Exploring high corrosion-resistant refractory high-entropy alloy via a combined experimental and simulation study

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In this work, we performed first-principles calculations, coupled with experiments, to explore HEAs with high corrosion resistance. The results revealed that TiNbTa-based HEAs exhibited a lower tendency for corrosion. However, the appearance of local chemical fluctuations (CFs) increased the corrosion tendency of TiNbTa-based HEAs. Comprehensive SHapley Additive exPlanations analyses uncovered that in a sample with configurational CFs, the atomic order near the surface was altered. Therefore, corrosion behavior was affected. Based on experiments, the annealed samples exhibited typical chemical segregation and declined corrosion resistance. Physical sciences/Materials science/Theory and computation Physical sciences/Materials science Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Introduction High-entropy alloys (HEAs) have attracted increasing attention due to their disordered atomic structure, exhibiting numerous desirable properties that cannot be achievable by traditional alloys 1,2,3 . The elevated configurational entropy in HEAs plays a pivotal role in stabilizing the formation of simple solid solution phases while impeding the development of detrimental intermetallic compounds 4,5 . The demand for new structural alloys with commendable mechanical properties and excellent corrosion resistance is particularly pronounced in application sectors such as aerospace, clean power, and biomedical industries. Refractory HEAs, composed of refractory metals, generally exhibit superior mechanical properties and resistance to general corrosion 6,7,8 , presenting promising prospects for diverse applications. Several refractory HEAs have demonstrated significant potential due to their remarkable strength. For example, during room temperature deformation, HEAs such as Nb 25 Mo 25 Ta 25 W 25 and V 20 Nb 20 Mo 20 Ta 20 W 20 alloys have shown high yield stress values of 1058 and 1246 MPa, respectively 9 . Recent studies has shown that exploration of chemical heterogeneity during the heat treatment process, such as short-range order and local chemical fluctuations (CFs), has opened up a new avenue for the development of high-strength HEAs 10,11,12 . A recent study reported evidence of consequential effects in NiCoCr, with the yield strength further increasing by 76% after annealing at 2073 K for 24h 13 . When the annealing duration of the TiZrHfNb alloy at 673 K was prolonged to 40 h, the hardness increased by 25% 14 . Meanwhile, CFs could lower the configurational entropy from its maximum value, corresponding to a random alloy, and change the expressions for free energy. CFs was also found to decrease the enthalpy of the system, influencing defect energetics and potentially affecting physical properties. Consequently, chemical heterogeneity may affect the corrosion properties of HEAs. It is well known that chemical heterogeneity is the primary cause of localized galvanic corrosion. Compared with a chemically homogeneous single-phase solid solution, the occurrence of elemental segregation behavior leads to the formation of different electrochemical potential regions within the alloy, which undoubtedly significantly increases its sensitivity to corrosion 15 . However, it is worth noting that certain chemical heterogeneities can enhance the corrosion resistance of an alloy. Taking the NiCoVAl x alloy as an example, an increase in the content of Al leads to a higher proportion of the B2 phase, which has a higher Volta potential, thereby improving the overall corrosion resistance of the alloy 16 . Since the emergence of CFs is widely considered to be the origin of elemental segregation 17 , it is particularly important to conduct in-depth research on the impact of CFs on the corrosion performance of alloys. However, only a few studies have reported on the corrosion behavior of refractory HEAs, with a significant gap in research on the effect of CFs on corrosion properties. Equiatomic TiZr(Hf, Ta, Nb) medium entropy alloys have been developed to achieve superior corrosion resistance compared with pure Ti 18 . MoNbTaTiZr HEAs have exhibited a distinctive combination of friction and corrosion resistance, outstanding mechanical properties, and biocompatibility, positioning them as potential bioimplants 19 . Recently, non-equiatomic TiNbTaZrMo HEAs with good biocompatibility have been designed 20 . Consequently, non-equiatomic HEAs, with extensive and unexplored composition spaces, present an opportunity to obtain highly corrosion-resistant alloys. However, systematic research on the effect of various elements and the corrosion resistance of refractory HEAs has remained insufficient, creating a bottleneck in designing corrosion-resistant HEAs. The ability to freely adjust alloy composition in HEAs, resulting in an enormous composition space, significantly complicates the determination of corrosion resistance of new materials. Therefore, an efficient and rapid forecasting method for corrosion resistance is urgently needed to guide experimental synthesis. The Monte Carlo (MC) molecular dynamics (MD) simulation method has proven useful for chemical heterogeneity investigations 21,22 . However, limitations in potential availability make it challenging to simulate in various composition models using the MD/MC method. Reliable interatomic potentials are considered essential for MD simulations 23 . However, only a limited number of potentials have been developed for HEAs, due to the brief history of HEAs and the substantial workload required to develop multi-elemental interatomic potentials. Density functional theory has emerged as a promising solution for addressing this challenge, as it can handle multi-elemental systems 24,25 . The effect of chemical heterogeneity on the mechanical properties of HEAs has been extensively investigated via the density functional theory (DFT)/MC method 26,27 , indicating that it will have a significant effect on critical parameters, notably the stacking-fault energy 26 and dislocation mobility 27 . In this work, we elucidated the chemical heterogeneity and corrosion resistance of Ti(Nb,Zr)(Zr,Nb,Ta)(Ta,Ha,V,Cr,Mo,W) quaternary refractory HEAs through a combination of MC simulations and experiments. The effect of CFs on the corrosion behavior of refractory HEAs was investigated using the DFT/MC method to determine the reasons for corrosion resistance variations. Results and discussion Generation of appropriate surface structures The calculated formation energies for the (110) surfaces of the bcc and (111) surfaces of the fcc in 16 refractory HEAs are presented in Fig. 1 , namely TiNbTaCr (TNTC), TiNbTaHf (TNTH), TiNbTaMo (TNTM), TiNbTaV (TNTV), TiNbTaW (TNTW), TiZrNbCr (TZNC), TiZrNbHf (TZNH), TiZrNbMo (TZNM), TiZrNbTa (TZNT), TiZrNbV (TZNV), TiZrNbW (TZNW), TiZrTaCr (TZTC), TiZrTaHf (TZTH), TiZrTaMo (TZTM), TiZrTaV (TZTV), and TiZrTaW (TZTW). A substantial number of atoms in the bcc and fcc slab structures were observed, and the calculated formation energies highlighted the stability of the generated structures. The bcc structure, with the lowest formation energy, was selected for corrosion behavior studies. Following electronic self-consistent calculations, the magnetic character of the initially set magnetic alloying element Cr persisted, while other systems became non-magnetic. Therefore, in subsequent calculations, only the magnetism of the alloying element Cr was considered. To computationally examine the effect of local chemical order on the corrosion behavior of these refractory HEAs, realistic models in the system were developed. Previous studies employed a systematic cluster expansion approach to explore local chemical heterogeneity in the TiZrNb, TiZrHfNb, and TiZrHfNbTa bcc refractory HEAs 28 . Although these studies indicated that CFs was expected to affect the mechanical properties, no systematic study has been conducted encompassing all refractory elements to explain the effect on the corrosion behavior of refractory HEAs. In this work, the DFT/MC method was employed to develop models for refractory HEA solid solutions with varying degrees of CFs. The most significant trends in potential energy change based on the DFT-based MC simulations are shown in Fig. 2 (a). Despite the relatively small number of swap trials per atom compared with classical MC simulations, the potential energy curves appeared to converge. The appearance of CFs reduced the free energy primarily by lowering the formation energy, ranging from 38 to 447 meV per atom. Simultaneously, it had a significant effect on the microstructure of the alloy. To describe the trends in local chemical ordering obtained by the MC simulations, we employed WCP to characterize. A positive value of WCP indicated that the atomic pair was unfavorable, while a negative value indicated that the atomic pair was favorable. The resulting indicated the segregation of different elements, with some elements showing significantly stronger segregation than others. This tendency was captured by the WCP in Fig. 2 (b–d), where some elements had a propensity to form clusters, and others favored neighbors of other types. As shown in Fig. 2 (b), there was a strong tendency to form X-Ta pairs (WCP 0). However, the results showed that the Ti-Hf pair was favorable (WCP = − 0.71), while the Hf-Ta pair was unfavorable (WCP = 0.44), which was attributed to the large atomic size of Hf, leading to segregation on the surface. Similar trends were also observed for the TiZrNb-based HEAs, where the Nb-X pair was favored (WCP < 0), and Zr-Cr, Zr-Mo, Zr-V, and Ti-Hf exhibited a strong trend to form pairs. Preferred atomic pairings between X-Ta, Ti-Hf, Zr-Cr, Zr-Mo, and Zr-V were observed in the TiZrTa-based HEAs as the WCP values were negative, confirming the energetic preference in the refractory alloys. Therefore, this result provided another perspective for understanding the corrosion behavior of refractory HEAs. Thus, the experimental identification of chemical heterogeneity in the refractory HEAs requires further investigation. Work function effects of refractory HEAs A high surface work function, derived from the electron potential energy, typically indicates a high corrosion potential and corrosion resistance for materials according to traditional theory 29,30,31 . For refractory HEAs with random compositional disorder, the calculated values of the work function are shown in Fig. 3 (a). The calculated work function values for different samples displayed a large range, spanning from 3.95 to 4.57 eV. Notably, the group of TiNbTa-based refractory HEAs exhibited a higher work function, suggesting potentially better corrosion resistance compared to the other two groups. The work function in the refractory HEAs could be quantitatively correlated with the degree of CFs, reflected by the total nonproportional number of local atomic pairs, WCP sum , as shown in Fig. 3 (b)–(d). For most HEAs, the work function was smaller in the more ordered sample, and a lower work function implied a higher probability of electron loss and a higher tendency for corrosion. However, for TiZrNbCr, TiZrTaCr, and TiZrTaV, the opposite trend was observed. The inconsistent influence of CFs on the work functions of different alloys highlighted the need for further examination. Subsequently, the effect of surface atomic distribution (first layer) was considered, revealing that CFs could lead to a change in surface atomic distribution. We explored the relationship between the surface atomic distribution and work function through a machine learning model 32,33 . Random forest 34,35,36,37,38 (RFR), a popular and efficient model based on the decision tree capable of both regression and classification, was employed. By incorporating the SHapley Additive exPlanations (SHAP) tool 39 and the RFR model, the relationship was explored according to the above calculation results. Regarding the effects of specific elements, the number of atoms of each element in the first layer was taken as the input, and the SHAP values of each element were plotted, as shown in Fig. 4 . We observed that, with more Zr and Ti atoms, the work function of the alloys tended to decrease, while for more Nb and Ta atoms, the work function of the alloys tended to increase. The observed trends could be attributed to the electronic configurations of the bonding shells of the constituent surface atoms 40 . Nb and Ta possessed more partially filled d orbitals compared with Ti and Zr, leading to greater energetic stability. Additionally, V and Cr had more partially filled d orbitals; however, due to their smaller atomic numbers relative to other elements, the corresponding regions were not conducive to improving the work function of the HEA surfaces. Potentiodynamic polarization measurements We synthesized 16 refractory HEAs using the conventional arc melting processing route, and the corrosion potential ( E corr ) was obtained by fitting potentiodynamic polarization curves. Figure 5 shows a strong correlation between the corrosion behavior and work function. The results established a trend of increasing corrosion resistance in the refractory HEAs with higher work function values. Notably, the TiNbTa-based refractory HEAs exhibited a lower corrosion tendency than the other groups, and TiNbTaMo demonstrated the highest E corr value of − 0.536 V SCE in this group. To further confirm the effect of chemical heterogeneity on corrosion resistance, a series of TiNbTaHf, TiNbTaMo, TiZrNbTa, and TiZrNbV samples was experimentally prepared by controlling the isothermal annealing time. The samples annealed at different durations showed different degrees of elemental aggregation. Figure 6 (a)–(d) illustrates the typical potentiodynamic polarization curves of each sample in 0.9 wt.% NaCl solution. According to the fitting results in Table 1 , compared with the as-cast samples, the corrosion tendency of the annealed samples was enhanced. With an extension of annealing time, E corr decreased, and the corrosion resistance deteriorated, aligning with the results of the work function DFT calculations. Table 1 Electrical parameters extracted from the potentiodynamic polarization curves of TiNbTaHf, TiNbTaMo, TiZrNbTa, and TiZrNbV annealed at different durations at 1273K in 0.9 wt.% NaCl solution. Annealing durations E corr (V SCE ) TiNbTaHf TiNbTaMo TiZrNbTa TiZrNbV 0 h −0.592 −0.536 −0.580 −0.573 12 h −0.642 −0.586 −0.624 −0.584 30 h −0.662 −0.712 −0.666 −0.663 Microstructure characterization To obtain further insight into the changes in corrosion behavior in our materials, the EDS element distribution mapping of TiZrNbTa and TiZrNbV annealed at 1273 K for 30 h and TiNbTaHf and TiNbTaMo annealed at 1273 K for 12 h were obtained using TEM, as shown in Figs. 7 and 8 . In the as-cast samples, each element was distributed homogeneously, and no distinct element segregation was detected. However, after annealing, element segregation in the alloy became apparent and intensified. In the annealed TiZrNbTa and TiZrNbV alloys, the Zr-lean phase was mainly composed of Nb and Ta/V elements, while the Zr elements were primarily enriched in the matrix of the Zr-rich phase, which was consistent with the previous calculation results of WCP. For annealed TiNbTaHf and TiNbTaMo, TiNbTaHf did not demonstrate distinct element segregation, while TiNbTaMo exhibited Ti-rich regions. Figure 9 shows the surface morphologies and elemental distribution near the Ti-rich regions of TiNbTaMo. The white square region in Fig. 9 b indicated the presence of nanoscale precipitates. A line scan (labeled as LS1 in Fig. 9 b) was performed to measure the composition of the precipitate and the matrix. The spatially resolved elemental concentrations along LS1 demonstrated segregation of Ti at the precipitate, as shown in Fig. 9 c. High-resolution TEM analysis (Fig. 9 d) of the annealed TiNbTaMo revealed that the precipitate and matrix exhibited the same crystal structure, as confirmed by the diffuse diffraction ring in the corresponding fast Fourier transform (FFT) images (R1 and R2 in Fig. 9 d). The above observations implied that the extension of annealing time further promoted segregation of elements. The local ordering between the atomic species also reflected strong affinity and interactions, explaining the segregation characteristics of chemical composition on an atomic scale 22, 41 . Although the observation of diffuse superlattice intensities through TEM is attributed to the presence of CFs 42 , there appears to be scant theoretical foundation for any form of CFs that aligns with electron diffraction patterns 43 . Meanwhile, the reported characteristics consistently correspond with those anticipated from symmetry-breaking effects, such as alterations in the stacking sequence. This indicates that determining CFs requires a high degree of caution. However, previous studies indicated that segregation was generally accompanied by the appearance of CFs 17,44 .The formation of CFs in HEAs will increase the energy barrier dominating the effective frictional resistance to dislocation movement 45,46 . Therefore, dislocation motion typically requires overcoming larger energy barriers, enhancing the strengthening effect. However, the introduction of CFs can lead to a decrease in corrosion resistance. In the regulation of mechanical properties, heat treatment 13,14 and the addition of large-sized atoms 47,48 can enlarge the scale of CFs, strengthening the alloy. However, it may lead to a decrease in the corrosion resistance of the alloy. Therefore, choosing a suitable treatment process is crucial. Conclusions In this work, a combined strategy employing first-principles calculations and experiments was used to explore refractory HEAs with high corrosion resistance. The influence of chemical heterogeneity on the corrosion behavior of the materials was investigated. The main conclusions obtained in this work were as follows. Based on the work function results of the RSS structure, the group of TiNbTa-based refractory HEAs had a higher work function, indicating a lower corrosion tendency and better corrosion resistance. The calculation results indicated that the introduction of CFs reduced the work function of most materials, with an adverse effect on the corrosion resistance. However, for a few refractory HEAs, the impact was not significant or had a favorable effect. Combined with SHAP analysis, we found that this effect was mainly caused by a change in the atomic ordered state of the surface. Electrochemical testing revealed that the TiNbTa-based refractory HEAs had a higher corrosion potential. The corrosion potential gradually decreased with prolonged annealing time, which was consistent with the calculated results. Microstructure characterization indicated that after annealing, the TiZrNbTa and TiZrNbV alloys exhibited Nb and Ta/V enrichment, which was in accordance with the simulation results. Meanwhile, the composition of TiNbTaHf remained uniform, and fine precipitates appeared in TiNbTaMo. In summary, we found that the group of TiNbTa-based refractory HEAs exhibited a lower corrosion tendency compared to the other two groups. However, the corrosion resistance of the materials was affected by the emergence of chemical heterogeneity. Through reasonable element regulation, it is expected to reduce or generate favorable effects. Future research on the comprehensive properties of these alloys should thus include consideration of the effects of chemical heterogeneity on corrosion resistance, to understand the degree to which chemical heterogeneity can be used as an independent structural variable to guide alloy design and optimization. It is expected to have good corrosion resistance while achieving better mechanical properties. Methodology DFT-based Monte Carlo simulations To generate the structures representing HEAs, MC simulations were employed. These simulations included the swap trials per atom, with acceptance probabilities determined based on Metropolis-Hastings sampling 49 . The supercell, consisting of 96 atoms, was generated as a special quasi-random structure to serve as the initial starting points, with the temperature used in the MC simulations set to 300 K. Energy calculations were performed using the Vienna ab initio simulation package (VASP) 50,51,52 . For each structure, MC simulations were executed over a total of 2000–2500 steps, equating to 21–26 swap trials per atom. DFT calculations DFT calculations were performed using VASP, with the interaction potential of the core electrons described using the projector augmented wave method 53 . The generalized-gradient approximation was adopted with Perdew-Burke-Ernzerhof 54 parameterization for the exchange correction function. The cutoff energy for the plane wave basis was set to 400 eV for the MC simulations and 600 eV for calculation of the work function. The k-points were meshed by 1 × 1 × 1 for the MC simulations and 2 × 2 × 1 for calculation of the work function 55 . The semi-core p electrons for all elements were treated as valence electrons when available 53,56 . Local chemical parameter The Warren-Cowley parameter (WCP) 57 was used to quantify the chemical ordering around an atomic species. The WCP was calculated using the following equation: $${WCP}_{ij}=1-{Z}_{ij}/{c}_{j}{Z}_{i}$$ 1 , where Z ij is the number of j -type atoms around i -type atoms, Z i is the total number of atoms around i -type atoms, and c j denotes the atomic fraction of j -type atoms in the HEA, with WCP = 0 corresponding to a random solution. A positive value of WCP indicated a tendency to decrease the number of i-j pairs, while a negative value corresponded to the opposite. In this investigation, WCP calculations were performed by counting the elemental types of the nearest neighbors. Experimental process The alloys were prepared from commercially pure Ti, Zr, Nb, Ta, Hf, V, Cr, Mo, and W metals with a purity of 99.9 wt.%. Each ingot with a weight of approximately 100 g was melted in a vacuum arc environment at least six times. Samples 10 × 10 × 2 mm in size were cut from each ingot for subsequent experiments. The exposed surfaces were then meticulously ground using #1000, #2000, #3000, and #5000 SiC sandpaper in sequential order. Electrochemical corrosion studies were conducted in an aerated 0.9 wt.% NaCl solution at 25°C. A Gamry Reference 3000 electrochemical workstation, equipped with a standard three-electrode system, was employed to measure the polarization curves. A saturated calomel electrode (SCE, E = 0.2415 V SHE ) served as the reference electrode, while the specimens functioned as the working electrodes, and a platinum foil served as the auxiliary electrode. The samples were mounted in contact with copper wire embedded in epoxy resin, then polished, degreased in alcohol, cleaned, and dried in warm air. Prior to the potentiodynamic polarization scan tests, cathodic pre-polarization at − 1.0 V SCE for 600 s was applied to spontaneously remove the air-formed oxides. Subsequently, the open circuit potential was measured for 30 min to ensure a steady-state potential. Potentiodynamic polarization curves were obtained at a scanning rate of 1 mV/s from an initial potential of − 0.6 V SCE versus E corr to a final potential of 1 V SCE . A transmission electron microscope (TEM, FEI Talos F200X) equipped with an energy dispersive spectrometer (EDS) was used to further analyze the nanoscale microstructure in the HEAs. Declarations Data availability The raw/processed data required to reproduce these findings can be obtained by contacting the corresponding author. Acknowledgements This research was funded by the Guangdong Province Key Area R&D Program (Grant No. 2019B030302011 and No. 2019B010940001) and the National Natural Science Foundation of China (Grant No. 52371050). Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References Ma, C. L., Li, J. G., Tan, Y., Tanaka R. & Hanada S. Microstructure and mechanical properties of Nb/Nb 5 Si 3 in situ composites in Nb–Mo–Si and Nb–W–Si systems. Mater. Sci. Eng. A 386, 375–383 (2004). Zhang, Y. et al. Microstructures and properties of high-entropy alloys. Prog. Mater. Sci. 61, 1–93 (2014). Miracle, D. B., & Senkov, O. N. A critical review of high entropy alloys and related concepts. Acta Mater. 122, 448–511 (2017). DiStefano, J. R. & Hendricks, J. W. Oxidation rates of niobium and tantalum alloys at low pressures. Oxid. Met. 41, 365–376 (1994). 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Additional Declarations (Not answered) Cite Share Download PDF Status: Published Journal Publication published 24 Jul, 2024 Read the published version in npj Materials Degradation → Version 1 posted Editorial decision: revise 18 Jun, 2024 Review # 1 received at journal 24 May, 2024 Review # 2 received at journal 22 May, 2024 Reviewer # 3 agreed at journal 21 May, 2024 Reviewer # 2 agreed at journal 14 May, 2024 Reviewer # 1 agreed at journal 14 May, 2024 Reviewers invited by journal 14 May, 2024 Editor assigned by journal 14 May, 2024 Submission checks completed at journal 09 May, 2024 First submitted to journal 07 May, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4384666","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":302227615,"identity":"7d63af77-0687-45b0-bfdb-7c7011a74eb1","order_by":0,"name":"Yu Yan","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAxklEQVRIiWNgGAWjYNCCCiCWAGIe4rWcAaomTQtjGylaDI6fPSbNO++wvb10A+ODt20M8uYEtZzJS5Pm3XY4sUfmALPh3DYGw50NhLQcyDEDaUngkUhgk+ZtY0gwOEBIy/k3QC1zDtsDtbD/Jk7LDZAtDYcZe4C2MBOlRfLGG2PLOcfSE3vuHGyWnHNOwnADIS1853MMb7ypsbZnn9188MObMht5grYoHGBgkYAwGRsYIGmAAJBvYGD+QFjZKBgFo2AUjGgAAGCjPMvkWnCxAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0003-4048-0603","institution":"University of Science and Technology Beijing","correspondingAuthor":true,"prefix":"","firstName":"Yu","middleName":"","lastName":"Yan","suffix":""},{"id":302227616,"identity":"e3f2eb6b-733a-4ac7-b34d-07636914e951","order_by":1,"name":"Xinpeng Zhao","email":"","orcid":"","institution":"University of Science and Technology Beijing","correspondingAuthor":false,"prefix":"","firstName":"Xinpeng","middleName":"","lastName":"Zhao","suffix":""},{"id":302227617,"identity":"5db2d897-a941-438a-8dac-86bb5656a904","order_by":2,"name":"Haiyou Huang","email":"","orcid":"","institution":"University of Science and Technology Beijing","correspondingAuthor":false,"prefix":"","firstName":"Haiyou","middleName":"","lastName":"Huang","suffix":""},{"id":302227618,"identity":"1667cc69-1ecb-4bbb-9030-0e76e6615b6c","order_by":3,"name":"Yanjing Su","email":"","orcid":"","institution":"University of Science and Technology Beijing","correspondingAuthor":false,"prefix":"","firstName":"Yanjing","middleName":"","lastName":"Su","suffix":""},{"id":302227619,"identity":"aacdc10d-5998-455a-9f21-e8045c981540","order_by":4,"name":"Lijie Qiao","email":"","orcid":"","institution":"University of Science and Technology Beijing","correspondingAuthor":false,"prefix":"","firstName":"Lijie","middleName":"","lastName":"Qiao","suffix":""}],"badges":[],"createdAt":"2024-05-07 17:46:12","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4384666/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4384666/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41529-024-00495-1","type":"published","date":"2024-07-24T04:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":57015452,"identity":"65ad5d63-2906-420b-afb9-6bc4fc86e2b1","added_by":"auto","created_at":"2024-05-23 12:36:11","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":237474,"visible":true,"origin":"","legend":"\u003cp\u003eCalculated formation energies for the (110) surfaces of the bcc and (111) surfaces of the fcc in various refractory HEAs.\u003c/p\u003e","description":"","filename":"floatimage1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4384666/v1/b417e748ce6c2f5b52243ab5.jpg"},{"id":57015429,"identity":"de7738c0-5eeb-4312-a220-fc423e46adaf","added_by":"auto","created_at":"2024-05-23 12:36:10","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":339633,"visible":true,"origin":"","legend":"\u003cp\u003eEvolution of energy and CFs in various refractory HEAs: (a) potential energy changes with the steps of the MC simulation; detailed values of WCP in the nearest neighbor shell for all atom pairs in the (b) TiNbTa-based (X = Cr, Hf, Mo, V, W), (c) TiZrNb-based (X = Cr, Hf, Mo, Ta, V, W), and (d) TiZrTa-based (X = Cr, Hf, Mo, V, W) refractory HEAs, where the lines and balls represent refractory HEAs with CFs, and the dashed lines represent an ideal random solid solution.\u003c/p\u003e","description":"","filename":"floatimage2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4384666/v1/95f774f26a4c2a33d935868f.jpg"},{"id":57015450,"identity":"3536774a-bf80-47db-a059-d2276c3993fc","added_by":"auto","created_at":"2024-05-23 12:36:10","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":247975,"visible":true,"origin":"","legend":"\u003cp\u003eWork function correlates strongly with local chemical ordering: (a) work function for the random solid solution structure (RSS); (b–d) work functions of three groups were plotted versus WCP\u003csub\u003esum\u003c/sub\u003e for the first neighbor shell, which were (b) TiNbTa-based (X = Cr, Hf, Mo, V, W), (c) TiZrNb-based (X=Cr, Hf, Mo, Ta, V, W), and (d) TiZrTa-based (X=Cr, Hf, Mo, V, W) for the refractory HEAs.\u003c/p\u003e","description":"","filename":"floatimage3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4384666/v1/4361bf2ae3026c1bc7eb8871.jpg"},{"id":57015451,"identity":"3a1ef79f-27d1-4462-9975-7a2482675fc1","added_by":"auto","created_at":"2024-05-23 12:36:11","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":72036,"visible":true,"origin":"","legend":"\u003cp\u003eIllustration showing the work function trends of the RSS and CFs surfaces (first layer) with specific elements, where the gray-shaded elements tendedto reduce the work function, while the golden-shaded elements tended to improve the work function.\u003c/p\u003e","description":"","filename":"floatimage4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4384666/v1/f43d041bcb147d1f5bfaab50.jpg"},{"id":57015415,"identity":"574c6b57-b327-41bf-aa83-f9b9667ef902","added_by":"auto","created_at":"2024-05-23 12:36:09","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":84142,"visible":true,"origin":"","legend":"\u003cp\u003eCorrelation between corrosion behavior and work function.\u003c/p\u003e","description":"","filename":"floatimage5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4384666/v1/f71b5d6a083581433ea1b783.jpg"},{"id":57015428,"identity":"9f840df2-bd78-4890-b5fd-363430235b04","added_by":"auto","created_at":"2024-05-23 12:36:09","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":217275,"visible":true,"origin":"","legend":"\u003cp\u003ePotentiodynamic polarization curves of the various refractory HEA samples before and after heat treatment in 0.9 wt.% NaCl solution: (a) TiNbTaHf, (b) TiNbTaMo, (c) TiZrNbTa, and (d) TiZrNbV.\u003c/p\u003e","description":"","filename":"floatimage6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4384666/v1/f1eb6f49f05988d5c5cd9a90.jpg"},{"id":57015449,"identity":"27ba64e1-3150-403e-a6c0-8e2d92d81de6","added_by":"auto","created_at":"2024-05-23 12:36:10","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":596050,"visible":true,"origin":"","legend":"\u003cp\u003eEDS element distribution mapping of the TiZrNbTa and TiZrNbV samples before and after heat treatment at 1273 K for 30 h: (a) as-cast TiZrNbTa, (b) annealed TiZrNbTa, (c) as-cast TiZrNbV, and (d) annealed TiZrNbV.\u003c/p\u003e","description":"","filename":"floatimage7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4384666/v1/6d09aa91766b0cfaba545ee0.jpg"},{"id":57015414,"identity":"ba0bb771-60fc-44b7-8e9c-3fe757345f98","added_by":"auto","created_at":"2024-05-23 12:36:09","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":868668,"visible":true,"origin":"","legend":"\u003cp\u003eEDS elemental distribution mapping of the TiNbTaHf and TiNbTaMo samples before and after heat treatment at 1273 K for 12 h: (a) as-cast TiNbTaHf, (b) annealed TiNbTaHf, (c) as-cast TiNbTaMo, and (d) annealed TiNbTaMo.\u003c/p\u003e","description":"","filename":"floatimage8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4384666/v1/747452bc12f35f1391d85164.jpg"},{"id":57015430,"identity":"7ec7eba0-06c3-4624-a8e3-5604425a3222","added_by":"auto","created_at":"2024-05-23 12:36:10","extension":"jpg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":337645,"visible":true,"origin":"","legend":"\u003cp\u003eTEM results of the Ti-rich regions in the annealed TiNbTaMo: (a) high magnification EDS element distribution mapping; (b) TEM dark-field image showing the precipitates; (c) concentration profiles along the LS1, as depicted in panel b; and (d) high-resolution TEM image of the precipitate region, and associated FFT images for the R1 and R2 regions.\u003c/p\u003e","description":"","filename":"floatimage9.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4384666/v1/32f16f7df65d598fa7871bc0.jpg"},{"id":61063803,"identity":"335a6581-da83-446b-a716-8c6c98fb6265","added_by":"auto","created_at":"2024-07-25 07:13:07","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3450121,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4384666/v1/c7e99149-7336-42cb-b240-24f45cf98612.pdf"}],"financialInterests":"(Not answered)","formattedTitle":"Exploring high corrosion-resistant refractory high-entropy alloy via a combined experimental and simulation study","fulltext":[{"header":"Introduction","content":"\u003cp\u003eHigh-entropy alloys (HEAs) have attracted increasing attention due to their disordered atomic structure, exhibiting numerous desirable properties that cannot be achievable by traditional alloys\u003csup\u003e1,2,3\u003c/sup\u003e. The elevated configurational entropy in HEAs plays a pivotal role in stabilizing the formation of simple solid solution phases while impeding the development of detrimental intermetallic compounds\u003csup\u003e4,5\u003c/sup\u003e. The demand for new structural alloys with commendable mechanical properties and excellent corrosion resistance is particularly pronounced in application sectors such as aerospace, clean power, and biomedical industries. Refractory HEAs, composed of refractory metals, generally exhibit superior mechanical properties and resistance to general corrosion\u003csup\u003e6,7,8\u003c/sup\u003e, presenting promising prospects for diverse applications. Several refractory HEAs have demonstrated significant potential due to their remarkable strength. For example, during room temperature deformation, HEAs such as Nb\u003csub\u003e25\u003c/sub\u003eMo\u003csub\u003e25\u003c/sub\u003eTa\u003csub\u003e25\u003c/sub\u003eW\u003csub\u003e25\u003c/sub\u003e and V\u003csub\u003e20\u003c/sub\u003eNb\u003csub\u003e20\u003c/sub\u003eMo\u003csub\u003e20\u003c/sub\u003eTa\u003csub\u003e20\u003c/sub\u003eW\u003csub\u003e20\u003c/sub\u003e alloys have shown high yield stress values of 1058 and 1246 MPa, respectively\u003csup\u003e9\u003c/sup\u003e. Recent studies has shown that exploration of chemical heterogeneity during the heat treatment process, such as short-range order and local chemical fluctuations (CFs), has opened up a new avenue for the development of high-strength HEAs\u003csup\u003e10,11,12\u003c/sup\u003e. A recent study reported evidence of consequential effects in NiCoCr, with the yield strength further increasing by 76% after annealing at 2073 K for 24h\u003csup\u003e13\u003c/sup\u003e. When the annealing duration of the TiZrHfNb alloy at 673 K was prolonged to 40 h, the hardness increased by 25%\u003csup\u003e14\u003c/sup\u003e. Meanwhile, CFs could lower the configurational entropy from its maximum value, corresponding to a random alloy, and change the expressions for free energy. CFs was also found to decrease the enthalpy of the system, influencing defect energetics and potentially affecting physical properties. Consequently, chemical heterogeneity may affect the corrosion properties of HEAs.\u003c/p\u003e \u003cp\u003eIt is well known that chemical heterogeneity is the primary cause of localized galvanic corrosion. Compared with a chemically homogeneous single-phase solid solution, the occurrence of elemental segregation behavior leads to the formation of different electrochemical potential regions within the alloy, which undoubtedly significantly increases its sensitivity to corrosion\u003csup\u003e15\u003c/sup\u003e. However, it is worth noting that certain chemical heterogeneities can enhance the corrosion resistance of an alloy. Taking the NiCoVAl\u003csub\u003ex\u003c/sub\u003e alloy as an example, an increase in the content of Al leads to a higher proportion of the B2 phase, which has a higher Volta potential, thereby improving the overall corrosion resistance of the alloy\u003csup\u003e16\u003c/sup\u003e. Since the emergence of CFs is widely considered to be the origin of elemental segregation\u003csup\u003e17\u003c/sup\u003e, it is particularly important to conduct in-depth research on the impact of CFs on the corrosion performance of alloys. However, only a few studies have reported on the corrosion behavior of refractory HEAs, with a significant gap in research on the effect of CFs on corrosion properties. Equiatomic TiZr(Hf, Ta, Nb) medium entropy alloys have been developed to achieve superior corrosion resistance compared with pure Ti\u003csup\u003e18\u003c/sup\u003e. MoNbTaTiZr HEAs have exhibited a distinctive combination of friction and corrosion resistance, outstanding mechanical properties, and biocompatibility, positioning them as potential bioimplants\u003csup\u003e19\u003c/sup\u003e. Recently, non-equiatomic TiNbTaZrMo HEAs with good biocompatibility have been designed\u003csup\u003e20\u003c/sup\u003e. Consequently, non-equiatomic HEAs, with extensive and unexplored composition spaces, present an opportunity to obtain highly corrosion-resistant alloys. However, systematic research on the effect of various elements and the corrosion resistance of refractory HEAs has remained insufficient, creating a bottleneck in designing corrosion-resistant HEAs. The ability to freely adjust alloy composition in HEAs, resulting in an enormous composition space, significantly complicates the determination of corrosion resistance of new materials. Therefore, an efficient and rapid forecasting method for corrosion resistance is urgently needed to guide experimental synthesis.\u003c/p\u003e \u003cp\u003eThe Monte Carlo (MC) molecular dynamics (MD) simulation method has proven useful for chemical heterogeneity investigations\u003csup\u003e21,22\u003c/sup\u003e. However, limitations in potential availability make it challenging to simulate in various composition models using the MD/MC method. Reliable interatomic potentials are considered essential for MD simulations\u003csup\u003e23\u003c/sup\u003e. However, only a limited number of potentials have been developed for HEAs, due to the brief history of HEAs and the substantial workload required to develop multi-elemental interatomic potentials. Density functional theory has emerged as a promising solution for addressing this challenge, as it can handle multi-elemental systems\u003csup\u003e24,25\u003c/sup\u003e. The effect of chemical heterogeneity on the mechanical properties of HEAs has been extensively investigated via the density functional theory (DFT)/MC method\u003csup\u003e26,27\u003c/sup\u003e, indicating that it will have a significant effect on critical parameters, notably the stacking-fault energy\u003csup\u003e26\u003c/sup\u003e and dislocation mobility\u003csup\u003e27\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eIn this work, we elucidated the chemical heterogeneity and corrosion resistance of Ti(Nb,Zr)(Zr,Nb,Ta)(Ta,Ha,V,Cr,Mo,W) quaternary refractory HEAs through a combination of MC simulations and experiments. The effect of CFs on the corrosion behavior of refractory HEAs was investigated using the DFT/MC method to determine the reasons for corrosion resistance variations.\u003c/p\u003e"},{"header":"Results and discussion","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eGeneration of appropriate surface structures\u003c/h2\u003e \u003cp\u003eThe calculated formation energies for the (110) surfaces of the bcc and (111) surfaces of the fcc in 16 refractory HEAs are presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, namely TiNbTaCr (TNTC), TiNbTaHf (TNTH), TiNbTaMo (TNTM), TiNbTaV (TNTV), TiNbTaW (TNTW), TiZrNbCr (TZNC), TiZrNbHf (TZNH), TiZrNbMo (TZNM), TiZrNbTa (TZNT), TiZrNbV (TZNV), TiZrNbW (TZNW), TiZrTaCr (TZTC), TiZrTaHf (TZTH), TiZrTaMo (TZTM), TiZrTaV (TZTV), and TiZrTaW (TZTW). A substantial number of atoms in the bcc and fcc slab structures were observed, and the calculated formation energies highlighted the stability of the generated structures. The bcc structure, with the lowest formation energy, was selected for corrosion behavior studies. Following electronic self-consistent calculations, the magnetic character of the initially set magnetic alloying element Cr persisted, while other systems became non-magnetic. Therefore, in subsequent calculations, only the magnetism of the alloying element Cr was considered.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo computationally examine the effect of local chemical order on the corrosion behavior of these refractory HEAs, realistic models in the system were developed. Previous studies employed a systematic cluster expansion approach to explore local chemical heterogeneity in the TiZrNb, TiZrHfNb, and TiZrHfNbTa bcc refractory HEAs\u003csup\u003e28\u003c/sup\u003e. Although these studies indicated that CFs was expected to affect the mechanical properties, no systematic study has been conducted encompassing all refractory elements to explain the effect on the corrosion behavior of refractory HEAs. In this work, the DFT/MC method was employed to develop models for refractory HEA solid solutions with varying degrees of CFs. The most significant trends in potential energy change based on the DFT-based MC simulations are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(a). Despite the relatively small number of swap trials per atom compared with classical MC simulations, the potential energy curves appeared to converge.\u003c/p\u003e \u003cp\u003eThe appearance of CFs reduced the free energy primarily by lowering the formation energy, ranging from 38 to 447 meV per atom. Simultaneously, it had a significant effect on the microstructure of the alloy. To describe the trends in local chemical ordering obtained by the MC simulations, we employed WCP to characterize. A positive value of WCP indicated that the atomic pair was unfavorable, while a negative value indicated that the atomic pair was favorable. The resulting indicated the segregation of different elements, with some elements showing significantly stronger segregation than others. This tendency was captured by the WCP in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(b\u0026ndash;d), where some elements had a propensity to form clusters, and others favored neighbors of other types. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(b), there was a strong tendency to form X-Ta pairs (WCP\u0026thinsp;\u0026lt;\u0026thinsp;0) in TiNbTa-based HEAs, except for Hf. By contrast, the Ti-X and X-X pairs were unfavorable (WCP\u0026thinsp;\u0026gt;\u0026thinsp;0). However, the results showed that the Ti-Hf pair was favorable (WCP\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;0.71), while the Hf-Ta pair was unfavorable (WCP\u0026thinsp;=\u0026thinsp;0.44), which was attributed to the large atomic size of Hf, leading to segregation on the surface. Similar trends were also observed for the TiZrNb-based HEAs, where the Nb-X pair was favored (WCP\u0026thinsp;\u0026lt;\u0026thinsp;0), and Zr-Cr, Zr-Mo, Zr-V, and Ti-Hf exhibited a strong trend to form pairs. Preferred atomic pairings between X-Ta, Ti-Hf, Zr-Cr, Zr-Mo, and Zr-V were observed in the TiZrTa-based HEAs as the WCP values were negative, confirming the energetic preference in the refractory alloys. Therefore, this result provided another perspective for understanding the corrosion behavior of refractory HEAs. Thus, the experimental identification of chemical heterogeneity in the refractory HEAs requires further investigation.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003eWork function effects of refractory HEAs\u003c/h2\u003e \u003cp\u003eA high surface work function, derived from the electron potential energy, typically indicates a high corrosion potential and corrosion resistance for materials according to traditional theory\u003csup\u003e29,30,31\u003c/sup\u003e. For refractory HEAs with random compositional disorder, the calculated values of the work function are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(a). The calculated work function values for different samples displayed a large range, spanning from 3.95 to 4.57 eV. Notably, the group of TiNbTa-based refractory HEAs exhibited a higher work function, suggesting potentially better corrosion resistance compared to the other two groups. The work function in the refractory HEAs could be quantitatively correlated with the degree of CFs, reflected by the total nonproportional number of local atomic pairs, WCP\u003csub\u003esum\u003c/sub\u003e, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(b)\u0026ndash;(d). For most HEAs, the work function was smaller in the more ordered sample, and a lower work function implied a higher probability of electron loss and a higher tendency for corrosion. However, for TiZrNbCr, TiZrTaCr, and TiZrTaV, the opposite trend was observed. The inconsistent influence of CFs on the work functions of different alloys highlighted the need for further examination.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eSubsequently, the effect of surface atomic distribution (first layer) was considered, revealing that CFs could lead to a change in surface atomic distribution. We explored the relationship between the surface atomic distribution and work function through a machine learning model\u003csup\u003e32,33\u003c/sup\u003e. Random forest\u003csup\u003e34,35,36,37,38\u003c/sup\u003e (RFR), a popular and efficient model based on the decision tree capable of both regression and classification, was employed. By incorporating the SHapley Additive exPlanations (SHAP) tool\u003csup\u003e39\u003c/sup\u003e and the RFR model, the relationship was explored according to the above calculation results. Regarding the effects of specific elements, the number of atoms of each element in the first layer was taken as the input, and the SHAP values of each element were plotted, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. We observed that, with more Zr and Ti atoms, the work function of the alloys tended to decrease, while for more Nb and Ta atoms, the work function of the alloys tended to increase. The observed trends could be attributed to the electronic configurations of the bonding shells of the constituent surface atoms\u003csup\u003e40\u003c/sup\u003e. Nb and Ta possessed more partially filled \u003cem\u003ed\u003c/em\u003e orbitals compared with Ti and Zr, leading to greater energetic stability. Additionally, V and Cr had more partially filled \u003cem\u003ed\u003c/em\u003e orbitals; however, due to their smaller atomic numbers relative to other elements, the corresponding regions were not conducive to improving the work function of the HEA surfaces.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003ePotentiodynamic polarization measurements\u003c/h2\u003e \u003cp\u003eWe synthesized 16 refractory HEAs using the conventional arc melting processing route, and the corrosion potential (\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003ecorr\u003c/em\u003e\u003c/sub\u003e) was obtained by fitting potentiodynamic polarization curves. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e shows a strong correlation between the corrosion behavior and work function. The results established a trend of increasing corrosion resistance in the refractory HEAs with higher work function values. Notably, the TiNbTa-based refractory HEAs exhibited a lower corrosion tendency than the other groups, and TiNbTaMo demonstrated the highest \u003cem\u003eE\u003c/em\u003e\u003csub\u003ecorr\u003c/sub\u003e value of \u0026minus;\u0026thinsp;0.536 V\u003csub\u003eSCE\u003c/sub\u003e in this group.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo further confirm the effect of chemical heterogeneity on corrosion resistance, a series of TiNbTaHf, TiNbTaMo, TiZrNbTa, and TiZrNbV samples was experimentally prepared by controlling the isothermal annealing time. The samples annealed at different durations showed different degrees of elemental aggregation. Figure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(a)\u0026ndash;(d) illustrates the typical potentiodynamic polarization curves of each sample in 0.9 wt.% NaCl solution. According to the fitting results in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, compared with the as-cast samples, the corrosion tendency of the annealed samples was enhanced. With an extension of annealing time, \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003ecorr\u003c/em\u003e\u003c/sub\u003e decreased, and the corrosion resistance deteriorated, aligning with the results of the work function DFT calculations.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eElectrical parameters extracted from the potentiodynamic polarization curves of TiNbTaHf, TiNbTaMo, TiZrNbTa, and TiZrNbV annealed at different durations at 1273K in 0.9 wt.% NaCl solution.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eAnnealing durations\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"4\" nameend=\"c5\" namest=\"c2\"\u003e \u003cp\u003eE\u003csub\u003ecorr\u003c/sub\u003e (V\u003csub\u003eSCE\u003c/sub\u003e)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTiNbTaHf\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTiNbTaMo\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eTiZrNbTa\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eTiZrNbV\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e0 h\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;0.592\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;0.536\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;0.580\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u0026minus;0.573\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e12 h\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;0.642\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;0.586\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;0.624\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u0026minus;0.584\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e30 h\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;0.662\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;0.712\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;0.666\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u0026minus;0.663\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003eMicrostructure characterization\u003c/h2\u003e \u003cp\u003eTo obtain further insight into the changes in corrosion behavior in our materials, the EDS element distribution mapping of TiZrNbTa and TiZrNbV annealed at 1273 K for 30 h and TiNbTaHf and TiNbTaMo annealed at 1273 K for 12 h were obtained using TEM, as shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e and \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e. In the as-cast samples, each element was distributed homogeneously, and no distinct element segregation was detected. However, after annealing, element segregation in the alloy became apparent and intensified. In the annealed TiZrNbTa and TiZrNbV alloys, the Zr-lean phase was mainly composed of Nb and Ta/V elements, while the Zr elements were primarily enriched in the matrix of the Zr-rich phase, which was consistent with the previous calculation results of WCP. For annealed TiNbTaHf and TiNbTaMo, TiNbTaHf did not demonstrate distinct element segregation, while TiNbTaMo exhibited Ti-rich regions.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e shows the surface morphologies and elemental distribution near the Ti-rich regions of TiNbTaMo. The white square region in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003eb indicated the presence of nanoscale precipitates. A line scan (labeled as LS1 in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003eb) was performed to measure the composition of the precipitate and the matrix. The spatially resolved elemental concentrations along LS1 demonstrated segregation of Ti at the precipitate, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003ec. High-resolution TEM analysis (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003ed) of the annealed TiNbTaMo revealed that the precipitate and matrix exhibited the same crystal structure, as confirmed by the diffuse diffraction ring in the corresponding fast Fourier transform (FFT) images (R1 and R2 in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003ed). The above observations implied that the extension of annealing time further promoted segregation of elements. The local ordering between the atomic species also reflected strong affinity and interactions, explaining the segregation characteristics of chemical composition on an atomic scale\u003csup\u003e22, 41\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eAlthough the observation of diffuse superlattice intensities through TEM is attributed to the presence of CFs\u003csup\u003e42\u003c/sup\u003e, there appears to be scant theoretical foundation for any form of CFs that aligns with electron diffraction patterns\u003csup\u003e43\u003c/sup\u003e. Meanwhile, the reported characteristics consistently correspond with those anticipated from symmetry-breaking effects, such as alterations in the stacking sequence. This indicates that determining CFs requires a high degree of caution. However, previous studies indicated that segregation was generally accompanied by the appearance of CFs\u003csup\u003e17,44\u003c/sup\u003e.The formation of CFs in HEAs will increase the energy barrier dominating the effective frictional resistance to dislocation movement\u003csup\u003e45,46\u003c/sup\u003e. Therefore, dislocation motion typically requires overcoming larger energy barriers, enhancing the strengthening effect. However, the introduction of CFs can lead to a decrease in corrosion resistance. In the regulation of mechanical properties, heat treatment\u003csup\u003e13,14\u003c/sup\u003e and the addition of large-sized atoms\u003csup\u003e47,48\u003c/sup\u003e can enlarge the scale of CFs, strengthening the alloy. However, it may lead to a decrease in the corrosion resistance of the alloy. Therefore, choosing a suitable treatment process is crucial.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"Conclusions","content":"\u003cp\u003eIn this work, a combined strategy employing first-principles calculations and experiments was used to explore refractory HEAs with high corrosion resistance. The influence of chemical heterogeneity on the corrosion behavior of the materials was investigated. The main conclusions obtained in this work were as follows.\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eBased on the work function results of the RSS structure, the group of TiNbTa-based refractory HEAs had a higher work function, indicating a lower corrosion tendency and better corrosion resistance.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe calculation results indicated that the introduction of CFs reduced the work function of most materials, with an adverse effect on the corrosion resistance. However, for a few refractory HEAs, the impact was not significant or had a favorable effect. Combined with SHAP analysis, we found that this effect was mainly caused by a change in the atomic ordered state of the surface.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eElectrochemical testing revealed that the TiNbTa-based refractory HEAs had a higher corrosion potential. The corrosion potential gradually decreased with prolonged annealing time, which was consistent with the calculated results.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eMicrostructure characterization indicated that after annealing, the TiZrNbTa and TiZrNbV alloys exhibited Nb and Ta/V enrichment, which was in accordance with the simulation results. Meanwhile, the composition of TiNbTaHf remained uniform, and fine precipitates appeared in TiNbTaMo.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eIn summary, we found that the group of TiNbTa-based refractory HEAs exhibited a lower corrosion tendency compared to the other two groups. However, the corrosion resistance of the materials was affected by the emergence of chemical heterogeneity. Through reasonable element regulation, it is expected to reduce or generate favorable effects. Future research on the comprehensive properties of these alloys should thus include consideration of the effects of chemical heterogeneity on corrosion resistance, to understand the degree to which chemical heterogeneity can be used as an independent structural variable to guide alloy design and optimization. It is expected to have good corrosion resistance while achieving better mechanical properties.\u003c/p\u003e"},{"header":"Methodology","content":"\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003eDFT-based Monte Carlo simulations\u003c/h2\u003e \u003cp\u003eTo generate the structures representing HEAs, MC simulations were employed. These simulations included the swap trials per atom, with acceptance probabilities determined based on Metropolis-Hastings sampling\u003csup\u003e49\u003c/sup\u003e. The supercell, consisting of 96 atoms, was generated as a special quasi-random structure to serve as the initial starting points, with the temperature used in the MC simulations set to 300 K. Energy calculations were performed using the Vienna ab initio simulation package (VASP) \u003csup\u003e50,51,52\u003c/sup\u003e. For each structure, MC simulations were executed over a total of 2000\u0026ndash;2500 steps, equating to 21\u0026ndash;26 swap trials per atom.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003eDFT calculations\u003c/h2\u003e \u003cp\u003eDFT calculations were performed using VASP, with the interaction potential of the core electrons described using the projector augmented wave method\u003csup\u003e53\u003c/sup\u003e. The generalized-gradient approximation was adopted with Perdew-Burke-Ernzerhof\u003csup\u003e54\u003c/sup\u003e parameterization for the exchange correction function. The cutoff energy for the plane wave basis was set to 400 eV for the MC simulations and 600 eV for calculation of the work function. The k-points were meshed by 1 \u0026times; 1 \u0026times; 1 for the MC simulations and 2 \u0026times; 2 \u0026times; 1 for calculation of the work function\u003csup\u003e55\u003c/sup\u003e. The semi-core p electrons for all elements were treated as valence electrons when available\u003csup\u003e53,56\u003c/sup\u003e.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003eLocal chemical parameter\u003c/h2\u003e \u003cp\u003eThe Warren-Cowley parameter (WCP)\u003csup\u003e57\u003c/sup\u003e was used to quantify the chemical ordering around an atomic species. The WCP was calculated using the following equation:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$${WCP}_{ij}=1-{Z}_{ij}/{c}_{j}{Z}_{i}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e,\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003eZ\u003c/em\u003e\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003e is the number of \u003cem\u003ej\u003c/em\u003e-type atoms around \u003cem\u003ei\u003c/em\u003e-type atoms, \u003cem\u003eZ\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e is the total number of atoms around \u003cem\u003ei\u003c/em\u003e-type atoms, and \u003cem\u003ec\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e denotes the atomic fraction of \u003cem\u003ej\u003c/em\u003e-type atoms in the HEA, with WCP\u0026thinsp;=\u0026thinsp;0 corresponding to a random solution. A positive value of WCP indicated a tendency to decrease the number of \u003cem\u003ei-j\u003c/em\u003e pairs, while a negative value corresponded to the opposite. In this investigation, WCP calculations were performed by counting the elemental types of the nearest neighbors.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003eExperimental process\u003c/h2\u003e \u003cp\u003eThe alloys were prepared from commercially pure Ti, Zr, Nb, Ta, Hf, V, Cr, Mo, and W metals with a purity of 99.9 wt.%. Each ingot with a weight of approximately 100 g was melted in a vacuum arc environment at least six times. Samples 10 \u0026times; 10 \u0026times; 2 mm in size were cut from each ingot for subsequent experiments. The exposed surfaces were then meticulously ground using #1000, #2000, #3000, and #5000 SiC sandpaper in sequential order.\u003c/p\u003e \u003cp\u003eElectrochemical corrosion studies were conducted in an aerated 0.9 wt.% NaCl solution at 25\u0026deg;C. A Gamry Reference 3000 electrochemical workstation, equipped with a standard three-electrode system, was employed to measure the polarization curves. A saturated calomel electrode (SCE, E\u0026thinsp;=\u0026thinsp;0.2415 V\u003csub\u003eSHE\u003c/sub\u003e) served as the reference electrode, while the specimens functioned as the working electrodes, and a platinum foil served as the auxiliary electrode. The samples were mounted in contact with copper wire embedded in epoxy resin, then polished, degreased in alcohol, cleaned, and dried in warm air. Prior to the potentiodynamic polarization scan tests, cathodic pre-polarization at \u0026minus;\u0026thinsp;1.0 V\u003csub\u003eSCE\u003c/sub\u003e for 600 s was applied to spontaneously remove the air-formed oxides. Subsequently, the open circuit potential was measured for 30 min to ensure a steady-state potential. Potentiodynamic polarization curves were obtained at a scanning rate of 1 mV/s from an initial potential of \u0026minus;\u0026thinsp;0.6 V\u003csub\u003eSCE\u003c/sub\u003e versus E\u003csub\u003ecorr\u003c/sub\u003e to a final potential of 1 V\u003csub\u003eSCE\u003c/sub\u003e.\u003c/p\u003e \u003cp\u003eA transmission electron microscope (TEM, FEI Talos F200X) equipped with an energy dispersive spectrometer (EDS) was used to further analyze the nanoscale microstructure in the HEAs.\u003c/p\u003e \u003c/div\u003e "},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe raw/processed data required to reproduce these findings can be obtained by contacting the corresponding author.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis research was funded by the Guangdong Province Key Area R\u0026amp;D Program (Grant No. 2019B030302011 and No. 2019B010940001) and the National Natural Science Foundation of China (Grant No. 52371050).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDeclaration of Competing Interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u0026nbsp;\u003cbr\u003e\u0026nbsp;\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eMa, C. 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In this work, we performed first-principles calculations, coupled with experiments, to explore HEAs with high corrosion resistance. The results revealed that TiNbTa-based HEAs exhibited a lower tendency for corrosion. However, the appearance of local chemical fluctuations (CFs) increased the corrosion tendency of TiNbTa-based HEAs. Comprehensive SHapley Additive exPlanations analyses uncovered that in a sample with configurational CFs, the atomic order near the surface was altered. Therefore, corrosion behavior was affected. Based on experiments, the annealed samples exhibited typical chemical segregation and declined corrosion resistance.\u003c/p\u003e","manuscriptTitle":"Exploring high corrosion-resistant refractory high-entropy alloy via a combined experimental and simulation study","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-05-23 12:36:00","doi":"10.21203/rs.3.rs-4384666/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"revise","date":"2024-06-18T09:30:56+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"This content is not available.","date":"2024-05-24T10:23:27+00:00","index":1,"fulltext":"This content is not available."},{"type":"editorInvitedReview","content":"This content is not available.","date":"2024-05-22T07:03:36+00:00","index":2,"fulltext":"This content is not available."},{"type":"reviewerAgreed","content":"This content is not available.","date":"2024-05-21T07:53:52+00:00","index":3,"fulltext":"This content is not available."},{"type":"reviewerAgreed","content":"This content is not available.","date":"2024-05-15T01:08:00+00:00","index":2,"fulltext":"This content is not available."},{"type":"reviewerAgreed","content":"This content is not available.","date":"2024-05-14T14:18:19+00:00","index":1,"fulltext":"This content is not available."},{"type":"reviewersInvited","content":"","date":"2024-05-14T08:13:18+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-05-14T08:01:14+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-05-09T10:12:42+00:00","index":"","fulltext":""},{"type":"submitted","content":"npj Materials Degradation","date":"2024-05-07T16:51:00+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"npj-materials-degradation","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"npjmatdeg","sideBox":"Learn more about [npj Materials Degradation](http://www.nature.com/npjmatdeg/)","snPcode":"41529","submissionUrl":"https://submission.springernature.com/new-submission/41529/3","title":"npj Materials Degradation","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"13b00889-fc96-48d9-8be1-5813320a3f83","owner":[],"postedDate":"May 23rd, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":31886494,"name":"Physical sciences/Materials science/Theory and computation"},{"id":31886495,"name":"Physical sciences/Materials science"}],"tags":[],"updatedAt":"2024-07-25T07:13:02+00:00","versionOfRecord":{"articleIdentity":"rs-4384666","link":"https://doi.org/10.1038/s41529-024-00495-1","journal":{"identity":"npj-materials-degradation","isVorOnly":false,"title":"npj Materials Degradation"},"publishedOn":"2024-07-24 04:00:00","publishedOnDateReadable":"July 24th, 2024"},"versionCreatedAt":"2024-05-23 12:36:00","video":"","vorDoi":"10.1038/s41529-024-00495-1","vorDoiUrl":"https://doi.org/10.1038/s41529-024-00495-1","workflowStages":[]},"version":"v1","identity":"rs-4384666","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4384666","identity":"rs-4384666","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}