Experimental methods

The Cr and AlCrNbSiTi HEA coatings were deposited on Zr-Sn-Nb alloy substrates (20 mm × 20 mm × 0.6 mm) using multi-arc ion plating technology. Three targets of the pure Ti (99.99%), pure Cr (99.99%), and Al₃₄Cr₂₂Nb₁₁Si₁₁Ti₂₂ alloy were used in the deposition process. Prior to deposition, the Zr alloy substrates were initially hand-polished with 2000 grit sandpaper, cleaned ultrasonically in acetone followed by ethanol to remove surface contaminants, and heated further to remove moisture. The deposition chamber was heated to 300 to remove the water vapor and evacuated to a base pressure below 6 × 10^-4 Pa. Subsequently, the substrate surfaces were etched using an arc-enhanced glow discharge (AEGD) process to remove contaminants (such as surface oxides) and to increase surface roughness. Cr and AlCrNbSiTi HEA coatings (of approximately 10 μm thickness) were then deposited individually on the substrates. The detailed deposition parameters are listed in Table 1.

The surface and cross-section morphology of the Cr and AlCrNbSiTi HEA coatings on the Zr alloy substrates were examined using a scanning electron microscope (SEM, Phenom XL). The samples for cross-section SEM were cut, sanded and polished (finally with a 0.05 μm Al₂O₃ water-based suspension). The fine structures and chemical compositions of the coatings were investigated using a transmission electron microscope (TEM, Talos F200X). TEM samples were prepared using a focused ion beam (FIB, Scios 2 DualBeam). The crystal structures of the coatings were studied using a grazing incident X-ray diffractometer (GIXRD, X’Pert MRD). The grazing incidence angle was 1 °, and the diffraction scan range was 10 ° < 2θ < 90 °, with a step size of 0.02 °.

The interface adhesion strength of the Cr and AlCrNbSiTi HEA coatings was tested using an automatic scratch tester (CASSTeP500_NHT3_MCT3) with a diamond ball cone indenter (apex angle was 120°±1.0°, and its radius (R) was 100 μm±10%). Scratch tests were made under a stepwise linearly increasing load (applied from 0 N to 10 N, 30 N) over the scratch length (2000 μm), and the corresponding scratch SEM morphology, friction (Ft), acoustical emission signal (AE), penetration depth (Pd), normal load (YFn), and friction coefficient (μ) images were recorded and subsequently analyzed.

Computational methods

First-principles calculations can provide an in-depth explanation of the origin of the coating performance [43, 44] and play a key role in predicting HEA coating performance [45]. Additionally, these calculations can explain the structure strength and other properties from the atomic or electronic level [43, 44, 46, 47], to supplement the experimental findings.

The special quasi-random structure (SQS) [48] approach was used to build the AlCrNbSiTi HEA models, and the mcsqs code from the alloy-theoretic automated toolkit (ATAT) [49] was utilized to generate the SQS models. The first and second nearest-neighbor pairs were optimized to ensure close proximity to the ideal mixing state. The SQS models were also screened according to Born’s dynamical stability criteria [50]. Fig. 1 shows the unrelaxed SQS models of HEA crystal structures with different alloy compositions, where the SQS model with FCC structure has 32 atoms. Based on the HEA SQS models, a series of HEA(111)/ Zr(0001) interfaces were built, one of which is shown in Fig. 2(b). Fig. 2(a) also shows the Cr(110)/Zr(0001) interface model. As shown in Fig. 2, the two Zr layers closest to the interface are denoted as Zr-1 and Zr-2, and the two coating atomic layers closest to the interface are labeled as Coating-1 and Coating-2. A, B, and C in Fig. 2 are the assumed fracture planes.

Fig. 1Full-screen View

(Color online) Unrelaxed SQS models of HEA alloy crystal structures: (a) Al₁₁Cr₉Nb₃Si₂Ti₇, (b) Al₁₃Cr₇Nb₃Si₂Ti₇, and (c) Al₁₅Cr₅Nb₃Si₂Ti₇

Fig. 2Full-screen View

(Color online) The unrelaxed models of (a) Cr/Zr and (b) FCC HEA/Zr interfaces. Zr-1 and Zr-2 indicate the atomic layers closest to the Zr substrate interface, and Coating-1 and Coating-2 denote the atomic layers closest to the Cr and HEA coatings interface. A, B, and C represent the different fracture planes between these atomic layers

The Vienna ab-initio simulation package (VASP) [51] was employed to perform electronic state calculations within the density functional theory (DFT) [52, 53]. Electron-ion interactions were described by the projector-augmented plane-wave (PAW) [54] method and the wave functions were expanded in a plane-wave basis set with a cutoff energy of 280 eV. A generalized gradient approximation (GGA) [55] of the exchange correlation energy was used in the PBE scheme. The total energy and Hellmann-Feynman forces were convergent within 10^-5 eV and 10^-2 eV/Å, respectively. The Monkhorst-Pack k-point meshes of 7 × 4 ×1 and 3 × 3 × 1 were used to sample the Brillouin zone [56] for the supercells of Cr/Zr and HEA/Zr interfaces, respectively. Ab-initio molecular dynamics (AIMD) simulations were also conducted to obtain the amorphous HEA structures. The HEA structures were subjected to pre-melting, melting, and then quenching to 0K to induce amorphicity. The FCC structured HEA was used solely to build the amorphous high-entropy alloy, and it was observed that this composition would not form an FCC structure. However, for comparison with amorphous structures, the FCC structured HEA was also investigated in this study.

Coating microstructure and adhesion strength

Figure 3(a, c) shows the surface SEM images of the Cr and AlCrNbSiTi HEA coatings, respectively. Both coatings exhibited a smooth cracks-free surface morphology. Droplets and voids (μm scale) were distributed on the Cr coating surface, generally formed during multi-arc ion plating [57]. On the contrary, the AlCrNbSiTi HEA coating exhibited a smoother surface. Fig. 3(b, d) shows the cross-sectional SEM images of the Cr and AlCrNbSiTi HEA coatings, respectively. Both coatings had a uniform thickness of approximately 10 μm with no defects (such as delamination, holes or cracks) found between coatings with the Zr substrate, indicating a good quality deposition well-adhered to the Zr substrate.

Fig. 3Full-screen View

(Color online) Surface and cross-sectional SEM images of the coatings: (a) Cr coating surface, (b) Cr coating cross-sectional, (c) AlCrNbSiTi HEA coating surface, and (d) AlCrNbSiTi HEA coating cross-sectional

Figure 4(a) shows the TEM images of the Cr coating. The Cr coating microstructure exhibited a typical columnar crystal structure, and the grain width of the columnar crystal was approximately 0.3 μm. The diffraction patterns along the [110] and [001] strip axes demonstrated typical BCC characteristics [57], as shown in Fig. 4(a). The high-resolution TEM (HRTEM) of the Cr coating is shown in Fig. 4(b), with a clearly-visible crystal structure. Fig. 4(c) shows the TEM image of the AlCrNbSiTi HEA coating. No obvious discernible microstructure were observed in the coating. The diffraction pattern of the AlCrNbSiTi HEA coating showed a typical amorphous structure characteristic, as shown in Fig. 4(c). The HRTEM of the AlCrNbSiTi HEA coating is shown in Fig. 4(d), where an obvious chaotic atomic structure was observed. Thus, from Fig. 4(c, d), it can be verified that the AlCrNbSiTi HEA coating deposited on the Zr alloy substrate is an amorphous structure. Furthermore, an energy dispersive X-ray spectrometry (EDS) composition analysis of the AlCrNbSiTi HEA coating was performed. The peaks of Al, Cr, Nb, Si and Ti were detected. All the elemental compositions - Al: 35.9, Cr: 21.1, Nb: 11.6, Si: 11.4, and Ti: 20.0 at.%, calculated by averaging over four data points were found to be agreeing with the Al₃₄Cr₂₂Nb₁₁Si₁₁Ti₂₂ target alloy composition, indicating a good coating deposition process.

Fig. 4Full-screen View

TEM images of coatings: (a) Cr coating, (b) HRTEM of Cr coating, (c) AlCrNbSiTi HEA coating, and (d) HRTEM of AlCrNbSiTi HEA coating

Figure 5 shows the GIXRD patterns of the Cr and AlCrNbSiTi HEA coatings, and the Zr substrate. The peaks of Zr, such as (002) and (103), in the top pattern (blue curve) were obvious. Most Cr coating peaks, in the bottom pattern (black curve), were similar to the Zr peaks, except for one extremely strong peak in the 64.6 ° position from Cr (200). The AlCrNbSiTi HEA coating peaks, in the middle pattern (red curve), were extremely similar to those of the Zr, and no obvious new peaks appeared. Notably, a broad peak appeared (between ∼38 °-∼45 °) after the Zr (101) peak, indicating the amorphous nature of AlCrNbSiTi HEA coating, in agreement with the TEM results.

Fig. 5Full-screen View

(Color online) GIXRD patterns of the Cr coating, AlCrNbSiTi HEA coating, and Zr substrate

Figure 6(a) and (b) show the scratch SEM morphology, Ft, AE, Pd, YFn, and μ images of the Cr and AlCrNbSiTi HEA coatings under 0-30 N normal load, respectively. As shown in Fig. 6(a), the Cr coating scratch was relatively flat with no obvious spalling, which indicated good adhesion between the Cr coating and Zr substrate. However, it is worth noting that once the scratch length exceeded 950 μm, cracks appeared on the scratch surface successively, corresponding to penetration depth (Pd) > 10 μm (the thickness of the coating). The friction (Ft) curve (black line in Fig. 6(a)) increased almost linearly to ∼ 15 N. The curve of friction coefficient (μ, the light blue line in Fig. 6(a)) increased rapidly to ∼ 0.2, and then gradually reached a slower increase to 0.5. The acoustic emission signal (AE) curve (red line in Fig. 6(a)) initially appeared stable at ∼ 2% (corresponding scratch length 0-380 μm), and then showed a wavy increasing trend to ∼ 14% (corresponding to scratch length 380-2000 μm). The AE wave peaks that appeared after the scratch length > 950 μm corresponded to the cracks in the SEM morphology. The Pd curve (green line in Fig. 6(a)) appeared to be linear increasing with the maximum scratch depth ∼ 23 μm, except for a bump after Pd ∼ 11 μm corresponding to scratch length 920-1000 μm, YFn ∼ 13N and a wave increase of AE from 4.5-9.5% which most likely occurred owing to the indenter reaching the interface between the Cr coating and Zr substrate.

Fig. 6Full-screen View

(Color online) Scratch SEM morphology and other coating information: (a) Cr coating under 0-30 N, (b) AlCrNbSiTi HEA coating under 0–30 N, and (c) AlCrNbSiTi HEA coating under 0–10 N. Ft represents friction, AE represents acoustical emission signal, Pd represents penetration depth, YFn represents normal load, and μ represents friction coefficient

The scratch on the AlCrNbSiTi HEA coating showed a significant difference with the Cr coating, shown in Fig. 6(b). Although the scratch initially appeared relatively flat (corresponding scratch length 0-320 μm), cracks similar to the Cr coating in Fig. 6(a) also appeared. Obvious spalling (brittle cracking similar to ceramics) was observed once the scratch length exceeded 320 μm (corresponding YFn > 5N), which indicated relatively poor adhesion between the AlCrNbSiTi coating and Zr substrate. The first large wave (increases rapidly from ∼ 5 to 13%) in the AE curve (red line in Fig. 6(b)) corresponds to the first spalling in the SEM morphology, subsequent waves in the AE curve suggest multiple brittle spalling. A significant increase in the Ft curve (black line in Fig. 6(b)), μ curve (light blue line in Fig. 6(b)), and Pd curve (green line in Fig. 6(b)) also corresponded to each spalling. To clearly obtain the coating breaking process, a scratch under 0-10 N normal load was also made for the AlCrNbSiTi HEA coatings (shown in Fig. 6(c)). The scratch results were similar to Fig. 6(b), more visible cracking and spalling was observed, which also indicated the brittle AlCrNbSiTi HEA coating property and relatively poor adhesion between the AlCrNbSiTi HEA coating and Zr substrate.

First-principles calculation

Table 2 lists the calculated lattice constants for BCC Cr and FCC HEA. The calculated lattice constant of Cr is found to be in good agreement with the experimental result [58]. As the Al content increased and Cr content decreased in HEA alloys, the HEA lattice constant increased from 7.792–7.910 Å as shown in Table 3. This is because the atomic size of Al is larger than that of Cr. To determine the adhesion between the coatings and Zr substrate, the interface energy, E_interface, is calculated as follows: $E_{\text{interface}}=E_{\text{total}}-E_{\text{coating}}-E_{\text{Zr}}\mathrm{,}$ (1) where E_total, E_coating, E_Zr are the calculated energies of the interface supercell, the coating, and the Zr substrate, respectively. A negative value indicates strong cohesion between the coatings and Zr substrate. It can be observed in Table 3 that the cohesion between the Cr/Zr interface is stronger than those between FCC HEA/Zr and amorphous HEA/Zr interfaces. Comparing the two HEA coatings, the cohesion strength is not affected by the FCC and amorphous structures of HEA. Moreover, the composition of Al₁₁Cr₉Nb₃Si₂Ti₇ was further examined to explore the cohesion mechanism between the HEA coatings and Zr substrate in the following sections.

To further investigate the cohesion between the coatings and Zr substrate, first-principles tensile tests were performed. A uniaxial tensile strain with a 2% increment in the interface normal direction was applied. In each strain step, the starting atomic configuration was obtained from the relaxed configuration of the preceding step. Figure 6 shows the result of the first-principles tensile test for the Cr/Zr interface. The maximum strength was 9.9 GPa at a strain of 12%. However, at 14% strain, the interface broke up between the layers Zr-1 and Zr-2. C is the final fracture plane as shown in the inset of Fig. 7. The Cr/Zr interface did not break along the A or B plane in Fig. 2. This means that the bonding strength across the C plane (i.e., bonds between Zr-1 and Zr-2 layers) determines the cohesion strength of Cr/Zr interface.

Fig. 7Full-screen View

(Color online) First-principles tensile test for Cr/Zr interface. The inset represents the atomic structure after the Cr/Zr interface breakup

To confirm the results in Fig. 7, first-principles tensile tests using a rigid separation method were performed. For the rigid separation method, the interface structures were separated at different planes (i.e., the A, B, and C planes in Fig. 2) with an increment of 0.1 Å in the interface normal direction, however, the atomic structures on both sides of the fracture plane were not relaxed. The results for the Cr/Zr interface are shown in Fig. 8 and Table 4. In Fig. 8, the separation energy for fracture plane A was consistently higher than those of the B and C planes during the tensile test. In Table 4, the maximum separation energy for the A plane was 0.48 ${\text{eV/Å}}^2$, and those for the B and C planes were only 0.26 ${\text{eV/Å}}^2$ and 0.21 ${\text{eV/Å}}^2$, respectively. Thus, it was most difficult to separate the interface structure at the A plane, meaning that the Cr-Cr bonds across the A plane are significantly stronger than the Cr-Zr bonds across the B plane and the Zr-Zr bonds across the C plane. As a result, the Cr/Zr interface breaks at the C plane preferentially, which is in good agreement with the results shown in Fig. 7.

Fig. 8Full-screen View

(Color online) Change tendency of separation energy ${\text{eV/Å}}^2$ during first-principles tensile test using rigid separation method for the Cr/Zr interface with respect to unseparated models. A, B, and C denote different fracture planes as shown in Fig. 2

As can be observed in Figs. 7 and 8, first-principles tensile tests have achieved identical results with and without the rigid separation method. Further, first-principles tensile tests with the rigid separation method have lower computational cost and can be used to calculate the separation energies for different fracture planes. Hence, this method was further used to identify the cohesion strength between the HEA coating and Zr substrate, and the results are shown in Fig. 9 and Table 4. The HEA coatings with both FCC and amorphous structures were both studied. In Fig. 9, for each fracture plane, the separation energies for FCC and amorphous HEAs have the similar values. The separation energy is listed in the following order: FCC/amorphous HEA-A > FCC/amorphous HEA-B > FCC/amorphous HEA-C. Therefore, the Zr-Zr bonding across the C plane is the weakest with the separation energy of 0.20 ${\text{eV/Å}}^2$ in Table 4, and the breakage would occur at the C plane of the FCC HEA/Zr and amorphous HEA/Zr interfaces. This is in good agreement with the results of the Cr/Zr interface in Fig. 8.

Fig. 9Full-screen View

(Color online) Change tendency of separation energy ${\text{eV/Å}}^2$ during first-principles tensile test using rigid separation method for FCC HEA/Zr and amorphous HEA/Zr interfaces with respect to unseparated models. A, B, and C denote different fracture planes as shown in Fig. 2

As can be observed in Table 4, the Cr-Cr bonding across the A plane of the Cr/Zr interface, with the separation energy of 0.48 ${\text{eV/Å}}^2$, is significantly stronger than the bonding across the A plane of the HEA/Zr interfaces. For the B plane, the Cr-Zr bonding in the Cr/Zr interface, with 0.26 ${\text{eV/Å}}^2$, is also stronger than the bonding between HEA and Zr atoms in the HEA/Zr interfaces. However, the bonding across the C plane is the Zr-Zr bonds for all interfaces, i.e., the bonds between Zr-1 and Zr-2 layers in Fig. 2, which results in similar separation energies as shown in Table 4.

To determine the underlaying mechanism in the cohesion of different interfaces, the charge densities for the Cr/Zr, FCC HEA/Zr, and amorphous HEA/Zr interfaces were investigated and are shown in Fig. 10. As demonstrated in Fig. 10 the charge densities in Cr and HEA coatings are significantly denser than those in the Zr substrate, and the charge densities in the amorphous HEA coating are random in Fig. 10(c) compared with those in Figs. 10(a) and 10(b). It can be observed that the charge densities between Zr-1 and Coating-1 atoms are higher than those between Zr-1 and Zr-2 atoms. This indicates that the bonding between the Zr-1 and Zr-2 layers is weaker and will preferentially break, which is in good agreement with the results of first-principles tensile test.

Fig. 10Full-screen View

(Color online) Charge densities for (a) Cr/Zr, (b) FCC HEA/Zr, and (c) amorphous HEA/Zr interfaces. The yellow and red isosurfaces indicate 0.03 and 0.06 electrons/Bohr³, respectively

Furthermore, the density of states for atoms in the Zr-1 and Coating-1 layers of the Cr/Zr and FCC HEA/Zr interfaces were calculated and are shown in Figs. 11 and 12, respectively. In Fig. 11, the density of states of Cr overlaps with that of Zr. Specifically, many hybridization peaks exist between the Cr-d and Zr-d electrons, indicating a relatively strong bonding between Cr and Zr. This confirms the results in Table 4 and Fig. 10. Similarly, in Figs. 12(b) and (d), an obvious overlap emerges between the density of states of Nb/Ti and Zr atoms with the existence of many hybridization peaks. However, in Figs. 12(a) and (c), no hybridization peaks are evident between Al/Si and Zr atoms, indicating a relatively weak bonding between Al/Si and Zr atoms. Hence, for the HEA coating, Cr, Nb, and Ti atoms form a stronger bonding with the Zr substrate than Al and Si atoms, and the cohesion between the HEA coating and Zr substrate is weaker than that between the Cr coating and Zr substrate, which also confirms the results shown in Table 4 and Fig. 10. Thus, reducing Al concentration improves the interface adhesion to a certain extent.

Fig. 11Full-screen View

(Color online) Density of states (electrons/eV) for Zr and Cr atoms in the Cr/Zr interface in Fig. 2(a)

Fig. 12Full-screen View

(Color online) Density of states (electrons/eV) for (a) Al, (b) Nb, (c)Si, and (d) Ti atoms in the FCC HEA/Zr interface in Fig. 2(b)

To investigate the mechanical properties of Cr, FCC HEA, and amorphous HEA coatings, the elastic constants were calculated. Because the chemical distribution in HEA SQS supercells can result in an anisotropic structure and scatter the elastic constants, an averaging approach [59] was applied to obtain the values of C₁₁, C₁₂, and C₄₄ as follows: $C_{11}=\left(c_{11}+c_{22}+c_{33}\right)/\mathrm{3,}$ (2) $C_{12}=\left(c_{12}+c_{23}+c_{13}\right)/\mathrm{3,}$ (3) $C_{44}=\left(c_{44}+c_{55}+c_{66}\right)/\mathrm{3,}$ (4) Using these average values, bulk modulus B, shear modulus G [60, 61], Young’s modulus E, and Cauchy pressure (Γ) were calculated as follows: $B=\left(c_{11}+2c_{12}\right)/\mathrm{3,}$ (5) $G=\left(G_V+G_R\right)/\mathrm{2,}$ (6) $G_V=\left(C_{11}-C_{12}+3C_{44}\right)/\mathrm{5,}$ (7) $G_R=\left[5\left(C_{11}-C_{12}\right)C_{44}\right]/\left[3\left(C_{11}-C_{12}\right)+4C_{44}\right]\mathrm{,}$ (8) $E=9BG/\left(3B+G\right)\mathrm{,}$ (9) $\text{Γ}=C_{11}-C_{44}\mathrm{,}$ (10) AIMD simulations were conducted to obtain the amorphous HEA structures with random structures in Fig. 13, investigated using the averaging approach.

Fig. 13Full-screen View

(Color online) Relaxed models of amorphous HEA alloy crystal structures: (a) Al11Cr9Nb3Si2Ti7, (b) Al13Cr7Nb3Si2Ti7, and (c) Al15Cr5Nb3Si2Ti7

The calculated elastic moduli (B,G and E), Pugh’s ratio B/G, and Cauchy pressure (Γ) for the Cr and HEA alloys are listed in Table 5. For BCC and FCC structures, B/G is larger than 1.75, implying that the examined alloys are ductile [62]. A negative value of Γ indicates a brittle alloy [63]. It is clear that the calculated B, G, and E of the Cr are significantly larger than those of the HEA coatings, thus the Cr coating possesses better mechanical properties. With the Cr reduction and Al addition in FCC HEA and amorphous HEA alloys, the values of B decrease monotonously. Meanwhile, Γ decreases into negative values, and B/G becomes less than 1.75 at low Cr content. Thus, low Cr and high Al content reduce the mechanical performances and increase the brittleness of HEA coatings, providing theoretical guidance for the preparation of improved coatings.

Finally, it should be emphasized that the SQS models used in this study solely represent the possible structures of HEA coatings. SQS models with other potential distributions and different properties may also exist. However, the first-principles calculations proposed herein illuminate the comparison of Cr and HEA coating properties with different compositions, and can be used as a theoretical guide for future coating development.

This study aimed to employ theoretical calculations to discover the underlying physical mechanisms in experiments, and demonstrated the utility of the combined approach of first-principles calculations and experimental research for the development of new HEA coatings. Although the adhesion performance of the HEAs prepared herein are not better than that of the Cr coatings, the advantage of HEA lies in the performance-based tunability of its composition, allowing HEA coating improvement based upon elemental composition alteration. Finally, a systematic evaluation of the service performance of improved AlCrNbSiTi HEA coatings was conducted, including high-temperature electrochemistry, hydrothermal corrosion conditions, high-temperature steam oxidation [41], and fretting corrosion performance [42].