Corrosion mechanism of an equimolar AlCoCrFeNi high-entropy alloy additively manufactured by electron beam melting

High-entropy alloys (HEAs) have emerged as a class of structural alloys with various attractive properties, and their application in additive manufacturing, which enables unprecedented thermal history and geometrical complexity, is promising for realising advanced materials. This study investigates the corrosion behaviour and passive film characteristics of an equimolar AlCoCrFeNi HEA additively manufactured by electron beam melting (EBM). Potentiodynamic polarisation in a 3.5 wt% NaCl solution revealed that the bottom part of the EBM specimen shows better corrosion performance than a conventionally prepared cast specimen in terms of both corrosion and passivation current density, while a continuous increase in the current density without any apparent passivity was observed during the anodic polarisation of the top part. The electrochemical impedance spectroscopic study indicated significant differences in the passive film characteristics between the specimens, and revealed an enhanced charge-transfer resistance and the formation of a more protective passive film of the bottom part. The elemental redistribution, in particular, the enrichment of Cr in the B2 phase during the post-melt high-temperature exposure of the alloy during EBM, was responsible for the improved stability of the passive film, retarding the selective dissolution of the B2 phase in the bottom part. These findings indicate that the microstructural evolution caused by ‘in situ annealing’ during the EBM process significantly influences the corrosion behaviour of the HEA.


INTRODUCTION
High-entropy alloys (HEAs) are multicomponent alloys composed of five or more elements in equimolar or near-equimolar proportions [1][2][3] . HEAs have many promising properties, such as significant solid-solution strengthening originating from severe lattice distortion 3,4 , excellent strength-ductility balance 5 , superior damage tolerance at cryogenic temperatures 6,7 and high wear resistance 8,9 , thus drawing considerable attention from the materials science community. It has been claimed that due to the unique alloying concept, the high mixing entropy of these alloys stabilises the solid-solution phases, such as in face-centred cubic (FCC) and body-centred cubic (BCC) structures. However, it does not necessarily assure the formation of a simple solid solution and, indeed, some HEAs show complex microstructures with the formation of secondary or intermetallic phases within the matrix 10,11 . Thus, such alloys do not have high configurational entropies and are often generally termed as 'compositionally complex alloys' (CCAs) [12][13][14] .
Recently, additive manufacturing (AM) has garnered significant attention as it enables the production of components with complex geometries directly from 3D computer-aided design data. Some such geometries cannot otherwise be fabricated through conventional manufacturing routes, such as casting, powder metallurgy and/or plastic deformation. Electron beam melting (EBM) is a powder-bed-fusion (PBF) AM technology that has been applied to many metallic materials 33 . A high-energy electron beam used as an energy source for selectively melting a metal powder bed can effectively prevent the formation of critical defects, such as cracks and lack of fusion under optimal processing parameters, thus enabling the production of fully dense metal components with superior mechanical properties.
In a previous study, equimolar AlCoCrFeNi HEA components were successfully fabricated using EBM. The as-built specimens were verified to have better mechanical properties and specifically better plastic deformability than those of specimens of the same alloy prepared using a conventional casting technique [34][35][36] . This result indicates that the microstructural evolution during AM, which is considerably different from that in conventional manufacturing, could significantly affect the properties of AM components. However, the corrosion behaviours of additively manufactured HEAs have been rarely reported [36][37][38][39][40] . Studies on corrosion were conducted on the EBM-built AlCoCrFeNi HEA 36 ; these revealed that the breakdown of passivity during 1 potentiodynamic polarisation measurements in artificial seawater occurred at a lower potential than that of the cast counterpart. However, the mechanism underlying the corrosion behaviour of the EBM materials has not been clarified yet.
A preheating procedure is unique to the EBM process; it is important to suppress the charge accumulation of powder particles and the resulting 'powder explosion' (namely, a 'smoke' event). Furthermore, residual stresses, which can cause the distortion and failure of components in other AM processes such as selective laser melting (SLM) 33,41 , are significantly reduced in the final products processed by EBM. However, this procedure makes EBM a completely hot process. The long build time at elevated temperatures allows microstructural evolutions such as grain growth 42 and phase transformation 43,44 during their fabrication. This 'in situ annealing' feature notably differentiates EBM from other PBF processes, such as SLM, in which the selective melting of raw powder is generally conducted without preheating.
In this study, the corrosion behaviours of an equimolar AlCoCrFeNi HEA prepared by EBM were examined at different build heights to examine the effect of post-melt high-temperature exposure. The mechanisms underlying the corrosion performance of the EBM specimen are discussed based on detailed microstructural examinations. Figure 1 depicts the typical microstructures of the studied AlCoCrFeNi HEA specimens, as observed by scanning electron microscopy (SEM), X-ray diffraction (XRD) and electron backscatter diffraction (EBSD) measurements. The back-scattered electron (BSE) images reveal the characteristic modulated structure of the matrices of all the samples, as shown in Fig. 1a-c. The XRD data indicate that the specimens are primarily composed of both ordered (B2) and disordered BCC phases. Thus, the modulated structures correspond to the duplex microstructure of the BCC and B2 phases (hereafter, this is denoted as the 'BCC/B2 matrix'). The modulated structure in the EBM specimens was markedly coarsened at the bottom section, while it was finer at the top section (with less than 200-nm width), as compared with that of the cast specimen. EBSD measurements revealed that in the EBM specimens, the 〈100〉 direction of the BCC/B2 matrix was strongly orientated along the build direction in the top part (Fig. 1d), which can be ascribed to the directional solidification along the building direction. Conversely, a more random orientational distribution, but a weaker 〈100〉 BCC/B2 texture, than that of the top part, was observed in the bottom part of the EBM specimen (Fig. 1e). Remarkably, the EBM specimens showed the evolution of the FCC phase at the grain boundaries of the BCC/B2 grains with an increase in the post-solidification period; the FCC-phase fraction (~30%) was considerably higher in the bottom part (Fig. 1h) than in the top part (Fig. 1g), where this fraction was almost negligible. The bright contrast for the FCC phase in the BSE images indicates that the average atomic number for the FCC phase is higher than that for the BCC/B2 matrix (in other words, it contains less Al). In contrast, the cast specimen almost exclusively showed a BCC/B2 matrix; it did not exhibit any specific strong texture (Fig. 1f), and the FCC phase was hardly identified (Fig. 1i) Fig. 1 Microstructures of the EBM and cast AlCoCrFeNi HEA specimens. a-c SEM-BSE images, d-f IPF maps and g-i phase maps obtained from the cross-section perpendicular to the build direction at the a, d, g top and b, e, h bottom sections of the EBM specimen and c, f, i cast specimen. The corresponding XRD patterns are also indicated in a-c.

Microstructures
pole figure maps show no significant grain-size difference between the two parts of the EBM specimens, while the cast specimens are found to have coarser grains. The average grain sizes of the BCC/B2 matrix of the EBM and cast specimens are~10 and 300 μm, respectively. Figure 2 depicts the results of scanning transmission electron microscopy (STEM) observations at different build heights of the EBM specimen. The high-angle annular dark-field (HAADF)-STEM images in Fig. 2a, g captured nanoscale elemental partitioning at each build height. The corresponding energy-dispersive X-ray spectroscopy (EDS) elemental mapping indicated that Al and Ni were preferentially distributed to the B2 phase, whereas the BCC phase contained a higher fraction of Cr and Fe, as shown in Fig. 2b, f and d, e, respectively. Although the elemental partitioning of Co between the BCC and B2 phases was not obvious in Fig. 2c, it was partitioned preferentially into the FCC phase, together with Cr and Fe, which was dominantly observed at the grain boundaries of the BCC/B2 matrix. A similar phase separation was observed in the bottom part, although the microstructure was coarsened, as shown in Fig. 2h-l. However, the results of the quantitative STEM-EDS analysis (Table 1) clarified the difference in chemical composition in the BCC/B2 matrix. Namely, the BCC phase at the top part has higher Cr and lower Ni contents than in the bottom counterpart, but the BCC phase at the bottom part still has a Cr content of 27.65 at.%. Although the chemical composition of the B2 phase is similar between the top and bottom samples, the B2 phase at the top part contained a much lower Cr content of~4 at% compared with the bottom part, which was as high as~7 at%. Accordingly, the elemental partitioning within the BCC/B2 matrix resulted in the difference in the lattice parameters between the BCC and B2 phases, causing the asymmetric BCC/B2 peaks in the XRD pattern (Fig. 1b). The FCC phase at both build heights showed an almost identical chemical composition. Furthermore, Cr-enriched particles were identified at the BCC/B2 interfaces of the bottom specimen (see the arrow in Fig. 2j for instance). This phase was enriched with Cr and contained Co and Fe, indicating that the small amount of nanosized particles in the bottom specimen consisted of the σ phase of an intermetallic compound, (Co, Fe)Cr 45 . The cast specimen exhibited an elemental partitioning tendency that is identical to the EBM specimen and is consistent with the literature 46,47 ; however, the modulated BCC/B2 structure was finer than those in the EBM specimen, and the fraction of the FCC phase was negligibly low (Supplementary Fig. 1).
Potentiodynamic characteristics Figure 3a depicts the variations in the open-circuit potential (E oc ) of the EBM and cast specimens immersed in a 3.5 wt% NaCl solution at room temperature. E oc is the measured voltage difference between the working electrode and the reference electrode when no current flows through the electrolytic cell, and it reflects the surface states of the metal when immersed in an electrolyte. Generally, with increasing immersion time, the E oc of  the bottom and cast specimens showed a gradual shift to positive values to attain stable surfaces with the electrolyte, indicating passivation during immersion. Conversely, the potential for the top part of the EBM specimen decreased continuously with increasing immersion time. The fluctuations in E oc indicate that the sample surface was not stable in the corrosive environment.
The final stabilised potential after 6-h immersion of the top specimen was much lower than those for the other specimens studied. Figure 3b-d depicts the typical cyclic polarisation curves obtained for the EBM and cast AlCoCrFeNi HEA specimens in a 3.5 wt% NaCl solution at room temperature. The arrows indicate the potential scan direction during cyclic polarisation measurements. While the current density of the top part increased continuously and did not show a clear passivity in the anodic region (Fig. 3b), the bottom counterpart demonstrated an obvious passivation (Fig. 3c). The cast specimen also showed the passivation in anodic polarisation, as shown in Fig. 3d. Notably, the passive current density for the bottom sample was apparently lower than that of the cast specimen. A positive hysteresis, which shows that the current density of the reverse scan exceeds that of the forward scan, was identified for all the specimens examined in this study, indicating that all the specimens were susceptible to pitting corrosion. The cast specimen demonstrated a repassivation tendency during cyclic polarisation, where the current density during the reverse scan decreased to reach a repassivation potential at which the current density corresponds to the passive current density value. Unlike the previous research on the corrosion behaviour of as-cast AlCoCrFeNi-based HEAs 48 , the repassivation potential was not always realised in the present cast specimen. Conversely, the EBM samples did not reach repassivation at both build heights. The area of the positive hysteresis loop is related to the pitting corrosion rate during the cycle 49 ; a larger area under the positive hysteresis loop for the bottom part of the EBM specimen indicates a more rapid growth of the nucleated pits upon their surfaces than that of the cast specimen. The metastable pits were observed at the bottom part of the EBM specimen.
The corrosion potential (E corr ) and corrosion current density (i corr ) values, which were obtained from the polarisation curves by Tafel fitting, are presented in Table 2. The results indicate that the cast specimen shows the highest E corr , while the top part of the EBM specimen shows a much lower E corr of −326 mV vs. Ag/AgCl. The bottom section shows an intermediate E corr . Conversely, the lowest i corr value was observed for the bottom specimen, followed by the cast counterpart. The top part showed the highest i corr value among the specimens. Furthermore, the pitting potential (E pit ), where the current density suddenly increased after showing the passive region, was almost the same (approximately 210 mV vs. Ag/AgCl) between the cast and EBM sample in the bottom section ( Table 2).
In summary, the bottom part of the EBM specimen has the best corrosion resistance both in terms of corrosion rate and passivity, while a more rapid growth of pits than that of the cast specimen was expected during cyclic polarisation.

Corroded surfaces
The surface morphologies of the top and bottom sections of the EBM specimens after the potentiodynamic polarisation tests are depicted in Fig. 4a, b, respectively. It is evident that the corrosion attack (namely, pitting corrosion) was localised in both samples, which is consistent with the results of cyclic polarisation tests, although the number of pits was much lower in the bottom part than in the others. The magnified images in Fig. 4d, e reveal that the BCC/B2 matrix of the EBM-built samples was susceptible to selective dissolution, while the grain-boundary FCC phase remained intact, without showing significant corrosion attack.  Consequently, network-like porous surfaces were created. A similar localised corrosion characteristic was observed in the cast sample, although the pit size was much larger than those of the EBM counterparts (Fig. 4c). Figure 4f suggested that the selective dissolution also occurred in the cast specimen.
Surface film structures Figure 5a, b, respectively, depicts the representative Nyquist and Bode diagrams for the EBM and cast specimens after 6 h of immersion in a 3.5 wt% NaCl solution at room temperature, as obtained by electrochemical impedance spectroscopy (EIS) at E oc . All the Nyquist plots show semicircular arcs with their centres depressed below the x-axis, which can be usually attributed to charge transfer on an inhomogeneous surface 50 . It is evident that the bottom section of the EBM sample exhibits the largest diameter of the depressed semicircle, while double semicircles with reduced diameters are observed for the remaining two samples. In the Bode plots, in contrast, the absolute values of impedance are almost independent of the frequency at frequencies >10 3 Hz in all cases, where the phase angle approached −10°, indicating that the solution resistance did not vary considerably. However, significant differences between the specimens were identified at medium-to-low frequencies with phase angles approaching −90°.
The electrochemical characteristics of the passive film for each specimen were quantitatively evaluated by modelling and fitting the experimental impedance spectra with the equivalent electrical circuit (EEC). Because the large phase-angle peak in the Bode diagram (Fig. 5b) indicates the electrochemical system associated with at least two time constants, the EEC consists of two RC groups. An EEC used in this study is displayed in Fig. 5c. The model has been used for Al-containing, B2-structured CCA 19 and alloys sensitive to pitting corrosion 51,52 . In this model, R s refers to the solution resistance. R f and Q f correspond to the resistance and capacitance of the passive film, respectively, whereas R ct and Q dl are the charge-transfer resistance and double-layer capacitance, respectively. A constant-phase element (CPE) was used to represent a shift from the ideal capacitor. As depicted in Fig. 5a, b, the simulated responses (solid lines) of the EEC in Fig. 5c agree well with the experimental results, indicating that the model is suitable for describing the passive film characteristics of the studied specimens in the 3.5 wt% NaCl solution. Table 3 lists the obtained electrochemical parameters for each specimen. There is no significant difference in the R s value. Notably, the top part of the EBM specimen showed the highest Q f value among the studied specimens, while no significant variations in the n f and R f were noticed. On the other hand, the lowest Q dl value was obtained for the bottom part, while a much higher value was obtained for the top part of the EBM specimen. The cast sample falls in the middle. Conversely, the R ct showed the opposite tendency, with the bottom and bottom parts showing the highest and lowest R ct values, respectively.

Surface chemistry
The survey X-ray photoelectron spectra (XPS) of the prepared specimens before and after immersion in a 3.5 wt% NaCl solution at room temperature show major peaks of the metals-the Al 2p, Co 2p, Cr 2p, Fe 2p and Ni 2p peaks-as well as the O 1s peak ( Supplementary Fig. 2). High-resolution narrow-scan XPS profiles of the specimens are presented in Fig. 6. The chemical compositions of the outermost surfaces before and after the immersion tests, calculated from the XPS data, are shown in Supplementary Tables 1-3. Further, to clarify the distributions of metallic elements at the immersed surfaces, the relative distributions of the metallic components in the surface oxides before and after the immersion tests are detailed in Fig. 7 and presented in Supplementary Table 4. All the metallic elements of the studied multicomponent alloy existed in both metal and oxide forms at detectable depths, although the fraction of each state was different among the specimens. Overall, no significant differences were identified among the XPS profiles of the specimens before immersion. Among the constitutive elements, Al (Fig. 6a), Co (Fig.  6b), Cr (Fig. 6c) and Fe (Fig. 6d) preferentially existed in their oxidised states, although the metallic state was preferred for Ni (Fig. 6e). The O 1s peaks could be deconvoluted into three peaks: O 2− , hydroxide (OH − ) and hydrates and/or adsorbed water (H 2 O). Before immersion in the 3.5 wt% NaCl solution, the hydroxide component was dominant in all the specimens (Fig. 6f).
Conversely, the oxidised state (Al 3+ ) was preferential for Al after immersion (Fig. 6g). Although the top part of the EBM specimen that was immersed for 1 h showed the lowest amount of Al 3+ Fig. 5 EIS results of the EBM and cast AlCoCrFeNi HEA specimens at E oc in a 3.5 wt% NaCl solution at room temperature. a Nyquist plots, b Bode plots and c the EEC employed for fitting the EIS data. Table 3. Electrochemical parameters obtained from EIS measurements for the EBM and cast AlCoCrFeNi HEA specimens in a 3.5 wt% NaCl solution for 6 h at room temperature. among the specimens, the significant variation between the samples disappeared after 6-h immersion (Fig. 7a). Remarkably, the increase of the Cr 3+ component in the outermost surface oxide occurred in all the samples during immersion (Fig. 6h), which suggests the occurrence of the passivation process.
Notably, the fraction of the Cr 3+ component was almost identical for all the samples. The Co(OH) 2 compound remained as the preferred chemical state of Co after immersion (Fig. 6i) Fig. 6 XPS characterisation of the EBM and cast AlCoCrFeNi HEA specimens prepared in this study. High-resolution spectra for a, g Al 2p, b, h Co 2p, c, i Cr 2p, d, j Fe 2p, e, k Ni 2p and f, l O 1s collected a-f before and g-l after static immersion in a 3.5 wt% NaCl solution for 6 h at room temperature. The spectral deconvolution into component peaks is also shown. progressive dissolution of Co(OH) 2 was observed in the bottom and cast samples at the early stage of immersion (at 1 h in Fig. 7b, c, respectively). Previously, the dissolution of cobalt has been observed in the passivation process of Co-Cr-based alloys [53][54][55][56] . Further, Fig. 6j, k revealed that Fe and Ni preferred Fe 3+ and Ni(OH) 2 , respectively, when immersed in the NaCl solution. Finally, immersion into the NaCl solution decreased the amount of the O 2− component, while the fraction of the OH − ions increased (Fig. 6l). Overall, the results of the XPS analysis suggested no apparent difference in the surface chemistry/state between the samples after immersion in terms of the metal components or the state of oxygen, despite the variation in the corrosion behaviour between the samples.

DISCUSSION
Both the EBM and cast specimens consisted primarily of the duplex BCC/B2 matrix, which was formed directly from the melt 46 .
In the EBM specimen, the modulated BCC/B2 matrix was developed preferentially at the top section, so that the 〈100〉 BCC/ B2 direction of the crystal was parallel to the build direction, whereas the bottom portion showed relatively random crystallographic orientations (Fig. 1). This indicates that as the EBM process proceeded, the microstructure tended to gradually transform into the stable 〈100〉 BCC/B2 fibre texture during solidification. Conversely, coarsening of the modulated BCC/ B2 structure occurred at the bottom part at the same time (Fig. 2), and the grain size of BCC/B2 increased slightly. Remarkably, the FCC phase was observed preferentially at the grain boundaries of the BCC/B2 grains. Although the formation of the grain-boundary FCC phase has been observed in AlCoCrFeNibased HEAs produced by laser PBF techniques 57,58 , the fraction of the FCC phase was much smaller than that at the bottom section of the EBM specimen. The results of the STEM-EDS mapping also imply the precipitation of a small amount of the Cr-enriched σ phase at the bottom section (Fig. 2). The coarsening of the modulated BCC/B2 structure, as well as the formation of the FCC and σ phases, can be explained by a solid-state phase transformation from the non-equilibrium microstructure formed just after solidification towards a thermally stable phase distribution 59 during the fabrication, because the EBM specimen was subjected to temperatures as high as the preheating temperature (950°C) for a certain period (~13 h in this case). Obviously, the bottom part was more affected by the high-temperature exposure than the top part. The cast specimen, on the other hand, showed a microstructure comparable to that of the top part, because the cast specimen was not maintained at high temperatures. The microstructural evolution of the equiatomic AlCoCrFeNi HEA during EBM and casting is schematised in Fig. 8. The most interesting finding of this study is the obvious difference in the corrosion behaviour along the build direction in the studied equiatomic AlCoCrFeNi HEA. The opposite tendency between the top and bottom parts was noticed in the E oc measurements, as shown in Fig. 3a. The potentiodynamic polarisation measurements (Fig. 3b-d) revealed that the bottom part of the EBM specimen showed higher E corr and lower i corr values than the top part (Table 2). Notably, the passivation behaviour was also considerably different between the specimens, although all the studied samples were susceptible to pitting corrosion. Whereas the bottom part of the EBM specimen, as well as the cast specimen, showed passivity during anodic polarisation, no apparent passivation behaviour was identified in the polarisation curve in the top part of the EBM specimen. Notably, the lower passive current density in the bottom part of the EBM specimen compared with that of the cast specimen indicates a higher passive film stability of the former in the current corrosive environment. A larger pitting overpotential (E pit − E corr ) for the bottom part of the EBM specimen than the cast counterpart also suggested the enhanced corrosion resistance. However, once stable pits nucleated on the EBM specimen surface, they grew more rapidly than those on the cast specimen. Repassivation was not obtained at either build height of the EBM specimen, as indicated by the cyclic polarisation tests.
Generally, the formation of pits in AlCoCrFeNi-based HEAs is closely related to a weakening of the passive films on the Crdepleted region. That is, the Cr-depleted dendrites in the cast specimen suffered from serious preferential dissolution, whereas the Cr-rich interdendritic regions remained largely resistant to corrosion 22,24 . This is consistent with the morphology of the corroded surface for the cast specimen, as shown in Fig. 4c. Conversely, such a dendritic-scale dissolution was completely suppressed in the EBM counterparts (Fig. 4a, b), because the rapid cooling during EBM, in principle, allows the production of components that are essentially free of segregations at interdendritic regions 33 . Notably, the pitting corrosion of the EBM and cast specimens proceeded in the modulated BCC/B2 matrix via a phase-specific selective dissolution at the nanoscale, as shown in Fig. 4d-f. Therefore, this enhanced the resistance to pitting corrosion at the bottom part of the EBM specimen in comparison with the cast counterpart. The suppression of the dendritic-scale pitting corrosion has been observed in the homogenisation of AlCoCrFeNi-based HEAs 30 . Such a microstructural difference could be an origin for the reduced repassivation ability in the EBM specimen during cyclic polarisation (Fig. 3b, c) when compared with the cast specimen, although further study is required to clarify the underlying mechanism.
The pitting corrosion of the EBM specimen correlates with the nanoscale elemental partitioning during fabrication. The quantitative STEM-EDS elemental analysis (Table 1) revealed that the B2 phase in the EBM specimen had a much lower Cr content (less than 10 at%) than the BCC phase (approximately 50 at%). Furthermore, the FCC phase at both sections of the EBM specimen had a similar Cr content (20 − 30 at%). Thus, it is highly likely that the passive films are formed on the BCC and FCC phases of the alloy substrates. This hypothesis is reasonable because the XPS surface analysis detected an increase in the Cr 3+ component during the static immersion (Fig. 7) and this correlated with the corroded surface observations that showed reduced corrosion during the polarisation tests (Fig. 4). Therefore, the selective dissolution that occurred at the Cr-lean, Al-Ni-enriched B2 phase must be a controlling process of the pitting corrosion, and this could explain why a continuous increase in the current density during the anodic polarisation occurred in the top sample.
An interesting observation that aids understanding of the enhanced corrosion resistance at the bottom part is the microstructural evolution during the 'in situ annealing' in the EBM process. The microstructural characterisation (Figs. 1 and 2) revealed that the bottom part had a higher FCC fraction and a weaker 〈100〉 BCC/B2 texture evolution when compared with the top part. Furthermore, the modulated BCC/B2 matrix was coarser at the bottom part. The phase distributions and crystallographic texture are possible influencing factors of the corrosion performance of metals [60][61][62] . Notably, these microstructural evolutions are associated with the elemental partitioning between the constitutive phases (Table 1). Importantly, in the modulated BCC/ B2 matrix, where corrosion occurred, the bottom part had a higher Cr content in the B2 phase than in the top part. Thus, a more severe dissolution at the B2 phase can be expected at the top part, hindering the passive region in the polarisation curve. This means that the redistribution of Cr that occurred with prolonged hightemperature exposure during the EBM process is essential for the corrosion performance. The spikes on the E oc curve of the bottom specimen can be correlated to the metastable pitting caused by the above-mentioned phase-specific selective dissolution. However, the surface chemistry variation originating from the phasespecific corrosion could not be detected by the XPS analysis, because the quantitative values determined by the XPS analysis were averaged over the analysed area (300 × 700 μm 2 ), which is much larger than the microstructural length as mentioned above.
Nonetheless, the corrosion behaviour and passive film characteristics depended significantly on the bulk of microstructures, as successfully captured by the EIS analysis (Fig. 5). The results indicated that although an identical EEC could be adapted for all the specimens prepared in this work, the EIS parameters of each specimen showed apparent differences. For example, the chargetransfer resistance (R ct ) was much higher at the bottom part of the EBM specimen, and lowest at the top. Polarisation resistance (R p ), which is generally used to estimate the corrosion resistance and is inversely proportionate to the corrosion rate, is described as follows: The R p values for the studied specimens are shown in Table 3. While the R f values of the specimens are almost identical, the R ct value of the bottom part is more than one order of magnitude higher than the R f value. This indicates that charge transfer is a critical factor for determining the electrochemical performance of the passive film. Consequently, the polarisation resistance of the bottom part of the EBM specimen was almost one order of magnitude larger than that of the top part, and three times larger than that of the cast specimen.
On the other hand, a lower Q value for the bottom part indicates the formation of a more homogeneous and less defective oxide film on the surface than that on the top part 63 . Furthermore, an effective capacitance (C eff ) can be obtained from the CPE parameters using the following equation [64][65][66] : C eff can be related to the thickness (t) of the passive film using the following equation 65 : where ε is the relative dielectric constant of the layer and ε 0 is the permittivity of vacuum (8.85 × 10 −14 F cm −1 ). Equation (2) was constructed for an EEC with a singular time constant. However, Mohanmedi et al. 67 calculated the C eff values for the EEC in Fig. 5c using the solution resistance (R s ), as follows 68 : Mohanmedi et al. 67 confirmed the validity of Eq. (4) by comparing the film thickness determined by EIS parameters with those measured through ellipsometry. The C eff values of the passive films formed on the samples used in the present study were also calculated. The results are shown in Table 3. The bottom sample possessed the lowest C eff value among the studied samples, which was less than half of that of the top part, and the cast sample falls in the middle; this trend agreed well with the corrosion behaviour deduced from the polarisation tests. As the C eff value is inversely proportional to the thickness of the passive film, the lowest Q f and highest C eff values in the bottom sample suggest the formation of a more homogeneous, compact, less defective passive film at the bottom section when immersed into the NaCl solution. The superior corrosion performance of the bottom part compared with that of the top part and the cast specimen can be explained by the more protective passive film formation and the enhanced R p value.
Moreover, both Q dl and n dl values also varied depending on the samples. Qiu et al. 19 reported a high Q dl value, which was similar to those for the top and bottom samples in this study, for pure Al immersed into a 0.6 M NaCl solution, whereas the single-phase AlTiVCr CCA with a better corrosion resistance had a much smaller value. The relatively small n dl values for the present specimens imply local heterogeneities in the surface oxide film 69 , although the bottom sample showed the highest value among the studied samples. Therefore, the subcircuit consisting of Q dl and n dl could be correlated with the B2 phase, which suffered from selective dissolution. The much lower Q dl and slightly higher n dl values for the bottom part of the EBM specimen would reflect the better corrosion resistance of the B2 phase among the studied samples. Conversely, the Q f and n f values seem to describe predominantly the passive film on the BCC and FCC phases, and the EEC model employed in this study suitably characterised the inhomogeneous passive films and the phase-specific selective corrosion behaviour.
The phase-specific pitting corrosion in AlCoCrFeNi-based HEAs can be described in terms of galvanic coupling between the constitutive phases 21,23 . Using scanning Kelvin probe force microscopy, Shi et al. 30 revealed an electrochemical potential difference between the BCC, B2 and FCC phases in the AlCoCrFeNi-based HEAs. The magnitude of the potential difference as a driving force for the nanoscale galvanic corrosion would depend on the composition, size and fraction of each constitutive phase, which could be affected by the building conditions. These findings clearly indicate that the microstructural evolution caused by 'in situ annealing' during the EBM process significantly influences the corrosion behaviour of the present HEA. In other words, rapidly solidified microstructures that are obtained by SLM and directed energy deposition, for instance, are similar to those observed in the top part of the EBM specimen, and are not always preferred if a high corrosion resistance is desired. Moreover, in terms of solidification segregation, the alloy microstructure at the bottom part must be different from the simply annealed coarse dendritic microstructures obtained by conventional casting. According to the microstructural observations and Vickers hardness measurements 35 , the microstructure that was not exposed to post melting at high temperatures during the EBM process, which should be avoided if good corrosion performance is to be achieved (i.e. the microstructure referred to as the 'top part' in this study), existed only near the top part (2 mm in height), and most parts of the specimens were homogeneous and had microstructures similar to that of the 'bottom part'. This suggests that EBM is a promising method for optimising the corrosion performance of almost all parts of the structural components of HEAs.

Sample preparation
Specimens examined in this study were produced by EBM and conventional casting. An Arcam A2X system (Arcam AB, Sweden) with an acceleration voltage of 60 kV was used to manufacture specimens with 20mm × 20-mm × 16-mm dimensions from a gas-atomised powder (the particle size ranged from 45 to 105 μm). The preheating temperature was set to 950°C. For comparison, cast specimens (15 mm in diameter and 300 mm in height) were also prepared by melting the same powder using a high-frequency induction furnace and a water-cooled copper mould. The chemical compositions of the EBM and cast specimens are shown in Table  4. The preparation processes have been previously described in detail 35 . The 'top' and 'bottom' specimens used in this paper were taken from locations 1 mm below the top and 1 mm above the bottom of the EBM specimens, respectively.

Microstructural characterisation
XRD (X'Pert MPD, PANalytical, Netherlands) was conducted using monochromatised Cu-Kα radiation to analyse the phase and structure of the alloys. The scanning range is from 2θ = 20°to 100°, and the step size is 0.08°. SEM was conducted on a JSM-7100F microscope (JEOL, Japan) with a field-emission gun operated at 15 kV. Field-emission SEM (XL30S-FEG, FEI, USA) at 20 kV was used for EBSD analyses. A TSL-OIM system (version 7.3, EDAX, USA) was used to collect and analyse the EBSD data with a step size of 0.25 or 2.5 μm, according to the magnification. The microstructural characterisations of the EBM samples were conducted on the specimen cross-section in a direction perpendicular to the build direction. Samples for microstructural analyses were ground with emery paper, polished with a 1-μm alumina suspension and then finished with a 0.04-μm colloidal silica suspension (OP-S, Struers, Japan).
A TITAN 3 G2 60-300S/TEM (FEI, USA) with a spherical aberration (Cs) corrector operating at 300 kV was used for HAADF-STEM observations and EDS mapping. The samples for observation were obtained by cutting 3mm-diameter disks from the top and bottom sections of the EBM specimens and then grinding them with a dimple grinder (Model 656, Gatan, USA) to form a thin film. After that, thin foils were formed by ionbeam milling (Model 691, PIPS, Gatan, USA).

Electrochemical characterisation
Electrochemical tests, including potentiodynamic polarisation and EIS, were performed using an SP-200 system (Bio-Logic Science Instruments, France) on a three-electrode flat cell consisting of a Pt mesh and Ag/AgCl electrode as the counter and reference electrodes, respectively. The samples with a measurement area of 1 cm 2 , which were cut from the top and bottom sections of the as-built materials and the as-cast counterparts, were used as working electrodes. Before each measurement, the samples were ground with 1000-grit emery paper, cleaned with acetone and dried with compressed air. The measurements were performed in a 3.5 wt% NaCl solution at room temperature (~25°C). The test solutions (~250 mL) were exposed to air during the measurements. After the polarisation tests, the surfaces were observed by SEM (JSM-7100F, JEOL, Japan) operated at 15 kV.
For each specimen, the E oc was measured for up to 6 h. The specimens were then anodically polarised within the range of −0.3 V vs. E oc to 0.5 V vs. Ag/AgCl at the scan rate of 1 mV s −1 . In order to investigate the susceptibility of the prepared alloy specimens to localised corrosion attacks (namely, pitting corrosion), cyclic potentiodynamic polarisation tests were performed from an initial potential of −0.3 V vs. E oc to a potential of 0.5 V vs. Ag/AgCl at forward and reverse scan rates of 1 mV s −1 with a peak current density of 5 mA cm −2 . The obtained data were analysed using the EC-Lab ® software (Bio-Logic Science Instruments, France).
The EIS measurements were performed after 6-h immersion at an amplitude of 10 mV at E oc in the frequency range of 100 kHz-10 mHz. In the EEC, the impedance of a CPE is defined as 69 where the exponent n (−1 ≤ n ≤ 1) is a coefficient that describes the deviation between the real capacitance and pure capacitance. Q and ω represent the general admittance function and the angular frequency, respectively. The CPE for n = 1 and 0 describes an ideal capacitor and an ideal resistor, respectively. The CPE for n = 0.5 represents a Warburg impedance with diffusional character. Finally, the CPE for 0.5 < n < 1 describes a frequency dispersion of time constants due to local heterogeneities in the dielectric material. A pure inductance yields n = −1.

Surface characterisation
Oxidation states and compositions of the surface oxide films were analysed before and after the immersion of the specimens in a 3.5 wt% NaCl solution for 6 h. For the analysis, XPS (Axis Ultra DLD, Shimadzu-Kratos, UK) was performed using monochromatised Al Kα X-ray radiation (15 kV, 10 mA) with an excitation energy of 1486.7 eV. The instrument was calibrated to give an Au 4f 7/2 metallic gold BE of 84.0 ± 0.1 eV. The spectrometer dispersion was adjusted to give a BE of 932.6 ± 0.1 eV for metallic Cu 2p 3/2 . A 300 × 700-μm area of the sample was analysed by XPS. The survey and narrow scans were made in 1 and 0.1-eV step sizes, respectively. The pass energy for collecting the survey and narrow spectra were 160 or 40 eV, respectively. Spectra from insulating samples were charge-corrected to give the adventitious C 1s signal at a binding energy of 284.8 eV. The chemical states of the elements were determined from the peak positions obtained by deconvoluting the high-resolution scan spectra. Spectra were analysed using CasaXPS software (ver. 2.3.15). A standard Shirley (or often linear) background was used for all reference samples of the spectra. Positions and the full width at half maximum (FWHM) of each peak are summarised in Supplemental Tables 1−3. The energy shifts as well as the FWHMs indicated an acceptable fit for all angles and potentials. The immersed alloy samples were cleaned with distilled water and then dried with air before the XPS measurements.