Analysis of Technologies for Applying High-Entropy Coatings by Physical Deposition Method

Introduction. In modern tribology, the issues of increasing the reliability, wear resistance and durability of friction units are relevant. Often, the stated tasks are solved by applying thin wear-resistant coatings to the tribocontact. Various approaches to strengthening friction surfaces are known, and they are discussed in the presented review. Particular attention is paid to the physical vapor deposition (PVD) method. The high level of PVD technologies allows applying coatings to the friction surface with such a structure and properties that can “adapt” to friction conditions in a wide range of loads and speeds. At the same time, a systematic approach to the selection of materials and modes of PVD application technology has not yet been formed. This piece of research is intended to partially fill this gap. The article presents a review of the literature on methods for applying PVD coatings to the tribocontact surface of modified and multicomponent layers.

The requirements for the substrate surface are due to the fact that the PVD coating accurately reproduces its relief. With a branched relief and high surface roughness, internal stresses accumulate fast in the growing (in thickness) coating — the causes of cracks and delamination. Therefore, the roughness value of the substrate surface must be at least class 10 (R_a £ 0.12 µm; R_z £ 0.6 µm) according to GOST 2789–73¹. This corresponds to the polished surface of steel.

A significant contribution to the development of technology for applying wear-resistant coatings using the physical deposition method was made by S.N. Grigoriev, S.V. Fedorov, A.K. Sinelshchikov, V.P. Zhed, V.I. Kolesnikov, A.I. Grigorov, Yu.G. Kabaldin, A.V. Bely, G.D. Karpenko, I.P. Tretyakov, L.S. Sablev, I.I. Aksenov, A.A. Andreev, V.G. Padalka [2].

The process under study goes through several stages [3].

1. Evaporation of a material (transition from a solid to a vaporous state).
2. Transfer of material vapors to the sample using inert gases.
3. Bombardment of the substrate surface by particles of material in the vapor phase to form an adhesive bond.
4. Origin and growth of the coating.

In mechanical engineering, solutions from leading global companies developing PVD coatings are widely used. Their innovations are applied to harden, reduce the coefficient of friction, and protect parts from corrosion.

Materials and Methods. In the framework of the presented research, materials in Russian and English, published in the Web of Science, eLibrary, Scopus, Medline, and CINAHL databases, were studied and reviewed. When forming queries by keywords, the authors abandoned the random selection of sources in favor of a systematic approach and were guided by a structured list of questions that they intended to consider. Exemplarily, having received a full understanding of how the initial stages of the coating process are described in the theoretical and applied literature, the authors entered new queries to obtain materials on the following stages. This method allowed us to create a representative sample of sources to solve the problems of this study. The collected data were processed using the funneling technique. The first narrowing of the funnel formed the structure of this article, discovered the basic topics of the review:

• vacuum-arc method of coating deposition;
• processes in the cathode region of the arc;
• processes on the anode and substrate;
• coatings obtained by the vacuum-arc method;
• magnetron sputtering technique;
• coating growth and structure formation mechanisms;
• properties of high-entropy alloys;
• composition of high-entropy alloys and coatings;
• research techniques for studying high-entropy coatings.

The following steps in narrowing the funnel allowed us to focus on the parameters of processes and materials that affect the qualities of coatings potentially suitable for use in mechanical engineering (e.g., heat resistance, hardness, adhesive strength). Numerical data were summarized in tables. Illustrations were used to visualize the basic processes, including those created by the authors of this article. At a certain stage of this work, the authors received a sufficient idea of the number and volume of studies devoted to this or that technology. They turned out to be different. Calculations, comparison and additional targeted search allowed us to conclude that there was a shortage of works considering this problem from the point of view of tribology.

Research Results

The cooperation of academic institutes and universities in Russia has significantly influenced the development of the theory and practice of the new direction. Vacuum-arc technologies are also actively developing in foreign research centers: Lawrence Berkeley National Laboratory (USA), Sydney University of Technology (Australia), Cambridge University (Great Britain), Fraunhofer Institute for Material and Beam Technology (Germany), Wuhan University of Science and Technology (China), etc. [2].

The main unit of vacuum-arc installations is an electric arc evaporator. For uninterrupted operation during coating application, a reliable starting of the evaporator, a stable arc discharge at a given current value, and localization of cathode spots are required. It is also important to have a simple design for quick replacement of ignitions and cathodes, and not to exceed the minimum droplet phase in plasma flows [2].

The authors analyzed this coating application method and noted a disadvantage — the formation of a droplet phase with a size of 0.1–40 μm. Due to this, surface heterogeneity is formed, which causes:

• increased roughness;
• low adhesion of the coating to the substrate;
• formation of internal stresses.

The above-mentioned disadvantages contribute to the formation of structural defects. To reduce the droplet phase, plasma flow separation using a magnetic field, and optimization of the electrical parameters of the vacuum coating installation are used.

Processes in the Cathode Region of the Arc. CS contain erosion products, which are characterized by three phases: microdroplet, vapor, and ionized [7]. The latter predominates when it comes to evaporation in cathodes made of refractory materials [8]. In cathodes made of low-melting metals, the ionized phase accounts for up to 10% [9]. Note that in the plasma flow of a molybdenum arc, the ionized phase accounts for 80–90% of all phases [10].

G.A. Mesyats et alias [8] developed an ectonic theory that described processes in the cathode region of a vacuum arc. According to this theory, the beginning of the CS cycle is the explosive emission of electrons (EEE), which contributes to the appearance of plasma. The potential difference between the electric discharge and the plasma is called the cathode fall potential (CFP). Its value is close to the value of the ionization potential of the metal — and this is the key feature of the phenomenon described. To determine the currents transferred through the CS, two of their characteristics are used — the minimum current and the average value. The minimum (threshold) current is the current at which the CS and arc exist. The parameters of the CS and the threshold current are the major characteristics of the cathode region and the arc discharge [11].

The authors [15] have determined that when some cells in the CS disintegrate, others are generated. The process can also occur outside the boundaries of a given CS, but within its plasma halo. This is how other cells are formed and, consequently, a new CS. In [15], it is concluded that CS move a distance of up to 300 μm. As the discharge current increases, the number and size of CP cells grow. Then, the CS is divided into fragments that repel each other [10].

In the early 20th century, J. Stark established that in the presence of a magnetic field perpendicular to the movement of the CS, it moved against the action of the Ampere force [16]. In the case of the CS of the 1st type, a strong plasma flow with a speed of 5–10 km/s will arise. The halo formed in the CS of the 2nd type has a plasma glow and moves in the opposite direction.

Considering the operation of the CS cells, we note that the consumption of the cathode mass directly depends on the erosion products and phase. In the ionized phase, the consumption is constant, but when the drop phase appears, it grows in accordance with the increase in the discharge that passes through the CS [2]. The erosion coefficient depends on the current, temperature and material of the cathode (in low-melting materials, destruction occurs faster than in refractory materials).

Thus, having considered the features of the formation of a vacuum-arc discharge and cathode spots, we can conclude that for stable implementation of vacuum-arc deposition, cathode materials with close values of the threshold current of the vacuum-arc discharge should be selected.

Processes on the Anode and Substrate. When the anode is applied, the vapor evaporating from the cathode surface condenses. The anode receives plasma energy. At the same time, its surface must have heat removal to the anode and perform reverse radiation into the plasma with subsequent evaporation of the anode material [21].

It is necessary to reduce the size of the anode to heat it to the melting and evaporation temperature. In this case, it is possible to apply coatings from the anode material with relatively high adhesion. When the anode is cooled to room temperature, brittle porous coatings with a high concentration of internal stresses are formed on its surface.

The energy of ions bombarding the substrate consists of their initial energy and the energy acquired in the Debye layer adjacent to the substrate when a negative potential is applied to it [1]:

(1)

where Е_i — ion energy; Е₀ — initial energy; Z — ion charge multiplicity; U_п — substrate potential.

The authors [22] revealed the dependence of the deposition rate on the substrate potential when applying plasma flows of chromium, molybdenum, zirconium and titanium (Fig. 2).

From Figure 2, it can be concluded that the potential value at which the processes of condensation and sputtering come into equilibrium depends on the nature of the evaporated material. As the potential value of the substrate increases, its material and the deposited particles are sputtered. Removal of substrate atoms (contaminants) leads to an increase in its temperature. Bombardment of hard alloy plates by chromium and titanium ions in a high vacuum at a potential of 1,000 V increases their average bending strength by 10–15% and reduces strength variation by 40–80% in a few minutes [23]. When the coating is subsequently applied, a diffusion zone up to 2–2.5 µm wide is formed. This treatment provides high adhesion of the coating to the substrate and makes it possible to harden steel with vacuum-arc coatings without losing their physical and mechanical characteristics [14]. With increasing gas pressure, the rate of discharge and speed decrease. This occurs when the active gas is released, which forms compounds with the evaporated gas.

Coatings Obtained Using the Vacuum-Arc Method. The vacuum-arc method (VAM) is used to obtain wear-resistant protective coatings with high physical and mechanical characteristics and a low friction factor. Over the years of developing vacuum technologies, scientists have produced numerous types of coatings for various branches of mechanical engineering. The most famous coatings are nitride (TiN, TiCN, TiAlN, TiMoN, TiSiN) and nanolayer composite (TiN/NbN, TiN/AlN, CrN/TiN, TiN/AlTiN) ones. Recently, the development of multicomponent high-entropy coatings has become a challenge.

Coatings obtained by VAM based on TiN with a nitrogen content of 37.5–52 at.% have been widely studied. Their main feature is a cellular microrelief with a cell size of 0.5–3 μm. The coating can contain two phases: Ti₂N with a hexagonal close-packed (hcp) lattice, and TiN with a face-centered cubic (fcc) lattice. Another characteristic of the coating is a columnar structure. The diameter of the columns is 200 nm, grains with a diameter of 25–75 nm are elongated in the direction of growth [2].

In nitride coatings, nitrogen affects microhardness. With increasing nitrogen pressure in the chamber, microhardness increases to 35–53 GPa, and with further growth, it decreases to 20–24 GPa. This is explained by a decrease in the activation of nitrogen particles at a pressure of more than 1 Pa [2]. Note that the electrical conductivity of the coatings in question depends on the nitrogen content. The friction factor is determined by humidity. If it is low (10%), then the friction factor for chromium steel reaches 0.8, at 50% humidity — about 0.6, and during running-in — about 0.2.

TiCN (titanium carbonitrides) coatings are formed through mixing N₂ with C₂H₂ or CH₄. They have a columnar structure with a column width of 260 nm. When acetylene is added, the microhardness increases to 50 GPa. Titanium carbonitrides are almost twice as resistant to erosion (compared to TiN coatings) [24].

Coatings Ti_1–хAl_хN are substitution solid solutions with a cubic lattice of the B1 TiN type at 0 ≤ х ≤ 0.6. They are highly resistant to oxidation at extensive temperatures. Microhardness grows to 30 GPa with an increase in aluminum in the coating composition and the formation of aluminum nitride [25]. The authors [26] found that when applying Ti₅₀Al₅₀N coating with a decrease in reference voltage from –300 V to –150 V, the concentration of aluminum in the coating composition decreased, and this affected the microhardness. With a decrease in reference voltage by 30 V, the microhardness value increased from 29.1 to 34.5 GPa.

The authors [27] applied a TiN coating by the vacuum-arc method and introduced MoS₂ into it through spraying molybdenum disulfide using the magnetron method. It was found that when introducing MoS_x, the hardness increased significantly (up to 30 GPa). The friction factor decreased to 0.15, and the wear rate decreased by 20 times.

Coatings TiSiN have attracted the interest of scientists because Si is an alloying element of transition metal nitrides. It is chemically related to nitrogen and has a minor atomic radius (if we are talking about transition metals). This is why TiSiN coatings have a high microhardness value (30–45 GPa) and a low elastic modulus (200–250 GPa). During tribological tests, silicon forms SiO₂ compound, and this solid lubricant reduces the friction factor to 0.5 [28].

When creating nanolayer composite coatings, layers of metals with different physical-mechanical properties, but close thermal expansion coefficients, alternate. The authors [29] studied nanolayer composite coatings made of materials with nanohardness of ~20 GPa. The TiN/NbN coating was found to have high nanohardness. The nanohardness of the TiN/VN coating was 55 GPa, and this is a very high figure for a nanolayer coating.

The use of the VAM is important in the creation of combined MeC(MeN)/a-C:H coatings with alternating nitride and carbon layers. Thus, in [30], TiAlN/DLC-Ti coatings were compared to DLC-Ti. The wear resistance of the combined coatings turned out to be twice as high as that of DLC-Ti, due to an increase in nanohardness to 24 GPa and Young's modulus — to 230 GPa.

The first magnetron sputtering systems (MSS) appeared in the early 1970s. At that time, cylindrical coaxial MSS of normal and inverse type were used. Their main problem was nonregular sputtering of the material due to the escape of electrons along the magnetic field lines. In this regard, the installations were modernized [34], technologies were developed, new types of magnetrons were created and introduced into production. Let us name some of them:

• magnetron with a flat cathode;
• magnetron with a balanced magnetic field;
• magnetron with an unbalanced magnetic field;
• unbalanced magnetrons with a vertical component of the magnetic field to the substrate;
• unbalanced magnetrons with magnetic field dispersion away from the substrate;
• unbalanced MSS with two magnetrons;
• magnetrons with devices for additional gas ionization;
• MSS with bipolar power supply.

The diagram of an unbalanced magnetron is shown in Figure 3.

The main elements of the device are: a cathode-target, an anode, and a magnetic system. Magnetrons are made so that a magnetic field is induced in parallel in the near-surface region of the target. As a result, secondary electrons are accelerated towards the targets. One magnetic pole is located in the center, and the second is at the edges of the cathode. This provides capturing the electrons that do not bombard the substrate itself. Thereby, the heating temperature of the target is reduced, but the degree of plasma ionization is increased [35].

The main advantages of this approach [36]:

• repetition of the exact composition of the target in a coating with a high-density structure;
• using any material for application to the substrate;
• applying coatings at low temperatures;
• controlling the quality of coatings through changing the parameters of the application process.

Among the most noticeable disadvantages are:

• low sputtering speed;
• low efficiency;
• weak adhesion of the coating to the substrate;
• instability of the phase components of the coating;
• cost of equipment.

Currently, it is required to obtain nitride and high-entropy coatings using magnetron sputtering. These include combined coatings, high-entropy coatings (HEC), as well as:

• cermet (TiN, ZrN, CrN, TiC, TiCN, TiAlN, AlCrN, TiBN, CrAlTiYN, Al2O3, SiO2);
• metal (Al, Ag, Au, Cu, Zn, Ti, Zr, Hf, Cr, Ta, Ni, Co, Si);
• nanocomposites (TiAlN/Si3N4, ZrN/Cu, TiN/CrN, TiN/AlN, CrN/AlN, TiN/CN).

Let us consider the main results of studies on coatings obtained by magnetron deposition method.

The authors [37] have determined that the magnetron type is suitable for depositing titanium nitride coatings with a thickness of 1 nm to 1 μm. For this purpose, they used a facility with pulsed sputtering on silicon substrates [38]. To maintain process stability, they varied the distance between the target and the substrate in the range of 50–100 mm and changed the nitrogen feed rate into the working chamber. Analysis of the obtained titanium nitride (TiN) coating has shown that with a decrease in the distance between the target and the substrate, the mechanical properties of the coating deteriorate, its quality decrease. This is explained by the fact that due to the close distance, the thermal effect increases, and the effect of thermal annealing occurs.

The authors [39] studied the growth rate of coatings on semiconductor substrates at room temperature. The feed rate and operating power of the magnetron control unit were varied.

Using the magnetron deposition method, superhard Ti_1–xAl_xN coatings were obtained at 0.5 ˃ х ˃ 0.6 with microhardness of 40 GPa. It is worth noting that the lattice parameter for TiN decreased from 0.4255 nm to 0.417 nm [40].

Coating TiMo(SN) alternated layers of molybdenum disulfide MoS₂ with TiN, so the microhardness increased from 4 GPa to 15–35 GPa with a friction factor of 0.02–0.1. MoS₂ was evaporated using a magnetron, and TiN was deposited using vacuum arc deposition. MoS2Ti with nanohardness of 10 GPa and Young's modulus of 142–169 GPa was applied to a CrN coating with nanohardness of 24–30 GPa and Young's modulus of 352–418 GPa. Due to molybdenum disulfide in the coating composition, the friction factor decreased by 91–95%, wear — by 50–95% [41]. Pure molybdenum disulfide was applied using a magnetron and studied without removing it from the chamber. Its friction factor was 0.002 [42]. Thus, adding MoS₂ to the coating composition reduces significantly the friction factor.

Nanostructured multilayer TiN/AlN coatings obtained by magnetron method showed high results in micro drilling and turning in comparison to TiN coatings. When drilling fiberglass, the durability of drills with TiN/AlN coating was 40% higher than without it, and 25% higher than with TiN coating [43].

An important property of coatings obtained by the magnetron method is adhesive strength. It provides evaluating the resistance of the surface to delamination. In [44], the adhesive strength of nitride coatings CrN, TiN on carbon steel S235 is evaluated. It is found that the application of a multilayer structure (sublayer + coating) provides for the adhesion improvement. Thus, for CrN coating, the value of adhesion strength without a sublayer is 37 N, with a Cr sublayer — 40 N. The indicators for TiN coating are 16 N (without a sublayer) and up to 24 N (with Ti sublayer). Adhesion strength increases when applying coatings to a harder base in the form of pure metals, close in composition to the basic coating.

The authors [45] studied the adhesive strength of AlTiNiAg and NiAg coatings obtained by the magnetron method. The coatings were applied to silicon structures and molybdenum thermocompensators of power semiconductor devices with annealing in vacuum, hydrogen, and without it. The adhesive strength was studied by scratch testing. The maximum adhesive strength was found in samples of a silicon structure with a four-layer AlTiNiAg coating (21.7 N) after annealing in vacuum. For molybdenum thermocompensators, the two-layer NiAg coatings annealed in vacuum turned out to be the strongest (13.5 N).

The review of the literature has established that magnetron sputtering is characterized by:

• ability to work with numerous materials;
• high accuracy of target composition repetition (at. %).

The method is widely used for applying thin layers to semiconductors, glass, and obtaining self-lubricating coatings with a low friction factor.

Coating Growth and Structure Formation Mechanisms. When coatings are applied, the structure formation occurs in several stages (Fig. 4). At the first stage, atoms are adsorbed from the plasma flow. The atom continues to move until a chemical bond with the surface atoms is formed. At this stage, the atom may not form a chemical bond with the substrate surface, depending on the material being applied and the method of application. After the atom is fixed to the surface, chemical bonds are formed with the newly arrived atoms — this is how the coating is formed. Diffusion processes may occur between the substrate and the film.

When an atom is adsorbed on a substrate, surface tension arises. The bonds between the atoms of the substrate and the coating are lengthened, therefore, the energy depends on the type of bond formation. The achievement of energy equilibrium is facilitated by the force of surface diffusion, which is determined by the temperature of the substrate and the energy of the atoms.

Figure 5 schematically shows three mechanisms of coating growth.

The layer-by-layer mechanism operates if the bond strength between the coating atoms is less than the bond strength between the coating and substrate atoms, and also if these forces are equal. In this case, the mismatch of the crystal lattices should be minimal. The condition for the island mode to be realized is that the bond between the coating atoms should be stronger than the bond between the coating and substrate atoms. The mixed mode occurs when the crystal lattice parameters of the coating and substrate are mismatched [1].

B.A. Movchan and A.V. Demchishin [46] were the authors of the first significant works on the mechanism of coating growth. In parallel, they developed physical deposition methods and proposed a diagram of the zone structure of coatings depending on the substrate temperature. The researchers have clearly shown that the microstructure of PVD coatings is conditionally divided into three zones with different homologous process temperatures (T_hm — ratio of the melting temperature of the coating to the substrate temperature Т_пл/Т_под).

This model was improved by J.A. Thornton [47]. He introduced the partial pressure of argon in the chamber and the intermediate zone T (between the first and second) into the diagram. The coating density in zone T is higher than in the neighboring zones, the surface roughness is less.

During the formation of the microstructure at different stages [48], nuclei are formed, islands increase in size and coalesce, polycrystalline islands and channels appear, and films grow (Fig. 6).

The formation of nuclei begins with the growth of isolated islands on the surface of the substrate. The size of the islands is 20–30 Å [49].

During the process of island coalescence, a driving force for grain coarsening is created due to the surface diffusion of atoms and grain boundary movement. The resulting low-energy islands absorb others. As a result, the new single-crystal island contributes to a decrease in the energy of the entire surface. The coarsening of the structure under coalescence depends on the temperature, the size of the islands, and determines their orientation [50]. At low temperatures and large island sizes, coarsening occurs more slowly due to grain boundary migration. During the coalescence of crystals, the grains coarsen until their boundaries become large and immobile.

It should be noted that vacuum technologies require preparation of the substrate for coating application. This is important because during coating growth, defects, such as porosity, internal stress, deformation of crystallites and the crystal lattice, may appear. They occur both in the vacuum-arc method and in the magnetron method.

If there is macro-roughness on the sample surface, high internal stresses are formed in the coating, which lead to delamination. Micro-roughness causes porosity of the coating and worsens its physical and mechanical properties. Defects appear on the surface and increase with the growth of the structure. The formation of a droplet phase is possible not only in vacuum-arc coatings, but also in magnetron sputtering of refractory materials [50]. Droplets on the surface are formed rather quickly and stochastically. The result is screw dislocations, which cause spiral growth of crystals. As shown in [51], during the coating process, the “craters” formed due to the separation of large particles are quickly filled with ions of the applied material. Therefore, defects due to the droplet phase are substructural and do not greatly affect the structure and properties of the coating.

Properties of High-Entropy Alloys. Research into HEA and coatings based on them has begun relatively recently. In 2002, Professor Jien-Wei Yeh (National Tsing Hua University, Taiwan) developed a new class of materials [52]. Physical and mechanical properties of HEA have attracted the attention of scientists. Over 20 years, about 5,000 papers on HEA have been published [53]. A characteristic feature of HEA is the mixing of 5 or more elements (each accounts for 5–35% at.). In this case, a substitution solid solution is formed. It is single-phase. A phase with a bcc-, fcc-, or bcc+fcc lattice is formed [54].

The key feature of HEA is the high entropy of mixing. It promotes the formation of solid solutions, which reduces the likelihood of intermetallic compounds. As a result, HEA are characterized by thermal stability, corrosion and wear resistance, increased plasticity at low temperatures, and resistance to ionizing radiation [55]. The average atomic concentration (el/at.) is often used to characterize the atomic-crystalline structure of multicomponent systems. In high-entropy alloys:

• at a concentration of up to 4 el/at., hcp lattice is formed;
• in the range from 4.25 to 7.2 el/at. — a bcc lattice;
• at a concentration from 7.2 to 8.3 el/at. — a two-phase structure with bcc and fcc lattices;
• a level above 8.4 el/at. corresponds to an fcc lattice [56].

The properties of the HEA are described by 5 parameters [57]:

• mixing entropy ΔS_mix;
• mixing enthalpy ΔH_mix;
• difference in atomic sizes δ;
• electronegative difference Dc;
• concentration of valence electrons VEC.

All criteria are calculated using expressions taking into account the atomic concentration of each i-th component of alloy c_i.

The entropy of the HEA consists of:

• entropy of electron motion (ΔS_B);
• entropy of atomic oscillation (ΔS_v);
• configurational entropy of mixing (ΔS_k);
• entropy of magnetic moments (ΔS_m) [58].

In a high-entropy alloy, configurational entropy (ΔS_k) is higher than that of the components ΔS_B, ΔS_v, ΔS_m. But this is not typical for common metals. Therefore, in high-entropy alloys, a single-phase solid solution is formed due to ΔS_k. With an increase in the number of elements (n), ΔS_k grows. This reduces the Gibbs energy ΔG = ΔH – T ΔS (ΔH — enthalpy, T — absolute temperature, ΔS — entropy) and maintains thermodynamic stability [59]. The entropy and enthalpy of high-entropy alloys are determined from the expressions:

(2)

(3)

where R — absolute gas constant, R = 8.314 J/(K×mol); c_i — atomic concentration of element i (at.%);  — enthalpy of binary alloys near the melting point of elements АВ, which are part of HEA.

At equiatomic concentration of components, the atomic concentration of an element is defined as c_i=1/n. This means that the entropy level is DS_mix = R × ln(n). At n≥5, the configurational entropy is: DS_mix ≥ 13.4 J/(K×mol), and the alloy is considered high-entropy.

Figure 7 shows the dependence of the mixing entropy on the number of elements [60].

In metals and simple alloys, atoms can occupy a place in the crystal lattice with equal probability. This is how they differ from high-energy alloys, in which the crystal lattice is distorted due to the substitution of several elements with different atomic sizes. If the sizes of atoms in the alloy structure differ significantly, then internal stresses are formed, which cause an increase in the strength properties of the coatings [58].

The distortion of the crystal lattice determines the strength of the HEA and reduces diffusion. Slowing down the diffusion enhances the formation and stabilization of the solid solution of the HEA, and also reduces the rate of crystal growth. The possibility of forming an amorphous structure is opened up, but the thermal and chemical stability increases [61].

To predict the formation of solid solutions, the difference in atomic radii (in %) is used. This parameter is denoted by δ. The formation of a structural phase in HEA is determined by:

(4)

where n — number of components in the alloy; c_i — content of the i-th component (at. %); r_i — atomic radius of the i-th component;  — average atomic radius .

To describe the difference in atomic sizes, paper [62] proposes to classify the elements of the HEA. Table 1 shows the classification and elements depending on the atomic size δ.

To exclude the formation of Laves phases, intermetalledes, and amorphous phases, theoretical parameter Ω is proposed, which takes into account the melting temperature of the components:

(5)

where T_m — average melting point of the components.

The average melting point is estimated together with the difference in atomic radii. High value Ω ˃ 1.1 and small value δ ˂ 6.6 predict the formation of solid solutions.

The authors [57] proposed a variant of predicting the formation of solid solutions by electronegativity:

(6)

where c_i — Pauling electronegativity for the i-th element; c_a — average electronegativity.

In this case, electronegativity is the average ionization energy of the valence electrons of free atoms. The authors [63] determined that solid solutions were formed in the ranges 3 < ∆χ < 6 and 1 < δ < 6%. It was also established that solid solutions with a bcc lattice exist with a greater mismatch of atomic radii and lower electronegativity (in comparison to the conditions for the fcc lattice).

The valence electron concentration (VEC) affects the stability of the structure of solid solutions and is defined as a weighted average value:

(7)

where c_i(VEC)_i — VEC for the i-th element.

When determining the electron concentration, special attention is paid to the stabilization of the solution due to the accumulation of electrons at low-energy levels [59]. The density of the structure and bonds per atom are estimated. At VEC ≥ 8, one fcc phase is formed. At 6.87 ≤ VEC ≤ 8, the bcc and fcc phases are mixed. At VEC ≤ 6.87, the alloy contains only the bcc phase. In [64], the influence of VEC on the formation of AlCoCuFeNi alloy lattice is analyzed. The bcc lattice was formed at low values of the valence electron concentration, and the fcc lattice — at high values.

The theoretical analysis allows us to determine the conditions for the formation of a solid solution:

• mixing enthalpy — 7 ≤ ∆H_mix≤ 22 kJ/mol;
• mixing entropy — 11 ≤ ∆S_mix≤ 19.5 J/(K·mol);
• difference in atomic sizes — 0 ≤ δ≤ 8.5%.

Composition of High-Entropy Alloys and Coatings. About 40 elements are known, from which approximately 500 materials can be obtained that meet all the criteria of high-entropy alloys [56].

In the literature, the elements of the HEA are divided into families. The first one is the most studied, it is based on 3d-transition elements: Fe, Co, Cr, Ni, Mn, Al, Ti, Cu, V. These are elements with high hardness, corrosion and wear resistance. One of the first and well-studied high-energy alloys is CoCrFeMnNi. This is the so-called Cantor alloy, proposed in 2004. The second family of HEA is based on refractory metals (Hf, Ta, Mo, Nb, V, W, Cr, Zr, Ti). The third includes low-melting elements (Al, Sn, Be, Li, Mg, Ti, Sc, Si, Zn). The fourth includes rare earth elements (Gd, Dy, Lu, Tm, Tb, Y). The fifth consists of high-entropy bronzes and brasses (Zn, Cu, Ni, Mn, Al, Sn). The sixth, the youngest, unites Au, Ag, Cu, Co, Cr, Ni, Pt, Pd, Ru, Rh [57]. Some elements belong to different families.

To reach high values of hardness and strength in modern nitride HEA, transition d-metals with negative enthalpy (ΔH) are used. The composition of nitride HEA and their hardness values are given in Table 2.

The authors [64] have found that the strength properties of high-entropy alloys are higher than those of numerous metallic alloys. The yield strength and Vickers hardness values of HEA are high — at the level of metallic glass, titanium and nickel alloys. NbCrMo_0,5Ta_0,5TiZr and Al_2,0CoCrCuFeNi occupy a special place. Their Vickers hardness is close to 1000, and the elastic limit exceeds this value.

Heat-resistant HEA are widely used and could be applied in the aerospace industry. The first such alloys based on Mo, Nb, Ta, W, V, had serious drawbacks — high density and low corrosion resistance. The problem is solved by replacing the specified elements with others — Cr, Ti, Zr, Al [65].

An important characteristic of heat-protective alloys and coatings is the thermal coefficient of linear expansion (TCLE). It affects the adhesion between the coating and the substrate, since in coatings with a low TCLE, thermal transformations occur at high temperatures, which cause “peeling”, delamination, and further destruction of the coating:

• diffusion processes between the coating and the substrate;
• phase transformations;
• plastic deformations;
• oxidations;
• compressive stresses.

To solve the problem of coating destruction under the influence of temperature, it is proposed to use a thermal barrier layer of high-entropy NiAlCrWTaYSiHf coating with a thickness of 20–30 μm [66]. This allows reducing the diffusion exchange, which causes an increase in the TCLE and adhesion between the combined coating and the substrate. It should be noted that for tribological coatings, this criterion is not relevant due to the small thickness of coatings.

The authors [67] performed annealing of two coatings:

• (Al₁Cr_30.8Nb_7.7Si_7.7Ti_30.7)₅₀N₅₀ at bias potential (–100) V;
• (Al₁Cr_30.8Nb_11.2Si_7.7Ti_21.2)₅₀N₅₀ at bias potential (–150) V.

The annealing was carried out at a temperature of 900°C for two hours. The study of the microstructure showed that oxide particles were formed on the surface of the coating. Their thickness for the coating (Al_23,1Cr_30,8Nb_7,7Si_7,7Ti_30,7)₅₀N₅₀ was 100 ± 12 nm, for the coating (Al_29,1Cr_30,8Nb_11,2Si_7,7Ti_21,2)₅₀N₅₀ — 80±7 nm. Under the oxide films, the structure of the coating did not change. The study confirmed that high-entropy coatings have high oxidation resistance and, in that indicator, surpassed most of the coatings in use.

To obtain high-entropy coatings, PVD deposition methods are widely used: vacuum arc and magnetron. The properties of several types of coatings from high-entropy alloys have been studied in detail: (AlCrTaTiZr)N, (TiAlCrNbY)C, (FeCoNiCrCuAl)N, (AlCrMoSiTi)N, (AlCrNbSiTiV)N, (TiAlCrSiV)N, (AlMoNbSiTaTiVZr)N, (TiVCrZrY)N, (TiHfZrVNb)N, (TiVCrZrHf)N.

The authors [68] obtained high-entropy nitride coatings using vacuum-arc deposition and magnetron sputtering. It has been found that metals of groups IV–V tend to form nitrides with a stable structure. The microstructure and hardness of high-entropy nitride coatings depend on the parameters of the deposition process. In processes with the same parameters, expansion in the number of components leads to an increase in the hardness of the coatings. Improved tribological properties are achieved by adding Mo or W elements, which reduce the friction factors. The addition of Al and Si increases oxidation resistance due to the formation of protective oxide layers.

In [69], the production of a CoCrFeNi film with a thickness of about 1 µm using ion-beam sputtering is shown. A film of similar composition and thickness was also obtained using the high-pressure torsion (HPT) technique. In the comparative analysis of the films, the textures and sizes of the crystallites were determined by X-ray diffraction, and the hardness was measured through nanoindentation. The hardness of the film obtained by PVD was 9.8 ± 0.3 GPa. This was greater than that of the HPT sample (7.3±0.3 GPa). The grain size of the crystallites was about 20 nm.

In [71], a CrTiNiZrCu coating on an AISI 201 steel substrate obtained through magnetron sputtering is described. Atomic force microscopy showed a cellular nanostructure of the high-entropy coating. Several models of its formation are described, and the main reasons for the formation of such nanostructures are established.

The authors [72] used a magnetron to form a CrNbTiMoZr coating with a nanohardness of 9.7 GPa and high tribological properties. In [73], multicomponent coatings based on AlCrTiV with the addition of Cu and Mo were considered. The researchers concluded that the corrosion properties of the coatings significantly exceeded the properties of the steel substrate AISI 304. This was explained by the formation of stable oxides.

In [74], the creation of a TiTaHfNbZr coating with a thickness of 800 nm on a substrate of Ti-6Al-4V alloy was described. It was obtained using magnetron sputtering. The tribological research showed that with an increase in load from 1 N to 3 N, the wear of the substrate without a coating increased significantly, whereas for samples with a TiTaHfNbZr coating the wear was insignificant.

In [75], vacuum arc and magnetron methods were used to obtain a (TiAlSiCrNiCuOC)N coating with a B1-type lattice, identical to TiN, with a superhardness of 47 GPa and a thermal stability of 900–1,000°C.

In [76], the production of a high-entropy nitride coating (TiZrHfVNb)N using the vacuum-arc method is shown. The reference voltage changed from –40 to (–200) V. The coating thickness was 4.78 μm. The results of nanoindentation showed that with a growth of the reference voltage, the following parameters increased:

• microhardness (from 19.34 GPa to 29.94 GPa);
• elasticity modulus (from 281 GPa to 384.1 GPa).

The data in Table 3 allow us to conclude that to obtain high-strength coatings, it is required to introduce transition metals into their composition. The addition of nitrogen strengthens covalent bonds in the coating and significantly increases the hardness. Coatings based on HEA are multi-parameter; therefore, to change the values of nanohardness and Young's modulus, it is necessary to vary the process parameters during application: nitrogen supply, substrate temperature, reference voltage.

Research on high-entropy coatings is based on the study of the coating structure, physical-mechanical properties, and thermal stability. Less attention is paid to tribological studies. Table 4 summarizes their key known results.

Table 4 shows that high-entropy coatings have a high friction factor. Note that (TiZrNbHfTa)C has an extremely low coefficient (0.15). This is explained by the formation of a free carbon phase, which acts as a solid lubricant and reduces the friction factor. The high wear resistance of HEA is associated with an increase in hardness when alloying transition metals, nitrogen, and greater resistance to plastic deformation.

Research Methods for High-Entropy Coatings. The microstructure of the HEC is examined using optical metallography. Scanning electron microscopy (SEM) is used to study fine details. Its major advantages are high resolution and clarity. In addition, SEM works with several types of induced radiation. In addition to X-rays, reflected and absorbed electrons, as well as cathodoluminescence, are used. In this way, it is possible to study the surface relief, phase and orientation contrasts, and conduct micro-X-ray spectral and energy-dispersive analysis. In some cases, the capabilities of electron microscopy and cross-sectional research are combined.

The chemical composition of the coatings is determined by an energy-dispersive X-ray detector. It allows point probing or scanning of a section by the area of the figure or by the distribution map of chemical elements. To increase the accuracy of determining the elemental and phase composition of the coatings, X-ray photoelectron spectroscopy and Auger electron spectroscopy methods are used. Survey spectra are recorded from the surface of the coatings. They are used to study the qualitative and quantitative composition of the surface. In addition, the spectra are used to determine the electron lines of the chemical elements of the surface, which makes it possible to effectively determine the chemical bond. This allows us to judge the phase in which the element is included.

X-ray structural analysis is used to determine the crystalline structure of high-entropy coatings. For this purpose, reflections with maximum intensity are identified on the X-ray diffraction pattern. Based on them, conclusions are made about the phase composition, the size of the coherent scattering regions, the parameters of the crystal lattice, and the deformation of the crystal lattice of the coating [87].

Such stress-strain properties of the coating as hardness (H) and elastic modulus (E) are measured through nanoindentation. In this case, the load curves are analyzed using the Oliver-Farr method [88]. For indentation in continuous measurement mode, Berkovich diamond indenter is used. In addition to hardness and elastic modulus, it is possible to determine:

H/E — indicator of tribological properties. The higher it is, the higher the wear resistance. Materials with H/E < 0.04 belong to the coarse-crystalline group (metals and alloys), and materials with H/E ≈ 0.05 – 0.09 belong to the group of fine-crystalline and nanomaterials (ceramics, coatings).

The tribological properties of the coatings are determined using friction machines by the “ball — disk” or “pin — plate” scheme. Based on the test results, such coating characteristics as wear and friction factor are assessed.

Discussion and Conclusion. The literature analysis performed by the authors of the presented article makes it possible to:

• consider widely used methods of applying PVD coatings;
• grasp the principle of creating cathode spots using explosive electron emission in the vacuum arc method;
• track the effect of discharge current in the process of forming cathode spots on the cathode;
• assess the importance of processes occurring on the anode and substrate.

One of the advantages of coatings obtained by vacuum-arc and magnetron methods is a wide range of materials for synthesizing coatings with high physical, mechanical and tribological characteristics.

Three classes of growth of coating formation are distinguished. The essence of the process is determined. This is nucleation with the growth of islands of 20–30 Å in size. We emphasize that any coating may have defects: porosity, internal stresses, deformation of crystallites and crystal lattice.

High-entropy alloys are formed by mixing five or more elements. High entropy promotes the formation of solid solutions. This feature determines thermal stability, wear resistance, increased plasticity at low temperatures, corrosion resistance, resistance to ionizing radiation. There are about 40 known elements that are included in high-entropy alloys; therefore, special criteria (parameters) have been developed for the precise selection of materials, prediction of stability and structural-phase state of high-entropy alloys:

• difference in atomic sizes of components d;
• mixing enthalpy DН_mix;
• mixing entropy DS_mix;
• difference in electronegativity of components Dc;
• valence electron concentration VEC.

Within the framework of this research, it is established that the issues related to nitride coatings obtained by vacuum-arc and magnetron methods are sufficiently explored in the literature. There are fundamental studies on the structure of coatings, their physical and mechanical properties, thermal stability. It is also known that high-entropy coatings are distinguished by high hardness with a face-centered cubic lattice, high thermal stability. Transition metals with the addition of nitrogen are widely used in the compositions of the coatings under consideration. The main type of high-entropy coatings is nitride. The coatings studied in this paper are characterized by a significant friction factor. However, due to their hardness and plasticity, they demonstrate high wear resistance.

It is difficult to say that high-entropy coatings can already replace traditional ones in mechanical engineering. However, over time, they will be widely used for elements that operate under high-temperature conditions.

Based on the literature analysis results, it should be noted that there is a limited number of papers considering this issue from the point of view of tribology. For further research, it is necessary to develop high-entropy coatings that will provide high hardness, wear resistance, and a low friction factor. This will make it possible to create coatings suitable for use in tribo-loaded units, and therefore, in the mechanical engineering production processes. Thus, it is expected to receive promising materials that will compete with traditional coatings.