Structural Particularities, Prediction, and Synthesis Methods in High-Entropy Alloys

Abstract

High-Entropy Alloys (HEAs) represent a transformative class of materials characterized by multiple principal elements and high configurational entropy. This review article provides an in-depth examination of their structural particularities, prediction methodologies, and synthesis techniques. HEAs exhibit unique structural stability due to high-entropy effects, severe lattice distortions, and slow diffusion processes. Predictive models, including thermodynamic and kinetic approaches, are essential for understanding phase stability. Various synthesis methods impact HEA properties, and advanced characterization techniques are crucial for their study. The article highlights current applications and future research directions, emphasizing the potential of HEAs in diverse technological fields.

1. Introduction

High-Entropy Alloys (HEAs) have emerged as a groundbreaking category of materials, characterized by their multi-principal element compositions and exceptional properties. Unlike traditional alloys, which typically consist of one or two primary elements with additional alloying elements, HEAs are composed of five or more elements in near-equimolar ratios. This compositional complexity leads to high configurational entropy, which stabilizes solid solution phases and imparts unique mechanical and physical properties.

The concept of HEAs was first introduced by Jien-Wei Yeh and Brian Cantor in the early 2000s [1]. Yeh proposed that alloys with multiple principal elements could form simple solid solution phases, such as face-centered cubic (FCC), body-centered cubic (BCC), and hexagonal close-packed (HCP) structures, instead of complex intermetallic compounds. This high-entropy effect is a key factor in the stability and performance of HEAs, distinguishing them from conventional alloys that often suffer from phase segregation and brittleness at high temperatures [2].

HEAs exhibit several remarkable properties, including high strength, excellent wear resistance, superior thermal stability, and good corrosion resistance. These properties make HEAs attractive for a wide range of applications from the aerospace and automotive industries to the energy and biomedical sectors. The high configurational entropy not only stabilizes the solid solution phases but also contributes to severe lattice distortions, which enhance the mechanical strength and hardness of HEAs. Additionally, the sluggish diffusion effect in HEAs results in slow atomic diffusion rates, leading to enhanced thermal stability and resistance to high-temperature deformation [3].

The development and optimization of HEAs require a deep understanding of their structural characteristics, phase stability, and the underlying mechanisms governing their unique properties. Various theoretical and computational models, such as the CALPHAD (CALculation of PHAse Diagrams) method, have been employed to predict phase stability and guide the design of new HEAs. These models consider the thermodynamic and kinetic aspects of HEAs, including Gibbs free energy calculations, mixing enthalpy, and entropy contributions [4]. The prediction of phase stability in HEAs is a complex task, given the vast compositional space and the interplay of multiple elements. However, advancements in computational techniques and high-throughput experiments have significantly enhanced our ability to design and develop new HEAs with tailored properties.

Synthesis methods play a crucial role in determining the microstructure and properties of HEAs. Techniques such as arc melting, mechanical alloying, and powder metallurgy are commonly used to produce HEAs. Each synthesis method has its own advantages and limitations, impacting the homogeneity, phase distribution, and overall performance of the resulting alloys. Post-synthesis treatments, such as heat treatment and thermomechanical processing, further influence the microstructure and mechanical properties of HEAs [5]. Advanced characterization techniques, including X-ray diffraction (XRD), scanning electron microscopy (SEM), and transmission electron microscopy (TEM), are essential for analyzing the phase composition, microstructural features, and defect structures in HEAs [6].

The exploration of HEAs is still in its early stages, with many challenges and opportunities lying ahead. Future research efforts are expected to focus on optimizing alloy compositions, understanding the fundamental mechanisms driving their properties, and exploring new applications for these versatile materials. The potential of HEAs to revolutionize materials science and engineering is immense, offering new pathways for developing next-generation materials with unprecedented performance and functionality [7].

In this review, we will delve into the structural particularities of HEAs, exploring their unique microstructural features and stability mechanisms. We will examine the various prediction and estimation concepts used to design and understand HEAs, highlighting the role of thermodynamic and kinetic models. Furthermore, we will discuss the synthesis methods employed to produce HEAs, emphasizing the impact of different techniques on their properties.

2. Structural Particularities of HEAs, Prediction and Estimation Concepts

High-Entropy Alloys (HEAs) are distinguished by their distinctive structural attributes, such as complex crystal structures, notable lattice distortions, and sluggish atomic diffusion. These particularities result in exceptional mechanical and thermal properties. Predicting and estimating the behaviors of HEAs involves advanced modeling techniques such as thermodynamic simulations, machine learning, and experimental validation to accurately optimize their performance.

2.1. Definition and Composition

One of the pioneering works in the field defines high-entropy alloys (HEAs) as “alloys composed of five or more principal elements in equimolar ratios” [1]. While the requirement for equimolar concentrations is restrictive, the same work extends this definition by specifying that “HEAs can contain principal elements with concentrations ranging from 5% to 35% atomic percent”. This broader definition implies that HEAs do not need to be equimolar, significantly increasing the number of possible high-entropy alloys. HEAs can also include minor elements to modify the alloy’s basic properties, further expanding the scope of HEAs [8].

The “high entropy” concept definition is based on the entropy value. An alternative definition, derived from Boltzmann’s theory, classifies alloys into low-entropy (SSS, ideal < 0.69 R, where SSS, ideal is the total configurational entropy in an ideal system and R is the gas constant), medium-entropy (0.69 R < SSS, ideal < 1.61 R), and high-entropy alloys (SSS, ideal > 1.61 R) [8]. Although Boltzmann’s equation provides a straightforward method for estimating SSS, which is ideal in alloy compositions, it assumes random atomic occupation of lattice sites.

2.2. Microstructural Stability

There are many factors that affect the microstructure and properties of complex alloys. Since high-entropy alloys contain at least five major elements, while conventional alloys are based on one or two metallic elements, there are different basic effects between these two categories. Three of the four basic effects developed and defined by Yeh [8] are high entropy, severe lattice distortion, and slow diffusion, and the fourth effect, proposed by Ranganathan [9], is the cocktail effect (Figure 1). From a thermodynamic point of view, the high-entropy effect could affect the formation of complex phases. For kinetics, the slow diffusion effect could slow down the phase transformation. From the structure perspective, the effect of severe lattice distortion could modify the properties to some extent. For properties, the cocktail effect brings a surplus to the predicted mixing amounts, usually due to mutual interactions between different atoms and severe lattice distortions.

2.2.1. High-Entropy Effect

The high-entropy effect is the concept behind high-entropy alloys and proposes an increase in configurational entropy in equimolar or near-equimolar alloys with 5 or more elements that can favor the formation of solid solution phases over intermetallic compounds. To support this concept, the configurational entropy is often evaluated in relation to the formation entropy of pure metals [1,8,9,10] or the formation enthalpies of certain metal compounds [11]. At the same time, only configurational entropy will be considered [12]. Among the terms that describe the components of entropy (configurational, vibrational, electronic, and magnetic), the configurational component turns out to be dominant over the other three [8]. The vibrational entropy is much higher in the ideal solid solution, but the thermodynamic processes that take place between the solid solution phases and the intermetallic compounds are quite complicated and a large part of the vibrational entropy cancels out in the initial and final phases. Finally, the first observations supporting this effect highlight the phases of the cast product, making the interpretation more complicated. The magnetic and electronic components of the entropy change are particular to the materials placed in magnetic or electric fields. Otherwise, these components have little or no influence on the total entropy of the system. Configurational entropy actually favors the formation of solid solution phases up to a certain level, which can be evaluated against the classical concepts of thermodynamics and against the microstructures reported in scientific papers [12].

2.2.2. Severe Lattice Distortion

The effect of severe lattice deformation is usually compared to single-dominant alloys, where the lattice nodes are mainly occupied by the dominant constituent. For multicomponent alloys, each element has the same possibility of occupying the network node, if the chemical ordering is not taken into account [13]. Significant lattice defects occur due to the varying atomic sizes within the densely packed complex phases. The dislocation at any given point in the atomic lattice is influenced by the specific atom at that location and the types of neighboring atoms. Such distortions that occur in the crystal lattice of a high-entropy alloy are more severe than when they occur in conventional alloys. The uncertainty that arises in the case of occupying the atom positions from these deformations contributes to the excess configurational entropy and contributes to the decrease in the intensity of the X-ray diffraction maxima [8,14]. The severe deformation of the crystal lattice is used to explain the increase in hardness, the reduction of electrical and thermal conductivity, and the reduction of the temperature dependence of these properties. Although this information appears to have a rational basis, research is still being conducted to quantify these effects and to be able to differentiate them from the effects of other processes. For instance, differences in elastic modulus between the constituent atoms can contribute to alloy hardening. Additionally, electrical and thermal conductivity may be affected by the electronic structures resulting from variations in the bonding states between atoms [13].

2.2.3. Slow Diffusion Effect

Specialized studies have shown that the diffusion process, which takes place in alloys with high entropy, is slow [1,8]. This statement is explained by the fact that nanocrystals and amorphous phases are formed during solidification and are based on qualitative interpretations of microstructural stability during cooling [12]. The first study to measure the retarded diffusion capability of high-entropy alloys was produced by Tsai et al. [15]. The authors used a simplified quasi-chemical model to investigate atomic diffusion in an ideal single-phase HEA (CoCrFeMnNi). Results were compared to similar phase (FCC) metal structures and concluded that diffusion is more sluggish in HEAs than in conventional alloys. Yeh [16] studied the formation of vacancies in high-entropy alloys and compared the diffusion coefficients for elements in pure metals, stainless steels, and HEAs. The study concluded that the order of diffusion rates in the three types of alloy systems is: HEA < stainless steels < pure metals. However, later studies performed by various research teams could not verify the initial statements and obtained diffusion behavior similar to conventional alloys [17,18]. Most of the studies related to either typical FCC or stable single-phase solid solution structures, but various compositions have been analyzed in the HEA or newly developed CCA systems and data may be considerably different. Due to the complex nature of the alloys, accurate measurements of the diffusion coefficients are difficult to obtain and more work is needed in the future to validate the original assumptions.

2.2.4. Cocktail Effect

The concept of “cocktail effect” is used for the first time by Prof. S. Ranganathan [9]. Unlike the other “base effects”, the “cocktail” effect is not a hypothesis and does not need to be proven. The “cocktail effect” [19] highlights that the extraordinary properties of materials often emerge from unexpected synergies. Similar unpredictable, synergistic outcomes can be observed in other material behaviors, including physical properties like the near-zero thermal coefficient of expansion; functional properties such as thermoelectric response or photovoltaic conversion; unique combinations of structural properties, like ultra-high hardness paired with good fracture resistance, fatigue resistance, or ductility. In all these instances, the properties are influenced by the material’s composition, microstructure, and electronic structure. The unusual combinations of elements and microstructures, featured by HEA, determine associations of properties that present a high grade of novelty [12,13].

This effect could be interpreted for alloys as a composite characteristic. The composite aspect arises from the notion of solid solution mixture formed by multiple primary components. Basically, this phenomenon refers to the specific property gain, acquired upon the intimate mixture of more than 5 elements within a single sample. The characteristic behavior of each phase present within HEA impacts its structural characteristics, such as morphology, grain size distribution, grains integrity, etc. Also, every individual element contributes to a specific property improvement. For example, this effect can alter material magnetization, flexibility, strength, coercivity, and electrical strength [20,21,22]. For example, the addition of Cr may promote the formation of BCC phase, thus raising the plasticity and lowering both hardness and strength. Also a list of different added elements and their influence with the cocktail effect was presented.

2.3. Prediction and Estimation Concepts

The prediction of phase formation in multicomponent alloys is a complex process fraught with numerous challenges. It is closely tied to achieving superior properties in newly developed materials compared to those conventionally used in the same spectrum of industrial applications. Over the years, extensive studies in this direction have led to the development of a series of empirical and parametric approaches [23,24]. The thermodynamic aspects of multicomponent alloy formation address the relationship between macroscopic variables (temperature, volume, and pressure) that describe the physical properties of materials and the heat radiation. On the other hand, chemical thermodynamics deals with energy transformations of multicomponent systems, that is, it studies the role of entropy in chemical reactions [13].

2.3.1. Gibbs Law

For a more efficient prediction of the number of phases in a multicomponent alloy, the phase rule proposed by Josiah Willard Gibbs in the 1870s can be applied [25]. Gibbs’ rule relates to the number of phases, P, in a multicomponent system at thermodynamic equilibrium, in connection with the degrees of freedom, F (the number of variables that can be independently adjusted without disturbing the equilibrium), and the number of components, N. At constant pressure, Gibbs’ phase rule is expressed by the equation:

$$P=N-F+1.$$

(1)

Given that phases defined by composition have (N − 1) degrees of freedom, and phases defined by temperature have 1 degree of freedom, the maximum number of degrees of freedom F is N. Conversely, the minimum number of degrees of freedom is 0, which corresponds to a point on a phase diagram where the number of phases is at its maximum, (N + 1). Any deviation in composition or temperature reduces the number of equilibrium phases. The minimum number of phases is 1 when the degrees of freedom equal the number of components in the system (i.e., F = N). Gibbs’ phase rule dictates the limits on the number of possible phases and determines the degrees of freedom for a given number of phases and components. However, it does not specify the exact number of phases present in a particular alloy or system at specific temperature and pressure conditions. In a system with N components, the number of phases can range from a minimum of 1 to a maximum of (N + 1) without contradicting Gibbs’ theorem [12]. Some researchers argue that the phase rule does not apply to High-Entropy Alloys (HEAs) [26].The fact that HEAs display fewer phases than the maximum possible is advantageous for validating the entropy effect [23,27,28]. Binary phase diagrams offer a clear method for examining the evolution and stability of a system, such as the mixture of alloy components under specific external conditions. In binary systems, the maximum number of phases is achieved when the degrees of freedom are zero, i.e., F = 0 [12].

The Hume–Rothery rules represent the oldest guidelines for obtaining solid solution alloys [29]. These rules indicate that solid solution formation is most likely in alloys where the constituent elements have comparable atomic sizes, crystal structures, electronegativities, and valencies. To predict solid solution phase formation in complex alloys, the HEA community has established new relationships involving atomic size difference (δ), relative electronegativity (Δχ), and the average valence electron concentration (VEC) [30,31]. Thermodynamic considerations are reflected through the mixing enthalpy ΔH_am and a parameter Ω which incorporates ΔH_am, the mixing entropy ΔS_am, and the melting temperature T_m [32]. The formulas for these parameters are as follows:

$$\delta =100\ast \sqrt{\sum c_i{\left(1-{\displaystyle \frac{r_i}{\overline{r}}}\right)}^2},$$

(2)

$$\mathsf{\Delta }\chi =100\ast \sqrt{\sum c_i{\left(1-{\displaystyle \frac{{\chi }_i}{\overline{\chi }}}\right)}^2},$$

(3)

$$VEC=\sum c_i{VEC}_I,$$

(4)

$${∆H}_{am}=\sum {4c}_i{c}_j\ast {∆H}_{ij},$$

(5)

$$\Omega =\left(\sum c_i{T}_{m,i}\right)\left(∆S_{mix}\right)/\left|∆H_{am}\right|,$$

(6)

where c_i, c_j—the mole fractions for elements i and j;

• r_i—the atomic radius of each element;
• χ_i—electronegativity of each component element;
• VEC_i—valence electron concentration for each element i;
• ΔH_i,j—binary enthalpy;
• T_m,i—melting point of element i;

$\overline{r }$—average atomic radius calculated with the formula:

$$\overline{ r}=\sum c_i{r}_i;$$

(7)

$\overline{\chi }$—average electronegativity calculated with the formula:

$$\overline{\chi }=\sum c_i{\chi }_i;$$

(8)

Studies in the specialized literature [33] have revealed correlations between the phases formed and parameters such as δ or VEC (Figure 2). Zhang et al. [34] discovered that solid solution formation tends to occur within the range of −15 kJ/mol ≤ ΔH_am ≤ 5 kJ/mol and 1% ≤ δ ≤ 6%. Conversely, Guo et al. [32] reported a narrower range of ΔH_am values for HEA formation: −5 kJ/mol ≤ ΔH_am ≤ 5 kJ/mol. In a subsequent study, Guo and Liu [30] identified the following simultaneous ranges for HEA formation: (i) −22 kJ/mol ≤ ΔH_am ≤ 7 kJ/mol, (ii) 0 ≤ δ ≤ 8.5, and (iii) 11 J/Kmol ≤ ΔS_am ≤ 19.5 J/Kmol. Positive values of the mixing enthalpy, ΔH_am, promote phase separation, whereas large negative values favor the formation of intermetallic compounds [35]. Electronegativity difference (Δχ) is also discussed as a main parameter in deciding the structure type in alloys and was determined to be lower than 6% for HEA containing only solid solutions [36,37].

Based on the same parameters and a set of different alloys, Guo et al. [30] suggested that a high value of VEC (>8.0) stabilizes the FCC phase, while a low value (<6.87) stabilizes the BCC phase. A value between these limits leads to the formation of a mixture of FCC and BCC phases [35]. Conversely, the valence electron concentration (VEC) can differentiate phases when dealing with a limited number of alloys within a specific alloy family. For example, in cast alloys such as Al_xCoCrCuFeNi and Al_xCoCrFeNi₂ (where 0 ≤ x ≤ 2) [32], VEC can distinguish between BCC and FCC phases. Similarly, VEC can predict the formation of the σ phase in heat-treated alloys containing Cr and Fe along with Al, Co, Mn, Ni, Ti, and/or V [38]. However, these correlations become less accurate as more elements are introduced. For instance, the same VEC range can predict both BCC + FCC phase formation in [31] and σ phase formation in another context [38]. The addition of Mn is assumed to make these predictions uncertain [31].

Most empirical approaches for predicting solid solution phases or intermetallic compounds in HEAs use parameters such as δ and ΔH_am or Ω [36,39,40,41]. The atomic size difference and ΔH_am are established empirical criteria for identifying amorphous alloys (AM) [40]. These parameters help distinguish between solid solution phases and amorphous phases in HEAs, although intermetallic compounds can overlap with both categories [34,39]. In an attempt to distinguish between solid solution domains and intermetallic compounds, the parameter Ω combines ΔH_am, ΔS_am, and T_m and was first used by Yang and Zhang [39]. By calculating both parameters, δ and Ω, the relationship between them was established (Figure 3), and a new rule for solid solution formation in high-entropy multicomponent alloys with high entropy was proposed.

Thus, when the parameter Ω > 1.1 and the parameter δ < 3.6%, exclusively solid solutions are formed. On the other hand, when Ω and δ fall within the ranges 1.1 < Ω < 10 and 3.6% < δ < 6.6%, both solid solutions and intermetallic compounds are formed, whereas if Ω > 10, only solid solutions are formed [39].

There has been intense research work in the materials community for the discovery of new and reliable HEAs that present single-phase or predominant solid solution structures, which amount to large data sets of alloys with calculated criteria values, validated by experimental trials. It is not the place here to present all of the known data, also presented in previous papers but to show an example of the values obtained.

Table 1. Calculated parameters and experimental results for typical HEA compositions.

Material	Parameters						Phase Type	Experimental [Reference]
	ΔSmix, J/molK	ΔHmix, kJ/mol	δ, %	Ω	Δχ, %	VEC
CoCrFeMnNi	13.38	−4.16	3.27	5.79	4.465	8	FCC	FCC [42]
CoCrFeNi	11.53	−3.75	0.3	5.75	4.853	8.25	FCC	FCC [43]
CoCrFeNiAl0.25	12.71	−6.75	3.47	3.42	5.315	7.94	BCC + FCC	FCC [44]
CrFeMnCuCo	13.38	4.16	3.14	5.56	4.108	8.2	FCC	FCC [42]
WMoNbTa	11.53	−6.5	2.32	5.6	3.765	5.5	BCC	BCC [45]
WMoNbTaV	13.38	−4.64	3.15	8.54	4.458	5.4	BCC	BCC [45]
NbTaHfZrTi	13.38	2.72	4.98	12.41	6.567	4.4	BCC	BCC [46]
CrMnFe1.5Ni0.5Al0.5	12.66	−7.26	5.15	3	4.822	7	BCC + FCC	BCC + IM [47]
CrMnFe1.5Ni0.5Al1.2	12.94	−11.29	6.02	1.85	5.244	6.46	BCC	BCC [47]
Cr0.5Fe0.5NiAlCo0.5MnV	15.75	−15.74	5.29	1.68	7.355	6.64	BCC	BCC [47]
CrNiCoMnV	13.38	−8.8	3.33	2.85	7.375	7.4	BCC + FCC	FCC + IM [42]
CrNiMnFeTi	13.38	−12.32	6.58	1.99	10.219	7	BCC + FCC	BCC + FCC + IM [42]
Al3.4Cu0.5Si0.2Zn0.5Mg0.2	8.15	−3.38	5.7	2.37	7.198	4.77	BCC	FCC + HCP + IM [48]
Al3Si0.8Zn0.3Mg0.7Mn0.2	9.75	−13.79	9.03	0.75	10.774	3.72	IM	FCC + IM [48]
Al20Be20Fe10Si15Ti35	12.69	−40.42	11.15	0.51	11.987	3.8	IM	IM [49]
Al65Cr5Cu5Si15Mn5Ti5	9.68	−20.22	7.7	0.58	8.023	3.95	IM	IM [50]
AlCrFeMnTi0.25	12.71	−11.74	6.27	1.77	6.283	5.88	BCC	BCC + L21 [51]

contains several compositions from the HEA family.

2.3.2. CALPHAD Method

Currently, most commercial software uses thermodynamic calculations that are very popular in the fields of materials science and engineering. Thermodynamic databases, which are integral to all thermodynamic software packages, are developed using the CALPHAD method (CALculation of PHAse Diagrams) [52]. Phase diagrams are like a map that helps design materials and optimize processes. They provide essential information about a particular alloy composition and temperature and also offer details about the present phases, their compositions, and transformation temperatures [52]. Although most binary phase diagrams and a limited number of ternary phase diagrams have been determined experimentally, many multi-component systems remain largely unexplored. Experimentally defining phase diagrams for multi-component systems is highly challenging because of the considerable effort required. However, in recent years, the CALPHAD method, when integrated with key experimental data, has proven to be increasingly effective in elucidating complex phase diagrams for such systems [53,54,55,56,57].

The CALPHAD method primarily focuses on developing thermodynamic functions based on experimental data from binary and ternary phase diagrams. For quaternary and higher-order systems, these methods are less commonly employed because the interactions in higher-order systems are often too weak to significantly impact the results and can be considered negligible [58]. However, the use of complex alloys is possible by combining and exploring binary and ternary data [59]. Thermodynamic functions for a specific set of elements are compiled into a database. These databases are created to replicate known data and predict phase equilibria for alloys where data is lacking. Typically, most databases are developed for alloy systems centered around a primary element. For instance, a thermodynamic database for the AlCoCrFeNi system was created by extrapolating data from binary and ternary systems across a broad range of compositions. The phase diagrams predicted using this database have been validated by experimental results [53].

Thermodynamic modeling based on the CALPHAD method makes significant contributions to the field of complex concentrated alloys. The reliability of CALPHAD calculations is assessed using the binary phase diagram fraction (fAB), which is defined as the ratio of the number of binary phase diagrams shared between the analyzed alloy and the thermodynamic database to the total number of binary systems for the alloy [55]. When fAB = 1, calculations tend to be the most accurate, whereas those with fAB ≥ 0.6 can still offer reliable predictions regarding the number and types of phases. In studies using CALPHAD for equimolar alloys composed of 3 to 6 elements, the phases most frequently identified include FCC, M5Si3 silicides, BCC, B2, and Laves (C15). Notably, for fAB = 1, the phases most commonly encountered are FCC, HCP, M5Si3, B2, and BCC, independent of the specific fAB value. Alloys that meet all four Hume–Rothery rules are always predicted to form solid solutions, though not every alloy predicted by this method adheres to all four rules. For example, alloys that form solid solutions can have a χ (electronegativity difference) of up to 30% and a VEC (valence electron concentration) of up to 55%. Among the Hume–Rothery conditions, the atomic size difference is the most important, ensuring that any alloy predicted to form solid solutions will have a δ value of 15% or lower. When fAB = 1, there is a strong agreement between the calculated and observed phases, a pattern that holds consistently across the entire dataset [53,60,61].

The widely recognized “high mixing entropy” theory suggests that High-Entropy Alloys (HEAs) are likely to form single-phase solid solutions (SS) due to their high configurational entropy. However, numerous studies have demonstrated that many HEAs display multiple phases, and the solid solutions in some single-phase HEAs may become unstable after prolonged annealing. To investigate and better understand the phase formation and stability of HEAs, various methods have been developed and proposed. For example, Yang and Zhang [39] suggested that the phase formation in HEAs is governed by a set of thermodynamic parameters, such as atomic size difference, mixing entropy, and mixing enthalpy. Wang and colleagues [62] applied the method of fundamental principles to refractory HEAs to forecast their phase formation behavior across the temperature-composition range.

Senkov and colleagues [57] applied phase diagram calculation methods (CALPHAD) to large quantities of HEAs, studying their phase formation behaviors and also developing several specialized commercial thermodynamic databases for HEAs. Other methods, such as machine learning, have also been applied to predict the phase formation behavior of HEAs [63].

In HEAs, the primary single-phase solid solution (SS) structures are BCC, FCC, or HCP. However, phases can also co-exist, such as BCC + HCP, BCC + FCC, FCC + HCP, and even combinations like BCC + FCC + HCP. Alongside these, intermetallic compound (IM) phases and amorphous phases may also form. The presence of intermetallic compounds in HEAs is generally undesirable because they often reduce ductility, negatively impacting mechanical performance and complicating processing. For this reason, achieving solid solution structures in HEAs is typically preferred [64].

Examples of HEA compositions with structures simulated by the CALPHAD method are presented in

Table 2. Results of CALPHAD simulations versus experimental for selected alloys.

Material	CALPHAD Results				Experimental [Reference]
	25 °C	400 °C	600 °C	800 °C
CoCrFeMnNi	FCC + BCC + sigma	FCC	FCC	FCC	FCC [42]
CoCrFeNi	BCC + sigma + IM	FCC + BCC + sigma	FCC + sigma	FCC	FCC [43]
CoCrFeNiAl0.25	BCC + sigma + IM	BCC + sigma + IM	FCC + sigma + IM	FCC	FCC [44]
CrFeMnCuCo	FCC + BCC + sigma+ IM	FCC + BCC + HCP + sigma	FCC + BCC	FCC + BCC	FCC [42]
WMoNbTa	BCC + IM	BCC	BCC	BCC	BCC [45]
WMoNbTaV	BCC + IM	BCC	BCC	BCC	BCC [45]
NbTaHfZrTi	HCP + BCC	BCC + HCP	BCC + HCP	BCC	BCC [46]
CrMnFe1.5Ni0.5Al0.5	SIGMA + BCC + IM	SIGMA + BCC + IM	SIGMA + FCC + BCC + IM	BCCC + FFCC + IM	BCC + IM [47]
CrMnFe1.5Ni0.5Al1.2	SIGMA + BCC + IM	BCC + SIGMA + IM	BCC + IM	BCC + IM	BCC [47]
Cr0.5Fe0.5NiAlCo0.5MnV	BCC + IM	BCC + IM	BCC + IM	BCC + FCC + IM	BCC [47]
CrNiCoMnV	FCC + BCC + IM	FCC + BCC	FCC + BCC	FCC + BCC	FCC + IM [42]
CrNiMnFeTi	FCC + IM	BCC + IM	BCC + IM	BCC + IM	BCC + FCC + IM [42]
Al3.4Cu0.5Si0.2Zn0.5Mg0.2	FCC + HCP + IM	BCC + FCC + IM	LIQUID	LIQUID	FCC + HCP + IM [48]
Al3Si0.8Zn0.3Mg0.7Mn0.2	FCC + IM	FCC + IM	IM	LIQUID	FCC + IM [48]
Al65Cr5Cu5Si15Mn5Ti5	BCC + IM	FCC + BCC + IM	FCC + BCC	LIQUID	IM [50]
AlCrFeMnTi0.25	BCC + FCC	BCC	BCC	BCC	BCC + L21 [51]

.

The VEC rule was recently revised for the AlCoCrFeNi alloy system, setting the BCC phase within a VEC range of 5.7 to 7.2, and the FCC phase above a VEC of 8.4. This revision highlights that the VEC range is generally influenced by factors such as temperature, concentration, and the specific constituent elements, provided no intermetallic or amorphous phases develop in the HEA. Furthermore, the VEC rule is found to be most applicable to HEAs primarily composed of 3d or 4d transition metals and is particularly reliable for equiatomic or semi-equiatomic HEAs. These constraints have impacted the accuracy of predicting the crystal structure types in HEAs [65].

To enhance the predictive power of the CALPHAD method, machine learning techniques are increasingly being integrated. These techniques can analyze vast amounts of data from thermodynamic databases and experimental results to identify patterns and improve the accuracy of phase predictions. Machine learning models can provide insights into the complex relationships between composition, processing conditions, and phase stability in HEAs.

Despite its successes, the CALPHAD method faces several challenges in the context of HEAs [66]. The high configurational entropy and potential for numerous competing phases in HEAs can complicate the development of accurate thermodynamic models. Additionally, the presence of intermetallic compounds and amorphous phases can further challenge the predictions. Future research aims to refine thermodynamic databases and enhance the integration of CALPHAD with advanced computational techniques, such as density functional theory (DFT) and machine learning. These advancements will improve the reliability of phase diagrams and property predictions, thereby facilitating the design of novel HEAs with tailored properties for specific applications.

3. Synthesis Methods and Their Influence on the Structure and Properties of HEA Alloys

3.1. Synthesis Methods for HEA Alloys

The processing methods for developing high-entropy alloys (HEAs) are quite similar to those used for conventional alloys. Various techniques for fabricating HEAs are documented in the literature, with casting, sputtering, spraying, and powder metallurgy being the most commonly employed methods [67]. Additionally, High-Pressure Torsion (HPT) has been utilized to create nanocrystalline materials characterized by high strength and structural stability [68]. Generally, the development of HEAs is categorized into three main groups (Figure 4). The first processing route involves the liquid state, which includes methods such as electric arc melting, electric resistance melting, induction melting, laser melting, laser cladding, and LENS (Laser Engineered Net Shaping) forming. The second route involves the solid-state approach, primarily through mechanical alloying followed by consolidation processes. Additionally, elements can be mixed in the vapor state using techniques such as sputtering, pulsed laser deposition (PLD), atomic layer deposition (ALD), molecular beam epitaxy (MBE), and vapor deposition to produce films on substrates [69].

Traditionally, melting and solidification processes have been extensively used for alloy synthesis, with the melting and casting method being employed for HEA production from the beginning. The Vacuum Arc Melting (VAM) technique is particularly effective for achieving the high temperatures required to handle the different melting points of elements in HEAs. Despite its effectiveness, the primary challenge of this method is the evaporation of metals with low boiling points, which makes it challenging to maintain accurate compositional control in HEAs [70]. The melting and casting method offers several benefits, including being time-efficient, cost-effective, and energy-saving. However, high-temperature segregation poses challenges, leading to the formation of dendritic and interdendritic structures. The cooling rate during solidification is crucial in shaping the microstructure and properties of the material. Various studies have shown that the growth of dendrites, the volume fraction in the interdendritic region, and the distribution of alloying elements are significantly influenced by the cooling rate [71].

Induction melting is based on the induction heating characterized by the Joule effect of induced currents resulting from the penetration of an electromagnetic field into a conductive material placed in a time-varying magnetic field. The energy transformation process is presented in Figure 5. Induction heating of a body involves three successive physical phenomena:

• The transfer of electromagnetic energy from the coil to the body to be heated;
• The generation of heat in the material as a result of the Joule effect;
• The transfer of heat through thermal conduction throughout the entire mass of the body.

Multicomponent High-Entropy Alloys (HEAs) are commonly produced by conventional induction melting or vacuum arc melting, followed by casting, which requires repeated remelting to achieve chemical homogeneity [72]. Typically, conventional casting with cooling rates of 10–20 K·s⁻¹ leads to substantial phase separation during HEA production, often requiring additional post-treatment to refine the microstructure and achieve the desired properties (Figure 6). Moreover, the inherent complexity and precise control required to produce bulk homogeneous alloys remains challenging for traditional manufacturing methods in the industry.

The melting temperatures of non-ferrous alloys vary widely due to the differing fusibilities of their constituent metals. Based on their melting points, these metals can be categorized as follows:

• Easily fusible metals, which melt at temperatures below 500 °C (e.g., Sn, Pb, Cd, Zn, etc.)
• Metals with medium melting temperatures, ranging from 500 °C to 1000 °C (e.g., Al, Mg, Sb, Ag, etc.)
• Metals with high melting temperatures, ranging from 1000 °C to 1500 °C (e.g., Cu, Au, Ni, Co, Mn, etc.)
• Refractory metals, which have melting temperatures above 1500 °C (e.g., Cr, Zr, Hf, Ti, W, Mo, etc.)

Under isobaric conditions, the phase transformation of metals during melting is isothermal [73]. Since melting is a process of transitioning from one condensed state to another, the pressure variations that may occur under real conditions are not significant enough to alter the phase transformation temperature. Calculations performed using the Clausius–Clapeyron equation yield negligible variations in melting temperature based on the pressure within the melting aggregates.

3.2. Influence of the Synthesis Method on the Structure and Properties of HEA Alloys

While there is a substantial body of literature reviewing the various synthesis methods for high-entropy alloys (HEAs), there is a noticeable gap when it comes to understanding how these synthesis methods influence the resulting structure and properties of HEAs. Numerous studies have detailed techniques such as casting, sputtering, spraying, and powder metallurgy, as well as advanced methods like High-Pressure Torsion (HPT). However, comprehensive analyses that correlate these fabrication processes with the microstructural characteristics and performance attributes of HEAs are relatively scarce. This is why this article can help address this gap by exploring the impact of different synthesis methods on the structural integrity and mechanical properties of HEAs, providing insights that are crucial for optimizing their development and application in advanced engineering fields.

3.2.1. Influence on the Microstructure of Different HEA Alloys

Figure 7 illustrates the impact of different production techniques on the microstructure of High-Entropy Alloys (HEAs). It highlights the advantages and disadvantages of arc melting, mechanical alloying, casting, and additive manufacturing in terms of achieving homogeneity, grain refinement, and controlling microstructural characteristics. These techniques are assessed for their ability to produce fine-grained and uniform structures, manage segregation, and handle contamination. Understanding these influences is crucial for optimizing the microstructural properties of HEAs for various engineering applications. In 2015, a group of researchers from Australia [74] published a study demonstrating the influence of synthesis methods on the structure of HEA alloys by comparing the microstructures of samples fabricated through direct laser synthesis (using an elemental powder mix, single solidification) and those produced via arc melting (undergoing five remelting cycles). They tested three types of Al_xCoCrFeNi alloys: Al_0.3CoCrFeNi with an FCC structure, Al_0.6CoCrFeNi with a dual FCC + BCC structure, and Al_0.85CoCrFeNi with a BCC structure. Their results revealed that both the Al_0.3 FCC and Al_0.85 BCC alloys exhibited similar microstructures and textures regardless of the processing method used, showing a pronounced 〈001〉 fiber texture aligned with the solidification direction. In the case of the FCC-BCC alloy (Al_0.6CoCrFeNi), arc melting resulted in a dendritic structure, whereas direct laser synthesis produced a Widmanstätten structure. This variation in microstructure was attributed to the faster solidification conditions during direct laser synthesis compared to arc melting.

In 2021, a group of South African researchers published a review article [5] highlighting several studies investigating the influence of synthesis methods through mechanical alloying and consolidation via SPS on the microstructure of various types of HEA alloys. Their primary conclusion was that during the mechanical alloying (MA) process, the energy generated as heat influences the formation of the phases. Severe plastic deformation during mechanical alloying (MA) results in a higher density of dislocations and induces strain within the lattice of the system. Key parameters, including grinding duration and speed, as well as the ball-to-powder ratio, are essential in determining phase evolution within powders. Furthermore, the initial structure of binary alloy pairs, the order of element addition, and the mixing sequence also impact phase development. During the consolidation process via spark plasma sintering (SPS), lattice distortion and the slow diffusion of elements further affect phase evolution in HEA alloys. Consequently, it can be concluded that the process parameters employed during MA and SPS have a significant influence on the microstructure and phases of HEA alloys.

According to the same review article from 2021 [5], phase changes occur during solidification (cooling) in the melting and casting processes of HEA alloys. The formation of phases during solidification is affected by how constituent elements move or are distributed within the alloy. However, the cooling rate, local atomic arrangement variations, and the different diffusion rates of elements can significantly influence the solid phases and the overall microstructure of the alloys. Alloys produced through melting and casting often display dendritic microstructures with segregations between the dendrites. Therefore, melting and casting techniques with higher cooling rates tend to favor the presence of a single dominant phase and limit the formation of secondary phases. Additionally, the formation of HEA phases during melting and casting relies more on the interactions between binary alloy pairs than on the individual constituent elements.

A group of researchers from Japan [75,76] published two studies several years apart about the synthesis of the AlCrFeCoNi HEA alloy using the additive manufacturing technique known as SEBM (Selective Electron Beam Melting) or selective laser melting. Their study revealed that the HEA produced using SEBM shows a microstructure with both BCC and B2 phases, similar to what has been reported for alloys made via melting and casting [77], despite the rapid solidification associated with SEBM. Additionally, an FCC phase was detected at the base of the HEA fabricated by SEBM. This FCC phase may have precipitated from the BCC or B2 phase at lower temperatures during the SEBM process. It is also possible that phase changes occurred during the preheating phase of the SEBM process. The presence of both BCC and FCC phases in the AlCrFeCoNi alloy was also confirmed by Ji et al. [78] who used a powder metallurgy approach (MA + SPS) to create the same HEA alloy.

Using the laser powder bed fusion (LPBF) additive manufacturing technique, Jung et al. [79] created an AlCrFeCoMnNi-type HEA alloy. The microstructure of this alloy displayed the presence of B2 (enriched with Ni–Al) and BCC (enriched with Fe–Cr) solid solutions. This outcome differs from the BCC and FCC phases observed in the alloy when synthesized through powder metallurgy or melting and casting methods [80,81].

When Gao et al. [82] utilized laser-based 3D printing technology to produce a CoCrFeMnNi-type HEA alloy, they observed fine BCC grains distributed along the grain boundaries of the FCC matrix. This observation contrasts with the single FCC phase reported by Kucza et al. [83], Tsai et al. [15], Pickering et al. [84], and Yao et al. [85], who processed the same HEA alloy using various melting and casting methods. Similarly, Joo et al. [86], confirmed the exclusive presence of the FCC phase in the CoCrFeMnNi alloy when produced using powder metallurgy methods.

3.2.2. Influence on the Mechanical Properties of Different HEA Alloys

The synthesis method used for high-entropy alloys (HEAs) plays a crucial role in determining their mechanical properties. Different fabrication techniques such as casting, mechanical alloying, powder metallurgy, and various additive manufacturing methods influence the microstructure, phase composition, and overall mechanical behavior of HEAs. For instance, traditional casting methods often result in dendritic microstructures with interdendritic segregation, which can impact the hardness, ductility, and tensile strength of the alloy [28]. On the other hand, methods like mechanical alloying combined with spark plasma sintering (SPS) can produce fine, homogeneous microstructures with enhanced mechanical properties due to the severe plastic deformation and rapid consolidation process.

Additive manufacturing (AM) techniques, such as selective laser melting (SLM) and laser powder bed fusion (LPBF), offer the advantage of rapid cooling rates, which can refine the microstructure and improve properties like strength and hardness. These methods can also introduce unique microstructural features such as fine BCC grains within an FCC matrix, as observed in some studies [87]. The choice of synthesis method can significantly influence the phase stability, grain size, and distribution of precipitates within the alloy, thereby affecting its mechanical performance. Consequently, understanding the relationship between synthesis techniques and the resulting mechanical properties is essential for optimizing HEAs for various engineering applications.

Table 3. Influence of the synthesis method of HEA alloys on their microstructure and mechanical properties.

Composition of HEA Alloy	Melting-Casting		MA + SPS		AM
	Phases	Mechanical Properties	Phases	Mechanical Properties	Phases	Mechanical Properties
CoCrFeNiMn	FCC [84,85]	-	FCC [88]	Rc = 1987 MPa Vickers hardness = 646 HV	FCC + BCC [82,89,90]	Rt = 601 MPa
CoCrFeNiAl0.3	FCC [91,92]	UTS = 528 MPa YTS = 257 MPa	FCC + BCC [78]	Rc = 1907 MPa Vickers hardness = 625 HV	FCC [93]	UTS = 896 MPa; YS = 730 MPa
CoCrFeNi	-	-	FCC + Cr7C3 [94]	Vickers hardness = 580 HV	FCC [95]	-
AlCoCrCuFeNi	FCC + BCC [96]	Hardness = 5.056 GPa Rc = 1.82 GPa	FCC + BCC [97]	Hardness = 8.13 GPa Elastic modulus = 172 GPa	BCC [98]	-
TiZrNbMo0.3V0.3	BCC [99]	YS = 1312 MPa	-	-	FCC + BCC [100]	-
Ni1.5Co1.5CrFeTi0.5	FCC [101]	YS = 896 MPa Rc = 1502 MPa Vickers hardness = 515 HV	FCC [102]	Vickers hardness = 442 HV Elastic modulus = 216 GPa Rt = 1384 MP	-	-

UTS = ultimate tensile strength; YTS = yield tensile strength; Rc = compression strength; Rt = tensile strength; YS = yield strength.

presents a brief review of some studies focused on the influence of different synthesis methods on the mechanical properties of HEA alloys.

4. Conclusions

High-Entropy Alloys (HEAs) have emerged as a groundbreaking class of materials with exceptional properties and a wide range of potential applications. This article has examined the influence of various synthesis methods on the microstructure and mechanical properties of HEAs. It has been demonstrated that different fabrication techniques, including casting, mechanical alloying, powder metallurgy, and additive manufacturing, significantly affect the phase composition, structural integrity, and mechanical performance of HEAs. The key findings of this brief review study include:

• Microstructural Impact: The choice of synthesis method leads to diverse microstructures. For example, direct laser synthesis and arc melting produce different textures and structures, such as dendritic and Widmanstätten, due to varying solidification conditions.
• Phase Evolution: The evolution of phases in HEAs is influenced by parameters like grinding duration, ball-to-powder ratio, initial structure, and mixing order during mechanical alloying and spark plasma sintering. Similarly, cooling rates and local atomic arrangements during melting and casting impact phase stability and microstructure.
• Mechanical Properties: The mechanical properties, including hardness, ductility, and tensile strength, are significantly influenced by the synthesis method. Additive manufacturing techniques like selective laser melting (SLM) and laser powder bed fusion (LPBF) enhance these properties through rapid cooling rates and refined microstructures.

In addition to traditional synthesis methods, the integration of advanced prediction methodologies and machine learning approaches has opened new avenues for HEA development. In particular, machine learning methods have demonstrated potential in forecasting phase formation and stability in HEAs by examining extensive datasets of thermodynamic and experimental data. These predictive models help identify optimal compositions and processing conditions, thereby accelerating the discovery and optimization of new HEAs with tailored properties.

The utilization of machine learning for predictive modeling represents a significant advancement in the field, enabling researchers to navigate the complex multi-component space of HEAs more efficiently. This approach not only enhances the understanding of the fundamental mechanisms governing HEA behavior but also guides the design of next-generation materials with superior performance characteristics.

In conclusion, the continued exploration of synthesis methods, coupled with advanced computational and machine-learning techniques, will play a crucial role in unlocking the full potential of HEAs. Future research should focus on refining these predictive models and expanding their applications to realize the extraordinary capabilities of HEAs in various engineering and technological domains.