High entropy effect

The high entropy effect is the most important effect because it can enhance the formation of solid solutions and makes the microstructure much simpler than expected. The prior knowledge expected to multi component alloys to have many different interactions among elements and thus form many different kinds of binary, ternary, and quaternary compounds and/or segregated phases. Thus, such alloys would possess complicated structure brittle by nature. This expectation in fact neglects the effect of high entropy effect. Indeed, according to the Second law of thermodynamics, the state having the lowest mixing Gibbs free energy  ${\displaystyle \Delta G_{mix}=\Delta H_{mix}-T\Delta S_{mix}}$ among all possible states would be the equilibrium state. Elemental phases based on one major element have small  Enthalpy of mixing (${\displaystyle \Delta H_{mix}}$) and a small Entropy of mixing (${\displaystyle \Delta S_{mix}}$), and compound phases have large ${\displaystyle \Delta H_{mix}}$  but small ${\displaystyle \Delta S_{mix}}$; on the other hand, solid-solution phases containing multiple elements have medium  ${\displaystyle \Delta H_{mix}}$ and high ${\displaystyle \Delta S_{mix}}$ . As a result, solid-solution phases become highly competitive for equilibrium state and more stable especially at high temperatures.^[30]

Severe lattice distortion effect

Because solid solution phases with multi-principal elements are usually found in HEAs, the conventional crystal structure concept is thus extended from a one or two element basis to a multi-element basis. every atom is surrounded by different kinds of atoms and thus suffers lattice strain and stress mainly due to atomic size difference. Besides the atomic size difference, both different bonding energy and crystal structure tendency among constituent elements are also believed to cause even higher lattice distortion because non-symmetrical bindings and electronic structure exist between an atom and its first neighbours. This distortion is believed to be the source of some of the mechanical, thermal, electrical, optical, and chemical behaviour of HEAs. Thus, overall lattice distortion would be more severe than that in traditional alloys in which most matrix atoms (or solvent atoms) have the same kind of atoms as their surroundings.^[30]

Sluggish diffusion effect

As explained in the last section, an HEA mainly contains random solid solution and/or ordered solid solution. Their matrices could be regarded as whole-solute matrices. In HEAs, those whole-solute matrices diffusion vacancy are surrounded by different element atoms, and thus have a specific lattice potential energy (LPE). This large fluctuation of LPE between lattice sites leads to low-LPE sites can serve as traps and hinder atomic diffusion.^[31] This leads to the sluggish diffusion effect.

Cocktail effect

Cocktail effect is used to emphasise the enhancement of the properties by at least five major elements. Because HEAs might have one or more phases, the whole properties are from the overall contribution of the constituent phases. Besides, each phase is solid solution and can be viewed as a composite with properties coming not only from the basic properties of constituant by the mixture rule but also from the interactions among all the constituant and from the severe lattice distortion. The Cocktail effect take into account the effect from the atomic-scale multicomponent phases and from the multi phases composite at the micro scale.^[32]

Phase formation

Gibbs' phase rule, ${\displaystyle F=C-P+2}$, can be used to determine an upper bound on the number of phases that will form in an equilibrium system. In his 2004 paper, Cantor created a 20-component alloy containing 5 at% of Mn, Cr, Fe, Co, Ni, Cu, Ag, W, Mo, Nb, Al, Cd, Sn, Pb, Bi, Zn, Ge, Si, Sb, and Mg. At constant pressure, the phase rule would allow for up to 21 phases at equilibrium, but far fewer actually formed. The predominant phase was a face-centered cubic solid-solution phase, containing mainly Cr, Mn, Fe, Co, and Ni. From that result, the CrMnFeCoNi alloy, which forms only a solid-solution phase, was developed.^[22]

The Hume-Rothery rules have historically been applied to determine whether a mixture will form a solid solution. Research into high-entropy alloys has found that in multi-component systems, these rules tend to be relaxed slightly. In particular, the rule that solvent and solute elements must have the same crystal structure does not seem to apply, as Cr, Mn, Fe, Co, and Ni have three different crystal structures as pure elements (and when the elements are present in equal concentrations, there can be no meaningful distinction between "solvent" and "solute" elements).^[25]

Thermodynamic mechanisms

Phase formation of HEA is determined by thermodynamics and geometry. When phase formation is controlled by thermodynamics and kinetics are ignored. ΔG_mix (Gibbs free energy of mixing) is defined as:

ΔG_mix = ΔH_mix - TΔS_mix

where H_mix is defined as enthalpy of mixing, T is temperature, and S_mix is entropy of mixing respectively. ΔH_mix and TΔS_mix continuously compete to determine the phase of the HEA material. Other important factors include atomic size of each element within the HEA, where Hume-Rothery rules and Akihisa Inoue [Wikidata]'s three empirical rules for bulk metallic glass play a role.

Disordered solids form when atomic size difference is small and ΔH_mix is not negative enough. This is because every atom is about the same size and can easily substitute for each other and ΔH_mix is not low enough to form a compound. More-ordered HEAs form as the size difference between the elements gets larger and ΔH_mix gets more negative. When the size difference of each individual element become too large, bulk metallic glasses form instead of HEAs. High temperature and high ΔS_mix also promote the formation of HEA because they significantly lower ΔG_mix, making the HEA easier to form because it is more stable than other phases such as intermetallics.^[36]

The multi-component alloys that Yeh developed also consisted mostly or entirely of solid-solution phases, contrary to what had been expected from earlier work in multi-component systems, primarily in the field of metallic glasses.^[21][37] Yeh attributed this result to the high configurational, or mixing, entropy of a random solid solution containing numerous elements. The mixing entropy for a random ideal solid solution can be calculated by:

${\displaystyle {\Delta }S_{mix}=-R\sum _{i=1}^{N}c_{i}\ln {c_{i}}}$

where R is the ideal gas constant, N is the number of components, and c_i is the atomic fraction of component i. From this it can be seen that alloys in which the components are present in equal proportions will have the highest entropy, and adding additional elements will increase the entropy. A five-component, equiatomic alloy will have a mixing entropy of 1.61R.^[21][38]

However, entropy alone is not sufficient to stabilize the solid-solution phase in every system. The enthalpy of mixing (ΔH), must also be taken into account. This can be calculated using:

${\displaystyle {\Delta }H_{mix}=\sum _{i=1,i{\neq }j}^{N}4{\Delta }H_{AB}^{mix}c_{i}c_{j}}$

where ${\displaystyle {\Delta }H_{AB}^{mix}}$ is the binary enthalpy of mixing for A and B.^[39] Zhang et al. found, empirically, that in order to form a complete solid solution, ΔH_mix should be between -10 and 5 kJ/mol.^[38] In addition, Otto et al. found that if the alloy contains any pair of elements that tend to form ordered compounds in their binary system, a multi-component alloy containing them is also likely to form ordered compounds.^[25]

Both of the thermodynamic parameters can be combined into a single, unitless parameter Ω:

${\displaystyle \Omega ={\frac {T_{m}{\Delta }S_{mix}}{\left\vert {\Delta }H_{mix}\right\vert }}}$

where T_m is the average melting point of the elements in the alloy. Ω should be greater than or equal to 1.1, which means entropy dominates over enthalpy at the point of solidification, to promote solid solution development.^[40][41]

Ω can be optimized by adjusting element composition. Waite J. C. has proposed an optimisation algorithm to maximize Ω and demonstrated that slight change in composition could cause huge increase of Ω.^[35]

Kinetic mechanisms

The atomic radii of the components must also be similar in order to form a solid solution. Zhang et al. proposed a parameter δ, average lattice mismatch, representing the difference in atomic radii:

${\displaystyle \delta ={\sqrt {\sum _{i=1}^{N}c_{i}\left(1-{\frac {r_{i}}{\bar {r}}}\right)^{2}}}}$

where r_i is the atomic radius of element i and ${\displaystyle {\bar {r}}=\sum _{i=1}^{N}c_{i}r_{i}}$. Formation of a solid-solution phase requires a δ ≤ 6.6%, which is an empirical number based on experiments on bulk metallic glasses (BMG).^[35] Exception are found on both side of 6.6%: some alloys with 4% < δ ≤ 6.6% do form intermetallics,^[38][40] and solid-solution phase do appear in alloy with δ > 9%^[41]

The multi-element lattice in HEAs is highly distorted because all elements are solute atoms and their atomic radii are different. δ helps evaluating the lattice strain caused by disorder crystal structure. When the atomic size difference (δ) is sufficiently large, the distorted lattice would collapse and a new phase such as an amorphous structure would be formed. The lattice distortion effect can result in solid solution hardening.^[2]

Other properties

For those alloys that do form solid solutions, an additional empirical parameter has been proposed to predict the crystal structure that will form. HEAs are usually FCC (face-centred cubic), BCC (body-centred cubic), HCP (hexagonal close-packed), or a mixture of the above structures, and each structure have their own advantages and disadvantages in terms of mechanical properties. There are many methods to predict the structure of HEA. Valence electron concentration (VEC) can be used to predict the stability of the HEA structure. The stability of physical properties of the HEA is closely associated with electron concentration (this is associated with the electron concentration rule from the Hume-Rothery rules).

When HEA is made with casting, only FCC structures are formed when VEC is larger than 8. When VEC is between 6.87 and 8, HEA is a mixture of BCC and FCC, and while VEC is below 6.87, the material is BCC. In order to produce certain crystal structure of HEA, certain phase stabilizing elements can be added. Experimentally, adding elements such as Al and Cr and help the formation of BCC HEA while Ni and Co can help forming FCC HEA.^[36]

Mechanical

The crystal structure of HEAs has been found to be the dominant factor in determining the mechanical properties. bcc HEAs typically have high yield strength and low ductility and vice versa for fcc HEAs. Some alloys have been particularly noted for their exceptional mechanical properties. A refractory alloy, VNbMoTaW maintains a high yield strength (>600 MPa (87 ksi)) even at a temperature of 1,400 °C (2,550 °F), significantly outperforming conventional superalloys such as Inconel 718. However, room temperature ductility is poor, less is known about other important high temperature properties such as creep resistance, and the density of the alloy is higher than conventional nickel-based superalloys.^[40]

CrMnFeCoNi has been found to have exceptional low-temperature mechanical properties and high fracture toughness, with both ductility and yield strength increasing as the test temperature was reduced from room temperature to 77 K (−321.1 °F). This was attributed to the onset of nanoscale twin boundary formation, an additional deformation mechanism that was not in effect at higher temperatures. At ultralow temperatures, inhomogenous deformation by serrations has been reported.^[68] As such, it may have applications as a structural material in low-temperature applications or, because of its high toughness, as an energy-absorbing material.^[69] However, later research showed that lower-entropy alloys with fewer elements or non-equiatomic compositions may have higher strength^[70] or higher toughness.^[71] No ductile to brittle transition was observed in the bcc AlCrFeCoNi alloy in tests as low as 77 K.^[40]

Al_0.5CrFeCoNiCu was found to have a high fatigue life and endurance limit, possibly exceeding some conventional steel and titanium alloys. But there was significant variability in the results, suggesting the material is very sensitive to defects introduced during manufacturing such as aluminum oxide particles and microcracks.^[72]

A single-phase nanocrystalline Al₂₀Li₂₀Mg₁₀Sc₂₀Ti₃₀ alloy was developed with a density of 2.67 g cm⁻³ and microhardness of 4.9 – 5.8 GPa, which would give it an estimated strength-to-weight ratio comparable to ceramic materials such as silicon carbide,^[12] though the high cost of scandium limits the possible uses.^[73]

Rather than bulk HEAs, small-scale HEA samples (e.g. NbMoTaW micro-pillars) exhibit extraordinarily high yield strengths of 4 – 10 GPa — one order of magnitude higher than that of its bulk form – and their ductility is considerably improved. Additionally, such HEA films show substantially enhanced stability for high-temperature, long-duration conditions (at 1,100 °C for 3 days). Small-scale HEAs combining these properties represent a new class of materials in small-dimension devices potentially for high-stress and high-temperature applications.^[45][26]

In 2018, new types of HEAs based on the careful placement of ordered oxygen complexes, a type of ordered interstitial complexes, have been produced. In particular, alloys of titanium, hafnium, and zirconium have been shown to have enhanced work hardening and ductility characteristics.^[74]

Bala et al. studied the effects of high-temperature exposure on the microstructure and mechanical properties of the Al5Ti5Co35Ni35Fe20 high-entropy alloy. After hot rolling and air-quenching, the alloy was exposed to a temperature range of 650-900 °C for 7 days. The air-quenching caused γ′ precipitation distributed uniformly throughout the microstructure. The high-temperature exposure resulted in growth of the γ′ particles and at temperatures higher than 700 °C, additional precipitation of γ′ was observed. The highest mechanical properties were obtained after exposure to 650 °C with a yield strength of 1050 MPa and an ultimate tensile yield strength of 1370 MPa. Increasing the temperature further decreased the mechanical properties.^[75]

Liu et al. studied a series of quaternary non-equimolar high-entropy alloys Al_xCr_15xCo_15xNi_70−x with x ranging from 0 to 35%. The lattice structure transitioned from FCC to BCC as Al content increased and with Al content in the range of 12.5 to 19.3 at%, the γ′ phase formed and strengthened the alloy at both room and elevated temperatures. With Al content at 19.3 at%, a lamellar eutectic structure formed composed of γ′ and B2 phases. Due to high γ′ phase fraction of 70 vol%, the alloy had a compressive yield strength of 925 MPa and fracture strain of 29% at room temperature and high yield strength at high temperatures as well with values of 789, 546, and 129 MPa at the temperatures of 973, 1123, and 1273K.^[76]

In general, refractory high-entropy alloys have exceptional strength at elevated temperatures but are brittle at room temperature. The TiZrNbHfTa alloy is an exception with plasticity of over 50% at room temperature. However, its strength at high temperature is insufficient. With the aim of increasing high temperature strength Chien-Chuang et al. modified the composition of TiZrNbHfTa, and studied the mechanical properties of the refractory high-entropy alloys: TiZrMoHfTa and TiZrNbMoHfTa. Both alloys have simple BCC structure. Their experiments showed that the yield strength of TiZrNbMoHfTa had a yield strength 6 times greater than TiZrMoHfTa at 1200 °C with a fracture strain of 12% retained in the alloy at room temperature.^[77]

Electrical and magnetic

CrFeCoNiCu is an fcc alloy that was found to be paramagnetic. But upon adding titanium, it forms a complex microstructure consisting of fcc solid solution, amorphous regions and nanoparticles of Laves phase, resulting in superparamagnetic behavior.^[78] High magnetic coercivity has been measured in a FeMnNiCoBi alloy.^[48] There are several magnetic high-entropy alloys which exhibit promising soft magnetic behavior with strong mechanical properties.^[79] Superconductivity was observed in TiZrNbHfTa alloys, with transition temperatures between 5.0 and 7.3 K.^[80]

Thermal Stability

Since high-entropy alloys are likely utilized in high temperature environment, the thermal stability is very important for designing HEA. This is especially critical for nano-crystalline where extra driving force exists for grain growth. Two aspects need to be considered for nano-crystalline HEAs: the stability of phases formed, which is dominated by the thermodynamics mechanism (see alloy design), and the retention of nanocrystallinity.^[81] The stability of nano-crystalline HEAs are controlled by many factors, including grain boundary diffusion, presence of oxide etc.

Other

The high concentrations of multiple elements leads to slow diffusion. The activation energy for diffusion was found to be higher for several elements in CrMnFeCoNi than in pure metals and stainless steels, leading to lower diffusion coefficients.^[82] Some equiatomic multicomponent alloys have also been reported to show good resistance to damage by energetic radiation.^[83] High-entropy alloys are investigated for hydrogen storage applications.^[84][85] Some high-entropy alloys such as TiZrCrMnFeNi show fast and reversible hydrogen storage at room temperature with good storage capacity for commercial applications.^[86] The high-entropy materials have high potential for a wider range of energy applications, particularly in the form of high-entropy ceramics.^[87][88]

Introduction

Most HEAs are prepared by vacuum arc melting, which obtains larger grain sizes at the µm-level. As a result, studies regarding high-performance high entropy alloy films (HEAFs) have attracted more material scientists. Compared to the preparation methods of the HEA bulk materials, HEAFs are easily achieved by rapid solidification with a faster cooling rate of 10^9 K/s.^[89] A rapid cooling rate can limit the diffusion of the constituent elements, inhibit phase separation, favor the formation of the single solid-solution phase or even an amorphous structure,^[90] and obtain a smaller grain size (nm) than those of HEA bulk materials (µm). So far, lots of technologies have been used to fabricate the HEAFs such as spraying, laser cladding, electrodeposition, and magnetron sputtering. Magnetron Sputtering technique is the most-used method to fabricate the HEAFs. An inert gas (Ar) is introduced in a vacuum chamber and it's accelerated by a high voltage that is applied between the substrate and the target.^[91] As a result, a target is bombarded by the energetic ions and some atoms are ejected from the target surface, then these atoms reach the substrate and condense on the substrate to form a thin film.^[91] The composition of each constituent element in HEAFs can be controlled by a given target and the operational parameters like power, gas flow, bias, and working distance between substrate and target during film deposition. Also, the oxide, nitride, and carbide films can be readily prepared by introducing reactive gases such as O₂, N₂, and C₂H₂. Until now, Li et al. summarized three routes to prepare HEAFs via the magnetron sputtering technique.^[90] First, a single HEA target can be used to fabricate the HEAFs. The related contents of the as-deposited films are approximately equal to that of the original target alloy even though each element has a different sputtering yield with the help of the pre-sputtering step.^[90] However, preparing a single HEA target is very time-consuming and difficult. For example, it's hard to produce an equiatomic CoCrFeMnNi alloy target due to the high evaporation rate of Mn. Thus, the additional amount of Mn is hard to expect and calculate to ensure each element is equiatomic. Secondly, HEAFs can be synthesized by co-sputtering deposition with various metal targets.^[90] A wide range of chemical compositions can be controlled by varying the processing conditions such as power, bias, gas flow, etc. Based on the published papers, lots of researchers doped different quantities of elements such as Al, Mo, V, Nb, Ti, and Nd into the CrMnFeCoNi system, which can modify the chemical composition and structure of the alloy and improve the mechanical properties. These HEAFs were prepared by co-sputtering deposition with a single CrMnFeCoNi alloy and Al/Ti/V/Mo/Nb targets.^{[92][93][94][95][96]} However, it needs trial and error to obtain the desired composition. Take Al_xCrMnFeCoNi films as an example.^[92] The crystalline structure changed from the single FCC phase for x = 0.07 to duplex FCC + BCC phases for x = 0.3, and eventually, to a single BCC phase for x = 1.0. The whole process was manipulated by varying both powers of CoCrFeMnNi and Al targets to obtain desired compositions, showing a phase transition from FCC to BCC phase with increasing Al contents. The last one is via the powder targets.^[90] The compositions of the target are simply adjusted by altering the weight fractions of the individual powders, but these powders must be well-mixed to ensure homogeneity. AlCrFeCoNiCu films were successfully deposited by sputtering pressed power targets.^[97]

Recently, there are more researchers investigated the mechanical properties of the HEAFs with nitrogen incorporation due to superior properties like high hardness. As above-mentioned, nitride-based HEAFs can be synthesized via magnetron sputtering by incorporating N₂ and Ar gases into the vacuum chamber. Adjusting the nitrogen flow ratio, R_N = N₂/(Ar + N₂), can obtain different amounts of nitrogen. Most of them increased the nitrogen flow ratio to study the correlation between phase transformation and mechanical properties.

Hardness and related modulus values

Both values of hardness and related modulus like reduced modulus (Er) or elastic modulus (E) will significantly increase through the magnetron sputtering method. This is because the rapid cooling rate can limit the growth of grain size, i.e., HEAFs have smaller grain sizes compared to bulk counterparts, which can inhibit the motion of dislocation and then lead to an increase in mechanical properties such as hardness and elastic modulus. For instance, CoCrFeMnNiAl_x films were successfully prepared by the co-sputtering method.^[92] The as-deposited CoCrFeMnNi film (Al₀) exhibited a single FCC structure with a lower hardness of around 5.71 GPa, and the addition of a small amount of Al atoms resulted in an increase to 5.91 GPa in the FCC structure of Al_0.07. With the further addition of Al, the hardness increased drastically to 8.36 GPa in the duplex FCC + BCC phases region. When the phase transformed to a single BCC structure, the Al_1.3 film reached a maximum hardness of 8.74 GPa. As a result, the structural transition from FCC to BCC led to hardness enhancements with the increasing Al content. It is worth noting that Al-doped CoCrFeMnNi HEAs have been processed and their mechanical properties have been characterized by Xian et al.^[98] and the measured hardness values are included in Hsu et al. work for comparison. Compared to Al-doped CoCrFeMnNi HEAs, Al-doped CoCrFeMnNi HEAFs had a much higher hardness, which could be attributed to the much smaller size of HEAFs (nm vs. µm). Also, the reduced modulus in Al₀ and Al_1.3 are 172.84 and 167.19 GPa, respectively.

In addition, the RF-sputtering technique was capable of depositing CoCrFeMnNiTi_x HEAFs by co-sputtering of CoCrFeMnNi alloy and Ti targets.^[93] The hardness increased drastically to 8.61 GPa for Ti_0.2 by adding Ti atoms to the CoCrFeMnNi alloy system, suggesting good solid solution strengthening effects. With the further addition of Ti, the Ti_0.8 film had a maximum hardness of 8.99 GPa. The increase in hardness was due to both the lattice distortion effect and the presence of the amorphous phase that was attributed to the addition of the larger Ti atoms to the CoCrFeMnNi alloy system. This is different from CoCrFeMnNiTix HEAs because the bulk alloy has intermetallic precipitate in the matrix. The reason is the difference in cooling rate, i.e., the preparation method of the bulk HEAs has slower cooling rate and thus intermetallic compound will appear in HEAs. Instead, HEAFs have higher cooling rate and limit the diffusion rate, so they seldom have intermetallic phases. And the reduced modulus in Ti_0.2 and Ti_0.8 are 157.81 and 151.42 GPa, respectively. Other HEAFs were successfully fabricated by the magnetron sputtering technique and the hardness and the related modulus values are listed in Table 1.

For nitride-HEAFs, Huang et al. prepared (AlCrNbSiTiV)N films and investigated the effect of nitrogen content on structure and mechanical properties.^[99] They found that both values of hardness (41 GPa) and elastic modulus (360 GPa) reached a maximum when R_N = 28%. The (AlCrMoTaTiZr)N_x film deposited at R_N = 40% with the highest hardness of 40.2 GPa and elastic modulus of 420 GPa.^[100] Chang et al. fabricated (TiVCrAlZr)N on silicon substrates under different R_N = 0 ~ 66.7%. At R_N = 50%, the hardness and elastic modulus of the films reached maximum values of 11 and 151 GPa.^[101] Liu et al. studied the (FeCoNiCuVZrAl)N HEAFs and increased the R_N ratio from 0 to 50%.^[102] They observed both values of hardness and elastic modulus exhibited maxima of 12 and 166 GPa with an amorphous structure at R_N = 30%. Other related nitride-based HEAFs are summarized in Table 2. Compared to pure metallic HEAFs (Table 1), most nitride-based films have larger hardness and elastic muduls due to the formation of binary compound consisting of nitrogen. However, there are still some films possessing relatively low hardness, which are smaller than 20 GPa, The reason is the inclusion of non-nitride-forming elements.^[90]

Until now, there are lots of studies focused on the HEAFs and designed different compositions and techniques. The grain size, phase transformation, structure, densification, residual stress, and the content of nitrogen, carbon, and oxygen also can affect the values of hardness and elastic modulus. Therefore, they still delve into the correlation between the microstructures and mechanical properties and the related applications.

Table 1. The published papers regarding the pure metallic HEAFs and their phase, hardness and related modulus values via magnetron sputtering method.

Table 2. Current publications regarding the nitride-based HEAFs and their structures, the related hardness and elastic modulus values.