age, the ancient human could use only natural materials, including stone, bone, and wood. After that, with the capability of reduction and extraction of copper, tin, lead, and iron from their ores, tools made of copper and iron were widely used in daily life, transportation, and construction during the Bronze Age and the Iron Age. Nowadays, more and more materials with specific properties and performance have been discovered and utilized due to the more efficient metallurgy techniques and material design paradigms, as shown in Figure 1.1 [2]. In the early stage of material design, one principal element is chosen and alloyed with other elements in trace amount to improve the properties of the original element. This design strategy is still dominant in our material design, such as Al alloys, Ni alloys, Fe alloys, and binary solid solution ceramics. Thus, information and understanding are highly developed on materials close to the corners and edges of a multicomponent phase diagram, with little known about those located at the center of the diagram [1, 3]. Recently, crystalline multi-principal element materials located at or near the center of the phase diagram with equal or near-equal atomic fraction of constituting elements have been introduced and have attracted increasing attention due to their unique compositions, microstructure, and unexpected properties. In this chapter, the basic concepts and information about these fascinating materials will be reviewed.

1.1 History of High-Entropy Materials

Attempts to synthesize multicomponent alloys were driven by the desire of metallic glasses with super-high glass-forming ability. After examining the works of Inoue et al. and Peker et al. [4, 5], Greer proposed a "confusion principle," which states that the more the number of elements involved, the lower is the chance that the alloy could select viable crystal structures, and the greater is the chance of glass formation [6]. He also pointed out that the most "confused" elements were those that differed most from each other in size. This principle has boosted the subsequent search of metallic glasses in multicomponent alloys with large atomic size difference [7-9].

Figure 1.1 Rising trend of alloy chemical complexity versus time (IMs: intermetallics or metallic compounds, HEA: high-entropy alloy). Source: Reproduced with permission from Cantor [1]/Springer Nature.

In 2004, two independent papers regarding multicomponent alloys have been published by Yeh et al. and Cantor et al. [10, 11]. Their results seemed to falsely verify the principle of confusion. In Cantor's paper, entitled "Microstructural development in equiatomic multicomponent alloys," the authors performed induction melting and melt quenching rapid solidification experiments on an equiatomic mixture of 20 elements (Mn, Cr, Fe, Co, Ni, Cu, Ag, W, Mo, Nb, Al, Cd, Sn, Pb, Bi, Zn, Ge, Si, Sb, and Mg) and 16 elements (Mn, Cr, Fe, Co, Ni, Cu, Ag, W, Mo, Nb, Al, Cd, Sn, Pb, Zn, and Mg) [11]. Surprisingly, instead of glassy phases, these alloys were multiphase, crystalline, and brittle, even after melt spinning. Moreover, they found that these alloys consisted predominantly of a single face-centered cubic (FCC) primary phase containing many elements but particularly rich in transition metals, notably Cr, Mn, Fe, Co, and Ni. Based on these results, they designed and prepared an equimolar Cr20Mn20Fe20Co20Ni20 alloy with a single FCC structure and a typical dendritic microstructure in the as-cast condition. They also found that the total number of phases was always well below the maximum equilibrium number allowed by the Gibbs phase rule and even further below the maximum number allowed under non-equilibrium solidification conditions. They argued that the confusion principle might not apply and other factors were more important in promoting glass formation rather than chemical complexity.

Simultaneously, Yeh et al. published the paper entitled "Nanostructured high-entropy alloys with multiple principal elements: novel alloy design concepts and outcomes," and clearly defined the term of high-entropy alloys (HEAs) [10]. By rough estimation of mixing entropies of multiple-principal-element alloys, they found that the mixing entropy of alloys with five or more constituent elements was larger than that of metal fusion and formation enthalpies of strong intermetallic (IM) compounds, indicating the preferred tendency of formation of random solid solutions during solidification of these alloys. Due to the central role of mixing entropy in stabilizing the solid solution, they defined these alloys as HEAs. They took the as-cast CuCoNiCrAlxFe alloy system as an example to illustrate that how simple the structure of these chemically complex alloys could be. In the same paper, they also concluded some conspicuous properties of HEAs, such as nanostructures resulting from difficulty in substitutional diffusion of elements, high hardness induced by multi-strengthening mechanisms, excellent resistance to annealing softening, wear, and oxidation. These promising properties made HEAs potentially suitable for many applications such as tools, molds, dies, mechanical parts as well as anticorrosive high-strength parts in chemical plants, integrated circuit (IC) foundries, and even marine applications. Moreover, unlike the commonly used traditional alloy systems, the number of HEAs was countless, even after excluding chemically incompatible elements that produced liquid immiscibility, and the concept of HEAs led to a whole new and uncharted territory, in which many possible new materials, phenomena, theories, and applications were awaited [9].

These two innovative works have ignited enthusiastic research on HEAs. It is worth mentioning that, before they published their groundbreaking works, years of related and ground works have been conducted. Cantor started the study of multicomponent alloys consisting of a large number of constituents in equal or near-equal proportions with his undergraduate students since the beginning of 1980s [12], while the exploration on multicomponent alloys by Yeh and his students could be traced back to 1995 [13].

The attempts to search high-entropy ceramics (HECs) were started by Chen et al. in their pursuit of promoting the hardness of HEA films by introducing non-metallic elements, such as nitrogen and oxygen [14-16]. They found that introducing nitrogen into Al0.5CoCrCuFeNi, Al2CoCrCuFeNi, and AlCrNiSiTi resulted in the amorphization and hardening of the nanostructured metallic solid solution [14, 15]. The oxidation of AlxCoCrCuFeNi (x = 0.5, 1, 2) HEAs led to the formation of a single cubic-spinel crystalline phase [16]. Although they synthesized the ceramics with multi-principal elements, the concept of high-entropy-stabilized ceramics was not used to describe these materials until Rost et al. published their work on high-entropy oxides (HEOs) with a single rock-salt phase and five different cations in equiatomic fractions [17]. This work has led to a significant increase in the number of publications about HEOs, and up to now, a large part of the publications is related to HEOs due to their fascinating mechanical and functional properties. Inspired by this work, high-entropy borides, high-entropy carbides, and other non-oxide HECs have been discovered and reported subsequently [18-21].

1.2 Definition of High-Entropy Materials

There are two generally accepted and widely used definitions for HEAs. One is based on composition and the other is based on configurational entropy. The first one was proposed in 2004 by Yeh et al. based on the compositional requirements [10]. They defined the HEAs as those containing at least five major principal elements with the concentration of each element being between 35 and 5 at.%. In their definition, the ratio of the major elements was not restricted to be equimolar, taking CuCo0.5Ni1.2CrAlFe1.5Ag0.02B0.1C0.15 as an example, leading to countless high entropy (HE) alloys with multiple principal elements. Moreover, HEAs were not required to be a single-phase solid solution according to this definition, and CuCoNiCrAlxFe alloys with 0.8 < x < 2.8 was an illustration.

The second definition is based on the magnitude of mixing entropy. According to the Boltzmann's thermodynamic statistics principle, the quantitative relationship between the entropy and complexion of the system is given by:

where k is the Boltzmann's constant, and ? is the thermodynamic probability, which represents the total number of microscopic states contained in the macroscopic state. With the increase in the number of microscopic states, the configuration entropy of the system increases. For a solid solution consisting of n kinds of atoms,...