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Anti-corrosive coatings to sustain large plastic deformation for pre-coated metallic bipolar plates of proton exchange membrane fuel cells

Li, Chuanzheng; Xu, Zhutian; Qiu, Diankai; Peng, Linfa

Abstract

Precoating process can substantially improve the manufacturing efficiency of metallic bipolar plates (BPPs) for the mass commercialization of proton exchange membrane fuel cells (PEMFCs). However, the anti-corrosive precoatings are prone to crack during the forming process of pre-coated BPPs, leading to the exposed substrate and deteriorated corrosion resistance. In this work, a formable Niobium based precoating is developed to sustain large plastic deformation by controlling the film microstructure with unbalanced magnetron sputtering process. With an optimal bias voltage of substrate, the precoatings with compact nanocrystalline microstructure are obtained to sustain a strain of 30% without evident cracks in uniaxial tensile tests, which is a superior ductility compared with previous precoatings. Furthermore, the applicability of precoatings is verified with electrochemical tests. The deformed samples maintain considerable corrosion resistance with the current density of 8E-6 A/cm2 and the contaminated ions dissolution of 0.07 ppm, which is comparable to the performance of traditional formed-then-coated metallic BPPs. Therefore, the mass production of precoated metallic BPPs is enabled with both improved manufacturing efficiency and maintained corrosion resistance after forming process.

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EFCF 2025: Low-Temp. Fuel Cells, Electrolysers & H2 Processing 1 – 4 July 2025, Lucerne Switzerland https://doi.org/10.5281/zenodo.17476223 A1103 Page 1/10 A1103 Anti-corrosive coatings to sustain large plastic deformation for pre-coated metallic bipolar plates of proton exchange membrane fuel cells Chuanzheng Li (1,2), Zhutian Xu* (1,2), Diankai Qiu (1,2), Linfa Peng (1,2) (1) Shanghai Key Laboratory of Digital Manufacture for Thin-Walled Structures, Shanghai Jiao Tong University, Shanghai/P. R. China; (2) State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai/P. R. China; *Contact corresponding authors: www.EFCF.com/ContactRequest Abstract Precoating process can substantially improve the manufacturing efficiency of metallic bipolar plates (BPPs) for the mass commercialization of proton exchange membrane fuel cells (PEMFCs). However, the anti-corrosive precoatings are prone to crack during the forming process of pre-coated BPPs, leading to the exposed substrate and deteriorated corrosion resistance. In this work, a formable Niobium based precoating is developed to sustain large plastic deformation by controlling the film microstructure with unbalanced magnetron sputtering process. With an optimal bias voltage of substrate, the precoatings with compact nanocrystalline microstructure are obtained to sustain a strain of 30% without evident cracks in uniaxial tensile tests, which is a superior ductility compared with previous precoatings. Furthermore, the applicability of precoatings is verified with electrochemical tests. The deformed samples maintain considerable corrosion resistance with the current density of 8E-6 A/cm2 and the contaminated ions dissolution of 0.07 ppm, which is comparable to the performance of traditional formed-then-coated metallic BPPs. Therefore, the mass production of precoated metallic BPPs is enabled with both improved manufacturing efficiency and maintained corrosion resistance after forming process. EFCF 2025: Low-Temp. Fuel Cells, Electrolysers & H2 Processing 1 – 4 July 2025, Lucerne Switzerland https://doi.org/10.5281/zenodo.17476223 A1103 Page 2/10 Introduction As a key component of proton exchange membrane fuel cells (PEMFCs), metallic bipolar plates (BPPs) account for 20−30% of the total cost and 60-80% of the overall weight of the fuel cell stack, which play an important role in isolating fuels and oxidant, distributing gases and water, and collecting generated current [1]. Protective and functional coatings on BPPs are commonly used to improve the corrosion resistance and lower the ICR. Nevertheless, as mass production is one of the main development trends of metallic BPPs, the time consumption of existing coating process becomes a great challenge [2]. Recently, pre-coating process has been proposed as a promising way for the mass production of metallic BPPs [3, 4]. Compared with the traditional forming-then-coating process with limited efficiency as illustrated in Fig. 1 (a), the pre-coating-then-forming process in Fig. 1 (b) can increase the production efficiency of metallic BPPs significantly. The pre-coatings are firstly prepared on metallic foils before forming process with large roll to roll foil coating line, leading to a considerable improvement of coating efficiency compared with the existing process [4]. Subsequently, the pre-coated metallic foils with satisfying performance could be directly stamped into the BPPs. Therefore, the total manufacturing efficiency is substantially improved, and the maximum production capacity could increase several times [5. Fig. 1 Schematics of (a) the traditional forming-then-coating process and (b) the novel precoating-then-forming process. However, forming process of pre-coated foils can lead to various defects of coatings, such as cracking, flaking, delamination and scratching. The damage of coating integrity can severely influence the performance of coatings of metallic BPPs, including the ICR and the corrosion resistance. Previous studies have been conducted on the ex-situ performances of pre-coated metallic BPPs [6-8]. In terms of several metal nitride coatings, it was revealed that the pre-coated-then-formed BPPs exhibited similar or even better ICR performance than traditional formed-then-coated BPPs in despite of the micro cracks of coatings [8]. When the coatings remained well adhesion to the substrates, the electron flow in through plane direction was hardly affected, and therefore the ICR of formed pre-coatings was not a critical problem. However, the corrosion was found to be more profound in the pre-coated-thenformed BPPs than the formed-then-coated BPPs for most cases of metal nitride pre-coatings due to the damaged integrity [6]. Recently, Haye et al. [7] also prepared chromium nitride coatings on 316L stainless steel by reactive magnetron sputtering. After biaxial deformation of 20% in x-axis and 5% in y-axis, the coatings still fulfilled the DOE 2020 targets on the ICR and corrosion resistance, although there were some defects including cracks and delamination. However, due to the damaged coating integrity, contaminated metallic ions can be dissolved when the stainless-steel substrate is exposed in the harsh corrosive environment. Therefore, the formed coatings must remain continuous without crack or EFCF 2025: Low-Temp. Fuel Cells, Electrolysers & H2 Processing 1 – 4 July 2025, Lucerne Switzerland https://doi.org/10.5281/zenodo.17476223 A1103 Page 3/10 delamination to avoid dissolved metallic ions, and high ductility is the fundamental requirement of the pre-coatings. To develop formable pre-coatings for metallic BPPs, Weil et al. [9] considered Niobium (Nb)- clad 304L stainless steel as a candidate material considering the great electrochemical properties and considerable ductility of Nb. After annealing treatment, the rolled Nb-clad stainless steel exhibited good ductility and could meet the requirement of stamping [10]. However, the elaborate annealing treatment must be conducted to avoid the brittle intermetallic layer at interface, and the thickness of Nb layer resulted in a high material cost [11]. Therefore, Nb-sputtered 316L stainless steel has been regarded as an alternative to the Nb-clad stainless steel for metallic BPPs. Kim et al. [12] deposited Niobium coating on 316L stainless steel by pulsed direct-current (DC) magnetron sputtering with different bias voltages of substrate. The microstructure and the corrosion resistance of the Nb coatings were optimized by controlling the bias voltage. However, when ductility is required, most protective and functional coatings prepared with physical vapor deposition (PVD) and chemical vapor deposition (CVD) process exhibit limited ductility, which are characterized by nanocrystalline or amorphous microstructure [13]. Freestanding nanocrystalline metallic films usually rupture at a very small elongation about 1%, and most polymer-supported metallic films rupture with limited elongations of less than 20% [14]. Therefore, the development of anti-corrosive coatings that can sustain large plastic deformation without cracks remains a great challenge. In that regard, considering the great features of Nb, a series of Nb coatings were deposited by unbalanced magnetron sputtering with different bias voltages of substrate in this study. The ductility of the deposited Nb coatings was investigated by evaluating the coating integrity after uniaxial tension tests, and the corrosion resistance of both as-deposited and formed coatings was evaluated by electrochemical corrosion tests and ions dissolution tests. The effect of bias voltage on the morphology and microstructure of coatings was characterized systematically, and the relationship between bias voltage of substrate and the coating performances including ductility and corrosion resistance was discussed. 1. Experiment details As illustrated in Fig. 2 (a), the Nb coatings were firstly prepared on 316L stainless steel (SS316L) foils with the thickness of 0.1 mm. The film microstructure was then investigated systematically with scanning electron microscope (SEM), transmission electron microscope (TEM), and X-ray diffraction (XRD), while the ductility of the Nb coatings was evaluated by uniaxial tensile tests. Furthermore, the corrosion resistance of as-deposited and deformed coatings was evaluated by electro-chemical tests. The detailed experimental procedure is as follows. The Nb coatings were deposited on SS316L foils by a closed field unbalanced magnetron sputter ion plating (CFUBMSIP) system (TEER UDP850). The magnetron field of all the neighbouring cathodes was closed, resulting in a higher density of electrons and ions in the chamber. Therefore, an intense effect of ion bombardment was enabled and a denser coating structure could be obtained. Before deposition, the substrates with the size of 200×100 mm were cleaned in acid, alkali, ethanol and deionized water ultrasonically. Subsequently, the substrates were fixed in the vacuum chamber, and the background pressure was pumped down to less than 4×10-3 Pa. After argon (99.999%) introduced into the chamber, the substrates were sputter-cleaned with a bias voltage of -650 V for 30 min to improve the adhesion of the coatings on the substrates. Finally, the Nb coatings were deposited by controlling the pulsed DC power sources of two Nb targets for 45 min. The frequency of pulsed power was 100 kHz and the duty ratio was 40%. The deposition pressure was approximately 0.1 Pa and the power of EFCF 2025: Low-Temp. Fuel Cells, Electrolysers & H2 Processing 1 – 4 July 2025, Lucerne Switzerland https://doi.org/10.5281/zenodo.17476223 A1103 Page 4/10 one Nb target was about 1800 W. The effect of ion bombardment on the deposited Nb coatings was investigated with different substrate bias voltages of -30, -60, -120, and -180 V. Fig. 2 (a) The schematic of experimental procedure and (b) the tensile specimens of the Nb-deposited samples (dimensions in mm). To evaluate the ductility of the coatings, uniaxial tensile specimens of the coated samples were fabricated by wire electro-discharge machining (WEDM) process following the standard ASTM-E8 as shown in Fig. 2 (b). The uniaxial tensile tests were conducted at room temperature with an Instron 5966 machine at a rate of 2 mm/min to different engineering strains of 10, 20 and 30%. After deformation, the surface integrity of the samples was investigated with a laser scanning confocal microscope KEYENCE VK200X. The resolution for XY directions was 0.02 μm and the resolution for Z axle was 0.012 μm. Surface defects, compactness and roughness of the coatings could be observed with the surface morphology. Field emission scanning electron microscope (FESEM, Inspect F50, FEI Ltd.) was used to characterize the surface of the as-deposited Nb coatings. Furthermore, to obtain the phase compositions and crystallinity of the deposited coatings, grazing incidence X-ray diffraction (GIXRD, D8 DaVinci, Bruker) was used with the Cu Kα radiation over a 2θ range from 10 to 90 ° and a step size of 0.02 °. Transmission electron microscope (TEM, JEM2100F, JEOL) was used to conduct TEM analysis of the coating microstructure. The TEM samples were prepared by ion thinning process, and the crystal structure and grain size of nanocrystalline in the Nb coatings under different deposition conditions was observed. In order to find out the applicability of the Nb coatings under the PEMFCs environment, the electrochemical corrosion behaviours of the Nb coatings before and after deformation were further investigated. Classical three-electrode electrochemical test with a Corr-Test 310 electrochemical workshop was used to analyse the corrosion behaviour of the coatings. The platinum gauze and the Hg/HgSO4 electrode served as the counter and the reference electrode, respectively, while the coated samples before and after deformation were prepared as the working electrode in circular corrosion cell with the diameter of 5 mm. The electrolyte was composed of H2SO4 solution (pH = 3, 80 ℃) with 0.1 ppm F-. Potentiostatic polarization tests at 1.6 V (vs. SHE) were carried out for 10 h to evaluate the corrosion resistance of the Nb coatings in extreme conditions. 2. Results and discussion Fig. 3 displays the laser confocal micrographs of the deformed coatings with different engineering strains. The coatings remain on the substrates without delamination in most cases, but the coating failure behaviors are significantly different under different conditions. EFCF 2025: Low-Temp. Fuel Cells, Electrolysers & H2 Processing 1 – 4 July 2025, Lucerne Switzerland https://doi.org/10.5281/zenodo.17476223 A1103 Page 5/10 For the samples deposited at the bias voltage of -30 V, a large number of cracks appear uniformly in the coating with the elongation of 10%. As shown in Fig. 3 (a), the number and the length of the cracks both increases with the strain. At the engineering strain of 30%, the coating become further buckled and warped as indicated by the black shadows, suggesting the adhesion between the coating and the substrate is lost and the SS316L substrate is evidently exposed. When the bias voltage increases to -60 V, the coating is free of crack with the engineering strain up to 20% as displayed in Fig. 3 (b). Furthermore, there are only few cracks on the sample surface at the strain of 30%, which indicates Nb coatings with considerable ductility is obtained with a bias voltage of -60 V. However, as the bias voltage further increases to -120 V, the ductility of the coatings deteriorates comparing to the samples deposited at -60 V. As displayed in Fig. 3 (c), micro cracks were observed on the sample surface when the strain is 20%. With the further increase of the elongation to 30%, more cracks are found in the coating. As illustrated in Fig. 3 (d), the sample deposited at - 180 V exhibits similar behavior like that at -30 V. Cracks emerge with the elongation of 10%, and following that the number of cracks grows substantially with the increase of elongation. Nevertheless, different from the coating failure condition at the bias voltage of -30 V, no decohesion of the coating is observed due to the enhanced ion bombardment by the greater bias voltage. Therefore, there is no warping of the coatings after large plastic deformation. By defining a proper threshold of binary images, the number and the area of defects including cracks and wrapping can be obtained with a MATLAB image processing package. The density of cracks 𝜌 and the area fraction of cracks 𝑟 are defined as: 100% t c t N A A r A  =    =   (1) in which 𝑁 is the number of cracks, while 𝐴𝑐 and 𝐴𝑡 are the crack area and the total measured area, respectively. As shown in Fig. 4, the density and the area fraction of cracks both increase with the engineering strain for all the coatings. The Nb coatings deposited at the bias voltage of -60 V can sustain more than 20% elongation without crack or delamination. The crack area fraction even remains negligible (<0.1%) when the engineering strain increases to 30%, which is a common deformation level at the fillet corner of the micro channels in the forming process of metallic BPPs. As a contrast, other Nb coatings deposited at lower or higher bias voltage start to crack at the engineering strain of 10% or 20%, and the crack area fraction become unacceptable when the engineering strain increases to 30%. Therefore, the optimal bias voltage of the substrate for deposition of Nb coatings is obtained, which is around -60 V. SEM micrographs of fracture morphology for the different coatings under different conditions are also shown in Fig. 5. The coating deposited at -30 V exhibits a typical brittle failure behavior, featuring intergranular cracks along the grain boundaries. When the bias voltage increases to -60 V, the fracture of coatings is dominated by the shear band and strain localization as shown in Fig. 5 (b). Moreover, the grains in the shear bands are elongated significantly, indicating that the fracture mechanism changes from brittle to ductile. As the bias voltages further increases to -120 V, a mixed fracture mechanism is revealed as shown in Fig. 5 (c), which consists of both shear band localizations and opening cracks normal to the tensile direction. The shear bands are similar to that on the samples deposited at -60 V. Finally, when the bias voltage is -180 V, the fracture is dominated by long opening cracks normal to the tensile direction as shown in Fig. 5 (d), which also indicates a brittle fracture behavior. EFCF 2025: Low-Temp. Fuel Cells, Electrolysers & H2 Processing 1 – 4 July 2025, Lucerne Switzerland https://doi.org/10.5281/zenodo.17476223 A1103 Page 6/10 Fig. 3 Laser confocal micrographs of the deformed samples deposited at different substrate bias voltages: (a) -30 V; (b) -60 V; (c) -120 V; (d) -180 V at three different engineering strains (10%, 20%, 30%). SEM micrographs of fracture morphology for the different coatings under different conditions are also shown in Fig. 5. The coating deposited at -30 V exhibits a typical brittle failure behavior, featuring intergranular cracks along the grain boundaries. When the bias voltage increases to -60 V, the fracture of coatings is dominated by the shear band and strain localization as shown in Fig. 5 (b). Moreover, the grains in the shear bands are elongated significantly, indicating that the fracture mechanism changes from brittle to ductile. As the bias voltages further increases to -120 V, a mixed fracture mechanism is revealed as shown in Fig. 5 (c), which consists of both shear band localizations and opening cracks normal to the tensile direction. The shear bands are similar to that on the samples deposited at -60 V. Finally, when the bias voltage is -180 V, the fracture is dominated by long opening cracks normal to the tensile direction as shown in Fig. 5 (d), which also indicates a brittle fracture behavior. To reveal the reason for different ductility of the Nb coatings deposited at different bias voltages, the surface morphology and microstructure are investigated as follows. As shown in Fig. 6 (a), the samples deposited at the bias voltage of -30 V exhibit a rough cauliflowerlike morphology with blocky and coarse columnar grains. Furthermore, the coatings are not fully compact, and lots of defects along the grain boundaries are observed including micro pinholes and micro cracks. With the increased bias voltage, the surfaces of coatings deposited at the bias voltage of -60 V become denser and smoother due to the energetic ion bombardment effect during the deposition process. In addition, the surface morphology as shown in Fig. 6 (b) shows distinguishable and uniform worm-like grains with compact grain boundaries, which can be reasonably attributed to a crystallization process. As the bias voltage increases to -120 V, the coating remains worm-like morphology as shown in Fig. 6 (c). However, there are some protuberances on the surface of the Nb coatings due to EFCF 2025: Low-Temp. Fuel Cells, Electrolysers & H2 Processing 1 – 4 July 2025, Lucerne Switzerland https://doi.org/10.5281/zenodo.17476223 A1103 Page 7/10 the higher energy of ion bombardments. When the bias voltage further increases to -180 V, cauliflower-like features similar to the coatings deposited at -30 V appears again as shown in Fig. 6 (d). However, finer and loose spherical clusters is observed instead of the granular microstructures observed at -30V. That is because the extremely-high bias voltage leads to excessive ion bombardment, which could destruct the crystalline process during the deposition process of Nb coatings. Fig. 4 (a) Crack density and (b) crack area fraction of the deformed Nb coatings deposited at different substrate bias voltages with the increased engineering strain. Fig. 5 SEM crack morphologies of the deformed Nb coatings deposited at different substrate bias voltages: (a) -30 V; (b) -60 V; (c) -120 V; (d) -180 V. The XRD patterns of the as-deposited Nb coatings deposited at different substrate bias voltages are illustrated in Fig. 7 (a). Five primary diffraction peaks of the Nb coating and the SS316L substrate are observed, which corresponds to the (110), (200) and (211) crystallographic planes of the Nb coatings, and (111) and (200) crystallographic planes of the austenite stainless steel substrate, respectively. The diffraction peaks indicate the asdeposited coating has a typical nanocrystalline microstructure. Moreover, the nano grains are mainly textured along the preferred orientations of (110) and (211), which is driven by the atom diffusion to low energy surfaces during the deposition process. To compare the crystallization state of different Nb coatings, the intensity and the full width at half-maximum (FWHM) of the Nb (110) and (211) preferred orientations are calculated. As shown in Fig. 7 (b), the intensities of both Nb (110) and Nb (211) diffraction peaks first increase with the substrate bias voltage, reaching the maximum at the bias voltage of -60 V. It suggests that the Nb coatings exhibit the best crystallization state at -60 V, further increases of bias voltage leads to the crystallization damage. The FWHM of both Nb (110) and Nb (211) diffraction peaks gradually increases with the bias voltage. According to the Debye-Scherrer method, the grain size decreases with the substrate bias voltage. When the bias voltage is greater than -120 V, the grain size becomes relatively small. Furthermore, it is found the peak positions of both Nb (110) and Nb (211) gradually shifts to the low angle direction when the bias voltage increases from -30 V to -180 V as shown in Fig. 7 (a), which indicates the enhancement of the ion bombardment effect. EFCF 2025: Low-Temp. Fuel Cells, Electrolysers & H2 Processing 1 – 4 July 2025, Lucerne Switzerland https://doi.org/10.5281/zenodo.17476223 A1103 Page 8/10 Fig. 6 SEM surface micrographs of the as-deposited Nb coatings deposited at different substrate bias voltages: (a) -30 V; (b) -60 V; (c) -120 V; (d) -180 V. Fig. 7 (a) XRD patterns of the as-deposited Nb coatings deposited at different substrate bias voltages; (b) intensity and FWHM of the preferred orientations. 3. Corrosion resistance performance The results of 1.6 V (vs. SHE) 10 h potentiostatic polarization tests before and after deformation are shown in Fig. 8 (a) and (b), respectively. As illustrated in Fig. 8 (a), the corrosion current densities of all as-deposited coatings during the potentiostatic polarization remain stable with the corrosion time. The stable corrosion current densities are all around 3E-6 A/cm2 after 10 h polarization as shown in Fig. 8 (c), suggesting the as-deposited Nb coatings exhibits excellent corrosion resistance. However, the corrosion current densities of most deformed coatings with the engineering strain of 20% increase significantly are shown in Fig. 8 (b). The deformation leads to the exposure of stainless-steel substrate for the cases at the bias voltages of -30, -120, and -180 V as shown in Fig. 3, resulting in an evident increase in the corrosion current density of more than an order of magnitude. As a contrast, due to the continuous crack-free coating surface as displayed in Fig. 3 (b), the corrosion current density of the deformed coatings deposited at -60 V still remains stable. The coatings after the strain of 20% still exhibit good corrosion resistance at a similar level to that before the deformation, which is about 8E-6 A/cm2 as shown in Fig. 8 (c). Furthermore, the corresponding ions dissolution results after 10 h polarization tests at 1.6 V (vs. SHE) are illustrated in Fig. 8 (d). The ions dissolution results are in good consistent with the corrosion current density results. The Fe ions dissolution is negligible (<0.1 ppm) and the Cr/Ni ions dissolution are not detected for the as-deposited Nb coatings and the crackfree deformed Nb coatings deposited at -60 V. As a contrast, due to the exposure of stainless-steel substrate in the corrosion solution induced by the fracture of the coating, the dissolved Fe ions of other deformed Nb samples increase significantly, which increases more than one magnitude compared with the counterparts without crack. Due to the largest area of substrate exposure, the Fe ions dissolution of Nb samples deposited at -30 V or - 120 V increase to around 1 ppm. Such a Fe ions dissolution can poison the catalyst of PEMFCs seriously, which is intolerable for the long-term stable operation of PEMFCs. Therefore, the ductility of coatings is a key factor that should be paid more attention for the application of protective coatings of precoated metallic BPPs. Compared with the previous EFCF 2025: Low-Temp. Fuel Cells, Electrolysers & H2 Processing 1 – 4 July 2025, Lucerne Switzerland https://doi.org/10.5281/zenodo.17476223 A1103 Page 9/10 coatings, the Nb coatings deposited at the bias voltage of -60 V exhibit excellent ductility to sustain large plastic deformation, and the corrosion resistance performance remains excellent even after the elongation of 20 %. Fig. 8 Corrosion behaviors of samples in 1.6 V (vs. SHE) potentiostatic polarization for 10 h: potentiostatic polarization curves (a) before deformation and (b) after 20% engineering strain. The corresponding (c) stable corrosion current densities of all the samples and (d) ions dissolution results in the corrosion solution after 20% strain. 4. Conclusive remarks In this research, an anti-corrosive Nb coating has been developed to sustain large plastic deformation, and the effect of bias voltage of substrate on the ductility and the corrosion resistance of the Nb coatings has been investigated. The coating obtained with the bias voltage of -60 V is revealed capable to sustain a 30% elongation without evident cracks, which exhibits similar corrosion resistance level before and after deformation. The corrosion current density remains 8E-6 A/cm2 and the dissolved ions is negligible after 20% elongation. Larger or smaller bias voltage both deteriorates the ductility of Nb coatings, and therefore the optimal bias voltage to prepare Nb coatings with the best combination of ductility and corrosion resistance is determined. In addition, based on the SEM, TEM, XRD results, the mechanism of ion bombardment effect by controlling the bias voltage on the deposition of Nb coatings is analysed. Too low bias voltage results in pinhole defects and loose grain boundary of the Nb coatings, which leads to stress concentration and early fracture. Too high bias voltage leads to excessive bombardment on the coating, which destroys the crystal structures and deteriorates the ductility. With proper ion bombardment effect, a compact Nb coating in good crystalline state could be prepared, which exhibits much better ductility than previous coatings. Acknowledgement This research was supported by the National Key R&D Program of China (Grant No. 2023YFB2504204), the Center for International Cooperation and Disciplinary Innovation (111 center, Grant No. B25017) and the State Key Laboratory of Mechanical System and Vibration (Grant No. MSVZD202402).